init commit ready for homework framwork
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Copyright (c) 2021 Lingqi Yan <lingqi@cs.ucsb.edu>, All rights reserved.
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Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:
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The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.
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THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
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# GAMES202 homework0
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# Blender MTL File: 'None'
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# Material Count: 1
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newmtl None
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Ns 500
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Ka 0.8 0.8 0.8
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Kd 0.8 0.8 0.8
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Ks 0.8 0.8 0.8
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d 1
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illum 2
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# Blender MTL File: 'None'
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# Material Count: 2
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newmtl 材质
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Ns 900.000000
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Ka 1.000000 1.000000 1.000000
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Kd 0.800000 0.800000 0.800000
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Ks 0.000000 0.000000 0.000000
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Ke 0.000000 0.000000 0.000000
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Ni 1.450000
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d 1.000000
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illum 1
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newmtl 材质
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Ns 900.000000
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Ka 1.000000 1.000000 1.000000
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Kd 0.270588 0.552941 0.874510
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Ks 0.000000 0.000000 0.000000
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Ke 0.000000 0.000000 0.000000
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Ni 1.450000
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d 1.000000
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illum 1
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# Blender MTL File: 'None'
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# Material Count: 1
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newmtl None
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Ns 500
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Ka 0.8 0.8 0.8
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Kd 0.0 1.0 0.0
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Ks 0.8 0.8 0.8
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d 1
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illum 2
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# Blender v2.91.0 OBJ File: ''
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# www.blender.org
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mtllib untitled.mtl
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o Cube
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v -3.594112 -3.594112 3.594112
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v -3.594112 3.594112 3.594112
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v -3.594112 -3.594112 -3.594112
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v -3.594112 3.594112 -3.594112
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v 3.594112 -3.594112 3.594112
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v 3.594112 3.594112 3.594112
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v 3.594112 -3.594112 -3.594112
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v 3.594112 3.594112 -3.594112
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vt 0.375000 0.000000
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vt 0.625000 0.000000
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vt 0.625000 0.250000
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vt 0.375000 0.250000
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vt 0.625000 0.500000
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vt 0.375000 0.500000
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vt 0.625000 0.750000
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vt 0.375000 0.750000
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vt 0.625000 1.000000
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vt 0.375000 1.000000
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vt 0.125000 0.500000
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vt 0.125000 0.750000
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vt 0.875000 0.500000
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vt 0.875000 0.750000
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vn -1.0000 0.0000 0.0000
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vn 0.0000 0.0000 -1.0000
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vn 1.0000 0.0000 0.0000
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vn 0.0000 0.0000 1.0000
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vn 0.0000 -1.0000 0.0000
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vn 0.0000 1.0000 0.0000
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usemtl None
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s off
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f 1/1/1 2/2/1 4/3/1 3/4/1
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f 3/4/2 4/3/2 8/5/2 7/6/2
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f 7/6/3 8/5/3 6/7/3 5/8/3
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f 5/8/4 6/7/4 2/9/4 1/10/4
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f 3/11/5 7/6/5 5/8/5 1/12/5
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f 8/5/6 4/13/6 2/14/6 6/7/6
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<!DOCTYPE html>
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<html>
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<head>
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<style>
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html,
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body {
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margin: 0;
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background-color: black;
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height: 100%;
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width: 100%;
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overflow: hidden;
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}
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#glcanvas {
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top: 0;
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width: 100%;
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height: 100%;
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}
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</style>
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<script src="lib/sh.js" defer></script>
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<script src="lib/three.js" defer></script>
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<script src="lib/bvhtree.js" defer></script>
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<script src="lib/OrbitControls.js" defer></script>
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<script src="lib/gl-matrix-min.js" defer></script>
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<script src="lib/RGBELoader.js" defer></script>
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<script src="lib/math.js" defer></script>
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<script type="text/javascript" src="lib/MTLLoader.js" defer></script>
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<script type="text/javascript" src="lib/OBJLoader.js" defer></script>
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<script type="text/javascript" src="lib/dat.gui.js" defer></script>
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<script src="src/utils/tools.js" defer></script>
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<script src="src/shaders/Shader.js" defer></script>
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<script src="src/shaders/InternalShader.js" defer></script>
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<script src="src/materials/Material.js" defer></script>
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<script src="src/materials/ShadowMaterial.js" defer></script>
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<script src="src/materials/PhongMaterial.js" defer></script>
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<script src="src/materials/SkyBoxMaterial.js" defer></script>
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<script src="src/textures/Texture.js" defer></script>
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<script src="src/textures/FBO.js" defer></script>
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<script src="src/textures/CubeTexture.js" defer></script>
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<script src="src/objects/Mesh.js" defer></script>
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<script src="src/loads/loadOBJ.js" defer></script>
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<script src="src/loads/loadShader.js" defer></script>
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<script src="src/lights/Light.js" defer></script>
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<script src="src/lights/DirectionalLight.js" defer></script>
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<script src="src/lights/PointLight.js" defer></script>
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<script src="src/renderers/WebGLRenderer.js" defer></script>
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<script src="src/renderers/MeshRender.js" defer></script>
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<script src="src/engine.js" defer></script>
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</head>
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<body>
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<canvas id="glcanvas"></canvas>
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</body>
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</html>
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/**
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* Loads a Wavefront .mtl file specifying materials
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*/
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THREE.MTLLoader = function ( manager ) {
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THREE.Loader.call( this, manager );
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};
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THREE.MTLLoader.prototype = Object.assign( Object.create( THREE.Loader.prototype ), {
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constructor: THREE.MTLLoader,
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/**
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* Loads and parses a MTL asset from a URL.
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*
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* @param {String} url - URL to the MTL file.
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* @param {Function} [onLoad] - Callback invoked with the loaded object.
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* @param {Function} [onProgress] - Callback for download progress.
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* @param {Function} [onError] - Callback for download errors.
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*
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* @see setPath setResourcePath
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*
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* @note In order for relative texture references to resolve correctly
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* you must call setResourcePath() explicitly prior to load.
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*/
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load: function ( url, onLoad, onProgress, onError ) {
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var scope = this;
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var path = ( this.path === '' ) ? THREE.LoaderUtils.extractUrlBase( url ) : this.path;
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var loader = new THREE.FileLoader( this.manager );
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loader.setPath( this.path );
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loader.setRequestHeader( this.requestHeader );
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loader.setWithCredentials( this.withCredentials );
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loader.load( url, function ( text ) {
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try {
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onLoad( scope.parse( text, path ) );
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} catch ( e ) {
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if ( onError ) {
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onError( e );
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} else {
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console.error( e );
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}
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scope.manager.itemError( url );
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}
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}, onProgress, onError );
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},
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setMaterialOptions: function ( value ) {
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this.materialOptions = value;
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return this;
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},
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/**
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* Parses a MTL file.
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*
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* @param {String} text - Content of MTL file
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* @return {THREE.MTLLoader.MaterialCreator}
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*
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* @see setPath setResourcePath
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*
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* @note In order for relative texture references to resolve correctly
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* you must call setResourcePath() explicitly prior to parse.
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*/
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parse: function ( text, path ) {
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var lines = text.split( '\n' );
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var info = {};
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var delimiter_pattern = /\s+/;
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var materialsInfo = {};
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for ( var i = 0; i < lines.length; i ++ ) {
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var line = lines[ i ];
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line = line.trim();
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if ( line.length === 0 || line.charAt( 0 ) === '#' ) {
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// Blank line or comment ignore
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continue;
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}
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var pos = line.indexOf( ' ' );
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var key = ( pos >= 0 ) ? line.substring( 0, pos ) : line;
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key = key.toLowerCase();
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var value = ( pos >= 0 ) ? line.substring( pos + 1 ) : '';
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value = value.trim();
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if ( key === 'newmtl' ) {
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// New material
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info = { name: value };
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materialsInfo[ value ] = info;
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} else {
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if ( key === 'ka' || key === 'kd' || key === 'ks' || key === 'ke' ) {
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var ss = value.split( delimiter_pattern, 3 );
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info[ key ] = [ parseFloat( ss[ 0 ] ), parseFloat( ss[ 1 ] ), parseFloat( ss[ 2 ] ) ];
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} else {
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info[ key ] = value;
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}
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}
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}
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var materialCreator = new THREE.MTLLoader.MaterialCreator( this.resourcePath || path, this.materialOptions );
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materialCreator.setCrossOrigin( this.crossOrigin );
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materialCreator.setManager( this.manager );
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materialCreator.setMaterials( materialsInfo );
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return materialCreator;
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}
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} );
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/**
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* Create a new THREE.MTLLoader.MaterialCreator
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* @param baseUrl - Url relative to which textures are loaded
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* @param options - Set of options on how to construct the materials
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* side: Which side to apply the material
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* THREE.FrontSide (default), THREE.BackSide, THREE.DoubleSide
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* wrap: What type of wrapping to apply for textures
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* THREE.RepeatWrapping (default), THREE.ClampToEdgeWrapping, THREE.MirroredRepeatWrapping
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* normalizeRGB: RGBs need to be normalized to 0-1 from 0-255
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* Default: false, assumed to be already normalized
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* ignoreZeroRGBs: Ignore values of RGBs (Ka,Kd,Ks) that are all 0's
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* Default: false
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* @constructor
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*/
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THREE.MTLLoader.MaterialCreator = function ( baseUrl, options ) {
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this.baseUrl = baseUrl || '';
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this.options = options;
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this.materialsInfo = {};
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this.materials = {};
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this.materialsArray = [];
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this.nameLookup = {};
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this.side = ( this.options && this.options.side ) ? this.options.side : THREE.FrontSide;
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this.wrap = ( this.options && this.options.wrap ) ? this.options.wrap : THREE.RepeatWrapping;
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};
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THREE.MTLLoader.MaterialCreator.prototype = {
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constructor: THREE.MTLLoader.MaterialCreator,
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crossOrigin: 'anonymous',
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setCrossOrigin: function ( value ) {
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this.crossOrigin = value;
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return this;
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},
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setManager: function ( value ) {
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this.manager = value;
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},
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setMaterials: function ( materialsInfo ) {
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this.materialsInfo = this.convert( materialsInfo );
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this.materials = {};
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this.materialsArray = [];
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this.nameLookup = {};
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},
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convert: function ( materialsInfo ) {
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if ( ! this.options ) return materialsInfo;
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var converted = {};
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for ( var mn in materialsInfo ) {
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// Convert materials info into normalized form based on options
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var mat = materialsInfo[ mn ];
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||||
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var covmat = {};
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||||
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converted[ mn ] = covmat;
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for ( var prop in mat ) {
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||||
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var save = true;
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||||
var value = mat[ prop ];
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||||
var lprop = prop.toLowerCase();
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||||
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switch ( lprop ) {
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||||
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||||
case 'kd':
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||||
case 'ka':
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case 'ks':
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||||
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||||
// Diffuse color (color under white light) using RGB values
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if ( this.options && this.options.normalizeRGB ) {
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||||
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value = [ value[ 0 ] / 255, value[ 1 ] / 255, value[ 2 ] / 255 ];
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||||
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}
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||||
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||||
if ( this.options && this.options.ignoreZeroRGBs ) {
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||||
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||||
if ( value[ 0 ] === 0 && value[ 1 ] === 0 && value[ 2 ] === 0 ) {
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||||
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// ignore
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||||
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||||
save = false;
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||||
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||||
}
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||||
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||||
}
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||||
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||||
break;
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||||
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||||
default:
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||||
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||||
break;
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||||
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||||
}
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||||
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||||
if ( save ) {
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||||
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||||
covmat[ lprop ] = value;
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||||
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||||
}
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||||
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||||
}
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||||
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||||
}
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||||
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||||
return converted;
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||||
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||||
},
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preload: function () {
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||||
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||||
for ( var mn in this.materialsInfo ) {
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||||
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this.create( mn );
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||||
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}
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||||
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},
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||||
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||||
getIndex: function ( materialName ) {
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||||
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return this.nameLookup[ materialName ];
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||||
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||||
},
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||||
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getAsArray: function () {
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||||
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||||
var index = 0;
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||||
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||||
for ( var mn in this.materialsInfo ) {
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||||
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||||
this.materialsArray[ index ] = this.create( mn );
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||||
this.nameLookup[ mn ] = index;
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||||
index ++;
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||||
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||||
}
|
||||
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||||
return this.materialsArray;
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||||
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||||
},
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||||
|
||||
create: function ( materialName ) {
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||||
|
||||
if ( this.materials[ materialName ] === undefined ) {
|
||||
|
||||
this.createMaterial_( materialName );
|
||||
|
||||
}
|
||||
|
||||
return this.materials[ materialName ];
|
||||
|
||||
},
|
||||
|
||||
createMaterial_: function ( materialName ) {
|
||||
|
||||
// Create material
|
||||
|
||||
var scope = this;
|
||||
var mat = this.materialsInfo[ materialName ];
|
||||
var params = {
|
||||
|
||||
name: materialName,
|
||||
side: this.side
|
||||
|
||||
};
|
||||
|
||||
function resolveURL( baseUrl, url ) {
|
||||
|
||||
if ( typeof url !== 'string' || url === '' )
|
||||
return '';
|
||||
|
||||
// Absolute URL
|
||||
if ( /^https?:\/\//i.test( url ) ) return url;
|
||||
|
||||
return baseUrl + url;
|
||||
|
||||
}
|
||||
|
||||
function setMapForType( mapType, value ) {
|
||||
|
||||
if ( params[ mapType ] ) return; // Keep the first encountered texture
|
||||
|
||||
var texParams = scope.getTextureParams( value, params );
|
||||
var map = scope.loadTexture( resolveURL( scope.baseUrl, texParams.url ) );
|
||||
|
||||
map.repeat.copy( texParams.scale );
|
||||
map.offset.copy( texParams.offset );
|
||||
|
||||
map.wrapS = scope.wrap;
|
||||
map.wrapT = scope.wrap;
|
||||
|
||||
params[ mapType ] = map;
|
||||
|
||||
}
|
||||
|
||||
for ( var prop in mat ) {
|
||||
|
||||
var value = mat[ prop ];
|
||||
var n;
|
||||
|
||||
if ( value === '' ) continue;
|
||||
|
||||
switch ( prop.toLowerCase() ) {
|
||||
|
||||
// Ns is material specular exponent
|
||||
|
||||
case 'kd':
|
||||
|
||||
// Diffuse color (color under white light) using RGB values
|
||||
|
||||
params.color = new THREE.Color().fromArray( value );
|
||||
|
||||
break;
|
||||
|
||||
case 'ks':
|
||||
|
||||
// Specular color (color when light is reflected from shiny surface) using RGB values
|
||||
params.specular = new THREE.Color().fromArray( value );
|
||||
|
||||
break;
|
||||
|
||||
case 'ke':
|
||||
|
||||
// Emissive using RGB values
|
||||
params.emissive = new THREE.Color().fromArray( value );
|
||||
|
||||
break;
|
||||
|
||||
case 'map_kd':
|
||||
|
||||
// Diffuse texture map
|
||||
|
||||
setMapForType( 'map', value );
|
||||
|
||||
break;
|
||||
|
||||
case 'map_ks':
|
||||
|
||||
// Specular map
|
||||
|
||||
setMapForType( 'specularMap', value );
|
||||
|
||||
break;
|
||||
|
||||
case 'map_ke':
|
||||
|
||||
// Emissive map
|
||||
|
||||
setMapForType( 'emissiveMap', value );
|
||||
|
||||
break;
|
||||
|
||||
case 'norm':
|
||||
|
||||
setMapForType( 'normalMap', value );
|
||||
|
||||
break;
|
||||
|
||||
case 'map_bump':
|
||||
case 'bump':
|
||||
|
||||
// Bump texture map
|
||||
|
||||
setMapForType( 'bumpMap', value );
|
||||
|
||||
break;
|
||||
|
||||
case 'map_d':
|
||||
|
||||
// Alpha map
|
||||
|
||||
setMapForType( 'alphaMap', value );
|
||||
params.transparent = true;
|
||||
|
||||
break;
|
||||
|
||||
case 'ns':
|
||||
|
||||
// The specular exponent (defines the focus of the specular highlight)
|
||||
// A high exponent results in a tight, concentrated highlight. Ns values normally range from 0 to 1000.
|
||||
|
||||
params.shininess = parseFloat( value );
|
||||
|
||||
break;
|
||||
|
||||
case 'd':
|
||||
n = parseFloat( value );
|
||||
|
||||
if ( n < 1 ) {
|
||||
|
||||
params.opacity = n;
|
||||
params.transparent = true;
|
||||
|
||||
}
|
||||
|
||||
break;
|
||||
|
||||
case 'tr':
|
||||
n = parseFloat( value );
|
||||
|
||||
if ( this.options && this.options.invertTrProperty ) n = 1 - n;
|
||||
|
||||
if ( n > 0 ) {
|
||||
|
||||
params.opacity = 1 - n;
|
||||
params.transparent = true;
|
||||
|
||||
}
|
||||
|
||||
break;
|
||||
|
||||
default:
|
||||
break;
|
||||
|
||||
}
|
||||
|
||||
}
|
||||
|
||||
this.materials[ materialName ] = new THREE.MeshPhongMaterial( params );
|
||||
return this.materials[ materialName ];
|
||||
|
||||
},
|
||||
|
||||
getTextureParams: function ( value, matParams ) {
|
||||
|
||||
var texParams = {
|
||||
|
||||
scale: new THREE.Vector2( 1, 1 ),
|
||||
offset: new THREE.Vector2( 0, 0 )
|
||||
|
||||
};
|
||||
|
||||
var items = value.split( /\s+/ );
|
||||
var pos;
|
||||
|
||||
pos = items.indexOf( '-bm' );
|
||||
|
||||
if ( pos >= 0 ) {
|
||||
|
||||
matParams.bumpScale = parseFloat( items[ pos + 1 ] );
|
||||
items.splice( pos, 2 );
|
||||
|
||||
}
|
||||
|
||||
pos = items.indexOf( '-s' );
|
||||
|
||||
if ( pos >= 0 ) {
|
||||
|
||||
texParams.scale.set( parseFloat( items[ pos + 1 ] ), parseFloat( items[ pos + 2 ] ) );
|
||||
items.splice( pos, 4 ); // we expect 3 parameters here!
|
||||
|
||||
}
|
||||
|
||||
pos = items.indexOf( '-o' );
|
||||
|
||||
if ( pos >= 0 ) {
|
||||
|
||||
texParams.offset.set( parseFloat( items[ pos + 1 ] ), parseFloat( items[ pos + 2 ] ) );
|
||||
items.splice( pos, 4 ); // we expect 3 parameters here!
|
||||
|
||||
}
|
||||
|
||||
texParams.url = items.join( ' ' ).trim();
|
||||
return texParams;
|
||||
|
||||
},
|
||||
|
||||
loadTexture: function ( url, mapping, onLoad, onProgress, onError ) {
|
||||
|
||||
var texture;
|
||||
var manager = ( this.manager !== undefined ) ? this.manager : THREE.DefaultLoadingManager;
|
||||
var loader = manager.getHandler( url );
|
||||
|
||||
if ( loader === null ) {
|
||||
|
||||
loader = new THREE.TextureLoader( manager );
|
||||
|
||||
}
|
||||
|
||||
if ( loader.setCrossOrigin ) loader.setCrossOrigin( this.crossOrigin );
|
||||
texture = loader.load( url, onLoad, onProgress, onError );
|
||||
|
||||
if ( mapping !== undefined ) texture.mapping = mapping;
|
||||
|
||||
return texture;
|
||||
|
||||
}
|
||||
|
||||
};
|
||||
|
|
@ -0,0 +1,900 @@
|
|||
THREE.OBJLoader = ( function () {
|
||||
|
||||
// o object_name | g group_name
|
||||
var object_pattern = /^[og]\s*(.+)?/;
|
||||
// mtllib file_reference
|
||||
var material_library_pattern = /^mtllib /;
|
||||
// usemtl material_name
|
||||
var material_use_pattern = /^usemtl /;
|
||||
// usemap map_name
|
||||
var map_use_pattern = /^usemap /;
|
||||
|
||||
var vA = new THREE.Vector3();
|
||||
var vB = new THREE.Vector3();
|
||||
var vC = new THREE.Vector3();
|
||||
|
||||
var ab = new THREE.Vector3();
|
||||
var cb = new THREE.Vector3();
|
||||
|
||||
function ParserState() {
|
||||
|
||||
var state = {
|
||||
objects: [],
|
||||
object: {},
|
||||
|
||||
vertices: [],
|
||||
normals: [],
|
||||
colors: [],
|
||||
uvs: [],
|
||||
|
||||
materials: {},
|
||||
materialLibraries: [],
|
||||
|
||||
startObject: function ( name, fromDeclaration ) {
|
||||
|
||||
// If the current object (initial from reset) is not from a g/o declaration in the parsed
|
||||
// file. We need to use it for the first parsed g/o to keep things in sync.
|
||||
if ( this.object && this.object.fromDeclaration === false ) {
|
||||
|
||||
this.object.name = name;
|
||||
this.object.fromDeclaration = ( fromDeclaration !== false );
|
||||
return;
|
||||
|
||||
}
|
||||
|
||||
var previousMaterial = ( this.object && typeof this.object.currentMaterial === 'function' ? this.object.currentMaterial() : undefined );
|
||||
|
||||
if ( this.object && typeof this.object._finalize === 'function' ) {
|
||||
|
||||
this.object._finalize( true );
|
||||
|
||||
}
|
||||
|
||||
this.object = {
|
||||
name: name || '',
|
||||
fromDeclaration: ( fromDeclaration !== false ),
|
||||
|
||||
geometry: {
|
||||
vertices: [],
|
||||
normals: [],
|
||||
colors: [],
|
||||
uvs: [],
|
||||
hasUVIndices: false
|
||||
},
|
||||
materials: [],
|
||||
smooth: true,
|
||||
|
||||
startMaterial: function ( name, libraries ) {
|
||||
|
||||
var previous = this._finalize( false );
|
||||
|
||||
// New usemtl declaration overwrites an inherited material, except if faces were declared
|
||||
// after the material, then it must be preserved for proper MultiMaterial continuation.
|
||||
if ( previous && ( previous.inherited || previous.groupCount <= 0 ) ) {
|
||||
|
||||
this.materials.splice( previous.index, 1 );
|
||||
|
||||
}
|
||||
|
||||
var material = {
|
||||
index: this.materials.length,
|
||||
name: name || '',
|
||||
mtllib: ( Array.isArray( libraries ) && libraries.length > 0 ? libraries[ libraries.length - 1 ] : '' ),
|
||||
smooth: ( previous !== undefined ? previous.smooth : this.smooth ),
|
||||
groupStart: ( previous !== undefined ? previous.groupEnd : 0 ),
|
||||
groupEnd: - 1,
|
||||
groupCount: - 1,
|
||||
inherited: false,
|
||||
|
||||
clone: function ( index ) {
|
||||
|
||||
var cloned = {
|
||||
index: ( typeof index === 'number' ? index : this.index ),
|
||||
name: this.name,
|
||||
mtllib: this.mtllib,
|
||||
smooth: this.smooth,
|
||||
groupStart: 0,
|
||||
groupEnd: - 1,
|
||||
groupCount: - 1,
|
||||
inherited: false
|
||||
};
|
||||
cloned.clone = this.clone.bind( cloned );
|
||||
return cloned;
|
||||
|
||||
}
|
||||
};
|
||||
|
||||
this.materials.push( material );
|
||||
|
||||
return material;
|
||||
|
||||
},
|
||||
|
||||
currentMaterial: function () {
|
||||
|
||||
if ( this.materials.length > 0 ) {
|
||||
|
||||
return this.materials[ this.materials.length - 1 ];
|
||||
|
||||
}
|
||||
|
||||
return undefined;
|
||||
|
||||
},
|
||||
|
||||
_finalize: function ( end ) {
|
||||
|
||||
var lastMultiMaterial = this.currentMaterial();
|
||||
if ( lastMultiMaterial && lastMultiMaterial.groupEnd === - 1 ) {
|
||||
|
||||
lastMultiMaterial.groupEnd = this.geometry.vertices.length / 3;
|
||||
lastMultiMaterial.groupCount = lastMultiMaterial.groupEnd - lastMultiMaterial.groupStart;
|
||||
lastMultiMaterial.inherited = false;
|
||||
|
||||
}
|
||||
|
||||
// Ignore objects tail materials if no face declarations followed them before a new o/g started.
|
||||
if ( end && this.materials.length > 1 ) {
|
||||
|
||||
for ( var mi = this.materials.length - 1; mi >= 0; mi -- ) {
|
||||
|
||||
if ( this.materials[ mi ].groupCount <= 0 ) {
|
||||
|
||||
this.materials.splice( mi, 1 );
|
||||
|
||||
}
|
||||
|
||||
}
|
||||
|
||||
}
|
||||
|
||||
// Guarantee at least one empty material, this makes the creation later more straight forward.
|
||||
if ( end && this.materials.length === 0 ) {
|
||||
|
||||
this.materials.push( {
|
||||
name: '',
|
||||
smooth: this.smooth
|
||||
} );
|
||||
|
||||
}
|
||||
|
||||
return lastMultiMaterial;
|
||||
|
||||
}
|
||||
};
|
||||
|
||||
// Inherit previous objects material.
|
||||
// Spec tells us that a declared material must be set to all objects until a new material is declared.
|
||||
// If a usemtl declaration is encountered while this new object is being parsed, it will
|
||||
// overwrite the inherited material. Exception being that there was already face declarations
|
||||
// to the inherited material, then it will be preserved for proper MultiMaterial continuation.
|
||||
|
||||
if ( previousMaterial && previousMaterial.name && typeof previousMaterial.clone === 'function' ) {
|
||||
|
||||
var declared = previousMaterial.clone( 0 );
|
||||
declared.inherited = true;
|
||||
this.object.materials.push( declared );
|
||||
|
||||
}
|
||||
|
||||
this.objects.push( this.object );
|
||||
|
||||
},
|
||||
|
||||
finalize: function () {
|
||||
|
||||
if ( this.object && typeof this.object._finalize === 'function' ) {
|
||||
|
||||
this.object._finalize( true );
|
||||
|
||||
}
|
||||
|
||||
},
|
||||
|
||||
parseVertexIndex: function ( value, len ) {
|
||||
|
||||
var index = parseInt( value, 10 );
|
||||
return ( index >= 0 ? index - 1 : index + len / 3 ) * 3;
|
||||
|
||||
},
|
||||
|
||||
parseNormalIndex: function ( value, len ) {
|
||||
|
||||
var index = parseInt( value, 10 );
|
||||
return ( index >= 0 ? index - 1 : index + len / 3 ) * 3;
|
||||
|
||||
},
|
||||
|
||||
parseUVIndex: function ( value, len ) {
|
||||
|
||||
var index = parseInt( value, 10 );
|
||||
return ( index >= 0 ? index - 1 : index + len / 2 ) * 2;
|
||||
|
||||
},
|
||||
|
||||
addVertex: function ( a, b, c ) {
|
||||
|
||||
var src = this.vertices;
|
||||
var dst = this.object.geometry.vertices;
|
||||
|
||||
dst.push( src[ a + 0 ], src[ a + 1 ], src[ a + 2 ] );
|
||||
dst.push( src[ b + 0 ], src[ b + 1 ], src[ b + 2 ] );
|
||||
dst.push( src[ c + 0 ], src[ c + 1 ], src[ c + 2 ] );
|
||||
|
||||
},
|
||||
|
||||
addVertexPoint: function ( a ) {
|
||||
|
||||
var src = this.vertices;
|
||||
var dst = this.object.geometry.vertices;
|
||||
|
||||
dst.push( src[ a + 0 ], src[ a + 1 ], src[ a + 2 ] );
|
||||
|
||||
},
|
||||
|
||||
addVertexLine: function ( a ) {
|
||||
|
||||
var src = this.vertices;
|
||||
var dst = this.object.geometry.vertices;
|
||||
|
||||
dst.push( src[ a + 0 ], src[ a + 1 ], src[ a + 2 ] );
|
||||
|
||||
},
|
||||
|
||||
addNormal: function ( a, b, c ) {
|
||||
|
||||
var src = this.normals;
|
||||
var dst = this.object.geometry.normals;
|
||||
|
||||
dst.push( src[ a + 0 ], src[ a + 1 ], src[ a + 2 ] );
|
||||
dst.push( src[ b + 0 ], src[ b + 1 ], src[ b + 2 ] );
|
||||
dst.push( src[ c + 0 ], src[ c + 1 ], src[ c + 2 ] );
|
||||
|
||||
},
|
||||
|
||||
addFaceNormal: function ( a, b, c ) {
|
||||
|
||||
var src = this.vertices;
|
||||
var dst = this.object.geometry.normals;
|
||||
|
||||
vA.fromArray( src, a );
|
||||
vB.fromArray( src, b );
|
||||
vC.fromArray( src, c );
|
||||
|
||||
cb.subVectors( vC, vB );
|
||||
ab.subVectors( vA, vB );
|
||||
cb.cross( ab );
|
||||
|
||||
cb.normalize();
|
||||
|
||||
dst.push( cb.x, cb.y, cb.z );
|
||||
dst.push( cb.x, cb.y, cb.z );
|
||||
dst.push( cb.x, cb.y, cb.z );
|
||||
|
||||
},
|
||||
|
||||
addColor: function ( a, b, c ) {
|
||||
|
||||
var src = this.colors;
|
||||
var dst = this.object.geometry.colors;
|
||||
|
||||
if ( src[ a ] !== undefined ) dst.push( src[ a + 0 ], src[ a + 1 ], src[ a + 2 ] );
|
||||
if ( src[ b ] !== undefined ) dst.push( src[ b + 0 ], src[ b + 1 ], src[ b + 2 ] );
|
||||
if ( src[ c ] !== undefined ) dst.push( src[ c + 0 ], src[ c + 1 ], src[ c + 2 ] );
|
||||
|
||||
},
|
||||
|
||||
addUV: function ( a, b, c ) {
|
||||
|
||||
var src = this.uvs;
|
||||
var dst = this.object.geometry.uvs;
|
||||
|
||||
dst.push( src[ a + 0 ], src[ a + 1 ] );
|
||||
dst.push( src[ b + 0 ], src[ b + 1 ] );
|
||||
dst.push( src[ c + 0 ], src[ c + 1 ] );
|
||||
|
||||
},
|
||||
|
||||
addDefaultUV: function () {
|
||||
|
||||
var dst = this.object.geometry.uvs;
|
||||
|
||||
dst.push( 0, 0 );
|
||||
dst.push( 0, 0 );
|
||||
dst.push( 0, 0 );
|
||||
|
||||
},
|
||||
|
||||
addUVLine: function ( a ) {
|
||||
|
||||
var src = this.uvs;
|
||||
var dst = this.object.geometry.uvs;
|
||||
|
||||
dst.push( src[ a + 0 ], src[ a + 1 ] );
|
||||
|
||||
},
|
||||
|
||||
addFace: function ( a, b, c, ua, ub, uc, na, nb, nc ) {
|
||||
|
||||
var vLen = this.vertices.length;
|
||||
|
||||
var ia = this.parseVertexIndex( a, vLen );
|
||||
var ib = this.parseVertexIndex( b, vLen );
|
||||
var ic = this.parseVertexIndex( c, vLen );
|
||||
|
||||
this.addVertex( ia, ib, ic );
|
||||
this.addColor( ia, ib, ic );
|
||||
|
||||
// normals
|
||||
|
||||
if ( na !== undefined && na !== '' ) {
|
||||
|
||||
var nLen = this.normals.length;
|
||||
|
||||
ia = this.parseNormalIndex( na, nLen );
|
||||
ib = this.parseNormalIndex( nb, nLen );
|
||||
ic = this.parseNormalIndex( nc, nLen );
|
||||
|
||||
this.addNormal( ia, ib, ic );
|
||||
|
||||
} else {
|
||||
|
||||
this.addFaceNormal( ia, ib, ic );
|
||||
|
||||
}
|
||||
|
||||
// uvs
|
||||
|
||||
if ( ua !== undefined && ua !== '' ) {
|
||||
|
||||
var uvLen = this.uvs.length;
|
||||
|
||||
ia = this.parseUVIndex( ua, uvLen );
|
||||
ib = this.parseUVIndex( ub, uvLen );
|
||||
ic = this.parseUVIndex( uc, uvLen );
|
||||
|
||||
this.addUV( ia, ib, ic );
|
||||
|
||||
this.object.geometry.hasUVIndices = true;
|
||||
|
||||
} else {
|
||||
|
||||
// add placeholder values (for inconsistent face definitions)
|
||||
|
||||
this.addDefaultUV();
|
||||
|
||||
}
|
||||
|
||||
},
|
||||
|
||||
addPointGeometry: function ( vertices ) {
|
||||
|
||||
this.object.geometry.type = 'Points';
|
||||
|
||||
var vLen = this.vertices.length;
|
||||
|
||||
for ( var vi = 0, l = vertices.length; vi < l; vi ++ ) {
|
||||
|
||||
var index = this.parseVertexIndex( vertices[ vi ], vLen );
|
||||
|
||||
this.addVertexPoint( index );
|
||||
this.addColor( index );
|
||||
|
||||
}
|
||||
|
||||
},
|
||||
|
||||
addLineGeometry: function ( vertices, uvs ) {
|
||||
|
||||
this.object.geometry.type = 'Line';
|
||||
|
||||
var vLen = this.vertices.length;
|
||||
var uvLen = this.uvs.length;
|
||||
|
||||
for ( var vi = 0, l = vertices.length; vi < l; vi ++ ) {
|
||||
|
||||
this.addVertexLine( this.parseVertexIndex( vertices[ vi ], vLen ) );
|
||||
|
||||
}
|
||||
|
||||
for ( var uvi = 0, l = uvs.length; uvi < l; uvi ++ ) {
|
||||
|
||||
this.addUVLine( this.parseUVIndex( uvs[ uvi ], uvLen ) );
|
||||
|
||||
}
|
||||
|
||||
}
|
||||
|
||||
};
|
||||
|
||||
state.startObject( '', false );
|
||||
|
||||
return state;
|
||||
|
||||
}
|
||||
|
||||
//
|
||||
|
||||
function OBJLoader( manager ) {
|
||||
|
||||
THREE.Loader.call( this, manager );
|
||||
|
||||
this.materials = null;
|
||||
|
||||
}
|
||||
|
||||
OBJLoader.prototype = Object.assign( Object.create( THREE.Loader.prototype ), {
|
||||
|
||||
constructor: OBJLoader,
|
||||
|
||||
load: function ( url, onLoad, onProgress, onError ) {
|
||||
|
||||
var scope = this;
|
||||
|
||||
var loader = new THREE.FileLoader( this.manager );
|
||||
loader.setPath( this.path );
|
||||
loader.setRequestHeader( this.requestHeader );
|
||||
loader.setWithCredentials( this.withCredentials );
|
||||
loader.load( url, function ( text ) {
|
||||
|
||||
try {
|
||||
|
||||
onLoad( scope.parse( text ) );
|
||||
|
||||
} catch ( e ) {
|
||||
|
||||
if ( onError ) {
|
||||
|
||||
onError( e );
|
||||
|
||||
} else {
|
||||
|
||||
console.error( e );
|
||||
|
||||
}
|
||||
|
||||
scope.manager.itemError( url );
|
||||
|
||||
}
|
||||
|
||||
}, onProgress, onError );
|
||||
|
||||
},
|
||||
|
||||
setMaterials: function ( materials ) {
|
||||
|
||||
this.materials = materials;
|
||||
|
||||
return this;
|
||||
|
||||
},
|
||||
|
||||
parse: function ( text ) {
|
||||
|
||||
var state = new ParserState();
|
||||
|
||||
if ( text.indexOf( '\r\n' ) !== - 1 ) {
|
||||
|
||||
// This is faster than String.split with regex that splits on both
|
||||
text = text.replace( /\r\n/g, '\n' );
|
||||
|
||||
}
|
||||
|
||||
if ( text.indexOf( '\\\n' ) !== - 1 ) {
|
||||
|
||||
// join lines separated by a line continuation character (\)
|
||||
text = text.replace( /\\\n/g, '' );
|
||||
|
||||
}
|
||||
|
||||
var lines = text.split( '\n' );
|
||||
var line = '', lineFirstChar = '';
|
||||
var lineLength = 0;
|
||||
var result = [];
|
||||
|
||||
// Faster to just trim left side of the line. Use if available.
|
||||
var trimLeft = ( typeof ''.trimLeft === 'function' );
|
||||
|
||||
for ( var i = 0, l = lines.length; i < l; i ++ ) {
|
||||
|
||||
line = lines[ i ];
|
||||
|
||||
line = trimLeft ? line.trimLeft() : line.trim();
|
||||
|
||||
lineLength = line.length;
|
||||
|
||||
if ( lineLength === 0 ) continue;
|
||||
|
||||
lineFirstChar = line.charAt( 0 );
|
||||
|
||||
// @todo invoke passed in handler if any
|
||||
if ( lineFirstChar === '#' ) continue;
|
||||
|
||||
if ( lineFirstChar === 'v' ) {
|
||||
|
||||
var data = line.split( /\s+/ );
|
||||
|
||||
switch ( data[ 0 ] ) {
|
||||
|
||||
case 'v':
|
||||
state.vertices.push(
|
||||
parseFloat( data[ 1 ] ),
|
||||
parseFloat( data[ 2 ] ),
|
||||
parseFloat( data[ 3 ] )
|
||||
);
|
||||
if ( data.length >= 7 ) {
|
||||
|
||||
state.colors.push(
|
||||
parseFloat( data[ 4 ] ),
|
||||
parseFloat( data[ 5 ] ),
|
||||
parseFloat( data[ 6 ] )
|
||||
|
||||
);
|
||||
|
||||
} else {
|
||||
|
||||
// if no colors are defined, add placeholders so color and vertex indices match
|
||||
|
||||
state.colors.push( undefined, undefined, undefined );
|
||||
|
||||
}
|
||||
|
||||
break;
|
||||
case 'vn':
|
||||
state.normals.push(
|
||||
parseFloat( data[ 1 ] ),
|
||||
parseFloat( data[ 2 ] ),
|
||||
parseFloat( data[ 3 ] )
|
||||
);
|
||||
break;
|
||||
case 'vt':
|
||||
state.uvs.push(
|
||||
parseFloat( data[ 1 ] ),
|
||||
parseFloat( data[ 2 ] )
|
||||
);
|
||||
break;
|
||||
|
||||
}
|
||||
|
||||
} else if ( lineFirstChar === 'f' ) {
|
||||
|
||||
var lineData = line.substr( 1 ).trim();
|
||||
var vertexData = lineData.split( /\s+/ );
|
||||
var faceVertices = [];
|
||||
|
||||
// Parse the face vertex data into an easy to work with format
|
||||
|
||||
for ( var j = 0, jl = vertexData.length; j < jl; j ++ ) {
|
||||
|
||||
var vertex = vertexData[ j ];
|
||||
|
||||
if ( vertex.length > 0 ) {
|
||||
|
||||
var vertexParts = vertex.split( '/' );
|
||||
faceVertices.push( vertexParts );
|
||||
|
||||
}
|
||||
|
||||
}
|
||||
|
||||
// Draw an edge between the first vertex and all subsequent vertices to form an n-gon
|
||||
|
||||
var v1 = faceVertices[ 0 ];
|
||||
|
||||
for ( var j = 1, jl = faceVertices.length - 1; j < jl; j ++ ) {
|
||||
|
||||
var v2 = faceVertices[ j ];
|
||||
var v3 = faceVertices[ j + 1 ];
|
||||
|
||||
state.addFace(
|
||||
v1[ 0 ], v2[ 0 ], v3[ 0 ],
|
||||
v1[ 1 ], v2[ 1 ], v3[ 1 ],
|
||||
v1[ 2 ], v2[ 2 ], v3[ 2 ]
|
||||
);
|
||||
|
||||
}
|
||||
|
||||
} else if ( lineFirstChar === 'l' ) {
|
||||
|
||||
var lineParts = line.substring( 1 ).trim().split( ' ' );
|
||||
var lineVertices = [], lineUVs = [];
|
||||
|
||||
if ( line.indexOf( '/' ) === - 1 ) {
|
||||
|
||||
lineVertices = lineParts;
|
||||
|
||||
} else {
|
||||
|
||||
for ( var li = 0, llen = lineParts.length; li < llen; li ++ ) {
|
||||
|
||||
var parts = lineParts[ li ].split( '/' );
|
||||
|
||||
if ( parts[ 0 ] !== '' ) lineVertices.push( parts[ 0 ] );
|
||||
if ( parts[ 1 ] !== '' ) lineUVs.push( parts[ 1 ] );
|
||||
|
||||
}
|
||||
|
||||
}
|
||||
|
||||
state.addLineGeometry( lineVertices, lineUVs );
|
||||
|
||||
} else if ( lineFirstChar === 'p' ) {
|
||||
|
||||
var lineData = line.substr( 1 ).trim();
|
||||
var pointData = lineData.split( ' ' );
|
||||
|
||||
state.addPointGeometry( pointData );
|
||||
|
||||
} else if ( ( result = object_pattern.exec( line ) ) !== null ) {
|
||||
|
||||
// o object_name
|
||||
// or
|
||||
// g group_name
|
||||
|
||||
// WORKAROUND: https://bugs.chromium.org/p/v8/issues/detail?id=2869
|
||||
// var name = result[ 0 ].substr( 1 ).trim();
|
||||
var name = ( ' ' + result[ 0 ].substr( 1 ).trim() ).substr( 1 );
|
||||
|
||||
state.startObject( name );
|
||||
|
||||
} else if ( material_use_pattern.test( line ) ) {
|
||||
|
||||
// material
|
||||
|
||||
state.object.startMaterial( line.substring( 7 ).trim(), state.materialLibraries );
|
||||
|
||||
} else if ( material_library_pattern.test( line ) ) {
|
||||
|
||||
// mtl file
|
||||
|
||||
state.materialLibraries.push( line.substring( 7 ).trim() );
|
||||
|
||||
} else if ( map_use_pattern.test( line ) ) {
|
||||
|
||||
// the line is parsed but ignored since the loader assumes textures are defined MTL files
|
||||
// (according to https://www.okino.com/conv/imp_wave.htm, 'usemap' is the old-style Wavefront texture reference method)
|
||||
|
||||
console.warn( 'THREE.OBJLoader: Rendering identifier "usemap" not supported. Textures must be defined in MTL files.' );
|
||||
|
||||
} else if ( lineFirstChar === 's' ) {
|
||||
|
||||
result = line.split( ' ' );
|
||||
|
||||
// smooth shading
|
||||
|
||||
// @todo Handle files that have varying smooth values for a set of faces inside one geometry,
|
||||
// but does not define a usemtl for each face set.
|
||||
// This should be detected and a dummy material created (later MultiMaterial and geometry groups).
|
||||
// This requires some care to not create extra material on each smooth value for "normal" obj files.
|
||||
// where explicit usemtl defines geometry groups.
|
||||
// Example asset: examples/models/obj/cerberus/Cerberus.obj
|
||||
|
||||
/*
|
||||
* http://paulbourke.net/dataformats/obj/
|
||||
* or
|
||||
* http://www.cs.utah.edu/~boulos/cs3505/obj_spec.pdf
|
||||
*
|
||||
* From chapter "Grouping" Syntax explanation "s group_number":
|
||||
* "group_number is the smoothing group number. To turn off smoothing groups, use a value of 0 or off.
|
||||
* Polygonal elements use group numbers to put elements in different smoothing groups. For free-form
|
||||
* surfaces, smoothing groups are either turned on or off; there is no difference between values greater
|
||||
* than 0."
|
||||
*/
|
||||
if ( result.length > 1 ) {
|
||||
|
||||
var value = result[ 1 ].trim().toLowerCase();
|
||||
state.object.smooth = ( value !== '0' && value !== 'off' );
|
||||
|
||||
} else {
|
||||
|
||||
// ZBrush can produce "s" lines #11707
|
||||
state.object.smooth = true;
|
||||
|
||||
}
|
||||
|
||||
var material = state.object.currentMaterial();
|
||||
if ( material ) material.smooth = state.object.smooth;
|
||||
|
||||
} else {
|
||||
|
||||
// Handle null terminated files without exception
|
||||
if ( line === '\0' ) continue;
|
||||
|
||||
console.warn( 'THREE.OBJLoader: Unexpected line: "' + line + '"' );
|
||||
|
||||
}
|
||||
|
||||
}
|
||||
|
||||
state.finalize();
|
||||
|
||||
var container = new THREE.Group();
|
||||
container.materialLibraries = [].concat( state.materialLibraries );
|
||||
|
||||
var hasPrimitives = ! ( state.objects.length === 1 && state.objects[ 0 ].geometry.vertices.length === 0 );
|
||||
|
||||
if ( hasPrimitives === true ) {
|
||||
|
||||
for ( var i = 0, l = state.objects.length; i < l; i ++ ) {
|
||||
|
||||
var object = state.objects[ i ];
|
||||
var geometry = object.geometry;
|
||||
var materials = object.materials;
|
||||
var isLine = ( geometry.type === 'Line' );
|
||||
var isPoints = ( geometry.type === 'Points' );
|
||||
var hasVertexColors = false;
|
||||
|
||||
// Skip o/g line declarations that did not follow with any faces
|
||||
if ( geometry.vertices.length === 0 ) continue;
|
||||
|
||||
var buffergeometry = new THREE.BufferGeometry();
|
||||
|
||||
buffergeometry.setAttribute( 'position', new THREE.Float32BufferAttribute( geometry.vertices, 3 ) );
|
||||
|
||||
if ( geometry.normals.length > 0 ) {
|
||||
|
||||
buffergeometry.setAttribute( 'normal', new THREE.Float32BufferAttribute( geometry.normals, 3 ) );
|
||||
|
||||
}
|
||||
|
||||
if ( geometry.colors.length > 0 ) {
|
||||
|
||||
hasVertexColors = true;
|
||||
buffergeometry.setAttribute( 'color', new THREE.Float32BufferAttribute( geometry.colors, 3 ) );
|
||||
|
||||
}
|
||||
|
||||
if ( geometry.hasUVIndices === true ) {
|
||||
|
||||
buffergeometry.setAttribute( 'uv', new THREE.Float32BufferAttribute( geometry.uvs, 2 ) );
|
||||
|
||||
}
|
||||
|
||||
// Create materials
|
||||
|
||||
var createdMaterials = [];
|
||||
|
||||
for ( var mi = 0, miLen = materials.length; mi < miLen; mi ++ ) {
|
||||
|
||||
var sourceMaterial = materials[ mi ];
|
||||
var materialHash = sourceMaterial.name + '_' + sourceMaterial.smooth + '_' + hasVertexColors;
|
||||
var material = state.materials[ materialHash ];
|
||||
|
||||
if ( this.materials !== null ) {
|
||||
|
||||
material = this.materials.create( sourceMaterial.name );
|
||||
|
||||
// mtl etc. loaders probably can't create line materials correctly, copy properties to a line material.
|
||||
if ( isLine && material && ! ( material instanceof THREE.LineBasicMaterial ) ) {
|
||||
|
||||
var materialLine = new THREE.LineBasicMaterial();
|
||||
THREE.Material.prototype.copy.call( materialLine, material );
|
||||
materialLine.color.copy( material.color );
|
||||
material = materialLine;
|
||||
|
||||
} else if ( isPoints && material && ! ( material instanceof THREE.PointsMaterial ) ) {
|
||||
|
||||
var materialPoints = new THREE.PointsMaterial( { size: 10, sizeAttenuation: false } );
|
||||
THREE.Material.prototype.copy.call( materialPoints, material );
|
||||
materialPoints.color.copy( material.color );
|
||||
materialPoints.map = material.map;
|
||||
material = materialPoints;
|
||||
|
||||
}
|
||||
|
||||
}
|
||||
|
||||
if ( material === undefined ) {
|
||||
|
||||
if ( isLine ) {
|
||||
|
||||
material = new THREE.LineBasicMaterial();
|
||||
|
||||
} else if ( isPoints ) {
|
||||
|
||||
material = new THREE.PointsMaterial( { size: 1, sizeAttenuation: false } );
|
||||
|
||||
} else {
|
||||
|
||||
material = new THREE.MeshPhongMaterial();
|
||||
|
||||
}
|
||||
|
||||
material.name = sourceMaterial.name;
|
||||
material.flatShading = sourceMaterial.smooth ? false : true;
|
||||
material.vertexColors = hasVertexColors;
|
||||
|
||||
state.materials[ materialHash ] = material;
|
||||
|
||||
}
|
||||
|
||||
createdMaterials.push( material );
|
||||
|
||||
}
|
||||
|
||||
// Create mesh
|
||||
|
||||
var mesh;
|
||||
|
||||
if ( createdMaterials.length > 1 ) {
|
||||
|
||||
for ( var mi = 0, miLen = materials.length; mi < miLen; mi ++ ) {
|
||||
|
||||
var sourceMaterial = materials[ mi ];
|
||||
buffergeometry.addGroup( sourceMaterial.groupStart, sourceMaterial.groupCount, mi );
|
||||
|
||||
}
|
||||
|
||||
if ( isLine ) {
|
||||
|
||||
mesh = new THREE.LineSegments( buffergeometry, createdMaterials );
|
||||
|
||||
} else if ( isPoints ) {
|
||||
|
||||
mesh = new THREE.Points( buffergeometry, createdMaterials );
|
||||
|
||||
} else {
|
||||
|
||||
mesh = new THREE.Mesh( buffergeometry, createdMaterials );
|
||||
|
||||
}
|
||||
|
||||
} else {
|
||||
|
||||
if ( isLine ) {
|
||||
|
||||
mesh = new THREE.LineSegments( buffergeometry, createdMaterials[ 0 ] );
|
||||
|
||||
} else if ( isPoints ) {
|
||||
|
||||
mesh = new THREE.Points( buffergeometry, createdMaterials[ 0 ] );
|
||||
|
||||
} else {
|
||||
|
||||
mesh = new THREE.Mesh( buffergeometry, createdMaterials[ 0 ] );
|
||||
|
||||
}
|
||||
|
||||
}
|
||||
|
||||
mesh.name = object.name;
|
||||
|
||||
container.add( mesh );
|
||||
|
||||
}
|
||||
|
||||
} else {
|
||||
|
||||
// if there is only the default parser state object with no geometry data, interpret data as point cloud
|
||||
|
||||
if ( state.vertices.length > 0 ) {
|
||||
|
||||
var material = new THREE.PointsMaterial( { size: 1, sizeAttenuation: false } );
|
||||
|
||||
var buffergeometry = new THREE.BufferGeometry();
|
||||
|
||||
buffergeometry.setAttribute( 'position', new THREE.Float32BufferAttribute( state.vertices, 3 ) );
|
||||
|
||||
if ( state.colors.length > 0 && state.colors[ 0 ] !== undefined ) {
|
||||
|
||||
buffergeometry.setAttribute( 'color', new THREE.Float32BufferAttribute( state.colors, 3 ) );
|
||||
material.vertexColors = true;
|
||||
|
||||
}
|
||||
|
||||
var points = new THREE.Points( buffergeometry, material );
|
||||
container.add( points );
|
||||
|
||||
}
|
||||
|
||||
}
|
||||
|
||||
return container;
|
||||
|
||||
}
|
||||
|
||||
} );
|
||||
|
||||
return OBJLoader;
|
||||
|
||||
} )();
|
||||
File diff suppressed because it is too large
Load Diff
|
|
@ -0,0 +1,489 @@
|
|||
( function () {
|
||||
|
||||
// http://en.wikipedia.org/wiki/RGBE_image_format
|
||||
|
||||
class RGBELoader extends THREE.DataTextureLoader {
|
||||
|
||||
constructor( manager ) {
|
||||
|
||||
super( manager );
|
||||
this.type = THREE.UnsignedByteType;
|
||||
|
||||
} // adapted from http://www.graphics.cornell.edu/~bjw/rgbe.html
|
||||
|
||||
|
||||
parse( buffer ) {
|
||||
|
||||
const
|
||||
/* return codes for rgbe routines */
|
||||
//RGBE_RETURN_SUCCESS = 0,
|
||||
RGBE_RETURN_FAILURE = - 1,
|
||||
|
||||
/* default error routine. change this to change error handling */
|
||||
rgbe_read_error = 1,
|
||||
rgbe_write_error = 2,
|
||||
rgbe_format_error = 3,
|
||||
rgbe_memory_error = 4,
|
||||
rgbe_error = function ( rgbe_error_code, msg ) {
|
||||
|
||||
switch ( rgbe_error_code ) {
|
||||
|
||||
case rgbe_read_error:
|
||||
console.error( 'THREE.RGBELoader Read Error: ' + ( msg || '' ) );
|
||||
break;
|
||||
|
||||
case rgbe_write_error:
|
||||
console.error( 'THREE.RGBELoader Write Error: ' + ( msg || '' ) );
|
||||
break;
|
||||
|
||||
case rgbe_format_error:
|
||||
console.error( 'THREE.RGBELoader Bad File Format: ' + ( msg || '' ) );
|
||||
break;
|
||||
|
||||
default:
|
||||
case rgbe_memory_error:
|
||||
console.error( 'THREE.RGBELoader: Error: ' + ( msg || '' ) );
|
||||
|
||||
}
|
||||
|
||||
return RGBE_RETURN_FAILURE;
|
||||
|
||||
},
|
||||
|
||||
/* offsets to red, green, and blue components in a data (float) pixel */
|
||||
//RGBE_DATA_RED = 0,
|
||||
//RGBE_DATA_GREEN = 1,
|
||||
//RGBE_DATA_BLUE = 2,
|
||||
|
||||
/* number of floats per pixel, use 4 since stored in rgba image format */
|
||||
//RGBE_DATA_SIZE = 4,
|
||||
|
||||
/* flags indicating which fields in an rgbe_header_info are valid */
|
||||
RGBE_VALID_PROGRAMTYPE = 1,
|
||||
RGBE_VALID_FORMAT = 2,
|
||||
RGBE_VALID_DIMENSIONS = 4,
|
||||
NEWLINE = '\n',
|
||||
fgets = function ( buffer, lineLimit, consume ) {
|
||||
|
||||
const chunkSize = 128;
|
||||
lineLimit = ! lineLimit ? 1024 : lineLimit;
|
||||
let p = buffer.pos,
|
||||
i = - 1,
|
||||
len = 0,
|
||||
s = '',
|
||||
chunk = String.fromCharCode.apply( null, new Uint16Array( buffer.subarray( p, p + chunkSize ) ) );
|
||||
|
||||
while ( 0 > ( i = chunk.indexOf( NEWLINE ) ) && len < lineLimit && p < buffer.byteLength ) {
|
||||
|
||||
s += chunk;
|
||||
len += chunk.length;
|
||||
p += chunkSize;
|
||||
chunk += String.fromCharCode.apply( null, new Uint16Array( buffer.subarray( p, p + chunkSize ) ) );
|
||||
|
||||
}
|
||||
|
||||
if ( - 1 < i ) {
|
||||
|
||||
/*for (i=l-1; i>=0; i--) {
|
||||
byteCode = m.charCodeAt(i);
|
||||
if (byteCode > 0x7f && byteCode <= 0x7ff) byteLen++;
|
||||
else if (byteCode > 0x7ff && byteCode <= 0xffff) byteLen += 2;
|
||||
if (byteCode >= 0xDC00 && byteCode <= 0xDFFF) i--; //trail surrogate
|
||||
}*/
|
||||
if ( false !== consume ) buffer.pos += len + i + 1;
|
||||
return s + chunk.slice( 0, i );
|
||||
|
||||
}
|
||||
|
||||
return false;
|
||||
|
||||
},
|
||||
|
||||
/* minimal header reading. modify if you want to parse more information */
|
||||
RGBE_ReadHeader = function ( buffer ) {
|
||||
|
||||
// regexes to parse header info fields
|
||||
const magic_token_re = /^#\?(\S+)/,
|
||||
gamma_re = /^\s*GAMMA\s*=\s*(\d+(\.\d+)?)\s*$/,
|
||||
exposure_re = /^\s*EXPOSURE\s*=\s*(\d+(\.\d+)?)\s*$/,
|
||||
format_re = /^\s*FORMAT=(\S+)\s*$/,
|
||||
dimensions_re = /^\s*\-Y\s+(\d+)\s+\+X\s+(\d+)\s*$/,
|
||||
// RGBE format header struct
|
||||
header = {
|
||||
valid: 0,
|
||||
|
||||
/* indicate which fields are valid */
|
||||
string: '',
|
||||
|
||||
/* the actual header string */
|
||||
comments: '',
|
||||
|
||||
/* comments found in header */
|
||||
programtype: 'RGBE',
|
||||
|
||||
/* listed at beginning of file to identify it after "#?". defaults to "RGBE" */
|
||||
format: '',
|
||||
|
||||
/* RGBE format, default 32-bit_rle_rgbe */
|
||||
gamma: 1.0,
|
||||
|
||||
/* image has already been gamma corrected with given gamma. defaults to 1.0 (no correction) */
|
||||
exposure: 1.0,
|
||||
|
||||
/* a value of 1.0 in an image corresponds to <exposure> watts/steradian/m^2. defaults to 1.0 */
|
||||
width: 0,
|
||||
height: 0
|
||||
/* image dimensions, width/height */
|
||||
|
||||
};
|
||||
let line, match;
|
||||
|
||||
if ( buffer.pos >= buffer.byteLength || ! ( line = fgets( buffer ) ) ) {
|
||||
|
||||
return rgbe_error( rgbe_read_error, 'no header found' );
|
||||
|
||||
}
|
||||
/* if you want to require the magic token then uncomment the next line */
|
||||
|
||||
|
||||
if ( ! ( match = line.match( magic_token_re ) ) ) {
|
||||
|
||||
return rgbe_error( rgbe_format_error, 'bad initial token' );
|
||||
|
||||
}
|
||||
|
||||
header.valid |= RGBE_VALID_PROGRAMTYPE;
|
||||
header.programtype = match[ 1 ];
|
||||
header.string += line + '\n';
|
||||
|
||||
while ( true ) {
|
||||
|
||||
line = fgets( buffer );
|
||||
if ( false === line ) break;
|
||||
header.string += line + '\n';
|
||||
|
||||
if ( '#' === line.charAt( 0 ) ) {
|
||||
|
||||
header.comments += line + '\n';
|
||||
continue; // comment line
|
||||
|
||||
}
|
||||
|
||||
if ( match = line.match( gamma_re ) ) {
|
||||
|
||||
header.gamma = parseFloat( match[ 1 ], 10 );
|
||||
|
||||
}
|
||||
|
||||
if ( match = line.match( exposure_re ) ) {
|
||||
|
||||
header.exposure = parseFloat( match[ 1 ], 10 );
|
||||
|
||||
}
|
||||
|
||||
if ( match = line.match( format_re ) ) {
|
||||
|
||||
header.valid |= RGBE_VALID_FORMAT;
|
||||
header.format = match[ 1 ]; //'32-bit_rle_rgbe';
|
||||
|
||||
}
|
||||
|
||||
if ( match = line.match( dimensions_re ) ) {
|
||||
|
||||
header.valid |= RGBE_VALID_DIMENSIONS;
|
||||
header.height = parseInt( match[ 1 ], 10 );
|
||||
header.width = parseInt( match[ 2 ], 10 );
|
||||
|
||||
}
|
||||
|
||||
if ( header.valid & RGBE_VALID_FORMAT && header.valid & RGBE_VALID_DIMENSIONS ) break;
|
||||
|
||||
}
|
||||
|
||||
if ( ! ( header.valid & RGBE_VALID_FORMAT ) ) {
|
||||
|
||||
return rgbe_error( rgbe_format_error, 'missing format specifier' );
|
||||
|
||||
}
|
||||
|
||||
if ( ! ( header.valid & RGBE_VALID_DIMENSIONS ) ) {
|
||||
|
||||
return rgbe_error( rgbe_format_error, 'missing image size specifier' );
|
||||
|
||||
}
|
||||
|
||||
return header;
|
||||
|
||||
},
|
||||
RGBE_ReadPixels_RLE = function ( buffer, w, h ) {
|
||||
|
||||
const scanline_width = w;
|
||||
|
||||
if ( // run length encoding is not allowed so read flat
|
||||
scanline_width < 8 || scanline_width > 0x7fff || // this file is not run length encoded
|
||||
2 !== buffer[ 0 ] || 2 !== buffer[ 1 ] || buffer[ 2 ] & 0x80 ) {
|
||||
|
||||
// return the flat buffer
|
||||
return new Uint8Array( buffer );
|
||||
|
||||
}
|
||||
|
||||
if ( scanline_width !== ( buffer[ 2 ] << 8 | buffer[ 3 ] ) ) {
|
||||
|
||||
return rgbe_error( rgbe_format_error, 'wrong scanline width' );
|
||||
|
||||
}
|
||||
|
||||
const data_rgba = new Uint8Array( 4 * w * h );
|
||||
|
||||
if ( ! data_rgba.length ) {
|
||||
|
||||
return rgbe_error( rgbe_memory_error, 'unable to allocate buffer space' );
|
||||
|
||||
}
|
||||
|
||||
let offset = 0,
|
||||
pos = 0;
|
||||
const ptr_end = 4 * scanline_width;
|
||||
const rgbeStart = new Uint8Array( 4 );
|
||||
const scanline_buffer = new Uint8Array( ptr_end );
|
||||
let num_scanlines = h; // read in each successive scanline
|
||||
|
||||
while ( num_scanlines > 0 && pos < buffer.byteLength ) {
|
||||
|
||||
if ( pos + 4 > buffer.byteLength ) {
|
||||
|
||||
return rgbe_error( rgbe_read_error );
|
||||
|
||||
}
|
||||
|
||||
rgbeStart[ 0 ] = buffer[ pos ++ ];
|
||||
rgbeStart[ 1 ] = buffer[ pos ++ ];
|
||||
rgbeStart[ 2 ] = buffer[ pos ++ ];
|
||||
rgbeStart[ 3 ] = buffer[ pos ++ ];
|
||||
|
||||
if ( 2 != rgbeStart[ 0 ] || 2 != rgbeStart[ 1 ] || ( rgbeStart[ 2 ] << 8 | rgbeStart[ 3 ] ) != scanline_width ) {
|
||||
|
||||
return rgbe_error( rgbe_format_error, 'bad rgbe scanline format' );
|
||||
|
||||
} // read each of the four channels for the scanline into the buffer
|
||||
// first red, then green, then blue, then exponent
|
||||
|
||||
|
||||
let ptr = 0,
|
||||
count;
|
||||
|
||||
while ( ptr < ptr_end && pos < buffer.byteLength ) {
|
||||
|
||||
count = buffer[ pos ++ ];
|
||||
const isEncodedRun = count > 128;
|
||||
if ( isEncodedRun ) count -= 128;
|
||||
|
||||
if ( 0 === count || ptr + count > ptr_end ) {
|
||||
|
||||
return rgbe_error( rgbe_format_error, 'bad scanline data' );
|
||||
|
||||
}
|
||||
|
||||
if ( isEncodedRun ) {
|
||||
|
||||
// a (encoded) run of the same value
|
||||
const byteValue = buffer[ pos ++ ];
|
||||
|
||||
for ( let i = 0; i < count; i ++ ) {
|
||||
|
||||
scanline_buffer[ ptr ++ ] = byteValue;
|
||||
|
||||
} //ptr += count;
|
||||
|
||||
} else {
|
||||
|
||||
// a literal-run
|
||||
scanline_buffer.set( buffer.subarray( pos, pos + count ), ptr );
|
||||
ptr += count;
|
||||
pos += count;
|
||||
|
||||
}
|
||||
|
||||
} // now convert data from buffer into rgba
|
||||
// first red, then green, then blue, then exponent (alpha)
|
||||
|
||||
|
||||
const l = scanline_width; //scanline_buffer.byteLength;
|
||||
|
||||
for ( let i = 0; i < l; i ++ ) {
|
||||
|
||||
let off = 0;
|
||||
data_rgba[ offset ] = scanline_buffer[ i + off ];
|
||||
off += scanline_width; //1;
|
||||
|
||||
data_rgba[ offset + 1 ] = scanline_buffer[ i + off ];
|
||||
off += scanline_width; //1;
|
||||
|
||||
data_rgba[ offset + 2 ] = scanline_buffer[ i + off ];
|
||||
off += scanline_width; //1;
|
||||
|
||||
data_rgba[ offset + 3 ] = scanline_buffer[ i + off ];
|
||||
offset += 4;
|
||||
|
||||
}
|
||||
|
||||
num_scanlines --;
|
||||
|
||||
}
|
||||
|
||||
return data_rgba;
|
||||
|
||||
};
|
||||
|
||||
const RGBEByteToRGBFloat = function ( sourceArray, sourceOffset, destArray, destOffset ) {
|
||||
|
||||
const e = sourceArray[ sourceOffset + 3 ];
|
||||
const scale = Math.pow( 2.0, e - 128.0 ) / 255.0;
|
||||
destArray[ destOffset + 0 ] = sourceArray[ sourceOffset + 0 ] * scale;
|
||||
destArray[ destOffset + 1 ] = sourceArray[ sourceOffset + 1 ] * scale;
|
||||
destArray[ destOffset + 2 ] = sourceArray[ sourceOffset + 2 ] * scale;
|
||||
|
||||
};
|
||||
|
||||
const RGBEByteToRGBHalf = function ( sourceArray, sourceOffset, destArray, destOffset ) {
|
||||
|
||||
const e = sourceArray[ sourceOffset + 3 ];
|
||||
const scale = Math.pow( 2.0, e - 128.0 ) / 255.0;
|
||||
destArray[ destOffset + 0 ] = THREE.DataUtils.toHalfFloat( sourceArray[ sourceOffset + 0 ] * scale );
|
||||
destArray[ destOffset + 1 ] = THREE.DataUtils.toHalfFloat( sourceArray[ sourceOffset + 1 ] * scale );
|
||||
destArray[ destOffset + 2 ] = THREE.DataUtils.toHalfFloat( sourceArray[ sourceOffset + 2 ] * scale );
|
||||
|
||||
};
|
||||
|
||||
const byteArray = new Uint8Array( buffer );
|
||||
byteArray.pos = 0;
|
||||
const rgbe_header_info = RGBE_ReadHeader( byteArray );
|
||||
|
||||
if ( RGBE_RETURN_FAILURE !== rgbe_header_info ) {
|
||||
|
||||
const w = rgbe_header_info.width,
|
||||
h = rgbe_header_info.height,
|
||||
image_rgba_data = RGBE_ReadPixels_RLE( byteArray.subarray( byteArray.pos ), w, h );
|
||||
|
||||
if ( RGBE_RETURN_FAILURE !== image_rgba_data ) {
|
||||
|
||||
let data, format, type;
|
||||
let numElements;
|
||||
|
||||
switch ( this.type ) {
|
||||
|
||||
case THREE.UnsignedByteType:
|
||||
data = image_rgba_data;
|
||||
format = THREE.RGBEFormat; // handled as THREE.RGBAFormat in shaders
|
||||
|
||||
type = THREE.UnsignedByteType;
|
||||
break;
|
||||
|
||||
case THREE.FloatType:
|
||||
numElements = image_rgba_data.length / 4 * 3;
|
||||
const floatArray = new Float32Array( numElements );
|
||||
|
||||
for ( let j = 0; j < numElements; j ++ ) {
|
||||
|
||||
RGBEByteToRGBFloat( image_rgba_data, j * 4, floatArray, j * 3 );
|
||||
|
||||
}
|
||||
|
||||
data = floatArray;
|
||||
format = THREE.RGBFormat;
|
||||
type = THREE.FloatType;
|
||||
break;
|
||||
|
||||
case THREE.HalfFloatType:
|
||||
numElements = image_rgba_data.length / 4 * 3;
|
||||
const halfArray = new Uint16Array( numElements );
|
||||
|
||||
for ( let j = 0; j < numElements; j ++ ) {
|
||||
|
||||
RGBEByteToRGBHalf( image_rgba_data, j * 4, halfArray, j * 3 );
|
||||
|
||||
}
|
||||
|
||||
data = halfArray;
|
||||
format = THREE.RGBFormat;
|
||||
type = THREE.HalfFloatType;
|
||||
break;
|
||||
|
||||
default:
|
||||
console.error( 'THREE.RGBELoader: unsupported type: ', this.type );
|
||||
break;
|
||||
|
||||
}
|
||||
|
||||
return {
|
||||
width: w,
|
||||
height: h,
|
||||
data: data,
|
||||
header: rgbe_header_info.string,
|
||||
gamma: rgbe_header_info.gamma,
|
||||
exposure: rgbe_header_info.exposure,
|
||||
format: format,
|
||||
type: type
|
||||
};
|
||||
|
||||
}
|
||||
|
||||
}
|
||||
|
||||
return null;
|
||||
|
||||
}
|
||||
|
||||
setDataType( value ) {
|
||||
|
||||
this.type = value;
|
||||
return this;
|
||||
|
||||
}
|
||||
|
||||
load( url, onLoad, onProgress, onError ) {
|
||||
|
||||
function onLoadCallback( texture, texData ) {
|
||||
|
||||
switch ( texture.type ) {
|
||||
|
||||
case THREE.UnsignedByteType:
|
||||
texture.encoding = THREE.RGBEEncoding;
|
||||
texture.minFilter = THREE.NearestFilter;
|
||||
texture.magFilter = THREE.NearestFilter;
|
||||
texture.generateMipmaps = false;
|
||||
texture.flipY = true;
|
||||
break;
|
||||
|
||||
case THREE.FloatType:
|
||||
texture.encoding = THREE.LinearEncoding;
|
||||
texture.minFilter = THREE.LinearFilter;
|
||||
texture.magFilter = THREE.LinearFilter;
|
||||
texture.generateMipmaps = false;
|
||||
texture.flipY = true;
|
||||
break;
|
||||
|
||||
case THREE.HalfFloatType:
|
||||
texture.encoding = THREE.LinearEncoding;
|
||||
texture.minFilter = THREE.LinearFilter;
|
||||
texture.magFilter = THREE.LinearFilter;
|
||||
texture.generateMipmaps = false;
|
||||
texture.flipY = true;
|
||||
break;
|
||||
|
||||
}
|
||||
|
||||
if ( onLoad ) onLoad( texture, texData );
|
||||
|
||||
}
|
||||
|
||||
return super.load( url, onLoadCallback, onProgress, onError );
|
||||
|
||||
}
|
||||
|
||||
}
|
||||
|
||||
THREE.RGBELoader = RGBELoader;
|
||||
|
||||
} )();
|
||||
|
|
@ -0,0 +1,648 @@
|
|||
/**
|
||||
* bvh-tree
|
||||
* A Bounding Volume Hierarchy data structure implementation.
|
||||
* https://github.com/benraziel/bvh-tree
|
||||
*
|
||||
* @author Ben Raziel
|
||||
*/
|
||||
var bvhtree = bvhtree || {};
|
||||
bvhtree.EPSILON = 1e-6;
|
||||
|
||||
/**
|
||||
* A 3D Vector class. Based on three.js Vector3
|
||||
*/
|
||||
bvhtree.BVHVector3 = function ( x, y, z ) {
|
||||
this.x = x || 0;
|
||||
this.y = y || 0;
|
||||
this.z = z || 0;
|
||||
|
||||
};
|
||||
|
||||
bvhtree.BVHVector3.prototype = {
|
||||
|
||||
constructor: bvhtree.BVHVector3,
|
||||
|
||||
copy: function ( v ) {
|
||||
|
||||
this.x = v.x;
|
||||
this.y = v.y;
|
||||
this.z = v.z;
|
||||
|
||||
return this;
|
||||
|
||||
},
|
||||
|
||||
set: function ( x, y, z ) {
|
||||
|
||||
this.x = x;
|
||||
this.y = y;
|
||||
this.z = z;
|
||||
|
||||
return this;
|
||||
},
|
||||
|
||||
setFromArray: function(array, firstElementPos) {
|
||||
this.x = array[firstElementPos];
|
||||
this.y = array[firstElementPos+1];
|
||||
this.z = array[firstElementPos+2];
|
||||
},
|
||||
|
||||
add: function ( v ) {
|
||||
|
||||
this.x += v.x;
|
||||
this.y += v.y;
|
||||
this.z += v.z;
|
||||
|
||||
return this;
|
||||
},
|
||||
|
||||
multiplyScalar: function ( scalar ) {
|
||||
|
||||
this.x *= scalar;
|
||||
this.y *= scalar;
|
||||
this.z *= scalar;
|
||||
|
||||
return this;
|
||||
|
||||
},
|
||||
|
||||
subVectors: function ( a, b ) {
|
||||
|
||||
this.x = a.x - b.x;
|
||||
this.y = a.y - b.y;
|
||||
this.z = a.z - b.z;
|
||||
|
||||
return this;
|
||||
|
||||
},
|
||||
|
||||
dot: function ( v ) {
|
||||
|
||||
return this.x * v.x + this.y * v.y + this.z * v.z;
|
||||
|
||||
},
|
||||
|
||||
cross: function ( v ) {
|
||||
var x = this.x, y = this.y, z = this.z;
|
||||
|
||||
this.x = y * v.z - z * v.y;
|
||||
this.y = z * v.x - x * v.z;
|
||||
this.z = x * v.y - y * v.x;
|
||||
|
||||
return this;
|
||||
},
|
||||
|
||||
crossVectors: function ( a, b ) {
|
||||
|
||||
var ax = a.x, ay = a.y, az = a.z;
|
||||
var bx = b.x, by = b.y, bz = b.z;
|
||||
|
||||
this.x = ay * bz - az * by;
|
||||
this.y = az * bx - ax * bz;
|
||||
this.z = ax * by - ay * bx;
|
||||
|
||||
return this;
|
||||
},
|
||||
|
||||
clone: function () {
|
||||
return new bvhtree.BVHVector3( this.x, this.y, this.z );
|
||||
}
|
||||
};
|
||||
|
||||
/**
|
||||
* @typedef {Object} Point A Point in 3D space
|
||||
* @property {number} x x coordinate of the point
|
||||
* @property {number} y y coordinate of the point
|
||||
* @property {number} z z coordinate of the point
|
||||
*
|
||||
* @typedef Point[3] Triangle A triangle in 3D space
|
||||
*/
|
||||
|
||||
/**
|
||||
* Constructs a bounding volume heirarchy from a list of triangles
|
||||
* @class
|
||||
* @param {Triangle[]} triangles an array of triangles to index. Each triangle is represented as an array of 3 xyz coordinates: [{x: X0, y: Y0, z: Z0}, {x: X1, y: Y1, z: Z1}, {x: X2, y: Y2, z: Z2}]
|
||||
* @param {number} [maxTrianglesPerNode=10] the maximum number of triangles in each node of the BVH tree. Once this value is reached, that node is split into two child nodes.
|
||||
*/
|
||||
bvhtree.BVH = function(triangles, maxTrianglesPerNode) {
|
||||
var trianglesArray = [];
|
||||
trianglesArray.length = triangles.length * 9;
|
||||
|
||||
for (var i = 0; i < triangles.length; i++) {
|
||||
var p0 = triangles[i][0];
|
||||
var p1 = triangles[i][1];
|
||||
var p2 = triangles[i][2];
|
||||
|
||||
trianglesArray[i*9] = p0.x;
|
||||
trianglesArray[i*9+1] = p0.y;
|
||||
trianglesArray[i*9+2] = p0.z;
|
||||
|
||||
trianglesArray[i*9+3] = p1.x;
|
||||
trianglesArray[i*9+4] = p1.y;
|
||||
trianglesArray[i*9+5] = p1.z;
|
||||
|
||||
trianglesArray[i*9+6] = p2.x;
|
||||
trianglesArray[i*9+7] = p2.y;
|
||||
trianglesArray[i*9+8] = p2.z;
|
||||
}
|
||||
|
||||
|
||||
this._trianglesArray = trianglesArray;
|
||||
this._maxTrianglesPerNode = maxTrianglesPerNode || 10;
|
||||
this._bboxArray = this.calcBoundingBoxes(trianglesArray);
|
||||
|
||||
// clone a helper array
|
||||
this._bboxHelper = new Float32Array(this._bboxArray.length);
|
||||
this._bboxHelper.set(this._bboxArray);
|
||||
|
||||
// create the root node, add all the triangles to it
|
||||
var triangleCount = trianglesArray.length / 9;
|
||||
var extents = this.calcExtents(0, triangleCount, bvhtree.EPSILON);
|
||||
this._rootNode = new bvhtree.BVHNode(extents[0], extents[1], 0, triangleCount, 0);
|
||||
|
||||
this._nodesToSplit = [this._rootNode];
|
||||
|
||||
while (this._nodesToSplit.length > 0) {
|
||||
var node = this._nodesToSplit.pop();
|
||||
this.splitNode(node);
|
||||
}
|
||||
};
|
||||
|
||||
/**
|
||||
* returns a list of all the triangles in the BVH which interected a specific node.
|
||||
* We use the BVH node structure to first cull out nodes which do not intereset the ray.
|
||||
* For rays that did intersect, we test intersection of the ray with each triangle
|
||||
* @param {Point} rayOrigin the origin position of the ray.
|
||||
* @param {Point} rayDirection the direction vector of the ray.
|
||||
* @param {Boolean} backfaceCulling if 'true', only intersections with front-faces of the mesh will be performed.
|
||||
* @return IntersectionResult[] an array of intersection result, one for each triangle which intersected the BVH
|
||||
*
|
||||
* @typedef {Object} IntersectionResult
|
||||
* @property Array[] triangle the triangle which the ray intersected
|
||||
* @property number triangleIndex the position of the interescting triangle in the input triangle array provided to the BVH constructor.
|
||||
* @property {Point} intersectionPoint the interesection point of the ray on the triangle.
|
||||
*/
|
||||
bvhtree.BVH.prototype.intersectRay = function(rayOrigin, rayDirection, backfaceCulling) {
|
||||
var nodesToIntersect = [this._rootNode];
|
||||
var trianglesInIntersectingNodes = []; // a list of nodes that intersect the ray (according to their bounding box)
|
||||
var intersectingTriangles = [];
|
||||
var i;
|
||||
|
||||
var invRayDirection = new bvhtree.BVHVector3(
|
||||
1.0 / rayDirection.x,
|
||||
1.0 / rayDirection.y,
|
||||
1.0 / rayDirection.z
|
||||
);
|
||||
|
||||
// go over the BVH tree, and extract the list of triangles that lie in nodes that intersect the ray.
|
||||
// note: these triangles may not intersect the ray themselves
|
||||
while (nodesToIntersect.length > 0) {
|
||||
var node = nodesToIntersect.pop();
|
||||
|
||||
if (bvhtree.BVH.intersectNodeBox(rayOrigin, invRayDirection, node)) {
|
||||
if (node._node0) {
|
||||
nodesToIntersect.push(node._node0);
|
||||
}
|
||||
|
||||
if (node._node1) {
|
||||
nodesToIntersect.push(node._node1);
|
||||
}
|
||||
|
||||
for (i = node._startIndex; i < node._endIndex; i++) {
|
||||
trianglesInIntersectingNodes.push(this._bboxArray[i*7]);
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// go over the list of candidate triangles, and check each of them using ray triangle intersection
|
||||
var a = new bvhtree.BVHVector3();
|
||||
var b = new bvhtree.BVHVector3();
|
||||
var c = new bvhtree.BVHVector3();
|
||||
var rayOriginVec3 = new bvhtree.BVHVector3(rayOrigin.x, rayOrigin.y, rayOrigin.z);
|
||||
var rayDirectionVec3 = new bvhtree.BVHVector3(rayDirection.x, rayDirection.y, rayDirection.z);
|
||||
|
||||
for (i = 0; i < trianglesInIntersectingNodes.length; i++) {
|
||||
var triIndex = trianglesInIntersectingNodes[i];
|
||||
|
||||
a.setFromArray(this._trianglesArray, triIndex*9);
|
||||
b.setFromArray(this._trianglesArray, triIndex*9+3);
|
||||
c.setFromArray(this._trianglesArray, triIndex*9+6);
|
||||
|
||||
var intersectionPoint = bvhtree.BVH.intersectRayTriangle(a, b, c, rayOriginVec3, rayDirectionVec3, backfaceCulling);
|
||||
|
||||
if (intersectionPoint) {
|
||||
intersectingTriangles.push({
|
||||
triangle: [a.clone(), b.clone(), c.clone()],
|
||||
triangleIndex: triIndex,
|
||||
intersectionPoint: intersectionPoint
|
||||
});
|
||||
}
|
||||
}
|
||||
|
||||
return intersectingTriangles;
|
||||
};
|
||||
|
||||
/**
|
||||
* Gets an array of triangle, and calculates the bounding box for each of them, and adds an index to the triangle's position in the array
|
||||
* Each bbox is saved as 7 values in a Float32Array: (position, minX, minY, minZ, maxX, maxY, maxZ)
|
||||
*/
|
||||
bvhtree.BVH.prototype.calcBoundingBoxes = function(trianglesArray) {
|
||||
var p0x, p0y, p0z;
|
||||
var p1x, p1y, p1z;
|
||||
var p2x, p2y, p2z;
|
||||
var minX, minY, minZ;
|
||||
var maxX, maxY, maxZ;
|
||||
|
||||
var triangleCount = trianglesArray.length / 9;
|
||||
var bboxArray = new Float32Array(triangleCount * 7);
|
||||
|
||||
for (var i = 0; i < triangleCount; i++) {
|
||||
p0x = trianglesArray[i*9];
|
||||
p0y = trianglesArray[i*9+1];
|
||||
p0z = trianglesArray[i*9+2];
|
||||
p1x = trianglesArray[i*9+3];
|
||||
p1y = trianglesArray[i*9+4];
|
||||
p1z = trianglesArray[i*9+5];
|
||||
p2x = trianglesArray[i*9+6];
|
||||
p2y = trianglesArray[i*9+7];
|
||||
p2z = trianglesArray[i*9+8];
|
||||
|
||||
minX = Math.min(Math.min(p0x, p1x), p2x);
|
||||
minY = Math.min(Math.min(p0y, p1y), p2y);
|
||||
minZ = Math.min(Math.min(p0z, p1z), p2z);
|
||||
maxX = Math.max(Math.max(p0x, p1x), p2x);
|
||||
maxY = Math.max(Math.max(p0y, p1y), p2y);
|
||||
maxZ = Math.max(Math.max(p0z, p1z), p2z);
|
||||
|
||||
bvhtree.BVH.setBox(bboxArray, i, i, minX, minY, minZ, maxX, maxY, maxZ);
|
||||
}
|
||||
|
||||
return bboxArray;
|
||||
};
|
||||
|
||||
/**
|
||||
* Calculates the extents (i.e the min and max coordinates) of a list of bounding boxes in the bboxArray
|
||||
* @param startIndex the index of the first triangle that we want to calc extents for
|
||||
* @param endIndex the index of the last triangle that we want to calc extents for
|
||||
* @param expandBy a small epsilon to expand the bbox by, for safety during ray-box intersections
|
||||
*/
|
||||
bvhtree.BVH.prototype.calcExtents = function(startIndex, endIndex, expandBy) {
|
||||
expandBy = expandBy || 0.0;
|
||||
|
||||
if (startIndex >= endIndex) {
|
||||
return [{'x': 0, 'y': 0, 'z': 0}, {'x': 0, 'y': 0, 'z': 0}];
|
||||
}
|
||||
|
||||
var minX = Number.MAX_VALUE;
|
||||
var minY = Number.MAX_VALUE;
|
||||
var minZ = Number.MAX_VALUE;
|
||||
var maxX = -Number.MAX_VALUE;
|
||||
var maxY = -Number.MAX_VALUE;
|
||||
var maxZ = -Number.MAX_VALUE;
|
||||
|
||||
for (var i = startIndex; i < endIndex; i++) {
|
||||
minX = Math.min(this._bboxArray[i*7+1], minX);
|
||||
minY = Math.min(this._bboxArray[i*7+2], minY);
|
||||
minZ = Math.min(this._bboxArray[i*7+3], minZ);
|
||||
maxX = Math.max(this._bboxArray[i*7+4], maxX);
|
||||
maxY = Math.max(this._bboxArray[i*7+5], maxY);
|
||||
maxZ = Math.max(this._bboxArray[i*7+6], maxZ);
|
||||
}
|
||||
|
||||
return [
|
||||
{'x': minX - expandBy, 'y': minY - expandBy, 'z': minZ - expandBy},
|
||||
{'x': maxX + expandBy, 'y': maxY + expandBy, 'z': maxZ + expandBy}
|
||||
];
|
||||
};
|
||||
|
||||
bvhtree.BVH.prototype.splitNode = function(node) {
|
||||
if ((node.elementCount() <= this._maxTrianglesPerNode) || (node.elementCount() === 0)) {
|
||||
return;
|
||||
}
|
||||
|
||||
var startIndex = node._startIndex;
|
||||
var endIndex = node._endIndex;
|
||||
|
||||
var leftNode = [ [],[],[] ];
|
||||
var rightNode = [ [],[],[] ];
|
||||
var extentCenters = [node.centerX(), node.centerY(), node.centerZ()];
|
||||
|
||||
var extentsLength = [
|
||||
node._extentsMax.x - node._extentsMin.x,
|
||||
node._extentsMax.y - node._extentsMin.y,
|
||||
node._extentsMax.z - node._extentsMin.z
|
||||
];
|
||||
|
||||
var objectCenter = [];
|
||||
objectCenter.length = 3;
|
||||
|
||||
for (var i = startIndex; i < endIndex; i++) {
|
||||
objectCenter[0] = (this._bboxArray[i * 7 + 1] + this._bboxArray[i * 7 + 4]) * 0.5; // center = (min + max) / 2
|
||||
objectCenter[1] = (this._bboxArray[i * 7 + 2] + this._bboxArray[i * 7 + 5]) * 0.5; // center = (min + max) / 2
|
||||
objectCenter[2] = (this._bboxArray[i * 7 + 3] + this._bboxArray[i * 7 + 6]) * 0.5; // center = (min + max) / 2
|
||||
|
||||
for (var j = 0; j < 3; j++) {
|
||||
if (objectCenter[j] < extentCenters[j]) {
|
||||
leftNode[j].push(i);
|
||||
}
|
||||
else {
|
||||
rightNode[j].push(i);
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// check if we couldn't split the node by any of the axes (x, y or z). halt here, dont try to split any more (cause it will always fail, and we'll enter an infinite loop
|
||||
var splitFailed = [];
|
||||
splitFailed.length = 3;
|
||||
|
||||
splitFailed[0] = (leftNode[0].length === 0) || (rightNode[0].length === 0);
|
||||
splitFailed[1] = (leftNode[1].length === 0) || (rightNode[1].length === 0);
|
||||
splitFailed[2] = (leftNode[2].length === 0) || (rightNode[2].length === 0);
|
||||
|
||||
if (splitFailed[0] && splitFailed[1] && splitFailed[2]) {
|
||||
return;
|
||||
}
|
||||
|
||||
// choose the longest split axis. if we can't split by it, choose next best one.
|
||||
var splitOrder = [0, 1, 2];
|
||||
|
||||
splitOrder.sort(function(axis0, axis1) {
|
||||
return (extentsLength[axis1] - extentsLength[axis0])
|
||||
});
|
||||
|
||||
var leftElements;
|
||||
var rightElements;
|
||||
|
||||
for (j = 0; j < 3; j++) {
|
||||
var candidateIndex = splitOrder[j];
|
||||
|
||||
if (!splitFailed[candidateIndex]) {
|
||||
leftElements = leftNode[candidateIndex];
|
||||
rightElements = rightNode[candidateIndex];
|
||||
|
||||
break;
|
||||
}
|
||||
}
|
||||
|
||||
// sort the elements in range (startIndex, endIndex) according to which node they should be at
|
||||
var node0Start = startIndex;
|
||||
var node0End = node0Start + leftElements.length;
|
||||
var node1Start = node0End;
|
||||
var node1End = endIndex;
|
||||
var currElement;
|
||||
|
||||
var helperPos = node._startIndex;
|
||||
var concatenatedElements = leftElements.concat(rightElements);
|
||||
|
||||
for (i = 0; i < concatenatedElements.length; i++) {
|
||||
currElement = concatenatedElements[i];
|
||||
bvhtree.BVH.copyBox(this._bboxArray, currElement, this._bboxHelper, helperPos);
|
||||
helperPos++;
|
||||
}
|
||||
|
||||
// copy results back to main array
|
||||
var subArr = this._bboxHelper.subarray(node._startIndex * 7, node._endIndex * 7);
|
||||
this._bboxArray.set(subArr, node._startIndex * 7);
|
||||
|
||||
// create 2 new nodes for the node we just split, and add links to them from the parent node
|
||||
var node0Extents = this.calcExtents(node0Start, node0End, bvhtree.EPSILON);
|
||||
var node1Extents = this.calcExtents(node1Start, node1End, bvhtree.EPSILON);
|
||||
|
||||
var node0 = new bvhtree.BVHNode(node0Extents[0], node0Extents[1], node0Start, node0End, node._level + 1);
|
||||
var node1 = new bvhtree.BVHNode(node1Extents[0], node1Extents[1], node1Start, node1End, node._level + 1);
|
||||
|
||||
node._node0 = node0;
|
||||
node._node1 = node1;
|
||||
node.clearShapes();
|
||||
|
||||
// add new nodes to the split queue
|
||||
this._nodesToSplit.push(node0);
|
||||
this._nodesToSplit.push(node1);
|
||||
};
|
||||
|
||||
bvhtree.BVH._calcTValues = function(minVal, maxVal, rayOriginCoord, invdir) {
|
||||
var res = {min: 0, max: 0};
|
||||
|
||||
if ( invdir >= 0 ) {
|
||||
res.min = ( minVal - rayOriginCoord ) * invdir;
|
||||
res.max = ( maxVal - rayOriginCoord ) * invdir;
|
||||
|
||||
} else {
|
||||
res.min = ( maxVal - rayOriginCoord ) * invdir;
|
||||
res.max = ( minVal - rayOriginCoord ) * invdir;
|
||||
}
|
||||
|
||||
return res;
|
||||
};
|
||||
|
||||
bvhtree.BVH.intersectNodeBox = function(rayOrigin, invRayDirection, node) {
|
||||
var t = bvhtree.BVH._calcTValues(node._extentsMin.x, node._extentsMax.x, rayOrigin.x, invRayDirection.x);
|
||||
var ty = bvhtree.BVH._calcTValues(node._extentsMin.y, node._extentsMax.y, rayOrigin.y, invRayDirection.y);
|
||||
|
||||
if ( ( t.min > ty.max ) || ( ty.min > t.max ) ) {
|
||||
return false;
|
||||
}
|
||||
|
||||
// These lines also handle the case where tmin or tmax is NaN
|
||||
// (result of 0 * Infinity). x !== x returns true if x is NaN
|
||||
if ( ty.min > t.min || t.min !== t.min ) {
|
||||
t.min = ty.min;
|
||||
}
|
||||
|
||||
if ( ty.max < t.max || t.max !== t.max ) {
|
||||
t.max = ty.max;
|
||||
}
|
||||
|
||||
var tz = bvhtree.BVH._calcTValues(node._extentsMin.z, node._extentsMax.z, rayOrigin.z, invRayDirection.z);
|
||||
|
||||
if ( ( t.min > tz.max ) || ( tz.min > t.max ) ) {
|
||||
return false;
|
||||
}
|
||||
|
||||
if ( tz.min > t.min || t.min !== t.min ) {
|
||||
t.min = tz.min;
|
||||
}
|
||||
|
||||
if ( tz.max < t.max || t.max !== t.max ) {
|
||||
t.max = tz.max;
|
||||
}
|
||||
|
||||
//return point closest to the ray (positive side)
|
||||
if (t.max < 0 ) {
|
||||
return false;
|
||||
}
|
||||
|
||||
return true;
|
||||
};
|
||||
|
||||
bvhtree.BVH.intersectRayTriangle = (function () {
|
||||
// Compute the offset origin, edges, and normal.
|
||||
var diff = new bvhtree.BVHVector3();
|
||||
var edge1 = new bvhtree.BVHVector3();
|
||||
var edge2 = new bvhtree.BVHVector3();
|
||||
var normal = new bvhtree.BVHVector3();
|
||||
|
||||
return function (a, b, c, rayOrigin, rayDirection, backfaceCulling) {
|
||||
|
||||
// from http://www.geometrictools.com/LibMathematics/Intersection/Wm5IntrRay3Triangle3.cpp
|
||||
|
||||
edge1.subVectors(b, a);
|
||||
edge2.subVectors(c, a);
|
||||
normal.crossVectors(edge1, edge2);
|
||||
|
||||
// Solve Q + t*D = b1*E1 + bL*E2 (Q = kDiff, D = ray direction,
|
||||
// E1 = kEdge1, E2 = kEdge2, N = Cross(E1,E2)) by
|
||||
// |Dot(D,N)|*b1 = sign(Dot(D,N))*Dot(D,Cross(Q,E2))
|
||||
// |Dot(D,N)|*b2 = sign(Dot(D,N))*Dot(D,Cross(E1,Q))
|
||||
// |Dot(D,N)|*t = -sign(Dot(D,N))*Dot(Q,N)
|
||||
var DdN = rayDirection.dot(normal);
|
||||
var sign;
|
||||
|
||||
if (DdN > 0) {
|
||||
|
||||
if (backfaceCulling) {
|
||||
return null;
|
||||
}
|
||||
|
||||
sign = 1;
|
||||
|
||||
} else if (DdN < 0) {
|
||||
|
||||
sign = -1;
|
||||
DdN = -DdN;
|
||||
|
||||
} else {
|
||||
|
||||
return null;
|
||||
|
||||
}
|
||||
|
||||
diff.subVectors(rayOrigin, a);
|
||||
var DdQxE2 = sign * rayDirection.dot(edge2.crossVectors(diff, edge2));
|
||||
|
||||
// b1 < 0, no intersection
|
||||
if (DdQxE2 < 0) {
|
||||
return null;
|
||||
}
|
||||
|
||||
var DdE1xQ = sign * rayDirection.dot(edge1.cross(diff));
|
||||
|
||||
// b2 < 0, no intersection
|
||||
if (DdE1xQ < 0) {
|
||||
return null;
|
||||
}
|
||||
|
||||
// b1+b2 > 1, no intersection
|
||||
if (DdQxE2 + DdE1xQ > DdN) {
|
||||
return null;
|
||||
}
|
||||
|
||||
// Line intersects triangle, check if ray does.
|
||||
var QdN = -sign * diff.dot(normal);
|
||||
|
||||
// t < 0, no intersection
|
||||
if (QdN < 0) {
|
||||
return null;
|
||||
}
|
||||
|
||||
// Ray intersects triangle.
|
||||
var t = QdN / DdN;
|
||||
var result = new bvhtree.BVHVector3();
|
||||
return result.copy( rayDirection ).multiplyScalar( t ).add( rayOrigin );
|
||||
};
|
||||
}());
|
||||
|
||||
bvhtree.BVH.setBox = function(bboxArray, pos, triangleId, minX, minY, minZ, maxX, maxY, maxZ) {
|
||||
bboxArray[pos*7] = triangleId;
|
||||
bboxArray[pos*7+1] = minX;
|
||||
bboxArray[pos*7+2] = minY;
|
||||
bboxArray[pos*7+3] = minZ;
|
||||
bboxArray[pos*7+4] = maxX;
|
||||
bboxArray[pos*7+5] = maxY;
|
||||
bboxArray[pos*7+6] = maxZ;
|
||||
};
|
||||
|
||||
bvhtree.BVH.copyBox = function(sourceArray, sourcePos, destArray, destPos) {
|
||||
destArray[destPos*7] = sourceArray[sourcePos*7];
|
||||
destArray[destPos*7+1] = sourceArray[sourcePos*7+1];
|
||||
destArray[destPos*7+2] = sourceArray[sourcePos*7+2];
|
||||
destArray[destPos*7+3] = sourceArray[sourcePos*7+3];
|
||||
destArray[destPos*7+4] = sourceArray[sourcePos*7+4];
|
||||
destArray[destPos*7+5] = sourceArray[sourcePos*7+5];
|
||||
destArray[destPos*7+6] = sourceArray[sourcePos*7+6];
|
||||
};
|
||||
|
||||
bvhtree.BVH.getBox = function(bboxArray, pos, outputBox) {
|
||||
outputBox.triangleId = bboxArray[pos*7];
|
||||
outputBox.minX = bboxArray[pos*7+1];
|
||||
outputBox.minY = bboxArray[pos*7+2];
|
||||
outputBox.minZ = bboxArray[pos*7+3];
|
||||
outputBox.maxX = bboxArray[pos*7+4];
|
||||
outputBox.maxY = bboxArray[pos*7+5];
|
||||
outputBox.maxZ = bboxArray[pos*7+6];
|
||||
};
|
||||
|
||||
|
||||
/**
|
||||
* A node in the BVH structure
|
||||
* @class
|
||||
* @param {Point} extentsMin the min coords of this node's bounding box ({x,y,z})
|
||||
* @param {Point} extentsMax the max coords of this node's bounding box ({x,y,z})
|
||||
* @param {number} startIndex an index in the bbox array, where the first element of this node is located
|
||||
* @param {number} endIndex an index in the bbox array, where the last of this node is located, plus 1 (meaning that its non-inclusive).
|
||||
* @param {number} the distance of this node from the root for the bvh tree. root node has level=0, its children have level=1 etc.
|
||||
*/
|
||||
bvhtree.BVHNode = function(extentsMin, extentsMax, startIndex, endIndex, level) {
|
||||
this._extentsMin = extentsMin;
|
||||
this._extentsMax = extentsMax;
|
||||
this._startIndex = startIndex;
|
||||
this._endIndex = endIndex;
|
||||
this._level = level;
|
||||
this._node0 = null;
|
||||
this._node1 = null;
|
||||
};
|
||||
|
||||
bvhtree.BVHNode.prototype.elementCount = function() {
|
||||
return this._endIndex - this._startIndex;
|
||||
};
|
||||
|
||||
bvhtree.BVHNode.prototype.centerX = function() {
|
||||
return (this._extentsMin.x + this._extentsMax.x) * 0.5;
|
||||
};
|
||||
|
||||
bvhtree.BVHNode.prototype.centerY = function() {
|
||||
return (this._extentsMin.y + this._extentsMax.y) * 0.5;
|
||||
};
|
||||
|
||||
bvhtree.BVHNode.prototype.centerZ = function() {
|
||||
return (this._extentsMin.z + this._extentsMax.z) * 0.5;
|
||||
};
|
||||
|
||||
bvhtree.BVHNode.prototype.clearShapes = function() {
|
||||
this._startIndex = -1;
|
||||
this._endIndex = -1;
|
||||
};
|
||||
|
||||
bvhtree.BVHNode.calcBoundingSphereRadius = function(extentsMin, extentsMax) {
|
||||
var centerX = (extentsMin.x + extentsMax.x) * 0.5;
|
||||
var centerY = (extentsMin.y + extentsMax.y) * 0.5;
|
||||
var centerZ = (extentsMin.z + extentsMax.z) * 0.5;
|
||||
|
||||
var extentsMinDistSqr =
|
||||
(centerX - extentsMin.x) * (centerX - extentsMin.x) +
|
||||
(centerY - extentsMin.y) * (centerY - extentsMin.y) +
|
||||
(centerZ - extentsMin.z) * (centerZ - extentsMin.z);
|
||||
|
||||
var extentsMaxDistSqr =
|
||||
(centerX - extentsMax.x) * (centerX - extentsMax.x) +
|
||||
(centerY - extentsMax.y) * (centerY - extentsMax.y) +
|
||||
(centerZ - extentsMax.z) * (centerZ - extentsMax.z);
|
||||
|
||||
return Math.sqrt(Math.max(extentsMinDistSqr, extentsMaxDistSqr));
|
||||
};
|
||||
|
||||
// commonjs module definiton
|
||||
if (typeof module !== 'undefined' && module.exports) {
|
||||
module.exports.BVH = bvhtree.BVH;
|
||||
module.exports.intersectRay = bvhtree.intersectRay;
|
||||
}
|
||||
File diff suppressed because one or more lines are too long
File diff suppressed because one or more lines are too long
Binary file not shown.
|
|
@ -0,0 +1,816 @@
|
|||
(function (global, factory) {
|
||||
typeof exports === 'object' && typeof module !== 'undefined' ? factory(exports, require('imgui-js')) :
|
||||
typeof define === 'function' && define.amd ? define(['exports', 'imgui-js'], factory) :
|
||||
(global = typeof globalThis !== 'undefined' ? globalThis : global || self, factory(global.ImGui_Impl = {}, global.ImGui));
|
||||
}(this, (function (exports, ImGui) { 'use strict';
|
||||
|
||||
let clipboard_text = "";
|
||||
let canvas = null;
|
||||
exports.gl = null;
|
||||
let g_ShaderHandle = null;
|
||||
let g_VertHandle = null;
|
||||
let g_FragHandle = null;
|
||||
let g_AttribLocationTex = null;
|
||||
let g_AttribLocationProjMtx = null;
|
||||
let g_AttribLocationPosition = -1;
|
||||
let g_AttribLocationUV = -1;
|
||||
let g_AttribLocationColor = -1;
|
||||
let g_VboHandle = null;
|
||||
let g_ElementsHandle = null;
|
||||
let g_FontTexture = null;
|
||||
exports.ctx = null;
|
||||
let prev_time = 0;
|
||||
function document_on_copy(event) {
|
||||
if (event.clipboardData) {
|
||||
event.clipboardData.setData("text/plain", clipboard_text);
|
||||
}
|
||||
// console.log(`${event.type}: "${clipboard_text}"`);
|
||||
event.preventDefault();
|
||||
}
|
||||
function document_on_cut(event) {
|
||||
if (event.clipboardData) {
|
||||
event.clipboardData.setData("text/plain", clipboard_text);
|
||||
}
|
||||
// console.log(`${event.type}: "${clipboard_text}"`);
|
||||
event.preventDefault();
|
||||
}
|
||||
function document_on_paste(event) {
|
||||
if (event.clipboardData) {
|
||||
clipboard_text = event.clipboardData.getData("text/plain");
|
||||
}
|
||||
// console.log(`${event.type}: "${clipboard_text}"`);
|
||||
event.preventDefault();
|
||||
}
|
||||
function window_on_resize() {
|
||||
if (canvas !== null) {
|
||||
const devicePixelRatio = window.devicePixelRatio || 1;
|
||||
canvas.width = Math.floor(canvas.scrollWidth * devicePixelRatio);
|
||||
canvas.height = Math.floor(canvas.scrollHeight * devicePixelRatio);
|
||||
}
|
||||
}
|
||||
function window_on_gamepadconnected(event /* GamepadEvent */) {
|
||||
console.log("Gamepad connected at index %d: %s. %d buttons, %d axes.", event.gamepad.index, event.gamepad.id, event.gamepad.buttons.length, event.gamepad.axes.length);
|
||||
}
|
||||
function window_on_gamepaddisconnected(event /* GamepadEvent */) {
|
||||
console.log("Gamepad disconnected at index %d: %s.", event.gamepad.index, event.gamepad.id);
|
||||
}
|
||||
function canvas_on_blur(event) {
|
||||
const io = ImGui.GetIO();
|
||||
io.KeyCtrl = false;
|
||||
io.KeyShift = false;
|
||||
io.KeyAlt = false;
|
||||
io.KeySuper = false;
|
||||
for (let i = 0; i < io.KeysDown.length; ++i) {
|
||||
io.KeysDown[i] = false;
|
||||
}
|
||||
for (let i = 0; i < io.MouseDown.length; ++i) {
|
||||
io.MouseDown[i] = false;
|
||||
}
|
||||
}
|
||||
const key_code_to_index = {
|
||||
"NumpadEnter": 176,
|
||||
};
|
||||
function canvas_on_keydown(event) {
|
||||
// console.log(event.type, event.key, event.code, event.keyCode);
|
||||
const io = ImGui.GetIO();
|
||||
io.KeyCtrl = event.ctrlKey;
|
||||
io.KeyShift = event.shiftKey;
|
||||
io.KeyAlt = event.altKey;
|
||||
io.KeySuper = event.metaKey;
|
||||
const key_index = key_code_to_index[event.code] || event.keyCode;
|
||||
ImGui.ASSERT(key_index >= 0 && key_index < ImGui.ARRAYSIZE(io.KeysDown));
|
||||
io.KeysDown[key_index] = true;
|
||||
// forward to the keypress event
|
||||
if ( /*io.WantCaptureKeyboard ||*/event.key === "Tab") {
|
||||
event.preventDefault();
|
||||
}
|
||||
}
|
||||
function canvas_on_keyup(event) {
|
||||
// console.log(event.type, event.key, event.code, event.keyCode);
|
||||
const io = ImGui.GetIO();
|
||||
io.KeyCtrl = event.ctrlKey;
|
||||
io.KeyShift = event.shiftKey;
|
||||
io.KeyAlt = event.altKey;
|
||||
io.KeySuper = event.metaKey;
|
||||
const key_index = key_code_to_index[event.code] || event.keyCode;
|
||||
ImGui.ASSERT(key_index >= 0 && key_index < ImGui.ARRAYSIZE(io.KeysDown));
|
||||
io.KeysDown[key_index] = false;
|
||||
if (io.WantCaptureKeyboard) {
|
||||
event.preventDefault();
|
||||
}
|
||||
}
|
||||
function canvas_on_keypress(event) {
|
||||
// console.log(event.type, event.key, event.code, event.keyCode);
|
||||
const io = ImGui.GetIO();
|
||||
io.AddInputCharacter(event.charCode);
|
||||
if (io.WantCaptureKeyboard) {
|
||||
event.preventDefault();
|
||||
}
|
||||
}
|
||||
function canvas_on_pointermove(event) {
|
||||
const io = ImGui.GetIO();
|
||||
io.MousePos.x = event.offsetX;
|
||||
io.MousePos.y = event.offsetY;
|
||||
if (io.WantCaptureMouse) {
|
||||
event.preventDefault();
|
||||
}
|
||||
}
|
||||
// MouseEvent.button
|
||||
// A number representing a given button:
|
||||
// 0: Main button pressed, usually the left button or the un-initialized state
|
||||
// 1: Auxiliary button pressed, usually the wheel button or the middle button (if present)
|
||||
// 2: Secondary button pressed, usually the right button
|
||||
// 3: Fourth button, typically the Browser Back button
|
||||
// 4: Fifth button, typically the Browser Forward button
|
||||
const mouse_button_map = [0, 2, 1, 3, 4];
|
||||
function canvas_on_pointerdown(event) {
|
||||
const io = ImGui.GetIO();
|
||||
io.MousePos.x = event.offsetX;
|
||||
io.MousePos.y = event.offsetY;
|
||||
io.MouseDown[mouse_button_map[event.button]] = true;
|
||||
// if (io.WantCaptureMouse) {
|
||||
// event.preventDefault();
|
||||
// }
|
||||
}
|
||||
function canvas_on_contextmenu(event) {
|
||||
const io = ImGui.GetIO();
|
||||
if (io.WantCaptureMouse) {
|
||||
event.preventDefault();
|
||||
}
|
||||
}
|
||||
function canvas_on_pointerup(event) {
|
||||
const io = ImGui.GetIO();
|
||||
io.MouseDown[mouse_button_map[event.button]] = false;
|
||||
if (io.WantCaptureMouse) {
|
||||
event.preventDefault();
|
||||
}
|
||||
}
|
||||
function canvas_on_wheel(event) {
|
||||
const io = ImGui.GetIO();
|
||||
let scale = 1.0;
|
||||
switch (event.deltaMode) {
|
||||
case event.DOM_DELTA_PIXEL:
|
||||
scale = 0.01;
|
||||
break;
|
||||
case event.DOM_DELTA_LINE:
|
||||
scale = 0.2;
|
||||
break;
|
||||
case event.DOM_DELTA_PAGE:
|
||||
scale = 1.0;
|
||||
break;
|
||||
}
|
||||
io.MouseWheelH = event.deltaX * scale;
|
||||
io.MouseWheel = -event.deltaY * scale; // Mouse wheel: 1 unit scrolls about 5 lines text.
|
||||
if (io.WantCaptureMouse) {
|
||||
event.preventDefault();
|
||||
}
|
||||
}
|
||||
function Init(value) {
|
||||
const io = ImGui.GetIO();
|
||||
if (typeof (window) !== "undefined") {
|
||||
io.BackendPlatformName = "imgui_impl_browser";
|
||||
ImGui.LoadIniSettingsFromMemory(window.localStorage.getItem("imgui.ini") || "");
|
||||
}
|
||||
else {
|
||||
io.BackendPlatformName = "imgui_impl_console";
|
||||
}
|
||||
if (typeof (navigator) !== "undefined") {
|
||||
io.ConfigMacOSXBehaviors = navigator.platform.match(/Mac/) !== null;
|
||||
}
|
||||
if (typeof (document) !== "undefined") {
|
||||
document.body.addEventListener("copy", document_on_copy);
|
||||
document.body.addEventListener("cut", document_on_cut);
|
||||
document.body.addEventListener("paste", document_on_paste);
|
||||
}
|
||||
io.SetClipboardTextFn = (user_data, text) => {
|
||||
clipboard_text = text;
|
||||
// console.log(`set clipboard_text: "${clipboard_text}"`);
|
||||
if (typeof navigator !== "undefined" && typeof navigator.clipboard !== "undefined") {
|
||||
// console.log(`clipboard.writeText: "${clipboard_text}"`);
|
||||
navigator.clipboard.writeText(clipboard_text).then(() => {
|
||||
// console.log(`clipboard.writeText: "${clipboard_text}" done.`);
|
||||
});
|
||||
}
|
||||
};
|
||||
io.GetClipboardTextFn = (user_data) => {
|
||||
// if (typeof navigator !== "undefined" && typeof (navigator as any).clipboard !== "undefined") {
|
||||
// console.log(`clipboard.readText: "${clipboard_text}"`);
|
||||
// (navigator as any).clipboard.readText().then((text: string): void => {
|
||||
// clipboard_text = text;
|
||||
// console.log(`clipboard.readText: "${clipboard_text}" done.`);
|
||||
// });
|
||||
// }
|
||||
// console.log(`get clipboard_text: "${clipboard_text}"`);
|
||||
return clipboard_text;
|
||||
};
|
||||
io.ClipboardUserData = null;
|
||||
if (typeof (window) !== "undefined") {
|
||||
window.addEventListener("resize", window_on_resize);
|
||||
window.addEventListener("gamepadconnected", window_on_gamepadconnected);
|
||||
window.addEventListener("gamepaddisconnected", window_on_gamepaddisconnected);
|
||||
}
|
||||
if (typeof (window) !== "undefined") {
|
||||
if (value instanceof (HTMLCanvasElement)) {
|
||||
canvas = value;
|
||||
value = canvas.getContext("webgl2", { alpha: false }) || canvas.getContext("webgl", { alpha: false }) || canvas.getContext("2d");
|
||||
}
|
||||
if (typeof WebGL2RenderingContext !== "undefined" && value instanceof (WebGL2RenderingContext)) {
|
||||
io.BackendRendererName = "imgui_impl_webgl2";
|
||||
canvas = canvas || value.canvas;
|
||||
exports.gl = value;
|
||||
}
|
||||
else if (typeof WebGLRenderingContext !== "undefined" && value instanceof (WebGLRenderingContext)) {
|
||||
io.BackendRendererName = "imgui_impl_webgl";
|
||||
canvas = canvas || value.canvas;
|
||||
exports.gl = value;
|
||||
}
|
||||
else if (typeof CanvasRenderingContext2D !== "undefined" && value instanceof (CanvasRenderingContext2D)) {
|
||||
io.BackendRendererName = "imgui_impl_2d";
|
||||
canvas = canvas || value.canvas;
|
||||
exports.ctx = value;
|
||||
}
|
||||
}
|
||||
if (canvas !== null) {
|
||||
window_on_resize();
|
||||
canvas.style.touchAction = "none"; // Disable browser handling of all panning and zooming gestures.
|
||||
canvas.addEventListener("blur", canvas_on_blur);
|
||||
canvas.addEventListener("keydown", canvas_on_keydown);
|
||||
canvas.addEventListener("keyup", canvas_on_keyup);
|
||||
canvas.addEventListener("keypress", canvas_on_keypress);
|
||||
canvas.addEventListener("pointermove", canvas_on_pointermove);
|
||||
canvas.addEventListener("pointerdown", canvas_on_pointerdown);
|
||||
canvas.addEventListener("contextmenu", canvas_on_contextmenu);
|
||||
canvas.addEventListener("pointerup", canvas_on_pointerup);
|
||||
canvas.addEventListener("wheel", canvas_on_wheel);
|
||||
}
|
||||
// Setup back-end capabilities flags
|
||||
io.BackendFlags |= ImGui.BackendFlags.HasMouseCursors; // We can honor GetMouseCursor() values (optional)
|
||||
// Keyboard mapping. ImGui will use those indices to peek into the io.KeyDown[] array.
|
||||
io.KeyMap[ImGui.Key.Tab] = 9;
|
||||
io.KeyMap[ImGui.Key.LeftArrow] = 37;
|
||||
io.KeyMap[ImGui.Key.RightArrow] = 39;
|
||||
io.KeyMap[ImGui.Key.UpArrow] = 38;
|
||||
io.KeyMap[ImGui.Key.DownArrow] = 40;
|
||||
io.KeyMap[ImGui.Key.PageUp] = 33;
|
||||
io.KeyMap[ImGui.Key.PageDown] = 34;
|
||||
io.KeyMap[ImGui.Key.Home] = 36;
|
||||
io.KeyMap[ImGui.Key.End] = 35;
|
||||
io.KeyMap[ImGui.Key.Insert] = 45;
|
||||
io.KeyMap[ImGui.Key.Delete] = 46;
|
||||
io.KeyMap[ImGui.Key.Backspace] = 8;
|
||||
io.KeyMap[ImGui.Key.Space] = 32;
|
||||
io.KeyMap[ImGui.Key.Enter] = 13;
|
||||
io.KeyMap[ImGui.Key.Escape] = 27;
|
||||
io.KeyMap[ImGui.Key.KeyPadEnter] = key_code_to_index["NumpadEnter"];
|
||||
io.KeyMap[ImGui.Key.A] = 65;
|
||||
io.KeyMap[ImGui.Key.C] = 67;
|
||||
io.KeyMap[ImGui.Key.V] = 86;
|
||||
io.KeyMap[ImGui.Key.X] = 88;
|
||||
io.KeyMap[ImGui.Key.Y] = 89;
|
||||
io.KeyMap[ImGui.Key.Z] = 90;
|
||||
CreateDeviceObjects();
|
||||
}
|
||||
function Shutdown() {
|
||||
DestroyDeviceObjects();
|
||||
if (canvas !== null) {
|
||||
canvas.removeEventListener("blur", canvas_on_blur);
|
||||
canvas.removeEventListener("keydown", canvas_on_keydown);
|
||||
canvas.removeEventListener("keyup", canvas_on_keyup);
|
||||
canvas.removeEventListener("keypress", canvas_on_keypress);
|
||||
canvas.removeEventListener("pointermove", canvas_on_pointermove);
|
||||
canvas.removeEventListener("pointerdown", canvas_on_pointerdown);
|
||||
canvas.removeEventListener("contextmenu", canvas_on_contextmenu);
|
||||
canvas.removeEventListener("pointerup", canvas_on_pointerup);
|
||||
canvas.removeEventListener("wheel", canvas_on_wheel);
|
||||
}
|
||||
exports.gl = null;
|
||||
exports.ctx = null;
|
||||
canvas = null;
|
||||
if (typeof (window) !== "undefined") {
|
||||
window.removeEventListener("resize", window_on_resize);
|
||||
window.removeEventListener("gamepadconnected", window_on_gamepadconnected);
|
||||
window.removeEventListener("gamepaddisconnected", window_on_gamepaddisconnected);
|
||||
}
|
||||
if (typeof (document) !== "undefined") {
|
||||
document.body.removeEventListener("copy", document_on_copy);
|
||||
document.body.removeEventListener("cut", document_on_cut);
|
||||
document.body.removeEventListener("paste", document_on_paste);
|
||||
}
|
||||
}
|
||||
function NewFrame(time) {
|
||||
const io = ImGui.GetIO();
|
||||
if (io.WantSaveIniSettings) {
|
||||
io.WantSaveIniSettings = false;
|
||||
if (typeof (window) !== "undefined") {
|
||||
window.localStorage.setItem("imgui.ini", ImGui.SaveIniSettingsToMemory());
|
||||
}
|
||||
}
|
||||
const w = canvas && canvas.scrollWidth || 640;
|
||||
const h = canvas && canvas.scrollHeight || 480;
|
||||
const display_w = exports.gl && exports.gl.drawingBufferWidth || w;
|
||||
const display_h = exports.gl && exports.gl.drawingBufferHeight || h;
|
||||
io.DisplaySize.x = w;
|
||||
io.DisplaySize.y = h;
|
||||
io.DisplayFramebufferScale.x = w > 0 ? (display_w / w) : 0;
|
||||
io.DisplayFramebufferScale.y = h > 0 ? (display_h / h) : 0;
|
||||
const dt = time - prev_time;
|
||||
prev_time = time;
|
||||
io.DeltaTime = dt / 1000;
|
||||
if (io.WantSetMousePos) {
|
||||
console.log("TODO: MousePos", io.MousePos.x, io.MousePos.y);
|
||||
}
|
||||
if (typeof (document) !== "undefined") {
|
||||
if (io.MouseDrawCursor) {
|
||||
document.body.style.cursor = "none";
|
||||
}
|
||||
else {
|
||||
switch (ImGui.GetMouseCursor()) {
|
||||
case ImGui.MouseCursor.None:
|
||||
document.body.style.cursor = "none";
|
||||
break;
|
||||
default:
|
||||
case ImGui.MouseCursor.Arrow:
|
||||
document.body.style.cursor = "default";
|
||||
break;
|
||||
case ImGui.MouseCursor.TextInput:
|
||||
document.body.style.cursor = "text";
|
||||
break; // When hovering over InputText, etc.
|
||||
case ImGui.MouseCursor.ResizeAll:
|
||||
document.body.style.cursor = "all-scroll";
|
||||
break; // Unused
|
||||
case ImGui.MouseCursor.ResizeNS:
|
||||
document.body.style.cursor = "ns-resize";
|
||||
break; // When hovering over an horizontal border
|
||||
case ImGui.MouseCursor.ResizeEW:
|
||||
document.body.style.cursor = "ew-resize";
|
||||
break; // When hovering over a vertical border or a column
|
||||
case ImGui.MouseCursor.ResizeNESW:
|
||||
document.body.style.cursor = "nesw-resize";
|
||||
break; // When hovering over the bottom-left corner of a window
|
||||
case ImGui.MouseCursor.ResizeNWSE:
|
||||
document.body.style.cursor = "nwse-resize";
|
||||
break; // When hovering over the bottom-right corner of a window
|
||||
case ImGui.MouseCursor.Hand:
|
||||
document.body.style.cursor = "move";
|
||||
break;
|
||||
case ImGui.MouseCursor.NotAllowed:
|
||||
document.body.style.cursor = "not-allowed";
|
||||
break;
|
||||
}
|
||||
}
|
||||
}
|
||||
// Gamepad navigation mapping [BETA]
|
||||
for (let i = 0; i < io.NavInputs.length; ++i) {
|
||||
// TODO: This is currently causing an issue and I have no gamepad to test with.
|
||||
// The error is: ''set' on proxy: trap returned falsish for property '21'
|
||||
// I think that the NavInputs are zeroed out by ImGui at the start of each frame anyway
|
||||
// so I am not sure if the following is even necessary.
|
||||
//io.NavInputs[i] = 0.0;
|
||||
}
|
||||
if (io.ConfigFlags & ImGui.ConfigFlags.NavEnableGamepad) {
|
||||
// Update gamepad inputs
|
||||
const gamepads = (typeof (navigator) !== "undefined" && typeof (navigator.getGamepads) === "function") ? navigator.getGamepads() : [];
|
||||
for (let i = 0; i < gamepads.length; ++i) {
|
||||
const gamepad = gamepads[i];
|
||||
if (!gamepad) {
|
||||
continue;
|
||||
}
|
||||
io.BackendFlags |= ImGui.BackendFlags.HasGamepad;
|
||||
const buttons_count = gamepad.buttons.length;
|
||||
const axes_count = gamepad.axes.length;
|
||||
function MAP_BUTTON(NAV_NO, BUTTON_NO) {
|
||||
if (!gamepad) {
|
||||
return;
|
||||
}
|
||||
if (buttons_count > BUTTON_NO && gamepad.buttons[BUTTON_NO].pressed)
|
||||
io.NavInputs[NAV_NO] = 1.0;
|
||||
}
|
||||
function MAP_ANALOG(NAV_NO, AXIS_NO, V0, V1) {
|
||||
if (!gamepad) {
|
||||
return;
|
||||
}
|
||||
let v = (axes_count > AXIS_NO) ? gamepad.axes[AXIS_NO] : V0;
|
||||
v = (v - V0) / (V1 - V0);
|
||||
if (v > 1.0)
|
||||
v = 1.0;
|
||||
if (io.NavInputs[NAV_NO] < v)
|
||||
io.NavInputs[NAV_NO] = v;
|
||||
}
|
||||
// TODO: map input based on vendor and product id
|
||||
// https://developer.mozilla.org/en-US/docs/Web/API/Gamepad/id
|
||||
const match = gamepad.id.match(/^([0-9a-f]{4})-([0-9a-f]{4})-.*$/);
|
||||
const match_chrome = gamepad.id.match(/^.*\(.*Vendor: ([0-9a-f]{4}) Product: ([0-9a-f]{4})\).*$/);
|
||||
const vendor = (match && match[1]) || (match_chrome && match_chrome[1]) || "0000";
|
||||
const product = (match && match[2]) || (match_chrome && match_chrome[2]) || "0000";
|
||||
switch (vendor + product) {
|
||||
case "046dc216": // Logitech Logitech Dual Action (Vendor: 046d Product: c216)
|
||||
MAP_BUTTON(ImGui.NavInput.Activate, 1); // Cross / A
|
||||
MAP_BUTTON(ImGui.NavInput.Cancel, 2); // Circle / B
|
||||
MAP_BUTTON(ImGui.NavInput.Menu, 0); // Square / X
|
||||
MAP_BUTTON(ImGui.NavInput.Input, 3); // Triangle / Y
|
||||
MAP_ANALOG(ImGui.NavInput.DpadLeft, 4, -0.3, -0.9); // D-Pad Left
|
||||
MAP_ANALOG(ImGui.NavInput.DpadRight, 4, +0.3, +0.9); // D-Pad Right
|
||||
MAP_ANALOG(ImGui.NavInput.DpadUp, 5, -0.3, -0.9); // D-Pad Up
|
||||
MAP_ANALOG(ImGui.NavInput.DpadDown, 5, +0.3, +0.9); // D-Pad Down
|
||||
MAP_BUTTON(ImGui.NavInput.FocusPrev, 4); // L1 / LB
|
||||
MAP_BUTTON(ImGui.NavInput.FocusNext, 5); // R1 / RB
|
||||
MAP_BUTTON(ImGui.NavInput.TweakSlow, 6); // L2 / LT
|
||||
MAP_BUTTON(ImGui.NavInput.TweakFast, 7); // R2 / RT
|
||||
MAP_ANALOG(ImGui.NavInput.LStickLeft, 0, -0.3, -0.9);
|
||||
MAP_ANALOG(ImGui.NavInput.LStickRight, 0, +0.3, +0.9);
|
||||
MAP_ANALOG(ImGui.NavInput.LStickUp, 1, -0.3, -0.9);
|
||||
MAP_ANALOG(ImGui.NavInput.LStickDown, 1, +0.3, +0.9);
|
||||
break;
|
||||
case "046dc21d": // Logitech Gamepad F310 (STANDARD GAMEPAD Vendor: 046d Product: c21d)
|
||||
MAP_BUTTON(ImGui.NavInput.Activate, 0); // Cross / A
|
||||
MAP_BUTTON(ImGui.NavInput.Cancel, 1); // Circle / B
|
||||
MAP_BUTTON(ImGui.NavInput.Menu, 2); // Square / X
|
||||
MAP_BUTTON(ImGui.NavInput.Input, 3); // Triangle / Y
|
||||
MAP_BUTTON(ImGui.NavInput.DpadLeft, 14); // D-Pad Left
|
||||
MAP_BUTTON(ImGui.NavInput.DpadRight, 15); // D-Pad Right
|
||||
MAP_BUTTON(ImGui.NavInput.DpadUp, 12); // D-Pad Up
|
||||
MAP_BUTTON(ImGui.NavInput.DpadDown, 13); // D-Pad Down
|
||||
MAP_BUTTON(ImGui.NavInput.FocusPrev, 4); // L1 / LB
|
||||
MAP_BUTTON(ImGui.NavInput.FocusNext, 5); // R1 / RB
|
||||
MAP_ANALOG(ImGui.NavInput.TweakSlow, 6, +0.3, +0.9); // L2 / LT
|
||||
MAP_ANALOG(ImGui.NavInput.TweakFast, 7, +0.3, +0.9); // R2 / RT
|
||||
MAP_ANALOG(ImGui.NavInput.LStickLeft, 0, -0.3, -0.9);
|
||||
MAP_ANALOG(ImGui.NavInput.LStickRight, 0, +0.3, +0.9);
|
||||
MAP_ANALOG(ImGui.NavInput.LStickUp, 1, -0.3, -0.9);
|
||||
MAP_ANALOG(ImGui.NavInput.LStickDown, 1, +0.3, +0.9);
|
||||
break;
|
||||
case "2dc86001": // 8Bitdo SN30 Pro 8Bitdo SN30 Pro (Vendor: 2dc8 Product: 6001)
|
||||
case "2dc86101": // 8Bitdo SN30 Pro (Vendor: 2dc8 Product: 6101)
|
||||
MAP_BUTTON(ImGui.NavInput.Activate, 1); // Cross / A
|
||||
MAP_BUTTON(ImGui.NavInput.Cancel, 0); // Circle / B
|
||||
MAP_BUTTON(ImGui.NavInput.Menu, 4); // Square / X
|
||||
MAP_BUTTON(ImGui.NavInput.Input, 3); // Triangle / Y
|
||||
MAP_ANALOG(ImGui.NavInput.DpadLeft, 6, -0.3, -0.9); // D-Pad Left
|
||||
MAP_ANALOG(ImGui.NavInput.DpadRight, 6, +0.3, +0.9); // D-Pad Right
|
||||
MAP_ANALOG(ImGui.NavInput.DpadUp, 7, -0.3, -0.9); // D-Pad Up
|
||||
MAP_ANALOG(ImGui.NavInput.DpadDown, 7, +0.3, +0.9); // D-Pad Down
|
||||
MAP_BUTTON(ImGui.NavInput.FocusPrev, 6); // L1 / LB
|
||||
MAP_BUTTON(ImGui.NavInput.FocusNext, 7); // R1 / RB
|
||||
MAP_BUTTON(ImGui.NavInput.TweakSlow, 8); // L2 / LT
|
||||
MAP_BUTTON(ImGui.NavInput.TweakFast, 9); // R2 / RT
|
||||
MAP_ANALOG(ImGui.NavInput.LStickLeft, 0, -0.3, -0.9);
|
||||
MAP_ANALOG(ImGui.NavInput.LStickRight, 0, +0.3, +0.9);
|
||||
MAP_ANALOG(ImGui.NavInput.LStickUp, 1, -0.3, -0.9);
|
||||
MAP_ANALOG(ImGui.NavInput.LStickDown, 1, +0.3, +0.9);
|
||||
break;
|
||||
default: // standard gamepad: https://w3c.github.io/gamepad/#remapping
|
||||
MAP_BUTTON(ImGui.NavInput.Activate, 0); // Cross / A
|
||||
MAP_BUTTON(ImGui.NavInput.Cancel, 1); // Circle / B
|
||||
MAP_BUTTON(ImGui.NavInput.Menu, 2); // Square / X
|
||||
MAP_BUTTON(ImGui.NavInput.Input, 3); // Triangle / Y
|
||||
MAP_BUTTON(ImGui.NavInput.DpadLeft, 14); // D-Pad Left
|
||||
MAP_BUTTON(ImGui.NavInput.DpadRight, 15); // D-Pad Right
|
||||
MAP_BUTTON(ImGui.NavInput.DpadUp, 12); // D-Pad Up
|
||||
MAP_BUTTON(ImGui.NavInput.DpadDown, 13); // D-Pad Down
|
||||
MAP_BUTTON(ImGui.NavInput.FocusPrev, 4); // L1 / LB
|
||||
MAP_BUTTON(ImGui.NavInput.FocusNext, 5); // R1 / RB
|
||||
MAP_BUTTON(ImGui.NavInput.TweakSlow, 6); // L2 / LT
|
||||
MAP_BUTTON(ImGui.NavInput.TweakFast, 7); // R2 / RT
|
||||
MAP_ANALOG(ImGui.NavInput.LStickLeft, 0, -0.3, -0.9);
|
||||
MAP_ANALOG(ImGui.NavInput.LStickRight, 0, +0.3, +0.9);
|
||||
MAP_ANALOG(ImGui.NavInput.LStickUp, 1, -0.3, -0.9);
|
||||
MAP_ANALOG(ImGui.NavInput.LStickDown, 1, +0.3, +0.9);
|
||||
break;
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
function RenderDrawData(draw_data = ImGui.GetDrawData()) {
|
||||
const io = ImGui.GetIO();
|
||||
if (draw_data === null) {
|
||||
throw new Error();
|
||||
}
|
||||
exports.gl || exports.ctx || console.log(draw_data);
|
||||
// Avoid rendering when minimized, scale coordinates for retina displays (screen coordinates != framebuffer coordinates)
|
||||
const fb_width = io.DisplaySize.x * io.DisplayFramebufferScale.x;
|
||||
const fb_height = io.DisplaySize.y * io.DisplayFramebufferScale.y;
|
||||
if (fb_width === 0 || fb_height === 0) {
|
||||
return;
|
||||
}
|
||||
draw_data.ScaleClipRects(io.DisplayFramebufferScale);
|
||||
const gl2 = typeof WebGL2RenderingContext !== "undefined" && exports.gl instanceof WebGL2RenderingContext && exports.gl || null;
|
||||
const gl_vao = exports.gl && exports.gl.getExtension("OES_vertex_array_object") || null;
|
||||
// Backup GL state
|
||||
const last_active_texture = exports.gl && exports.gl.getParameter(exports.gl.ACTIVE_TEXTURE) || null;
|
||||
const last_program = exports.gl && exports.gl.getParameter(exports.gl.CURRENT_PROGRAM) || null;
|
||||
const last_texture = exports.gl && exports.gl.getParameter(exports.gl.TEXTURE_BINDING_2D) || null;
|
||||
const last_array_buffer = exports.gl && exports.gl.getParameter(exports.gl.ARRAY_BUFFER_BINDING) || null;
|
||||
const last_element_array_buffer = exports.gl && exports.gl.getParameter(exports.gl.ELEMENT_ARRAY_BUFFER_BINDING) || null;
|
||||
const last_vertex_array_object = gl2 && gl2.getParameter(gl2.VERTEX_ARRAY_BINDING) || exports.gl && gl_vao && exports.gl.getParameter(gl_vao.VERTEX_ARRAY_BINDING_OES) || null;
|
||||
// GLint last_polygon_mode[2]; glGetIntegerv(GL_POLYGON_MODE, last_polygon_mode);
|
||||
const last_viewport = exports.gl && exports.gl.getParameter(exports.gl.VIEWPORT) || null;
|
||||
const last_scissor_box = exports.gl && exports.gl.getParameter(exports.gl.SCISSOR_BOX) || null;
|
||||
const last_blend_src_rgb = exports.gl && exports.gl.getParameter(exports.gl.BLEND_SRC_RGB) || null;
|
||||
const last_blend_dst_rgb = exports.gl && exports.gl.getParameter(exports.gl.BLEND_DST_RGB) || null;
|
||||
const last_blend_src_alpha = exports.gl && exports.gl.getParameter(exports.gl.BLEND_SRC_ALPHA) || null;
|
||||
const last_blend_dst_alpha = exports.gl && exports.gl.getParameter(exports.gl.BLEND_DST_ALPHA) || null;
|
||||
const last_blend_equation_rgb = exports.gl && exports.gl.getParameter(exports.gl.BLEND_EQUATION_RGB) || null;
|
||||
const last_blend_equation_alpha = exports.gl && exports.gl.getParameter(exports.gl.BLEND_EQUATION_ALPHA) || null;
|
||||
const last_enable_blend = exports.gl && exports.gl.getParameter(exports.gl.BLEND) || null;
|
||||
const last_enable_cull_face = exports.gl && exports.gl.getParameter(exports.gl.CULL_FACE) || null;
|
||||
const last_enable_depth_test = exports.gl && exports.gl.getParameter(exports.gl.DEPTH_TEST) || null;
|
||||
const last_enable_scissor_test = exports.gl && exports.gl.getParameter(exports.gl.SCISSOR_TEST) || null;
|
||||
// Setup desired GL state
|
||||
// Recreate the VAO every time (this is to easily allow multiple GL contexts to be rendered to. VAO are not shared among GL contexts)
|
||||
// The renderer would actually work without any VAO bound, but then our VertexAttrib calls would overwrite the default one currently bound.
|
||||
const vertex_array_object = gl2 && gl2.createVertexArray() || gl_vao && gl_vao.createVertexArrayOES();
|
||||
// Setup render state: alpha-blending enabled, no face culling, no depth testing, scissor enabled, polygon fill
|
||||
exports.gl && exports.gl.enable(exports.gl.BLEND);
|
||||
exports.gl && exports.gl.blendEquation(exports.gl.FUNC_ADD);
|
||||
exports.gl && exports.gl.blendFunc(exports.gl.SRC_ALPHA, exports.gl.ONE_MINUS_SRC_ALPHA);
|
||||
exports.gl && exports.gl.disable(exports.gl.CULL_FACE);
|
||||
exports.gl && exports.gl.disable(exports.gl.DEPTH_TEST);
|
||||
exports.gl && exports.gl.enable(exports.gl.SCISSOR_TEST);
|
||||
// glPolygonMode(GL_FRONT_AND_BACK, GL_FILL);
|
||||
// Setup viewport, orthographic projection matrix
|
||||
// Our visible imgui space lies from draw_data->DisplayPps (top left) to draw_data->DisplayPos+data_data->DisplaySize (bottom right). DisplayMin is typically (0,0) for single viewport apps.
|
||||
exports.gl && exports.gl.viewport(0, 0, fb_width, fb_height);
|
||||
const L = draw_data.DisplayPos.x;
|
||||
const R = draw_data.DisplayPos.x + draw_data.DisplaySize.x;
|
||||
const T = draw_data.DisplayPos.y;
|
||||
const B = draw_data.DisplayPos.y + draw_data.DisplaySize.y;
|
||||
const ortho_projection = new Float32Array([
|
||||
2.0 / (R - L), 0.0, 0.0, 0.0,
|
||||
0.0, 2.0 / (T - B), 0.0, 0.0,
|
||||
0.0, 0.0, -1.0, 0.0,
|
||||
(R + L) / (L - R), (T + B) / (B - T), 0.0, 1.0,
|
||||
]);
|
||||
exports.gl && exports.gl.useProgram(g_ShaderHandle);
|
||||
exports.gl && exports.gl.uniform1i(g_AttribLocationTex, 0);
|
||||
exports.gl && g_AttribLocationProjMtx && exports.gl.uniformMatrix4fv(g_AttribLocationProjMtx, false, ortho_projection);
|
||||
gl2 && gl2.bindVertexArray(vertex_array_object) || gl_vao && gl_vao.bindVertexArrayOES(vertex_array_object);
|
||||
// Render command lists
|
||||
exports.gl && exports.gl.bindBuffer(exports.gl.ARRAY_BUFFER, g_VboHandle);
|
||||
exports.gl && exports.gl.enableVertexAttribArray(g_AttribLocationPosition);
|
||||
exports.gl && exports.gl.enableVertexAttribArray(g_AttribLocationUV);
|
||||
exports.gl && exports.gl.enableVertexAttribArray(g_AttribLocationColor);
|
||||
exports.gl && exports.gl.vertexAttribPointer(g_AttribLocationPosition, 2, exports.gl.FLOAT, false, ImGui.DrawVertSize, ImGui.DrawVertPosOffset);
|
||||
exports.gl && exports.gl.vertexAttribPointer(g_AttribLocationUV, 2, exports.gl.FLOAT, false, ImGui.DrawVertSize, ImGui.DrawVertUVOffset);
|
||||
exports.gl && exports.gl.vertexAttribPointer(g_AttribLocationColor, 4, exports.gl.UNSIGNED_BYTE, true, ImGui.DrawVertSize, ImGui.DrawVertColOffset);
|
||||
// Draw
|
||||
const pos = draw_data.DisplayPos;
|
||||
const idx_buffer_type = exports.gl && ((ImGui.DrawIdxSize === 4) ? exports.gl.UNSIGNED_INT : exports.gl.UNSIGNED_SHORT) || 0;
|
||||
draw_data.IterateDrawLists((draw_list) => {
|
||||
exports.gl || exports.ctx || console.log(draw_list);
|
||||
exports.gl || exports.ctx || console.log("VtxBuffer.length", draw_list.VtxBuffer.length);
|
||||
exports.gl || exports.ctx || console.log("IdxBuffer.length", draw_list.IdxBuffer.length);
|
||||
let idx_buffer_offset = 0;
|
||||
exports.gl && exports.gl.bindBuffer(exports.gl.ARRAY_BUFFER, g_VboHandle);
|
||||
exports.gl && exports.gl.bufferData(exports.gl.ARRAY_BUFFER, draw_list.VtxBuffer, exports.gl.STREAM_DRAW);
|
||||
exports.gl && exports.gl.bindBuffer(exports.gl.ELEMENT_ARRAY_BUFFER, g_ElementsHandle);
|
||||
exports.gl && exports.gl.bufferData(exports.gl.ELEMENT_ARRAY_BUFFER, draw_list.IdxBuffer, exports.gl.STREAM_DRAW);
|
||||
draw_list.IterateDrawCmds((draw_cmd) => {
|
||||
exports.gl || exports.ctx || console.log(draw_cmd);
|
||||
exports.gl || exports.ctx || console.log("ElemCount", draw_cmd.ElemCount);
|
||||
exports.gl || exports.ctx || console.log("ClipRect", draw_cmd.ClipRect.x, fb_height - draw_cmd.ClipRect.w, draw_cmd.ClipRect.z - draw_cmd.ClipRect.x, draw_cmd.ClipRect.w - draw_cmd.ClipRect.y);
|
||||
exports.gl || exports.ctx || console.log("TextureId", draw_cmd.TextureId);
|
||||
if (!exports.gl && !exports.ctx) {
|
||||
console.log("i: pos.x pos.y uv.x uv.y col");
|
||||
for (let i = 0; i < Math.min(3, draw_cmd.ElemCount); ++i) {
|
||||
const view = new ImGui.DrawVert(draw_list.VtxBuffer.buffer, draw_list.VtxBuffer.byteOffset + i * ImGui.DrawVertSize);
|
||||
console.log(`${i}: ${view.pos[0].toFixed(2)} ${view.pos[1].toFixed(2)} ${view.uv[0].toFixed(5)} ${view.uv[1].toFixed(5)} ${("00000000" + view.col[0].toString(16)).substr(-8)}`);
|
||||
}
|
||||
}
|
||||
if (draw_cmd.UserCallback !== null) {
|
||||
// User callback (registered via ImDrawList::AddCallback)
|
||||
draw_cmd.UserCallback(draw_list, draw_cmd);
|
||||
}
|
||||
else {
|
||||
const clip_rect = new ImGui.Vec4(draw_cmd.ClipRect.x - pos.x, draw_cmd.ClipRect.y - pos.y, draw_cmd.ClipRect.z - pos.x, draw_cmd.ClipRect.w - pos.y);
|
||||
if (clip_rect.x < fb_width && clip_rect.y < fb_height && clip_rect.z >= 0.0 && clip_rect.w >= 0.0) {
|
||||
// Apply scissor/clipping rectangle
|
||||
exports.gl && exports.gl.scissor(clip_rect.x, fb_height - clip_rect.w, clip_rect.z - clip_rect.x, clip_rect.w - clip_rect.y);
|
||||
// Bind texture, Draw
|
||||
exports.gl && exports.gl.activeTexture(exports.gl.TEXTURE0);
|
||||
exports.gl && exports.gl.bindTexture(exports.gl.TEXTURE_2D, draw_cmd.TextureId);
|
||||
exports.gl && exports.gl.drawElements(exports.gl.TRIANGLES, draw_cmd.ElemCount, idx_buffer_type, idx_buffer_offset);
|
||||
if (exports.ctx) {
|
||||
exports.ctx.save();
|
||||
exports.ctx.beginPath();
|
||||
exports.ctx.rect(clip_rect.x, clip_rect.y, clip_rect.z - clip_rect.x, clip_rect.w - clip_rect.y);
|
||||
exports.ctx.clip();
|
||||
const idx = ImGui.DrawIdxSize === 4 ?
|
||||
new Uint32Array(draw_list.IdxBuffer.buffer, draw_list.IdxBuffer.byteOffset + idx_buffer_offset) :
|
||||
new Uint16Array(draw_list.IdxBuffer.buffer, draw_list.IdxBuffer.byteOffset + idx_buffer_offset);
|
||||
for (let i = 0; i < draw_cmd.ElemCount; i += 3) {
|
||||
const i0 = idx[i + 0];
|
||||
const i1 = idx[i + 1];
|
||||
const i2 = idx[i + 2];
|
||||
const v0 = new ImGui.DrawVert(draw_list.VtxBuffer.buffer, draw_list.VtxBuffer.byteOffset + i0 * ImGui.DrawVertSize);
|
||||
const v1 = new ImGui.DrawVert(draw_list.VtxBuffer.buffer, draw_list.VtxBuffer.byteOffset + i1 * ImGui.DrawVertSize);
|
||||
const v2 = new ImGui.DrawVert(draw_list.VtxBuffer.buffer, draw_list.VtxBuffer.byteOffset + i2 * ImGui.DrawVertSize);
|
||||
const i3 = idx[i + 3];
|
||||
const i4 = idx[i + 4];
|
||||
const i5 = idx[i + 5];
|
||||
const v3 = new ImGui.DrawVert(draw_list.VtxBuffer.buffer, draw_list.VtxBuffer.byteOffset + i3 * ImGui.DrawVertSize);
|
||||
const v4 = new ImGui.DrawVert(draw_list.VtxBuffer.buffer, draw_list.VtxBuffer.byteOffset + i4 * ImGui.DrawVertSize);
|
||||
const v5 = new ImGui.DrawVert(draw_list.VtxBuffer.buffer, draw_list.VtxBuffer.byteOffset + i5 * ImGui.DrawVertSize);
|
||||
let quad = true;
|
||||
let minmin = v0;
|
||||
let minmax = v0;
|
||||
let maxmin = v0;
|
||||
let maxmax = v0;
|
||||
for (const v of [v1, v2, v3, v4, v5]) {
|
||||
let found = false;
|
||||
if (v.pos[0] <= minmin.pos[0] && v.pos[1] <= minmin.pos[1]) {
|
||||
minmin = v;
|
||||
found = true;
|
||||
}
|
||||
if (v.pos[0] <= minmax.pos[0] && v.pos[1] >= minmax.pos[1]) {
|
||||
minmax = v;
|
||||
found = true;
|
||||
}
|
||||
if (v.pos[0] >= maxmin.pos[0] && v.pos[1] <= maxmin.pos[1]) {
|
||||
maxmin = v;
|
||||
found = true;
|
||||
}
|
||||
if (v.pos[0] >= maxmax.pos[0] && v.pos[1] >= maxmax.pos[1]) {
|
||||
maxmax = v;
|
||||
found = true;
|
||||
}
|
||||
if (!found) {
|
||||
quad = false;
|
||||
}
|
||||
}
|
||||
quad = quad && (minmin.pos[0] === minmax.pos[0]);
|
||||
quad = quad && (maxmin.pos[0] === maxmax.pos[0]);
|
||||
quad = quad && (minmin.pos[1] === maxmin.pos[1]);
|
||||
quad = quad && (minmax.pos[1] === maxmax.pos[1]);
|
||||
if (quad) {
|
||||
if (minmin.uv[0] === maxmax.uv[0] || minmin.uv[1] === maxmax.uv[1]) {
|
||||
// one vertex color
|
||||
exports.ctx.beginPath();
|
||||
exports.ctx.rect(minmin.pos[0], minmin.pos[1], maxmax.pos[0] - minmin.pos[0], maxmax.pos[1] - minmin.pos[1]);
|
||||
exports.ctx.fillStyle = `rgba(${v0.col[0] >> 0 & 0xff}, ${v0.col[0] >> 8 & 0xff}, ${v0.col[0] >> 16 & 0xff}, ${(v0.col[0] >> 24 & 0xff) / 0xff})`;
|
||||
exports.ctx.fill();
|
||||
}
|
||||
else {
|
||||
// no vertex color
|
||||
const image = draw_cmd.TextureId; // HACK
|
||||
const width = image instanceof HTMLVideoElement ? image.videoWidth : image.width;
|
||||
const height = image instanceof HTMLVideoElement ? image.videoHeight : image.height;
|
||||
image && exports.ctx.drawImage(image, minmin.uv[0] * width, minmin.uv[1] * height, (maxmax.uv[0] - minmin.uv[0]) * width, (maxmax.uv[1] - minmin.uv[1]) * height, minmin.pos[0], minmin.pos[1], maxmax.pos[0] - minmin.pos[0], maxmax.pos[1] - minmin.pos[1]);
|
||||
// ctx.beginPath();
|
||||
// ctx.rect(minmin.pos[0], minmin.pos[1], maxmax.pos[0] - minmin.pos[0], maxmax.pos[1] - minmin.pos[1]);
|
||||
// ctx.strokeStyle = "yellow";
|
||||
// ctx.stroke();
|
||||
}
|
||||
i += 3;
|
||||
}
|
||||
else {
|
||||
// one vertex color, no texture
|
||||
exports.ctx.beginPath();
|
||||
exports.ctx.moveTo(v0.pos[0], v0.pos[1]);
|
||||
exports.ctx.lineTo(v1.pos[0], v1.pos[1]);
|
||||
exports.ctx.lineTo(v2.pos[0], v2.pos[1]);
|
||||
exports.ctx.closePath();
|
||||
exports.ctx.fillStyle = `rgba(${v0.col[0] >> 0 & 0xff}, ${v0.col[0] >> 8 & 0xff}, ${v0.col[0] >> 16 & 0xff}, ${(v0.col[0] >> 24 & 0xff) / 0xff})`;
|
||||
exports.ctx.fill();
|
||||
}
|
||||
}
|
||||
exports.ctx.restore();
|
||||
}
|
||||
}
|
||||
}
|
||||
idx_buffer_offset += draw_cmd.ElemCount * ImGui.DrawIdxSize;
|
||||
});
|
||||
});
|
||||
// Destroy the temporary VAO
|
||||
gl2 && gl2.deleteVertexArray(vertex_array_object) || gl_vao && gl_vao.deleteVertexArrayOES(vertex_array_object);
|
||||
// Restore modified GL state
|
||||
exports.gl && (last_program !== null) && exports.gl.useProgram(last_program);
|
||||
exports.gl && (last_texture !== null) && exports.gl.bindTexture(exports.gl.TEXTURE_2D, last_texture);
|
||||
exports.gl && (last_active_texture !== null) && exports.gl.activeTexture(last_active_texture);
|
||||
gl2 && gl2.bindVertexArray(last_vertex_array_object) || gl_vao && gl_vao.bindVertexArrayOES(last_vertex_array_object);
|
||||
exports.gl && (last_array_buffer !== null) && exports.gl.bindBuffer(exports.gl.ARRAY_BUFFER, last_array_buffer);
|
||||
exports.gl && (last_element_array_buffer !== null) && exports.gl.bindBuffer(exports.gl.ELEMENT_ARRAY_BUFFER, last_element_array_buffer);
|
||||
exports.gl && (last_blend_equation_rgb !== null && last_blend_equation_alpha !== null) && exports.gl.blendEquationSeparate(last_blend_equation_rgb, last_blend_equation_alpha);
|
||||
exports.gl && (last_blend_src_rgb !== null && last_blend_src_alpha !== null && last_blend_dst_rgb !== null && last_blend_dst_alpha !== null) && exports.gl.blendFuncSeparate(last_blend_src_rgb, last_blend_src_alpha, last_blend_dst_rgb, last_blend_dst_alpha);
|
||||
exports.gl && (last_enable_blend ? exports.gl.enable(exports.gl.BLEND) : exports.gl.disable(exports.gl.BLEND));
|
||||
exports.gl && (last_enable_cull_face ? exports.gl.enable(exports.gl.CULL_FACE) : exports.gl.disable(exports.gl.CULL_FACE));
|
||||
exports.gl && (last_enable_depth_test ? exports.gl.enable(exports.gl.DEPTH_TEST) : exports.gl.disable(exports.gl.DEPTH_TEST));
|
||||
exports.gl && (last_enable_scissor_test ? exports.gl.enable(exports.gl.SCISSOR_TEST) : exports.gl.disable(exports.gl.SCISSOR_TEST));
|
||||
// glPolygonMode(GL_FRONT_AND_BACK, (GLenum)last_polygon_mode[0]);
|
||||
exports.gl && (last_viewport !== null) && exports.gl.viewport(last_viewport[0], last_viewport[1], last_viewport[2], last_viewport[3]);
|
||||
exports.gl && (last_scissor_box !== null) && exports.gl.scissor(last_scissor_box[0], last_scissor_box[1], last_scissor_box[2], last_scissor_box[3]);
|
||||
}
|
||||
function CreateFontsTexture() {
|
||||
const io = ImGui.GetIO();
|
||||
// Backup GL state
|
||||
const last_texture = exports.gl && exports.gl.getParameter(exports.gl.TEXTURE_BINDING_2D);
|
||||
// Build texture atlas
|
||||
// const width: number = 256;
|
||||
// const height: number = 256;
|
||||
// const pixels: Uint8Array = new Uint8Array(4 * width * height).fill(0xff);
|
||||
const { width, height, pixels } = io.Fonts.GetTexDataAsRGBA32(); // Load as RGBA 32-bits (75% of the memory is wasted, but default font is so small) because it is more likely to be compatible with user's existing shaders. If your ImTextureId represent a higher-level concept than just a GL texture id, consider calling GetTexDataAsAlpha8() instead to save on GPU memory.
|
||||
// console.log(`font texture ${width} x ${height} @ ${pixels.length}`);
|
||||
// Upload texture to graphics system
|
||||
g_FontTexture = exports.gl && exports.gl.createTexture();
|
||||
exports.gl && exports.gl.bindTexture(exports.gl.TEXTURE_2D, g_FontTexture);
|
||||
exports.gl && exports.gl.texParameteri(exports.gl.TEXTURE_2D, exports.gl.TEXTURE_MIN_FILTER, exports.gl.LINEAR);
|
||||
exports.gl && exports.gl.texParameteri(exports.gl.TEXTURE_2D, exports.gl.TEXTURE_MAG_FILTER, exports.gl.LINEAR);
|
||||
// gl && gl.pixelStorei(gl.UNPACK_ROW_LENGTH); // WebGL2
|
||||
exports.gl && exports.gl.texImage2D(exports.gl.TEXTURE_2D, 0, exports.gl.RGBA, width, height, 0, exports.gl.RGBA, exports.gl.UNSIGNED_BYTE, pixels);
|
||||
// Store our identifier
|
||||
io.Fonts.TexID = g_FontTexture || { foo: "bar" };
|
||||
// console.log("font texture id", g_FontTexture);
|
||||
if (exports.ctx) {
|
||||
const image_canvas = document.createElement("canvas");
|
||||
image_canvas.width = width;
|
||||
image_canvas.height = height;
|
||||
const image_ctx = image_canvas.getContext("2d");
|
||||
if (image_ctx === null) {
|
||||
throw new Error();
|
||||
}
|
||||
const image_data = image_ctx.getImageData(0, 0, width, height);
|
||||
image_data.data.set(pixels);
|
||||
image_ctx.putImageData(image_data, 0, 0);
|
||||
io.Fonts.TexID = image_canvas;
|
||||
}
|
||||
// Restore modified GL state
|
||||
exports.gl && last_texture && exports.gl.bindTexture(exports.gl.TEXTURE_2D, last_texture);
|
||||
}
|
||||
function DestroyFontsTexture() {
|
||||
const io = ImGui.GetIO();
|
||||
io.Fonts.TexID = null;
|
||||
exports.gl && exports.gl.deleteTexture(g_FontTexture);
|
||||
g_FontTexture = null;
|
||||
}
|
||||
function CreateDeviceObjects() {
|
||||
const vertex_shader = [
|
||||
"uniform mat4 ProjMtx;",
|
||||
"attribute vec2 Position;",
|
||||
"attribute vec2 UV;",
|
||||
"attribute vec4 Color;",
|
||||
"varying vec2 Frag_UV;",
|
||||
"varying vec4 Frag_Color;",
|
||||
"void main() {",
|
||||
" Frag_UV = UV;",
|
||||
" Frag_Color = Color;",
|
||||
" gl_Position = ProjMtx * vec4(Position.xy,0,1);",
|
||||
"}",
|
||||
];
|
||||
const fragment_shader = [
|
||||
"precision mediump float;",
|
||||
"uniform sampler2D Texture;",
|
||||
"varying vec2 Frag_UV;",
|
||||
"varying vec4 Frag_Color;",
|
||||
"void main() {",
|
||||
" gl_FragColor = Frag_Color * texture2D(Texture, Frag_UV);",
|
||||
"}",
|
||||
];
|
||||
g_ShaderHandle = exports.gl && exports.gl.createProgram();
|
||||
g_VertHandle = exports.gl && exports.gl.createShader(exports.gl.VERTEX_SHADER);
|
||||
g_FragHandle = exports.gl && exports.gl.createShader(exports.gl.FRAGMENT_SHADER);
|
||||
exports.gl && exports.gl.shaderSource(g_VertHandle, vertex_shader.join("\n"));
|
||||
exports.gl && exports.gl.shaderSource(g_FragHandle, fragment_shader.join("\n"));
|
||||
exports.gl && exports.gl.compileShader(g_VertHandle);
|
||||
exports.gl && exports.gl.compileShader(g_FragHandle);
|
||||
exports.gl && exports.gl.attachShader(g_ShaderHandle, g_VertHandle);
|
||||
exports.gl && exports.gl.attachShader(g_ShaderHandle, g_FragHandle);
|
||||
exports.gl && exports.gl.linkProgram(g_ShaderHandle);
|
||||
g_AttribLocationTex = exports.gl && exports.gl.getUniformLocation(g_ShaderHandle, "Texture");
|
||||
g_AttribLocationProjMtx = exports.gl && exports.gl.getUniformLocation(g_ShaderHandle, "ProjMtx");
|
||||
g_AttribLocationPosition = exports.gl && exports.gl.getAttribLocation(g_ShaderHandle, "Position") || 0;
|
||||
g_AttribLocationUV = exports.gl && exports.gl.getAttribLocation(g_ShaderHandle, "UV") || 0;
|
||||
g_AttribLocationColor = exports.gl && exports.gl.getAttribLocation(g_ShaderHandle, "Color") || 0;
|
||||
g_VboHandle = exports.gl && exports.gl.createBuffer();
|
||||
g_ElementsHandle = exports.gl && exports.gl.createBuffer();
|
||||
CreateFontsTexture();
|
||||
}
|
||||
function DestroyDeviceObjects() {
|
||||
DestroyFontsTexture();
|
||||
exports.gl && exports.gl.deleteBuffer(g_VboHandle);
|
||||
g_VboHandle = null;
|
||||
exports.gl && exports.gl.deleteBuffer(g_ElementsHandle);
|
||||
g_ElementsHandle = null;
|
||||
g_AttribLocationTex = null;
|
||||
g_AttribLocationProjMtx = null;
|
||||
g_AttribLocationPosition = -1;
|
||||
g_AttribLocationUV = -1;
|
||||
g_AttribLocationColor = -1;
|
||||
exports.gl && exports.gl.deleteProgram(g_ShaderHandle);
|
||||
g_ShaderHandle = null;
|
||||
exports.gl && exports.gl.deleteShader(g_VertHandle);
|
||||
g_VertHandle = null;
|
||||
exports.gl && exports.gl.deleteShader(g_FragHandle);
|
||||
g_FragHandle = null;
|
||||
}
|
||||
|
||||
exports.CreateDeviceObjects = CreateDeviceObjects;
|
||||
exports.CreateFontsTexture = CreateFontsTexture;
|
||||
exports.DestroyDeviceObjects = DestroyDeviceObjects;
|
||||
exports.DestroyFontsTexture = DestroyFontsTexture;
|
||||
exports.Init = Init;
|
||||
exports.NewFrame = NewFrame;
|
||||
exports.RenderDrawData = RenderDrawData;
|
||||
exports.Shutdown = Shutdown;
|
||||
|
||||
Object.defineProperty(exports, '__esModule', { value: true });
|
||||
|
||||
})));
|
||||
Binary file not shown.
|
|
@ -0,0 +1,780 @@
|
|||
|
||||
// order n
|
||||
function SHEval(fX, fY, fZ, order)
|
||||
{
|
||||
return SHEvalFct[order - 3](fX, fY, fZ);
|
||||
}
|
||||
|
||||
SHEvalFct = [
|
||||
SHEval3,
|
||||
SHEval4,
|
||||
SHEval5,
|
||||
SHEval6,
|
||||
SHEval7,
|
||||
SHEval8,
|
||||
SHEval9,
|
||||
SHEval10
|
||||
];
|
||||
|
||||
// order 3
|
||||
function SHEval3(fX, fY, fZ) {
|
||||
var fC0,fC1,fS0,fS1,fTmpA,fTmpB,fTmpC;
|
||||
var fZ2 = fZ*fZ;
|
||||
var pSH = new Array(9);
|
||||
|
||||
pSH[0] = 0.2820947917738781;
|
||||
pSH[2] = 0.4886025119029199*fZ;
|
||||
pSH[6] = 0.9461746957575601*fZ2 + -0.3153915652525201;
|
||||
fC0 = fX;
|
||||
fS0 = fY;
|
||||
|
||||
fTmpA = -0.48860251190292;
|
||||
pSH[3] = fTmpA*fC0;
|
||||
pSH[1] = fTmpA*fS0;
|
||||
fTmpB = -1.092548430592079*fZ;
|
||||
pSH[7] = fTmpB*fC0;
|
||||
pSH[5] = fTmpB*fS0;
|
||||
fC1 = fX*fC0 - fY*fS0;
|
||||
fS1 = fX*fS0 + fY*fC0;
|
||||
|
||||
fTmpC = 0.5462742152960395;
|
||||
pSH[8] = fTmpC*fC1;
|
||||
pSH[4] = fTmpC*fS1;
|
||||
|
||||
return pSH;
|
||||
}
|
||||
|
||||
// order 4
|
||||
function SHEval4(fX, fY, fZ)
|
||||
{
|
||||
var fC0,fC1,fS0,fS1,fTmpA,fTmpB,fTmpC;
|
||||
var fZ2 = fZ*fZ;
|
||||
var pSH = new Array(16);
|
||||
|
||||
pSH[0] = 0.2820947917738781;
|
||||
pSH[2] = 0.4886025119029199*fZ;
|
||||
pSH[6] = 0.9461746957575601*fZ2 + -0.3153915652525201;
|
||||
pSH[12] = fZ*(1.865881662950577*fZ2 + -1.119528997770346);
|
||||
fC0 = fX;
|
||||
fS0 = fY;
|
||||
|
||||
fTmpA = -0.48860251190292;
|
||||
pSH[3] = fTmpA*fC0;
|
||||
pSH[1] = fTmpA*fS0;
|
||||
fTmpB = -1.092548430592079*fZ;
|
||||
pSH[7] = fTmpB*fC0;
|
||||
pSH[5] = fTmpB*fS0;
|
||||
fTmpC = -2.285228997322329*fZ2 + 0.4570457994644658;
|
||||
pSH[13] = fTmpC*fC0;
|
||||
pSH[11] = fTmpC*fS0;
|
||||
fC1 = fX*fC0 - fY*fS0;
|
||||
fS1 = fX*fS0 + fY*fC0;
|
||||
|
||||
fTmpA = 0.5462742152960395;
|
||||
pSH[8] = fTmpA*fC1;
|
||||
pSH[4] = fTmpA*fS1;
|
||||
fTmpB = 1.445305721320277*fZ;
|
||||
pSH[14] = fTmpB*fC1;
|
||||
pSH[10] = fTmpB*fS1;
|
||||
fC0 = fX*fC1 - fY*fS1;
|
||||
fS0 = fX*fS1 + fY*fC1;
|
||||
|
||||
fTmpC = -0.5900435899266435;
|
||||
pSH[15] = fTmpC*fC0;
|
||||
pSH[9] = fTmpC*fS0;
|
||||
|
||||
return pSH;
|
||||
}
|
||||
|
||||
// order 5
|
||||
function SHEval5(fX, fY, fZ)
|
||||
{
|
||||
var fC0,fC1,fS0,fS1,fTmpA,fTmpB,fTmpC;
|
||||
var fZ2 = fZ*fZ;
|
||||
var pSH = new Array(25);
|
||||
|
||||
pSH[0] = 0.2820947917738781;
|
||||
pSH[2] = 0.4886025119029199*fZ;
|
||||
pSH[6] = 0.9461746957575601*fZ2 + -0.3153915652525201;
|
||||
pSH[12] = fZ*(1.865881662950577*fZ2 + -1.119528997770346);
|
||||
pSH[20] = 1.984313483298443*fZ*pSH[12] + -1.006230589874905*pSH[6];
|
||||
fC0 = fX;
|
||||
fS0 = fY;
|
||||
|
||||
fTmpA = -0.48860251190292;
|
||||
pSH[3] = fTmpA*fC0;
|
||||
pSH[1] = fTmpA*fS0;
|
||||
fTmpB = -1.092548430592079*fZ;
|
||||
pSH[7] = fTmpB*fC0;
|
||||
pSH[5] = fTmpB*fS0;
|
||||
fTmpC = -2.285228997322329*fZ2 + 0.4570457994644658;
|
||||
pSH[13] = fTmpC*fC0;
|
||||
pSH[11] = fTmpC*fS0;
|
||||
fTmpA = fZ*(-4.683325804901025*fZ2 + 2.007139630671868);
|
||||
pSH[21] = fTmpA*fC0;
|
||||
pSH[19] = fTmpA*fS0;
|
||||
fC1 = fX*fC0 - fY*fS0;
|
||||
fS1 = fX*fS0 + fY*fC0;
|
||||
|
||||
fTmpA = 0.5462742152960395;
|
||||
pSH[8] = fTmpA*fC1;
|
||||
pSH[4] = fTmpA*fS1;
|
||||
fTmpB = 1.445305721320277*fZ;
|
||||
pSH[14] = fTmpB*fC1;
|
||||
pSH[10] = fTmpB*fS1;
|
||||
fTmpC = 3.31161143515146*fZ2 + -0.47308734787878;
|
||||
pSH[22] = fTmpC*fC1;
|
||||
pSH[18] = fTmpC*fS1;
|
||||
fC0 = fX*fC1 - fY*fS1;
|
||||
fS0 = fX*fS1 + fY*fC1;
|
||||
|
||||
fTmpA = -0.5900435899266435;
|
||||
pSH[15] = fTmpA*fC0;
|
||||
pSH[9] = fTmpA*fS0;
|
||||
fTmpB = -1.770130769779931*fZ;
|
||||
pSH[23] = fTmpB*fC0;
|
||||
pSH[17] = fTmpB*fS0;
|
||||
fC1 = fX*fC0 - fY*fS0;
|
||||
fS1 = fX*fS0 + fY*fC0;
|
||||
|
||||
fTmpC = 0.6258357354491763;
|
||||
pSH[24] = fTmpC*fC1;
|
||||
pSH[16] = fTmpC*fS1;
|
||||
|
||||
return pSH;
|
||||
}
|
||||
|
||||
// order 6
|
||||
function SHEval6(fX, fY, fZ)
|
||||
{
|
||||
var fC0,fC1,fS0,fS1,fTmpA,fTmpB,fTmpC;
|
||||
var fZ2 = fZ*fZ;
|
||||
var pSH = new Array(36);
|
||||
|
||||
pSH[0] = 0.2820947917738781;
|
||||
pSH[2] = 0.4886025119029199*fZ;
|
||||
pSH[6] = 0.9461746957575601*fZ2 + -0.3153915652525201;
|
||||
pSH[12] = fZ*(1.865881662950577*fZ2 + -1.119528997770346);
|
||||
pSH[20] = 1.984313483298443*fZ*pSH[12] + -1.006230589874905*pSH[6];
|
||||
pSH[30] = 1.98997487421324*fZ*pSH[20] + -1.002853072844814*pSH[12];
|
||||
fC0 = fX;
|
||||
fS0 = fY;
|
||||
|
||||
fTmpA = -0.48860251190292;
|
||||
pSH[3] = fTmpA*fC0;
|
||||
pSH[1] = fTmpA*fS0;
|
||||
fTmpB = -1.092548430592079*fZ;
|
||||
pSH[7] = fTmpB*fC0;
|
||||
pSH[5] = fTmpB*fS0;
|
||||
fTmpC = -2.285228997322329*fZ2 + 0.4570457994644658;
|
||||
pSH[13] = fTmpC*fC0;
|
||||
pSH[11] = fTmpC*fS0;
|
||||
fTmpA = fZ*(-4.683325804901025*fZ2 + 2.007139630671868);
|
||||
pSH[21] = fTmpA*fC0;
|
||||
pSH[19] = fTmpA*fS0;
|
||||
fTmpB = 2.03100960115899*fZ*fTmpA + -0.991031208965115*fTmpC;
|
||||
pSH[31] = fTmpB*fC0;
|
||||
pSH[29] = fTmpB*fS0;
|
||||
fC1 = fX*fC0 - fY*fS0;
|
||||
fS1 = fX*fS0 + fY*fC0;
|
||||
|
||||
fTmpA = 0.5462742152960395;
|
||||
pSH[8] = fTmpA*fC1;
|
||||
pSH[4] = fTmpA*fS1;
|
||||
fTmpB = 1.445305721320277*fZ;
|
||||
pSH[14] = fTmpB*fC1;
|
||||
pSH[10] = fTmpB*fS1;
|
||||
fTmpC = 3.31161143515146*fZ2 + -0.47308734787878;
|
||||
pSH[22] = fTmpC*fC1;
|
||||
pSH[18] = fTmpC*fS1;
|
||||
fTmpA = fZ*(7.190305177459987*fZ2 + -2.396768392486662);
|
||||
pSH[32] = fTmpA*fC1;
|
||||
pSH[28] = fTmpA*fS1;
|
||||
fC0 = fX*fC1 - fY*fS1;
|
||||
fS0 = fX*fS1 + fY*fC1;
|
||||
|
||||
fTmpA = -0.5900435899266435;
|
||||
pSH[15] = fTmpA*fC0;
|
||||
pSH[9] = fTmpA*fS0;
|
||||
fTmpB = -1.770130769779931*fZ;
|
||||
pSH[23] = fTmpB*fC0;
|
||||
pSH[17] = fTmpB*fS0;
|
||||
fTmpC = -4.403144694917254*fZ2 + 0.4892382994352505;
|
||||
pSH[33] = fTmpC*fC0;
|
||||
pSH[27] = fTmpC*fS0;
|
||||
fC1 = fX*fC0 - fY*fS0;
|
||||
fS1 = fX*fS0 + fY*fC0;
|
||||
|
||||
fTmpA = 0.6258357354491763;
|
||||
pSH[24] = fTmpA*fC1;
|
||||
pSH[16] = fTmpA*fS1;
|
||||
fTmpB = 2.075662314881041*fZ;
|
||||
pSH[34] = fTmpB*fC1;
|
||||
pSH[26] = fTmpB*fS1;
|
||||
fC0 = fX*fC1 - fY*fS1;
|
||||
fS0 = fX*fS1 + fY*fC1;
|
||||
|
||||
fTmpC = -0.6563820568401703;
|
||||
pSH[35] = fTmpC*fC0;
|
||||
pSH[25] = fTmpC*fS0;
|
||||
|
||||
return pSH;
|
||||
}
|
||||
|
||||
// order 7
|
||||
function SHEval7(fX, fY, fZ)
|
||||
{
|
||||
var fC0,fC1,fS0,fS1,fTmpA,fTmpB,fTmpC;
|
||||
var fZ2 = fZ*fZ;
|
||||
var pSH = new Array(49);
|
||||
|
||||
pSH[0] = 0.2820947917738781;
|
||||
pSH[2] = 0.4886025119029199*fZ;
|
||||
pSH[6] = 0.9461746957575601*fZ2 + -0.3153915652525201;
|
||||
pSH[12] = fZ*(1.865881662950577*fZ2 + -1.119528997770346);
|
||||
pSH[20] = 1.984313483298443*fZ*pSH[12] + -1.006230589874905*pSH[6];
|
||||
pSH[30] = 1.98997487421324*fZ*pSH[20] + -1.002853072844814*pSH[12];
|
||||
pSH[42] = 1.993043457183567*fZ*pSH[30] + -1.001542020962219*pSH[20];
|
||||
fC0 = fX;
|
||||
fS0 = fY;
|
||||
|
||||
fTmpA = -0.48860251190292;
|
||||
pSH[3] = fTmpA*fC0;
|
||||
pSH[1] = fTmpA*fS0;
|
||||
fTmpB = -1.092548430592079*fZ;
|
||||
pSH[7] = fTmpB*fC0;
|
||||
pSH[5] = fTmpB*fS0;
|
||||
fTmpC = -2.285228997322329*fZ2 + 0.4570457994644658;
|
||||
pSH[13] = fTmpC*fC0;
|
||||
pSH[11] = fTmpC*fS0;
|
||||
fTmpA = fZ*(-4.683325804901025*fZ2 + 2.007139630671868);
|
||||
pSH[21] = fTmpA*fC0;
|
||||
pSH[19] = fTmpA*fS0;
|
||||
fTmpB = 2.03100960115899*fZ*fTmpA + -0.991031208965115*fTmpC;
|
||||
pSH[31] = fTmpB*fC0;
|
||||
pSH[29] = fTmpB*fS0;
|
||||
fTmpC = 2.021314989237028*fZ*fTmpB + -0.9952267030562385*fTmpA;
|
||||
pSH[43] = fTmpC*fC0;
|
||||
pSH[41] = fTmpC*fS0;
|
||||
fC1 = fX*fC0 - fY*fS0;
|
||||
fS1 = fX*fS0 + fY*fC0;
|
||||
|
||||
fTmpA = 0.5462742152960395;
|
||||
pSH[8] = fTmpA*fC1;
|
||||
pSH[4] = fTmpA*fS1;
|
||||
fTmpB = 1.445305721320277*fZ;
|
||||
pSH[14] = fTmpB*fC1;
|
||||
pSH[10] = fTmpB*fS1;
|
||||
fTmpC = 3.31161143515146*fZ2 + -0.47308734787878;
|
||||
pSH[22] = fTmpC*fC1;
|
||||
pSH[18] = fTmpC*fS1;
|
||||
fTmpA = fZ*(7.190305177459987*fZ2 + -2.396768392486662);
|
||||
pSH[32] = fTmpA*fC1;
|
||||
pSH[28] = fTmpA*fS1;
|
||||
fTmpB = 2.11394181566097*fZ*fTmpA + -0.9736101204623268*fTmpC;
|
||||
pSH[44] = fTmpB*fC1;
|
||||
pSH[40] = fTmpB*fS1;
|
||||
fC0 = fX*fC1 - fY*fS1;
|
||||
fS0 = fX*fS1 + fY*fC1;
|
||||
|
||||
fTmpA = -0.5900435899266435;
|
||||
pSH[15] = fTmpA*fC0;
|
||||
pSH[9] = fTmpA*fS0;
|
||||
fTmpB = -1.770130769779931*fZ;
|
||||
pSH[23] = fTmpB*fC0;
|
||||
pSH[17] = fTmpB*fS0;
|
||||
fTmpC = -4.403144694917254*fZ2 + 0.4892382994352505;
|
||||
pSH[33] = fTmpC*fC0;
|
||||
pSH[27] = fTmpC*fS0;
|
||||
fTmpA = fZ*(-10.13325785466416*fZ2 + 2.763615778544771);
|
||||
pSH[45] = fTmpA*fC0;
|
||||
pSH[39] = fTmpA*fS0;
|
||||
fC1 = fX*fC0 - fY*fS0;
|
||||
fS1 = fX*fS0 + fY*fC0;
|
||||
|
||||
fTmpA = 0.6258357354491763;
|
||||
pSH[24] = fTmpA*fC1;
|
||||
pSH[16] = fTmpA*fS1;
|
||||
fTmpB = 2.075662314881041*fZ;
|
||||
pSH[34] = fTmpB*fC1;
|
||||
pSH[26] = fTmpB*fS1;
|
||||
fTmpC = 5.550213908015966*fZ2 + -0.5045649007287241;
|
||||
pSH[46] = fTmpC*fC1;
|
||||
pSH[38] = fTmpC*fS1;
|
||||
fC0 = fX*fC1 - fY*fS1;
|
||||
fS0 = fX*fS1 + fY*fC1;
|
||||
|
||||
fTmpA = -0.6563820568401703;
|
||||
pSH[35] = fTmpA*fC0;
|
||||
pSH[25] = fTmpA*fS0;
|
||||
fTmpB = -2.366619162231753*fZ;
|
||||
pSH[47] = fTmpB*fC0;
|
||||
pSH[37] = fTmpB*fS0;
|
||||
fC1 = fX*fC0 - fY*fS0;
|
||||
fS1 = fX*fS0 + fY*fC0;
|
||||
|
||||
fTmpC = 0.6831841051919144;
|
||||
pSH[48] = fTmpC*fC1;
|
||||
pSH[36] = fTmpC*fS1;
|
||||
|
||||
return pSH;
|
||||
}
|
||||
|
||||
// order 8
|
||||
function SHEval8(fX, fY, fZ)
|
||||
{
|
||||
var fC0,fC1,fS0,fS1,fTmpA,fTmpB,fTmpC;
|
||||
var fZ2 = fZ*fZ;
|
||||
var pSH = new Array(64);
|
||||
|
||||
pSH[0] = 0.2820947917738781;
|
||||
pSH[2] = 0.4886025119029199*fZ;
|
||||
pSH[6] = 0.9461746957575601*fZ2 + -0.3153915652525201;
|
||||
pSH[12] = fZ*(1.865881662950577*fZ2 + -1.119528997770346);
|
||||
pSH[20] = 1.984313483298443*fZ*pSH[12] + -1.006230589874905*pSH[6];
|
||||
pSH[30] = 1.98997487421324*fZ*pSH[20] + -1.002853072844814*pSH[12];
|
||||
pSH[42] = 1.993043457183567*fZ*pSH[30] + -1.001542020962219*pSH[20];
|
||||
pSH[56] = 1.994891434824135*fZ*pSH[42] + -1.000927213921958*pSH[30];
|
||||
fC0 = fX;
|
||||
fS0 = fY;
|
||||
|
||||
fTmpA = -0.48860251190292;
|
||||
pSH[3] = fTmpA*fC0;
|
||||
pSH[1] = fTmpA*fS0;
|
||||
fTmpB = -1.092548430592079*fZ;
|
||||
pSH[7] = fTmpB*fC0;
|
||||
pSH[5] = fTmpB*fS0;
|
||||
fTmpC = -2.285228997322329*fZ2 + 0.4570457994644658;
|
||||
pSH[13] = fTmpC*fC0;
|
||||
pSH[11] = fTmpC*fS0;
|
||||
fTmpA = fZ*(-4.683325804901025*fZ2 + 2.007139630671868);
|
||||
pSH[21] = fTmpA*fC0;
|
||||
pSH[19] = fTmpA*fS0;
|
||||
fTmpB = 2.03100960115899*fZ*fTmpA + -0.991031208965115*fTmpC;
|
||||
pSH[31] = fTmpB*fC0;
|
||||
pSH[29] = fTmpB*fS0;
|
||||
fTmpC = 2.021314989237028*fZ*fTmpB + -0.9952267030562385*fTmpA;
|
||||
pSH[43] = fTmpC*fC0;
|
||||
pSH[41] = fTmpC*fS0;
|
||||
fTmpA = 2.015564437074638*fZ*fTmpC + -0.9971550440218319*fTmpB;
|
||||
pSH[57] = fTmpA*fC0;
|
||||
pSH[55] = fTmpA*fS0;
|
||||
fC1 = fX*fC0 - fY*fS0;
|
||||
fS1 = fX*fS0 + fY*fC0;
|
||||
|
||||
fTmpA = 0.5462742152960395;
|
||||
pSH[8] = fTmpA*fC1;
|
||||
pSH[4] = fTmpA*fS1;
|
||||
fTmpB = 1.445305721320277*fZ;
|
||||
pSH[14] = fTmpB*fC1;
|
||||
pSH[10] = fTmpB*fS1;
|
||||
fTmpC = 3.31161143515146*fZ2 + -0.47308734787878;
|
||||
pSH[22] = fTmpC*fC1;
|
||||
pSH[18] = fTmpC*fS1;
|
||||
fTmpA = fZ*(7.190305177459987*fZ2 + -2.396768392486662);
|
||||
pSH[32] = fTmpA*fC1;
|
||||
pSH[28] = fTmpA*fS1;
|
||||
fTmpB = 2.11394181566097*fZ*fTmpA + -0.9736101204623268*fTmpC;
|
||||
pSH[44] = fTmpB*fC1;
|
||||
pSH[40] = fTmpB*fS1;
|
||||
fTmpC = 2.081665999466133*fZ*fTmpB + -0.9847319278346618*fTmpA;
|
||||
pSH[58] = fTmpC*fC1;
|
||||
pSH[54] = fTmpC*fS1;
|
||||
fC0 = fX*fC1 - fY*fS1;
|
||||
fS0 = fX*fS1 + fY*fC1;
|
||||
|
||||
fTmpA = -0.5900435899266435;
|
||||
pSH[15] = fTmpA*fC0;
|
||||
pSH[9] = fTmpA*fS0;
|
||||
fTmpB = -1.770130769779931*fZ;
|
||||
pSH[23] = fTmpB*fC0;
|
||||
pSH[17] = fTmpB*fS0;
|
||||
fTmpC = -4.403144694917254*fZ2 + 0.4892382994352505;
|
||||
pSH[33] = fTmpC*fC0;
|
||||
pSH[27] = fTmpC*fS0;
|
||||
fTmpA = fZ*(-10.13325785466416*fZ2 + 2.763615778544771);
|
||||
pSH[45] = fTmpA*fC0;
|
||||
pSH[39] = fTmpA*fS0;
|
||||
fTmpB = 2.207940216581962*fZ*fTmpA + -0.959403223600247*fTmpC;
|
||||
pSH[59] = fTmpB*fC0;
|
||||
pSH[53] = fTmpB*fS0;
|
||||
fC1 = fX*fC0 - fY*fS0;
|
||||
fS1 = fX*fS0 + fY*fC0;
|
||||
|
||||
fTmpA = 0.6258357354491763;
|
||||
pSH[24] = fTmpA*fC1;
|
||||
pSH[16] = fTmpA*fS1;
|
||||
fTmpB = 2.075662314881041*fZ;
|
||||
pSH[34] = fTmpB*fC1;
|
||||
pSH[26] = fTmpB*fS1;
|
||||
fTmpC = 5.550213908015966*fZ2 + -0.5045649007287241;
|
||||
pSH[46] = fTmpC*fC1;
|
||||
pSH[38] = fTmpC*fS1;
|
||||
fTmpA = fZ*(13.49180504672677*fZ2 + -3.113493472321562);
|
||||
pSH[60] = fTmpA*fC1;
|
||||
pSH[52] = fTmpA*fS1;
|
||||
fC0 = fX*fC1 - fY*fS1;
|
||||
fS0 = fX*fS1 + fY*fC1;
|
||||
|
||||
fTmpA = -0.6563820568401703;
|
||||
pSH[35] = fTmpA*fC0;
|
||||
pSH[25] = fTmpA*fS0;
|
||||
fTmpB = -2.366619162231753*fZ;
|
||||
pSH[47] = fTmpB*fC0;
|
||||
pSH[37] = fTmpB*fS0;
|
||||
fTmpC = -6.745902523363385*fZ2 + 0.5189155787202604;
|
||||
pSH[61] = fTmpC*fC0;
|
||||
pSH[51] = fTmpC*fS0;
|
||||
fC1 = fX*fC0 - fY*fS0;
|
||||
fS1 = fX*fS0 + fY*fC0;
|
||||
|
||||
fTmpA = 0.6831841051919144;
|
||||
pSH[48] = fTmpA*fC1;
|
||||
pSH[36] = fTmpA*fS1;
|
||||
fTmpB = 2.645960661801901*fZ;
|
||||
pSH[62] = fTmpB*fC1;
|
||||
pSH[50] = fTmpB*fS1;
|
||||
fC0 = fX*fC1 - fY*fS1;
|
||||
fS0 = fX*fS1 + fY*fC1;
|
||||
|
||||
fTmpC = -0.7071627325245963;
|
||||
pSH[63] = fTmpC*fC0;
|
||||
pSH[49] = fTmpC*fS0;
|
||||
|
||||
return pSH;
|
||||
}
|
||||
|
||||
// order 9
|
||||
function SHEval9(fX, fY, fZ)
|
||||
{
|
||||
var fC0,fC1,fS0,fS1,fTmpA,fTmpB,fTmpC;
|
||||
var fZ2 = fZ*fZ;
|
||||
var pSH = new Array(81);
|
||||
|
||||
pSH[0] = 0.2820947917738781;
|
||||
pSH[2] = 0.4886025119029199*fZ;
|
||||
pSH[6] = 0.9461746957575601*fZ2 + -0.3153915652525201;
|
||||
pSH[12] = fZ*(1.865881662950577*fZ2 + -1.119528997770346);
|
||||
pSH[20] = 1.984313483298443*fZ*pSH[12] + -1.006230589874905*pSH[6];
|
||||
pSH[30] = 1.98997487421324*fZ*pSH[20] + -1.002853072844814*pSH[12];
|
||||
pSH[42] = 1.993043457183567*fZ*pSH[30] + -1.001542020962219*pSH[20];
|
||||
pSH[56] = 1.994891434824135*fZ*pSH[42] + -1.000927213921958*pSH[30];
|
||||
pSH[72] = 1.996089927833914*fZ*pSH[56] + -1.000600781069515*pSH[42];
|
||||
fC0 = fX;
|
||||
fS0 = fY;
|
||||
|
||||
fTmpA = -0.48860251190292;
|
||||
pSH[3] = fTmpA*fC0;
|
||||
pSH[1] = fTmpA*fS0;
|
||||
fTmpB = -1.092548430592079*fZ;
|
||||
pSH[7] = fTmpB*fC0;
|
||||
pSH[5] = fTmpB*fS0;
|
||||
fTmpC = -2.285228997322329*fZ2 + 0.4570457994644658;
|
||||
pSH[13] = fTmpC*fC0;
|
||||
pSH[11] = fTmpC*fS0;
|
||||
fTmpA = fZ*(-4.683325804901025*fZ2 + 2.007139630671868);
|
||||
pSH[21] = fTmpA*fC0;
|
||||
pSH[19] = fTmpA*fS0;
|
||||
fTmpB = 2.03100960115899*fZ*fTmpA + -0.991031208965115*fTmpC;
|
||||
pSH[31] = fTmpB*fC0;
|
||||
pSH[29] = fTmpB*fS0;
|
||||
fTmpC = 2.021314989237028*fZ*fTmpB + -0.9952267030562385*fTmpA;
|
||||
pSH[43] = fTmpC*fC0;
|
||||
pSH[41] = fTmpC*fS0;
|
||||
fTmpA = 2.015564437074638*fZ*fTmpC + -0.9971550440218319*fTmpB;
|
||||
pSH[57] = fTmpA*fC0;
|
||||
pSH[55] = fTmpA*fS0;
|
||||
fTmpB = 2.011869540407391*fZ*fTmpA + -0.9981668178901745*fTmpC;
|
||||
pSH[73] = fTmpB*fC0;
|
||||
pSH[71] = fTmpB*fS0;
|
||||
fC1 = fX*fC0 - fY*fS0;
|
||||
fS1 = fX*fS0 + fY*fC0;
|
||||
|
||||
fTmpA = 0.5462742152960395;
|
||||
pSH[8] = fTmpA*fC1;
|
||||
pSH[4] = fTmpA*fS1;
|
||||
fTmpB = 1.445305721320277*fZ;
|
||||
pSH[14] = fTmpB*fC1;
|
||||
pSH[10] = fTmpB*fS1;
|
||||
fTmpC = 3.31161143515146*fZ2 + -0.47308734787878;
|
||||
pSH[22] = fTmpC*fC1;
|
||||
pSH[18] = fTmpC*fS1;
|
||||
fTmpA = fZ*(7.190305177459987*fZ2 + -2.396768392486662);
|
||||
pSH[32] = fTmpA*fC1;
|
||||
pSH[28] = fTmpA*fS1;
|
||||
fTmpB = 2.11394181566097*fZ*fTmpA + -0.9736101204623268*fTmpC;
|
||||
pSH[44] = fTmpB*fC1;
|
||||
pSH[40] = fTmpB*fS1;
|
||||
fTmpC = 2.081665999466133*fZ*fTmpB + -0.9847319278346618*fTmpA;
|
||||
pSH[58] = fTmpC*fC1;
|
||||
pSH[54] = fTmpC*fS1;
|
||||
fTmpA = 2.06155281280883*fZ*fTmpC + -0.9903379376602873*fTmpB;
|
||||
pSH[74] = fTmpA*fC1;
|
||||
pSH[70] = fTmpA*fS1;
|
||||
fC0 = fX*fC1 - fY*fS1;
|
||||
fS0 = fX*fS1 + fY*fC1;
|
||||
|
||||
fTmpA = -0.5900435899266435;
|
||||
pSH[15] = fTmpA*fC0;
|
||||
pSH[9] = fTmpA*fS0;
|
||||
fTmpB = -1.770130769779931*fZ;
|
||||
pSH[23] = fTmpB*fC0;
|
||||
pSH[17] = fTmpB*fS0;
|
||||
fTmpC = -4.403144694917254*fZ2 + 0.4892382994352505;
|
||||
pSH[33] = fTmpC*fC0;
|
||||
pSH[27] = fTmpC*fS0;
|
||||
fTmpA = fZ*(-10.13325785466416*fZ2 + 2.763615778544771);
|
||||
pSH[45] = fTmpA*fC0;
|
||||
pSH[39] = fTmpA*fS0;
|
||||
fTmpB = 2.207940216581962*fZ*fTmpA + -0.959403223600247*fTmpC;
|
||||
pSH[59] = fTmpB*fC0;
|
||||
pSH[53] = fTmpB*fS0;
|
||||
fTmpC = 2.15322168769582*fZ*fTmpB + -0.9752173865600178*fTmpA;
|
||||
pSH[75] = fTmpC*fC0;
|
||||
pSH[69] = fTmpC*fS0;
|
||||
fC1 = fX*fC0 - fY*fS0;
|
||||
fS1 = fX*fS0 + fY*fC0;
|
||||
|
||||
fTmpA = 0.6258357354491763;
|
||||
pSH[24] = fTmpA*fC1;
|
||||
pSH[16] = fTmpA*fS1;
|
||||
fTmpB = 2.075662314881041*fZ;
|
||||
pSH[34] = fTmpB*fC1;
|
||||
pSH[26] = fTmpB*fS1;
|
||||
fTmpC = 5.550213908015966*fZ2 + -0.5045649007287241;
|
||||
pSH[46] = fTmpC*fC1;
|
||||
pSH[38] = fTmpC*fS1;
|
||||
fTmpA = fZ*(13.49180504672677*fZ2 + -3.113493472321562);
|
||||
pSH[60] = fTmpA*fC1;
|
||||
pSH[52] = fTmpA*fS1;
|
||||
fTmpB = 2.304886114323221*fZ*fTmpA + -0.9481763873554654*fTmpC;
|
||||
pSH[76] = fTmpB*fC1;
|
||||
pSH[68] = fTmpB*fS1;
|
||||
fC0 = fX*fC1 - fY*fS1;
|
||||
fS0 = fX*fS1 + fY*fC1;
|
||||
|
||||
fTmpA = -0.6563820568401703;
|
||||
pSH[35] = fTmpA*fC0;
|
||||
pSH[25] = fTmpA*fS0;
|
||||
fTmpB = -2.366619162231753*fZ;
|
||||
pSH[47] = fTmpB*fC0;
|
||||
pSH[37] = fTmpB*fS0;
|
||||
fTmpC = -6.745902523363385*fZ2 + 0.5189155787202604;
|
||||
pSH[61] = fTmpC*fC0;
|
||||
pSH[51] = fTmpC*fS0;
|
||||
fTmpA = fZ*(-17.24955311049054*fZ2 + 3.449910622098108);
|
||||
pSH[77] = fTmpA*fC0;
|
||||
pSH[67] = fTmpA*fS0;
|
||||
fC1 = fX*fC0 - fY*fS0;
|
||||
fS1 = fX*fS0 + fY*fC0;
|
||||
|
||||
fTmpA = 0.6831841051919144;
|
||||
pSH[48] = fTmpA*fC1;
|
||||
pSH[36] = fTmpA*fS1;
|
||||
fTmpB = 2.645960661801901*fZ;
|
||||
pSH[62] = fTmpB*fC1;
|
||||
pSH[50] = fTmpB*fS1;
|
||||
fTmpC = 7.984991490893139*fZ2 + -0.5323327660595426;
|
||||
pSH[78] = fTmpC*fC1;
|
||||
pSH[66] = fTmpC*fS1;
|
||||
fC0 = fX*fC1 - fY*fS1;
|
||||
fS0 = fX*fS1 + fY*fC1;
|
||||
|
||||
fTmpA = -0.7071627325245963;
|
||||
pSH[63] = fTmpA*fC0;
|
||||
pSH[49] = fTmpA*fS0;
|
||||
fTmpB = -2.91570664069932*fZ;
|
||||
pSH[79] = fTmpB*fC0;
|
||||
pSH[65] = fTmpB*fS0;
|
||||
fC1 = fX*fC0 - fY*fS0;
|
||||
fS1 = fX*fS0 + fY*fC0;
|
||||
|
||||
fTmpC = 0.72892666017483;
|
||||
pSH[80] = fTmpC*fC1;
|
||||
pSH[64] = fTmpC*fS1;
|
||||
|
||||
return pSH;
|
||||
}
|
||||
|
||||
// order 10
|
||||
function SHEval10(fX, fY, fZ)
|
||||
{
|
||||
var fC0,fC1,fS0,fS1,fTmpA,fTmpB,fTmpC;
|
||||
var fZ2 = fZ*fZ;
|
||||
var pSH = new Array(100);
|
||||
|
||||
pSH[0] = 0.2820947917738781;
|
||||
pSH[2] = 0.4886025119029199*fZ;
|
||||
pSH[6] = 0.9461746957575601*fZ2 + -0.3153915652525201;
|
||||
pSH[12] = fZ*(1.865881662950577*fZ2 + -1.119528997770346);
|
||||
pSH[20] = 1.984313483298443*fZ*pSH[12] + -1.006230589874905*pSH[6];
|
||||
pSH[30] = 1.98997487421324*fZ*pSH[20] + -1.002853072844814*pSH[12];
|
||||
pSH[42] = 1.993043457183567*fZ*pSH[30] + -1.001542020962219*pSH[20];
|
||||
pSH[56] = 1.994891434824135*fZ*pSH[42] + -1.000927213921958*pSH[30];
|
||||
pSH[72] = 1.996089927833914*fZ*pSH[56] + -1.000600781069515*pSH[42];
|
||||
pSH[90] = 1.996911195067937*fZ*pSH[72] + -1.000411437993134*pSH[56];
|
||||
fC0 = fX;
|
||||
fS0 = fY;
|
||||
|
||||
fTmpA = -0.48860251190292;
|
||||
pSH[3] = fTmpA*fC0;
|
||||
pSH[1] = fTmpA*fS0;
|
||||
fTmpB = -1.092548430592079*fZ;
|
||||
pSH[7] = fTmpB*fC0;
|
||||
pSH[5] = fTmpB*fS0;
|
||||
fTmpC = -2.285228997322329*fZ2 + 0.4570457994644658;
|
||||
pSH[13] = fTmpC*fC0;
|
||||
pSH[11] = fTmpC*fS0;
|
||||
fTmpA = fZ*(-4.683325804901025*fZ2 + 2.007139630671868);
|
||||
pSH[21] = fTmpA*fC0;
|
||||
pSH[19] = fTmpA*fS0;
|
||||
fTmpB = 2.03100960115899*fZ*fTmpA + -0.991031208965115*fTmpC;
|
||||
pSH[31] = fTmpB*fC0;
|
||||
pSH[29] = fTmpB*fS0;
|
||||
fTmpC = 2.021314989237028*fZ*fTmpB + -0.9952267030562385*fTmpA;
|
||||
pSH[43] = fTmpC*fC0;
|
||||
pSH[41] = fTmpC*fS0;
|
||||
fTmpA = 2.015564437074638*fZ*fTmpC + -0.9971550440218319*fTmpB;
|
||||
pSH[57] = fTmpA*fC0;
|
||||
pSH[55] = fTmpA*fS0;
|
||||
fTmpB = 2.011869540407391*fZ*fTmpA + -0.9981668178901745*fTmpC;
|
||||
pSH[73] = fTmpB*fC0;
|
||||
pSH[71] = fTmpB*fS0;
|
||||
fTmpC = 2.009353129741012*fZ*fTmpB + -0.9987492177719088*fTmpA;
|
||||
pSH[91] = fTmpC*fC0;
|
||||
pSH[89] = fTmpC*fS0;
|
||||
fC1 = fX*fC0 - fY*fS0;
|
||||
fS1 = fX*fS0 + fY*fC0;
|
||||
|
||||
fTmpA = 0.5462742152960395;
|
||||
pSH[8] = fTmpA*fC1;
|
||||
pSH[4] = fTmpA*fS1;
|
||||
fTmpB = 1.445305721320277*fZ;
|
||||
pSH[14] = fTmpB*fC1;
|
||||
pSH[10] = fTmpB*fS1;
|
||||
fTmpC = 3.31161143515146*fZ2 + -0.47308734787878;
|
||||
pSH[22] = fTmpC*fC1;
|
||||
pSH[18] = fTmpC*fS1;
|
||||
fTmpA = fZ*(7.190305177459987*fZ2 + -2.396768392486662);
|
||||
pSH[32] = fTmpA*fC1;
|
||||
pSH[28] = fTmpA*fS1;
|
||||
fTmpB = 2.11394181566097*fZ*fTmpA + -0.9736101204623268*fTmpC;
|
||||
pSH[44] = fTmpB*fC1;
|
||||
pSH[40] = fTmpB*fS1;
|
||||
fTmpC = 2.081665999466133*fZ*fTmpB + -0.9847319278346618*fTmpA;
|
||||
pSH[58] = fTmpC*fC1;
|
||||
pSH[54] = fTmpC*fS1;
|
||||
fTmpA = 2.06155281280883*fZ*fTmpC + -0.9903379376602873*fTmpB;
|
||||
pSH[74] = fTmpA*fC1;
|
||||
pSH[70] = fTmpA*fS1;
|
||||
fTmpB = 2.048122358357819*fZ*fTmpA + -0.9934852726704042*fTmpC;
|
||||
pSH[92] = fTmpB*fC1;
|
||||
pSH[88] = fTmpB*fS1;
|
||||
fC0 = fX*fC1 - fY*fS1;
|
||||
fS0 = fX*fS1 + fY*fC1;
|
||||
|
||||
fTmpA = -0.5900435899266435;
|
||||
pSH[15] = fTmpA*fC0;
|
||||
pSH[9] = fTmpA*fS0;
|
||||
fTmpB = -1.770130769779931*fZ;
|
||||
pSH[23] = fTmpB*fC0;
|
||||
pSH[17] = fTmpB*fS0;
|
||||
fTmpC = -4.403144694917254*fZ2 + 0.4892382994352505;
|
||||
pSH[33] = fTmpC*fC0;
|
||||
pSH[27] = fTmpC*fS0;
|
||||
fTmpA = fZ*(-10.13325785466416*fZ2 + 2.763615778544771);
|
||||
pSH[45] = fTmpA*fC0;
|
||||
pSH[39] = fTmpA*fS0;
|
||||
fTmpB = 2.207940216581962*fZ*fTmpA + -0.959403223600247*fTmpC;
|
||||
pSH[59] = fTmpB*fC0;
|
||||
pSH[53] = fTmpB*fS0;
|
||||
fTmpC = 2.15322168769582*fZ*fTmpB + -0.9752173865600178*fTmpA;
|
||||
pSH[75] = fTmpC*fC0;
|
||||
pSH[69] = fTmpC*fS0;
|
||||
fTmpA = 2.118044171189805*fZ*fTmpC + -0.9836628449792094*fTmpB;
|
||||
pSH[93] = fTmpA*fC0;
|
||||
pSH[87] = fTmpA*fS0;
|
||||
fC1 = fX*fC0 - fY*fS0;
|
||||
fS1 = fX*fS0 + fY*fC0;
|
||||
|
||||
fTmpA = 0.6258357354491763;
|
||||
pSH[24] = fTmpA*fC1;
|
||||
pSH[16] = fTmpA*fS1;
|
||||
fTmpB = 2.075662314881041*fZ;
|
||||
pSH[34] = fTmpB*fC1;
|
||||
pSH[26] = fTmpB*fS1;
|
||||
fTmpC = 5.550213908015966*fZ2 + -0.5045649007287241;
|
||||
pSH[46] = fTmpC*fC1;
|
||||
pSH[38] = fTmpC*fS1;
|
||||
fTmpA = fZ*(13.49180504672677*fZ2 + -3.113493472321562);
|
||||
pSH[60] = fTmpA*fC1;
|
||||
pSH[52] = fTmpA*fS1;
|
||||
fTmpB = 2.304886114323221*fZ*fTmpA + -0.9481763873554654*fTmpC;
|
||||
pSH[76] = fTmpB*fC1;
|
||||
pSH[68] = fTmpB*fS1;
|
||||
fTmpC = 2.229177150706235*fZ*fTmpB + -0.9671528397231821*fTmpA;
|
||||
pSH[94] = fTmpC*fC1;
|
||||
pSH[86] = fTmpC*fS1;
|
||||
fC0 = fX*fC1 - fY*fS1;
|
||||
fS0 = fX*fS1 + fY*fC1;
|
||||
|
||||
fTmpA = -0.6563820568401703;
|
||||
pSH[35] = fTmpA*fC0;
|
||||
pSH[25] = fTmpA*fS0;
|
||||
fTmpB = -2.366619162231753*fZ;
|
||||
pSH[47] = fTmpB*fC0;
|
||||
pSH[37] = fTmpB*fS0;
|
||||
fTmpC = -6.745902523363385*fZ2 + 0.5189155787202604;
|
||||
pSH[61] = fTmpC*fC0;
|
||||
pSH[51] = fTmpC*fS0;
|
||||
fTmpA = fZ*(-17.24955311049054*fZ2 + 3.449910622098108);
|
||||
pSH[77] = fTmpA*fC0;
|
||||
pSH[67] = fTmpA*fS0;
|
||||
fTmpB = 2.401636346922062*fZ*fTmpA + -0.9392246042043708*fTmpC;
|
||||
pSH[95] = fTmpB*fC0;
|
||||
pSH[85] = fTmpB*fS0;
|
||||
fC1 = fX*fC0 - fY*fS0;
|
||||
fS1 = fX*fS0 + fY*fC0;
|
||||
|
||||
fTmpA = 0.6831841051919144;
|
||||
pSH[48] = fTmpA*fC1;
|
||||
pSH[36] = fTmpA*fS1;
|
||||
fTmpB = 2.645960661801901*fZ;
|
||||
pSH[62] = fTmpB*fC1;
|
||||
pSH[50] = fTmpB*fS1;
|
||||
fTmpC = 7.984991490893139*fZ2 + -0.5323327660595426;
|
||||
pSH[78] = fTmpC*fC1;
|
||||
pSH[66] = fTmpC*fS1;
|
||||
fTmpA = fZ*(21.39289019090864*fZ2 + -3.775215916042701);
|
||||
pSH[96] = fTmpA*fC1;
|
||||
pSH[84] = fTmpA*fS1;
|
||||
fC0 = fX*fC1 - fY*fS1;
|
||||
fS0 = fX*fS1 + fY*fC1;
|
||||
|
||||
fTmpA = -0.7071627325245963;
|
||||
pSH[63] = fTmpA*fC0;
|
||||
pSH[49] = fTmpA*fS0;
|
||||
fTmpB = -2.91570664069932*fZ;
|
||||
pSH[79] = fTmpB*fC0;
|
||||
pSH[65] = fTmpB*fS0;
|
||||
fTmpC = -9.263393182848905*fZ2 + 0.5449054813440533;
|
||||
pSH[97] = fTmpC*fC0;
|
||||
pSH[83] = fTmpC*fS0;
|
||||
fC1 = fX*fC0 - fY*fS0;
|
||||
fS1 = fX*fS0 + fY*fC0;
|
||||
|
||||
fTmpA = 0.72892666017483;
|
||||
pSH[80] = fTmpA*fC1;
|
||||
pSH[64] = fTmpA*fS1;
|
||||
fTmpB = 3.177317648954698*fZ;
|
||||
pSH[98] = fTmpB*fC1;
|
||||
pSH[82] = fTmpB*fS1;
|
||||
fC0 = fX*fC1 - fY*fS1;
|
||||
fS0 = fX*fS1 + fY*fC1;
|
||||
|
||||
fTmpC = -0.7489009518531884;
|
||||
pSH[99] = fTmpC*fC0;
|
||||
pSH[81] = fTmpC*fS0;
|
||||
|
||||
return pSH;
|
||||
}
|
||||
Binary file not shown.
|
|
@ -0,0 +1,133 @@
|
|||
cmake_minimum_required (VERSION 3.2)
|
||||
project(nori)
|
||||
|
||||
add_subdirectory(ext ext_build)
|
||||
|
||||
include_directories(
|
||||
# Nori include files
|
||||
${CMAKE_CURRENT_SOURCE_DIR}/include
|
||||
# tinyformat string formatting library
|
||||
${TFM_INCLUDE_DIR}
|
||||
# Eigen linear algebra library
|
||||
SYSTEM ${EIGEN_INCLUDE_DIR}
|
||||
# OpenEXR high dynamic range bitmap library
|
||||
SYSTEM ${OPENEXR_INCLUDE_DIRS}
|
||||
# Intel Thread Building Blocks
|
||||
SYSTEM ${TBB_INCLUDE_DIR}
|
||||
# Pseudorandom number generator
|
||||
${PCG32_INCLUDE_DIR}
|
||||
# PugiXML parser
|
||||
${PUGIXML_INCLUDE_DIR}
|
||||
# Helper functions for statistical hypothesis tests
|
||||
${HYPOTHESIS_INCLUDE_DIR}
|
||||
# GLFW library for OpenGL context creation
|
||||
SYSTEM ${GLFW_INCLUDE_DIR}
|
||||
# GLEW library for accessing OpenGL functions
|
||||
SYSTEM ${GLEW_INCLUDE_DIR}
|
||||
# NanoVG drawing library
|
||||
SYSTEM ${NANOVG_INCLUDE_DIR}
|
||||
# NanoGUI user interface library
|
||||
SYSTEM ${NANOGUI_INCLUDE_DIR}
|
||||
SYSTEM ${NANOGUI_EXTRA_INCS}
|
||||
# Portable filesystem API
|
||||
SYSTEM ${FILESYSTEM_INCLUDE_DIR}
|
||||
# STB Image Write
|
||||
SYSTEM ${STB_IMAGE_WRITE_INCLUDE_DIR}
|
||||
|
||||
SYSTEM ${SH_INCLUDE_DIRS}
|
||||
)
|
||||
|
||||
# The following lines build the main executable. If you add a source
|
||||
# code file to Nori, be sure to include it in this list.
|
||||
add_executable(nori
|
||||
|
||||
# Header files
|
||||
include/nori/bbox.h
|
||||
include/nori/bitmap.h
|
||||
include/nori/block.h
|
||||
include/nori/bsdf.h
|
||||
include/nori/accel.h
|
||||
include/nori/camera.h
|
||||
include/nori/color.h
|
||||
include/nori/common.h
|
||||
include/nori/dpdf.h
|
||||
include/nori/frame.h
|
||||
include/nori/integrator.h
|
||||
include/nori/emitter.h
|
||||
include/nori/mesh.h
|
||||
include/nori/object.h
|
||||
include/nori/parser.h
|
||||
include/nori/proplist.h
|
||||
include/nori/ray.h
|
||||
include/nori/rfilter.h
|
||||
include/nori/sampler.h
|
||||
include/nori/scene.h
|
||||
include/nori/timer.h
|
||||
include/nori/transform.h
|
||||
include/nori/vector.h
|
||||
include/nori/warp.h
|
||||
|
||||
# Source code files
|
||||
src/bitmap.cpp
|
||||
src/block.cpp
|
||||
src/accel.cpp
|
||||
src/chi2test.cpp
|
||||
src/common.cpp
|
||||
src/diffuse.cpp
|
||||
src/gui.cpp
|
||||
src/independent.cpp
|
||||
src/main.cpp
|
||||
src/mesh.cpp
|
||||
src/obj.cpp
|
||||
src/object.cpp
|
||||
src/parser.cpp
|
||||
src/perspective.cpp
|
||||
src/proplist.cpp
|
||||
src/rfilter.cpp
|
||||
src/scene.cpp
|
||||
src/ttest.cpp
|
||||
src/warp.cpp
|
||||
src/microfacet.cpp
|
||||
src/mirror.cpp
|
||||
src/dielectric.cpp
|
||||
src/prt.cpp
|
||||
ext/spherical-harmonics/sh/spherical_harmonics.cc
|
||||
ext/spherical-harmonics/sh/default_image.cc
|
||||
)
|
||||
|
||||
add_definitions(${NANOGUI_EXTRA_DEFS})
|
||||
|
||||
# The following lines build the warping test application
|
||||
add_executable(warptest
|
||||
include/nori/warp.h
|
||||
src/warp.cpp
|
||||
src/warptest.cpp
|
||||
src/microfacet.cpp
|
||||
src/object.cpp
|
||||
src/proplist.cpp
|
||||
src/common.cpp
|
||||
)
|
||||
|
||||
if (WIN32)
|
||||
target_link_libraries(nori tbb_static pugixml IlmImf nanogui ${NANOGUI_EXTRA_LIBS} zlibstatic)
|
||||
else()
|
||||
target_link_libraries(nori tbb_static pugixml IlmImf nanogui ${NANOGUI_EXTRA_LIBS})
|
||||
endif()
|
||||
|
||||
target_link_libraries(warptest tbb_static nanogui ${NANOGUI_EXTRA_LIBS})
|
||||
|
||||
# Force colored output for the ninja generator
|
||||
if (CMAKE_GENERATOR STREQUAL "Ninja")
|
||||
if (CMAKE_CXX_COMPILER_ID MATCHES "Clang")
|
||||
set(CMAKE_C_FLAGS "${CMAKE_C_FLAGS} -fcolor-diagnostics")
|
||||
set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -fcolor-diagnostics")
|
||||
elseif (CMAKE_CXX_COMPILER_ID MATCHES "GNU")
|
||||
set(CMAKE_C_FLAGS "${CMAKE_C_FLAGS} -fdiagnostics-color=always")
|
||||
set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -fdiagnostics-color=always")
|
||||
endif()
|
||||
endif()
|
||||
|
||||
target_compile_features(warptest PRIVATE cxx_std_17)
|
||||
target_compile_features(nori PRIVATE cxx_std_17)
|
||||
|
||||
# vim: set et ts=2 sw=2 ft=cmake nospell:
|
||||
|
|
@ -0,0 +1,24 @@
|
|||
[](https://rgl.s3.eu-central-1.amazonaws.com/media/uploads/wjakob/2017/02/20/cs440-rgl.jpg)
|
||||
|
||||
## Nori Version 2
|
||||
|
||||
|
||||
Nori is a simple ray tracer written in C++. It runs on Windows, Linux, and
|
||||
Mac OS and provides basic functionality that is required to complete the
|
||||
assignments in the course Advanced Computer Graphics taught at EPFL.
|
||||
|
||||
### Course information and framework documentation
|
||||
|
||||
For access to course information including slides and reading material, visit the main [Advanced Computer Graphics website](https://rgl.epfl.ch/courses/ACG17). The Nori 2 framework and coding assignments will be described on the [Nori website](https://wjakob.github.io/nori).
|
||||
|
||||
### Note to researchers and students from other institutions
|
||||
|
||||
Last year's version of Nori including a full set of assignment descriptions can
|
||||
be found in the following [archive](https://github.com/wjakob/nori-old).
|
||||
|
||||
|
||||
### Known Issues
|
||||
There is a known issue with the NanoGUI version that Nori uses: on Linux systems with an integrated Intel GPU, a bug in the Mesa graphics drivers causes the GUI to freeze on startup. A workaround is to temporarily switch to an older Mesa driver to run Nori. This can be done by running
|
||||
```
|
||||
export MESA_LOADER_DRIVER_OVERRIDE=i965
|
||||
```
|
||||
|
|
@ -0,0 +1,228 @@
|
|||
# =======================================================================
|
||||
# WARNING WARNING WARNING WARNING WARNING WARNING
|
||||
# =======================================================================
|
||||
# Remember to put on SAFETY GOGGLES before looking at this file. You
|
||||
# are most certainly not expected to read or understand any of it.
|
||||
# =======================================================================
|
||||
#
|
||||
# This CMake file is responsible for compiling dependency libraries and
|
||||
# setting up suitable compiler flags for various platforms. You do not
|
||||
# need to read or change anything in this file; see CMakeLists.txt in
|
||||
# the main Nori folder instead.
|
||||
|
||||
include(CheckCXXCompilerFlag)
|
||||
|
||||
if(NOT IS_DIRECTORY "${CMAKE_CURRENT_SOURCE_DIR}/openexr/OpenEXR")
|
||||
message(FATAL_ERROR "The Nori dependencies are missing! "
|
||||
"You probably did not clone the project with --recursive. It is possible to recover "
|
||||
"by calling \"git submodule update --init --recursive\"")
|
||||
endif()
|
||||
|
||||
# Set a default build configuration (Release)
|
||||
if(NOT CMAKE_BUILD_TYPE AND NOT CMAKE_CONFIGURATION_TYPES)
|
||||
message(STATUS "Setting build type to 'Release' as none was specified.")
|
||||
set(CMAKE_BUILD_TYPE Release CACHE STRING "Choose the type of build." FORCE)
|
||||
set_property(CACHE CMAKE_BUILD_TYPE PROPERTY STRINGS "Debug" "Release"
|
||||
"MinSizeRel" "RelWithDebInfo")
|
||||
endif()
|
||||
string(TOUPPER "${CMAKE_BUILD_TYPE}" U_CMAKE_BUILD_TYPE)
|
||||
|
||||
# Enable folders for projects in Visual Studio
|
||||
if (CMAKE_GENERATOR MATCHES "Visual Studio")
|
||||
set_property(GLOBAL PROPERTY USE_FOLDERS ON)
|
||||
endif()
|
||||
|
||||
if (APPLE)
|
||||
set(CMAKE_MACOSX_RPATH ON)
|
||||
endif()
|
||||
|
||||
if (CMAKE_CXX_COMPILER_ID MATCHES "Clang" OR CMAKE_CXX_COMPILER_ID MATCHES "GNU")
|
||||
CHECK_CXX_COMPILER_FLAG("-std=c++14" HAS_CPP14_FLAG)
|
||||
CHECK_CXX_COMPILER_FLAG("-std=c++11" HAS_CPP11_FLAG)
|
||||
|
||||
if (HAS_CPP14_FLAG)
|
||||
set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -std=c++14")
|
||||
elseif (HAS_CPP11_FLAG)
|
||||
set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -std=c++11")
|
||||
else()
|
||||
message(FATAL_ERROR "Unsupported compiler -- Nori requires C++11 support!")
|
||||
endif()
|
||||
|
||||
# Prefer libc++ in conjunction with Clang
|
||||
if (CMAKE_CXX_COMPILER_ID MATCHES "Clang")
|
||||
CHECK_CXX_COMPILER_FLAG("-stdlib=libc++" HAS_LIBCPP)
|
||||
if (HAS_LIBCPP)
|
||||
set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -stdlib=libc++ -D_LIBCPP_VERSION")
|
||||
set(CMAKE_EXE_LINKER_FLAGS "${CMAKE_EXE_LINKER_FLAGS} -stdlib=libc++")
|
||||
set(CMAKE_SHARED_LINKER_FLAGS "${CMAKE_SHARED_LINKER_FLAGS} -stdlib=libc++")
|
||||
message(STATUS "Nori: using libc++.")
|
||||
else()
|
||||
message(WARNING "libc++ is recommended in conjunction with clang. Please insteall the libc++ development headers, provided e.g. by the packages 'libc++-dev' and 'libc++abi-dev' on Debian/Ubuntu.")
|
||||
endif()
|
||||
endif()
|
||||
|
||||
# Enable link time optimization and set the default symbol
|
||||
# visibility to hidden (very important to obtain small binaries)
|
||||
if (NOT ${U_CMAKE_BUILD_TYPE} MATCHES DEBUG)
|
||||
# Default symbol visibility
|
||||
set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -fvisibility=hidden")
|
||||
endif()
|
||||
|
||||
# Disable specific GCC 7 warnings
|
||||
if (CMAKE_COMPILER_IS_GNUCC AND CMAKE_CXX_COMPILER_VERSION VERSION_GREATER 7.0)
|
||||
set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -Wno-deprecated-declarations -Wno-misleading-indentation -Wformat-truncation=0 -Wno-int-in-bool-context -Wimplicit-fallthrough=0")
|
||||
endif()
|
||||
endif()
|
||||
|
||||
# Sanitize build environment for static build with C++11
|
||||
if (MSVC)
|
||||
# Disable annoying secure CRT warnings
|
||||
set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} /D_CRT_SECURE_NO_WARNINGS")
|
||||
|
||||
# We'll select the TBB library ourselves
|
||||
set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} /D__TBB_NO_IMPLICIT_LINKAGE")
|
||||
|
||||
# Parallel build on MSVC (all targets)
|
||||
set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} /MP")
|
||||
|
||||
if (NOT CMAKE_SIZEOF_VOID_P EQUAL 8)
|
||||
set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} /arch:SSE2")
|
||||
|
||||
# Disable Eigen vectorization for Windows 32 bit builds (issues with unaligned access segfaults)
|
||||
set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} /DEIGEN_DONT_ALIGN")
|
||||
endif()
|
||||
|
||||
# Static build
|
||||
set(CompilerFlags
|
||||
CMAKE_CXX_FLAGS CMAKE_CXX_FLAGS_DEBUG CMAKE_CXX_FLAGS_RELEASE
|
||||
CMAKE_CXX_FLAGS_MINSIZEREL CMAKE_CXX_FLAGS_RELWITHDEBINFO
|
||||
CMAKE_C_FLAGS CMAKE_C_FLAGS_DEBUG CMAKE_C_FLAGS_RELEASE
|
||||
CMAKE_C_FLAGS_MINSIZEREL CMAKE_C_FLAGS_RELWITHDEBINFO)
|
||||
foreach(CompilerFlag ${CompilerFlags})
|
||||
string(REPLACE "/MD" "/MT" ${CompilerFlag} "${${CompilerFlag}}")
|
||||
endforeach()
|
||||
endif()
|
||||
|
||||
if (WIN32)
|
||||
# Build zlib (only on Windows)
|
||||
set(ZLIB_BUILD_STATIC_LIBS ON CACHE BOOL " " FORCE)
|
||||
set(ZLIB_BUILD_SHARED_LIBS OFF CACHE BOOL " " FORCE)
|
||||
add_subdirectory(zlib)
|
||||
|
||||
set(ZLIB_INCLUDE_DIR "${CMAKE_CURRENT_SOURCE_DIR}/zlib" CACHE PATH " " FORCE)
|
||||
if (CMAKE_GENERATOR STREQUAL "Ninja")
|
||||
set(ZLIB_LIBRARY "${CMAKE_CURRENT_BINARY_DIR}/zlib/zlibstatic.lib" CACHE FILEPATH " " FORCE)
|
||||
else()
|
||||
set(ZLIB_LIBRARY "${CMAKE_CURRENT_BINARY_DIR}/zlib/$<CONFIGURATION>/zlibstatic.lib" CACHE FILEPATH " " FORCE)
|
||||
endif()
|
||||
|
||||
set_property(TARGET zlibstatic PROPERTY FOLDER "dependencies")
|
||||
include_directories(${ZLIB_INCLUDE_DIR} "${CMAKE_CURRENT_BINARY_DIR}/zlib")
|
||||
endif()
|
||||
|
||||
# Build OpenER
|
||||
set(ILMBASE_BUILD_SHARED_LIBS OFF CACHE BOOL " " FORCE)
|
||||
set(OPENEXR_BUILD_SHARED_LIBS OFF CACHE BOOL " " FORCE)
|
||||
set(ILMBASE_NAMESPACE_VERSIONING OFF CACHE BOOL " " FORCE)
|
||||
set(OPENEXR_NAMESPACE_VERSIONING OFF CACHE BOOL " " FORCE)
|
||||
add_subdirectory(openexr)
|
||||
set_property(TARGET IexMath eLut toFloat b44ExpLogTable dwaLookups IlmThread Half Iex Imath IlmImf PROPERTY FOLDER "dependencies")
|
||||
|
||||
# Build Thread Building Blocks (main shared libraries only)
|
||||
set(TBB_BUILD_SHARED OFF CACHE BOOL " " FORCE)
|
||||
set(TBB_BUILD_STATIC ON CACHE BOOL " " FORCE)
|
||||
set(TBB_BUILD_TBBMALLOC OFF CACHE BOOL " " FORCE)
|
||||
set(TBB_BUILD_TBBMALLOC_PROXY OFF CACHE BOOL " " FORCE)
|
||||
set(TBB_BUILD_TESTS OFF CACHE BOOL " " FORCE)
|
||||
add_subdirectory(tbb)
|
||||
set_property(TARGET tbb_static tbb_def_files PROPERTY FOLDER "dependencies")
|
||||
|
||||
if (APPLE)
|
||||
set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -DGL_SILENCE_DEPRECATION=1")
|
||||
endif()
|
||||
|
||||
# Build NanoGUI
|
||||
# Use OpenGL backend for UI. In the future, this can be removed to use Metal on MacOS
|
||||
set(NANOGUI_BACKEND "OpenGL" CACHE BOOL " " FORCE)
|
||||
set(NANOGUI_BUILD_EXAMPLES OFF CACHE BOOL " " FORCE)
|
||||
set(NANOGUI_BUILD_SHARED OFF CACHE BOOL " " FORCE)
|
||||
set(NANOGUI_BUILD_PYTHON OFF CACHE BOOL " " FORCE)
|
||||
add_subdirectory(nanogui)
|
||||
set_property(TARGET glfw glfw_objects nanogui PROPERTY FOLDER "dependencies")
|
||||
|
||||
# Build the pugixml parser
|
||||
add_library(pugixml STATIC pugixml/src/pugixml.cpp)
|
||||
set_property(TARGET pugixml PROPERTY
|
||||
LIBRARY_OUTPUT_DIRECTORY "${CMAKE_CURRENT_BINARY_DIR}/pugixml")
|
||||
set_property(TARGET pugixml PROPERTY FOLDER "dependencies")
|
||||
|
||||
set(OPENEXR_INCLUDE_DIRS
|
||||
${CMAKE_CURRENT_SOURCE_DIR}/openexr/IlmBase/Imath
|
||||
${CMAKE_CURRENT_SOURCE_DIR}/openexr/IlmBase/Iex
|
||||
${CMAKE_CURRENT_SOURCE_DIR}/openexr/IlmBase/Half
|
||||
${CMAKE_CURRENT_SOURCE_DIR}/openexr/OpenEXR/IlmImf
|
||||
${CMAKE_CURRENT_BINARY_DIR}/openexr/OpenEXR/config
|
||||
${CMAKE_CURRENT_BINARY_DIR}/openexr/IlmBase/config)
|
||||
set(PCG32_INCLUDE_DIR
|
||||
${CMAKE_CURRENT_SOURCE_DIR}/pcg32)
|
||||
set(TFM_INCLUDE_DIR
|
||||
${CMAKE_CURRENT_SOURCE_DIR}/tinyformat)
|
||||
set(HYPOTHESIS_INCLUDE_DIR
|
||||
${CMAKE_CURRENT_SOURCE_DIR}/hypothesis)
|
||||
set(GLFW_INCLUDE_DIR
|
||||
${CMAKE_CURRENT_SOURCE_DIR}/nanogui/ext/glfw/include)
|
||||
set(GLEW_INCLUDE_DIR
|
||||
${CMAKE_CURRENT_SOURCE_DIR}/nanogui/ext/glew/include)
|
||||
set(NANOVG_INCLUDE_DIR
|
||||
${CMAKE_CURRENT_SOURCE_DIR}/nanogui/ext/nanovg/src)
|
||||
set(STB_IMAGE_WRITE_INCLUDE_DIR
|
||||
${CMAKE_CURRENT_SOURCE_DIR}/nanogui/ext/nanovg/example)
|
||||
set(NANOGUI_INCLUDE_DIR
|
||||
${CMAKE_CURRENT_SOURCE_DIR}/nanogui/include)
|
||||
set(EIGEN_INCLUDE_DIR
|
||||
${CMAKE_CURRENT_SOURCE_DIR}/eigen)
|
||||
set(SH_INCLUDE_DIRS
|
||||
${CMAKE_CURRENT_SOURCE_DIR}/spherical-harmonics)
|
||||
set(TBB_INCLUDE_DIR
|
||||
${CMAKE_CURRENT_SOURCE_DIR}/tbb/include)
|
||||
set(FILESYSTEM_INCLUDE_DIR
|
||||
${CMAKE_CURRENT_SOURCE_DIR}/filesystem)
|
||||
set(PUGIXML_INCLUDE_DIR
|
||||
${CMAKE_CURRENT_SOURCE_DIR}/pugixml/src)
|
||||
|
||||
# Compile remainder of the codebase with compiler warnings turned on
|
||||
if(MSVC)
|
||||
if(CMAKE_CXX_FLAGS MATCHES "/W[0-4]")
|
||||
string(REGEX REPLACE "/W[0-4]" "/W4" CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS}")
|
||||
else()
|
||||
set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} /W4")
|
||||
endif()
|
||||
elseif (CMAKE_CXX_COMPILER_ID MATCHES "Clang" OR CMAKE_CXX_COMPILER_ID MATCHES "GNU")
|
||||
# Re-enable disabled warnings
|
||||
# if(CMAKE_CXX_FLAGS MATCHES "-Wno-[^ ]+")
|
||||
# string(REGEX REPLACE "-Wno-[^ ]+" "" CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS}")
|
||||
# endif()
|
||||
|
||||
set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -Wall -Wextra -Wno-unused-parameter")
|
||||
if (CMAKE_CXX_COMPILER_ID MATCHES "Clang")
|
||||
set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -Wno-gnu-anonymous-struct -Wno-c99-extensions -Wno-nested-anon-types -Wno-deprecated-register")
|
||||
endif()
|
||||
endif()
|
||||
|
||||
set(CompilerFlags
|
||||
CMAKE_CXX_FLAGS CMAKE_CXX_FLAGS_DEBUG CMAKE_CXX_FLAGS_RELEASE
|
||||
CMAKE_CXX_FLAGS_MINSIZEREL CMAKE_CXX_FLAGS_RELWITHDEBINFO CMAKE_C_FLAGS
|
||||
CMAKE_C_FLAGS_DEBUG CMAKE_C_FLAGS_RELEASE CMAKE_C_FLAGS_MINSIZEREL
|
||||
CMAKE_C_FLAGS_RELWITHDEBINFO COMPILE_DEFINITIONS U_CMAKE_BUILD_TYPE
|
||||
CMAKE_MACOSX_RPATH
|
||||
OPENEXR_INCLUDE_DIRS PCG32_INCLUDE_DIR TFM_INCLUDE_DIR
|
||||
HYPOTHESIS_INCLUDE_DIR GLFW_INCLUDE_DIR GLEW_INCLUDE_DIR
|
||||
NANOVG_INCLUDE_DIR NANOGUI_EXTRA_INCS NANOGUI_EXTRA_DEFS
|
||||
NANOGUI_EXTRA_LIBS NANOGUI_INCLUDE_DIR EIGEN_INCLUDE_DIR
|
||||
STB_IMAGE_WRITE_INCLUDE_DIR TBB_INCLUDE_DIR
|
||||
FILESYSTEM_INCLUDE_DIR PUGIXML_INCLUDE_DIR
|
||||
SH_INCLUDE_DIRS
|
||||
)
|
||||
foreach(CompilerFlag ${CompilerFlags})
|
||||
set(${CompilerFlag} "${${CompilerFlag}}" PARENT_SCOPE)
|
||||
endforeach()
|
||||
|
|
@ -0,0 +1,15 @@
|
|||
### Overview of dependency libraries used by Nori
|
||||
|
||||
Nori requires several utility libraries to function correctly; a full list with
|
||||
explanations is given below. You should feel free to use any of their
|
||||
functionality in your own submissions—however, you are not required to do so.
|
||||
|
||||
* `filesystem`: tiny self-contained library for manipulating file paths
|
||||
* `hypothesis`: utility functions for statistical hypothesis tests
|
||||
* `nanogui`: minimalistic GUI library for OpenGL
|
||||
* `openexr`: High dynamic range image format library
|
||||
* `pcg32`: tiny self-contained pseudorandom number generator
|
||||
* `pugixml`: light-weight XML processing library
|
||||
* `tbb`: Intel's Boost Thread Building Blocks for multithreading
|
||||
* `tinyformat`: type-safe C++11 version of `sprintf` and friends
|
||||
* `zlib`: data compression library, used by `openexr`
|
||||
|
|
@ -0,0 +1,37 @@
|
|||
qrc_*cxx
|
||||
*.orig
|
||||
*.pyc
|
||||
*.diff
|
||||
diff
|
||||
*.save
|
||||
save
|
||||
*.old
|
||||
*.gmo
|
||||
*.qm
|
||||
core
|
||||
core.*
|
||||
*.bak
|
||||
*~
|
||||
*build*
|
||||
*.moc.*
|
||||
*.moc
|
||||
ui_*
|
||||
CMakeCache.txt
|
||||
tags
|
||||
.*.swp
|
||||
activity.png
|
||||
*.out
|
||||
*.php*
|
||||
*.log
|
||||
*.orig
|
||||
*.rej
|
||||
log
|
||||
patch
|
||||
*.patch
|
||||
a
|
||||
a.*
|
||||
lapack/testing
|
||||
lapack/reference
|
||||
.*project
|
||||
.settings
|
||||
Makefile
|
||||
|
|
@ -0,0 +1,11 @@
|
|||
[patterns]
|
||||
*.sh = LF
|
||||
*.MINPACK = CRLF
|
||||
scripts/*.in = LF
|
||||
debug/msvc/*.dat = CRLF
|
||||
debug/msvc/*.natvis = CRLF
|
||||
unsupported/test/mpreal/*.* = CRLF
|
||||
** = native
|
||||
|
||||
[repository]
|
||||
native = LF
|
||||
|
|
@ -0,0 +1,621 @@
|
|||
project(Eigen3)
|
||||
|
||||
cmake_minimum_required(VERSION 2.8.5)
|
||||
|
||||
# guard against in-source builds
|
||||
|
||||
if(${CMAKE_SOURCE_DIR} STREQUAL ${CMAKE_BINARY_DIR})
|
||||
message(FATAL_ERROR "In-source builds not allowed. Please make a new directory (called a build directory) and run CMake from there. You may need to remove CMakeCache.txt. ")
|
||||
endif()
|
||||
|
||||
# Alias Eigen_*_DIR to Eigen3_*_DIR:
|
||||
|
||||
set(Eigen_SOURCE_DIR ${Eigen3_SOURCE_DIR})
|
||||
set(Eigen_BINARY_DIR ${Eigen3_BINARY_DIR})
|
||||
|
||||
# guard against bad build-type strings
|
||||
|
||||
if (NOT CMAKE_BUILD_TYPE)
|
||||
set(CMAKE_BUILD_TYPE "Release")
|
||||
endif()
|
||||
|
||||
string(TOLOWER "${CMAKE_BUILD_TYPE}" cmake_build_type_tolower)
|
||||
if( NOT cmake_build_type_tolower STREQUAL "debug"
|
||||
AND NOT cmake_build_type_tolower STREQUAL "release"
|
||||
AND NOT cmake_build_type_tolower STREQUAL "relwithdebinfo")
|
||||
message(FATAL_ERROR "Unknown build type \"${CMAKE_BUILD_TYPE}\". Allowed values are Debug, Release, RelWithDebInfo (case-insensitive).")
|
||||
endif()
|
||||
|
||||
|
||||
#############################################################################
|
||||
# retrieve version infomation #
|
||||
#############################################################################
|
||||
|
||||
# automatically parse the version number
|
||||
file(READ "${PROJECT_SOURCE_DIR}/Eigen/src/Core/util/Macros.h" _eigen_version_header)
|
||||
string(REGEX MATCH "define[ \t]+EIGEN_WORLD_VERSION[ \t]+([0-9]+)" _eigen_world_version_match "${_eigen_version_header}")
|
||||
set(EIGEN_WORLD_VERSION "${CMAKE_MATCH_1}")
|
||||
string(REGEX MATCH "define[ \t]+EIGEN_MAJOR_VERSION[ \t]+([0-9]+)" _eigen_major_version_match "${_eigen_version_header}")
|
||||
set(EIGEN_MAJOR_VERSION "${CMAKE_MATCH_1}")
|
||||
string(REGEX MATCH "define[ \t]+EIGEN_MINOR_VERSION[ \t]+([0-9]+)" _eigen_minor_version_match "${_eigen_version_header}")
|
||||
set(EIGEN_MINOR_VERSION "${CMAKE_MATCH_1}")
|
||||
set(EIGEN_VERSION_NUMBER ${EIGEN_WORLD_VERSION}.${EIGEN_MAJOR_VERSION}.${EIGEN_MINOR_VERSION})
|
||||
|
||||
# if we are not in a mercurial clone
|
||||
if(IS_DIRECTORY ${CMAKE_SOURCE_DIR}/.hg)
|
||||
# if the mercurial program is absent or this will leave the EIGEN_HG_CHANGESET string empty,
|
||||
# but won't stop CMake.
|
||||
execute_process(COMMAND hg tip -R ${CMAKE_SOURCE_DIR} OUTPUT_VARIABLE EIGEN_HGTIP_OUTPUT)
|
||||
execute_process(COMMAND hg branch -R ${CMAKE_SOURCE_DIR} OUTPUT_VARIABLE EIGEN_BRANCH_OUTPUT)
|
||||
endif()
|
||||
|
||||
# if this is the default (aka development) branch, extract the mercurial changeset number from the hg tip output...
|
||||
if(EIGEN_BRANCH_OUTPUT MATCHES "default")
|
||||
string(REGEX MATCH "^changeset: *[0-9]*:([0-9;a-f]+).*" EIGEN_HG_CHANGESET_MATCH "${EIGEN_HGTIP_OUTPUT}")
|
||||
set(EIGEN_HG_CHANGESET "${CMAKE_MATCH_1}")
|
||||
endif(EIGEN_BRANCH_OUTPUT MATCHES "default")
|
||||
#...and show it next to the version number
|
||||
if(EIGEN_HG_CHANGESET)
|
||||
set(EIGEN_VERSION "${EIGEN_VERSION_NUMBER} (mercurial changeset ${EIGEN_HG_CHANGESET})")
|
||||
else(EIGEN_HG_CHANGESET)
|
||||
set(EIGEN_VERSION "${EIGEN_VERSION_NUMBER}")
|
||||
endif(EIGEN_HG_CHANGESET)
|
||||
|
||||
|
||||
include(CheckCXXCompilerFlag)
|
||||
include(GNUInstallDirs)
|
||||
|
||||
set(CMAKE_MODULE_PATH ${PROJECT_SOURCE_DIR}/cmake)
|
||||
|
||||
|
||||
option(EIGEN_TEST_CXX11 "Enable testing with C++11 and C++11 features (e.g. Tensor module)." OFF)
|
||||
|
||||
|
||||
macro(ei_add_cxx_compiler_flag FLAG)
|
||||
string(REGEX REPLACE "-" "" SFLAG1 ${FLAG})
|
||||
string(REGEX REPLACE "\\+" "p" SFLAG ${SFLAG1})
|
||||
check_cxx_compiler_flag(${FLAG} COMPILER_SUPPORT_${SFLAG})
|
||||
if(COMPILER_SUPPORT_${SFLAG})
|
||||
set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} ${FLAG}")
|
||||
endif()
|
||||
endmacro(ei_add_cxx_compiler_flag)
|
||||
|
||||
check_cxx_compiler_flag("-std=c++11" EIGEN_COMPILER_SUPPORT_CPP11)
|
||||
|
||||
if(EIGEN_TEST_CXX11)
|
||||
set(CMAKE_CXX_STANDARD 11)
|
||||
set(CMAKE_CXX_EXTENSIONS OFF)
|
||||
if(EIGEN_COMPILER_SUPPORT_CPP11)
|
||||
set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -std=c++11")
|
||||
endif()
|
||||
else()
|
||||
#set(CMAKE_CXX_STANDARD 03)
|
||||
#set(CMAKE_CXX_EXTENSIONS OFF)
|
||||
ei_add_cxx_compiler_flag("-std=c++03")
|
||||
endif()
|
||||
|
||||
#############################################################################
|
||||
# find how to link to the standard libraries #
|
||||
#############################################################################
|
||||
|
||||
find_package(StandardMathLibrary)
|
||||
|
||||
|
||||
set(EIGEN_TEST_CUSTOM_LINKER_FLAGS "" CACHE STRING "Additional linker flags when linking unit tests.")
|
||||
set(EIGEN_TEST_CUSTOM_CXX_FLAGS "" CACHE STRING "Additional compiler flags when compiling unit tests.")
|
||||
|
||||
set(EIGEN_STANDARD_LIBRARIES_TO_LINK_TO "")
|
||||
|
||||
if(NOT STANDARD_MATH_LIBRARY_FOUND)
|
||||
|
||||
message(FATAL_ERROR
|
||||
"Can't link to the standard math library. Please report to the Eigen developers, telling them about your platform.")
|
||||
|
||||
else()
|
||||
|
||||
if(EIGEN_STANDARD_LIBRARIES_TO_LINK_TO)
|
||||
set(EIGEN_STANDARD_LIBRARIES_TO_LINK_TO "${EIGEN_STANDARD_LIBRARIES_TO_LINK_TO} ${STANDARD_MATH_LIBRARY}")
|
||||
else()
|
||||
set(EIGEN_STANDARD_LIBRARIES_TO_LINK_TO "${STANDARD_MATH_LIBRARY}")
|
||||
endif()
|
||||
|
||||
endif()
|
||||
|
||||
if(EIGEN_STANDARD_LIBRARIES_TO_LINK_TO)
|
||||
message(STATUS "Standard libraries to link to explicitly: ${EIGEN_STANDARD_LIBRARIES_TO_LINK_TO}")
|
||||
else()
|
||||
message(STATUS "Standard libraries to link to explicitly: none")
|
||||
endif()
|
||||
|
||||
option(EIGEN_BUILD_BTL "Build benchmark suite" OFF)
|
||||
|
||||
# Disable pkgconfig only for native Windows builds
|
||||
if(NOT WIN32 OR NOT CMAKE_HOST_SYSTEM_NAME MATCHES Windows)
|
||||
option(EIGEN_BUILD_PKGCONFIG "Build pkg-config .pc file for Eigen" ON)
|
||||
endif()
|
||||
|
||||
set(CMAKE_INCLUDE_CURRENT_DIR ON)
|
||||
|
||||
option(EIGEN_SPLIT_LARGE_TESTS "Split large tests into smaller executables" ON)
|
||||
|
||||
option(EIGEN_DEFAULT_TO_ROW_MAJOR "Use row-major as default matrix storage order" OFF)
|
||||
if(EIGEN_DEFAULT_TO_ROW_MAJOR)
|
||||
add_definitions("-DEIGEN_DEFAULT_TO_ROW_MAJOR")
|
||||
endif()
|
||||
|
||||
set(EIGEN_TEST_MAX_SIZE "320" CACHE STRING "Maximal matrix/vector size, default is 320")
|
||||
|
||||
if(NOT MSVC)
|
||||
# We assume that other compilers are partly compatible with GNUCC
|
||||
|
||||
# clang outputs some warnings for unknown flags that are not caught by check_cxx_compiler_flag
|
||||
# adding -Werror turns such warnings into errors
|
||||
check_cxx_compiler_flag("-Werror" COMPILER_SUPPORT_WERROR)
|
||||
if(COMPILER_SUPPORT_WERROR)
|
||||
set(CMAKE_REQUIRED_FLAGS "-Werror")
|
||||
endif()
|
||||
ei_add_cxx_compiler_flag("-pedantic")
|
||||
ei_add_cxx_compiler_flag("-Wall")
|
||||
ei_add_cxx_compiler_flag("-Wextra")
|
||||
#ei_add_cxx_compiler_flag("-Weverything") # clang
|
||||
|
||||
ei_add_cxx_compiler_flag("-Wundef")
|
||||
ei_add_cxx_compiler_flag("-Wcast-align")
|
||||
ei_add_cxx_compiler_flag("-Wchar-subscripts")
|
||||
ei_add_cxx_compiler_flag("-Wnon-virtual-dtor")
|
||||
ei_add_cxx_compiler_flag("-Wunused-local-typedefs")
|
||||
ei_add_cxx_compiler_flag("-Wpointer-arith")
|
||||
ei_add_cxx_compiler_flag("-Wwrite-strings")
|
||||
ei_add_cxx_compiler_flag("-Wformat-security")
|
||||
ei_add_cxx_compiler_flag("-Wshorten-64-to-32")
|
||||
ei_add_cxx_compiler_flag("-Wlogical-op")
|
||||
ei_add_cxx_compiler_flag("-Wenum-conversion")
|
||||
ei_add_cxx_compiler_flag("-Wc++11-extensions")
|
||||
ei_add_cxx_compiler_flag("-Wdouble-promotion")
|
||||
# ei_add_cxx_compiler_flag("-Wconversion")
|
||||
|
||||
# -Wshadow is insanely too strict with gcc, hopefully it will become usable with gcc 6
|
||||
# if(NOT CMAKE_COMPILER_IS_GNUCXX OR (CMAKE_CXX_COMPILER_VERSION VERSION_GREATER "5.0.0"))
|
||||
if(NOT CMAKE_COMPILER_IS_GNUCXX)
|
||||
ei_add_cxx_compiler_flag("-Wshadow")
|
||||
endif()
|
||||
|
||||
ei_add_cxx_compiler_flag("-Wno-psabi")
|
||||
ei_add_cxx_compiler_flag("-Wno-variadic-macros")
|
||||
ei_add_cxx_compiler_flag("-Wno-long-long")
|
||||
|
||||
ei_add_cxx_compiler_flag("-fno-check-new")
|
||||
ei_add_cxx_compiler_flag("-fno-common")
|
||||
ei_add_cxx_compiler_flag("-fstrict-aliasing")
|
||||
ei_add_cxx_compiler_flag("-wd981") # disable ICC's "operands are evaluated in unspecified order" remark
|
||||
ei_add_cxx_compiler_flag("-wd2304") # disable ICC's "warning #2304: non-explicit constructor with single argument may cause implicit type conversion" produced by -Wnon-virtual-dtor
|
||||
|
||||
|
||||
# The -ansi flag must be added last, otherwise it is also used as a linker flag by check_cxx_compiler_flag making it fails
|
||||
# Moreover we should not set both -strict-ansi and -ansi
|
||||
check_cxx_compiler_flag("-strict-ansi" COMPILER_SUPPORT_STRICTANSI)
|
||||
ei_add_cxx_compiler_flag("-Qunused-arguments") # disable clang warning: argument unused during compilation: '-ansi'
|
||||
|
||||
if(COMPILER_SUPPORT_STRICTANSI)
|
||||
set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -strict-ansi")
|
||||
else()
|
||||
ei_add_cxx_compiler_flag("-ansi")
|
||||
endif()
|
||||
|
||||
if(ANDROID_NDK)
|
||||
ei_add_cxx_compiler_flag("-pie")
|
||||
ei_add_cxx_compiler_flag("-fPIE")
|
||||
endif()
|
||||
|
||||
set(CMAKE_REQUIRED_FLAGS "")
|
||||
|
||||
option(EIGEN_TEST_SSE2 "Enable/Disable SSE2 in tests/examples" OFF)
|
||||
if(EIGEN_TEST_SSE2)
|
||||
set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -msse2")
|
||||
message(STATUS "Enabling SSE2 in tests/examples")
|
||||
endif()
|
||||
|
||||
option(EIGEN_TEST_SSE3 "Enable/Disable SSE3 in tests/examples" OFF)
|
||||
if(EIGEN_TEST_SSE3)
|
||||
set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -msse3")
|
||||
message(STATUS "Enabling SSE3 in tests/examples")
|
||||
endif()
|
||||
|
||||
option(EIGEN_TEST_SSSE3 "Enable/Disable SSSE3 in tests/examples" OFF)
|
||||
if(EIGEN_TEST_SSSE3)
|
||||
set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -mssse3")
|
||||
message(STATUS "Enabling SSSE3 in tests/examples")
|
||||
endif()
|
||||
|
||||
option(EIGEN_TEST_SSE4_1 "Enable/Disable SSE4.1 in tests/examples" OFF)
|
||||
if(EIGEN_TEST_SSE4_1)
|
||||
set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -msse4.1")
|
||||
message(STATUS "Enabling SSE4.1 in tests/examples")
|
||||
endif()
|
||||
|
||||
option(EIGEN_TEST_SSE4_2 "Enable/Disable SSE4.2 in tests/examples" OFF)
|
||||
if(EIGEN_TEST_SSE4_2)
|
||||
set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -msse4.2")
|
||||
message(STATUS "Enabling SSE4.2 in tests/examples")
|
||||
endif()
|
||||
|
||||
option(EIGEN_TEST_AVX "Enable/Disable AVX in tests/examples" OFF)
|
||||
if(EIGEN_TEST_AVX)
|
||||
set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -mavx")
|
||||
message(STATUS "Enabling AVX in tests/examples")
|
||||
endif()
|
||||
|
||||
option(EIGEN_TEST_FMA "Enable/Disable FMA in tests/examples" OFF)
|
||||
if(EIGEN_TEST_FMA AND NOT EIGEN_TEST_NEON)
|
||||
set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -mfma")
|
||||
message(STATUS "Enabling FMA in tests/examples")
|
||||
endif()
|
||||
|
||||
option(EIGEN_TEST_AVX512 "Enable/Disable AVX512 in tests/examples" OFF)
|
||||
if(EIGEN_TEST_AVX512)
|
||||
set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -mavx512f -fabi-version=6 -DEIGEN_ENABLE_AVX512")
|
||||
message(STATUS "Enabling AVX512 in tests/examples")
|
||||
endif()
|
||||
|
||||
option(EIGEN_TEST_F16C "Enable/Disable F16C in tests/examples" OFF)
|
||||
if(EIGEN_TEST_F16C)
|
||||
set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -mf16c")
|
||||
message(STATUS "Enabling F16C in tests/examples")
|
||||
endif()
|
||||
|
||||
option(EIGEN_TEST_ALTIVEC "Enable/Disable AltiVec in tests/examples" OFF)
|
||||
if(EIGEN_TEST_ALTIVEC)
|
||||
set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -maltivec -mabi=altivec")
|
||||
message(STATUS "Enabling AltiVec in tests/examples")
|
||||
endif()
|
||||
|
||||
option(EIGEN_TEST_VSX "Enable/Disable VSX in tests/examples" OFF)
|
||||
if(EIGEN_TEST_VSX)
|
||||
set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -m64 -mvsx")
|
||||
message(STATUS "Enabling VSX in tests/examples")
|
||||
endif()
|
||||
|
||||
option(EIGEN_TEST_NEON "Enable/Disable Neon in tests/examples" OFF)
|
||||
if(EIGEN_TEST_NEON)
|
||||
if(EIGEN_TEST_FMA)
|
||||
set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -mfpu=neon-vfpv4")
|
||||
else()
|
||||
set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -mfpu=neon")
|
||||
endif()
|
||||
set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -mfloat-abi=hard")
|
||||
message(STATUS "Enabling NEON in tests/examples")
|
||||
endif()
|
||||
|
||||
option(EIGEN_TEST_NEON64 "Enable/Disable Neon in tests/examples" OFF)
|
||||
if(EIGEN_TEST_NEON64)
|
||||
set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS}")
|
||||
message(STATUS "Enabling NEON in tests/examples")
|
||||
endif()
|
||||
|
||||
option(EIGEN_TEST_ZVECTOR "Enable/Disable S390X(zEC13) ZVECTOR in tests/examples" OFF)
|
||||
if(EIGEN_TEST_ZVECTOR)
|
||||
set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -march=z13 -mzvector")
|
||||
message(STATUS "Enabling S390X(zEC13) ZVECTOR in tests/examples")
|
||||
endif()
|
||||
|
||||
check_cxx_compiler_flag("-fopenmp" COMPILER_SUPPORT_OPENMP)
|
||||
if(COMPILER_SUPPORT_OPENMP)
|
||||
option(EIGEN_TEST_OPENMP "Enable/Disable OpenMP in tests/examples" OFF)
|
||||
if(EIGEN_TEST_OPENMP)
|
||||
set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -fopenmp")
|
||||
message(STATUS "Enabling OpenMP in tests/examples")
|
||||
endif()
|
||||
endif()
|
||||
|
||||
else(NOT MSVC)
|
||||
|
||||
# C4127 - conditional expression is constant
|
||||
# C4714 - marked as __forceinline not inlined (I failed to deactivate it selectively)
|
||||
# We can disable this warning in the unit tests since it is clear that it occurs
|
||||
# because we are oftentimes returning objects that have a destructor or may
|
||||
# throw exceptions - in particular in the unit tests we are throwing extra many
|
||||
# exceptions to cover indexing errors.
|
||||
# C4505 - unreferenced local function has been removed (impossible to deactive selectively)
|
||||
set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} /EHsc /wd4127 /wd4505 /wd4714")
|
||||
|
||||
# replace all /Wx by /W4
|
||||
string(REGEX REPLACE "/W[0-9]" "/W4" CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS}")
|
||||
|
||||
check_cxx_compiler_flag("/openmp" COMPILER_SUPPORT_OPENMP)
|
||||
if(COMPILER_SUPPORT_OPENMP)
|
||||
option(EIGEN_TEST_OPENMP "Enable/Disable OpenMP in tests/examples" OFF)
|
||||
if(EIGEN_TEST_OPENMP)
|
||||
set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} /openmp")
|
||||
message(STATUS "Enabling OpenMP in tests/examples")
|
||||
endif()
|
||||
endif()
|
||||
|
||||
option(EIGEN_TEST_SSE2 "Enable/Disable SSE2 in tests/examples" OFF)
|
||||
if(EIGEN_TEST_SSE2)
|
||||
if(NOT CMAKE_CL_64)
|
||||
# arch is not supported on 64 bit systems, SSE is enabled automatically.
|
||||
set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} /arch:SSE2")
|
||||
endif(NOT CMAKE_CL_64)
|
||||
message(STATUS "Enabling SSE2 in tests/examples")
|
||||
endif(EIGEN_TEST_SSE2)
|
||||
endif(NOT MSVC)
|
||||
|
||||
option(EIGEN_TEST_NO_EXPLICIT_VECTORIZATION "Disable explicit vectorization in tests/examples" OFF)
|
||||
option(EIGEN_TEST_X87 "Force using X87 instructions. Implies no vectorization." OFF)
|
||||
option(EIGEN_TEST_32BIT "Force generating 32bit code." OFF)
|
||||
|
||||
if(EIGEN_TEST_X87)
|
||||
set(EIGEN_TEST_NO_EXPLICIT_VECTORIZATION ON)
|
||||
if(CMAKE_COMPILER_IS_GNUCXX)
|
||||
set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -mfpmath=387")
|
||||
message(STATUS "Forcing use of x87 instructions in tests/examples")
|
||||
else()
|
||||
message(STATUS "EIGEN_TEST_X87 ignored on your compiler")
|
||||
endif()
|
||||
endif()
|
||||
|
||||
if(EIGEN_TEST_32BIT)
|
||||
if(CMAKE_COMPILER_IS_GNUCXX)
|
||||
set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -m32")
|
||||
message(STATUS "Forcing generation of 32-bit code in tests/examples")
|
||||
else()
|
||||
message(STATUS "EIGEN_TEST_32BIT ignored on your compiler")
|
||||
endif()
|
||||
endif()
|
||||
|
||||
if(EIGEN_TEST_NO_EXPLICIT_VECTORIZATION)
|
||||
add_definitions(-DEIGEN_DONT_VECTORIZE=1)
|
||||
message(STATUS "Disabling vectorization in tests/examples")
|
||||
endif()
|
||||
|
||||
option(EIGEN_TEST_NO_EXPLICIT_ALIGNMENT "Disable explicit alignment (hence vectorization) in tests/examples" OFF)
|
||||
if(EIGEN_TEST_NO_EXPLICIT_ALIGNMENT)
|
||||
add_definitions(-DEIGEN_DONT_ALIGN=1)
|
||||
message(STATUS "Disabling alignment in tests/examples")
|
||||
endif()
|
||||
|
||||
option(EIGEN_TEST_NO_EXCEPTIONS "Disables C++ exceptions" OFF)
|
||||
if(EIGEN_TEST_NO_EXCEPTIONS)
|
||||
ei_add_cxx_compiler_flag("-fno-exceptions")
|
||||
message(STATUS "Disabling exceptions in tests/examples")
|
||||
endif()
|
||||
|
||||
set(EIGEN_CUDA_COMPUTE_ARCH 30 CACHE STRING "The CUDA compute architecture level to target when compiling CUDA code")
|
||||
|
||||
include_directories(${CMAKE_CURRENT_SOURCE_DIR} ${CMAKE_CURRENT_BINARY_DIR})
|
||||
|
||||
# Backward compatibility support for EIGEN_INCLUDE_INSTALL_DIR
|
||||
if(EIGEN_INCLUDE_INSTALL_DIR)
|
||||
message(WARNING "EIGEN_INCLUDE_INSTALL_DIR is deprecated. Use INCLUDE_INSTALL_DIR instead.")
|
||||
endif()
|
||||
|
||||
if(EIGEN_INCLUDE_INSTALL_DIR AND NOT INCLUDE_INSTALL_DIR)
|
||||
set(INCLUDE_INSTALL_DIR ${EIGEN_INCLUDE_INSTALL_DIR}
|
||||
CACHE STRING "The directory relative to CMAKE_PREFIX_PATH where Eigen header files are installed")
|
||||
else()
|
||||
set(INCLUDE_INSTALL_DIR
|
||||
"${CMAKE_INSTALL_INCLUDEDIR}/eigen3"
|
||||
CACHE STRING "The directory relative to CMAKE_PREFIX_PATH where Eigen header files are installed"
|
||||
)
|
||||
endif()
|
||||
set(CMAKEPACKAGE_INSTALL_DIR
|
||||
"${CMAKE_INSTALL_DATADIR}/eigen3/cmake"
|
||||
CACHE STRING "The directory relative to CMAKE_PREFIX_PATH where Eigen3Config.cmake is installed"
|
||||
)
|
||||
set(PKGCONFIG_INSTALL_DIR
|
||||
"${CMAKE_INSTALL_DATADIR}/pkgconfig"
|
||||
CACHE STRING "The directory relative to CMAKE_PREFIX_PATH where eigen3.pc is installed"
|
||||
)
|
||||
|
||||
foreach(var INCLUDE_INSTALL_DIR CMAKEPACKAGE_INSTALL_DIR PKGCONFIG_INSTALL_DIR)
|
||||
if(IS_ABSOLUTE "${${var}}")
|
||||
message(FATAL_ERROR "${var} must be relative to CMAKE_PREFIX_PATH. Got: ${${var}}")
|
||||
endif()
|
||||
endforeach()
|
||||
|
||||
# similar to set_target_properties but append the property instead of overwriting it
|
||||
macro(ei_add_target_property target prop value)
|
||||
|
||||
get_target_property(previous ${target} ${prop})
|
||||
# if the property wasn't previously set, ${previous} is now "previous-NOTFOUND" which cmake allows catching with plain if()
|
||||
if(NOT previous)
|
||||
set(previous "")
|
||||
endif(NOT previous)
|
||||
set_target_properties(${target} PROPERTIES ${prop} "${previous} ${value}")
|
||||
endmacro(ei_add_target_property)
|
||||
|
||||
install(FILES
|
||||
signature_of_eigen3_matrix_library
|
||||
DESTINATION ${INCLUDE_INSTALL_DIR} COMPONENT Devel
|
||||
)
|
||||
|
||||
if(EIGEN_BUILD_PKGCONFIG)
|
||||
configure_file(eigen3.pc.in eigen3.pc @ONLY)
|
||||
install(FILES ${CMAKE_CURRENT_BINARY_DIR}/eigen3.pc
|
||||
DESTINATION ${PKGCONFIG_INSTALL_DIR}
|
||||
)
|
||||
endif()
|
||||
|
||||
add_subdirectory(Eigen)
|
||||
|
||||
add_subdirectory(doc EXCLUDE_FROM_ALL)
|
||||
|
||||
option(BUILD_TESTING "Enable creation of Eigen tests." ON)
|
||||
if(BUILD_TESTING)
|
||||
include(EigenConfigureTesting)
|
||||
|
||||
if(EIGEN_LEAVE_TEST_IN_ALL_TARGET)
|
||||
add_subdirectory(test) # can't do EXCLUDE_FROM_ALL here, breaks CTest
|
||||
else()
|
||||
add_subdirectory(test EXCLUDE_FROM_ALL)
|
||||
endif()
|
||||
endif()
|
||||
|
||||
if(EIGEN_LEAVE_TEST_IN_ALL_TARGET)
|
||||
add_subdirectory(blas)
|
||||
add_subdirectory(lapack)
|
||||
else()
|
||||
add_subdirectory(blas EXCLUDE_FROM_ALL)
|
||||
add_subdirectory(lapack EXCLUDE_FROM_ALL)
|
||||
endif()
|
||||
|
||||
# add SYCL
|
||||
option(EIGEN_TEST_SYCL "Add Sycl support." OFF)
|
||||
if(EIGEN_TEST_SYCL)
|
||||
set (CMAKE_MODULE_PATH "${CMAKE_ROOT}/Modules" "cmake/Modules/" "${CMAKE_MODULE_PATH}")
|
||||
include(FindComputeCpp)
|
||||
endif()
|
||||
|
||||
add_subdirectory(unsupported)
|
||||
|
||||
add_subdirectory(demos EXCLUDE_FROM_ALL)
|
||||
|
||||
# must be after test and unsupported, for configuring buildtests.in
|
||||
add_subdirectory(scripts EXCLUDE_FROM_ALL)
|
||||
|
||||
# TODO: consider also replacing EIGEN_BUILD_BTL by a custom target "make btl"?
|
||||
if(EIGEN_BUILD_BTL)
|
||||
add_subdirectory(bench/btl EXCLUDE_FROM_ALL)
|
||||
endif(EIGEN_BUILD_BTL)
|
||||
|
||||
if(NOT WIN32)
|
||||
add_subdirectory(bench/spbench EXCLUDE_FROM_ALL)
|
||||
endif(NOT WIN32)
|
||||
|
||||
configure_file(scripts/cdashtesting.cmake.in cdashtesting.cmake @ONLY)
|
||||
|
||||
if(BUILD_TESTING)
|
||||
ei_testing_print_summary()
|
||||
endif()
|
||||
|
||||
message(STATUS "")
|
||||
message(STATUS "Configured Eigen ${EIGEN_VERSION_NUMBER}")
|
||||
message(STATUS "")
|
||||
|
||||
option(EIGEN_FAILTEST "Enable failtests." OFF)
|
||||
if(EIGEN_FAILTEST)
|
||||
add_subdirectory(failtest)
|
||||
endif()
|
||||
|
||||
string(TOLOWER "${CMAKE_GENERATOR}" cmake_generator_tolower)
|
||||
if(cmake_generator_tolower MATCHES "makefile")
|
||||
message(STATUS "Some things you can do now:")
|
||||
message(STATUS "--------------+--------------------------------------------------------------")
|
||||
message(STATUS "Command | Description")
|
||||
message(STATUS "--------------+--------------------------------------------------------------")
|
||||
message(STATUS "make install | Install Eigen. Headers will be installed to:")
|
||||
message(STATUS " | <CMAKE_INSTALL_PREFIX>/<INCLUDE_INSTALL_DIR>")
|
||||
message(STATUS " | Using the following values:")
|
||||
message(STATUS " | CMAKE_INSTALL_PREFIX: ${CMAKE_INSTALL_PREFIX}")
|
||||
message(STATUS " | INCLUDE_INSTALL_DIR: ${INCLUDE_INSTALL_DIR}")
|
||||
message(STATUS " | Change the install location of Eigen headers using:")
|
||||
message(STATUS " | cmake . -DCMAKE_INSTALL_PREFIX=yourprefix")
|
||||
message(STATUS " | Or:")
|
||||
message(STATUS " | cmake . -DINCLUDE_INSTALL_DIR=yourdir")
|
||||
message(STATUS "make doc | Generate the API documentation, requires Doxygen & LaTeX")
|
||||
message(STATUS "make check | Build and run the unit-tests. Read this page:")
|
||||
message(STATUS " | http://eigen.tuxfamily.org/index.php?title=Tests")
|
||||
message(STATUS "make blas | Build BLAS library (not the same thing as Eigen)")
|
||||
message(STATUS "make uninstall| Removes files installed by make install")
|
||||
message(STATUS "--------------+--------------------------------------------------------------")
|
||||
else()
|
||||
message(STATUS "To build/run the unit tests, read this page:")
|
||||
message(STATUS " http://eigen.tuxfamily.org/index.php?title=Tests")
|
||||
endif()
|
||||
|
||||
message(STATUS "")
|
||||
|
||||
|
||||
set ( EIGEN_VERSION_STRING ${EIGEN_VERSION_NUMBER} )
|
||||
set ( EIGEN_VERSION_MAJOR ${EIGEN_WORLD_VERSION} )
|
||||
set ( EIGEN_VERSION_MINOR ${EIGEN_MAJOR_VERSION} )
|
||||
set ( EIGEN_VERSION_PATCH ${EIGEN_MINOR_VERSION} )
|
||||
set ( EIGEN_DEFINITIONS "")
|
||||
set ( EIGEN_INCLUDE_DIR "${CMAKE_INSTALL_PREFIX}/${INCLUDE_INSTALL_DIR}" )
|
||||
set ( EIGEN_ROOT_DIR ${CMAKE_INSTALL_PREFIX} )
|
||||
|
||||
# Interface libraries require at least CMake 3.0
|
||||
if (NOT CMAKE_VERSION VERSION_LESS 3.0)
|
||||
include (CMakePackageConfigHelpers)
|
||||
|
||||
# Imported target support
|
||||
add_library (eigen INTERFACE)
|
||||
|
||||
target_compile_definitions (eigen INTERFACE ${EIGEN_DEFINITIONS})
|
||||
target_include_directories (eigen INTERFACE
|
||||
$<BUILD_INTERFACE:${CMAKE_CURRENT_SOURCE_DIR}>
|
||||
$<INSTALL_INTERFACE:${INCLUDE_INSTALL_DIR}>
|
||||
)
|
||||
|
||||
# Export as title case Eigen
|
||||
set_target_properties (eigen PROPERTIES EXPORT_NAME Eigen)
|
||||
|
||||
install (TARGETS eigen EXPORT Eigen3Targets)
|
||||
|
||||
configure_package_config_file (
|
||||
${CMAKE_CURRENT_SOURCE_DIR}/cmake/Eigen3Config.cmake.in
|
||||
${CMAKE_CURRENT_BINARY_DIR}/Eigen3Config.cmake
|
||||
PATH_VARS EIGEN_INCLUDE_DIR EIGEN_ROOT_DIR
|
||||
INSTALL_DESTINATION ${CMAKEPACKAGE_INSTALL_DIR}
|
||||
NO_CHECK_REQUIRED_COMPONENTS_MACRO # Eigen does not provide components
|
||||
)
|
||||
# Remove CMAKE_SIZEOF_VOID_P from Eigen3ConfigVersion.cmake since Eigen does
|
||||
# not depend on architecture specific settings or libraries. More
|
||||
# specifically, an Eigen3Config.cmake generated from a 64 bit target can be
|
||||
# used for 32 bit targets as well (and vice versa).
|
||||
set (_Eigen3_CMAKE_SIZEOF_VOID_P ${CMAKE_SIZEOF_VOID_P})
|
||||
unset (CMAKE_SIZEOF_VOID_P)
|
||||
write_basic_package_version_file (Eigen3ConfigVersion.cmake
|
||||
VERSION ${EIGEN_VERSION_NUMBER}
|
||||
COMPATIBILITY SameMajorVersion)
|
||||
set (CMAKE_SIZEOF_VOID_P ${_Eigen3_CMAKE_SIZEOF_VOID_P})
|
||||
|
||||
# The Eigen target will be located in the Eigen3 namespace. Other CMake
|
||||
# targets can refer to it using Eigen3::Eigen.
|
||||
export (TARGETS eigen NAMESPACE Eigen3:: FILE Eigen3Targets.cmake)
|
||||
# Export Eigen3 package to CMake registry such that it can be easily found by
|
||||
# CMake even if it has not been installed to a standard directory.
|
||||
export (PACKAGE Eigen3)
|
||||
|
||||
install (EXPORT Eigen3Targets NAMESPACE Eigen3:: DESTINATION ${CMAKEPACKAGE_INSTALL_DIR})
|
||||
|
||||
else (NOT CMAKE_VERSION VERSION_LESS 3.0)
|
||||
# Fallback to legacy Eigen3Config.cmake without the imported target
|
||||
|
||||
# If CMakePackageConfigHelpers module is available (CMake >= 2.8.8)
|
||||
# create a relocatable Config file, otherwise leave the hardcoded paths
|
||||
include(CMakePackageConfigHelpers OPTIONAL RESULT_VARIABLE CPCH_PATH)
|
||||
|
||||
if(CPCH_PATH)
|
||||
configure_package_config_file (
|
||||
${CMAKE_CURRENT_SOURCE_DIR}/cmake/Eigen3ConfigLegacy.cmake.in
|
||||
${CMAKE_CURRENT_BINARY_DIR}/Eigen3Config.cmake
|
||||
PATH_VARS EIGEN_INCLUDE_DIR EIGEN_ROOT_DIR
|
||||
INSTALL_DESTINATION ${CMAKEPACKAGE_INSTALL_DIR}
|
||||
NO_CHECK_REQUIRED_COMPONENTS_MACRO # Eigen does not provide components
|
||||
)
|
||||
else()
|
||||
# The PACKAGE_* variables are defined by the configure_package_config_file
|
||||
# but without it we define them manually to the hardcoded paths
|
||||
set(PACKAGE_INIT "")
|
||||
set(PACKAGE_EIGEN_INCLUDE_DIR ${EIGEN_INCLUDE_DIR})
|
||||
set(PACKAGE_EIGEN_ROOT_DIR ${EIGEN_ROOT_DIR})
|
||||
configure_file ( ${CMAKE_CURRENT_SOURCE_DIR}/cmake/Eigen3ConfigLegacy.cmake.in
|
||||
${CMAKE_CURRENT_BINARY_DIR}/Eigen3Config.cmake
|
||||
@ONLY ESCAPE_QUOTES )
|
||||
endif()
|
||||
|
||||
write_basic_package_version_file( Eigen3ConfigVersion.cmake
|
||||
VERSION ${EIGEN_VERSION_NUMBER}
|
||||
COMPATIBILITY SameMajorVersion )
|
||||
|
||||
endif (NOT CMAKE_VERSION VERSION_LESS 3.0)
|
||||
|
||||
install ( FILES ${CMAKE_CURRENT_SOURCE_DIR}/cmake/UseEigen3.cmake
|
||||
${CMAKE_CURRENT_BINARY_DIR}/Eigen3Config.cmake
|
||||
${CMAKE_CURRENT_BINARY_DIR}/Eigen3ConfigVersion.cmake
|
||||
DESTINATION ${CMAKEPACKAGE_INSTALL_DIR} )
|
||||
|
||||
# Add uninstall target
|
||||
add_custom_target ( uninstall
|
||||
COMMAND ${CMAKE_COMMAND} -P ${CMAKE_CURRENT_SOURCE_DIR}/cmake/EigenUninstall.cmake)
|
||||
|
|
@ -0,0 +1,26 @@
|
|||
/*
|
||||
Copyright (c) 2011, Intel Corporation. All rights reserved.
|
||||
|
||||
Redistribution and use in source and binary forms, with or without modification,
|
||||
are permitted provided that the following conditions are met:
|
||||
|
||||
* Redistributions of source code must retain the above copyright notice, this
|
||||
list of conditions and the following disclaimer.
|
||||
* Redistributions in binary form must reproduce the above copyright notice,
|
||||
this list of conditions and the following disclaimer in the documentation
|
||||
and/or other materials provided with the distribution.
|
||||
* Neither the name of Intel Corporation nor the names of its contributors may
|
||||
be used to endorse or promote products derived from this software without
|
||||
specific prior written permission.
|
||||
|
||||
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
|
||||
ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
|
||||
WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
|
||||
DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
|
||||
ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
|
||||
(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
|
||||
LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
|
||||
ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
|
||||
(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
|
||||
SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
|
||||
*/
|
||||
|
|
@ -0,0 +1,674 @@
|
|||
GNU GENERAL PUBLIC LICENSE
|
||||
Version 3, 29 June 2007
|
||||
|
||||
Copyright (C) 2007 Free Software Foundation, Inc. <http://fsf.org/>
|
||||
Everyone is permitted to copy and distribute verbatim copies
|
||||
of this license document, but changing it is not allowed.
|
||||
|
||||
Preamble
|
||||
|
||||
The GNU General Public License is a free, copyleft license for
|
||||
software and other kinds of works.
|
||||
|
||||
The licenses for most software and other practical works are designed
|
||||
to take away your freedom to share and change the works. By contrast,
|
||||
the GNU General Public License is intended to guarantee your freedom to
|
||||
share and change all versions of a program--to make sure it remains free
|
||||
software for all its users. We, the Free Software Foundation, use the
|
||||
GNU General Public License for most of our software; it applies also to
|
||||
any other work released this way by its authors. You can apply it to
|
||||
your programs, too.
|
||||
|
||||
When we speak of free software, we are referring to freedom, not
|
||||
price. Our General Public Licenses are designed to make sure that you
|
||||
have the freedom to distribute copies of free software (and charge for
|
||||
them if you wish), that you receive source code or can get it if you
|
||||
want it, that you can change the software or use pieces of it in new
|
||||
free programs, and that you know you can do these things.
|
||||
|
||||
To protect your rights, we need to prevent others from denying you
|
||||
these rights or asking you to surrender the rights. Therefore, you have
|
||||
certain responsibilities if you distribute copies of the software, or if
|
||||
you modify it: responsibilities to respect the freedom of others.
|
||||
|
||||
For example, if you distribute copies of such a program, whether
|
||||
gratis or for a fee, you must pass on to the recipients the same
|
||||
freedoms that you received. You must make sure that they, too, receive
|
||||
or can get the source code. And you must show them these terms so they
|
||||
know their rights.
|
||||
|
||||
Developers that use the GNU GPL protect your rights with two steps:
|
||||
(1) assert copyright on the software, and (2) offer you this License
|
||||
giving you legal permission to copy, distribute and/or modify it.
|
||||
|
||||
For the developers' and authors' protection, the GPL clearly explains
|
||||
that there is no warranty for this free software. For both users' and
|
||||
authors' sake, the GPL requires that modified versions be marked as
|
||||
changed, so that their problems will not be attributed erroneously to
|
||||
authors of previous versions.
|
||||
|
||||
Some devices are designed to deny users access to install or run
|
||||
modified versions of the software inside them, although the manufacturer
|
||||
can do so. This is fundamentally incompatible with the aim of
|
||||
protecting users' freedom to change the software. The systematic
|
||||
pattern of such abuse occurs in the area of products for individuals to
|
||||
use, which is precisely where it is most unacceptable. Therefore, we
|
||||
have designed this version of the GPL to prohibit the practice for those
|
||||
products. If such problems arise substantially in other domains, we
|
||||
stand ready to extend this provision to those domains in future versions
|
||||
of the GPL, as needed to protect the freedom of users.
|
||||
|
||||
Finally, every program is threatened constantly by software patents.
|
||||
States should not allow patents to restrict development and use of
|
||||
software on general-purpose computers, but in those that do, we wish to
|
||||
avoid the special danger that patents applied to a free program could
|
||||
make it effectively proprietary. To prevent this, the GPL assures that
|
||||
patents cannot be used to render the program non-free.
|
||||
|
||||
The precise terms and conditions for copying, distribution and
|
||||
modification follow.
|
||||
|
||||
TERMS AND CONDITIONS
|
||||
|
||||
0. Definitions.
|
||||
|
||||
"This License" refers to version 3 of the GNU General Public License.
|
||||
|
||||
"Copyright" also means copyright-like laws that apply to other kinds of
|
||||
works, such as semiconductor masks.
|
||||
|
||||
"The Program" refers to any copyrightable work licensed under this
|
||||
License. Each licensee is addressed as "you". "Licensees" and
|
||||
"recipients" may be individuals or organizations.
|
||||
|
||||
To "modify" a work means to copy from or adapt all or part of the work
|
||||
in a fashion requiring copyright permission, other than the making of an
|
||||
exact copy. The resulting work is called a "modified version" of the
|
||||
earlier work or a work "based on" the earlier work.
|
||||
|
||||
A "covered work" means either the unmodified Program or a work based
|
||||
on the Program.
|
||||
|
||||
To "propagate" a work means to do anything with it that, without
|
||||
permission, would make you directly or secondarily liable for
|
||||
infringement under applicable copyright law, except executing it on a
|
||||
computer or modifying a private copy. Propagation includes copying,
|
||||
distribution (with or without modification), making available to the
|
||||
public, and in some countries other activities as well.
|
||||
|
||||
To "convey" a work means any kind of propagation that enables other
|
||||
parties to make or receive copies. Mere interaction with a user through
|
||||
a computer network, with no transfer of a copy, is not conveying.
|
||||
|
||||
An interactive user interface displays "Appropriate Legal Notices"
|
||||
to the extent that it includes a convenient and prominently visible
|
||||
feature that (1) displays an appropriate copyright notice, and (2)
|
||||
tells the user that there is no warranty for the work (except to the
|
||||
extent that warranties are provided), that licensees may convey the
|
||||
work under this License, and how to view a copy of this License. If
|
||||
the interface presents a list of user commands or options, such as a
|
||||
menu, a prominent item in the list meets this criterion.
|
||||
|
||||
1. Source Code.
|
||||
|
||||
The "source code" for a work means the preferred form of the work
|
||||
for making modifications to it. "Object code" means any non-source
|
||||
form of a work.
|
||||
|
||||
A "Standard Interface" means an interface that either is an official
|
||||
standard defined by a recognized standards body, or, in the case of
|
||||
interfaces specified for a particular programming language, one that
|
||||
is widely used among developers working in that language.
|
||||
|
||||
The "System Libraries" of an executable work include anything, other
|
||||
than the work as a whole, that (a) is included in the normal form of
|
||||
packaging a Major Component, but which is not part of that Major
|
||||
Component, and (b) serves only to enable use of the work with that
|
||||
Major Component, or to implement a Standard Interface for which an
|
||||
implementation is available to the public in source code form. A
|
||||
"Major Component", in this context, means a major essential component
|
||||
(kernel, window system, and so on) of the specific operating system
|
||||
(if any) on which the executable work runs, or a compiler used to
|
||||
produce the work, or an object code interpreter used to run it.
|
||||
|
||||
The "Corresponding Source" for a work in object code form means all
|
||||
the source code needed to generate, install, and (for an executable
|
||||
work) run the object code and to modify the work, including scripts to
|
||||
control those activities. However, it does not include the work's
|
||||
System Libraries, or general-purpose tools or generally available free
|
||||
programs which are used unmodified in performing those activities but
|
||||
which are not part of the work. For example, Corresponding Source
|
||||
includes interface definition files associated with source files for
|
||||
the work, and the source code for shared libraries and dynamically
|
||||
linked subprograms that the work is specifically designed to require,
|
||||
such as by intimate data communication or control flow between those
|
||||
subprograms and other parts of the work.
|
||||
|
||||
The Corresponding Source need not include anything that users
|
||||
can regenerate automatically from other parts of the Corresponding
|
||||
Source.
|
||||
|
||||
The Corresponding Source for a work in source code form is that
|
||||
same work.
|
||||
|
||||
2. Basic Permissions.
|
||||
|
||||
All rights granted under this License are granted for the term of
|
||||
copyright on the Program, and are irrevocable provided the stated
|
||||
conditions are met. This License explicitly affirms your unlimited
|
||||
permission to run the unmodified Program. The output from running a
|
||||
covered work is covered by this License only if the output, given its
|
||||
content, constitutes a covered work. This License acknowledges your
|
||||
rights of fair use or other equivalent, as provided by copyright law.
|
||||
|
||||
You may make, run and propagate covered works that you do not
|
||||
convey, without conditions so long as your license otherwise remains
|
||||
in force. You may convey covered works to others for the sole purpose
|
||||
of having them make modifications exclusively for you, or provide you
|
||||
with facilities for running those works, provided that you comply with
|
||||
the terms of this License in conveying all material for which you do
|
||||
not control copyright. Those thus making or running the covered works
|
||||
for you must do so exclusively on your behalf, under your direction
|
||||
and control, on terms that prohibit them from making any copies of
|
||||
your copyrighted material outside their relationship with you.
|
||||
|
||||
Conveying under any other circumstances is permitted solely under
|
||||
the conditions stated below. Sublicensing is not allowed; section 10
|
||||
makes it unnecessary.
|
||||
|
||||
3. Protecting Users' Legal Rights From Anti-Circumvention Law.
|
||||
|
||||
No covered work shall be deemed part of an effective technological
|
||||
measure under any applicable law fulfilling obligations under article
|
||||
11 of the WIPO copyright treaty adopted on 20 December 1996, or
|
||||
similar laws prohibiting or restricting circumvention of such
|
||||
measures.
|
||||
|
||||
When you convey a covered work, you waive any legal power to forbid
|
||||
circumvention of technological measures to the extent such circumvention
|
||||
is effected by exercising rights under this License with respect to
|
||||
the covered work, and you disclaim any intention to limit operation or
|
||||
modification of the work as a means of enforcing, against the work's
|
||||
users, your or third parties' legal rights to forbid circumvention of
|
||||
technological measures.
|
||||
|
||||
4. Conveying Verbatim Copies.
|
||||
|
||||
You may convey verbatim copies of the Program's source code as you
|
||||
receive it, in any medium, provided that you conspicuously and
|
||||
appropriately publish on each copy an appropriate copyright notice;
|
||||
keep intact all notices stating that this License and any
|
||||
non-permissive terms added in accord with section 7 apply to the code;
|
||||
keep intact all notices of the absence of any warranty; and give all
|
||||
recipients a copy of this License along with the Program.
|
||||
|
||||
You may charge any price or no price for each copy that you convey,
|
||||
and you may offer support or warranty protection for a fee.
|
||||
|
||||
5. Conveying Modified Source Versions.
|
||||
|
||||
You may convey a work based on the Program, or the modifications to
|
||||
produce it from the Program, in the form of source code under the
|
||||
terms of section 4, provided that you also meet all of these conditions:
|
||||
|
||||
a) The work must carry prominent notices stating that you modified
|
||||
it, and giving a relevant date.
|
||||
|
||||
b) The work must carry prominent notices stating that it is
|
||||
released under this License and any conditions added under section
|
||||
7. This requirement modifies the requirement in section 4 to
|
||||
"keep intact all notices".
|
||||
|
||||
c) You must license the entire work, as a whole, under this
|
||||
License to anyone who comes into possession of a copy. This
|
||||
License will therefore apply, along with any applicable section 7
|
||||
additional terms, to the whole of the work, and all its parts,
|
||||
regardless of how they are packaged. This License gives no
|
||||
permission to license the work in any other way, but it does not
|
||||
invalidate such permission if you have separately received it.
|
||||
|
||||
d) If the work has interactive user interfaces, each must display
|
||||
Appropriate Legal Notices; however, if the Program has interactive
|
||||
interfaces that do not display Appropriate Legal Notices, your
|
||||
work need not make them do so.
|
||||
|
||||
A compilation of a covered work with other separate and independent
|
||||
works, which are not by their nature extensions of the covered work,
|
||||
and which are not combined with it such as to form a larger program,
|
||||
in or on a volume of a storage or distribution medium, is called an
|
||||
"aggregate" if the compilation and its resulting copyright are not
|
||||
used to limit the access or legal rights of the compilation's users
|
||||
beyond what the individual works permit. Inclusion of a covered work
|
||||
in an aggregate does not cause this License to apply to the other
|
||||
parts of the aggregate.
|
||||
|
||||
6. Conveying Non-Source Forms.
|
||||
|
||||
You may convey a covered work in object code form under the terms
|
||||
of sections 4 and 5, provided that you also convey the
|
||||
machine-readable Corresponding Source under the terms of this License,
|
||||
in one of these ways:
|
||||
|
||||
a) Convey the object code in, or embodied in, a physical product
|
||||
(including a physical distribution medium), accompanied by the
|
||||
Corresponding Source fixed on a durable physical medium
|
||||
customarily used for software interchange.
|
||||
|
||||
b) Convey the object code in, or embodied in, a physical product
|
||||
(including a physical distribution medium), accompanied by a
|
||||
written offer, valid for at least three years and valid for as
|
||||
long as you offer spare parts or customer support for that product
|
||||
model, to give anyone who possesses the object code either (1) a
|
||||
copy of the Corresponding Source for all the software in the
|
||||
product that is covered by this License, on a durable physical
|
||||
medium customarily used for software interchange, for a price no
|
||||
more than your reasonable cost of physically performing this
|
||||
conveying of source, or (2) access to copy the
|
||||
Corresponding Source from a network server at no charge.
|
||||
|
||||
c) Convey individual copies of the object code with a copy of the
|
||||
written offer to provide the Corresponding Source. This
|
||||
alternative is allowed only occasionally and noncommercially, and
|
||||
only if you received the object code with such an offer, in accord
|
||||
with subsection 6b.
|
||||
|
||||
d) Convey the object code by offering access from a designated
|
||||
place (gratis or for a charge), and offer equivalent access to the
|
||||
Corresponding Source in the same way through the same place at no
|
||||
further charge. You need not require recipients to copy the
|
||||
Corresponding Source along with the object code. If the place to
|
||||
copy the object code is a network server, the Corresponding Source
|
||||
may be on a different server (operated by you or a third party)
|
||||
that supports equivalent copying facilities, provided you maintain
|
||||
clear directions next to the object code saying where to find the
|
||||
Corresponding Source. Regardless of what server hosts the
|
||||
Corresponding Source, you remain obligated to ensure that it is
|
||||
available for as long as needed to satisfy these requirements.
|
||||
|
||||
e) Convey the object code using peer-to-peer transmission, provided
|
||||
you inform other peers where the object code and Corresponding
|
||||
Source of the work are being offered to the general public at no
|
||||
charge under subsection 6d.
|
||||
|
||||
A separable portion of the object code, whose source code is excluded
|
||||
from the Corresponding Source as a System Library, need not be
|
||||
included in conveying the object code work.
|
||||
|
||||
A "User Product" is either (1) a "consumer product", which means any
|
||||
tangible personal property which is normally used for personal, family,
|
||||
or household purposes, or (2) anything designed or sold for incorporation
|
||||
into a dwelling. In determining whether a product is a consumer product,
|
||||
doubtful cases shall be resolved in favor of coverage. For a particular
|
||||
product received by a particular user, "normally used" refers to a
|
||||
typical or common use of that class of product, regardless of the status
|
||||
of the particular user or of the way in which the particular user
|
||||
actually uses, or expects or is expected to use, the product. A product
|
||||
is a consumer product regardless of whether the product has substantial
|
||||
commercial, industrial or non-consumer uses, unless such uses represent
|
||||
the only significant mode of use of the product.
|
||||
|
||||
"Installation Information" for a User Product means any methods,
|
||||
procedures, authorization keys, or other information required to install
|
||||
and execute modified versions of a covered work in that User Product from
|
||||
a modified version of its Corresponding Source. The information must
|
||||
suffice to ensure that the continued functioning of the modified object
|
||||
code is in no case prevented or interfered with solely because
|
||||
modification has been made.
|
||||
|
||||
If you convey an object code work under this section in, or with, or
|
||||
specifically for use in, a User Product, and the conveying occurs as
|
||||
part of a transaction in which the right of possession and use of the
|
||||
User Product is transferred to the recipient in perpetuity or for a
|
||||
fixed term (regardless of how the transaction is characterized), the
|
||||
Corresponding Source conveyed under this section must be accompanied
|
||||
by the Installation Information. But this requirement does not apply
|
||||
if neither you nor any third party retains the ability to install
|
||||
modified object code on the User Product (for example, the work has
|
||||
been installed in ROM).
|
||||
|
||||
The requirement to provide Installation Information does not include a
|
||||
requirement to continue to provide support service, warranty, or updates
|
||||
for a work that has been modified or installed by the recipient, or for
|
||||
the User Product in which it has been modified or installed. Access to a
|
||||
network may be denied when the modification itself materially and
|
||||
adversely affects the operation of the network or violates the rules and
|
||||
protocols for communication across the network.
|
||||
|
||||
Corresponding Source conveyed, and Installation Information provided,
|
||||
in accord with this section must be in a format that is publicly
|
||||
documented (and with an implementation available to the public in
|
||||
source code form), and must require no special password or key for
|
||||
unpacking, reading or copying.
|
||||
|
||||
7. Additional Terms.
|
||||
|
||||
"Additional permissions" are terms that supplement the terms of this
|
||||
License by making exceptions from one or more of its conditions.
|
||||
Additional permissions that are applicable to the entire Program shall
|
||||
be treated as though they were included in this License, to the extent
|
||||
that they are valid under applicable law. If additional permissions
|
||||
apply only to part of the Program, that part may be used separately
|
||||
under those permissions, but the entire Program remains governed by
|
||||
this License without regard to the additional permissions.
|
||||
|
||||
When you convey a copy of a covered work, you may at your option
|
||||
remove any additional permissions from that copy, or from any part of
|
||||
it. (Additional permissions may be written to require their own
|
||||
removal in certain cases when you modify the work.) You may place
|
||||
additional permissions on material, added by you to a covered work,
|
||||
for which you have or can give appropriate copyright permission.
|
||||
|
||||
Notwithstanding any other provision of this License, for material you
|
||||
add to a covered work, you may (if authorized by the copyright holders of
|
||||
that material) supplement the terms of this License with terms:
|
||||
|
||||
a) Disclaiming warranty or limiting liability differently from the
|
||||
terms of sections 15 and 16 of this License; or
|
||||
|
||||
b) Requiring preservation of specified reasonable legal notices or
|
||||
author attributions in that material or in the Appropriate Legal
|
||||
Notices displayed by works containing it; or
|
||||
|
||||
c) Prohibiting misrepresentation of the origin of that material, or
|
||||
requiring that modified versions of such material be marked in
|
||||
reasonable ways as different from the original version; or
|
||||
|
||||
d) Limiting the use for publicity purposes of names of licensors or
|
||||
authors of the material; or
|
||||
|
||||
e) Declining to grant rights under trademark law for use of some
|
||||
trade names, trademarks, or service marks; or
|
||||
|
||||
f) Requiring indemnification of licensors and authors of that
|
||||
material by anyone who conveys the material (or modified versions of
|
||||
it) with contractual assumptions of liability to the recipient, for
|
||||
any liability that these contractual assumptions directly impose on
|
||||
those licensors and authors.
|
||||
|
||||
All other non-permissive additional terms are considered "further
|
||||
restrictions" within the meaning of section 10. If the Program as you
|
||||
received it, or any part of it, contains a notice stating that it is
|
||||
governed by this License along with a term that is a further
|
||||
restriction, you may remove that term. If a license document contains
|
||||
a further restriction but permits relicensing or conveying under this
|
||||
License, you may add to a covered work material governed by the terms
|
||||
of that license document, provided that the further restriction does
|
||||
not survive such relicensing or conveying.
|
||||
|
||||
If you add terms to a covered work in accord with this section, you
|
||||
must place, in the relevant source files, a statement of the
|
||||
additional terms that apply to those files, or a notice indicating
|
||||
where to find the applicable terms.
|
||||
|
||||
Additional terms, permissive or non-permissive, may be stated in the
|
||||
form of a separately written license, or stated as exceptions;
|
||||
the above requirements apply either way.
|
||||
|
||||
8. Termination.
|
||||
|
||||
You may not propagate or modify a covered work except as expressly
|
||||
provided under this License. Any attempt otherwise to propagate or
|
||||
modify it is void, and will automatically terminate your rights under
|
||||
this License (including any patent licenses granted under the third
|
||||
paragraph of section 11).
|
||||
|
||||
However, if you cease all violation of this License, then your
|
||||
license from a particular copyright holder is reinstated (a)
|
||||
provisionally, unless and until the copyright holder explicitly and
|
||||
finally terminates your license, and (b) permanently, if the copyright
|
||||
holder fails to notify you of the violation by some reasonable means
|
||||
prior to 60 days after the cessation.
|
||||
|
||||
Moreover, your license from a particular copyright holder is
|
||||
reinstated permanently if the copyright holder notifies you of the
|
||||
violation by some reasonable means, this is the first time you have
|
||||
received notice of violation of this License (for any work) from that
|
||||
copyright holder, and you cure the violation prior to 30 days after
|
||||
your receipt of the notice.
|
||||
|
||||
Termination of your rights under this section does not terminate the
|
||||
licenses of parties who have received copies or rights from you under
|
||||
this License. If your rights have been terminated and not permanently
|
||||
reinstated, you do not qualify to receive new licenses for the same
|
||||
material under section 10.
|
||||
|
||||
9. Acceptance Not Required for Having Copies.
|
||||
|
||||
You are not required to accept this License in order to receive or
|
||||
run a copy of the Program. Ancillary propagation of a covered work
|
||||
occurring solely as a consequence of using peer-to-peer transmission
|
||||
to receive a copy likewise does not require acceptance. However,
|
||||
nothing other than this License grants you permission to propagate or
|
||||
modify any covered work. These actions infringe copyright if you do
|
||||
not accept this License. Therefore, by modifying or propagating a
|
||||
covered work, you indicate your acceptance of this License to do so.
|
||||
|
||||
10. Automatic Licensing of Downstream Recipients.
|
||||
|
||||
Each time you convey a covered work, the recipient automatically
|
||||
receives a license from the original licensors, to run, modify and
|
||||
propagate that work, subject to this License. You are not responsible
|
||||
for enforcing compliance by third parties with this License.
|
||||
|
||||
An "entity transaction" is a transaction transferring control of an
|
||||
organization, or substantially all assets of one, or subdividing an
|
||||
organization, or merging organizations. If propagation of a covered
|
||||
work results from an entity transaction, each party to that
|
||||
transaction who receives a copy of the work also receives whatever
|
||||
licenses to the work the party's predecessor in interest had or could
|
||||
give under the previous paragraph, plus a right to possession of the
|
||||
Corresponding Source of the work from the predecessor in interest, if
|
||||
the predecessor has it or can get it with reasonable efforts.
|
||||
|
||||
You may not impose any further restrictions on the exercise of the
|
||||
rights granted or affirmed under this License. For example, you may
|
||||
not impose a license fee, royalty, or other charge for exercise of
|
||||
rights granted under this License, and you may not initiate litigation
|
||||
(including a cross-claim or counterclaim in a lawsuit) alleging that
|
||||
any patent claim is infringed by making, using, selling, offering for
|
||||
sale, or importing the Program or any portion of it.
|
||||
|
||||
11. Patents.
|
||||
|
||||
A "contributor" is a copyright holder who authorizes use under this
|
||||
License of the Program or a work on which the Program is based. The
|
||||
work thus licensed is called the contributor's "contributor version".
|
||||
|
||||
A contributor's "essential patent claims" are all patent claims
|
||||
owned or controlled by the contributor, whether already acquired or
|
||||
hereafter acquired, that would be infringed by some manner, permitted
|
||||
by this License, of making, using, or selling its contributor version,
|
||||
but do not include claims that would be infringed only as a
|
||||
consequence of further modification of the contributor version. For
|
||||
purposes of this definition, "control" includes the right to grant
|
||||
patent sublicenses in a manner consistent with the requirements of
|
||||
this License.
|
||||
|
||||
Each contributor grants you a non-exclusive, worldwide, royalty-free
|
||||
patent license under the contributor's essential patent claims, to
|
||||
make, use, sell, offer for sale, import and otherwise run, modify and
|
||||
propagate the contents of its contributor version.
|
||||
|
||||
In the following three paragraphs, a "patent license" is any express
|
||||
agreement or commitment, however denominated, not to enforce a patent
|
||||
(such as an express permission to practice a patent or covenant not to
|
||||
sue for patent infringement). To "grant" such a patent license to a
|
||||
party means to make such an agreement or commitment not to enforce a
|
||||
patent against the party.
|
||||
|
||||
If you convey a covered work, knowingly relying on a patent license,
|
||||
and the Corresponding Source of the work is not available for anyone
|
||||
to copy, free of charge and under the terms of this License, through a
|
||||
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If, pursuant to or in connection with a single transaction or
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|
||||
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||||
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Nothing in this License shall be construed as excluding or limiting
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||||
|
||||
12. No Surrender of Others' Freedom.
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||||
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||||
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|
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|
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|
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|
||||
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|
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|
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||||
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||||
|
||||
The Free Software Foundation may publish revised and/or new versions of
|
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|
||||
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|
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THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY
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17. Interpretation of Sections 15 and 16.
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|
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If the disclaimer of warranty and limitation of liability provided
|
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END OF TERMS AND CONDITIONS
|
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|
||||
How to Apply These Terms to Your New Programs
|
||||
|
||||
If you develop a new program, and you want it to be of the greatest
|
||||
possible use to the public, the best way to achieve this is to make it
|
||||
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|
||||
|
||||
To do so, attach the following notices to the program. It is safest
|
||||
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|
||||
state the exclusion of warranty; and each file should have at least
|
||||
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|
||||
|
||||
<one line to give the program's name and a brief idea of what it does.>
|
||||
Copyright (C) <year> <name of author>
|
||||
|
||||
This program is free software: you can redistribute it and/or modify
|
||||
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|
||||
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|
||||
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|
||||
|
||||
This program is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
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|
||||
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|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with this program. If not, see <http://www.gnu.org/licenses/>.
|
||||
|
||||
Also add information on how to contact you by electronic and paper mail.
|
||||
|
||||
If the program does terminal interaction, make it output a short
|
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notice like this when it starts in an interactive mode:
|
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|
||||
<program> Copyright (C) <year> <name of author>
|
||||
This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'.
|
||||
This is free software, and you are welcome to redistribute it
|
||||
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|
||||
|
||||
The hypothetical commands `show w' and `show c' should show the appropriate
|
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|
||||
might be different; for a GUI interface, you would use an "about box".
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|
||||
You should also get your employer (if you work as a programmer) or school,
|
||||
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|
||||
For more information on this, and how to apply and follow the GNU GPL, see
|
||||
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|
||||
|
||||
The GNU General Public License does not permit incorporating your program
|
||||
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|
||||
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|
||||
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|
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|
||||
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|
||||
|
|
@ -0,0 +1,502 @@
|
|||
GNU LESSER GENERAL PUBLIC LICENSE
|
||||
Version 2.1, February 1999
|
||||
|
||||
Copyright (C) 1991, 1999 Free Software Foundation, Inc.
|
||||
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|
||||
Everyone is permitted to copy and distribute verbatim copies
|
||||
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|
||||
|
||||
[This is the first released version of the Lesser GPL. It also counts
|
||||
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|
||||
the version number 2.1.]
|
||||
|
||||
Preamble
|
||||
|
||||
The licenses for most software are designed to take away your
|
||||
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|
||||
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|
||||
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|
||||
This license, the Lesser General Public License, applies to some
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|
||||
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|
||||
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|
||||
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|
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When we speak of free software, we are referring to freedom of use,
|
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To protect your rights, we need to make restrictions that forbid
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|
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|
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|
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The precise terms and conditions for copying, distribution and
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|
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|
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|
||||
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|
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These requirements apply to the modified work as a whole. If
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||||
that is part of the Library, the object code for the work may be a
|
||||
derivative work of the Library even though the source code is not.
|
||||
Whether this is true is especially significant if the work can be
|
||||
linked without the Library, or if the work is itself a library. The
|
||||
threshold for this to be true is not precisely defined by law.
|
||||
|
||||
If such an object file uses only numerical parameters, data
|
||||
structure layouts and accessors, and small macros and small inline
|
||||
functions (ten lines or less in length), then the use of the object
|
||||
file is unrestricted, regardless of whether it is legally a derivative
|
||||
work. (Executables containing this object code plus portions of the
|
||||
Library will still fall under Section 6.)
|
||||
|
||||
Otherwise, if the work is a derivative of the Library, you may
|
||||
distribute the object code for the work under the terms of Section 6.
|
||||
Any executables containing that work also fall under Section 6,
|
||||
whether or not they are linked directly with the Library itself.
|
||||
|
||||
6. As an exception to the Sections above, you may also combine or
|
||||
link a "work that uses the Library" with the Library to produce a
|
||||
work containing portions of the Library, and distribute that work
|
||||
under terms of your choice, provided that the terms permit
|
||||
modification of the work for the customer's own use and reverse
|
||||
engineering for debugging such modifications.
|
||||
|
||||
You must give prominent notice with each copy of the work that the
|
||||
Library is used in it and that the Library and its use are covered by
|
||||
this License. You must supply a copy of this License. If the work
|
||||
during execution displays copyright notices, you must include the
|
||||
copyright notice for the Library among them, as well as a reference
|
||||
directing the user to the copy of this License. Also, you must do one
|
||||
of these things:
|
||||
|
||||
a) Accompany the work with the complete corresponding
|
||||
machine-readable source code for the Library including whatever
|
||||
changes were used in the work (which must be distributed under
|
||||
Sections 1 and 2 above); and, if the work is an executable linked
|
||||
with the Library, with the complete machine-readable "work that
|
||||
uses the Library", as object code and/or source code, so that the
|
||||
user can modify the Library and then relink to produce a modified
|
||||
executable containing the modified Library. (It is understood
|
||||
that the user who changes the contents of definitions files in the
|
||||
Library will not necessarily be able to recompile the application
|
||||
to use the modified definitions.)
|
||||
|
||||
b) Use a suitable shared library mechanism for linking with the
|
||||
Library. A suitable mechanism is one that (1) uses at run time a
|
||||
copy of the library already present on the user's computer system,
|
||||
rather than copying library functions into the executable, and (2)
|
||||
will operate properly with a modified version of the library, if
|
||||
the user installs one, as long as the modified version is
|
||||
interface-compatible with the version that the work was made with.
|
||||
|
||||
c) Accompany the work with a written offer, valid for at
|
||||
least three years, to give the same user the materials
|
||||
specified in Subsection 6a, above, for a charge no more
|
||||
than the cost of performing this distribution.
|
||||
|
||||
d) If distribution of the work is made by offering access to copy
|
||||
from a designated place, offer equivalent access to copy the above
|
||||
specified materials from the same place.
|
||||
|
||||
e) Verify that the user has already received a copy of these
|
||||
materials or that you have already sent this user a copy.
|
||||
|
||||
For an executable, the required form of the "work that uses the
|
||||
Library" must include any data and utility programs needed for
|
||||
reproducing the executable from it. However, as a special exception,
|
||||
the materials to be distributed need not include anything that is
|
||||
normally distributed (in either source or binary form) with the major
|
||||
components (compiler, kernel, and so on) of the operating system on
|
||||
which the executable runs, unless that component itself accompanies
|
||||
the executable.
|
||||
|
||||
It may happen that this requirement contradicts the license
|
||||
restrictions of other proprietary libraries that do not normally
|
||||
accompany the operating system. Such a contradiction means you cannot
|
||||
use both them and the Library together in an executable that you
|
||||
distribute.
|
||||
|
||||
7. You may place library facilities that are a work based on the
|
||||
Library side-by-side in a single library together with other library
|
||||
facilities not covered by this License, and distribute such a combined
|
||||
library, provided that the separate distribution of the work based on
|
||||
the Library and of the other library facilities is otherwise
|
||||
permitted, and provided that you do these two things:
|
||||
|
||||
a) Accompany the combined library with a copy of the same work
|
||||
based on the Library, uncombined with any other library
|
||||
facilities. This must be distributed under the terms of the
|
||||
Sections above.
|
||||
|
||||
b) Give prominent notice with the combined library of the fact
|
||||
that part of it is a work based on the Library, and explaining
|
||||
where to find the accompanying uncombined form of the same work.
|
||||
|
||||
8. You may not copy, modify, sublicense, link with, or distribute
|
||||
the Library except as expressly provided under this License. Any
|
||||
attempt otherwise to copy, modify, sublicense, link with, or
|
||||
distribute the Library is void, and will automatically terminate your
|
||||
rights under this License. However, parties who have received copies,
|
||||
or rights, from you under this License will not have their licenses
|
||||
terminated so long as such parties remain in full compliance.
|
||||
|
||||
9. You are not required to accept this License, since you have not
|
||||
signed it. However, nothing else grants you permission to modify or
|
||||
distribute the Library or its derivative works. These actions are
|
||||
prohibited by law if you do not accept this License. Therefore, by
|
||||
modifying or distributing the Library (or any work based on the
|
||||
Library), you indicate your acceptance of this License to do so, and
|
||||
all its terms and conditions for copying, distributing or modifying
|
||||
the Library or works based on it.
|
||||
|
||||
10. Each time you redistribute the Library (or any work based on the
|
||||
Library), the recipient automatically receives a license from the
|
||||
original licensor to copy, distribute, link with or modify the Library
|
||||
subject to these terms and conditions. You may not impose any further
|
||||
restrictions on the recipients' exercise of the rights granted herein.
|
||||
You are not responsible for enforcing compliance by third parties with
|
||||
this License.
|
||||
|
||||
11. If, as a consequence of a court judgment or allegation of patent
|
||||
infringement or for any other reason (not limited to patent issues),
|
||||
conditions are imposed on you (whether by court order, agreement or
|
||||
otherwise) that contradict the conditions of this License, they do not
|
||||
excuse you from the conditions of this License. If you cannot
|
||||
distribute so as to satisfy simultaneously your obligations under this
|
||||
License and any other pertinent obligations, then as a consequence you
|
||||
may not distribute the Library at all. For example, if a patent
|
||||
license would not permit royalty-free redistribution of the Library by
|
||||
all those who receive copies directly or indirectly through you, then
|
||||
the only way you could satisfy both it and this License would be to
|
||||
refrain entirely from distribution of the Library.
|
||||
|
||||
If any portion of this section is held invalid or unenforceable under any
|
||||
particular circumstance, the balance of the section is intended to apply,
|
||||
and the section as a whole is intended to apply in other circumstances.
|
||||
|
||||
It is not the purpose of this section to induce you to infringe any
|
||||
patents or other property right claims or to contest validity of any
|
||||
such claims; this section has the sole purpose of protecting the
|
||||
integrity of the free software distribution system which is
|
||||
implemented by public license practices. Many people have made
|
||||
generous contributions to the wide range of software distributed
|
||||
through that system in reliance on consistent application of that
|
||||
system; it is up to the author/donor to decide if he or she is willing
|
||||
to distribute software through any other system and a licensee cannot
|
||||
impose that choice.
|
||||
|
||||
This section is intended to make thoroughly clear what is believed to
|
||||
be a consequence of the rest of this License.
|
||||
|
||||
12. If the distribution and/or use of the Library is restricted in
|
||||
certain countries either by patents or by copyrighted interfaces, the
|
||||
original copyright holder who places the Library under this License may add
|
||||
an explicit geographical distribution limitation excluding those countries,
|
||||
so that distribution is permitted only in or among countries not thus
|
||||
excluded. In such case, this License incorporates the limitation as if
|
||||
written in the body of this License.
|
||||
|
||||
13. The Free Software Foundation may publish revised and/or new
|
||||
versions of the Lesser General Public License from time to time.
|
||||
Such new versions will be similar in spirit to the present version,
|
||||
but may differ in detail to address new problems or concerns.
|
||||
|
||||
Each version is given a distinguishing version number. If the Library
|
||||
specifies a version number of this License which applies to it and
|
||||
"any later version", you have the option of following the terms and
|
||||
conditions either of that version or of any later version published by
|
||||
the Free Software Foundation. If the Library does not specify a
|
||||
license version number, you may choose any version ever published by
|
||||
the Free Software Foundation.
|
||||
|
||||
14. If you wish to incorporate parts of the Library into other free
|
||||
programs whose distribution conditions are incompatible with these,
|
||||
write to the author to ask for permission. For software which is
|
||||
copyrighted by the Free Software Foundation, write to the Free
|
||||
Software Foundation; we sometimes make exceptions for this. Our
|
||||
decision will be guided by the two goals of preserving the free status
|
||||
of all derivatives of our free software and of promoting the sharing
|
||||
and reuse of software generally.
|
||||
|
||||
NO WARRANTY
|
||||
|
||||
15. BECAUSE THE LIBRARY IS LICENSED FREE OF CHARGE, THERE IS NO
|
||||
WARRANTY FOR THE LIBRARY, TO THE EXTENT PERMITTED BY APPLICABLE LAW.
|
||||
EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT HOLDERS AND/OR
|
||||
OTHER PARTIES PROVIDE THE LIBRARY "AS IS" WITHOUT WARRANTY OF ANY
|
||||
KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, THE
|
||||
IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
|
||||
PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE
|
||||
LIBRARY IS WITH YOU. SHOULD THE LIBRARY PROVE DEFECTIVE, YOU ASSUME
|
||||
THE COST OF ALL NECESSARY SERVICING, REPAIR OR CORRECTION.
|
||||
|
||||
16. IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN
|
||||
WRITING WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MAY MODIFY
|
||||
AND/OR REDISTRIBUTE THE LIBRARY AS PERMITTED ABOVE, BE LIABLE TO YOU
|
||||
FOR DAMAGES, INCLUDING ANY GENERAL, SPECIAL, INCIDENTAL OR
|
||||
CONSEQUENTIAL DAMAGES ARISING OUT OF THE USE OR INABILITY TO USE THE
|
||||
LIBRARY (INCLUDING BUT NOT LIMITED TO LOSS OF DATA OR DATA BEING
|
||||
RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD PARTIES OR A
|
||||
FAILURE OF THE LIBRARY TO OPERATE WITH ANY OTHER SOFTWARE), EVEN IF
|
||||
SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH
|
||||
DAMAGES.
|
||||
|
||||
END OF TERMS AND CONDITIONS
|
||||
|
||||
How to Apply These Terms to Your New Libraries
|
||||
|
||||
If you develop a new library, and you want it to be of the greatest
|
||||
possible use to the public, we recommend making it free software that
|
||||
everyone can redistribute and change. You can do so by permitting
|
||||
redistribution under these terms (or, alternatively, under the terms of the
|
||||
ordinary General Public License).
|
||||
|
||||
To apply these terms, attach the following notices to the library. It is
|
||||
safest to attach them to the start of each source file to most effectively
|
||||
convey the exclusion of warranty; and each file should have at least the
|
||||
"copyright" line and a pointer to where the full notice is found.
|
||||
|
||||
<one line to give the library's name and a brief idea of what it does.>
|
||||
Copyright (C) <year> <name of author>
|
||||
|
||||
This library is free software; you can redistribute it and/or
|
||||
modify it under the terms of the GNU Lesser General Public
|
||||
License as published by the Free Software Foundation; either
|
||||
version 2.1 of the License, or (at your option) any later version.
|
||||
|
||||
This library is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
|
||||
Lesser General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU Lesser General Public
|
||||
License along with this library; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
Also add information on how to contact you by electronic and paper mail.
|
||||
|
||||
You should also get your employer (if you work as a programmer) or your
|
||||
school, if any, to sign a "copyright disclaimer" for the library, if
|
||||
necessary. Here is a sample; alter the names:
|
||||
|
||||
Yoyodyne, Inc., hereby disclaims all copyright interest in the
|
||||
library `Frob' (a library for tweaking knobs) written by James Random Hacker.
|
||||
|
||||
<signature of Ty Coon>, 1 April 1990
|
||||
Ty Coon, President of Vice
|
||||
|
||||
That's all there is to it!
|
||||
|
|
@ -0,0 +1,52 @@
|
|||
Minpack Copyright Notice (1999) University of Chicago. All rights reserved
|
||||
|
||||
Redistribution and use in source and binary forms, with or
|
||||
without modification, are permitted provided that the
|
||||
following conditions are met:
|
||||
|
||||
1. Redistributions of source code must retain the above
|
||||
copyright notice, this list of conditions and the following
|
||||
disclaimer.
|
||||
|
||||
2. Redistributions in binary form must reproduce the above
|
||||
copyright notice, this list of conditions and the following
|
||||
disclaimer in the documentation and/or other materials
|
||||
provided with the distribution.
|
||||
|
||||
3. The end-user documentation included with the
|
||||
redistribution, if any, must include the following
|
||||
acknowledgment:
|
||||
|
||||
"This product includes software developed by the
|
||||
University of Chicago, as Operator of Argonne National
|
||||
Laboratory.
|
||||
|
||||
Alternately, this acknowledgment may appear in the software
|
||||
itself, if and wherever such third-party acknowledgments
|
||||
normally appear.
|
||||
|
||||
4. WARRANTY DISCLAIMER. THE SOFTWARE IS SUPPLIED "AS IS"
|
||||
WITHOUT WARRANTY OF ANY KIND. THE COPYRIGHT HOLDER, THE
|
||||
UNITED STATES, THE UNITED STATES DEPARTMENT OF ENERGY, AND
|
||||
THEIR EMPLOYEES: (1) DISCLAIM ANY WARRANTIES, EXPRESS OR
|
||||
IMPLIED, INCLUDING BUT NOT LIMITED TO ANY IMPLIED WARRANTIES
|
||||
OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE, TITLE
|
||||
OR NON-INFRINGEMENT, (2) DO NOT ASSUME ANY LEGAL LIABILITY
|
||||
OR RESPONSIBILITY FOR THE ACCURACY, COMPLETENESS, OR
|
||||
USEFULNESS OF THE SOFTWARE, (3) DO NOT REPRESENT THAT USE OF
|
||||
THE SOFTWARE WOULD NOT INFRINGE PRIVATELY OWNED RIGHTS, (4)
|
||||
DO NOT WARRANT THAT THE SOFTWARE WILL FUNCTION
|
||||
UNINTERRUPTED, THAT IT IS ERROR-FREE OR THAT ANY ERRORS WILL
|
||||
BE CORRECTED.
|
||||
|
||||
5. LIMITATION OF LIABILITY. IN NO EVENT WILL THE COPYRIGHT
|
||||
HOLDER, THE UNITED STATES, THE UNITED STATES DEPARTMENT OF
|
||||
ENERGY, OR THEIR EMPLOYEES: BE LIABLE FOR ANY INDIRECT,
|
||||
INCIDENTAL, CONSEQUENTIAL, SPECIAL OR PUNITIVE DAMAGES OF
|
||||
ANY KIND OR NATURE, INCLUDING BUT NOT LIMITED TO LOSS OF
|
||||
PROFITS OR LOSS OF DATA, FOR ANY REASON WHATSOEVER, WHETHER
|
||||
SUCH LIABILITY IS ASSERTED ON THE BASIS OF CONTRACT, TORT
|
||||
(INCLUDING NEGLIGENCE OR STRICT LIABILITY), OR OTHERWISE,
|
||||
EVEN IF ANY OF SAID PARTIES HAS BEEN WARNED OF THE
|
||||
POSSIBILITY OF SUCH LOSS OR DAMAGES.
|
||||
|
||||
|
|
@ -0,0 +1,373 @@
|
|||
Mozilla Public License Version 2.0
|
||||
==================================
|
||||
|
||||
1. Definitions
|
||||
--------------
|
||||
|
||||
1.1. "Contributor"
|
||||
means each individual or legal entity that creates, contributes to
|
||||
the creation of, or owns Covered Software.
|
||||
|
||||
1.2. "Contributor Version"
|
||||
means the combination of the Contributions of others (if any) used
|
||||
by a Contributor and that particular Contributor's Contribution.
|
||||
|
||||
1.3. "Contribution"
|
||||
means Covered Software of a particular Contributor.
|
||||
|
||||
1.4. "Covered Software"
|
||||
means Source Code Form to which the initial Contributor has attached
|
||||
the notice in Exhibit A, the Executable Form of such Source Code
|
||||
Form, and Modifications of such Source Code Form, in each case
|
||||
including portions thereof.
|
||||
|
||||
1.5. "Incompatible With Secondary Licenses"
|
||||
means
|
||||
|
||||
(a) that the initial Contributor has attached the notice described
|
||||
in Exhibit B to the Covered Software; or
|
||||
|
||||
(b) that the Covered Software was made available under the terms of
|
||||
version 1.1 or earlier of the License, but not also under the
|
||||
terms of a Secondary License.
|
||||
|
||||
1.6. "Executable Form"
|
||||
means any form of the work other than Source Code Form.
|
||||
|
||||
1.7. "Larger Work"
|
||||
means a work that combines Covered Software with other material, in
|
||||
a separate file or files, that is not Covered Software.
|
||||
|
||||
1.8. "License"
|
||||
means this document.
|
||||
|
||||
1.9. "Licensable"
|
||||
means having the right to grant, to the maximum extent possible,
|
||||
whether at the time of the initial grant or subsequently, any and
|
||||
all of the rights conveyed by this License.
|
||||
|
||||
1.10. "Modifications"
|
||||
means any of the following:
|
||||
|
||||
(a) any file in Source Code Form that results from an addition to,
|
||||
deletion from, or modification of the contents of Covered
|
||||
Software; or
|
||||
|
||||
(b) any new file in Source Code Form that contains any Covered
|
||||
Software.
|
||||
|
||||
1.11. "Patent Claims" of a Contributor
|
||||
means any patent claim(s), including without limitation, method,
|
||||
process, and apparatus claims, in any patent Licensable by such
|
||||
Contributor that would be infringed, but for the grant of the
|
||||
License, by the making, using, selling, offering for sale, having
|
||||
made, import, or transfer of either its Contributions or its
|
||||
Contributor Version.
|
||||
|
||||
1.12. "Secondary License"
|
||||
means either the GNU General Public License, Version 2.0, the GNU
|
||||
Lesser General Public License, Version 2.1, the GNU Affero General
|
||||
Public License, Version 3.0, or any later versions of those
|
||||
licenses.
|
||||
|
||||
1.13. "Source Code Form"
|
||||
means the form of the work preferred for making modifications.
|
||||
|
||||
1.14. "You" (or "Your")
|
||||
means an individual or a legal entity exercising rights under this
|
||||
License. For legal entities, "You" includes any entity that
|
||||
controls, is controlled by, or is under common control with You. For
|
||||
purposes of this definition, "control" means (a) the power, direct
|
||||
or indirect, to cause the direction or management of such entity,
|
||||
whether by contract or otherwise, or (b) ownership of more than
|
||||
fifty percent (50%) of the outstanding shares or beneficial
|
||||
ownership of such entity.
|
||||
|
||||
2. License Grants and Conditions
|
||||
--------------------------------
|
||||
|
||||
2.1. Grants
|
||||
|
||||
Each Contributor hereby grants You a world-wide, royalty-free,
|
||||
non-exclusive license:
|
||||
|
||||
(a) under intellectual property rights (other than patent or trademark)
|
||||
Licensable by such Contributor to use, reproduce, make available,
|
||||
modify, display, perform, distribute, and otherwise exploit its
|
||||
Contributions, either on an unmodified basis, with Modifications, or
|
||||
as part of a Larger Work; and
|
||||
|
||||
(b) under Patent Claims of such Contributor to make, use, sell, offer
|
||||
for sale, have made, import, and otherwise transfer either its
|
||||
Contributions or its Contributor Version.
|
||||
|
||||
2.2. Effective Date
|
||||
|
||||
The licenses granted in Section 2.1 with respect to any Contribution
|
||||
become effective for each Contribution on the date the Contributor first
|
||||
distributes such Contribution.
|
||||
|
||||
2.3. Limitations on Grant Scope
|
||||
|
||||
The licenses granted in this Section 2 are the only rights granted under
|
||||
this License. No additional rights or licenses will be implied from the
|
||||
distribution or licensing of Covered Software under this License.
|
||||
Notwithstanding Section 2.1(b) above, no patent license is granted by a
|
||||
Contributor:
|
||||
|
||||
(a) for any code that a Contributor has removed from Covered Software;
|
||||
or
|
||||
|
||||
(b) for infringements caused by: (i) Your and any other third party's
|
||||
modifications of Covered Software, or (ii) the combination of its
|
||||
Contributions with other software (except as part of its Contributor
|
||||
Version); or
|
||||
|
||||
(c) under Patent Claims infringed by Covered Software in the absence of
|
||||
its Contributions.
|
||||
|
||||
This License does not grant any rights in the trademarks, service marks,
|
||||
or logos of any Contributor (except as may be necessary to comply with
|
||||
the notice requirements in Section 3.4).
|
||||
|
||||
2.4. Subsequent Licenses
|
||||
|
||||
No Contributor makes additional grants as a result of Your choice to
|
||||
distribute the Covered Software under a subsequent version of this
|
||||
License (see Section 10.2) or under the terms of a Secondary License (if
|
||||
permitted under the terms of Section 3.3).
|
||||
|
||||
2.5. Representation
|
||||
|
||||
Each Contributor represents that the Contributor believes its
|
||||
Contributions are its original creation(s) or it has sufficient rights
|
||||
to grant the rights to its Contributions conveyed by this License.
|
||||
|
||||
2.6. Fair Use
|
||||
|
||||
This License is not intended to limit any rights You have under
|
||||
applicable copyright doctrines of fair use, fair dealing, or other
|
||||
equivalents.
|
||||
|
||||
2.7. Conditions
|
||||
|
||||
Sections 3.1, 3.2, 3.3, and 3.4 are conditions of the licenses granted
|
||||
in Section 2.1.
|
||||
|
||||
3. Responsibilities
|
||||
-------------------
|
||||
|
||||
3.1. Distribution of Source Form
|
||||
|
||||
All distribution of Covered Software in Source Code Form, including any
|
||||
Modifications that You create or to which You contribute, must be under
|
||||
the terms of this License. You must inform recipients that the Source
|
||||
Code Form of the Covered Software is governed by the terms of this
|
||||
License, and how they can obtain a copy of this License. You may not
|
||||
attempt to alter or restrict the recipients' rights in the Source Code
|
||||
Form.
|
||||
|
||||
3.2. Distribution of Executable Form
|
||||
|
||||
If You distribute Covered Software in Executable Form then:
|
||||
|
||||
(a) such Covered Software must also be made available in Source Code
|
||||
Form, as described in Section 3.1, and You must inform recipients of
|
||||
the Executable Form how they can obtain a copy of such Source Code
|
||||
Form by reasonable means in a timely manner, at a charge no more
|
||||
than the cost of distribution to the recipient; and
|
||||
|
||||
(b) You may distribute such Executable Form under the terms of this
|
||||
License, or sublicense it under different terms, provided that the
|
||||
license for the Executable Form does not attempt to limit or alter
|
||||
the recipients' rights in the Source Code Form under this License.
|
||||
|
||||
3.3. Distribution of a Larger Work
|
||||
|
||||
You may create and distribute a Larger Work under terms of Your choice,
|
||||
provided that You also comply with the requirements of this License for
|
||||
the Covered Software. If the Larger Work is a combination of Covered
|
||||
Software with a work governed by one or more Secondary Licenses, and the
|
||||
Covered Software is not Incompatible With Secondary Licenses, this
|
||||
License permits You to additionally distribute such Covered Software
|
||||
under the terms of such Secondary License(s), so that the recipient of
|
||||
the Larger Work may, at their option, further distribute the Covered
|
||||
Software under the terms of either this License or such Secondary
|
||||
License(s).
|
||||
|
||||
3.4. Notices
|
||||
|
||||
You may not remove or alter the substance of any license notices
|
||||
(including copyright notices, patent notices, disclaimers of warranty,
|
||||
or limitations of liability) contained within the Source Code Form of
|
||||
the Covered Software, except that You may alter any license notices to
|
||||
the extent required to remedy known factual inaccuracies.
|
||||
|
||||
3.5. Application of Additional Terms
|
||||
|
||||
You may choose to offer, and to charge a fee for, warranty, support,
|
||||
indemnity or liability obligations to one or more recipients of Covered
|
||||
Software. However, You may do so only on Your own behalf, and not on
|
||||
behalf of any Contributor. You must make it absolutely clear that any
|
||||
such warranty, support, indemnity, or liability obligation is offered by
|
||||
You alone, and You hereby agree to indemnify every Contributor for any
|
||||
liability incurred by such Contributor as a result of warranty, support,
|
||||
indemnity or liability terms You offer. You may include additional
|
||||
disclaimers of warranty and limitations of liability specific to any
|
||||
jurisdiction.
|
||||
|
||||
4. Inability to Comply Due to Statute or Regulation
|
||||
---------------------------------------------------
|
||||
|
||||
If it is impossible for You to comply with any of the terms of this
|
||||
License with respect to some or all of the Covered Software due to
|
||||
statute, judicial order, or regulation then You must: (a) comply with
|
||||
the terms of this License to the maximum extent possible; and (b)
|
||||
describe the limitations and the code they affect. Such description must
|
||||
be placed in a text file included with all distributions of the Covered
|
||||
Software under this License. Except to the extent prohibited by statute
|
||||
or regulation, such description must be sufficiently detailed for a
|
||||
recipient of ordinary skill to be able to understand it.
|
||||
|
||||
5. Termination
|
||||
--------------
|
||||
|
||||
5.1. The rights granted under this License will terminate automatically
|
||||
if You fail to comply with any of its terms. However, if You become
|
||||
compliant, then the rights granted under this License from a particular
|
||||
Contributor are reinstated (a) provisionally, unless and until such
|
||||
Contributor explicitly and finally terminates Your grants, and (b) on an
|
||||
ongoing basis, if such Contributor fails to notify You of the
|
||||
non-compliance by some reasonable means prior to 60 days after You have
|
||||
come back into compliance. Moreover, Your grants from a particular
|
||||
Contributor are reinstated on an ongoing basis if such Contributor
|
||||
notifies You of the non-compliance by some reasonable means, this is the
|
||||
first time You have received notice of non-compliance with this License
|
||||
from such Contributor, and You become compliant prior to 30 days after
|
||||
Your receipt of the notice.
|
||||
|
||||
5.2. If You initiate litigation against any entity by asserting a patent
|
||||
infringement claim (excluding declaratory judgment actions,
|
||||
counter-claims, and cross-claims) alleging that a Contributor Version
|
||||
directly or indirectly infringes any patent, then the rights granted to
|
||||
You by any and all Contributors for the Covered Software under Section
|
||||
2.1 of this License shall terminate.
|
||||
|
||||
5.3. In the event of termination under Sections 5.1 or 5.2 above, all
|
||||
end user license agreements (excluding distributors and resellers) which
|
||||
have been validly granted by You or Your distributors under this License
|
||||
prior to termination shall survive termination.
|
||||
|
||||
************************************************************************
|
||||
* *
|
||||
* 6. Disclaimer of Warranty *
|
||||
* ------------------------- *
|
||||
* *
|
||||
* Covered Software is provided under this License on an "as is" *
|
||||
* basis, without warranty of any kind, either expressed, implied, or *
|
||||
* statutory, including, without limitation, warranties that the *
|
||||
* Covered Software is free of defects, merchantable, fit for a *
|
||||
* particular purpose or non-infringing. The entire risk as to the *
|
||||
* quality and performance of the Covered Software is with You. *
|
||||
* Should any Covered Software prove defective in any respect, You *
|
||||
* (not any Contributor) assume the cost of any necessary servicing, *
|
||||
* repair, or correction. This disclaimer of warranty constitutes an *
|
||||
* essential part of this License. No use of any Covered Software is *
|
||||
* authorized under this License except under this disclaimer. *
|
||||
* *
|
||||
************************************************************************
|
||||
|
||||
************************************************************************
|
||||
* *
|
||||
* 7. Limitation of Liability *
|
||||
* -------------------------- *
|
||||
* *
|
||||
* Under no circumstances and under no legal theory, whether tort *
|
||||
* (including negligence), contract, or otherwise, shall any *
|
||||
* Contributor, or anyone who distributes Covered Software as *
|
||||
* permitted above, be liable to You for any direct, indirect, *
|
||||
* special, incidental, or consequential damages of any character *
|
||||
* including, without limitation, damages for lost profits, loss of *
|
||||
* goodwill, work stoppage, computer failure or malfunction, or any *
|
||||
* and all other commercial damages or losses, even if such party *
|
||||
* shall have been informed of the possibility of such damages. This *
|
||||
* limitation of liability shall not apply to liability for death or *
|
||||
* personal injury resulting from such party's negligence to the *
|
||||
* extent applicable law prohibits such limitation. Some *
|
||||
* jurisdictions do not allow the exclusion or limitation of *
|
||||
* incidental or consequential damages, so this exclusion and *
|
||||
* limitation may not apply to You. *
|
||||
* *
|
||||
************************************************************************
|
||||
|
||||
8. Litigation
|
||||
-------------
|
||||
|
||||
Any litigation relating to this License may be brought only in the
|
||||
courts of a jurisdiction where the defendant maintains its principal
|
||||
place of business and such litigation shall be governed by laws of that
|
||||
jurisdiction, without reference to its conflict-of-law provisions.
|
||||
Nothing in this Section shall prevent a party's ability to bring
|
||||
cross-claims or counter-claims.
|
||||
|
||||
9. Miscellaneous
|
||||
----------------
|
||||
|
||||
This License represents the complete agreement concerning the subject
|
||||
matter hereof. If any provision of this License is held to be
|
||||
unenforceable, such provision shall be reformed only to the extent
|
||||
necessary to make it enforceable. Any law or regulation which provides
|
||||
that the language of a contract shall be construed against the drafter
|
||||
shall not be used to construe this License against a Contributor.
|
||||
|
||||
10. Versions of the License
|
||||
---------------------------
|
||||
|
||||
10.1. New Versions
|
||||
|
||||
Mozilla Foundation is the license steward. Except as provided in Section
|
||||
10.3, no one other than the license steward has the right to modify or
|
||||
publish new versions of this License. Each version will be given a
|
||||
distinguishing version number.
|
||||
|
||||
10.2. Effect of New Versions
|
||||
|
||||
You may distribute the Covered Software under the terms of the version
|
||||
of the License under which You originally received the Covered Software,
|
||||
or under the terms of any subsequent version published by the license
|
||||
steward.
|
||||
|
||||
10.3. Modified Versions
|
||||
|
||||
If you create software not governed by this License, and you want to
|
||||
create a new license for such software, you may create and use a
|
||||
modified version of this License if you rename the license and remove
|
||||
any references to the name of the license steward (except to note that
|
||||
such modified license differs from this License).
|
||||
|
||||
10.4. Distributing Source Code Form that is Incompatible With Secondary
|
||||
Licenses
|
||||
|
||||
If You choose to distribute Source Code Form that is Incompatible With
|
||||
Secondary Licenses under the terms of this version of the License, the
|
||||
notice described in Exhibit B of this License must be attached.
|
||||
|
||||
Exhibit A - Source Code Form License Notice
|
||||
-------------------------------------------
|
||||
|
||||
This Source Code Form is subject to the terms of the Mozilla Public
|
||||
License, v. 2.0. If a copy of the MPL was not distributed with this
|
||||
file, You can obtain one at http://mozilla.org/MPL/2.0/.
|
||||
|
||||
If it is not possible or desirable to put the notice in a particular
|
||||
file, then You may include the notice in a location (such as a LICENSE
|
||||
file in a relevant directory) where a recipient would be likely to look
|
||||
for such a notice.
|
||||
|
||||
You may add additional accurate notices of copyright ownership.
|
||||
|
||||
Exhibit B - "Incompatible With Secondary Licenses" Notice
|
||||
---------------------------------------------------------
|
||||
|
||||
This Source Code Form is "Incompatible With Secondary Licenses", as
|
||||
defined by the Mozilla Public License, v. 2.0.
|
||||
|
|
@ -0,0 +1,18 @@
|
|||
Eigen is primarily MPL2 licensed. See COPYING.MPL2 and these links:
|
||||
http://www.mozilla.org/MPL/2.0/
|
||||
http://www.mozilla.org/MPL/2.0/FAQ.html
|
||||
|
||||
Some files contain third-party code under BSD or LGPL licenses, whence the other
|
||||
COPYING.* files here.
|
||||
|
||||
All the LGPL code is either LGPL 2.1-only, or LGPL 2.1-or-later.
|
||||
For this reason, the COPYING.LGPL file contains the LGPL 2.1 text.
|
||||
|
||||
If you want to guarantee that the Eigen code that you are #including is licensed
|
||||
under the MPL2 and possibly more permissive licenses (like BSD), #define this
|
||||
preprocessor symbol:
|
||||
EIGEN_MPL2_ONLY
|
||||
For example, with most compilers, you could add this to your project CXXFLAGS:
|
||||
-DEIGEN_MPL2_ONLY
|
||||
This will cause a compilation error to be generated if you #include any code that is
|
||||
LGPL licensed.
|
||||
|
|
@ -0,0 +1,13 @@
|
|||
## This file should be placed in the root directory of your project.
|
||||
## Then modify the CMakeLists.txt file in the root directory of your
|
||||
## project to incorporate the testing dashboard.
|
||||
## # The following are required to uses Dart and the Cdash dashboard
|
||||
## ENABLE_TESTING()
|
||||
## INCLUDE(CTest)
|
||||
set(CTEST_PROJECT_NAME "Eigen")
|
||||
set(CTEST_NIGHTLY_START_TIME "00:00:00 UTC")
|
||||
|
||||
set(CTEST_DROP_METHOD "http")
|
||||
set(CTEST_DROP_SITE "my.cdash.org")
|
||||
set(CTEST_DROP_LOCATION "/submit.php?project=Eigen")
|
||||
set(CTEST_DROP_SITE_CDASH TRUE)
|
||||
|
|
@ -0,0 +1,4 @@
|
|||
|
||||
set(CTEST_CUSTOM_MAXIMUM_NUMBER_OF_WARNINGS "2000")
|
||||
set(CTEST_CUSTOM_MAXIMUM_NUMBER_OF_ERRORS "2000")
|
||||
list(APPEND CTEST_CUSTOM_ERROR_EXCEPTION @EIGEN_CTEST_ERROR_EXCEPTION@)
|
||||
|
|
@ -0,0 +1,19 @@
|
|||
include(RegexUtils)
|
||||
test_escape_string_as_regex()
|
||||
|
||||
file(GLOB Eigen_directory_files "*")
|
||||
|
||||
escape_string_as_regex(ESCAPED_CMAKE_CURRENT_SOURCE_DIR "${CMAKE_CURRENT_SOURCE_DIR}")
|
||||
|
||||
foreach(f ${Eigen_directory_files})
|
||||
if(NOT f MATCHES "\\.txt" AND NOT f MATCHES "${ESCAPED_CMAKE_CURRENT_SOURCE_DIR}/[.].+" AND NOT f MATCHES "${ESCAPED_CMAKE_CURRENT_SOURCE_DIR}/src")
|
||||
list(APPEND Eigen_directory_files_to_install ${f})
|
||||
endif()
|
||||
endforeach(f ${Eigen_directory_files})
|
||||
|
||||
install(FILES
|
||||
${Eigen_directory_files_to_install}
|
||||
DESTINATION ${INCLUDE_INSTALL_DIR}/Eigen COMPONENT Devel
|
||||
)
|
||||
|
||||
install(DIRECTORY src DESTINATION ${INCLUDE_INSTALL_DIR}/Eigen COMPONENT Devel FILES_MATCHING PATTERN "*.h")
|
||||
|
|
@ -0,0 +1,46 @@
|
|||
// This file is part of Eigen, a lightweight C++ template library
|
||||
// for linear algebra.
|
||||
//
|
||||
// This Source Code Form is subject to the terms of the Mozilla
|
||||
// Public License v. 2.0. If a copy of the MPL was not distributed
|
||||
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
|
||||
|
||||
#ifndef EIGEN_CHOLESKY_MODULE_H
|
||||
#define EIGEN_CHOLESKY_MODULE_H
|
||||
|
||||
#include "Core"
|
||||
#include "Jacobi"
|
||||
|
||||
#include "src/Core/util/DisableStupidWarnings.h"
|
||||
|
||||
/** \defgroup Cholesky_Module Cholesky module
|
||||
*
|
||||
*
|
||||
*
|
||||
* This module provides two variants of the Cholesky decomposition for selfadjoint (hermitian) matrices.
|
||||
* Those decompositions are also accessible via the following methods:
|
||||
* - MatrixBase::llt()
|
||||
* - MatrixBase::ldlt()
|
||||
* - SelfAdjointView::llt()
|
||||
* - SelfAdjointView::ldlt()
|
||||
*
|
||||
* \code
|
||||
* #include <Eigen/Cholesky>
|
||||
* \endcode
|
||||
*/
|
||||
|
||||
#include "src/Cholesky/LLT.h"
|
||||
#include "src/Cholesky/LDLT.h"
|
||||
#ifdef EIGEN_USE_LAPACKE
|
||||
#ifdef EIGEN_USE_MKL
|
||||
#include "mkl_lapacke.h"
|
||||
#else
|
||||
#include "src/misc/lapacke.h"
|
||||
#endif
|
||||
#include "src/Cholesky/LLT_LAPACKE.h"
|
||||
#endif
|
||||
|
||||
#include "src/Core/util/ReenableStupidWarnings.h"
|
||||
|
||||
#endif // EIGEN_CHOLESKY_MODULE_H
|
||||
/* vim: set filetype=cpp et sw=2 ts=2 ai: */
|
||||
|
|
@ -0,0 +1,48 @@
|
|||
// This file is part of Eigen, a lightweight C++ template library
|
||||
// for linear algebra.
|
||||
//
|
||||
// This Source Code Form is subject to the terms of the Mozilla
|
||||
// Public License v. 2.0. If a copy of the MPL was not distributed
|
||||
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
|
||||
|
||||
#ifndef EIGEN_CHOLMODSUPPORT_MODULE_H
|
||||
#define EIGEN_CHOLMODSUPPORT_MODULE_H
|
||||
|
||||
#include "SparseCore"
|
||||
|
||||
#include "src/Core/util/DisableStupidWarnings.h"
|
||||
|
||||
extern "C" {
|
||||
#include <cholmod.h>
|
||||
}
|
||||
|
||||
/** \ingroup Support_modules
|
||||
* \defgroup CholmodSupport_Module CholmodSupport module
|
||||
*
|
||||
* This module provides an interface to the Cholmod library which is part of the <a href="http://www.suitesparse.com">suitesparse</a> package.
|
||||
* It provides the two following main factorization classes:
|
||||
* - class CholmodSupernodalLLT: a supernodal LLT Cholesky factorization.
|
||||
* - class CholmodDecomposiiton: a general L(D)LT Cholesky factorization with automatic or explicit runtime selection of the underlying factorization method (supernodal or simplicial).
|
||||
*
|
||||
* For the sake of completeness, this module also propose the two following classes:
|
||||
* - class CholmodSimplicialLLT
|
||||
* - class CholmodSimplicialLDLT
|
||||
* Note that these classes does not bring any particular advantage compared to the built-in
|
||||
* SimplicialLLT and SimplicialLDLT factorization classes.
|
||||
*
|
||||
* \code
|
||||
* #include <Eigen/CholmodSupport>
|
||||
* \endcode
|
||||
*
|
||||
* In order to use this module, the cholmod headers must be accessible from the include paths, and your binary must be linked to the cholmod library and its dependencies.
|
||||
* The dependencies depend on how cholmod has been compiled.
|
||||
* For a cmake based project, you can use our FindCholmod.cmake module to help you in this task.
|
||||
*
|
||||
*/
|
||||
|
||||
#include "src/CholmodSupport/CholmodSupport.h"
|
||||
|
||||
#include "src/Core/util/ReenableStupidWarnings.h"
|
||||
|
||||
#endif // EIGEN_CHOLMODSUPPORT_MODULE_H
|
||||
|
||||
|
|
@ -0,0 +1,7 @@
|
|||
#include "Core"
|
||||
#include "LU"
|
||||
#include "Cholesky"
|
||||
#include "QR"
|
||||
#include "SVD"
|
||||
#include "Geometry"
|
||||
#include "Eigenvalues"
|
||||
|
|
@ -0,0 +1,2 @@
|
|||
#include "Dense"
|
||||
#include "Sparse"
|
||||
|
|
@ -0,0 +1,61 @@
|
|||
// This file is part of Eigen, a lightweight C++ template library
|
||||
// for linear algebra.
|
||||
//
|
||||
// This Source Code Form is subject to the terms of the Mozilla
|
||||
// Public License v. 2.0. If a copy of the MPL was not distributed
|
||||
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
|
||||
|
||||
#ifndef EIGEN_EIGENVALUES_MODULE_H
|
||||
#define EIGEN_EIGENVALUES_MODULE_H
|
||||
|
||||
#include "Core"
|
||||
|
||||
#include "Cholesky"
|
||||
#include "Jacobi"
|
||||
#include "Householder"
|
||||
#include "LU"
|
||||
#include "Geometry"
|
||||
|
||||
#include "src/Core/util/DisableStupidWarnings.h"
|
||||
|
||||
/** \defgroup Eigenvalues_Module Eigenvalues module
|
||||
*
|
||||
*
|
||||
*
|
||||
* This module mainly provides various eigenvalue solvers.
|
||||
* This module also provides some MatrixBase methods, including:
|
||||
* - MatrixBase::eigenvalues(),
|
||||
* - MatrixBase::operatorNorm()
|
||||
*
|
||||
* \code
|
||||
* #include <Eigen/Eigenvalues>
|
||||
* \endcode
|
||||
*/
|
||||
|
||||
#include "src/misc/RealSvd2x2.h"
|
||||
#include "src/Eigenvalues/Tridiagonalization.h"
|
||||
#include "src/Eigenvalues/RealSchur.h"
|
||||
#include "src/Eigenvalues/EigenSolver.h"
|
||||
#include "src/Eigenvalues/SelfAdjointEigenSolver.h"
|
||||
#include "src/Eigenvalues/GeneralizedSelfAdjointEigenSolver.h"
|
||||
#include "src/Eigenvalues/HessenbergDecomposition.h"
|
||||
#include "src/Eigenvalues/ComplexSchur.h"
|
||||
#include "src/Eigenvalues/ComplexEigenSolver.h"
|
||||
#include "src/Eigenvalues/RealQZ.h"
|
||||
#include "src/Eigenvalues/GeneralizedEigenSolver.h"
|
||||
#include "src/Eigenvalues/MatrixBaseEigenvalues.h"
|
||||
#ifdef EIGEN_USE_LAPACKE
|
||||
#ifdef EIGEN_USE_MKL
|
||||
#include "mkl_lapacke.h"
|
||||
#else
|
||||
#include "src/misc/lapacke.h"
|
||||
#endif
|
||||
#include "src/Eigenvalues/RealSchur_LAPACKE.h"
|
||||
#include "src/Eigenvalues/ComplexSchur_LAPACKE.h"
|
||||
#include "src/Eigenvalues/SelfAdjointEigenSolver_LAPACKE.h"
|
||||
#endif
|
||||
|
||||
#include "src/Core/util/ReenableStupidWarnings.h"
|
||||
|
||||
#endif // EIGEN_EIGENVALUES_MODULE_H
|
||||
/* vim: set filetype=cpp et sw=2 ts=2 ai: */
|
||||
|
|
@ -0,0 +1,62 @@
|
|||
// This file is part of Eigen, a lightweight C++ template library
|
||||
// for linear algebra.
|
||||
//
|
||||
// This Source Code Form is subject to the terms of the Mozilla
|
||||
// Public License v. 2.0. If a copy of the MPL was not distributed
|
||||
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
|
||||
|
||||
#ifndef EIGEN_GEOMETRY_MODULE_H
|
||||
#define EIGEN_GEOMETRY_MODULE_H
|
||||
|
||||
#include "Core"
|
||||
|
||||
#include "SVD"
|
||||
#include "LU"
|
||||
#include <limits>
|
||||
|
||||
#include "src/Core/util/DisableStupidWarnings.h"
|
||||
|
||||
/** \defgroup Geometry_Module Geometry module
|
||||
*
|
||||
* This module provides support for:
|
||||
* - fixed-size homogeneous transformations
|
||||
* - translation, scaling, 2D and 3D rotations
|
||||
* - \link Quaternion quaternions \endlink
|
||||
* - cross products (\ref MatrixBase::cross, \ref MatrixBase::cross3)
|
||||
* - orthognal vector generation (\ref MatrixBase::unitOrthogonal)
|
||||
* - some linear components: \link ParametrizedLine parametrized-lines \endlink and \link Hyperplane hyperplanes \endlink
|
||||
* - \link AlignedBox axis aligned bounding boxes \endlink
|
||||
* - \link umeyama least-square transformation fitting \endlink
|
||||
*
|
||||
* \code
|
||||
* #include <Eigen/Geometry>
|
||||
* \endcode
|
||||
*/
|
||||
|
||||
#include "src/Geometry/OrthoMethods.h"
|
||||
#include "src/Geometry/EulerAngles.h"
|
||||
|
||||
#include "src/Geometry/Homogeneous.h"
|
||||
#include "src/Geometry/RotationBase.h"
|
||||
#include "src/Geometry/Rotation2D.h"
|
||||
#include "src/Geometry/Quaternion.h"
|
||||
#include "src/Geometry/AngleAxis.h"
|
||||
#include "src/Geometry/Transform.h"
|
||||
#include "src/Geometry/Translation.h"
|
||||
#include "src/Geometry/Scaling.h"
|
||||
#include "src/Geometry/Hyperplane.h"
|
||||
#include "src/Geometry/ParametrizedLine.h"
|
||||
#include "src/Geometry/AlignedBox.h"
|
||||
#include "src/Geometry/Umeyama.h"
|
||||
|
||||
// Use the SSE optimized version whenever possible. At the moment the
|
||||
// SSE version doesn't compile when AVX is enabled
|
||||
#if defined EIGEN_VECTORIZE_SSE && !defined EIGEN_VECTORIZE_AVX
|
||||
#include "src/Geometry/arch/Geometry_SSE.h"
|
||||
#endif
|
||||
|
||||
#include "src/Core/util/ReenableStupidWarnings.h"
|
||||
|
||||
#endif // EIGEN_GEOMETRY_MODULE_H
|
||||
/* vim: set filetype=cpp et sw=2 ts=2 ai: */
|
||||
|
||||
|
|
@ -0,0 +1,30 @@
|
|||
// This file is part of Eigen, a lightweight C++ template library
|
||||
// for linear algebra.
|
||||
//
|
||||
// This Source Code Form is subject to the terms of the Mozilla
|
||||
// Public License v. 2.0. If a copy of the MPL was not distributed
|
||||
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
|
||||
|
||||
#ifndef EIGEN_HOUSEHOLDER_MODULE_H
|
||||
#define EIGEN_HOUSEHOLDER_MODULE_H
|
||||
|
||||
#include "Core"
|
||||
|
||||
#include "src/Core/util/DisableStupidWarnings.h"
|
||||
|
||||
/** \defgroup Householder_Module Householder module
|
||||
* This module provides Householder transformations.
|
||||
*
|
||||
* \code
|
||||
* #include <Eigen/Householder>
|
||||
* \endcode
|
||||
*/
|
||||
|
||||
#include "src/Householder/Householder.h"
|
||||
#include "src/Householder/HouseholderSequence.h"
|
||||
#include "src/Householder/BlockHouseholder.h"
|
||||
|
||||
#include "src/Core/util/ReenableStupidWarnings.h"
|
||||
|
||||
#endif // EIGEN_HOUSEHOLDER_MODULE_H
|
||||
/* vim: set filetype=cpp et sw=2 ts=2 ai: */
|
||||
|
|
@ -0,0 +1,48 @@
|
|||
// This file is part of Eigen, a lightweight C++ template library
|
||||
// for linear algebra.
|
||||
//
|
||||
// This Source Code Form is subject to the terms of the Mozilla
|
||||
// Public License v. 2.0. If a copy of the MPL was not distributed
|
||||
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
|
||||
|
||||
#ifndef EIGEN_ITERATIVELINEARSOLVERS_MODULE_H
|
||||
#define EIGEN_ITERATIVELINEARSOLVERS_MODULE_H
|
||||
|
||||
#include "SparseCore"
|
||||
#include "OrderingMethods"
|
||||
|
||||
#include "src/Core/util/DisableStupidWarnings.h"
|
||||
|
||||
/**
|
||||
* \defgroup IterativeLinearSolvers_Module IterativeLinearSolvers module
|
||||
*
|
||||
* This module currently provides iterative methods to solve problems of the form \c A \c x = \c b, where \c A is a squared matrix, usually very large and sparse.
|
||||
* Those solvers are accessible via the following classes:
|
||||
* - ConjugateGradient for selfadjoint (hermitian) matrices,
|
||||
* - LeastSquaresConjugateGradient for rectangular least-square problems,
|
||||
* - BiCGSTAB for general square matrices.
|
||||
*
|
||||
* These iterative solvers are associated with some preconditioners:
|
||||
* - IdentityPreconditioner - not really useful
|
||||
* - DiagonalPreconditioner - also called Jacobi preconditioner, work very well on diagonal dominant matrices.
|
||||
* - IncompleteLUT - incomplete LU factorization with dual thresholding
|
||||
*
|
||||
* Such problems can also be solved using the direct sparse decomposition modules: SparseCholesky, CholmodSupport, UmfPackSupport, SuperLUSupport.
|
||||
*
|
||||
\code
|
||||
#include <Eigen/IterativeLinearSolvers>
|
||||
\endcode
|
||||
*/
|
||||
|
||||
#include "src/IterativeLinearSolvers/SolveWithGuess.h"
|
||||
#include "src/IterativeLinearSolvers/IterativeSolverBase.h"
|
||||
#include "src/IterativeLinearSolvers/BasicPreconditioners.h"
|
||||
#include "src/IterativeLinearSolvers/ConjugateGradient.h"
|
||||
#include "src/IterativeLinearSolvers/LeastSquareConjugateGradient.h"
|
||||
#include "src/IterativeLinearSolvers/BiCGSTAB.h"
|
||||
#include "src/IterativeLinearSolvers/IncompleteLUT.h"
|
||||
#include "src/IterativeLinearSolvers/IncompleteCholesky.h"
|
||||
|
||||
#include "src/Core/util/ReenableStupidWarnings.h"
|
||||
|
||||
#endif // EIGEN_ITERATIVELINEARSOLVERS_MODULE_H
|
||||
|
|
@ -0,0 +1,33 @@
|
|||
// This file is part of Eigen, a lightweight C++ template library
|
||||
// for linear algebra.
|
||||
//
|
||||
// This Source Code Form is subject to the terms of the Mozilla
|
||||
// Public License v. 2.0. If a copy of the MPL was not distributed
|
||||
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
|
||||
|
||||
#ifndef EIGEN_JACOBI_MODULE_H
|
||||
#define EIGEN_JACOBI_MODULE_H
|
||||
|
||||
#include "Core"
|
||||
|
||||
#include "src/Core/util/DisableStupidWarnings.h"
|
||||
|
||||
/** \defgroup Jacobi_Module Jacobi module
|
||||
* This module provides Jacobi and Givens rotations.
|
||||
*
|
||||
* \code
|
||||
* #include <Eigen/Jacobi>
|
||||
* \endcode
|
||||
*
|
||||
* In addition to listed classes, it defines the two following MatrixBase methods to apply a Jacobi or Givens rotation:
|
||||
* - MatrixBase::applyOnTheLeft()
|
||||
* - MatrixBase::applyOnTheRight().
|
||||
*/
|
||||
|
||||
#include "src/Jacobi/Jacobi.h"
|
||||
|
||||
#include "src/Core/util/ReenableStupidWarnings.h"
|
||||
|
||||
#endif // EIGEN_JACOBI_MODULE_H
|
||||
/* vim: set filetype=cpp et sw=2 ts=2 ai: */
|
||||
|
||||
|
|
@ -0,0 +1,50 @@
|
|||
// This file is part of Eigen, a lightweight C++ template library
|
||||
// for linear algebra.
|
||||
//
|
||||
// This Source Code Form is subject to the terms of the Mozilla
|
||||
// Public License v. 2.0. If a copy of the MPL was not distributed
|
||||
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
|
||||
|
||||
#ifndef EIGEN_LU_MODULE_H
|
||||
#define EIGEN_LU_MODULE_H
|
||||
|
||||
#include "Core"
|
||||
|
||||
#include "src/Core/util/DisableStupidWarnings.h"
|
||||
|
||||
/** \defgroup LU_Module LU module
|
||||
* This module includes %LU decomposition and related notions such as matrix inversion and determinant.
|
||||
* This module defines the following MatrixBase methods:
|
||||
* - MatrixBase::inverse()
|
||||
* - MatrixBase::determinant()
|
||||
*
|
||||
* \code
|
||||
* #include <Eigen/LU>
|
||||
* \endcode
|
||||
*/
|
||||
|
||||
#include "src/misc/Kernel.h"
|
||||
#include "src/misc/Image.h"
|
||||
#include "src/LU/FullPivLU.h"
|
||||
#include "src/LU/PartialPivLU.h"
|
||||
#ifdef EIGEN_USE_LAPACKE
|
||||
#ifdef EIGEN_USE_MKL
|
||||
#include "mkl_lapacke.h"
|
||||
#else
|
||||
#include "src/misc/lapacke.h"
|
||||
#endif
|
||||
#include "src/LU/PartialPivLU_LAPACKE.h"
|
||||
#endif
|
||||
#include "src/LU/Determinant.h"
|
||||
#include "src/LU/InverseImpl.h"
|
||||
|
||||
// Use the SSE optimized version whenever possible. At the moment the
|
||||
// SSE version doesn't compile when AVX is enabled
|
||||
#if defined EIGEN_VECTORIZE_SSE && !defined EIGEN_VECTORIZE_AVX
|
||||
#include "src/LU/arch/Inverse_SSE.h"
|
||||
#endif
|
||||
|
||||
#include "src/Core/util/ReenableStupidWarnings.h"
|
||||
|
||||
#endif // EIGEN_LU_MODULE_H
|
||||
/* vim: set filetype=cpp et sw=2 ts=2 ai: */
|
||||
|
|
@ -0,0 +1,35 @@
|
|||
// This file is part of Eigen, a lightweight C++ template library
|
||||
// for linear algebra.
|
||||
//
|
||||
// This Source Code Form is subject to the terms of the Mozilla
|
||||
// Public License v. 2.0. If a copy of the MPL was not distributed
|
||||
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
|
||||
|
||||
#ifndef EIGEN_METISSUPPORT_MODULE_H
|
||||
#define EIGEN_METISSUPPORT_MODULE_H
|
||||
|
||||
#include "SparseCore"
|
||||
|
||||
#include "src/Core/util/DisableStupidWarnings.h"
|
||||
|
||||
extern "C" {
|
||||
#include <metis.h>
|
||||
}
|
||||
|
||||
|
||||
/** \ingroup Support_modules
|
||||
* \defgroup MetisSupport_Module MetisSupport module
|
||||
*
|
||||
* \code
|
||||
* #include <Eigen/MetisSupport>
|
||||
* \endcode
|
||||
* This module defines an interface to the METIS reordering package (http://glaros.dtc.umn.edu/gkhome/views/metis).
|
||||
* It can be used just as any other built-in method as explained in \link OrderingMethods_Module here. \endlink
|
||||
*/
|
||||
|
||||
|
||||
#include "src/MetisSupport/MetisSupport.h"
|
||||
|
||||
#include "src/Core/util/ReenableStupidWarnings.h"
|
||||
|
||||
#endif // EIGEN_METISSUPPORT_MODULE_H
|
||||
|
|
@ -0,0 +1,73 @@
|
|||
// This file is part of Eigen, a lightweight C++ template library
|
||||
// for linear algebra.
|
||||
//
|
||||
// This Source Code Form is subject to the terms of the Mozilla
|
||||
// Public License v. 2.0. If a copy of the MPL was not distributed
|
||||
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
|
||||
|
||||
#ifndef EIGEN_ORDERINGMETHODS_MODULE_H
|
||||
#define EIGEN_ORDERINGMETHODS_MODULE_H
|
||||
|
||||
#include "SparseCore"
|
||||
|
||||
#include "src/Core/util/DisableStupidWarnings.h"
|
||||
|
||||
/**
|
||||
* \defgroup OrderingMethods_Module OrderingMethods module
|
||||
*
|
||||
* This module is currently for internal use only
|
||||
*
|
||||
* It defines various built-in and external ordering methods for sparse matrices.
|
||||
* They are typically used to reduce the number of elements during
|
||||
* the sparse matrix decomposition (LLT, LU, QR).
|
||||
* Precisely, in a preprocessing step, a permutation matrix P is computed using
|
||||
* those ordering methods and applied to the columns of the matrix.
|
||||
* Using for instance the sparse Cholesky decomposition, it is expected that
|
||||
* the nonzeros elements in LLT(A*P) will be much smaller than that in LLT(A).
|
||||
*
|
||||
*
|
||||
* Usage :
|
||||
* \code
|
||||
* #include <Eigen/OrderingMethods>
|
||||
* \endcode
|
||||
*
|
||||
* A simple usage is as a template parameter in the sparse decomposition classes :
|
||||
*
|
||||
* \code
|
||||
* SparseLU<MatrixType, COLAMDOrdering<int> > solver;
|
||||
* \endcode
|
||||
*
|
||||
* \code
|
||||
* SparseQR<MatrixType, COLAMDOrdering<int> > solver;
|
||||
* \endcode
|
||||
*
|
||||
* It is possible as well to call directly a particular ordering method for your own purpose,
|
||||
* \code
|
||||
* AMDOrdering<int> ordering;
|
||||
* PermutationMatrix<Dynamic, Dynamic, int> perm;
|
||||
* SparseMatrix<double> A;
|
||||
* //Fill the matrix ...
|
||||
*
|
||||
* ordering(A, perm); // Call AMD
|
||||
* \endcode
|
||||
*
|
||||
* \note Some of these methods (like AMD or METIS), need the sparsity pattern
|
||||
* of the input matrix to be symmetric. When the matrix is structurally unsymmetric,
|
||||
* Eigen computes internally the pattern of \f$A^T*A\f$ before calling the method.
|
||||
* If your matrix is already symmetric (at leat in structure), you can avoid that
|
||||
* by calling the method with a SelfAdjointView type.
|
||||
*
|
||||
* \code
|
||||
* // Call the ordering on the pattern of the lower triangular matrix A
|
||||
* ordering(A.selfadjointView<Lower>(), perm);
|
||||
* \endcode
|
||||
*/
|
||||
|
||||
#ifndef EIGEN_MPL2_ONLY
|
||||
#include "src/OrderingMethods/Amd.h"
|
||||
#endif
|
||||
|
||||
#include "src/OrderingMethods/Ordering.h"
|
||||
#include "src/Core/util/ReenableStupidWarnings.h"
|
||||
|
||||
#endif // EIGEN_ORDERINGMETHODS_MODULE_H
|
||||
|
|
@ -0,0 +1,48 @@
|
|||
// This file is part of Eigen, a lightweight C++ template library
|
||||
// for linear algebra.
|
||||
//
|
||||
// This Source Code Form is subject to the terms of the Mozilla
|
||||
// Public License v. 2.0. If a copy of the MPL was not distributed
|
||||
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
|
||||
|
||||
#ifndef EIGEN_PASTIXSUPPORT_MODULE_H
|
||||
#define EIGEN_PASTIXSUPPORT_MODULE_H
|
||||
|
||||
#include "SparseCore"
|
||||
|
||||
#include "src/Core/util/DisableStupidWarnings.h"
|
||||
|
||||
extern "C" {
|
||||
#include <pastix_nompi.h>
|
||||
#include <pastix.h>
|
||||
}
|
||||
|
||||
#ifdef complex
|
||||
#undef complex
|
||||
#endif
|
||||
|
||||
/** \ingroup Support_modules
|
||||
* \defgroup PaStiXSupport_Module PaStiXSupport module
|
||||
*
|
||||
* This module provides an interface to the <a href="http://pastix.gforge.inria.fr/">PaSTiX</a> library.
|
||||
* PaSTiX is a general \b supernodal, \b parallel and \b opensource sparse solver.
|
||||
* It provides the two following main factorization classes:
|
||||
* - class PastixLLT : a supernodal, parallel LLt Cholesky factorization.
|
||||
* - class PastixLDLT: a supernodal, parallel LDLt Cholesky factorization.
|
||||
* - class PastixLU : a supernodal, parallel LU factorization (optimized for a symmetric pattern).
|
||||
*
|
||||
* \code
|
||||
* #include <Eigen/PaStiXSupport>
|
||||
* \endcode
|
||||
*
|
||||
* In order to use this module, the PaSTiX headers must be accessible from the include paths, and your binary must be linked to the PaSTiX library and its dependencies.
|
||||
* The dependencies depend on how PaSTiX has been compiled.
|
||||
* For a cmake based project, you can use our FindPaSTiX.cmake module to help you in this task.
|
||||
*
|
||||
*/
|
||||
|
||||
#include "src/PaStiXSupport/PaStiXSupport.h"
|
||||
|
||||
#include "src/Core/util/ReenableStupidWarnings.h"
|
||||
|
||||
#endif // EIGEN_PASTIXSUPPORT_MODULE_H
|
||||
|
|
@ -0,0 +1,35 @@
|
|||
// This file is part of Eigen, a lightweight C++ template library
|
||||
// for linear algebra.
|
||||
//
|
||||
// This Source Code Form is subject to the terms of the Mozilla
|
||||
// Public License v. 2.0. If a copy of the MPL was not distributed
|
||||
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
|
||||
|
||||
#ifndef EIGEN_PARDISOSUPPORT_MODULE_H
|
||||
#define EIGEN_PARDISOSUPPORT_MODULE_H
|
||||
|
||||
#include "SparseCore"
|
||||
|
||||
#include "src/Core/util/DisableStupidWarnings.h"
|
||||
|
||||
#include <mkl_pardiso.h>
|
||||
|
||||
/** \ingroup Support_modules
|
||||
* \defgroup PardisoSupport_Module PardisoSupport module
|
||||
*
|
||||
* This module brings support for the Intel(R) MKL PARDISO direct sparse solvers.
|
||||
*
|
||||
* \code
|
||||
* #include <Eigen/PardisoSupport>
|
||||
* \endcode
|
||||
*
|
||||
* In order to use this module, the MKL headers must be accessible from the include paths, and your binary must be linked to the MKL library and its dependencies.
|
||||
* See this \ref TopicUsingIntelMKL "page" for more information on MKL-Eigen integration.
|
||||
*
|
||||
*/
|
||||
|
||||
#include "src/PardisoSupport/PardisoSupport.h"
|
||||
|
||||
#include "src/Core/util/ReenableStupidWarnings.h"
|
||||
|
||||
#endif // EIGEN_PARDISOSUPPORT_MODULE_H
|
||||
|
|
@ -0,0 +1,51 @@
|
|||
// This file is part of Eigen, a lightweight C++ template library
|
||||
// for linear algebra.
|
||||
//
|
||||
// This Source Code Form is subject to the terms of the Mozilla
|
||||
// Public License v. 2.0. If a copy of the MPL was not distributed
|
||||
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
|
||||
|
||||
#ifndef EIGEN_QR_MODULE_H
|
||||
#define EIGEN_QR_MODULE_H
|
||||
|
||||
#include "Core"
|
||||
|
||||
#include "Cholesky"
|
||||
#include "Jacobi"
|
||||
#include "Householder"
|
||||
|
||||
#include "src/Core/util/DisableStupidWarnings.h"
|
||||
|
||||
/** \defgroup QR_Module QR module
|
||||
*
|
||||
*
|
||||
*
|
||||
* This module provides various QR decompositions
|
||||
* This module also provides some MatrixBase methods, including:
|
||||
* - MatrixBase::householderQr()
|
||||
* - MatrixBase::colPivHouseholderQr()
|
||||
* - MatrixBase::fullPivHouseholderQr()
|
||||
*
|
||||
* \code
|
||||
* #include <Eigen/QR>
|
||||
* \endcode
|
||||
*/
|
||||
|
||||
#include "src/QR/HouseholderQR.h"
|
||||
#include "src/QR/FullPivHouseholderQR.h"
|
||||
#include "src/QR/ColPivHouseholderQR.h"
|
||||
#include "src/QR/CompleteOrthogonalDecomposition.h"
|
||||
#ifdef EIGEN_USE_LAPACKE
|
||||
#ifdef EIGEN_USE_MKL
|
||||
#include "mkl_lapacke.h"
|
||||
#else
|
||||
#include "src/misc/lapacke.h"
|
||||
#endif
|
||||
#include "src/QR/HouseholderQR_LAPACKE.h"
|
||||
#include "src/QR/ColPivHouseholderQR_LAPACKE.h"
|
||||
#endif
|
||||
|
||||
#include "src/Core/util/ReenableStupidWarnings.h"
|
||||
|
||||
#endif // EIGEN_QR_MODULE_H
|
||||
/* vim: set filetype=cpp et sw=2 ts=2 ai: */
|
||||
|
|
@ -0,0 +1,40 @@
|
|||
// This file is part of Eigen, a lightweight C++ template library
|
||||
// for linear algebra.
|
||||
//
|
||||
// This Source Code Form is subject to the terms of the Mozilla
|
||||
// Public License v. 2.0. If a copy of the MPL was not distributed
|
||||
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
|
||||
|
||||
#ifndef EIGEN_QTMALLOC_MODULE_H
|
||||
#define EIGEN_QTMALLOC_MODULE_H
|
||||
|
||||
#include "Core"
|
||||
|
||||
#if (!EIGEN_MALLOC_ALREADY_ALIGNED)
|
||||
|
||||
#include "src/Core/util/DisableStupidWarnings.h"
|
||||
|
||||
void *qMalloc(std::size_t size)
|
||||
{
|
||||
return Eigen::internal::aligned_malloc(size);
|
||||
}
|
||||
|
||||
void qFree(void *ptr)
|
||||
{
|
||||
Eigen::internal::aligned_free(ptr);
|
||||
}
|
||||
|
||||
void *qRealloc(void *ptr, std::size_t size)
|
||||
{
|
||||
void* newPtr = Eigen::internal::aligned_malloc(size);
|
||||
std::memcpy(newPtr, ptr, size);
|
||||
Eigen::internal::aligned_free(ptr);
|
||||
return newPtr;
|
||||
}
|
||||
|
||||
#include "src/Core/util/ReenableStupidWarnings.h"
|
||||
|
||||
#endif
|
||||
|
||||
#endif // EIGEN_QTMALLOC_MODULE_H
|
||||
/* vim: set filetype=cpp et sw=2 ts=2 ai: */
|
||||
|
|
@ -0,0 +1,34 @@
|
|||
// This file is part of Eigen, a lightweight C++ template library
|
||||
// for linear algebra.
|
||||
//
|
||||
// This Source Code Form is subject to the terms of the Mozilla
|
||||
// Public License v. 2.0. If a copy of the MPL was not distributed
|
||||
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
|
||||
|
||||
#ifndef EIGEN_SPQRSUPPORT_MODULE_H
|
||||
#define EIGEN_SPQRSUPPORT_MODULE_H
|
||||
|
||||
#include "SparseCore"
|
||||
|
||||
#include "src/Core/util/DisableStupidWarnings.h"
|
||||
|
||||
#include "SuiteSparseQR.hpp"
|
||||
|
||||
/** \ingroup Support_modules
|
||||
* \defgroup SPQRSupport_Module SuiteSparseQR module
|
||||
*
|
||||
* This module provides an interface to the SPQR library, which is part of the <a href="http://www.suitesparse.com">suitesparse</a> package.
|
||||
*
|
||||
* \code
|
||||
* #include <Eigen/SPQRSupport>
|
||||
* \endcode
|
||||
*
|
||||
* In order to use this module, the SPQR headers must be accessible from the include paths, and your binary must be linked to the SPQR library and its dependencies (Cholmod, AMD, COLAMD,...).
|
||||
* For a cmake based project, you can use our FindSPQR.cmake and FindCholmod.Cmake modules
|
||||
*
|
||||
*/
|
||||
|
||||
#include "src/CholmodSupport/CholmodSupport.h"
|
||||
#include "src/SPQRSupport/SuiteSparseQRSupport.h"
|
||||
|
||||
#endif
|
||||
|
|
@ -0,0 +1,51 @@
|
|||
// This file is part of Eigen, a lightweight C++ template library
|
||||
// for linear algebra.
|
||||
//
|
||||
// This Source Code Form is subject to the terms of the Mozilla
|
||||
// Public License v. 2.0. If a copy of the MPL was not distributed
|
||||
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
|
||||
|
||||
#ifndef EIGEN_SVD_MODULE_H
|
||||
#define EIGEN_SVD_MODULE_H
|
||||
|
||||
#include "QR"
|
||||
#include "Householder"
|
||||
#include "Jacobi"
|
||||
|
||||
#include "src/Core/util/DisableStupidWarnings.h"
|
||||
|
||||
/** \defgroup SVD_Module SVD module
|
||||
*
|
||||
*
|
||||
*
|
||||
* This module provides SVD decomposition for matrices (both real and complex).
|
||||
* Two decomposition algorithms are provided:
|
||||
* - JacobiSVD implementing two-sided Jacobi iterations is numerically very accurate, fast for small matrices, but very slow for larger ones.
|
||||
* - BDCSVD implementing a recursive divide & conquer strategy on top of an upper-bidiagonalization which remains fast for large problems.
|
||||
* These decompositions are accessible via the respective classes and following MatrixBase methods:
|
||||
* - MatrixBase::jacobiSvd()
|
||||
* - MatrixBase::bdcSvd()
|
||||
*
|
||||
* \code
|
||||
* #include <Eigen/SVD>
|
||||
* \endcode
|
||||
*/
|
||||
|
||||
#include "src/misc/RealSvd2x2.h"
|
||||
#include "src/SVD/UpperBidiagonalization.h"
|
||||
#include "src/SVD/SVDBase.h"
|
||||
#include "src/SVD/JacobiSVD.h"
|
||||
#include "src/SVD/BDCSVD.h"
|
||||
#if defined(EIGEN_USE_LAPACKE) && !defined(EIGEN_USE_LAPACKE_STRICT)
|
||||
#ifdef EIGEN_USE_MKL
|
||||
#include "mkl_lapacke.h"
|
||||
#else
|
||||
#include "src/misc/lapacke.h"
|
||||
#endif
|
||||
#include "src/SVD/JacobiSVD_LAPACKE.h"
|
||||
#endif
|
||||
|
||||
#include "src/Core/util/ReenableStupidWarnings.h"
|
||||
|
||||
#endif // EIGEN_SVD_MODULE_H
|
||||
/* vim: set filetype=cpp et sw=2 ts=2 ai: */
|
||||
|
|
@ -0,0 +1,36 @@
|
|||
// This file is part of Eigen, a lightweight C++ template library
|
||||
// for linear algebra.
|
||||
//
|
||||
// This Source Code Form is subject to the terms of the Mozilla
|
||||
// Public License v. 2.0. If a copy of the MPL was not distributed
|
||||
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
|
||||
|
||||
#ifndef EIGEN_SPARSE_MODULE_H
|
||||
#define EIGEN_SPARSE_MODULE_H
|
||||
|
||||
/** \defgroup Sparse_Module Sparse meta-module
|
||||
*
|
||||
* Meta-module including all related modules:
|
||||
* - \ref SparseCore_Module
|
||||
* - \ref OrderingMethods_Module
|
||||
* - \ref SparseCholesky_Module
|
||||
* - \ref SparseLU_Module
|
||||
* - \ref SparseQR_Module
|
||||
* - \ref IterativeLinearSolvers_Module
|
||||
*
|
||||
\code
|
||||
#include <Eigen/Sparse>
|
||||
\endcode
|
||||
*/
|
||||
|
||||
#include "SparseCore"
|
||||
#include "OrderingMethods"
|
||||
#ifndef EIGEN_MPL2_ONLY
|
||||
#include "SparseCholesky"
|
||||
#endif
|
||||
#include "SparseLU"
|
||||
#include "SparseQR"
|
||||
#include "IterativeLinearSolvers"
|
||||
|
||||
#endif // EIGEN_SPARSE_MODULE_H
|
||||
|
||||
|
|
@ -0,0 +1,45 @@
|
|||
// This file is part of Eigen, a lightweight C++ template library
|
||||
// for linear algebra.
|
||||
//
|
||||
// Copyright (C) 2008-2013 Gael Guennebaud <gael.guennebaud@inria.fr>
|
||||
//
|
||||
// This Source Code Form is subject to the terms of the Mozilla
|
||||
// Public License v. 2.0. If a copy of the MPL was not distributed
|
||||
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
|
||||
|
||||
#ifndef EIGEN_SPARSECHOLESKY_MODULE_H
|
||||
#define EIGEN_SPARSECHOLESKY_MODULE_H
|
||||
|
||||
#include "SparseCore"
|
||||
#include "OrderingMethods"
|
||||
|
||||
#include "src/Core/util/DisableStupidWarnings.h"
|
||||
|
||||
/**
|
||||
* \defgroup SparseCholesky_Module SparseCholesky module
|
||||
*
|
||||
* This module currently provides two variants of the direct sparse Cholesky decomposition for selfadjoint (hermitian) matrices.
|
||||
* Those decompositions are accessible via the following classes:
|
||||
* - SimplicialLLt,
|
||||
* - SimplicialLDLt
|
||||
*
|
||||
* Such problems can also be solved using the ConjugateGradient solver from the IterativeLinearSolvers module.
|
||||
*
|
||||
* \code
|
||||
* #include <Eigen/SparseCholesky>
|
||||
* \endcode
|
||||
*/
|
||||
|
||||
#ifdef EIGEN_MPL2_ONLY
|
||||
#error The SparseCholesky module has nothing to offer in MPL2 only mode
|
||||
#endif
|
||||
|
||||
#include "src/SparseCholesky/SimplicialCholesky.h"
|
||||
|
||||
#ifndef EIGEN_MPL2_ONLY
|
||||
#include "src/SparseCholesky/SimplicialCholesky_impl.h"
|
||||
#endif
|
||||
|
||||
#include "src/Core/util/ReenableStupidWarnings.h"
|
||||
|
||||
#endif // EIGEN_SPARSECHOLESKY_MODULE_H
|
||||
|
|
@ -0,0 +1,69 @@
|
|||
// This file is part of Eigen, a lightweight C++ template library
|
||||
// for linear algebra.
|
||||
//
|
||||
// This Source Code Form is subject to the terms of the Mozilla
|
||||
// Public License v. 2.0. If a copy of the MPL was not distributed
|
||||
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
|
||||
|
||||
#ifndef EIGEN_SPARSECORE_MODULE_H
|
||||
#define EIGEN_SPARSECORE_MODULE_H
|
||||
|
||||
#include "Core"
|
||||
|
||||
#include "src/Core/util/DisableStupidWarnings.h"
|
||||
|
||||
#include <vector>
|
||||
#include <map>
|
||||
#include <cstdlib>
|
||||
#include <cstring>
|
||||
#include <algorithm>
|
||||
|
||||
/**
|
||||
* \defgroup SparseCore_Module SparseCore module
|
||||
*
|
||||
* This module provides a sparse matrix representation, and basic associated matrix manipulations
|
||||
* and operations.
|
||||
*
|
||||
* See the \ref TutorialSparse "Sparse tutorial"
|
||||
*
|
||||
* \code
|
||||
* #include <Eigen/SparseCore>
|
||||
* \endcode
|
||||
*
|
||||
* This module depends on: Core.
|
||||
*/
|
||||
|
||||
#include "src/SparseCore/SparseUtil.h"
|
||||
#include "src/SparseCore/SparseMatrixBase.h"
|
||||
#include "src/SparseCore/SparseAssign.h"
|
||||
#include "src/SparseCore/CompressedStorage.h"
|
||||
#include "src/SparseCore/AmbiVector.h"
|
||||
#include "src/SparseCore/SparseCompressedBase.h"
|
||||
#include "src/SparseCore/SparseMatrix.h"
|
||||
#include "src/SparseCore/SparseMap.h"
|
||||
#include "src/SparseCore/MappedSparseMatrix.h"
|
||||
#include "src/SparseCore/SparseVector.h"
|
||||
#include "src/SparseCore/SparseRef.h"
|
||||
#include "src/SparseCore/SparseCwiseUnaryOp.h"
|
||||
#include "src/SparseCore/SparseCwiseBinaryOp.h"
|
||||
#include "src/SparseCore/SparseTranspose.h"
|
||||
#include "src/SparseCore/SparseBlock.h"
|
||||
#include "src/SparseCore/SparseDot.h"
|
||||
#include "src/SparseCore/SparseRedux.h"
|
||||
#include "src/SparseCore/SparseView.h"
|
||||
#include "src/SparseCore/SparseDiagonalProduct.h"
|
||||
#include "src/SparseCore/ConservativeSparseSparseProduct.h"
|
||||
#include "src/SparseCore/SparseSparseProductWithPruning.h"
|
||||
#include "src/SparseCore/SparseProduct.h"
|
||||
#include "src/SparseCore/SparseDenseProduct.h"
|
||||
#include "src/SparseCore/SparseSelfAdjointView.h"
|
||||
#include "src/SparseCore/SparseTriangularView.h"
|
||||
#include "src/SparseCore/TriangularSolver.h"
|
||||
#include "src/SparseCore/SparsePermutation.h"
|
||||
#include "src/SparseCore/SparseFuzzy.h"
|
||||
#include "src/SparseCore/SparseSolverBase.h"
|
||||
|
||||
#include "src/Core/util/ReenableStupidWarnings.h"
|
||||
|
||||
#endif // EIGEN_SPARSECORE_MODULE_H
|
||||
|
||||
|
|
@ -0,0 +1,46 @@
|
|||
// This file is part of Eigen, a lightweight C++ template library
|
||||
// for linear algebra.
|
||||
//
|
||||
// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
|
||||
// Copyright (C) 2012 Gael Guennebaud <gael.guennebaud@inria.fr>
|
||||
//
|
||||
// This Source Code Form is subject to the terms of the Mozilla
|
||||
// Public License v. 2.0. If a copy of the MPL was not distributed
|
||||
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
|
||||
|
||||
#ifndef EIGEN_SPARSELU_MODULE_H
|
||||
#define EIGEN_SPARSELU_MODULE_H
|
||||
|
||||
#include "SparseCore"
|
||||
|
||||
/**
|
||||
* \defgroup SparseLU_Module SparseLU module
|
||||
* This module defines a supernodal factorization of general sparse matrices.
|
||||
* The code is fully optimized for supernode-panel updates with specialized kernels.
|
||||
* Please, see the documentation of the SparseLU class for more details.
|
||||
*/
|
||||
|
||||
// Ordering interface
|
||||
#include "OrderingMethods"
|
||||
|
||||
#include "src/SparseLU/SparseLU_gemm_kernel.h"
|
||||
|
||||
#include "src/SparseLU/SparseLU_Structs.h"
|
||||
#include "src/SparseLU/SparseLU_SupernodalMatrix.h"
|
||||
#include "src/SparseLU/SparseLUImpl.h"
|
||||
#include "src/SparseCore/SparseColEtree.h"
|
||||
#include "src/SparseLU/SparseLU_Memory.h"
|
||||
#include "src/SparseLU/SparseLU_heap_relax_snode.h"
|
||||
#include "src/SparseLU/SparseLU_relax_snode.h"
|
||||
#include "src/SparseLU/SparseLU_pivotL.h"
|
||||
#include "src/SparseLU/SparseLU_panel_dfs.h"
|
||||
#include "src/SparseLU/SparseLU_kernel_bmod.h"
|
||||
#include "src/SparseLU/SparseLU_panel_bmod.h"
|
||||
#include "src/SparseLU/SparseLU_column_dfs.h"
|
||||
#include "src/SparseLU/SparseLU_column_bmod.h"
|
||||
#include "src/SparseLU/SparseLU_copy_to_ucol.h"
|
||||
#include "src/SparseLU/SparseLU_pruneL.h"
|
||||
#include "src/SparseLU/SparseLU_Utils.h"
|
||||
#include "src/SparseLU/SparseLU.h"
|
||||
|
||||
#endif // EIGEN_SPARSELU_MODULE_H
|
||||
|
|
@ -0,0 +1,36 @@
|
|||
// This file is part of Eigen, a lightweight C++ template library
|
||||
// for linear algebra.
|
||||
//
|
||||
// This Source Code Form is subject to the terms of the Mozilla
|
||||
// Public License v. 2.0. If a copy of the MPL was not distributed
|
||||
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
|
||||
|
||||
#ifndef EIGEN_SPARSEQR_MODULE_H
|
||||
#define EIGEN_SPARSEQR_MODULE_H
|
||||
|
||||
#include "SparseCore"
|
||||
#include "OrderingMethods"
|
||||
#include "src/Core/util/DisableStupidWarnings.h"
|
||||
|
||||
/** \defgroup SparseQR_Module SparseQR module
|
||||
* \brief Provides QR decomposition for sparse matrices
|
||||
*
|
||||
* This module provides a simplicial version of the left-looking Sparse QR decomposition.
|
||||
* The columns of the input matrix should be reordered to limit the fill-in during the
|
||||
* decomposition. Built-in methods (COLAMD, AMD) or external methods (METIS) can be used to this end.
|
||||
* See the \link OrderingMethods_Module OrderingMethods\endlink module for the list
|
||||
* of built-in and external ordering methods.
|
||||
*
|
||||
* \code
|
||||
* #include <Eigen/SparseQR>
|
||||
* \endcode
|
||||
*
|
||||
*
|
||||
*/
|
||||
|
||||
#include "src/SparseCore/SparseColEtree.h"
|
||||
#include "src/SparseQR/SparseQR.h"
|
||||
|
||||
#include "src/Core/util/ReenableStupidWarnings.h"
|
||||
|
||||
#endif
|
||||
|
|
@ -0,0 +1,27 @@
|
|||
// This file is part of Eigen, a lightweight C++ template library
|
||||
// for linear algebra.
|
||||
//
|
||||
// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
|
||||
// Copyright (C) 2009 Hauke Heibel <hauke.heibel@googlemail.com>
|
||||
//
|
||||
// This Source Code Form is subject to the terms of the Mozilla
|
||||
// Public License v. 2.0. If a copy of the MPL was not distributed
|
||||
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
|
||||
|
||||
#ifndef EIGEN_STDDEQUE_MODULE_H
|
||||
#define EIGEN_STDDEQUE_MODULE_H
|
||||
|
||||
#include "Core"
|
||||
#include <deque>
|
||||
|
||||
#if EIGEN_COMP_MSVC && EIGEN_OS_WIN64 && (EIGEN_MAX_STATIC_ALIGN_BYTES<=16) /* MSVC auto aligns up to 16 bytes in 64 bit builds */
|
||||
|
||||
#define EIGEN_DEFINE_STL_DEQUE_SPECIALIZATION(...)
|
||||
|
||||
#else
|
||||
|
||||
#include "src/StlSupport/StdDeque.h"
|
||||
|
||||
#endif
|
||||
|
||||
#endif // EIGEN_STDDEQUE_MODULE_H
|
||||
|
|
@ -0,0 +1,26 @@
|
|||
// This file is part of Eigen, a lightweight C++ template library
|
||||
// for linear algebra.
|
||||
//
|
||||
// Copyright (C) 2009 Hauke Heibel <hauke.heibel@googlemail.com>
|
||||
//
|
||||
// This Source Code Form is subject to the terms of the Mozilla
|
||||
// Public License v. 2.0. If a copy of the MPL was not distributed
|
||||
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
|
||||
|
||||
#ifndef EIGEN_STDLIST_MODULE_H
|
||||
#define EIGEN_STDLIST_MODULE_H
|
||||
|
||||
#include "Core"
|
||||
#include <list>
|
||||
|
||||
#if EIGEN_COMP_MSVC && EIGEN_OS_WIN64 && (EIGEN_MAX_STATIC_ALIGN_BYTES<=16) /* MSVC auto aligns up to 16 bytes in 64 bit builds */
|
||||
|
||||
#define EIGEN_DEFINE_STL_LIST_SPECIALIZATION(...)
|
||||
|
||||
#else
|
||||
|
||||
#include "src/StlSupport/StdList.h"
|
||||
|
||||
#endif
|
||||
|
||||
#endif // EIGEN_STDLIST_MODULE_H
|
||||
|
|
@ -0,0 +1,27 @@
|
|||
// This file is part of Eigen, a lightweight C++ template library
|
||||
// for linear algebra.
|
||||
//
|
||||
// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
|
||||
// Copyright (C) 2009 Hauke Heibel <hauke.heibel@googlemail.com>
|
||||
//
|
||||
// This Source Code Form is subject to the terms of the Mozilla
|
||||
// Public License v. 2.0. If a copy of the MPL was not distributed
|
||||
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
|
||||
|
||||
#ifndef EIGEN_STDVECTOR_MODULE_H
|
||||
#define EIGEN_STDVECTOR_MODULE_H
|
||||
|
||||
#include "Core"
|
||||
#include <vector>
|
||||
|
||||
#if EIGEN_COMP_MSVC && EIGEN_OS_WIN64 && (EIGEN_MAX_STATIC_ALIGN_BYTES<=16) /* MSVC auto aligns up to 16 bytes in 64 bit builds */
|
||||
|
||||
#define EIGEN_DEFINE_STL_VECTOR_SPECIALIZATION(...)
|
||||
|
||||
#else
|
||||
|
||||
#include "src/StlSupport/StdVector.h"
|
||||
|
||||
#endif
|
||||
|
||||
#endif // EIGEN_STDVECTOR_MODULE_H
|
||||
|
|
@ -0,0 +1,64 @@
|
|||
// This file is part of Eigen, a lightweight C++ template library
|
||||
// for linear algebra.
|
||||
//
|
||||
// This Source Code Form is subject to the terms of the Mozilla
|
||||
// Public License v. 2.0. If a copy of the MPL was not distributed
|
||||
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
|
||||
|
||||
#ifndef EIGEN_SUPERLUSUPPORT_MODULE_H
|
||||
#define EIGEN_SUPERLUSUPPORT_MODULE_H
|
||||
|
||||
#include "SparseCore"
|
||||
|
||||
#include "src/Core/util/DisableStupidWarnings.h"
|
||||
|
||||
#ifdef EMPTY
|
||||
#define EIGEN_EMPTY_WAS_ALREADY_DEFINED
|
||||
#endif
|
||||
|
||||
typedef int int_t;
|
||||
#include <slu_Cnames.h>
|
||||
#include <supermatrix.h>
|
||||
#include <slu_util.h>
|
||||
|
||||
// slu_util.h defines a preprocessor token named EMPTY which is really polluting,
|
||||
// so we remove it in favor of a SUPERLU_EMPTY token.
|
||||
// If EMPTY was already defined then we don't undef it.
|
||||
|
||||
#if defined(EIGEN_EMPTY_WAS_ALREADY_DEFINED)
|
||||
# undef EIGEN_EMPTY_WAS_ALREADY_DEFINED
|
||||
#elif defined(EMPTY)
|
||||
# undef EMPTY
|
||||
#endif
|
||||
|
||||
#define SUPERLU_EMPTY (-1)
|
||||
|
||||
namespace Eigen { struct SluMatrix; }
|
||||
|
||||
/** \ingroup Support_modules
|
||||
* \defgroup SuperLUSupport_Module SuperLUSupport module
|
||||
*
|
||||
* This module provides an interface to the <a href="http://crd-legacy.lbl.gov/~xiaoye/SuperLU/">SuperLU</a> library.
|
||||
* It provides the following factorization class:
|
||||
* - class SuperLU: a supernodal sequential LU factorization.
|
||||
* - class SuperILU: a supernodal sequential incomplete LU factorization (to be used as a preconditioner for iterative methods).
|
||||
*
|
||||
* \warning This wrapper requires at least versions 4.0 of SuperLU. The 3.x versions are not supported.
|
||||
*
|
||||
* \warning When including this module, you have to use SUPERLU_EMPTY instead of EMPTY which is no longer defined because it is too polluting.
|
||||
*
|
||||
* \code
|
||||
* #include <Eigen/SuperLUSupport>
|
||||
* \endcode
|
||||
*
|
||||
* In order to use this module, the superlu headers must be accessible from the include paths, and your binary must be linked to the superlu library and its dependencies.
|
||||
* The dependencies depend on how superlu has been compiled.
|
||||
* For a cmake based project, you can use our FindSuperLU.cmake module to help you in this task.
|
||||
*
|
||||
*/
|
||||
|
||||
#include "src/SuperLUSupport/SuperLUSupport.h"
|
||||
|
||||
#include "src/Core/util/ReenableStupidWarnings.h"
|
||||
|
||||
#endif // EIGEN_SUPERLUSUPPORT_MODULE_H
|
||||
|
|
@ -0,0 +1,40 @@
|
|||
// This file is part of Eigen, a lightweight C++ template library
|
||||
// for linear algebra.
|
||||
//
|
||||
// This Source Code Form is subject to the terms of the Mozilla
|
||||
// Public License v. 2.0. If a copy of the MPL was not distributed
|
||||
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
|
||||
|
||||
#ifndef EIGEN_UMFPACKSUPPORT_MODULE_H
|
||||
#define EIGEN_UMFPACKSUPPORT_MODULE_H
|
||||
|
||||
#include "SparseCore"
|
||||
|
||||
#include "src/Core/util/DisableStupidWarnings.h"
|
||||
|
||||
extern "C" {
|
||||
#include <umfpack.h>
|
||||
}
|
||||
|
||||
/** \ingroup Support_modules
|
||||
* \defgroup UmfPackSupport_Module UmfPackSupport module
|
||||
*
|
||||
* This module provides an interface to the UmfPack library which is part of the <a href="http://www.suitesparse.com">suitesparse</a> package.
|
||||
* It provides the following factorization class:
|
||||
* - class UmfPackLU: a multifrontal sequential LU factorization.
|
||||
*
|
||||
* \code
|
||||
* #include <Eigen/UmfPackSupport>
|
||||
* \endcode
|
||||
*
|
||||
* In order to use this module, the umfpack headers must be accessible from the include paths, and your binary must be linked to the umfpack library and its dependencies.
|
||||
* The dependencies depend on how umfpack has been compiled.
|
||||
* For a cmake based project, you can use our FindUmfPack.cmake module to help you in this task.
|
||||
*
|
||||
*/
|
||||
|
||||
#include "src/UmfPackSupport/UmfPackSupport.h"
|
||||
|
||||
#include "src/Core/util/ReenableStupidWarnings.h"
|
||||
|
||||
#endif // EIGEN_UMFPACKSUPPORT_MODULE_H
|
||||
|
|
@ -0,0 +1,673 @@
|
|||
// This file is part of Eigen, a lightweight C++ template library
|
||||
// for linear algebra.
|
||||
//
|
||||
// Copyright (C) 2008-2011 Gael Guennebaud <gael.guennebaud@inria.fr>
|
||||
// Copyright (C) 2009 Keir Mierle <mierle@gmail.com>
|
||||
// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
|
||||
// Copyright (C) 2011 Timothy E. Holy <tim.holy@gmail.com >
|
||||
//
|
||||
// This Source Code Form is subject to the terms of the Mozilla
|
||||
// Public License v. 2.0. If a copy of the MPL was not distributed
|
||||
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
|
||||
|
||||
#ifndef EIGEN_LDLT_H
|
||||
#define EIGEN_LDLT_H
|
||||
|
||||
namespace Eigen {
|
||||
|
||||
namespace internal {
|
||||
template<typename MatrixType, int UpLo> struct LDLT_Traits;
|
||||
|
||||
// PositiveSemiDef means positive semi-definite and non-zero; same for NegativeSemiDef
|
||||
enum SignMatrix { PositiveSemiDef, NegativeSemiDef, ZeroSign, Indefinite };
|
||||
}
|
||||
|
||||
/** \ingroup Cholesky_Module
|
||||
*
|
||||
* \class LDLT
|
||||
*
|
||||
* \brief Robust Cholesky decomposition of a matrix with pivoting
|
||||
*
|
||||
* \tparam _MatrixType the type of the matrix of which to compute the LDL^T Cholesky decomposition
|
||||
* \tparam _UpLo the triangular part that will be used for the decompositon: Lower (default) or Upper.
|
||||
* The other triangular part won't be read.
|
||||
*
|
||||
* Perform a robust Cholesky decomposition of a positive semidefinite or negative semidefinite
|
||||
* matrix \f$ A \f$ such that \f$ A = P^TLDL^*P \f$, where P is a permutation matrix, L
|
||||
* is lower triangular with a unit diagonal and D is a diagonal matrix.
|
||||
*
|
||||
* The decomposition uses pivoting to ensure stability, so that L will have
|
||||
* zeros in the bottom right rank(A) - n submatrix. Avoiding the square root
|
||||
* on D also stabilizes the computation.
|
||||
*
|
||||
* Remember that Cholesky decompositions are not rank-revealing. Also, do not use a Cholesky
|
||||
* decomposition to determine whether a system of equations has a solution.
|
||||
*
|
||||
* This class supports the \link InplaceDecomposition inplace decomposition \endlink mechanism.
|
||||
*
|
||||
* \sa MatrixBase::ldlt(), SelfAdjointView::ldlt(), class LLT
|
||||
*/
|
||||
template<typename _MatrixType, int _UpLo> class LDLT
|
||||
{
|
||||
public:
|
||||
typedef _MatrixType MatrixType;
|
||||
enum {
|
||||
RowsAtCompileTime = MatrixType::RowsAtCompileTime,
|
||||
ColsAtCompileTime = MatrixType::ColsAtCompileTime,
|
||||
MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
|
||||
MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime,
|
||||
UpLo = _UpLo
|
||||
};
|
||||
typedef typename MatrixType::Scalar Scalar;
|
||||
typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
|
||||
typedef Eigen::Index Index; ///< \deprecated since Eigen 3.3
|
||||
typedef typename MatrixType::StorageIndex StorageIndex;
|
||||
typedef Matrix<Scalar, RowsAtCompileTime, 1, 0, MaxRowsAtCompileTime, 1> TmpMatrixType;
|
||||
|
||||
typedef Transpositions<RowsAtCompileTime, MaxRowsAtCompileTime> TranspositionType;
|
||||
typedef PermutationMatrix<RowsAtCompileTime, MaxRowsAtCompileTime> PermutationType;
|
||||
|
||||
typedef internal::LDLT_Traits<MatrixType,UpLo> Traits;
|
||||
|
||||
/** \brief Default Constructor.
|
||||
*
|
||||
* The default constructor is useful in cases in which the user intends to
|
||||
* perform decompositions via LDLT::compute(const MatrixType&).
|
||||
*/
|
||||
LDLT()
|
||||
: m_matrix(),
|
||||
m_transpositions(),
|
||||
m_sign(internal::ZeroSign),
|
||||
m_isInitialized(false)
|
||||
{}
|
||||
|
||||
/** \brief Default Constructor with memory preallocation
|
||||
*
|
||||
* Like the default constructor but with preallocation of the internal data
|
||||
* according to the specified problem \a size.
|
||||
* \sa LDLT()
|
||||
*/
|
||||
explicit LDLT(Index size)
|
||||
: m_matrix(size, size),
|
||||
m_transpositions(size),
|
||||
m_temporary(size),
|
||||
m_sign(internal::ZeroSign),
|
||||
m_isInitialized(false)
|
||||
{}
|
||||
|
||||
/** \brief Constructor with decomposition
|
||||
*
|
||||
* This calculates the decomposition for the input \a matrix.
|
||||
*
|
||||
* \sa LDLT(Index size)
|
||||
*/
|
||||
template<typename InputType>
|
||||
explicit LDLT(const EigenBase<InputType>& matrix)
|
||||
: m_matrix(matrix.rows(), matrix.cols()),
|
||||
m_transpositions(matrix.rows()),
|
||||
m_temporary(matrix.rows()),
|
||||
m_sign(internal::ZeroSign),
|
||||
m_isInitialized(false)
|
||||
{
|
||||
compute(matrix.derived());
|
||||
}
|
||||
|
||||
/** \brief Constructs a LDLT factorization from a given matrix
|
||||
*
|
||||
* This overloaded constructor is provided for \link InplaceDecomposition inplace decomposition \endlink when \c MatrixType is a Eigen::Ref.
|
||||
*
|
||||
* \sa LDLT(const EigenBase&)
|
||||
*/
|
||||
template<typename InputType>
|
||||
explicit LDLT(EigenBase<InputType>& matrix)
|
||||
: m_matrix(matrix.derived()),
|
||||
m_transpositions(matrix.rows()),
|
||||
m_temporary(matrix.rows()),
|
||||
m_sign(internal::ZeroSign),
|
||||
m_isInitialized(false)
|
||||
{
|
||||
compute(matrix.derived());
|
||||
}
|
||||
|
||||
/** Clear any existing decomposition
|
||||
* \sa rankUpdate(w,sigma)
|
||||
*/
|
||||
void setZero()
|
||||
{
|
||||
m_isInitialized = false;
|
||||
}
|
||||
|
||||
/** \returns a view of the upper triangular matrix U */
|
||||
inline typename Traits::MatrixU matrixU() const
|
||||
{
|
||||
eigen_assert(m_isInitialized && "LDLT is not initialized.");
|
||||
return Traits::getU(m_matrix);
|
||||
}
|
||||
|
||||
/** \returns a view of the lower triangular matrix L */
|
||||
inline typename Traits::MatrixL matrixL() const
|
||||
{
|
||||
eigen_assert(m_isInitialized && "LDLT is not initialized.");
|
||||
return Traits::getL(m_matrix);
|
||||
}
|
||||
|
||||
/** \returns the permutation matrix P as a transposition sequence.
|
||||
*/
|
||||
inline const TranspositionType& transpositionsP() const
|
||||
{
|
||||
eigen_assert(m_isInitialized && "LDLT is not initialized.");
|
||||
return m_transpositions;
|
||||
}
|
||||
|
||||
/** \returns the coefficients of the diagonal matrix D */
|
||||
inline Diagonal<const MatrixType> vectorD() const
|
||||
{
|
||||
eigen_assert(m_isInitialized && "LDLT is not initialized.");
|
||||
return m_matrix.diagonal();
|
||||
}
|
||||
|
||||
/** \returns true if the matrix is positive (semidefinite) */
|
||||
inline bool isPositive() const
|
||||
{
|
||||
eigen_assert(m_isInitialized && "LDLT is not initialized.");
|
||||
return m_sign == internal::PositiveSemiDef || m_sign == internal::ZeroSign;
|
||||
}
|
||||
|
||||
/** \returns true if the matrix is negative (semidefinite) */
|
||||
inline bool isNegative(void) const
|
||||
{
|
||||
eigen_assert(m_isInitialized && "LDLT is not initialized.");
|
||||
return m_sign == internal::NegativeSemiDef || m_sign == internal::ZeroSign;
|
||||
}
|
||||
|
||||
/** \returns a solution x of \f$ A x = b \f$ using the current decomposition of A.
|
||||
*
|
||||
* This function also supports in-place solves using the syntax <tt>x = decompositionObject.solve(x)</tt> .
|
||||
*
|
||||
* \note_about_checking_solutions
|
||||
*
|
||||
* More precisely, this method solves \f$ A x = b \f$ using the decomposition \f$ A = P^T L D L^* P \f$
|
||||
* by solving the systems \f$ P^T y_1 = b \f$, \f$ L y_2 = y_1 \f$, \f$ D y_3 = y_2 \f$,
|
||||
* \f$ L^* y_4 = y_3 \f$ and \f$ P x = y_4 \f$ in succession. If the matrix \f$ A \f$ is singular, then
|
||||
* \f$ D \f$ will also be singular (all the other matrices are invertible). In that case, the
|
||||
* least-square solution of \f$ D y_3 = y_2 \f$ is computed. This does not mean that this function
|
||||
* computes the least-square solution of \f$ A x = b \f$ is \f$ A \f$ is singular.
|
||||
*
|
||||
* \sa MatrixBase::ldlt(), SelfAdjointView::ldlt()
|
||||
*/
|
||||
template<typename Rhs>
|
||||
inline const Solve<LDLT, Rhs>
|
||||
solve(const MatrixBase<Rhs>& b) const
|
||||
{
|
||||
eigen_assert(m_isInitialized && "LDLT is not initialized.");
|
||||
eigen_assert(m_matrix.rows()==b.rows()
|
||||
&& "LDLT::solve(): invalid number of rows of the right hand side matrix b");
|
||||
return Solve<LDLT, Rhs>(*this, b.derived());
|
||||
}
|
||||
|
||||
template<typename Derived>
|
||||
bool solveInPlace(MatrixBase<Derived> &bAndX) const;
|
||||
|
||||
template<typename InputType>
|
||||
LDLT& compute(const EigenBase<InputType>& matrix);
|
||||
|
||||
/** \returns an estimate of the reciprocal condition number of the matrix of
|
||||
* which \c *this is the LDLT decomposition.
|
||||
*/
|
||||
RealScalar rcond() const
|
||||
{
|
||||
eigen_assert(m_isInitialized && "LDLT is not initialized.");
|
||||
return internal::rcond_estimate_helper(m_l1_norm, *this);
|
||||
}
|
||||
|
||||
template <typename Derived>
|
||||
LDLT& rankUpdate(const MatrixBase<Derived>& w, const RealScalar& alpha=1);
|
||||
|
||||
/** \returns the internal LDLT decomposition matrix
|
||||
*
|
||||
* TODO: document the storage layout
|
||||
*/
|
||||
inline const MatrixType& matrixLDLT() const
|
||||
{
|
||||
eigen_assert(m_isInitialized && "LDLT is not initialized.");
|
||||
return m_matrix;
|
||||
}
|
||||
|
||||
MatrixType reconstructedMatrix() const;
|
||||
|
||||
/** \returns the adjoint of \c *this, that is, a const reference to the decomposition itself as the underlying matrix is self-adjoint.
|
||||
*
|
||||
* This method is provided for compatibility with other matrix decompositions, thus enabling generic code such as:
|
||||
* \code x = decomposition.adjoint().solve(b) \endcode
|
||||
*/
|
||||
const LDLT& adjoint() const { return *this; };
|
||||
|
||||
inline Index rows() const { return m_matrix.rows(); }
|
||||
inline Index cols() const { return m_matrix.cols(); }
|
||||
|
||||
/** \brief Reports whether previous computation was successful.
|
||||
*
|
||||
* \returns \c Success if computation was succesful,
|
||||
* \c NumericalIssue if the factorization failed because of a zero pivot.
|
||||
*/
|
||||
ComputationInfo info() const
|
||||
{
|
||||
eigen_assert(m_isInitialized && "LDLT is not initialized.");
|
||||
return m_info;
|
||||
}
|
||||
|
||||
#ifndef EIGEN_PARSED_BY_DOXYGEN
|
||||
template<typename RhsType, typename DstType>
|
||||
EIGEN_DEVICE_FUNC
|
||||
void _solve_impl(const RhsType &rhs, DstType &dst) const;
|
||||
#endif
|
||||
|
||||
protected:
|
||||
|
||||
static void check_template_parameters()
|
||||
{
|
||||
EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar);
|
||||
}
|
||||
|
||||
/** \internal
|
||||
* Used to compute and store the Cholesky decomposition A = L D L^* = U^* D U.
|
||||
* The strict upper part is used during the decomposition, the strict lower
|
||||
* part correspond to the coefficients of L (its diagonal is equal to 1 and
|
||||
* is not stored), and the diagonal entries correspond to D.
|
||||
*/
|
||||
MatrixType m_matrix;
|
||||
RealScalar m_l1_norm;
|
||||
TranspositionType m_transpositions;
|
||||
TmpMatrixType m_temporary;
|
||||
internal::SignMatrix m_sign;
|
||||
bool m_isInitialized;
|
||||
ComputationInfo m_info;
|
||||
};
|
||||
|
||||
namespace internal {
|
||||
|
||||
template<int UpLo> struct ldlt_inplace;
|
||||
|
||||
template<> struct ldlt_inplace<Lower>
|
||||
{
|
||||
template<typename MatrixType, typename TranspositionType, typename Workspace>
|
||||
static bool unblocked(MatrixType& mat, TranspositionType& transpositions, Workspace& temp, SignMatrix& sign)
|
||||
{
|
||||
using std::abs;
|
||||
typedef typename MatrixType::Scalar Scalar;
|
||||
typedef typename MatrixType::RealScalar RealScalar;
|
||||
typedef typename TranspositionType::StorageIndex IndexType;
|
||||
eigen_assert(mat.rows()==mat.cols());
|
||||
const Index size = mat.rows();
|
||||
bool found_zero_pivot = false;
|
||||
bool ret = true;
|
||||
|
||||
if (size <= 1)
|
||||
{
|
||||
transpositions.setIdentity();
|
||||
if(size==0) sign = ZeroSign;
|
||||
else if (numext::real(mat.coeff(0,0)) > static_cast<RealScalar>(0) ) sign = PositiveSemiDef;
|
||||
else if (numext::real(mat.coeff(0,0)) < static_cast<RealScalar>(0)) sign = NegativeSemiDef;
|
||||
else sign = ZeroSign;
|
||||
return true;
|
||||
}
|
||||
|
||||
for (Index k = 0; k < size; ++k)
|
||||
{
|
||||
// Find largest diagonal element
|
||||
Index index_of_biggest_in_corner;
|
||||
mat.diagonal().tail(size-k).cwiseAbs().maxCoeff(&index_of_biggest_in_corner);
|
||||
index_of_biggest_in_corner += k;
|
||||
|
||||
transpositions.coeffRef(k) = IndexType(index_of_biggest_in_corner);
|
||||
if(k != index_of_biggest_in_corner)
|
||||
{
|
||||
// apply the transposition while taking care to consider only
|
||||
// the lower triangular part
|
||||
Index s = size-index_of_biggest_in_corner-1; // trailing size after the biggest element
|
||||
mat.row(k).head(k).swap(mat.row(index_of_biggest_in_corner).head(k));
|
||||
mat.col(k).tail(s).swap(mat.col(index_of_biggest_in_corner).tail(s));
|
||||
std::swap(mat.coeffRef(k,k),mat.coeffRef(index_of_biggest_in_corner,index_of_biggest_in_corner));
|
||||
for(Index i=k+1;i<index_of_biggest_in_corner;++i)
|
||||
{
|
||||
Scalar tmp = mat.coeffRef(i,k);
|
||||
mat.coeffRef(i,k) = numext::conj(mat.coeffRef(index_of_biggest_in_corner,i));
|
||||
mat.coeffRef(index_of_biggest_in_corner,i) = numext::conj(tmp);
|
||||
}
|
||||
if(NumTraits<Scalar>::IsComplex)
|
||||
mat.coeffRef(index_of_biggest_in_corner,k) = numext::conj(mat.coeff(index_of_biggest_in_corner,k));
|
||||
}
|
||||
|
||||
// partition the matrix:
|
||||
// A00 | - | -
|
||||
// lu = A10 | A11 | -
|
||||
// A20 | A21 | A22
|
||||
Index rs = size - k - 1;
|
||||
Block<MatrixType,Dynamic,1> A21(mat,k+1,k,rs,1);
|
||||
Block<MatrixType,1,Dynamic> A10(mat,k,0,1,k);
|
||||
Block<MatrixType,Dynamic,Dynamic> A20(mat,k+1,0,rs,k);
|
||||
|
||||
if(k>0)
|
||||
{
|
||||
temp.head(k) = mat.diagonal().real().head(k).asDiagonal() * A10.adjoint();
|
||||
mat.coeffRef(k,k) -= (A10 * temp.head(k)).value();
|
||||
if(rs>0)
|
||||
A21.noalias() -= A20 * temp.head(k);
|
||||
}
|
||||
|
||||
// In some previous versions of Eigen (e.g., 3.2.1), the scaling was omitted if the pivot
|
||||
// was smaller than the cutoff value. However, since LDLT is not rank-revealing
|
||||
// we should only make sure that we do not introduce INF or NaN values.
|
||||
// Remark that LAPACK also uses 0 as the cutoff value.
|
||||
RealScalar realAkk = numext::real(mat.coeffRef(k,k));
|
||||
bool pivot_is_valid = (abs(realAkk) > RealScalar(0));
|
||||
|
||||
if(k==0 && !pivot_is_valid)
|
||||
{
|
||||
// The entire diagonal is zero, there is nothing more to do
|
||||
// except filling the transpositions, and checking whether the matrix is zero.
|
||||
sign = ZeroSign;
|
||||
for(Index j = 0; j<size; ++j)
|
||||
{
|
||||
transpositions.coeffRef(j) = IndexType(j);
|
||||
ret = ret && (mat.col(j).tail(size-j-1).array()==Scalar(0)).all();
|
||||
}
|
||||
return ret;
|
||||
}
|
||||
|
||||
if((rs>0) && pivot_is_valid)
|
||||
A21 /= realAkk;
|
||||
else if(rs>0)
|
||||
ret = ret && (A21.array()==Scalar(0)).all();
|
||||
|
||||
if(found_zero_pivot && pivot_is_valid) ret = false; // factorization failed
|
||||
else if(!pivot_is_valid) found_zero_pivot = true;
|
||||
|
||||
if (sign == PositiveSemiDef) {
|
||||
if (realAkk < static_cast<RealScalar>(0)) sign = Indefinite;
|
||||
} else if (sign == NegativeSemiDef) {
|
||||
if (realAkk > static_cast<RealScalar>(0)) sign = Indefinite;
|
||||
} else if (sign == ZeroSign) {
|
||||
if (realAkk > static_cast<RealScalar>(0)) sign = PositiveSemiDef;
|
||||
else if (realAkk < static_cast<RealScalar>(0)) sign = NegativeSemiDef;
|
||||
}
|
||||
}
|
||||
|
||||
return ret;
|
||||
}
|
||||
|
||||
// Reference for the algorithm: Davis and Hager, "Multiple Rank
|
||||
// Modifications of a Sparse Cholesky Factorization" (Algorithm 1)
|
||||
// Trivial rearrangements of their computations (Timothy E. Holy)
|
||||
// allow their algorithm to work for rank-1 updates even if the
|
||||
// original matrix is not of full rank.
|
||||
// Here only rank-1 updates are implemented, to reduce the
|
||||
// requirement for intermediate storage and improve accuracy
|
||||
template<typename MatrixType, typename WDerived>
|
||||
static bool updateInPlace(MatrixType& mat, MatrixBase<WDerived>& w, const typename MatrixType::RealScalar& sigma=1)
|
||||
{
|
||||
using numext::isfinite;
|
||||
typedef typename MatrixType::Scalar Scalar;
|
||||
typedef typename MatrixType::RealScalar RealScalar;
|
||||
|
||||
const Index size = mat.rows();
|
||||
eigen_assert(mat.cols() == size && w.size()==size);
|
||||
|
||||
RealScalar alpha = 1;
|
||||
|
||||
// Apply the update
|
||||
for (Index j = 0; j < size; j++)
|
||||
{
|
||||
// Check for termination due to an original decomposition of low-rank
|
||||
if (!(isfinite)(alpha))
|
||||
break;
|
||||
|
||||
// Update the diagonal terms
|
||||
RealScalar dj = numext::real(mat.coeff(j,j));
|
||||
Scalar wj = w.coeff(j);
|
||||
RealScalar swj2 = sigma*numext::abs2(wj);
|
||||
RealScalar gamma = dj*alpha + swj2;
|
||||
|
||||
mat.coeffRef(j,j) += swj2/alpha;
|
||||
alpha += swj2/dj;
|
||||
|
||||
|
||||
// Update the terms of L
|
||||
Index rs = size-j-1;
|
||||
w.tail(rs) -= wj * mat.col(j).tail(rs);
|
||||
if(gamma != 0)
|
||||
mat.col(j).tail(rs) += (sigma*numext::conj(wj)/gamma)*w.tail(rs);
|
||||
}
|
||||
return true;
|
||||
}
|
||||
|
||||
template<typename MatrixType, typename TranspositionType, typename Workspace, typename WType>
|
||||
static bool update(MatrixType& mat, const TranspositionType& transpositions, Workspace& tmp, const WType& w, const typename MatrixType::RealScalar& sigma=1)
|
||||
{
|
||||
// Apply the permutation to the input w
|
||||
tmp = transpositions * w;
|
||||
|
||||
return ldlt_inplace<Lower>::updateInPlace(mat,tmp,sigma);
|
||||
}
|
||||
};
|
||||
|
||||
template<> struct ldlt_inplace<Upper>
|
||||
{
|
||||
template<typename MatrixType, typename TranspositionType, typename Workspace>
|
||||
static EIGEN_STRONG_INLINE bool unblocked(MatrixType& mat, TranspositionType& transpositions, Workspace& temp, SignMatrix& sign)
|
||||
{
|
||||
Transpose<MatrixType> matt(mat);
|
||||
return ldlt_inplace<Lower>::unblocked(matt, transpositions, temp, sign);
|
||||
}
|
||||
|
||||
template<typename MatrixType, typename TranspositionType, typename Workspace, typename WType>
|
||||
static EIGEN_STRONG_INLINE bool update(MatrixType& mat, TranspositionType& transpositions, Workspace& tmp, WType& w, const typename MatrixType::RealScalar& sigma=1)
|
||||
{
|
||||
Transpose<MatrixType> matt(mat);
|
||||
return ldlt_inplace<Lower>::update(matt, transpositions, tmp, w.conjugate(), sigma);
|
||||
}
|
||||
};
|
||||
|
||||
template<typename MatrixType> struct LDLT_Traits<MatrixType,Lower>
|
||||
{
|
||||
typedef const TriangularView<const MatrixType, UnitLower> MatrixL;
|
||||
typedef const TriangularView<const typename MatrixType::AdjointReturnType, UnitUpper> MatrixU;
|
||||
static inline MatrixL getL(const MatrixType& m) { return MatrixL(m); }
|
||||
static inline MatrixU getU(const MatrixType& m) { return MatrixU(m.adjoint()); }
|
||||
};
|
||||
|
||||
template<typename MatrixType> struct LDLT_Traits<MatrixType,Upper>
|
||||
{
|
||||
typedef const TriangularView<const typename MatrixType::AdjointReturnType, UnitLower> MatrixL;
|
||||
typedef const TriangularView<const MatrixType, UnitUpper> MatrixU;
|
||||
static inline MatrixL getL(const MatrixType& m) { return MatrixL(m.adjoint()); }
|
||||
static inline MatrixU getU(const MatrixType& m) { return MatrixU(m); }
|
||||
};
|
||||
|
||||
} // end namespace internal
|
||||
|
||||
/** Compute / recompute the LDLT decomposition A = L D L^* = U^* D U of \a matrix
|
||||
*/
|
||||
template<typename MatrixType, int _UpLo>
|
||||
template<typename InputType>
|
||||
LDLT<MatrixType,_UpLo>& LDLT<MatrixType,_UpLo>::compute(const EigenBase<InputType>& a)
|
||||
{
|
||||
check_template_parameters();
|
||||
|
||||
eigen_assert(a.rows()==a.cols());
|
||||
const Index size = a.rows();
|
||||
|
||||
m_matrix = a.derived();
|
||||
|
||||
// Compute matrix L1 norm = max abs column sum.
|
||||
m_l1_norm = RealScalar(0);
|
||||
// TODO move this code to SelfAdjointView
|
||||
for (Index col = 0; col < size; ++col) {
|
||||
RealScalar abs_col_sum;
|
||||
if (_UpLo == Lower)
|
||||
abs_col_sum = m_matrix.col(col).tail(size - col).template lpNorm<1>() + m_matrix.row(col).head(col).template lpNorm<1>();
|
||||
else
|
||||
abs_col_sum = m_matrix.col(col).head(col).template lpNorm<1>() + m_matrix.row(col).tail(size - col).template lpNorm<1>();
|
||||
if (abs_col_sum > m_l1_norm)
|
||||
m_l1_norm = abs_col_sum;
|
||||
}
|
||||
|
||||
m_transpositions.resize(size);
|
||||
m_isInitialized = false;
|
||||
m_temporary.resize(size);
|
||||
m_sign = internal::ZeroSign;
|
||||
|
||||
m_info = internal::ldlt_inplace<UpLo>::unblocked(m_matrix, m_transpositions, m_temporary, m_sign) ? Success : NumericalIssue;
|
||||
|
||||
m_isInitialized = true;
|
||||
return *this;
|
||||
}
|
||||
|
||||
/** Update the LDLT decomposition: given A = L D L^T, efficiently compute the decomposition of A + sigma w w^T.
|
||||
* \param w a vector to be incorporated into the decomposition.
|
||||
* \param sigma a scalar, +1 for updates and -1 for "downdates," which correspond to removing previously-added column vectors. Optional; default value is +1.
|
||||
* \sa setZero()
|
||||
*/
|
||||
template<typename MatrixType, int _UpLo>
|
||||
template<typename Derived>
|
||||
LDLT<MatrixType,_UpLo>& LDLT<MatrixType,_UpLo>::rankUpdate(const MatrixBase<Derived>& w, const typename LDLT<MatrixType,_UpLo>::RealScalar& sigma)
|
||||
{
|
||||
typedef typename TranspositionType::StorageIndex IndexType;
|
||||
const Index size = w.rows();
|
||||
if (m_isInitialized)
|
||||
{
|
||||
eigen_assert(m_matrix.rows()==size);
|
||||
}
|
||||
else
|
||||
{
|
||||
m_matrix.resize(size,size);
|
||||
m_matrix.setZero();
|
||||
m_transpositions.resize(size);
|
||||
for (Index i = 0; i < size; i++)
|
||||
m_transpositions.coeffRef(i) = IndexType(i);
|
||||
m_temporary.resize(size);
|
||||
m_sign = sigma>=0 ? internal::PositiveSemiDef : internal::NegativeSemiDef;
|
||||
m_isInitialized = true;
|
||||
}
|
||||
|
||||
internal::ldlt_inplace<UpLo>::update(m_matrix, m_transpositions, m_temporary, w, sigma);
|
||||
|
||||
return *this;
|
||||
}
|
||||
|
||||
#ifndef EIGEN_PARSED_BY_DOXYGEN
|
||||
template<typename _MatrixType, int _UpLo>
|
||||
template<typename RhsType, typename DstType>
|
||||
void LDLT<_MatrixType,_UpLo>::_solve_impl(const RhsType &rhs, DstType &dst) const
|
||||
{
|
||||
eigen_assert(rhs.rows() == rows());
|
||||
// dst = P b
|
||||
dst = m_transpositions * rhs;
|
||||
|
||||
// dst = L^-1 (P b)
|
||||
matrixL().solveInPlace(dst);
|
||||
|
||||
// dst = D^-1 (L^-1 P b)
|
||||
// more precisely, use pseudo-inverse of D (see bug 241)
|
||||
using std::abs;
|
||||
const typename Diagonal<const MatrixType>::RealReturnType vecD(vectorD());
|
||||
// In some previous versions, tolerance was set to the max of 1/highest (or rather numeric_limits::min())
|
||||
// and the maximal diagonal entry * epsilon as motivated by LAPACK's xGELSS:
|
||||
// RealScalar tolerance = numext::maxi(vecD.array().abs().maxCoeff() * NumTraits<RealScalar>::epsilon(),RealScalar(1) / NumTraits<RealScalar>::highest());
|
||||
// However, LDLT is not rank revealing, and so adjusting the tolerance wrt to the highest
|
||||
// diagonal element is not well justified and leads to numerical issues in some cases.
|
||||
// Moreover, Lapack's xSYTRS routines use 0 for the tolerance.
|
||||
// Using numeric_limits::min() gives us more robustness to denormals.
|
||||
RealScalar tolerance = (std::numeric_limits<RealScalar>::min)();
|
||||
|
||||
for (Index i = 0; i < vecD.size(); ++i)
|
||||
{
|
||||
if(abs(vecD(i)) > tolerance)
|
||||
dst.row(i) /= vecD(i);
|
||||
else
|
||||
dst.row(i).setZero();
|
||||
}
|
||||
|
||||
// dst = L^-T (D^-1 L^-1 P b)
|
||||
matrixU().solveInPlace(dst);
|
||||
|
||||
// dst = P^-1 (L^-T D^-1 L^-1 P b) = A^-1 b
|
||||
dst = m_transpositions.transpose() * dst;
|
||||
}
|
||||
#endif
|
||||
|
||||
/** \internal use x = ldlt_object.solve(x);
|
||||
*
|
||||
* This is the \em in-place version of solve().
|
||||
*
|
||||
* \param bAndX represents both the right-hand side matrix b and result x.
|
||||
*
|
||||
* \returns true always! If you need to check for existence of solutions, use another decomposition like LU, QR, or SVD.
|
||||
*
|
||||
* This version avoids a copy when the right hand side matrix b is not
|
||||
* needed anymore.
|
||||
*
|
||||
* \sa LDLT::solve(), MatrixBase::ldlt()
|
||||
*/
|
||||
template<typename MatrixType,int _UpLo>
|
||||
template<typename Derived>
|
||||
bool LDLT<MatrixType,_UpLo>::solveInPlace(MatrixBase<Derived> &bAndX) const
|
||||
{
|
||||
eigen_assert(m_isInitialized && "LDLT is not initialized.");
|
||||
eigen_assert(m_matrix.rows() == bAndX.rows());
|
||||
|
||||
bAndX = this->solve(bAndX);
|
||||
|
||||
return true;
|
||||
}
|
||||
|
||||
/** \returns the matrix represented by the decomposition,
|
||||
* i.e., it returns the product: P^T L D L^* P.
|
||||
* This function is provided for debug purpose. */
|
||||
template<typename MatrixType, int _UpLo>
|
||||
MatrixType LDLT<MatrixType,_UpLo>::reconstructedMatrix() const
|
||||
{
|
||||
eigen_assert(m_isInitialized && "LDLT is not initialized.");
|
||||
const Index size = m_matrix.rows();
|
||||
MatrixType res(size,size);
|
||||
|
||||
// P
|
||||
res.setIdentity();
|
||||
res = transpositionsP() * res;
|
||||
// L^* P
|
||||
res = matrixU() * res;
|
||||
// D(L^*P)
|
||||
res = vectorD().real().asDiagonal() * res;
|
||||
// L(DL^*P)
|
||||
res = matrixL() * res;
|
||||
// P^T (LDL^*P)
|
||||
res = transpositionsP().transpose() * res;
|
||||
|
||||
return res;
|
||||
}
|
||||
|
||||
/** \cholesky_module
|
||||
* \returns the Cholesky decomposition with full pivoting without square root of \c *this
|
||||
* \sa MatrixBase::ldlt()
|
||||
*/
|
||||
template<typename MatrixType, unsigned int UpLo>
|
||||
inline const LDLT<typename SelfAdjointView<MatrixType, UpLo>::PlainObject, UpLo>
|
||||
SelfAdjointView<MatrixType, UpLo>::ldlt() const
|
||||
{
|
||||
return LDLT<PlainObject,UpLo>(m_matrix);
|
||||
}
|
||||
|
||||
/** \cholesky_module
|
||||
* \returns the Cholesky decomposition with full pivoting without square root of \c *this
|
||||
* \sa SelfAdjointView::ldlt()
|
||||
*/
|
||||
template<typename Derived>
|
||||
inline const LDLT<typename MatrixBase<Derived>::PlainObject>
|
||||
MatrixBase<Derived>::ldlt() const
|
||||
{
|
||||
return LDLT<PlainObject>(derived());
|
||||
}
|
||||
|
||||
} // end namespace Eigen
|
||||
|
||||
#endif // EIGEN_LDLT_H
|
||||
|
|
@ -0,0 +1,542 @@
|
|||
// This file is part of Eigen, a lightweight C++ template library
|
||||
// for linear algebra.
|
||||
//
|
||||
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
|
||||
//
|
||||
// This Source Code Form is subject to the terms of the Mozilla
|
||||
// Public License v. 2.0. If a copy of the MPL was not distributed
|
||||
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
|
||||
|
||||
#ifndef EIGEN_LLT_H
|
||||
#define EIGEN_LLT_H
|
||||
|
||||
namespace Eigen {
|
||||
|
||||
namespace internal{
|
||||
template<typename MatrixType, int UpLo> struct LLT_Traits;
|
||||
}
|
||||
|
||||
/** \ingroup Cholesky_Module
|
||||
*
|
||||
* \class LLT
|
||||
*
|
||||
* \brief Standard Cholesky decomposition (LL^T) of a matrix and associated features
|
||||
*
|
||||
* \tparam _MatrixType the type of the matrix of which we are computing the LL^T Cholesky decomposition
|
||||
* \tparam _UpLo the triangular part that will be used for the decompositon: Lower (default) or Upper.
|
||||
* The other triangular part won't be read.
|
||||
*
|
||||
* This class performs a LL^T Cholesky decomposition of a symmetric, positive definite
|
||||
* matrix A such that A = LL^* = U^*U, where L is lower triangular.
|
||||
*
|
||||
* While the Cholesky decomposition is particularly useful to solve selfadjoint problems like D^*D x = b,
|
||||
* for that purpose, we recommend the Cholesky decomposition without square root which is more stable
|
||||
* and even faster. Nevertheless, this standard Cholesky decomposition remains useful in many other
|
||||
* situations like generalised eigen problems with hermitian matrices.
|
||||
*
|
||||
* Remember that Cholesky decompositions are not rank-revealing. This LLT decomposition is only stable on positive definite matrices,
|
||||
* use LDLT instead for the semidefinite case. Also, do not use a Cholesky decomposition to determine whether a system of equations
|
||||
* has a solution.
|
||||
*
|
||||
* Example: \include LLT_example.cpp
|
||||
* Output: \verbinclude LLT_example.out
|
||||
*
|
||||
* \b Performance: for best performance, it is recommended to use a column-major storage format
|
||||
* with the Lower triangular part (the default), or, equivalently, a row-major storage format
|
||||
* with the Upper triangular part. Otherwise, you might get a 20% slowdown for the full factorization
|
||||
* step, and rank-updates can be up to 3 times slower.
|
||||
*
|
||||
* This class supports the \link InplaceDecomposition inplace decomposition \endlink mechanism.
|
||||
*
|
||||
* Note that during the decomposition, only the lower (or upper, as defined by _UpLo) triangular part of A is considered.
|
||||
* Therefore, the strict lower part does not have to store correct values.
|
||||
*
|
||||
* \sa MatrixBase::llt(), SelfAdjointView::llt(), class LDLT
|
||||
*/
|
||||
template<typename _MatrixType, int _UpLo> class LLT
|
||||
{
|
||||
public:
|
||||
typedef _MatrixType MatrixType;
|
||||
enum {
|
||||
RowsAtCompileTime = MatrixType::RowsAtCompileTime,
|
||||
ColsAtCompileTime = MatrixType::ColsAtCompileTime,
|
||||
MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime
|
||||
};
|
||||
typedef typename MatrixType::Scalar Scalar;
|
||||
typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
|
||||
typedef Eigen::Index Index; ///< \deprecated since Eigen 3.3
|
||||
typedef typename MatrixType::StorageIndex StorageIndex;
|
||||
|
||||
enum {
|
||||
PacketSize = internal::packet_traits<Scalar>::size,
|
||||
AlignmentMask = int(PacketSize)-1,
|
||||
UpLo = _UpLo
|
||||
};
|
||||
|
||||
typedef internal::LLT_Traits<MatrixType,UpLo> Traits;
|
||||
|
||||
/**
|
||||
* \brief Default Constructor.
|
||||
*
|
||||
* The default constructor is useful in cases in which the user intends to
|
||||
* perform decompositions via LLT::compute(const MatrixType&).
|
||||
*/
|
||||
LLT() : m_matrix(), m_isInitialized(false) {}
|
||||
|
||||
/** \brief Default Constructor with memory preallocation
|
||||
*
|
||||
* Like the default constructor but with preallocation of the internal data
|
||||
* according to the specified problem \a size.
|
||||
* \sa LLT()
|
||||
*/
|
||||
explicit LLT(Index size) : m_matrix(size, size),
|
||||
m_isInitialized(false) {}
|
||||
|
||||
template<typename InputType>
|
||||
explicit LLT(const EigenBase<InputType>& matrix)
|
||||
: m_matrix(matrix.rows(), matrix.cols()),
|
||||
m_isInitialized(false)
|
||||
{
|
||||
compute(matrix.derived());
|
||||
}
|
||||
|
||||
/** \brief Constructs a LDLT factorization from a given matrix
|
||||
*
|
||||
* This overloaded constructor is provided for \link InplaceDecomposition inplace decomposition \endlink when
|
||||
* \c MatrixType is a Eigen::Ref.
|
||||
*
|
||||
* \sa LLT(const EigenBase&)
|
||||
*/
|
||||
template<typename InputType>
|
||||
explicit LLT(EigenBase<InputType>& matrix)
|
||||
: m_matrix(matrix.derived()),
|
||||
m_isInitialized(false)
|
||||
{
|
||||
compute(matrix.derived());
|
||||
}
|
||||
|
||||
/** \returns a view of the upper triangular matrix U */
|
||||
inline typename Traits::MatrixU matrixU() const
|
||||
{
|
||||
eigen_assert(m_isInitialized && "LLT is not initialized.");
|
||||
return Traits::getU(m_matrix);
|
||||
}
|
||||
|
||||
/** \returns a view of the lower triangular matrix L */
|
||||
inline typename Traits::MatrixL matrixL() const
|
||||
{
|
||||
eigen_assert(m_isInitialized && "LLT is not initialized.");
|
||||
return Traits::getL(m_matrix);
|
||||
}
|
||||
|
||||
/** \returns the solution x of \f$ A x = b \f$ using the current decomposition of A.
|
||||
*
|
||||
* Since this LLT class assumes anyway that the matrix A is invertible, the solution
|
||||
* theoretically exists and is unique regardless of b.
|
||||
*
|
||||
* Example: \include LLT_solve.cpp
|
||||
* Output: \verbinclude LLT_solve.out
|
||||
*
|
||||
* \sa solveInPlace(), MatrixBase::llt(), SelfAdjointView::llt()
|
||||
*/
|
||||
template<typename Rhs>
|
||||
inline const Solve<LLT, Rhs>
|
||||
solve(const MatrixBase<Rhs>& b) const
|
||||
{
|
||||
eigen_assert(m_isInitialized && "LLT is not initialized.");
|
||||
eigen_assert(m_matrix.rows()==b.rows()
|
||||
&& "LLT::solve(): invalid number of rows of the right hand side matrix b");
|
||||
return Solve<LLT, Rhs>(*this, b.derived());
|
||||
}
|
||||
|
||||
template<typename Derived>
|
||||
void solveInPlace(const MatrixBase<Derived> &bAndX) const;
|
||||
|
||||
template<typename InputType>
|
||||
LLT& compute(const EigenBase<InputType>& matrix);
|
||||
|
||||
/** \returns an estimate of the reciprocal condition number of the matrix of
|
||||
* which \c *this is the Cholesky decomposition.
|
||||
*/
|
||||
RealScalar rcond() const
|
||||
{
|
||||
eigen_assert(m_isInitialized && "LLT is not initialized.");
|
||||
eigen_assert(m_info == Success && "LLT failed because matrix appears to be negative");
|
||||
return internal::rcond_estimate_helper(m_l1_norm, *this);
|
||||
}
|
||||
|
||||
/** \returns the LLT decomposition matrix
|
||||
*
|
||||
* TODO: document the storage layout
|
||||
*/
|
||||
inline const MatrixType& matrixLLT() const
|
||||
{
|
||||
eigen_assert(m_isInitialized && "LLT is not initialized.");
|
||||
return m_matrix;
|
||||
}
|
||||
|
||||
MatrixType reconstructedMatrix() const;
|
||||
|
||||
|
||||
/** \brief Reports whether previous computation was successful.
|
||||
*
|
||||
* \returns \c Success if computation was succesful,
|
||||
* \c NumericalIssue if the matrix.appears not to be positive definite.
|
||||
*/
|
||||
ComputationInfo info() const
|
||||
{
|
||||
eigen_assert(m_isInitialized && "LLT is not initialized.");
|
||||
return m_info;
|
||||
}
|
||||
|
||||
/** \returns the adjoint of \c *this, that is, a const reference to the decomposition itself as the underlying matrix is self-adjoint.
|
||||
*
|
||||
* This method is provided for compatibility with other matrix decompositions, thus enabling generic code such as:
|
||||
* \code x = decomposition.adjoint().solve(b) \endcode
|
||||
*/
|
||||
const LLT& adjoint() const { return *this; };
|
||||
|
||||
inline Index rows() const { return m_matrix.rows(); }
|
||||
inline Index cols() const { return m_matrix.cols(); }
|
||||
|
||||
template<typename VectorType>
|
||||
LLT rankUpdate(const VectorType& vec, const RealScalar& sigma = 1);
|
||||
|
||||
#ifndef EIGEN_PARSED_BY_DOXYGEN
|
||||
template<typename RhsType, typename DstType>
|
||||
EIGEN_DEVICE_FUNC
|
||||
void _solve_impl(const RhsType &rhs, DstType &dst) const;
|
||||
#endif
|
||||
|
||||
protected:
|
||||
|
||||
static void check_template_parameters()
|
||||
{
|
||||
EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar);
|
||||
}
|
||||
|
||||
/** \internal
|
||||
* Used to compute and store L
|
||||
* The strict upper part is not used and even not initialized.
|
||||
*/
|
||||
MatrixType m_matrix;
|
||||
RealScalar m_l1_norm;
|
||||
bool m_isInitialized;
|
||||
ComputationInfo m_info;
|
||||
};
|
||||
|
||||
namespace internal {
|
||||
|
||||
template<typename Scalar, int UpLo> struct llt_inplace;
|
||||
|
||||
template<typename MatrixType, typename VectorType>
|
||||
static Index llt_rank_update_lower(MatrixType& mat, const VectorType& vec, const typename MatrixType::RealScalar& sigma)
|
||||
{
|
||||
using std::sqrt;
|
||||
typedef typename MatrixType::Scalar Scalar;
|
||||
typedef typename MatrixType::RealScalar RealScalar;
|
||||
typedef typename MatrixType::ColXpr ColXpr;
|
||||
typedef typename internal::remove_all<ColXpr>::type ColXprCleaned;
|
||||
typedef typename ColXprCleaned::SegmentReturnType ColXprSegment;
|
||||
typedef Matrix<Scalar,Dynamic,1> TempVectorType;
|
||||
typedef typename TempVectorType::SegmentReturnType TempVecSegment;
|
||||
|
||||
Index n = mat.cols();
|
||||
eigen_assert(mat.rows()==n && vec.size()==n);
|
||||
|
||||
TempVectorType temp;
|
||||
|
||||
if(sigma>0)
|
||||
{
|
||||
// This version is based on Givens rotations.
|
||||
// It is faster than the other one below, but only works for updates,
|
||||
// i.e., for sigma > 0
|
||||
temp = sqrt(sigma) * vec;
|
||||
|
||||
for(Index i=0; i<n; ++i)
|
||||
{
|
||||
JacobiRotation<Scalar> g;
|
||||
g.makeGivens(mat(i,i), -temp(i), &mat(i,i));
|
||||
|
||||
Index rs = n-i-1;
|
||||
if(rs>0)
|
||||
{
|
||||
ColXprSegment x(mat.col(i).tail(rs));
|
||||
TempVecSegment y(temp.tail(rs));
|
||||
apply_rotation_in_the_plane(x, y, g);
|
||||
}
|
||||
}
|
||||
}
|
||||
else
|
||||
{
|
||||
temp = vec;
|
||||
RealScalar beta = 1;
|
||||
for(Index j=0; j<n; ++j)
|
||||
{
|
||||
RealScalar Ljj = numext::real(mat.coeff(j,j));
|
||||
RealScalar dj = numext::abs2(Ljj);
|
||||
Scalar wj = temp.coeff(j);
|
||||
RealScalar swj2 = sigma*numext::abs2(wj);
|
||||
RealScalar gamma = dj*beta + swj2;
|
||||
|
||||
RealScalar x = dj + swj2/beta;
|
||||
if (x<=RealScalar(0))
|
||||
return j;
|
||||
RealScalar nLjj = sqrt(x);
|
||||
mat.coeffRef(j,j) = nLjj;
|
||||
beta += swj2/dj;
|
||||
|
||||
// Update the terms of L
|
||||
Index rs = n-j-1;
|
||||
if(rs)
|
||||
{
|
||||
temp.tail(rs) -= (wj/Ljj) * mat.col(j).tail(rs);
|
||||
if(gamma != 0)
|
||||
mat.col(j).tail(rs) = (nLjj/Ljj) * mat.col(j).tail(rs) + (nLjj * sigma*numext::conj(wj)/gamma)*temp.tail(rs);
|
||||
}
|
||||
}
|
||||
}
|
||||
return -1;
|
||||
}
|
||||
|
||||
template<typename Scalar> struct llt_inplace<Scalar, Lower>
|
||||
{
|
||||
typedef typename NumTraits<Scalar>::Real RealScalar;
|
||||
template<typename MatrixType>
|
||||
static Index unblocked(MatrixType& mat)
|
||||
{
|
||||
using std::sqrt;
|
||||
|
||||
eigen_assert(mat.rows()==mat.cols());
|
||||
const Index size = mat.rows();
|
||||
for(Index k = 0; k < size; ++k)
|
||||
{
|
||||
Index rs = size-k-1; // remaining size
|
||||
|
||||
Block<MatrixType,Dynamic,1> A21(mat,k+1,k,rs,1);
|
||||
Block<MatrixType,1,Dynamic> A10(mat,k,0,1,k);
|
||||
Block<MatrixType,Dynamic,Dynamic> A20(mat,k+1,0,rs,k);
|
||||
|
||||
RealScalar x = numext::real(mat.coeff(k,k));
|
||||
if (k>0) x -= A10.squaredNorm();
|
||||
if (x<=RealScalar(0))
|
||||
return k;
|
||||
mat.coeffRef(k,k) = x = sqrt(x);
|
||||
if (k>0 && rs>0) A21.noalias() -= A20 * A10.adjoint();
|
||||
if (rs>0) A21 /= x;
|
||||
}
|
||||
return -1;
|
||||
}
|
||||
|
||||
template<typename MatrixType>
|
||||
static Index blocked(MatrixType& m)
|
||||
{
|
||||
eigen_assert(m.rows()==m.cols());
|
||||
Index size = m.rows();
|
||||
if(size<32)
|
||||
return unblocked(m);
|
||||
|
||||
Index blockSize = size/8;
|
||||
blockSize = (blockSize/16)*16;
|
||||
blockSize = (std::min)((std::max)(blockSize,Index(8)), Index(128));
|
||||
|
||||
for (Index k=0; k<size; k+=blockSize)
|
||||
{
|
||||
// partition the matrix:
|
||||
// A00 | - | -
|
||||
// lu = A10 | A11 | -
|
||||
// A20 | A21 | A22
|
||||
Index bs = (std::min)(blockSize, size-k);
|
||||
Index rs = size - k - bs;
|
||||
Block<MatrixType,Dynamic,Dynamic> A11(m,k, k, bs,bs);
|
||||
Block<MatrixType,Dynamic,Dynamic> A21(m,k+bs,k, rs,bs);
|
||||
Block<MatrixType,Dynamic,Dynamic> A22(m,k+bs,k+bs,rs,rs);
|
||||
|
||||
Index ret;
|
||||
if((ret=unblocked(A11))>=0) return k+ret;
|
||||
if(rs>0) A11.adjoint().template triangularView<Upper>().template solveInPlace<OnTheRight>(A21);
|
||||
if(rs>0) A22.template selfadjointView<Lower>().rankUpdate(A21,typename NumTraits<RealScalar>::Literal(-1)); // bottleneck
|
||||
}
|
||||
return -1;
|
||||
}
|
||||
|
||||
template<typename MatrixType, typename VectorType>
|
||||
static Index rankUpdate(MatrixType& mat, const VectorType& vec, const RealScalar& sigma)
|
||||
{
|
||||
return Eigen::internal::llt_rank_update_lower(mat, vec, sigma);
|
||||
}
|
||||
};
|
||||
|
||||
template<typename Scalar> struct llt_inplace<Scalar, Upper>
|
||||
{
|
||||
typedef typename NumTraits<Scalar>::Real RealScalar;
|
||||
|
||||
template<typename MatrixType>
|
||||
static EIGEN_STRONG_INLINE Index unblocked(MatrixType& mat)
|
||||
{
|
||||
Transpose<MatrixType> matt(mat);
|
||||
return llt_inplace<Scalar, Lower>::unblocked(matt);
|
||||
}
|
||||
template<typename MatrixType>
|
||||
static EIGEN_STRONG_INLINE Index blocked(MatrixType& mat)
|
||||
{
|
||||
Transpose<MatrixType> matt(mat);
|
||||
return llt_inplace<Scalar, Lower>::blocked(matt);
|
||||
}
|
||||
template<typename MatrixType, typename VectorType>
|
||||
static Index rankUpdate(MatrixType& mat, const VectorType& vec, const RealScalar& sigma)
|
||||
{
|
||||
Transpose<MatrixType> matt(mat);
|
||||
return llt_inplace<Scalar, Lower>::rankUpdate(matt, vec.conjugate(), sigma);
|
||||
}
|
||||
};
|
||||
|
||||
template<typename MatrixType> struct LLT_Traits<MatrixType,Lower>
|
||||
{
|
||||
typedef const TriangularView<const MatrixType, Lower> MatrixL;
|
||||
typedef const TriangularView<const typename MatrixType::AdjointReturnType, Upper> MatrixU;
|
||||
static inline MatrixL getL(const MatrixType& m) { return MatrixL(m); }
|
||||
static inline MatrixU getU(const MatrixType& m) { return MatrixU(m.adjoint()); }
|
||||
static bool inplace_decomposition(MatrixType& m)
|
||||
{ return llt_inplace<typename MatrixType::Scalar, Lower>::blocked(m)==-1; }
|
||||
};
|
||||
|
||||
template<typename MatrixType> struct LLT_Traits<MatrixType,Upper>
|
||||
{
|
||||
typedef const TriangularView<const typename MatrixType::AdjointReturnType, Lower> MatrixL;
|
||||
typedef const TriangularView<const MatrixType, Upper> MatrixU;
|
||||
static inline MatrixL getL(const MatrixType& m) { return MatrixL(m.adjoint()); }
|
||||
static inline MatrixU getU(const MatrixType& m) { return MatrixU(m); }
|
||||
static bool inplace_decomposition(MatrixType& m)
|
||||
{ return llt_inplace<typename MatrixType::Scalar, Upper>::blocked(m)==-1; }
|
||||
};
|
||||
|
||||
} // end namespace internal
|
||||
|
||||
/** Computes / recomputes the Cholesky decomposition A = LL^* = U^*U of \a matrix
|
||||
*
|
||||
* \returns a reference to *this
|
||||
*
|
||||
* Example: \include TutorialLinAlgComputeTwice.cpp
|
||||
* Output: \verbinclude TutorialLinAlgComputeTwice.out
|
||||
*/
|
||||
template<typename MatrixType, int _UpLo>
|
||||
template<typename InputType>
|
||||
LLT<MatrixType,_UpLo>& LLT<MatrixType,_UpLo>::compute(const EigenBase<InputType>& a)
|
||||
{
|
||||
check_template_parameters();
|
||||
|
||||
eigen_assert(a.rows()==a.cols());
|
||||
const Index size = a.rows();
|
||||
m_matrix.resize(size, size);
|
||||
if (!internal::is_same_dense(m_matrix, a.derived()))
|
||||
m_matrix = a.derived();
|
||||
|
||||
// Compute matrix L1 norm = max abs column sum.
|
||||
m_l1_norm = RealScalar(0);
|
||||
// TODO move this code to SelfAdjointView
|
||||
for (Index col = 0; col < size; ++col) {
|
||||
RealScalar abs_col_sum;
|
||||
if (_UpLo == Lower)
|
||||
abs_col_sum = m_matrix.col(col).tail(size - col).template lpNorm<1>() + m_matrix.row(col).head(col).template lpNorm<1>();
|
||||
else
|
||||
abs_col_sum = m_matrix.col(col).head(col).template lpNorm<1>() + m_matrix.row(col).tail(size - col).template lpNorm<1>();
|
||||
if (abs_col_sum > m_l1_norm)
|
||||
m_l1_norm = abs_col_sum;
|
||||
}
|
||||
|
||||
m_isInitialized = true;
|
||||
bool ok = Traits::inplace_decomposition(m_matrix);
|
||||
m_info = ok ? Success : NumericalIssue;
|
||||
|
||||
return *this;
|
||||
}
|
||||
|
||||
/** Performs a rank one update (or dowdate) of the current decomposition.
|
||||
* If A = LL^* before the rank one update,
|
||||
* then after it we have LL^* = A + sigma * v v^* where \a v must be a vector
|
||||
* of same dimension.
|
||||
*/
|
||||
template<typename _MatrixType, int _UpLo>
|
||||
template<typename VectorType>
|
||||
LLT<_MatrixType,_UpLo> LLT<_MatrixType,_UpLo>::rankUpdate(const VectorType& v, const RealScalar& sigma)
|
||||
{
|
||||
EIGEN_STATIC_ASSERT_VECTOR_ONLY(VectorType);
|
||||
eigen_assert(v.size()==m_matrix.cols());
|
||||
eigen_assert(m_isInitialized);
|
||||
if(internal::llt_inplace<typename MatrixType::Scalar, UpLo>::rankUpdate(m_matrix,v,sigma)>=0)
|
||||
m_info = NumericalIssue;
|
||||
else
|
||||
m_info = Success;
|
||||
|
||||
return *this;
|
||||
}
|
||||
|
||||
#ifndef EIGEN_PARSED_BY_DOXYGEN
|
||||
template<typename _MatrixType,int _UpLo>
|
||||
template<typename RhsType, typename DstType>
|
||||
void LLT<_MatrixType,_UpLo>::_solve_impl(const RhsType &rhs, DstType &dst) const
|
||||
{
|
||||
dst = rhs;
|
||||
solveInPlace(dst);
|
||||
}
|
||||
#endif
|
||||
|
||||
/** \internal use x = llt_object.solve(x);
|
||||
*
|
||||
* This is the \em in-place version of solve().
|
||||
*
|
||||
* \param bAndX represents both the right-hand side matrix b and result x.
|
||||
*
|
||||
* This version avoids a copy when the right hand side matrix b is not needed anymore.
|
||||
*
|
||||
* \warning The parameter is only marked 'const' to make the C++ compiler accept a temporary expression here.
|
||||
* This function will const_cast it, so constness isn't honored here.
|
||||
*
|
||||
* \sa LLT::solve(), MatrixBase::llt()
|
||||
*/
|
||||
template<typename MatrixType, int _UpLo>
|
||||
template<typename Derived>
|
||||
void LLT<MatrixType,_UpLo>::solveInPlace(const MatrixBase<Derived> &bAndX) const
|
||||
{
|
||||
eigen_assert(m_isInitialized && "LLT is not initialized.");
|
||||
eigen_assert(m_matrix.rows()==bAndX.rows());
|
||||
matrixL().solveInPlace(bAndX);
|
||||
matrixU().solveInPlace(bAndX);
|
||||
}
|
||||
|
||||
/** \returns the matrix represented by the decomposition,
|
||||
* i.e., it returns the product: L L^*.
|
||||
* This function is provided for debug purpose. */
|
||||
template<typename MatrixType, int _UpLo>
|
||||
MatrixType LLT<MatrixType,_UpLo>::reconstructedMatrix() const
|
||||
{
|
||||
eigen_assert(m_isInitialized && "LLT is not initialized.");
|
||||
return matrixL() * matrixL().adjoint().toDenseMatrix();
|
||||
}
|
||||
|
||||
/** \cholesky_module
|
||||
* \returns the LLT decomposition of \c *this
|
||||
* \sa SelfAdjointView::llt()
|
||||
*/
|
||||
template<typename Derived>
|
||||
inline const LLT<typename MatrixBase<Derived>::PlainObject>
|
||||
MatrixBase<Derived>::llt() const
|
||||
{
|
||||
return LLT<PlainObject>(derived());
|
||||
}
|
||||
|
||||
/** \cholesky_module
|
||||
* \returns the LLT decomposition of \c *this
|
||||
* \sa SelfAdjointView::llt()
|
||||
*/
|
||||
template<typename MatrixType, unsigned int UpLo>
|
||||
inline const LLT<typename SelfAdjointView<MatrixType, UpLo>::PlainObject, UpLo>
|
||||
SelfAdjointView<MatrixType, UpLo>::llt() const
|
||||
{
|
||||
return LLT<PlainObject,UpLo>(m_matrix);
|
||||
}
|
||||
|
||||
} // end namespace Eigen
|
||||
|
||||
#endif // EIGEN_LLT_H
|
||||
|
|
@ -0,0 +1,99 @@
|
|||
/*
|
||||
Copyright (c) 2011, Intel Corporation. All rights reserved.
|
||||
|
||||
Redistribution and use in source and binary forms, with or without modification,
|
||||
are permitted provided that the following conditions are met:
|
||||
|
||||
* Redistributions of source code must retain the above copyright notice, this
|
||||
list of conditions and the following disclaimer.
|
||||
* Redistributions in binary form must reproduce the above copyright notice,
|
||||
this list of conditions and the following disclaimer in the documentation
|
||||
and/or other materials provided with the distribution.
|
||||
* Neither the name of Intel Corporation nor the names of its contributors may
|
||||
be used to endorse or promote products derived from this software without
|
||||
specific prior written permission.
|
||||
|
||||
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
|
||||
ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
|
||||
WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
|
||||
DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
|
||||
ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
|
||||
(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
|
||||
LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
|
||||
ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
|
||||
(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
|
||||
SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
|
||||
|
||||
********************************************************************************
|
||||
* Content : Eigen bindings to LAPACKe
|
||||
* LLt decomposition based on LAPACKE_?potrf function.
|
||||
********************************************************************************
|
||||
*/
|
||||
|
||||
#ifndef EIGEN_LLT_LAPACKE_H
|
||||
#define EIGEN_LLT_LAPACKE_H
|
||||
|
||||
namespace Eigen {
|
||||
|
||||
namespace internal {
|
||||
|
||||
template<typename Scalar> struct lapacke_llt;
|
||||
|
||||
#define EIGEN_LAPACKE_LLT(EIGTYPE, BLASTYPE, LAPACKE_PREFIX) \
|
||||
template<> struct lapacke_llt<EIGTYPE> \
|
||||
{ \
|
||||
template<typename MatrixType> \
|
||||
static inline Index potrf(MatrixType& m, char uplo) \
|
||||
{ \
|
||||
lapack_int matrix_order; \
|
||||
lapack_int size, lda, info, StorageOrder; \
|
||||
EIGTYPE* a; \
|
||||
eigen_assert(m.rows()==m.cols()); \
|
||||
/* Set up parameters for ?potrf */ \
|
||||
size = convert_index<lapack_int>(m.rows()); \
|
||||
StorageOrder = MatrixType::Flags&RowMajorBit?RowMajor:ColMajor; \
|
||||
matrix_order = StorageOrder==RowMajor ? LAPACK_ROW_MAJOR : LAPACK_COL_MAJOR; \
|
||||
a = &(m.coeffRef(0,0)); \
|
||||
lda = convert_index<lapack_int>(m.outerStride()); \
|
||||
\
|
||||
info = LAPACKE_##LAPACKE_PREFIX##potrf( matrix_order, uplo, size, (BLASTYPE*)a, lda ); \
|
||||
info = (info==0) ? -1 : info>0 ? info-1 : size; \
|
||||
return info; \
|
||||
} \
|
||||
}; \
|
||||
template<> struct llt_inplace<EIGTYPE, Lower> \
|
||||
{ \
|
||||
template<typename MatrixType> \
|
||||
static Index blocked(MatrixType& m) \
|
||||
{ \
|
||||
return lapacke_llt<EIGTYPE>::potrf(m, 'L'); \
|
||||
} \
|
||||
template<typename MatrixType, typename VectorType> \
|
||||
static Index rankUpdate(MatrixType& mat, const VectorType& vec, const typename MatrixType::RealScalar& sigma) \
|
||||
{ return Eigen::internal::llt_rank_update_lower(mat, vec, sigma); } \
|
||||
}; \
|
||||
template<> struct llt_inplace<EIGTYPE, Upper> \
|
||||
{ \
|
||||
template<typename MatrixType> \
|
||||
static Index blocked(MatrixType& m) \
|
||||
{ \
|
||||
return lapacke_llt<EIGTYPE>::potrf(m, 'U'); \
|
||||
} \
|
||||
template<typename MatrixType, typename VectorType> \
|
||||
static Index rankUpdate(MatrixType& mat, const VectorType& vec, const typename MatrixType::RealScalar& sigma) \
|
||||
{ \
|
||||
Transpose<MatrixType> matt(mat); \
|
||||
return llt_inplace<EIGTYPE, Lower>::rankUpdate(matt, vec.conjugate(), sigma); \
|
||||
} \
|
||||
};
|
||||
|
||||
EIGEN_LAPACKE_LLT(double, double, d)
|
||||
EIGEN_LAPACKE_LLT(float, float, s)
|
||||
EIGEN_LAPACKE_LLT(dcomplex, lapack_complex_double, z)
|
||||
EIGEN_LAPACKE_LLT(scomplex, lapack_complex_float, c)
|
||||
|
||||
} // end namespace internal
|
||||
|
||||
} // end namespace Eigen
|
||||
|
||||
#endif // EIGEN_LLT_LAPACKE_H
|
||||
|
|
@ -0,0 +1,639 @@
|
|||
// This file is part of Eigen, a lightweight C++ template library
|
||||
// for linear algebra.
|
||||
//
|
||||
// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
|
||||
//
|
||||
// This Source Code Form is subject to the terms of the Mozilla
|
||||
// Public License v. 2.0. If a copy of the MPL was not distributed
|
||||
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
|
||||
|
||||
#ifndef EIGEN_CHOLMODSUPPORT_H
|
||||
#define EIGEN_CHOLMODSUPPORT_H
|
||||
|
||||
namespace Eigen {
|
||||
|
||||
namespace internal {
|
||||
|
||||
template<typename Scalar> struct cholmod_configure_matrix;
|
||||
|
||||
template<> struct cholmod_configure_matrix<double> {
|
||||
template<typename CholmodType>
|
||||
static void run(CholmodType& mat) {
|
||||
mat.xtype = CHOLMOD_REAL;
|
||||
mat.dtype = CHOLMOD_DOUBLE;
|
||||
}
|
||||
};
|
||||
|
||||
template<> struct cholmod_configure_matrix<std::complex<double> > {
|
||||
template<typename CholmodType>
|
||||
static void run(CholmodType& mat) {
|
||||
mat.xtype = CHOLMOD_COMPLEX;
|
||||
mat.dtype = CHOLMOD_DOUBLE;
|
||||
}
|
||||
};
|
||||
|
||||
// Other scalar types are not yet suppotred by Cholmod
|
||||
// template<> struct cholmod_configure_matrix<float> {
|
||||
// template<typename CholmodType>
|
||||
// static void run(CholmodType& mat) {
|
||||
// mat.xtype = CHOLMOD_REAL;
|
||||
// mat.dtype = CHOLMOD_SINGLE;
|
||||
// }
|
||||
// };
|
||||
//
|
||||
// template<> struct cholmod_configure_matrix<std::complex<float> > {
|
||||
// template<typename CholmodType>
|
||||
// static void run(CholmodType& mat) {
|
||||
// mat.xtype = CHOLMOD_COMPLEX;
|
||||
// mat.dtype = CHOLMOD_SINGLE;
|
||||
// }
|
||||
// };
|
||||
|
||||
} // namespace internal
|
||||
|
||||
/** Wraps the Eigen sparse matrix \a mat into a Cholmod sparse matrix object.
|
||||
* Note that the data are shared.
|
||||
*/
|
||||
template<typename _Scalar, int _Options, typename _StorageIndex>
|
||||
cholmod_sparse viewAsCholmod(Ref<SparseMatrix<_Scalar,_Options,_StorageIndex> > mat)
|
||||
{
|
||||
cholmod_sparse res;
|
||||
res.nzmax = mat.nonZeros();
|
||||
res.nrow = mat.rows();
|
||||
res.ncol = mat.cols();
|
||||
res.p = mat.outerIndexPtr();
|
||||
res.i = mat.innerIndexPtr();
|
||||
res.x = mat.valuePtr();
|
||||
res.z = 0;
|
||||
res.sorted = 1;
|
||||
if(mat.isCompressed())
|
||||
{
|
||||
res.packed = 1;
|
||||
res.nz = 0;
|
||||
}
|
||||
else
|
||||
{
|
||||
res.packed = 0;
|
||||
res.nz = mat.innerNonZeroPtr();
|
||||
}
|
||||
|
||||
res.dtype = 0;
|
||||
res.stype = -1;
|
||||
|
||||
if (internal::is_same<_StorageIndex,int>::value)
|
||||
{
|
||||
res.itype = CHOLMOD_INT;
|
||||
}
|
||||
else if (internal::is_same<_StorageIndex,long>::value)
|
||||
{
|
||||
res.itype = CHOLMOD_LONG;
|
||||
}
|
||||
else
|
||||
{
|
||||
eigen_assert(false && "Index type not supported yet");
|
||||
}
|
||||
|
||||
// setup res.xtype
|
||||
internal::cholmod_configure_matrix<_Scalar>::run(res);
|
||||
|
||||
res.stype = 0;
|
||||
|
||||
return res;
|
||||
}
|
||||
|
||||
template<typename _Scalar, int _Options, typename _Index>
|
||||
const cholmod_sparse viewAsCholmod(const SparseMatrix<_Scalar,_Options,_Index>& mat)
|
||||
{
|
||||
cholmod_sparse res = viewAsCholmod(Ref<SparseMatrix<_Scalar,_Options,_Index> >(mat.const_cast_derived()));
|
||||
return res;
|
||||
}
|
||||
|
||||
template<typename _Scalar, int _Options, typename _Index>
|
||||
const cholmod_sparse viewAsCholmod(const SparseVector<_Scalar,_Options,_Index>& mat)
|
||||
{
|
||||
cholmod_sparse res = viewAsCholmod(Ref<SparseMatrix<_Scalar,_Options,_Index> >(mat.const_cast_derived()));
|
||||
return res;
|
||||
}
|
||||
|
||||
/** Returns a view of the Eigen sparse matrix \a mat as Cholmod sparse matrix.
|
||||
* The data are not copied but shared. */
|
||||
template<typename _Scalar, int _Options, typename _Index, unsigned int UpLo>
|
||||
cholmod_sparse viewAsCholmod(const SparseSelfAdjointView<const SparseMatrix<_Scalar,_Options,_Index>, UpLo>& mat)
|
||||
{
|
||||
cholmod_sparse res = viewAsCholmod(Ref<SparseMatrix<_Scalar,_Options,_Index> >(mat.matrix().const_cast_derived()));
|
||||
|
||||
if(UpLo==Upper) res.stype = 1;
|
||||
if(UpLo==Lower) res.stype = -1;
|
||||
|
||||
return res;
|
||||
}
|
||||
|
||||
/** Returns a view of the Eigen \b dense matrix \a mat as Cholmod dense matrix.
|
||||
* The data are not copied but shared. */
|
||||
template<typename Derived>
|
||||
cholmod_dense viewAsCholmod(MatrixBase<Derived>& mat)
|
||||
{
|
||||
EIGEN_STATIC_ASSERT((internal::traits<Derived>::Flags&RowMajorBit)==0,THIS_METHOD_IS_ONLY_FOR_COLUMN_MAJOR_MATRICES);
|
||||
typedef typename Derived::Scalar Scalar;
|
||||
|
||||
cholmod_dense res;
|
||||
res.nrow = mat.rows();
|
||||
res.ncol = mat.cols();
|
||||
res.nzmax = res.nrow * res.ncol;
|
||||
res.d = Derived::IsVectorAtCompileTime ? mat.derived().size() : mat.derived().outerStride();
|
||||
res.x = (void*)(mat.derived().data());
|
||||
res.z = 0;
|
||||
|
||||
internal::cholmod_configure_matrix<Scalar>::run(res);
|
||||
|
||||
return res;
|
||||
}
|
||||
|
||||
/** Returns a view of the Cholmod sparse matrix \a cm as an Eigen sparse matrix.
|
||||
* The data are not copied but shared. */
|
||||
template<typename Scalar, int Flags, typename StorageIndex>
|
||||
MappedSparseMatrix<Scalar,Flags,StorageIndex> viewAsEigen(cholmod_sparse& cm)
|
||||
{
|
||||
return MappedSparseMatrix<Scalar,Flags,StorageIndex>
|
||||
(cm.nrow, cm.ncol, static_cast<StorageIndex*>(cm.p)[cm.ncol],
|
||||
static_cast<StorageIndex*>(cm.p), static_cast<StorageIndex*>(cm.i),static_cast<Scalar*>(cm.x) );
|
||||
}
|
||||
|
||||
enum CholmodMode {
|
||||
CholmodAuto, CholmodSimplicialLLt, CholmodSupernodalLLt, CholmodLDLt
|
||||
};
|
||||
|
||||
|
||||
/** \ingroup CholmodSupport_Module
|
||||
* \class CholmodBase
|
||||
* \brief The base class for the direct Cholesky factorization of Cholmod
|
||||
* \sa class CholmodSupernodalLLT, class CholmodSimplicialLDLT, class CholmodSimplicialLLT
|
||||
*/
|
||||
template<typename _MatrixType, int _UpLo, typename Derived>
|
||||
class CholmodBase : public SparseSolverBase<Derived>
|
||||
{
|
||||
protected:
|
||||
typedef SparseSolverBase<Derived> Base;
|
||||
using Base::derived;
|
||||
using Base::m_isInitialized;
|
||||
public:
|
||||
typedef _MatrixType MatrixType;
|
||||
enum { UpLo = _UpLo };
|
||||
typedef typename MatrixType::Scalar Scalar;
|
||||
typedef typename MatrixType::RealScalar RealScalar;
|
||||
typedef MatrixType CholMatrixType;
|
||||
typedef typename MatrixType::StorageIndex StorageIndex;
|
||||
enum {
|
||||
ColsAtCompileTime = MatrixType::ColsAtCompileTime,
|
||||
MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime
|
||||
};
|
||||
|
||||
public:
|
||||
|
||||
CholmodBase()
|
||||
: m_cholmodFactor(0), m_info(Success), m_factorizationIsOk(false), m_analysisIsOk(false)
|
||||
{
|
||||
EIGEN_STATIC_ASSERT((internal::is_same<double,RealScalar>::value), CHOLMOD_SUPPORTS_DOUBLE_PRECISION_ONLY);
|
||||
m_shiftOffset[0] = m_shiftOffset[1] = 0.0;
|
||||
cholmod_start(&m_cholmod);
|
||||
}
|
||||
|
||||
explicit CholmodBase(const MatrixType& matrix)
|
||||
: m_cholmodFactor(0), m_info(Success), m_factorizationIsOk(false), m_analysisIsOk(false)
|
||||
{
|
||||
EIGEN_STATIC_ASSERT((internal::is_same<double,RealScalar>::value), CHOLMOD_SUPPORTS_DOUBLE_PRECISION_ONLY);
|
||||
m_shiftOffset[0] = m_shiftOffset[1] = 0.0;
|
||||
cholmod_start(&m_cholmod);
|
||||
compute(matrix);
|
||||
}
|
||||
|
||||
~CholmodBase()
|
||||
{
|
||||
if(m_cholmodFactor)
|
||||
cholmod_free_factor(&m_cholmodFactor, &m_cholmod);
|
||||
cholmod_finish(&m_cholmod);
|
||||
}
|
||||
|
||||
inline StorageIndex cols() const { return internal::convert_index<StorageIndex, Index>(m_cholmodFactor->n); }
|
||||
inline StorageIndex rows() const { return internal::convert_index<StorageIndex, Index>(m_cholmodFactor->n); }
|
||||
|
||||
/** \brief Reports whether previous computation was successful.
|
||||
*
|
||||
* \returns \c Success if computation was succesful,
|
||||
* \c NumericalIssue if the matrix.appears to be negative.
|
||||
*/
|
||||
ComputationInfo info() const
|
||||
{
|
||||
eigen_assert(m_isInitialized && "Decomposition is not initialized.");
|
||||
return m_info;
|
||||
}
|
||||
|
||||
/** Computes the sparse Cholesky decomposition of \a matrix */
|
||||
Derived& compute(const MatrixType& matrix)
|
||||
{
|
||||
analyzePattern(matrix);
|
||||
factorize(matrix);
|
||||
return derived();
|
||||
}
|
||||
|
||||
/** Performs a symbolic decomposition on the sparsity pattern of \a matrix.
|
||||
*
|
||||
* This function is particularly useful when solving for several problems having the same structure.
|
||||
*
|
||||
* \sa factorize()
|
||||
*/
|
||||
void analyzePattern(const MatrixType& matrix)
|
||||
{
|
||||
if(m_cholmodFactor)
|
||||
{
|
||||
cholmod_free_factor(&m_cholmodFactor, &m_cholmod);
|
||||
m_cholmodFactor = 0;
|
||||
}
|
||||
cholmod_sparse A = viewAsCholmod(matrix.template selfadjointView<UpLo>());
|
||||
m_cholmodFactor = cholmod_analyze(&A, &m_cholmod);
|
||||
|
||||
this->m_isInitialized = true;
|
||||
this->m_info = Success;
|
||||
m_analysisIsOk = true;
|
||||
m_factorizationIsOk = false;
|
||||
}
|
||||
|
||||
/** Performs a numeric decomposition of \a matrix
|
||||
*
|
||||
* The given matrix must have the same sparsity pattern as the matrix on which the symbolic decomposition has been performed.
|
||||
*
|
||||
* \sa analyzePattern()
|
||||
*/
|
||||
void factorize(const MatrixType& matrix)
|
||||
{
|
||||
eigen_assert(m_analysisIsOk && "You must first call analyzePattern()");
|
||||
cholmod_sparse A = viewAsCholmod(matrix.template selfadjointView<UpLo>());
|
||||
cholmod_factorize_p(&A, m_shiftOffset, 0, 0, m_cholmodFactor, &m_cholmod);
|
||||
|
||||
// If the factorization failed, minor is the column at which it did. On success minor == n.
|
||||
this->m_info = (m_cholmodFactor->minor == m_cholmodFactor->n ? Success : NumericalIssue);
|
||||
m_factorizationIsOk = true;
|
||||
}
|
||||
|
||||
/** Returns a reference to the Cholmod's configuration structure to get a full control over the performed operations.
|
||||
* See the Cholmod user guide for details. */
|
||||
cholmod_common& cholmod() { return m_cholmod; }
|
||||
|
||||
#ifndef EIGEN_PARSED_BY_DOXYGEN
|
||||
/** \internal */
|
||||
template<typename Rhs,typename Dest>
|
||||
void _solve_impl(const MatrixBase<Rhs> &b, MatrixBase<Dest> &dest) const
|
||||
{
|
||||
eigen_assert(m_factorizationIsOk && "The decomposition is not in a valid state for solving, you must first call either compute() or symbolic()/numeric()");
|
||||
const Index size = m_cholmodFactor->n;
|
||||
EIGEN_UNUSED_VARIABLE(size);
|
||||
eigen_assert(size==b.rows());
|
||||
|
||||
// Cholmod needs column-major stoarge without inner-stride, which corresponds to the default behavior of Ref.
|
||||
Ref<const Matrix<typename Rhs::Scalar,Dynamic,Dynamic,ColMajor> > b_ref(b.derived());
|
||||
|
||||
cholmod_dense b_cd = viewAsCholmod(b_ref);
|
||||
cholmod_dense* x_cd = cholmod_solve(CHOLMOD_A, m_cholmodFactor, &b_cd, &m_cholmod);
|
||||
if(!x_cd)
|
||||
{
|
||||
this->m_info = NumericalIssue;
|
||||
return;
|
||||
}
|
||||
// TODO optimize this copy by swapping when possible (be careful with alignment, etc.)
|
||||
dest = Matrix<Scalar,Dest::RowsAtCompileTime,Dest::ColsAtCompileTime>::Map(reinterpret_cast<Scalar*>(x_cd->x),b.rows(),b.cols());
|
||||
cholmod_free_dense(&x_cd, &m_cholmod);
|
||||
}
|
||||
|
||||
/** \internal */
|
||||
template<typename RhsDerived, typename DestDerived>
|
||||
void _solve_impl(const SparseMatrixBase<RhsDerived> &b, SparseMatrixBase<DestDerived> &dest) const
|
||||
{
|
||||
eigen_assert(m_factorizationIsOk && "The decomposition is not in a valid state for solving, you must first call either compute() or symbolic()/numeric()");
|
||||
const Index size = m_cholmodFactor->n;
|
||||
EIGEN_UNUSED_VARIABLE(size);
|
||||
eigen_assert(size==b.rows());
|
||||
|
||||
// note: cs stands for Cholmod Sparse
|
||||
Ref<SparseMatrix<typename RhsDerived::Scalar,ColMajor,typename RhsDerived::StorageIndex> > b_ref(b.const_cast_derived());
|
||||
cholmod_sparse b_cs = viewAsCholmod(b_ref);
|
||||
cholmod_sparse* x_cs = cholmod_spsolve(CHOLMOD_A, m_cholmodFactor, &b_cs, &m_cholmod);
|
||||
if(!x_cs)
|
||||
{
|
||||
this->m_info = NumericalIssue;
|
||||
return;
|
||||
}
|
||||
// TODO optimize this copy by swapping when possible (be careful with alignment, etc.)
|
||||
dest.derived() = viewAsEigen<typename DestDerived::Scalar,ColMajor,typename DestDerived::StorageIndex>(*x_cs);
|
||||
cholmod_free_sparse(&x_cs, &m_cholmod);
|
||||
}
|
||||
#endif // EIGEN_PARSED_BY_DOXYGEN
|
||||
|
||||
|
||||
/** Sets the shift parameter that will be used to adjust the diagonal coefficients during the numerical factorization.
|
||||
*
|
||||
* During the numerical factorization, an offset term is added to the diagonal coefficients:\n
|
||||
* \c d_ii = \a offset + \c d_ii
|
||||
*
|
||||
* The default is \a offset=0.
|
||||
*
|
||||
* \returns a reference to \c *this.
|
||||
*/
|
||||
Derived& setShift(const RealScalar& offset)
|
||||
{
|
||||
m_shiftOffset[0] = double(offset);
|
||||
return derived();
|
||||
}
|
||||
|
||||
/** \returns the determinant of the underlying matrix from the current factorization */
|
||||
Scalar determinant() const
|
||||
{
|
||||
using std::exp;
|
||||
return exp(logDeterminant());
|
||||
}
|
||||
|
||||
/** \returns the log determinant of the underlying matrix from the current factorization */
|
||||
Scalar logDeterminant() const
|
||||
{
|
||||
using std::log;
|
||||
using numext::real;
|
||||
eigen_assert(m_factorizationIsOk && "The decomposition is not in a valid state for solving, you must first call either compute() or symbolic()/numeric()");
|
||||
|
||||
RealScalar logDet = 0;
|
||||
Scalar *x = static_cast<Scalar*>(m_cholmodFactor->x);
|
||||
if (m_cholmodFactor->is_super)
|
||||
{
|
||||
// Supernodal factorization stored as a packed list of dense column-major blocs,
|
||||
// as described by the following structure:
|
||||
|
||||
// super[k] == index of the first column of the j-th super node
|
||||
StorageIndex *super = static_cast<StorageIndex*>(m_cholmodFactor->super);
|
||||
// pi[k] == offset to the description of row indices
|
||||
StorageIndex *pi = static_cast<StorageIndex*>(m_cholmodFactor->pi);
|
||||
// px[k] == offset to the respective dense block
|
||||
StorageIndex *px = static_cast<StorageIndex*>(m_cholmodFactor->px);
|
||||
|
||||
Index nb_super_nodes = m_cholmodFactor->nsuper;
|
||||
for (Index k=0; k < nb_super_nodes; ++k)
|
||||
{
|
||||
StorageIndex ncols = super[k + 1] - super[k];
|
||||
StorageIndex nrows = pi[k + 1] - pi[k];
|
||||
|
||||
Map<const Array<Scalar,1,Dynamic>, 0, InnerStride<> > sk(x + px[k], ncols, InnerStride<>(nrows+1));
|
||||
logDet += sk.real().log().sum();
|
||||
}
|
||||
}
|
||||
else
|
||||
{
|
||||
// Simplicial factorization stored as standard CSC matrix.
|
||||
StorageIndex *p = static_cast<StorageIndex*>(m_cholmodFactor->p);
|
||||
Index size = m_cholmodFactor->n;
|
||||
for (Index k=0; k<size; ++k)
|
||||
logDet += log(real( x[p[k]] ));
|
||||
}
|
||||
if (m_cholmodFactor->is_ll)
|
||||
logDet *= 2.0;
|
||||
return logDet;
|
||||
};
|
||||
|
||||
template<typename Stream>
|
||||
void dumpMemory(Stream& /*s*/)
|
||||
{}
|
||||
|
||||
protected:
|
||||
mutable cholmod_common m_cholmod;
|
||||
cholmod_factor* m_cholmodFactor;
|
||||
double m_shiftOffset[2];
|
||||
mutable ComputationInfo m_info;
|
||||
int m_factorizationIsOk;
|
||||
int m_analysisIsOk;
|
||||
};
|
||||
|
||||
/** \ingroup CholmodSupport_Module
|
||||
* \class CholmodSimplicialLLT
|
||||
* \brief A simplicial direct Cholesky (LLT) factorization and solver based on Cholmod
|
||||
*
|
||||
* This class allows to solve for A.X = B sparse linear problems via a simplicial LL^T Cholesky factorization
|
||||
* using the Cholmod library.
|
||||
* This simplicial variant is equivalent to Eigen's built-in SimplicialLLT class. Therefore, it has little practical interest.
|
||||
* The sparse matrix A must be selfadjoint and positive definite. The vectors or matrices
|
||||
* X and B can be either dense or sparse.
|
||||
*
|
||||
* \tparam _MatrixType the type of the sparse matrix A, it must be a SparseMatrix<>
|
||||
* \tparam _UpLo the triangular part that will be used for the computations. It can be Lower
|
||||
* or Upper. Default is Lower.
|
||||
*
|
||||
* \implsparsesolverconcept
|
||||
*
|
||||
* This class supports all kind of SparseMatrix<>: row or column major; upper, lower, or both; compressed or non compressed.
|
||||
*
|
||||
* \warning Only double precision real and complex scalar types are supported by Cholmod.
|
||||
*
|
||||
* \sa \ref TutorialSparseSolverConcept, class CholmodSupernodalLLT, class SimplicialLLT
|
||||
*/
|
||||
template<typename _MatrixType, int _UpLo = Lower>
|
||||
class CholmodSimplicialLLT : public CholmodBase<_MatrixType, _UpLo, CholmodSimplicialLLT<_MatrixType, _UpLo> >
|
||||
{
|
||||
typedef CholmodBase<_MatrixType, _UpLo, CholmodSimplicialLLT> Base;
|
||||
using Base::m_cholmod;
|
||||
|
||||
public:
|
||||
|
||||
typedef _MatrixType MatrixType;
|
||||
|
||||
CholmodSimplicialLLT() : Base() { init(); }
|
||||
|
||||
CholmodSimplicialLLT(const MatrixType& matrix) : Base()
|
||||
{
|
||||
init();
|
||||
this->compute(matrix);
|
||||
}
|
||||
|
||||
~CholmodSimplicialLLT() {}
|
||||
protected:
|
||||
void init()
|
||||
{
|
||||
m_cholmod.final_asis = 0;
|
||||
m_cholmod.supernodal = CHOLMOD_SIMPLICIAL;
|
||||
m_cholmod.final_ll = 1;
|
||||
}
|
||||
};
|
||||
|
||||
|
||||
/** \ingroup CholmodSupport_Module
|
||||
* \class CholmodSimplicialLDLT
|
||||
* \brief A simplicial direct Cholesky (LDLT) factorization and solver based on Cholmod
|
||||
*
|
||||
* This class allows to solve for A.X = B sparse linear problems via a simplicial LDL^T Cholesky factorization
|
||||
* using the Cholmod library.
|
||||
* This simplicial variant is equivalent to Eigen's built-in SimplicialLDLT class. Therefore, it has little practical interest.
|
||||
* The sparse matrix A must be selfadjoint and positive definite. The vectors or matrices
|
||||
* X and B can be either dense or sparse.
|
||||
*
|
||||
* \tparam _MatrixType the type of the sparse matrix A, it must be a SparseMatrix<>
|
||||
* \tparam _UpLo the triangular part that will be used for the computations. It can be Lower
|
||||
* or Upper. Default is Lower.
|
||||
*
|
||||
* \implsparsesolverconcept
|
||||
*
|
||||
* This class supports all kind of SparseMatrix<>: row or column major; upper, lower, or both; compressed or non compressed.
|
||||
*
|
||||
* \warning Only double precision real and complex scalar types are supported by Cholmod.
|
||||
*
|
||||
* \sa \ref TutorialSparseSolverConcept, class CholmodSupernodalLLT, class SimplicialLDLT
|
||||
*/
|
||||
template<typename _MatrixType, int _UpLo = Lower>
|
||||
class CholmodSimplicialLDLT : public CholmodBase<_MatrixType, _UpLo, CholmodSimplicialLDLT<_MatrixType, _UpLo> >
|
||||
{
|
||||
typedef CholmodBase<_MatrixType, _UpLo, CholmodSimplicialLDLT> Base;
|
||||
using Base::m_cholmod;
|
||||
|
||||
public:
|
||||
|
||||
typedef _MatrixType MatrixType;
|
||||
|
||||
CholmodSimplicialLDLT() : Base() { init(); }
|
||||
|
||||
CholmodSimplicialLDLT(const MatrixType& matrix) : Base()
|
||||
{
|
||||
init();
|
||||
this->compute(matrix);
|
||||
}
|
||||
|
||||
~CholmodSimplicialLDLT() {}
|
||||
protected:
|
||||
void init()
|
||||
{
|
||||
m_cholmod.final_asis = 1;
|
||||
m_cholmod.supernodal = CHOLMOD_SIMPLICIAL;
|
||||
}
|
||||
};
|
||||
|
||||
/** \ingroup CholmodSupport_Module
|
||||
* \class CholmodSupernodalLLT
|
||||
* \brief A supernodal Cholesky (LLT) factorization and solver based on Cholmod
|
||||
*
|
||||
* This class allows to solve for A.X = B sparse linear problems via a supernodal LL^T Cholesky factorization
|
||||
* using the Cholmod library.
|
||||
* This supernodal variant performs best on dense enough problems, e.g., 3D FEM, or very high order 2D FEM.
|
||||
* The sparse matrix A must be selfadjoint and positive definite. The vectors or matrices
|
||||
* X and B can be either dense or sparse.
|
||||
*
|
||||
* \tparam _MatrixType the type of the sparse matrix A, it must be a SparseMatrix<>
|
||||
* \tparam _UpLo the triangular part that will be used for the computations. It can be Lower
|
||||
* or Upper. Default is Lower.
|
||||
*
|
||||
* \implsparsesolverconcept
|
||||
*
|
||||
* This class supports all kind of SparseMatrix<>: row or column major; upper, lower, or both; compressed or non compressed.
|
||||
*
|
||||
* \warning Only double precision real and complex scalar types are supported by Cholmod.
|
||||
*
|
||||
* \sa \ref TutorialSparseSolverConcept
|
||||
*/
|
||||
template<typename _MatrixType, int _UpLo = Lower>
|
||||
class CholmodSupernodalLLT : public CholmodBase<_MatrixType, _UpLo, CholmodSupernodalLLT<_MatrixType, _UpLo> >
|
||||
{
|
||||
typedef CholmodBase<_MatrixType, _UpLo, CholmodSupernodalLLT> Base;
|
||||
using Base::m_cholmod;
|
||||
|
||||
public:
|
||||
|
||||
typedef _MatrixType MatrixType;
|
||||
|
||||
CholmodSupernodalLLT() : Base() { init(); }
|
||||
|
||||
CholmodSupernodalLLT(const MatrixType& matrix) : Base()
|
||||
{
|
||||
init();
|
||||
this->compute(matrix);
|
||||
}
|
||||
|
||||
~CholmodSupernodalLLT() {}
|
||||
protected:
|
||||
void init()
|
||||
{
|
||||
m_cholmod.final_asis = 1;
|
||||
m_cholmod.supernodal = CHOLMOD_SUPERNODAL;
|
||||
}
|
||||
};
|
||||
|
||||
/** \ingroup CholmodSupport_Module
|
||||
* \class CholmodDecomposition
|
||||
* \brief A general Cholesky factorization and solver based on Cholmod
|
||||
*
|
||||
* This class allows to solve for A.X = B sparse linear problems via a LL^T or LDL^T Cholesky factorization
|
||||
* using the Cholmod library. The sparse matrix A must be selfadjoint and positive definite. The vectors or matrices
|
||||
* X and B can be either dense or sparse.
|
||||
*
|
||||
* This variant permits to change the underlying Cholesky method at runtime.
|
||||
* On the other hand, it does not provide access to the result of the factorization.
|
||||
* The default is to let Cholmod automatically choose between a simplicial and supernodal factorization.
|
||||
*
|
||||
* \tparam _MatrixType the type of the sparse matrix A, it must be a SparseMatrix<>
|
||||
* \tparam _UpLo the triangular part that will be used for the computations. It can be Lower
|
||||
* or Upper. Default is Lower.
|
||||
*
|
||||
* \implsparsesolverconcept
|
||||
*
|
||||
* This class supports all kind of SparseMatrix<>: row or column major; upper, lower, or both; compressed or non compressed.
|
||||
*
|
||||
* \warning Only double precision real and complex scalar types are supported by Cholmod.
|
||||
*
|
||||
* \sa \ref TutorialSparseSolverConcept
|
||||
*/
|
||||
template<typename _MatrixType, int _UpLo = Lower>
|
||||
class CholmodDecomposition : public CholmodBase<_MatrixType, _UpLo, CholmodDecomposition<_MatrixType, _UpLo> >
|
||||
{
|
||||
typedef CholmodBase<_MatrixType, _UpLo, CholmodDecomposition> Base;
|
||||
using Base::m_cholmod;
|
||||
|
||||
public:
|
||||
|
||||
typedef _MatrixType MatrixType;
|
||||
|
||||
CholmodDecomposition() : Base() { init(); }
|
||||
|
||||
CholmodDecomposition(const MatrixType& matrix) : Base()
|
||||
{
|
||||
init();
|
||||
this->compute(matrix);
|
||||
}
|
||||
|
||||
~CholmodDecomposition() {}
|
||||
|
||||
void setMode(CholmodMode mode)
|
||||
{
|
||||
switch(mode)
|
||||
{
|
||||
case CholmodAuto:
|
||||
m_cholmod.final_asis = 1;
|
||||
m_cholmod.supernodal = CHOLMOD_AUTO;
|
||||
break;
|
||||
case CholmodSimplicialLLt:
|
||||
m_cholmod.final_asis = 0;
|
||||
m_cholmod.supernodal = CHOLMOD_SIMPLICIAL;
|
||||
m_cholmod.final_ll = 1;
|
||||
break;
|
||||
case CholmodSupernodalLLt:
|
||||
m_cholmod.final_asis = 1;
|
||||
m_cholmod.supernodal = CHOLMOD_SUPERNODAL;
|
||||
break;
|
||||
case CholmodLDLt:
|
||||
m_cholmod.final_asis = 1;
|
||||
m_cholmod.supernodal = CHOLMOD_SIMPLICIAL;
|
||||
break;
|
||||
default:
|
||||
break;
|
||||
}
|
||||
}
|
||||
protected:
|
||||
void init()
|
||||
{
|
||||
m_cholmod.final_asis = 1;
|
||||
m_cholmod.supernodal = CHOLMOD_AUTO;
|
||||
}
|
||||
};
|
||||
|
||||
} // end namespace Eigen
|
||||
|
||||
#endif // EIGEN_CHOLMODSUPPORT_H
|
||||
|
|
@ -0,0 +1,346 @@
|
|||
// This file is part of Eigen, a lightweight C++ template library
|
||||
// for linear algebra.
|
||||
//
|
||||
// Copyright (C) 2009 Claire Maurice
|
||||
// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
|
||||
// Copyright (C) 2010,2012 Jitse Niesen <jitse@maths.leeds.ac.uk>
|
||||
//
|
||||
// This Source Code Form is subject to the terms of the Mozilla
|
||||
// Public License v. 2.0. If a copy of the MPL was not distributed
|
||||
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
|
||||
|
||||
#ifndef EIGEN_COMPLEX_EIGEN_SOLVER_H
|
||||
#define EIGEN_COMPLEX_EIGEN_SOLVER_H
|
||||
|
||||
#include "./ComplexSchur.h"
|
||||
|
||||
namespace Eigen {
|
||||
|
||||
/** \eigenvalues_module \ingroup Eigenvalues_Module
|
||||
*
|
||||
*
|
||||
* \class ComplexEigenSolver
|
||||
*
|
||||
* \brief Computes eigenvalues and eigenvectors of general complex matrices
|
||||
*
|
||||
* \tparam _MatrixType the type of the matrix of which we are
|
||||
* computing the eigendecomposition; this is expected to be an
|
||||
* instantiation of the Matrix class template.
|
||||
*
|
||||
* The eigenvalues and eigenvectors of a matrix \f$ A \f$ are scalars
|
||||
* \f$ \lambda \f$ and vectors \f$ v \f$ such that \f$ Av = \lambda v
|
||||
* \f$. If \f$ D \f$ is a diagonal matrix with the eigenvalues on
|
||||
* the diagonal, and \f$ V \f$ is a matrix with the eigenvectors as
|
||||
* its columns, then \f$ A V = V D \f$. The matrix \f$ V \f$ is
|
||||
* almost always invertible, in which case we have \f$ A = V D V^{-1}
|
||||
* \f$. This is called the eigendecomposition.
|
||||
*
|
||||
* The main function in this class is compute(), which computes the
|
||||
* eigenvalues and eigenvectors of a given function. The
|
||||
* documentation for that function contains an example showing the
|
||||
* main features of the class.
|
||||
*
|
||||
* \sa class EigenSolver, class SelfAdjointEigenSolver
|
||||
*/
|
||||
template<typename _MatrixType> class ComplexEigenSolver
|
||||
{
|
||||
public:
|
||||
|
||||
/** \brief Synonym for the template parameter \p _MatrixType. */
|
||||
typedef _MatrixType MatrixType;
|
||||
|
||||
enum {
|
||||
RowsAtCompileTime = MatrixType::RowsAtCompileTime,
|
||||
ColsAtCompileTime = MatrixType::ColsAtCompileTime,
|
||||
Options = MatrixType::Options,
|
||||
MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
|
||||
MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime
|
||||
};
|
||||
|
||||
/** \brief Scalar type for matrices of type #MatrixType. */
|
||||
typedef typename MatrixType::Scalar Scalar;
|
||||
typedef typename NumTraits<Scalar>::Real RealScalar;
|
||||
typedef Eigen::Index Index; ///< \deprecated since Eigen 3.3
|
||||
|
||||
/** \brief Complex scalar type for #MatrixType.
|
||||
*
|
||||
* This is \c std::complex<Scalar> if #Scalar is real (e.g.,
|
||||
* \c float or \c double) and just \c Scalar if #Scalar is
|
||||
* complex.
|
||||
*/
|
||||
typedef std::complex<RealScalar> ComplexScalar;
|
||||
|
||||
/** \brief Type for vector of eigenvalues as returned by eigenvalues().
|
||||
*
|
||||
* This is a column vector with entries of type #ComplexScalar.
|
||||
* The length of the vector is the size of #MatrixType.
|
||||
*/
|
||||
typedef Matrix<ComplexScalar, ColsAtCompileTime, 1, Options&(~RowMajor), MaxColsAtCompileTime, 1> EigenvalueType;
|
||||
|
||||
/** \brief Type for matrix of eigenvectors as returned by eigenvectors().
|
||||
*
|
||||
* This is a square matrix with entries of type #ComplexScalar.
|
||||
* The size is the same as the size of #MatrixType.
|
||||
*/
|
||||
typedef Matrix<ComplexScalar, RowsAtCompileTime, ColsAtCompileTime, Options, MaxRowsAtCompileTime, MaxColsAtCompileTime> EigenvectorType;
|
||||
|
||||
/** \brief Default constructor.
|
||||
*
|
||||
* The default constructor is useful in cases in which the user intends to
|
||||
* perform decompositions via compute().
|
||||
*/
|
||||
ComplexEigenSolver()
|
||||
: m_eivec(),
|
||||
m_eivalues(),
|
||||
m_schur(),
|
||||
m_isInitialized(false),
|
||||
m_eigenvectorsOk(false),
|
||||
m_matX()
|
||||
{}
|
||||
|
||||
/** \brief Default Constructor with memory preallocation
|
||||
*
|
||||
* Like the default constructor but with preallocation of the internal data
|
||||
* according to the specified problem \a size.
|
||||
* \sa ComplexEigenSolver()
|
||||
*/
|
||||
explicit ComplexEigenSolver(Index size)
|
||||
: m_eivec(size, size),
|
||||
m_eivalues(size),
|
||||
m_schur(size),
|
||||
m_isInitialized(false),
|
||||
m_eigenvectorsOk(false),
|
||||
m_matX(size, size)
|
||||
{}
|
||||
|
||||
/** \brief Constructor; computes eigendecomposition of given matrix.
|
||||
*
|
||||
* \param[in] matrix Square matrix whose eigendecomposition is to be computed.
|
||||
* \param[in] computeEigenvectors If true, both the eigenvectors and the
|
||||
* eigenvalues are computed; if false, only the eigenvalues are
|
||||
* computed.
|
||||
*
|
||||
* This constructor calls compute() to compute the eigendecomposition.
|
||||
*/
|
||||
template<typename InputType>
|
||||
explicit ComplexEigenSolver(const EigenBase<InputType>& matrix, bool computeEigenvectors = true)
|
||||
: m_eivec(matrix.rows(),matrix.cols()),
|
||||
m_eivalues(matrix.cols()),
|
||||
m_schur(matrix.rows()),
|
||||
m_isInitialized(false),
|
||||
m_eigenvectorsOk(false),
|
||||
m_matX(matrix.rows(),matrix.cols())
|
||||
{
|
||||
compute(matrix.derived(), computeEigenvectors);
|
||||
}
|
||||
|
||||
/** \brief Returns the eigenvectors of given matrix.
|
||||
*
|
||||
* \returns A const reference to the matrix whose columns are the eigenvectors.
|
||||
*
|
||||
* \pre Either the constructor
|
||||
* ComplexEigenSolver(const MatrixType& matrix, bool) or the member
|
||||
* function compute(const MatrixType& matrix, bool) has been called before
|
||||
* to compute the eigendecomposition of a matrix, and
|
||||
* \p computeEigenvectors was set to true (the default).
|
||||
*
|
||||
* This function returns a matrix whose columns are the eigenvectors. Column
|
||||
* \f$ k \f$ is an eigenvector corresponding to eigenvalue number \f$ k
|
||||
* \f$ as returned by eigenvalues(). The eigenvectors are normalized to
|
||||
* have (Euclidean) norm equal to one. The matrix returned by this
|
||||
* function is the matrix \f$ V \f$ in the eigendecomposition \f$ A = V D
|
||||
* V^{-1} \f$, if it exists.
|
||||
*
|
||||
* Example: \include ComplexEigenSolver_eigenvectors.cpp
|
||||
* Output: \verbinclude ComplexEigenSolver_eigenvectors.out
|
||||
*/
|
||||
const EigenvectorType& eigenvectors() const
|
||||
{
|
||||
eigen_assert(m_isInitialized && "ComplexEigenSolver is not initialized.");
|
||||
eigen_assert(m_eigenvectorsOk && "The eigenvectors have not been computed together with the eigenvalues.");
|
||||
return m_eivec;
|
||||
}
|
||||
|
||||
/** \brief Returns the eigenvalues of given matrix.
|
||||
*
|
||||
* \returns A const reference to the column vector containing the eigenvalues.
|
||||
*
|
||||
* \pre Either the constructor
|
||||
* ComplexEigenSolver(const MatrixType& matrix, bool) or the member
|
||||
* function compute(const MatrixType& matrix, bool) has been called before
|
||||
* to compute the eigendecomposition of a matrix.
|
||||
*
|
||||
* This function returns a column vector containing the
|
||||
* eigenvalues. Eigenvalues are repeated according to their
|
||||
* algebraic multiplicity, so there are as many eigenvalues as
|
||||
* rows in the matrix. The eigenvalues are not sorted in any particular
|
||||
* order.
|
||||
*
|
||||
* Example: \include ComplexEigenSolver_eigenvalues.cpp
|
||||
* Output: \verbinclude ComplexEigenSolver_eigenvalues.out
|
||||
*/
|
||||
const EigenvalueType& eigenvalues() const
|
||||
{
|
||||
eigen_assert(m_isInitialized && "ComplexEigenSolver is not initialized.");
|
||||
return m_eivalues;
|
||||
}
|
||||
|
||||
/** \brief Computes eigendecomposition of given matrix.
|
||||
*
|
||||
* \param[in] matrix Square matrix whose eigendecomposition is to be computed.
|
||||
* \param[in] computeEigenvectors If true, both the eigenvectors and the
|
||||
* eigenvalues are computed; if false, only the eigenvalues are
|
||||
* computed.
|
||||
* \returns Reference to \c *this
|
||||
*
|
||||
* This function computes the eigenvalues of the complex matrix \p matrix.
|
||||
* The eigenvalues() function can be used to retrieve them. If
|
||||
* \p computeEigenvectors is true, then the eigenvectors are also computed
|
||||
* and can be retrieved by calling eigenvectors().
|
||||
*
|
||||
* The matrix is first reduced to Schur form using the
|
||||
* ComplexSchur class. The Schur decomposition is then used to
|
||||
* compute the eigenvalues and eigenvectors.
|
||||
*
|
||||
* The cost of the computation is dominated by the cost of the
|
||||
* Schur decomposition, which is \f$ O(n^3) \f$ where \f$ n \f$
|
||||
* is the size of the matrix.
|
||||
*
|
||||
* Example: \include ComplexEigenSolver_compute.cpp
|
||||
* Output: \verbinclude ComplexEigenSolver_compute.out
|
||||
*/
|
||||
template<typename InputType>
|
||||
ComplexEigenSolver& compute(const EigenBase<InputType>& matrix, bool computeEigenvectors = true);
|
||||
|
||||
/** \brief Reports whether previous computation was successful.
|
||||
*
|
||||
* \returns \c Success if computation was succesful, \c NoConvergence otherwise.
|
||||
*/
|
||||
ComputationInfo info() const
|
||||
{
|
||||
eigen_assert(m_isInitialized && "ComplexEigenSolver is not initialized.");
|
||||
return m_schur.info();
|
||||
}
|
||||
|
||||
/** \brief Sets the maximum number of iterations allowed. */
|
||||
ComplexEigenSolver& setMaxIterations(Index maxIters)
|
||||
{
|
||||
m_schur.setMaxIterations(maxIters);
|
||||
return *this;
|
||||
}
|
||||
|
||||
/** \brief Returns the maximum number of iterations. */
|
||||
Index getMaxIterations()
|
||||
{
|
||||
return m_schur.getMaxIterations();
|
||||
}
|
||||
|
||||
protected:
|
||||
|
||||
static void check_template_parameters()
|
||||
{
|
||||
EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar);
|
||||
}
|
||||
|
||||
EigenvectorType m_eivec;
|
||||
EigenvalueType m_eivalues;
|
||||
ComplexSchur<MatrixType> m_schur;
|
||||
bool m_isInitialized;
|
||||
bool m_eigenvectorsOk;
|
||||
EigenvectorType m_matX;
|
||||
|
||||
private:
|
||||
void doComputeEigenvectors(RealScalar matrixnorm);
|
||||
void sortEigenvalues(bool computeEigenvectors);
|
||||
};
|
||||
|
||||
|
||||
template<typename MatrixType>
|
||||
template<typename InputType>
|
||||
ComplexEigenSolver<MatrixType>&
|
||||
ComplexEigenSolver<MatrixType>::compute(const EigenBase<InputType>& matrix, bool computeEigenvectors)
|
||||
{
|
||||
check_template_parameters();
|
||||
|
||||
// this code is inspired from Jampack
|
||||
eigen_assert(matrix.cols() == matrix.rows());
|
||||
|
||||
// Do a complex Schur decomposition, A = U T U^*
|
||||
// The eigenvalues are on the diagonal of T.
|
||||
m_schur.compute(matrix.derived(), computeEigenvectors);
|
||||
|
||||
if(m_schur.info() == Success)
|
||||
{
|
||||
m_eivalues = m_schur.matrixT().diagonal();
|
||||
if(computeEigenvectors)
|
||||
doComputeEigenvectors(m_schur.matrixT().norm());
|
||||
sortEigenvalues(computeEigenvectors);
|
||||
}
|
||||
|
||||
m_isInitialized = true;
|
||||
m_eigenvectorsOk = computeEigenvectors;
|
||||
return *this;
|
||||
}
|
||||
|
||||
|
||||
template<typename MatrixType>
|
||||
void ComplexEigenSolver<MatrixType>::doComputeEigenvectors(RealScalar matrixnorm)
|
||||
{
|
||||
const Index n = m_eivalues.size();
|
||||
|
||||
matrixnorm = numext::maxi(matrixnorm,(std::numeric_limits<RealScalar>::min)());
|
||||
|
||||
// Compute X such that T = X D X^(-1), where D is the diagonal of T.
|
||||
// The matrix X is unit triangular.
|
||||
m_matX = EigenvectorType::Zero(n, n);
|
||||
for(Index k=n-1 ; k>=0 ; k--)
|
||||
{
|
||||
m_matX.coeffRef(k,k) = ComplexScalar(1.0,0.0);
|
||||
// Compute X(i,k) using the (i,k) entry of the equation X T = D X
|
||||
for(Index i=k-1 ; i>=0 ; i--)
|
||||
{
|
||||
m_matX.coeffRef(i,k) = -m_schur.matrixT().coeff(i,k);
|
||||
if(k-i-1>0)
|
||||
m_matX.coeffRef(i,k) -= (m_schur.matrixT().row(i).segment(i+1,k-i-1) * m_matX.col(k).segment(i+1,k-i-1)).value();
|
||||
ComplexScalar z = m_schur.matrixT().coeff(i,i) - m_schur.matrixT().coeff(k,k);
|
||||
if(z==ComplexScalar(0))
|
||||
{
|
||||
// If the i-th and k-th eigenvalue are equal, then z equals 0.
|
||||
// Use a small value instead, to prevent division by zero.
|
||||
numext::real_ref(z) = NumTraits<RealScalar>::epsilon() * matrixnorm;
|
||||
}
|
||||
m_matX.coeffRef(i,k) = m_matX.coeff(i,k) / z;
|
||||
}
|
||||
}
|
||||
|
||||
// Compute V as V = U X; now A = U T U^* = U X D X^(-1) U^* = V D V^(-1)
|
||||
m_eivec.noalias() = m_schur.matrixU() * m_matX;
|
||||
// .. and normalize the eigenvectors
|
||||
for(Index k=0 ; k<n ; k++)
|
||||
{
|
||||
m_eivec.col(k).normalize();
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
template<typename MatrixType>
|
||||
void ComplexEigenSolver<MatrixType>::sortEigenvalues(bool computeEigenvectors)
|
||||
{
|
||||
const Index n = m_eivalues.size();
|
||||
for (Index i=0; i<n; i++)
|
||||
{
|
||||
Index k;
|
||||
m_eivalues.cwiseAbs().tail(n-i).minCoeff(&k);
|
||||
if (k != 0)
|
||||
{
|
||||
k += i;
|
||||
std::swap(m_eivalues[k],m_eivalues[i]);
|
||||
if(computeEigenvectors)
|
||||
m_eivec.col(i).swap(m_eivec.col(k));
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
} // end namespace Eigen
|
||||
|
||||
#endif // EIGEN_COMPLEX_EIGEN_SOLVER_H
|
||||
|
|
@ -0,0 +1,462 @@
|
|||
// This file is part of Eigen, a lightweight C++ template library
|
||||
// for linear algebra.
|
||||
//
|
||||
// Copyright (C) 2009 Claire Maurice
|
||||
// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
|
||||
// Copyright (C) 2010,2012 Jitse Niesen <jitse@maths.leeds.ac.uk>
|
||||
//
|
||||
// This Source Code Form is subject to the terms of the Mozilla
|
||||
// Public License v. 2.0. If a copy of the MPL was not distributed
|
||||
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
|
||||
|
||||
#ifndef EIGEN_COMPLEX_SCHUR_H
|
||||
#define EIGEN_COMPLEX_SCHUR_H
|
||||
|
||||
#include "./HessenbergDecomposition.h"
|
||||
|
||||
namespace Eigen {
|
||||
|
||||
namespace internal {
|
||||
template<typename MatrixType, bool IsComplex> struct complex_schur_reduce_to_hessenberg;
|
||||
}
|
||||
|
||||
/** \eigenvalues_module \ingroup Eigenvalues_Module
|
||||
*
|
||||
*
|
||||
* \class ComplexSchur
|
||||
*
|
||||
* \brief Performs a complex Schur decomposition of a real or complex square matrix
|
||||
*
|
||||
* \tparam _MatrixType the type of the matrix of which we are
|
||||
* computing the Schur decomposition; this is expected to be an
|
||||
* instantiation of the Matrix class template.
|
||||
*
|
||||
* Given a real or complex square matrix A, this class computes the
|
||||
* Schur decomposition: \f$ A = U T U^*\f$ where U is a unitary
|
||||
* complex matrix, and T is a complex upper triangular matrix. The
|
||||
* diagonal of the matrix T corresponds to the eigenvalues of the
|
||||
* matrix A.
|
||||
*
|
||||
* Call the function compute() to compute the Schur decomposition of
|
||||
* a given matrix. Alternatively, you can use the
|
||||
* ComplexSchur(const MatrixType&, bool) constructor which computes
|
||||
* the Schur decomposition at construction time. Once the
|
||||
* decomposition is computed, you can use the matrixU() and matrixT()
|
||||
* functions to retrieve the matrices U and V in the decomposition.
|
||||
*
|
||||
* \note This code is inspired from Jampack
|
||||
*
|
||||
* \sa class RealSchur, class EigenSolver, class ComplexEigenSolver
|
||||
*/
|
||||
template<typename _MatrixType> class ComplexSchur
|
||||
{
|
||||
public:
|
||||
typedef _MatrixType MatrixType;
|
||||
enum {
|
||||
RowsAtCompileTime = MatrixType::RowsAtCompileTime,
|
||||
ColsAtCompileTime = MatrixType::ColsAtCompileTime,
|
||||
Options = MatrixType::Options,
|
||||
MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
|
||||
MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime
|
||||
};
|
||||
|
||||
/** \brief Scalar type for matrices of type \p _MatrixType. */
|
||||
typedef typename MatrixType::Scalar Scalar;
|
||||
typedef typename NumTraits<Scalar>::Real RealScalar;
|
||||
typedef Eigen::Index Index; ///< \deprecated since Eigen 3.3
|
||||
|
||||
/** \brief Complex scalar type for \p _MatrixType.
|
||||
*
|
||||
* This is \c std::complex<Scalar> if #Scalar is real (e.g.,
|
||||
* \c float or \c double) and just \c Scalar if #Scalar is
|
||||
* complex.
|
||||
*/
|
||||
typedef std::complex<RealScalar> ComplexScalar;
|
||||
|
||||
/** \brief Type for the matrices in the Schur decomposition.
|
||||
*
|
||||
* This is a square matrix with entries of type #ComplexScalar.
|
||||
* The size is the same as the size of \p _MatrixType.
|
||||
*/
|
||||
typedef Matrix<ComplexScalar, RowsAtCompileTime, ColsAtCompileTime, Options, MaxRowsAtCompileTime, MaxColsAtCompileTime> ComplexMatrixType;
|
||||
|
||||
/** \brief Default constructor.
|
||||
*
|
||||
* \param [in] size Positive integer, size of the matrix whose Schur decomposition will be computed.
|
||||
*
|
||||
* The default constructor is useful in cases in which the user
|
||||
* intends to perform decompositions via compute(). The \p size
|
||||
* parameter is only used as a hint. It is not an error to give a
|
||||
* wrong \p size, but it may impair performance.
|
||||
*
|
||||
* \sa compute() for an example.
|
||||
*/
|
||||
explicit ComplexSchur(Index size = RowsAtCompileTime==Dynamic ? 1 : RowsAtCompileTime)
|
||||
: m_matT(size,size),
|
||||
m_matU(size,size),
|
||||
m_hess(size),
|
||||
m_isInitialized(false),
|
||||
m_matUisUptodate(false),
|
||||
m_maxIters(-1)
|
||||
{}
|
||||
|
||||
/** \brief Constructor; computes Schur decomposition of given matrix.
|
||||
*
|
||||
* \param[in] matrix Square matrix whose Schur decomposition is to be computed.
|
||||
* \param[in] computeU If true, both T and U are computed; if false, only T is computed.
|
||||
*
|
||||
* This constructor calls compute() to compute the Schur decomposition.
|
||||
*
|
||||
* \sa matrixT() and matrixU() for examples.
|
||||
*/
|
||||
template<typename InputType>
|
||||
explicit ComplexSchur(const EigenBase<InputType>& matrix, bool computeU = true)
|
||||
: m_matT(matrix.rows(),matrix.cols()),
|
||||
m_matU(matrix.rows(),matrix.cols()),
|
||||
m_hess(matrix.rows()),
|
||||
m_isInitialized(false),
|
||||
m_matUisUptodate(false),
|
||||
m_maxIters(-1)
|
||||
{
|
||||
compute(matrix.derived(), computeU);
|
||||
}
|
||||
|
||||
/** \brief Returns the unitary matrix in the Schur decomposition.
|
||||
*
|
||||
* \returns A const reference to the matrix U.
|
||||
*
|
||||
* It is assumed that either the constructor
|
||||
* ComplexSchur(const MatrixType& matrix, bool computeU) or the
|
||||
* member function compute(const MatrixType& matrix, bool computeU)
|
||||
* has been called before to compute the Schur decomposition of a
|
||||
* matrix, and that \p computeU was set to true (the default
|
||||
* value).
|
||||
*
|
||||
* Example: \include ComplexSchur_matrixU.cpp
|
||||
* Output: \verbinclude ComplexSchur_matrixU.out
|
||||
*/
|
||||
const ComplexMatrixType& matrixU() const
|
||||
{
|
||||
eigen_assert(m_isInitialized && "ComplexSchur is not initialized.");
|
||||
eigen_assert(m_matUisUptodate && "The matrix U has not been computed during the ComplexSchur decomposition.");
|
||||
return m_matU;
|
||||
}
|
||||
|
||||
/** \brief Returns the triangular matrix in the Schur decomposition.
|
||||
*
|
||||
* \returns A const reference to the matrix T.
|
||||
*
|
||||
* It is assumed that either the constructor
|
||||
* ComplexSchur(const MatrixType& matrix, bool computeU) or the
|
||||
* member function compute(const MatrixType& matrix, bool computeU)
|
||||
* has been called before to compute the Schur decomposition of a
|
||||
* matrix.
|
||||
*
|
||||
* Note that this function returns a plain square matrix. If you want to reference
|
||||
* only the upper triangular part, use:
|
||||
* \code schur.matrixT().triangularView<Upper>() \endcode
|
||||
*
|
||||
* Example: \include ComplexSchur_matrixT.cpp
|
||||
* Output: \verbinclude ComplexSchur_matrixT.out
|
||||
*/
|
||||
const ComplexMatrixType& matrixT() const
|
||||
{
|
||||
eigen_assert(m_isInitialized && "ComplexSchur is not initialized.");
|
||||
return m_matT;
|
||||
}
|
||||
|
||||
/** \brief Computes Schur decomposition of given matrix.
|
||||
*
|
||||
* \param[in] matrix Square matrix whose Schur decomposition is to be computed.
|
||||
* \param[in] computeU If true, both T and U are computed; if false, only T is computed.
|
||||
|
||||
* \returns Reference to \c *this
|
||||
*
|
||||
* The Schur decomposition is computed by first reducing the
|
||||
* matrix to Hessenberg form using the class
|
||||
* HessenbergDecomposition. The Hessenberg matrix is then reduced
|
||||
* to triangular form by performing QR iterations with a single
|
||||
* shift. The cost of computing the Schur decomposition depends
|
||||
* on the number of iterations; as a rough guide, it may be taken
|
||||
* on the number of iterations; as a rough guide, it may be taken
|
||||
* to be \f$25n^3\f$ complex flops, or \f$10n^3\f$ complex flops
|
||||
* if \a computeU is false.
|
||||
*
|
||||
* Example: \include ComplexSchur_compute.cpp
|
||||
* Output: \verbinclude ComplexSchur_compute.out
|
||||
*
|
||||
* \sa compute(const MatrixType&, bool, Index)
|
||||
*/
|
||||
template<typename InputType>
|
||||
ComplexSchur& compute(const EigenBase<InputType>& matrix, bool computeU = true);
|
||||
|
||||
/** \brief Compute Schur decomposition from a given Hessenberg matrix
|
||||
* \param[in] matrixH Matrix in Hessenberg form H
|
||||
* \param[in] matrixQ orthogonal matrix Q that transform a matrix A to H : A = Q H Q^T
|
||||
* \param computeU Computes the matriX U of the Schur vectors
|
||||
* \return Reference to \c *this
|
||||
*
|
||||
* This routine assumes that the matrix is already reduced in Hessenberg form matrixH
|
||||
* using either the class HessenbergDecomposition or another mean.
|
||||
* It computes the upper quasi-triangular matrix T of the Schur decomposition of H
|
||||
* When computeU is true, this routine computes the matrix U such that
|
||||
* A = U T U^T = (QZ) T (QZ)^T = Q H Q^T where A is the initial matrix
|
||||
*
|
||||
* NOTE Q is referenced if computeU is true; so, if the initial orthogonal matrix
|
||||
* is not available, the user should give an identity matrix (Q.setIdentity())
|
||||
*
|
||||
* \sa compute(const MatrixType&, bool)
|
||||
*/
|
||||
template<typename HessMatrixType, typename OrthMatrixType>
|
||||
ComplexSchur& computeFromHessenberg(const HessMatrixType& matrixH, const OrthMatrixType& matrixQ, bool computeU=true);
|
||||
|
||||
/** \brief Reports whether previous computation was successful.
|
||||
*
|
||||
* \returns \c Success if computation was succesful, \c NoConvergence otherwise.
|
||||
*/
|
||||
ComputationInfo info() const
|
||||
{
|
||||
eigen_assert(m_isInitialized && "ComplexSchur is not initialized.");
|
||||
return m_info;
|
||||
}
|
||||
|
||||
/** \brief Sets the maximum number of iterations allowed.
|
||||
*
|
||||
* If not specified by the user, the maximum number of iterations is m_maxIterationsPerRow times the size
|
||||
* of the matrix.
|
||||
*/
|
||||
ComplexSchur& setMaxIterations(Index maxIters)
|
||||
{
|
||||
m_maxIters = maxIters;
|
||||
return *this;
|
||||
}
|
||||
|
||||
/** \brief Returns the maximum number of iterations. */
|
||||
Index getMaxIterations()
|
||||
{
|
||||
return m_maxIters;
|
||||
}
|
||||
|
||||
/** \brief Maximum number of iterations per row.
|
||||
*
|
||||
* If not otherwise specified, the maximum number of iterations is this number times the size of the
|
||||
* matrix. It is currently set to 30.
|
||||
*/
|
||||
static const int m_maxIterationsPerRow = 30;
|
||||
|
||||
protected:
|
||||
ComplexMatrixType m_matT, m_matU;
|
||||
HessenbergDecomposition<MatrixType> m_hess;
|
||||
ComputationInfo m_info;
|
||||
bool m_isInitialized;
|
||||
bool m_matUisUptodate;
|
||||
Index m_maxIters;
|
||||
|
||||
private:
|
||||
bool subdiagonalEntryIsNeglegible(Index i);
|
||||
ComplexScalar computeShift(Index iu, Index iter);
|
||||
void reduceToTriangularForm(bool computeU);
|
||||
friend struct internal::complex_schur_reduce_to_hessenberg<MatrixType, NumTraits<Scalar>::IsComplex>;
|
||||
};
|
||||
|
||||
/** If m_matT(i+1,i) is neglegible in floating point arithmetic
|
||||
* compared to m_matT(i,i) and m_matT(j,j), then set it to zero and
|
||||
* return true, else return false. */
|
||||
template<typename MatrixType>
|
||||
inline bool ComplexSchur<MatrixType>::subdiagonalEntryIsNeglegible(Index i)
|
||||
{
|
||||
RealScalar d = numext::norm1(m_matT.coeff(i,i)) + numext::norm1(m_matT.coeff(i+1,i+1));
|
||||
RealScalar sd = numext::norm1(m_matT.coeff(i+1,i));
|
||||
if (internal::isMuchSmallerThan(sd, d, NumTraits<RealScalar>::epsilon()))
|
||||
{
|
||||
m_matT.coeffRef(i+1,i) = ComplexScalar(0);
|
||||
return true;
|
||||
}
|
||||
return false;
|
||||
}
|
||||
|
||||
|
||||
/** Compute the shift in the current QR iteration. */
|
||||
template<typename MatrixType>
|
||||
typename ComplexSchur<MatrixType>::ComplexScalar ComplexSchur<MatrixType>::computeShift(Index iu, Index iter)
|
||||
{
|
||||
using std::abs;
|
||||
if (iter == 10 || iter == 20)
|
||||
{
|
||||
// exceptional shift, taken from http://www.netlib.org/eispack/comqr.f
|
||||
return abs(numext::real(m_matT.coeff(iu,iu-1))) + abs(numext::real(m_matT.coeff(iu-1,iu-2)));
|
||||
}
|
||||
|
||||
// compute the shift as one of the eigenvalues of t, the 2x2
|
||||
// diagonal block on the bottom of the active submatrix
|
||||
Matrix<ComplexScalar,2,2> t = m_matT.template block<2,2>(iu-1,iu-1);
|
||||
RealScalar normt = t.cwiseAbs().sum();
|
||||
t /= normt; // the normalization by sf is to avoid under/overflow
|
||||
|
||||
ComplexScalar b = t.coeff(0,1) * t.coeff(1,0);
|
||||
ComplexScalar c = t.coeff(0,0) - t.coeff(1,1);
|
||||
ComplexScalar disc = sqrt(c*c + RealScalar(4)*b);
|
||||
ComplexScalar det = t.coeff(0,0) * t.coeff(1,1) - b;
|
||||
ComplexScalar trace = t.coeff(0,0) + t.coeff(1,1);
|
||||
ComplexScalar eival1 = (trace + disc) / RealScalar(2);
|
||||
ComplexScalar eival2 = (trace - disc) / RealScalar(2);
|
||||
RealScalar eival1_norm = numext::norm1(eival1);
|
||||
RealScalar eival2_norm = numext::norm1(eival2);
|
||||
// A division by zero can only occur if eival1==eival2==0.
|
||||
// In this case, det==0, and all we have to do is checking that eival2_norm!=0
|
||||
if(eival1_norm > eival2_norm)
|
||||
eival2 = det / eival1;
|
||||
else if(eival2_norm!=RealScalar(0))
|
||||
eival1 = det / eival2;
|
||||
|
||||
// choose the eigenvalue closest to the bottom entry of the diagonal
|
||||
if(numext::norm1(eival1-t.coeff(1,1)) < numext::norm1(eival2-t.coeff(1,1)))
|
||||
return normt * eival1;
|
||||
else
|
||||
return normt * eival2;
|
||||
}
|
||||
|
||||
|
||||
template<typename MatrixType>
|
||||
template<typename InputType>
|
||||
ComplexSchur<MatrixType>& ComplexSchur<MatrixType>::compute(const EigenBase<InputType>& matrix, bool computeU)
|
||||
{
|
||||
m_matUisUptodate = false;
|
||||
eigen_assert(matrix.cols() == matrix.rows());
|
||||
|
||||
if(matrix.cols() == 1)
|
||||
{
|
||||
m_matT = matrix.derived().template cast<ComplexScalar>();
|
||||
if(computeU) m_matU = ComplexMatrixType::Identity(1,1);
|
||||
m_info = Success;
|
||||
m_isInitialized = true;
|
||||
m_matUisUptodate = computeU;
|
||||
return *this;
|
||||
}
|
||||
|
||||
internal::complex_schur_reduce_to_hessenberg<MatrixType, NumTraits<Scalar>::IsComplex>::run(*this, matrix.derived(), computeU);
|
||||
computeFromHessenberg(m_matT, m_matU, computeU);
|
||||
return *this;
|
||||
}
|
||||
|
||||
template<typename MatrixType>
|
||||
template<typename HessMatrixType, typename OrthMatrixType>
|
||||
ComplexSchur<MatrixType>& ComplexSchur<MatrixType>::computeFromHessenberg(const HessMatrixType& matrixH, const OrthMatrixType& matrixQ, bool computeU)
|
||||
{
|
||||
m_matT = matrixH;
|
||||
if(computeU)
|
||||
m_matU = matrixQ;
|
||||
reduceToTriangularForm(computeU);
|
||||
return *this;
|
||||
}
|
||||
namespace internal {
|
||||
|
||||
/* Reduce given matrix to Hessenberg form */
|
||||
template<typename MatrixType, bool IsComplex>
|
||||
struct complex_schur_reduce_to_hessenberg
|
||||
{
|
||||
// this is the implementation for the case IsComplex = true
|
||||
static void run(ComplexSchur<MatrixType>& _this, const MatrixType& matrix, bool computeU)
|
||||
{
|
||||
_this.m_hess.compute(matrix);
|
||||
_this.m_matT = _this.m_hess.matrixH();
|
||||
if(computeU) _this.m_matU = _this.m_hess.matrixQ();
|
||||
}
|
||||
};
|
||||
|
||||
template<typename MatrixType>
|
||||
struct complex_schur_reduce_to_hessenberg<MatrixType, false>
|
||||
{
|
||||
static void run(ComplexSchur<MatrixType>& _this, const MatrixType& matrix, bool computeU)
|
||||
{
|
||||
typedef typename ComplexSchur<MatrixType>::ComplexScalar ComplexScalar;
|
||||
|
||||
// Note: m_hess is over RealScalar; m_matT and m_matU is over ComplexScalar
|
||||
_this.m_hess.compute(matrix);
|
||||
_this.m_matT = _this.m_hess.matrixH().template cast<ComplexScalar>();
|
||||
if(computeU)
|
||||
{
|
||||
// This may cause an allocation which seems to be avoidable
|
||||
MatrixType Q = _this.m_hess.matrixQ();
|
||||
_this.m_matU = Q.template cast<ComplexScalar>();
|
||||
}
|
||||
}
|
||||
};
|
||||
|
||||
} // end namespace internal
|
||||
|
||||
// Reduce the Hessenberg matrix m_matT to triangular form by QR iteration.
|
||||
template<typename MatrixType>
|
||||
void ComplexSchur<MatrixType>::reduceToTriangularForm(bool computeU)
|
||||
{
|
||||
Index maxIters = m_maxIters;
|
||||
if (maxIters == -1)
|
||||
maxIters = m_maxIterationsPerRow * m_matT.rows();
|
||||
|
||||
// The matrix m_matT is divided in three parts.
|
||||
// Rows 0,...,il-1 are decoupled from the rest because m_matT(il,il-1) is zero.
|
||||
// Rows il,...,iu is the part we are working on (the active submatrix).
|
||||
// Rows iu+1,...,end are already brought in triangular form.
|
||||
Index iu = m_matT.cols() - 1;
|
||||
Index il;
|
||||
Index iter = 0; // number of iterations we are working on the (iu,iu) element
|
||||
Index totalIter = 0; // number of iterations for whole matrix
|
||||
|
||||
while(true)
|
||||
{
|
||||
// find iu, the bottom row of the active submatrix
|
||||
while(iu > 0)
|
||||
{
|
||||
if(!subdiagonalEntryIsNeglegible(iu-1)) break;
|
||||
iter = 0;
|
||||
--iu;
|
||||
}
|
||||
|
||||
// if iu is zero then we are done; the whole matrix is triangularized
|
||||
if(iu==0) break;
|
||||
|
||||
// if we spent too many iterations, we give up
|
||||
iter++;
|
||||
totalIter++;
|
||||
if(totalIter > maxIters) break;
|
||||
|
||||
// find il, the top row of the active submatrix
|
||||
il = iu-1;
|
||||
while(il > 0 && !subdiagonalEntryIsNeglegible(il-1))
|
||||
{
|
||||
--il;
|
||||
}
|
||||
|
||||
/* perform the QR step using Givens rotations. The first rotation
|
||||
creates a bulge; the (il+2,il) element becomes nonzero. This
|
||||
bulge is chased down to the bottom of the active submatrix. */
|
||||
|
||||
ComplexScalar shift = computeShift(iu, iter);
|
||||
JacobiRotation<ComplexScalar> rot;
|
||||
rot.makeGivens(m_matT.coeff(il,il) - shift, m_matT.coeff(il+1,il));
|
||||
m_matT.rightCols(m_matT.cols()-il).applyOnTheLeft(il, il+1, rot.adjoint());
|
||||
m_matT.topRows((std::min)(il+2,iu)+1).applyOnTheRight(il, il+1, rot);
|
||||
if(computeU) m_matU.applyOnTheRight(il, il+1, rot);
|
||||
|
||||
for(Index i=il+1 ; i<iu ; i++)
|
||||
{
|
||||
rot.makeGivens(m_matT.coeffRef(i,i-1), m_matT.coeffRef(i+1,i-1), &m_matT.coeffRef(i,i-1));
|
||||
m_matT.coeffRef(i+1,i-1) = ComplexScalar(0);
|
||||
m_matT.rightCols(m_matT.cols()-i).applyOnTheLeft(i, i+1, rot.adjoint());
|
||||
m_matT.topRows((std::min)(i+2,iu)+1).applyOnTheRight(i, i+1, rot);
|
||||
if(computeU) m_matU.applyOnTheRight(i, i+1, rot);
|
||||
}
|
||||
}
|
||||
|
||||
if(totalIter <= maxIters)
|
||||
m_info = Success;
|
||||
else
|
||||
m_info = NoConvergence;
|
||||
|
||||
m_isInitialized = true;
|
||||
m_matUisUptodate = computeU;
|
||||
}
|
||||
|
||||
} // end namespace Eigen
|
||||
|
||||
#endif // EIGEN_COMPLEX_SCHUR_H
|
||||
|
|
@ -0,0 +1,91 @@
|
|||
/*
|
||||
Copyright (c) 2011, Intel Corporation. All rights reserved.
|
||||
|
||||
Redistribution and use in source and binary forms, with or without modification,
|
||||
are permitted provided that the following conditions are met:
|
||||
|
||||
* Redistributions of source code must retain the above copyright notice, this
|
||||
list of conditions and the following disclaimer.
|
||||
* Redistributions in binary form must reproduce the above copyright notice,
|
||||
this list of conditions and the following disclaimer in the documentation
|
||||
and/or other materials provided with the distribution.
|
||||
* Neither the name of Intel Corporation nor the names of its contributors may
|
||||
be used to endorse or promote products derived from this software without
|
||||
specific prior written permission.
|
||||
|
||||
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
|
||||
ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
|
||||
WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
|
||||
DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
|
||||
ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
|
||||
(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
|
||||
LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
|
||||
ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
|
||||
(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
|
||||
SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
|
||||
|
||||
********************************************************************************
|
||||
* Content : Eigen bindings to LAPACKe
|
||||
* Complex Schur needed to complex unsymmetrical eigenvalues/eigenvectors.
|
||||
********************************************************************************
|
||||
*/
|
||||
|
||||
#ifndef EIGEN_COMPLEX_SCHUR_LAPACKE_H
|
||||
#define EIGEN_COMPLEX_SCHUR_LAPACKE_H
|
||||
|
||||
namespace Eigen {
|
||||
|
||||
/** \internal Specialization for the data types supported by LAPACKe */
|
||||
|
||||
#define EIGEN_LAPACKE_SCHUR_COMPLEX(EIGTYPE, LAPACKE_TYPE, LAPACKE_PREFIX, LAPACKE_PREFIX_U, EIGCOLROW, LAPACKE_COLROW) \
|
||||
template<> template<typename InputType> inline \
|
||||
ComplexSchur<Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW> >& \
|
||||
ComplexSchur<Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW> >::compute(const EigenBase<InputType>& matrix, bool computeU) \
|
||||
{ \
|
||||
typedef Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW> MatrixType; \
|
||||
typedef MatrixType::RealScalar RealScalar; \
|
||||
typedef std::complex<RealScalar> ComplexScalar; \
|
||||
\
|
||||
eigen_assert(matrix.cols() == matrix.rows()); \
|
||||
\
|
||||
m_matUisUptodate = false; \
|
||||
if(matrix.cols() == 1) \
|
||||
{ \
|
||||
m_matT = matrix.derived().template cast<ComplexScalar>(); \
|
||||
if(computeU) m_matU = ComplexMatrixType::Identity(1,1); \
|
||||
m_info = Success; \
|
||||
m_isInitialized = true; \
|
||||
m_matUisUptodate = computeU; \
|
||||
return *this; \
|
||||
} \
|
||||
lapack_int n = internal::convert_index<lapack_int>(matrix.cols()), sdim, info; \
|
||||
lapack_int matrix_order = LAPACKE_COLROW; \
|
||||
char jobvs, sort='N'; \
|
||||
LAPACK_##LAPACKE_PREFIX_U##_SELECT1 select = 0; \
|
||||
jobvs = (computeU) ? 'V' : 'N'; \
|
||||
m_matU.resize(n, n); \
|
||||
lapack_int ldvs = internal::convert_index<lapack_int>(m_matU.outerStride()); \
|
||||
m_matT = matrix; \
|
||||
lapack_int lda = internal::convert_index<lapack_int>(m_matT.outerStride()); \
|
||||
Matrix<EIGTYPE, Dynamic, Dynamic> w; \
|
||||
w.resize(n, 1);\
|
||||
info = LAPACKE_##LAPACKE_PREFIX##gees( matrix_order, jobvs, sort, select, n, (LAPACKE_TYPE*)m_matT.data(), lda, &sdim, (LAPACKE_TYPE*)w.data(), (LAPACKE_TYPE*)m_matU.data(), ldvs ); \
|
||||
if(info == 0) \
|
||||
m_info = Success; \
|
||||
else \
|
||||
m_info = NoConvergence; \
|
||||
\
|
||||
m_isInitialized = true; \
|
||||
m_matUisUptodate = computeU; \
|
||||
return *this; \
|
||||
\
|
||||
}
|
||||
|
||||
EIGEN_LAPACKE_SCHUR_COMPLEX(dcomplex, lapack_complex_double, z, Z, ColMajor, LAPACK_COL_MAJOR)
|
||||
EIGEN_LAPACKE_SCHUR_COMPLEX(scomplex, lapack_complex_float, c, C, ColMajor, LAPACK_COL_MAJOR)
|
||||
EIGEN_LAPACKE_SCHUR_COMPLEX(dcomplex, lapack_complex_double, z, Z, RowMajor, LAPACK_ROW_MAJOR)
|
||||
EIGEN_LAPACKE_SCHUR_COMPLEX(scomplex, lapack_complex_float, c, C, RowMajor, LAPACK_ROW_MAJOR)
|
||||
|
||||
} // end namespace Eigen
|
||||
|
||||
#endif // EIGEN_COMPLEX_SCHUR_LAPACKE_H
|
||||
|
|
@ -0,0 +1,622 @@
|
|||
// This file is part of Eigen, a lightweight C++ template library
|
||||
// for linear algebra.
|
||||
//
|
||||
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
|
||||
// Copyright (C) 2010,2012 Jitse Niesen <jitse@maths.leeds.ac.uk>
|
||||
//
|
||||
// This Source Code Form is subject to the terms of the Mozilla
|
||||
// Public License v. 2.0. If a copy of the MPL was not distributed
|
||||
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
|
||||
|
||||
#ifndef EIGEN_EIGENSOLVER_H
|
||||
#define EIGEN_EIGENSOLVER_H
|
||||
|
||||
#include "./RealSchur.h"
|
||||
|
||||
namespace Eigen {
|
||||
|
||||
/** \eigenvalues_module \ingroup Eigenvalues_Module
|
||||
*
|
||||
*
|
||||
* \class EigenSolver
|
||||
*
|
||||
* \brief Computes eigenvalues and eigenvectors of general matrices
|
||||
*
|
||||
* \tparam _MatrixType the type of the matrix of which we are computing the
|
||||
* eigendecomposition; this is expected to be an instantiation of the Matrix
|
||||
* class template. Currently, only real matrices are supported.
|
||||
*
|
||||
* The eigenvalues and eigenvectors of a matrix \f$ A \f$ are scalars
|
||||
* \f$ \lambda \f$ and vectors \f$ v \f$ such that \f$ Av = \lambda v \f$. If
|
||||
* \f$ D \f$ is a diagonal matrix with the eigenvalues on the diagonal, and
|
||||
* \f$ V \f$ is a matrix with the eigenvectors as its columns, then \f$ A V =
|
||||
* V D \f$. The matrix \f$ V \f$ is almost always invertible, in which case we
|
||||
* have \f$ A = V D V^{-1} \f$. This is called the eigendecomposition.
|
||||
*
|
||||
* The eigenvalues and eigenvectors of a matrix may be complex, even when the
|
||||
* matrix is real. However, we can choose real matrices \f$ V \f$ and \f$ D
|
||||
* \f$ satisfying \f$ A V = V D \f$, just like the eigendecomposition, if the
|
||||
* matrix \f$ D \f$ is not required to be diagonal, but if it is allowed to
|
||||
* have blocks of the form
|
||||
* \f[ \begin{bmatrix} u & v \\ -v & u \end{bmatrix} \f]
|
||||
* (where \f$ u \f$ and \f$ v \f$ are real numbers) on the diagonal. These
|
||||
* blocks correspond to complex eigenvalue pairs \f$ u \pm iv \f$. We call
|
||||
* this variant of the eigendecomposition the pseudo-eigendecomposition.
|
||||
*
|
||||
* Call the function compute() to compute the eigenvalues and eigenvectors of
|
||||
* a given matrix. Alternatively, you can use the
|
||||
* EigenSolver(const MatrixType&, bool) constructor which computes the
|
||||
* eigenvalues and eigenvectors at construction time. Once the eigenvalue and
|
||||
* eigenvectors are computed, they can be retrieved with the eigenvalues() and
|
||||
* eigenvectors() functions. The pseudoEigenvalueMatrix() and
|
||||
* pseudoEigenvectors() methods allow the construction of the
|
||||
* pseudo-eigendecomposition.
|
||||
*
|
||||
* The documentation for EigenSolver(const MatrixType&, bool) contains an
|
||||
* example of the typical use of this class.
|
||||
*
|
||||
* \note The implementation is adapted from
|
||||
* <a href="http://math.nist.gov/javanumerics/jama/">JAMA</a> (public domain).
|
||||
* Their code is based on EISPACK.
|
||||
*
|
||||
* \sa MatrixBase::eigenvalues(), class ComplexEigenSolver, class SelfAdjointEigenSolver
|
||||
*/
|
||||
template<typename _MatrixType> class EigenSolver
|
||||
{
|
||||
public:
|
||||
|
||||
/** \brief Synonym for the template parameter \p _MatrixType. */
|
||||
typedef _MatrixType MatrixType;
|
||||
|
||||
enum {
|
||||
RowsAtCompileTime = MatrixType::RowsAtCompileTime,
|
||||
ColsAtCompileTime = MatrixType::ColsAtCompileTime,
|
||||
Options = MatrixType::Options,
|
||||
MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
|
||||
MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime
|
||||
};
|
||||
|
||||
/** \brief Scalar type for matrices of type #MatrixType. */
|
||||
typedef typename MatrixType::Scalar Scalar;
|
||||
typedef typename NumTraits<Scalar>::Real RealScalar;
|
||||
typedef Eigen::Index Index; ///< \deprecated since Eigen 3.3
|
||||
|
||||
/** \brief Complex scalar type for #MatrixType.
|
||||
*
|
||||
* This is \c std::complex<Scalar> if #Scalar is real (e.g.,
|
||||
* \c float or \c double) and just \c Scalar if #Scalar is
|
||||
* complex.
|
||||
*/
|
||||
typedef std::complex<RealScalar> ComplexScalar;
|
||||
|
||||
/** \brief Type for vector of eigenvalues as returned by eigenvalues().
|
||||
*
|
||||
* This is a column vector with entries of type #ComplexScalar.
|
||||
* The length of the vector is the size of #MatrixType.
|
||||
*/
|
||||
typedef Matrix<ComplexScalar, ColsAtCompileTime, 1, Options & ~RowMajor, MaxColsAtCompileTime, 1> EigenvalueType;
|
||||
|
||||
/** \brief Type for matrix of eigenvectors as returned by eigenvectors().
|
||||
*
|
||||
* This is a square matrix with entries of type #ComplexScalar.
|
||||
* The size is the same as the size of #MatrixType.
|
||||
*/
|
||||
typedef Matrix<ComplexScalar, RowsAtCompileTime, ColsAtCompileTime, Options, MaxRowsAtCompileTime, MaxColsAtCompileTime> EigenvectorsType;
|
||||
|
||||
/** \brief Default constructor.
|
||||
*
|
||||
* The default constructor is useful in cases in which the user intends to
|
||||
* perform decompositions via EigenSolver::compute(const MatrixType&, bool).
|
||||
*
|
||||
* \sa compute() for an example.
|
||||
*/
|
||||
EigenSolver() : m_eivec(), m_eivalues(), m_isInitialized(false), m_realSchur(), m_matT(), m_tmp() {}
|
||||
|
||||
/** \brief Default constructor with memory preallocation
|
||||
*
|
||||
* Like the default constructor but with preallocation of the internal data
|
||||
* according to the specified problem \a size.
|
||||
* \sa EigenSolver()
|
||||
*/
|
||||
explicit EigenSolver(Index size)
|
||||
: m_eivec(size, size),
|
||||
m_eivalues(size),
|
||||
m_isInitialized(false),
|
||||
m_eigenvectorsOk(false),
|
||||
m_realSchur(size),
|
||||
m_matT(size, size),
|
||||
m_tmp(size)
|
||||
{}
|
||||
|
||||
/** \brief Constructor; computes eigendecomposition of given matrix.
|
||||
*
|
||||
* \param[in] matrix Square matrix whose eigendecomposition is to be computed.
|
||||
* \param[in] computeEigenvectors If true, both the eigenvectors and the
|
||||
* eigenvalues are computed; if false, only the eigenvalues are
|
||||
* computed.
|
||||
*
|
||||
* This constructor calls compute() to compute the eigenvalues
|
||||
* and eigenvectors.
|
||||
*
|
||||
* Example: \include EigenSolver_EigenSolver_MatrixType.cpp
|
||||
* Output: \verbinclude EigenSolver_EigenSolver_MatrixType.out
|
||||
*
|
||||
* \sa compute()
|
||||
*/
|
||||
template<typename InputType>
|
||||
explicit EigenSolver(const EigenBase<InputType>& matrix, bool computeEigenvectors = true)
|
||||
: m_eivec(matrix.rows(), matrix.cols()),
|
||||
m_eivalues(matrix.cols()),
|
||||
m_isInitialized(false),
|
||||
m_eigenvectorsOk(false),
|
||||
m_realSchur(matrix.cols()),
|
||||
m_matT(matrix.rows(), matrix.cols()),
|
||||
m_tmp(matrix.cols())
|
||||
{
|
||||
compute(matrix.derived(), computeEigenvectors);
|
||||
}
|
||||
|
||||
/** \brief Returns the eigenvectors of given matrix.
|
||||
*
|
||||
* \returns %Matrix whose columns are the (possibly complex) eigenvectors.
|
||||
*
|
||||
* \pre Either the constructor
|
||||
* EigenSolver(const MatrixType&,bool) or the member function
|
||||
* compute(const MatrixType&, bool) has been called before, and
|
||||
* \p computeEigenvectors was set to true (the default).
|
||||
*
|
||||
* Column \f$ k \f$ of the returned matrix is an eigenvector corresponding
|
||||
* to eigenvalue number \f$ k \f$ as returned by eigenvalues(). The
|
||||
* eigenvectors are normalized to have (Euclidean) norm equal to one. The
|
||||
* matrix returned by this function is the matrix \f$ V \f$ in the
|
||||
* eigendecomposition \f$ A = V D V^{-1} \f$, if it exists.
|
||||
*
|
||||
* Example: \include EigenSolver_eigenvectors.cpp
|
||||
* Output: \verbinclude EigenSolver_eigenvectors.out
|
||||
*
|
||||
* \sa eigenvalues(), pseudoEigenvectors()
|
||||
*/
|
||||
EigenvectorsType eigenvectors() const;
|
||||
|
||||
/** \brief Returns the pseudo-eigenvectors of given matrix.
|
||||
*
|
||||
* \returns Const reference to matrix whose columns are the pseudo-eigenvectors.
|
||||
*
|
||||
* \pre Either the constructor
|
||||
* EigenSolver(const MatrixType&,bool) or the member function
|
||||
* compute(const MatrixType&, bool) has been called before, and
|
||||
* \p computeEigenvectors was set to true (the default).
|
||||
*
|
||||
* The real matrix \f$ V \f$ returned by this function and the
|
||||
* block-diagonal matrix \f$ D \f$ returned by pseudoEigenvalueMatrix()
|
||||
* satisfy \f$ AV = VD \f$.
|
||||
*
|
||||
* Example: \include EigenSolver_pseudoEigenvectors.cpp
|
||||
* Output: \verbinclude EigenSolver_pseudoEigenvectors.out
|
||||
*
|
||||
* \sa pseudoEigenvalueMatrix(), eigenvectors()
|
||||
*/
|
||||
const MatrixType& pseudoEigenvectors() const
|
||||
{
|
||||
eigen_assert(m_isInitialized && "EigenSolver is not initialized.");
|
||||
eigen_assert(m_eigenvectorsOk && "The eigenvectors have not been computed together with the eigenvalues.");
|
||||
return m_eivec;
|
||||
}
|
||||
|
||||
/** \brief Returns the block-diagonal matrix in the pseudo-eigendecomposition.
|
||||
*
|
||||
* \returns A block-diagonal matrix.
|
||||
*
|
||||
* \pre Either the constructor
|
||||
* EigenSolver(const MatrixType&,bool) or the member function
|
||||
* compute(const MatrixType&, bool) has been called before.
|
||||
*
|
||||
* The matrix \f$ D \f$ returned by this function is real and
|
||||
* block-diagonal. The blocks on the diagonal are either 1-by-1 or 2-by-2
|
||||
* blocks of the form
|
||||
* \f$ \begin{bmatrix} u & v \\ -v & u \end{bmatrix} \f$.
|
||||
* These blocks are not sorted in any particular order.
|
||||
* The matrix \f$ D \f$ and the matrix \f$ V \f$ returned by
|
||||
* pseudoEigenvectors() satisfy \f$ AV = VD \f$.
|
||||
*
|
||||
* \sa pseudoEigenvectors() for an example, eigenvalues()
|
||||
*/
|
||||
MatrixType pseudoEigenvalueMatrix() const;
|
||||
|
||||
/** \brief Returns the eigenvalues of given matrix.
|
||||
*
|
||||
* \returns A const reference to the column vector containing the eigenvalues.
|
||||
*
|
||||
* \pre Either the constructor
|
||||
* EigenSolver(const MatrixType&,bool) or the member function
|
||||
* compute(const MatrixType&, bool) has been called before.
|
||||
*
|
||||
* The eigenvalues are repeated according to their algebraic multiplicity,
|
||||
* so there are as many eigenvalues as rows in the matrix. The eigenvalues
|
||||
* are not sorted in any particular order.
|
||||
*
|
||||
* Example: \include EigenSolver_eigenvalues.cpp
|
||||
* Output: \verbinclude EigenSolver_eigenvalues.out
|
||||
*
|
||||
* \sa eigenvectors(), pseudoEigenvalueMatrix(),
|
||||
* MatrixBase::eigenvalues()
|
||||
*/
|
||||
const EigenvalueType& eigenvalues() const
|
||||
{
|
||||
eigen_assert(m_isInitialized && "EigenSolver is not initialized.");
|
||||
return m_eivalues;
|
||||
}
|
||||
|
||||
/** \brief Computes eigendecomposition of given matrix.
|
||||
*
|
||||
* \param[in] matrix Square matrix whose eigendecomposition is to be computed.
|
||||
* \param[in] computeEigenvectors If true, both the eigenvectors and the
|
||||
* eigenvalues are computed; if false, only the eigenvalues are
|
||||
* computed.
|
||||
* \returns Reference to \c *this
|
||||
*
|
||||
* This function computes the eigenvalues of the real matrix \p matrix.
|
||||
* The eigenvalues() function can be used to retrieve them. If
|
||||
* \p computeEigenvectors is true, then the eigenvectors are also computed
|
||||
* and can be retrieved by calling eigenvectors().
|
||||
*
|
||||
* The matrix is first reduced to real Schur form using the RealSchur
|
||||
* class. The Schur decomposition is then used to compute the eigenvalues
|
||||
* and eigenvectors.
|
||||
*
|
||||
* The cost of the computation is dominated by the cost of the
|
||||
* Schur decomposition, which is very approximately \f$ 25n^3 \f$
|
||||
* (where \f$ n \f$ is the size of the matrix) if \p computeEigenvectors
|
||||
* is true, and \f$ 10n^3 \f$ if \p computeEigenvectors is false.
|
||||
*
|
||||
* This method reuses of the allocated data in the EigenSolver object.
|
||||
*
|
||||
* Example: \include EigenSolver_compute.cpp
|
||||
* Output: \verbinclude EigenSolver_compute.out
|
||||
*/
|
||||
template<typename InputType>
|
||||
EigenSolver& compute(const EigenBase<InputType>& matrix, bool computeEigenvectors = true);
|
||||
|
||||
/** \returns NumericalIssue if the input contains INF or NaN values or overflow occured. Returns Success otherwise. */
|
||||
ComputationInfo info() const
|
||||
{
|
||||
eigen_assert(m_isInitialized && "EigenSolver is not initialized.");
|
||||
return m_info;
|
||||
}
|
||||
|
||||
/** \brief Sets the maximum number of iterations allowed. */
|
||||
EigenSolver& setMaxIterations(Index maxIters)
|
||||
{
|
||||
m_realSchur.setMaxIterations(maxIters);
|
||||
return *this;
|
||||
}
|
||||
|
||||
/** \brief Returns the maximum number of iterations. */
|
||||
Index getMaxIterations()
|
||||
{
|
||||
return m_realSchur.getMaxIterations();
|
||||
}
|
||||
|
||||
private:
|
||||
void doComputeEigenvectors();
|
||||
|
||||
protected:
|
||||
|
||||
static void check_template_parameters()
|
||||
{
|
||||
EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar);
|
||||
EIGEN_STATIC_ASSERT(!NumTraits<Scalar>::IsComplex, NUMERIC_TYPE_MUST_BE_REAL);
|
||||
}
|
||||
|
||||
MatrixType m_eivec;
|
||||
EigenvalueType m_eivalues;
|
||||
bool m_isInitialized;
|
||||
bool m_eigenvectorsOk;
|
||||
ComputationInfo m_info;
|
||||
RealSchur<MatrixType> m_realSchur;
|
||||
MatrixType m_matT;
|
||||
|
||||
typedef Matrix<Scalar, ColsAtCompileTime, 1, Options & ~RowMajor, MaxColsAtCompileTime, 1> ColumnVectorType;
|
||||
ColumnVectorType m_tmp;
|
||||
};
|
||||
|
||||
template<typename MatrixType>
|
||||
MatrixType EigenSolver<MatrixType>::pseudoEigenvalueMatrix() const
|
||||
{
|
||||
eigen_assert(m_isInitialized && "EigenSolver is not initialized.");
|
||||
const RealScalar precision = RealScalar(2)*NumTraits<RealScalar>::epsilon();
|
||||
Index n = m_eivalues.rows();
|
||||
MatrixType matD = MatrixType::Zero(n,n);
|
||||
for (Index i=0; i<n; ++i)
|
||||
{
|
||||
if (internal::isMuchSmallerThan(numext::imag(m_eivalues.coeff(i)), numext::real(m_eivalues.coeff(i)), precision))
|
||||
matD.coeffRef(i,i) = numext::real(m_eivalues.coeff(i));
|
||||
else
|
||||
{
|
||||
matD.template block<2,2>(i,i) << numext::real(m_eivalues.coeff(i)), numext::imag(m_eivalues.coeff(i)),
|
||||
-numext::imag(m_eivalues.coeff(i)), numext::real(m_eivalues.coeff(i));
|
||||
++i;
|
||||
}
|
||||
}
|
||||
return matD;
|
||||
}
|
||||
|
||||
template<typename MatrixType>
|
||||
typename EigenSolver<MatrixType>::EigenvectorsType EigenSolver<MatrixType>::eigenvectors() const
|
||||
{
|
||||
eigen_assert(m_isInitialized && "EigenSolver is not initialized.");
|
||||
eigen_assert(m_eigenvectorsOk && "The eigenvectors have not been computed together with the eigenvalues.");
|
||||
const RealScalar precision = RealScalar(2)*NumTraits<RealScalar>::epsilon();
|
||||
Index n = m_eivec.cols();
|
||||
EigenvectorsType matV(n,n);
|
||||
for (Index j=0; j<n; ++j)
|
||||
{
|
||||
if (internal::isMuchSmallerThan(numext::imag(m_eivalues.coeff(j)), numext::real(m_eivalues.coeff(j)), precision) || j+1==n)
|
||||
{
|
||||
// we have a real eigen value
|
||||
matV.col(j) = m_eivec.col(j).template cast<ComplexScalar>();
|
||||
matV.col(j).normalize();
|
||||
}
|
||||
else
|
||||
{
|
||||
// we have a pair of complex eigen values
|
||||
for (Index i=0; i<n; ++i)
|
||||
{
|
||||
matV.coeffRef(i,j) = ComplexScalar(m_eivec.coeff(i,j), m_eivec.coeff(i,j+1));
|
||||
matV.coeffRef(i,j+1) = ComplexScalar(m_eivec.coeff(i,j), -m_eivec.coeff(i,j+1));
|
||||
}
|
||||
matV.col(j).normalize();
|
||||
matV.col(j+1).normalize();
|
||||
++j;
|
||||
}
|
||||
}
|
||||
return matV;
|
||||
}
|
||||
|
||||
template<typename MatrixType>
|
||||
template<typename InputType>
|
||||
EigenSolver<MatrixType>&
|
||||
EigenSolver<MatrixType>::compute(const EigenBase<InputType>& matrix, bool computeEigenvectors)
|
||||
{
|
||||
check_template_parameters();
|
||||
|
||||
using std::sqrt;
|
||||
using std::abs;
|
||||
using numext::isfinite;
|
||||
eigen_assert(matrix.cols() == matrix.rows());
|
||||
|
||||
// Reduce to real Schur form.
|
||||
m_realSchur.compute(matrix.derived(), computeEigenvectors);
|
||||
|
||||
m_info = m_realSchur.info();
|
||||
|
||||
if (m_info == Success)
|
||||
{
|
||||
m_matT = m_realSchur.matrixT();
|
||||
if (computeEigenvectors)
|
||||
m_eivec = m_realSchur.matrixU();
|
||||
|
||||
// Compute eigenvalues from matT
|
||||
m_eivalues.resize(matrix.cols());
|
||||
Index i = 0;
|
||||
while (i < matrix.cols())
|
||||
{
|
||||
if (i == matrix.cols() - 1 || m_matT.coeff(i+1, i) == Scalar(0))
|
||||
{
|
||||
m_eivalues.coeffRef(i) = m_matT.coeff(i, i);
|
||||
if(!(isfinite)(m_eivalues.coeffRef(i)))
|
||||
{
|
||||
m_isInitialized = true;
|
||||
m_eigenvectorsOk = false;
|
||||
m_info = NumericalIssue;
|
||||
return *this;
|
||||
}
|
||||
++i;
|
||||
}
|
||||
else
|
||||
{
|
||||
Scalar p = Scalar(0.5) * (m_matT.coeff(i, i) - m_matT.coeff(i+1, i+1));
|
||||
Scalar z;
|
||||
// Compute z = sqrt(abs(p * p + m_matT.coeff(i+1, i) * m_matT.coeff(i, i+1)));
|
||||
// without overflow
|
||||
{
|
||||
Scalar t0 = m_matT.coeff(i+1, i);
|
||||
Scalar t1 = m_matT.coeff(i, i+1);
|
||||
Scalar maxval = numext::maxi<Scalar>(abs(p),numext::maxi<Scalar>(abs(t0),abs(t1)));
|
||||
t0 /= maxval;
|
||||
t1 /= maxval;
|
||||
Scalar p0 = p/maxval;
|
||||
z = maxval * sqrt(abs(p0 * p0 + t0 * t1));
|
||||
}
|
||||
|
||||
m_eivalues.coeffRef(i) = ComplexScalar(m_matT.coeff(i+1, i+1) + p, z);
|
||||
m_eivalues.coeffRef(i+1) = ComplexScalar(m_matT.coeff(i+1, i+1) + p, -z);
|
||||
if(!((isfinite)(m_eivalues.coeffRef(i)) && (isfinite)(m_eivalues.coeffRef(i+1))))
|
||||
{
|
||||
m_isInitialized = true;
|
||||
m_eigenvectorsOk = false;
|
||||
m_info = NumericalIssue;
|
||||
return *this;
|
||||
}
|
||||
i += 2;
|
||||
}
|
||||
}
|
||||
|
||||
// Compute eigenvectors.
|
||||
if (computeEigenvectors)
|
||||
doComputeEigenvectors();
|
||||
}
|
||||
|
||||
m_isInitialized = true;
|
||||
m_eigenvectorsOk = computeEigenvectors;
|
||||
|
||||
return *this;
|
||||
}
|
||||
|
||||
|
||||
template<typename MatrixType>
|
||||
void EigenSolver<MatrixType>::doComputeEigenvectors()
|
||||
{
|
||||
using std::abs;
|
||||
const Index size = m_eivec.cols();
|
||||
const Scalar eps = NumTraits<Scalar>::epsilon();
|
||||
|
||||
// inefficient! this is already computed in RealSchur
|
||||
Scalar norm(0);
|
||||
for (Index j = 0; j < size; ++j)
|
||||
{
|
||||
norm += m_matT.row(j).segment((std::max)(j-1,Index(0)), size-(std::max)(j-1,Index(0))).cwiseAbs().sum();
|
||||
}
|
||||
|
||||
// Backsubstitute to find vectors of upper triangular form
|
||||
if (norm == Scalar(0))
|
||||
{
|
||||
return;
|
||||
}
|
||||
|
||||
for (Index n = size-1; n >= 0; n--)
|
||||
{
|
||||
Scalar p = m_eivalues.coeff(n).real();
|
||||
Scalar q = m_eivalues.coeff(n).imag();
|
||||
|
||||
// Scalar vector
|
||||
if (q == Scalar(0))
|
||||
{
|
||||
Scalar lastr(0), lastw(0);
|
||||
Index l = n;
|
||||
|
||||
m_matT.coeffRef(n,n) = Scalar(1);
|
||||
for (Index i = n-1; i >= 0; i--)
|
||||
{
|
||||
Scalar w = m_matT.coeff(i,i) - p;
|
||||
Scalar r = m_matT.row(i).segment(l,n-l+1).dot(m_matT.col(n).segment(l, n-l+1));
|
||||
|
||||
if (m_eivalues.coeff(i).imag() < Scalar(0))
|
||||
{
|
||||
lastw = w;
|
||||
lastr = r;
|
||||
}
|
||||
else
|
||||
{
|
||||
l = i;
|
||||
if (m_eivalues.coeff(i).imag() == Scalar(0))
|
||||
{
|
||||
if (w != Scalar(0))
|
||||
m_matT.coeffRef(i,n) = -r / w;
|
||||
else
|
||||
m_matT.coeffRef(i,n) = -r / (eps * norm);
|
||||
}
|
||||
else // Solve real equations
|
||||
{
|
||||
Scalar x = m_matT.coeff(i,i+1);
|
||||
Scalar y = m_matT.coeff(i+1,i);
|
||||
Scalar denom = (m_eivalues.coeff(i).real() - p) * (m_eivalues.coeff(i).real() - p) + m_eivalues.coeff(i).imag() * m_eivalues.coeff(i).imag();
|
||||
Scalar t = (x * lastr - lastw * r) / denom;
|
||||
m_matT.coeffRef(i,n) = t;
|
||||
if (abs(x) > abs(lastw))
|
||||
m_matT.coeffRef(i+1,n) = (-r - w * t) / x;
|
||||
else
|
||||
m_matT.coeffRef(i+1,n) = (-lastr - y * t) / lastw;
|
||||
}
|
||||
|
||||
// Overflow control
|
||||
Scalar t = abs(m_matT.coeff(i,n));
|
||||
if ((eps * t) * t > Scalar(1))
|
||||
m_matT.col(n).tail(size-i) /= t;
|
||||
}
|
||||
}
|
||||
}
|
||||
else if (q < Scalar(0) && n > 0) // Complex vector
|
||||
{
|
||||
Scalar lastra(0), lastsa(0), lastw(0);
|
||||
Index l = n-1;
|
||||
|
||||
// Last vector component imaginary so matrix is triangular
|
||||
if (abs(m_matT.coeff(n,n-1)) > abs(m_matT.coeff(n-1,n)))
|
||||
{
|
||||
m_matT.coeffRef(n-1,n-1) = q / m_matT.coeff(n,n-1);
|
||||
m_matT.coeffRef(n-1,n) = -(m_matT.coeff(n,n) - p) / m_matT.coeff(n,n-1);
|
||||
}
|
||||
else
|
||||
{
|
||||
ComplexScalar cc = ComplexScalar(Scalar(0),-m_matT.coeff(n-1,n)) / ComplexScalar(m_matT.coeff(n-1,n-1)-p,q);
|
||||
m_matT.coeffRef(n-1,n-1) = numext::real(cc);
|
||||
m_matT.coeffRef(n-1,n) = numext::imag(cc);
|
||||
}
|
||||
m_matT.coeffRef(n,n-1) = Scalar(0);
|
||||
m_matT.coeffRef(n,n) = Scalar(1);
|
||||
for (Index i = n-2; i >= 0; i--)
|
||||
{
|
||||
Scalar ra = m_matT.row(i).segment(l, n-l+1).dot(m_matT.col(n-1).segment(l, n-l+1));
|
||||
Scalar sa = m_matT.row(i).segment(l, n-l+1).dot(m_matT.col(n).segment(l, n-l+1));
|
||||
Scalar w = m_matT.coeff(i,i) - p;
|
||||
|
||||
if (m_eivalues.coeff(i).imag() < Scalar(0))
|
||||
{
|
||||
lastw = w;
|
||||
lastra = ra;
|
||||
lastsa = sa;
|
||||
}
|
||||
else
|
||||
{
|
||||
l = i;
|
||||
if (m_eivalues.coeff(i).imag() == RealScalar(0))
|
||||
{
|
||||
ComplexScalar cc = ComplexScalar(-ra,-sa) / ComplexScalar(w,q);
|
||||
m_matT.coeffRef(i,n-1) = numext::real(cc);
|
||||
m_matT.coeffRef(i,n) = numext::imag(cc);
|
||||
}
|
||||
else
|
||||
{
|
||||
// Solve complex equations
|
||||
Scalar x = m_matT.coeff(i,i+1);
|
||||
Scalar y = m_matT.coeff(i+1,i);
|
||||
Scalar vr = (m_eivalues.coeff(i).real() - p) * (m_eivalues.coeff(i).real() - p) + m_eivalues.coeff(i).imag() * m_eivalues.coeff(i).imag() - q * q;
|
||||
Scalar vi = (m_eivalues.coeff(i).real() - p) * Scalar(2) * q;
|
||||
if ((vr == Scalar(0)) && (vi == Scalar(0)))
|
||||
vr = eps * norm * (abs(w) + abs(q) + abs(x) + abs(y) + abs(lastw));
|
||||
|
||||
ComplexScalar cc = ComplexScalar(x*lastra-lastw*ra+q*sa,x*lastsa-lastw*sa-q*ra) / ComplexScalar(vr,vi);
|
||||
m_matT.coeffRef(i,n-1) = numext::real(cc);
|
||||
m_matT.coeffRef(i,n) = numext::imag(cc);
|
||||
if (abs(x) > (abs(lastw) + abs(q)))
|
||||
{
|
||||
m_matT.coeffRef(i+1,n-1) = (-ra - w * m_matT.coeff(i,n-1) + q * m_matT.coeff(i,n)) / x;
|
||||
m_matT.coeffRef(i+1,n) = (-sa - w * m_matT.coeff(i,n) - q * m_matT.coeff(i,n-1)) / x;
|
||||
}
|
||||
else
|
||||
{
|
||||
cc = ComplexScalar(-lastra-y*m_matT.coeff(i,n-1),-lastsa-y*m_matT.coeff(i,n)) / ComplexScalar(lastw,q);
|
||||
m_matT.coeffRef(i+1,n-1) = numext::real(cc);
|
||||
m_matT.coeffRef(i+1,n) = numext::imag(cc);
|
||||
}
|
||||
}
|
||||
|
||||
// Overflow control
|
||||
Scalar t = numext::maxi<Scalar>(abs(m_matT.coeff(i,n-1)),abs(m_matT.coeff(i,n)));
|
||||
if ((eps * t) * t > Scalar(1))
|
||||
m_matT.block(i, n-1, size-i, 2) /= t;
|
||||
|
||||
}
|
||||
}
|
||||
|
||||
// We handled a pair of complex conjugate eigenvalues, so need to skip them both
|
||||
n--;
|
||||
}
|
||||
else
|
||||
{
|
||||
eigen_assert(0 && "Internal bug in EigenSolver (INF or NaN has not been detected)"); // this should not happen
|
||||
}
|
||||
}
|
||||
|
||||
// Back transformation to get eigenvectors of original matrix
|
||||
for (Index j = size-1; j >= 0; j--)
|
||||
{
|
||||
m_tmp.noalias() = m_eivec.leftCols(j+1) * m_matT.col(j).segment(0, j+1);
|
||||
m_eivec.col(j) = m_tmp;
|
||||
}
|
||||
}
|
||||
|
||||
} // end namespace Eigen
|
||||
|
||||
#endif // EIGEN_EIGENSOLVER_H
|
||||
|
|
@ -0,0 +1,418 @@
|
|||
// This file is part of Eigen, a lightweight C++ template library
|
||||
// for linear algebra.
|
||||
//
|
||||
// Copyright (C) 2012-2016 Gael Guennebaud <gael.guennebaud@inria.fr>
|
||||
// Copyright (C) 2010,2012 Jitse Niesen <jitse@maths.leeds.ac.uk>
|
||||
// Copyright (C) 2016 Tobias Wood <tobias@spinicist.org.uk>
|
||||
//
|
||||
// This Source Code Form is subject to the terms of the Mozilla
|
||||
// Public License v. 2.0. If a copy of the MPL was not distributed
|
||||
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
|
||||
|
||||
#ifndef EIGEN_GENERALIZEDEIGENSOLVER_H
|
||||
#define EIGEN_GENERALIZEDEIGENSOLVER_H
|
||||
|
||||
#include "./RealQZ.h"
|
||||
|
||||
namespace Eigen {
|
||||
|
||||
/** \eigenvalues_module \ingroup Eigenvalues_Module
|
||||
*
|
||||
*
|
||||
* \class GeneralizedEigenSolver
|
||||
*
|
||||
* \brief Computes the generalized eigenvalues and eigenvectors of a pair of general matrices
|
||||
*
|
||||
* \tparam _MatrixType the type of the matrices of which we are computing the
|
||||
* eigen-decomposition; this is expected to be an instantiation of the Matrix
|
||||
* class template. Currently, only real matrices are supported.
|
||||
*
|
||||
* The generalized eigenvalues and eigenvectors of a matrix pair \f$ A \f$ and \f$ B \f$ are scalars
|
||||
* \f$ \lambda \f$ and vectors \f$ v \f$ such that \f$ Av = \lambda Bv \f$. If
|
||||
* \f$ D \f$ is a diagonal matrix with the eigenvalues on the diagonal, and
|
||||
* \f$ V \f$ is a matrix with the eigenvectors as its columns, then \f$ A V =
|
||||
* B V D \f$. The matrix \f$ V \f$ is almost always invertible, in which case we
|
||||
* have \f$ A = B V D V^{-1} \f$. This is called the generalized eigen-decomposition.
|
||||
*
|
||||
* The generalized eigenvalues and eigenvectors of a matrix pair may be complex, even when the
|
||||
* matrices are real. Moreover, the generalized eigenvalue might be infinite if the matrix B is
|
||||
* singular. To workaround this difficulty, the eigenvalues are provided as a pair of complex \f$ \alpha \f$
|
||||
* and real \f$ \beta \f$ such that: \f$ \lambda_i = \alpha_i / \beta_i \f$. If \f$ \beta_i \f$ is (nearly) zero,
|
||||
* then one can consider the well defined left eigenvalue \f$ \mu = \beta_i / \alpha_i\f$ such that:
|
||||
* \f$ \mu_i A v_i = B v_i \f$, or even \f$ \mu_i u_i^T A = u_i^T B \f$ where \f$ u_i \f$ is
|
||||
* called the left eigenvector.
|
||||
*
|
||||
* Call the function compute() to compute the generalized eigenvalues and eigenvectors of
|
||||
* a given matrix pair. Alternatively, you can use the
|
||||
* GeneralizedEigenSolver(const MatrixType&, const MatrixType&, bool) constructor which computes the
|
||||
* eigenvalues and eigenvectors at construction time. Once the eigenvalue and
|
||||
* eigenvectors are computed, they can be retrieved with the eigenvalues() and
|
||||
* eigenvectors() functions.
|
||||
*
|
||||
* Here is an usage example of this class:
|
||||
* Example: \include GeneralizedEigenSolver.cpp
|
||||
* Output: \verbinclude GeneralizedEigenSolver.out
|
||||
*
|
||||
* \sa MatrixBase::eigenvalues(), class ComplexEigenSolver, class SelfAdjointEigenSolver
|
||||
*/
|
||||
template<typename _MatrixType> class GeneralizedEigenSolver
|
||||
{
|
||||
public:
|
||||
|
||||
/** \brief Synonym for the template parameter \p _MatrixType. */
|
||||
typedef _MatrixType MatrixType;
|
||||
|
||||
enum {
|
||||
RowsAtCompileTime = MatrixType::RowsAtCompileTime,
|
||||
ColsAtCompileTime = MatrixType::ColsAtCompileTime,
|
||||
Options = MatrixType::Options,
|
||||
MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
|
||||
MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime
|
||||
};
|
||||
|
||||
/** \brief Scalar type for matrices of type #MatrixType. */
|
||||
typedef typename MatrixType::Scalar Scalar;
|
||||
typedef typename NumTraits<Scalar>::Real RealScalar;
|
||||
typedef Eigen::Index Index; ///< \deprecated since Eigen 3.3
|
||||
|
||||
/** \brief Complex scalar type for #MatrixType.
|
||||
*
|
||||
* This is \c std::complex<Scalar> if #Scalar is real (e.g.,
|
||||
* \c float or \c double) and just \c Scalar if #Scalar is
|
||||
* complex.
|
||||
*/
|
||||
typedef std::complex<RealScalar> ComplexScalar;
|
||||
|
||||
/** \brief Type for vector of real scalar values eigenvalues as returned by betas().
|
||||
*
|
||||
* This is a column vector with entries of type #Scalar.
|
||||
* The length of the vector is the size of #MatrixType.
|
||||
*/
|
||||
typedef Matrix<Scalar, ColsAtCompileTime, 1, Options & ~RowMajor, MaxColsAtCompileTime, 1> VectorType;
|
||||
|
||||
/** \brief Type for vector of complex scalar values eigenvalues as returned by alphas().
|
||||
*
|
||||
* This is a column vector with entries of type #ComplexScalar.
|
||||
* The length of the vector is the size of #MatrixType.
|
||||
*/
|
||||
typedef Matrix<ComplexScalar, ColsAtCompileTime, 1, Options & ~RowMajor, MaxColsAtCompileTime, 1> ComplexVectorType;
|
||||
|
||||
/** \brief Expression type for the eigenvalues as returned by eigenvalues().
|
||||
*/
|
||||
typedef CwiseBinaryOp<internal::scalar_quotient_op<ComplexScalar,Scalar>,ComplexVectorType,VectorType> EigenvalueType;
|
||||
|
||||
/** \brief Type for matrix of eigenvectors as returned by eigenvectors().
|
||||
*
|
||||
* This is a square matrix with entries of type #ComplexScalar.
|
||||
* The size is the same as the size of #MatrixType.
|
||||
*/
|
||||
typedef Matrix<ComplexScalar, RowsAtCompileTime, ColsAtCompileTime, Options, MaxRowsAtCompileTime, MaxColsAtCompileTime> EigenvectorsType;
|
||||
|
||||
/** \brief Default constructor.
|
||||
*
|
||||
* The default constructor is useful in cases in which the user intends to
|
||||
* perform decompositions via EigenSolver::compute(const MatrixType&, bool).
|
||||
*
|
||||
* \sa compute() for an example.
|
||||
*/
|
||||
GeneralizedEigenSolver()
|
||||
: m_eivec(),
|
||||
m_alphas(),
|
||||
m_betas(),
|
||||
m_valuesOkay(false),
|
||||
m_vectorsOkay(false),
|
||||
m_realQZ()
|
||||
{}
|
||||
|
||||
/** \brief Default constructor with memory preallocation
|
||||
*
|
||||
* Like the default constructor but with preallocation of the internal data
|
||||
* according to the specified problem \a size.
|
||||
* \sa GeneralizedEigenSolver()
|
||||
*/
|
||||
explicit GeneralizedEigenSolver(Index size)
|
||||
: m_eivec(size, size),
|
||||
m_alphas(size),
|
||||
m_betas(size),
|
||||
m_valuesOkay(false),
|
||||
m_vectorsOkay(false),
|
||||
m_realQZ(size),
|
||||
m_tmp(size)
|
||||
{}
|
||||
|
||||
/** \brief Constructor; computes the generalized eigendecomposition of given matrix pair.
|
||||
*
|
||||
* \param[in] A Square matrix whose eigendecomposition is to be computed.
|
||||
* \param[in] B Square matrix whose eigendecomposition is to be computed.
|
||||
* \param[in] computeEigenvectors If true, both the eigenvectors and the
|
||||
* eigenvalues are computed; if false, only the eigenvalues are computed.
|
||||
*
|
||||
* This constructor calls compute() to compute the generalized eigenvalues
|
||||
* and eigenvectors.
|
||||
*
|
||||
* \sa compute()
|
||||
*/
|
||||
GeneralizedEigenSolver(const MatrixType& A, const MatrixType& B, bool computeEigenvectors = true)
|
||||
: m_eivec(A.rows(), A.cols()),
|
||||
m_alphas(A.cols()),
|
||||
m_betas(A.cols()),
|
||||
m_valuesOkay(false),
|
||||
m_vectorsOkay(false),
|
||||
m_realQZ(A.cols()),
|
||||
m_tmp(A.cols())
|
||||
{
|
||||
compute(A, B, computeEigenvectors);
|
||||
}
|
||||
|
||||
/* \brief Returns the computed generalized eigenvectors.
|
||||
*
|
||||
* \returns %Matrix whose columns are the (possibly complex) right eigenvectors.
|
||||
* i.e. the eigenvectors that solve (A - l*B)x = 0. The ordering matches the eigenvalues.
|
||||
*
|
||||
* \pre Either the constructor
|
||||
* GeneralizedEigenSolver(const MatrixType&,const MatrixType&, bool) or the member function
|
||||
* compute(const MatrixType&, const MatrixType& bool) has been called before, and
|
||||
* \p computeEigenvectors was set to true (the default).
|
||||
*
|
||||
* \sa eigenvalues()
|
||||
*/
|
||||
EigenvectorsType eigenvectors() const {
|
||||
eigen_assert(m_vectorsOkay && "Eigenvectors for GeneralizedEigenSolver were not calculated.");
|
||||
return m_eivec;
|
||||
}
|
||||
|
||||
/** \brief Returns an expression of the computed generalized eigenvalues.
|
||||
*
|
||||
* \returns An expression of the column vector containing the eigenvalues.
|
||||
*
|
||||
* It is a shortcut for \code this->alphas().cwiseQuotient(this->betas()); \endcode
|
||||
* Not that betas might contain zeros. It is therefore not recommended to use this function,
|
||||
* but rather directly deal with the alphas and betas vectors.
|
||||
*
|
||||
* \pre Either the constructor
|
||||
* GeneralizedEigenSolver(const MatrixType&,const MatrixType&,bool) or the member function
|
||||
* compute(const MatrixType&,const MatrixType&,bool) has been called before.
|
||||
*
|
||||
* The eigenvalues are repeated according to their algebraic multiplicity,
|
||||
* so there are as many eigenvalues as rows in the matrix. The eigenvalues
|
||||
* are not sorted in any particular order.
|
||||
*
|
||||
* \sa alphas(), betas(), eigenvectors()
|
||||
*/
|
||||
EigenvalueType eigenvalues() const
|
||||
{
|
||||
eigen_assert(m_valuesOkay && "GeneralizedEigenSolver is not initialized.");
|
||||
return EigenvalueType(m_alphas,m_betas);
|
||||
}
|
||||
|
||||
/** \returns A const reference to the vectors containing the alpha values
|
||||
*
|
||||
* This vector permits to reconstruct the j-th eigenvalues as alphas(i)/betas(j).
|
||||
*
|
||||
* \sa betas(), eigenvalues() */
|
||||
ComplexVectorType alphas() const
|
||||
{
|
||||
eigen_assert(m_valuesOkay && "GeneralizedEigenSolver is not initialized.");
|
||||
return m_alphas;
|
||||
}
|
||||
|
||||
/** \returns A const reference to the vectors containing the beta values
|
||||
*
|
||||
* This vector permits to reconstruct the j-th eigenvalues as alphas(i)/betas(j).
|
||||
*
|
||||
* \sa alphas(), eigenvalues() */
|
||||
VectorType betas() const
|
||||
{
|
||||
eigen_assert(m_valuesOkay && "GeneralizedEigenSolver is not initialized.");
|
||||
return m_betas;
|
||||
}
|
||||
|
||||
/** \brief Computes generalized eigendecomposition of given matrix.
|
||||
*
|
||||
* \param[in] A Square matrix whose eigendecomposition is to be computed.
|
||||
* \param[in] B Square matrix whose eigendecomposition is to be computed.
|
||||
* \param[in] computeEigenvectors If true, both the eigenvectors and the
|
||||
* eigenvalues are computed; if false, only the eigenvalues are
|
||||
* computed.
|
||||
* \returns Reference to \c *this
|
||||
*
|
||||
* This function computes the eigenvalues of the real matrix \p matrix.
|
||||
* The eigenvalues() function can be used to retrieve them. If
|
||||
* \p computeEigenvectors is true, then the eigenvectors are also computed
|
||||
* and can be retrieved by calling eigenvectors().
|
||||
*
|
||||
* The matrix is first reduced to real generalized Schur form using the RealQZ
|
||||
* class. The generalized Schur decomposition is then used to compute the eigenvalues
|
||||
* and eigenvectors.
|
||||
*
|
||||
* The cost of the computation is dominated by the cost of the
|
||||
* generalized Schur decomposition.
|
||||
*
|
||||
* This method reuses of the allocated data in the GeneralizedEigenSolver object.
|
||||
*/
|
||||
GeneralizedEigenSolver& compute(const MatrixType& A, const MatrixType& B, bool computeEigenvectors = true);
|
||||
|
||||
ComputationInfo info() const
|
||||
{
|
||||
eigen_assert(m_valuesOkay && "EigenSolver is not initialized.");
|
||||
return m_realQZ.info();
|
||||
}
|
||||
|
||||
/** Sets the maximal number of iterations allowed.
|
||||
*/
|
||||
GeneralizedEigenSolver& setMaxIterations(Index maxIters)
|
||||
{
|
||||
m_realQZ.setMaxIterations(maxIters);
|
||||
return *this;
|
||||
}
|
||||
|
||||
protected:
|
||||
|
||||
static void check_template_parameters()
|
||||
{
|
||||
EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar);
|
||||
EIGEN_STATIC_ASSERT(!NumTraits<Scalar>::IsComplex, NUMERIC_TYPE_MUST_BE_REAL);
|
||||
}
|
||||
|
||||
EigenvectorsType m_eivec;
|
||||
ComplexVectorType m_alphas;
|
||||
VectorType m_betas;
|
||||
bool m_valuesOkay, m_vectorsOkay;
|
||||
RealQZ<MatrixType> m_realQZ;
|
||||
ComplexVectorType m_tmp;
|
||||
};
|
||||
|
||||
template<typename MatrixType>
|
||||
GeneralizedEigenSolver<MatrixType>&
|
||||
GeneralizedEigenSolver<MatrixType>::compute(const MatrixType& A, const MatrixType& B, bool computeEigenvectors)
|
||||
{
|
||||
check_template_parameters();
|
||||
|
||||
using std::sqrt;
|
||||
using std::abs;
|
||||
eigen_assert(A.cols() == A.rows() && B.cols() == A.rows() && B.cols() == B.rows());
|
||||
Index size = A.cols();
|
||||
m_valuesOkay = false;
|
||||
m_vectorsOkay = false;
|
||||
// Reduce to generalized real Schur form:
|
||||
// A = Q S Z and B = Q T Z
|
||||
m_realQZ.compute(A, B, computeEigenvectors);
|
||||
if (m_realQZ.info() == Success)
|
||||
{
|
||||
// Resize storage
|
||||
m_alphas.resize(size);
|
||||
m_betas.resize(size);
|
||||
if (computeEigenvectors)
|
||||
{
|
||||
m_eivec.resize(size,size);
|
||||
m_tmp.resize(size);
|
||||
}
|
||||
|
||||
// Aliases:
|
||||
Map<VectorType> v(reinterpret_cast<Scalar*>(m_tmp.data()), size);
|
||||
ComplexVectorType &cv = m_tmp;
|
||||
const MatrixType &mS = m_realQZ.matrixS();
|
||||
const MatrixType &mT = m_realQZ.matrixT();
|
||||
|
||||
Index i = 0;
|
||||
while (i < size)
|
||||
{
|
||||
if (i == size - 1 || mS.coeff(i+1, i) == Scalar(0))
|
||||
{
|
||||
// Real eigenvalue
|
||||
m_alphas.coeffRef(i) = mS.diagonal().coeff(i);
|
||||
m_betas.coeffRef(i) = mT.diagonal().coeff(i);
|
||||
if (computeEigenvectors)
|
||||
{
|
||||
v.setConstant(Scalar(0.0));
|
||||
v.coeffRef(i) = Scalar(1.0);
|
||||
// For singular eigenvalues do nothing more
|
||||
if(abs(m_betas.coeffRef(i)) >= (std::numeric_limits<RealScalar>::min)())
|
||||
{
|
||||
// Non-singular eigenvalue
|
||||
const Scalar alpha = real(m_alphas.coeffRef(i));
|
||||
const Scalar beta = m_betas.coeffRef(i);
|
||||
for (Index j = i-1; j >= 0; j--)
|
||||
{
|
||||
const Index st = j+1;
|
||||
const Index sz = i-j;
|
||||
if (j > 0 && mS.coeff(j, j-1) != Scalar(0))
|
||||
{
|
||||
// 2x2 block
|
||||
Matrix<Scalar, 2, 1> rhs = (alpha*mT.template block<2,Dynamic>(j-1,st,2,sz) - beta*mS.template block<2,Dynamic>(j-1,st,2,sz)) .lazyProduct( v.segment(st,sz) );
|
||||
Matrix<Scalar, 2, 2> lhs = beta * mS.template block<2,2>(j-1,j-1) - alpha * mT.template block<2,2>(j-1,j-1);
|
||||
v.template segment<2>(j-1) = lhs.partialPivLu().solve(rhs);
|
||||
j--;
|
||||
}
|
||||
else
|
||||
{
|
||||
v.coeffRef(j) = -v.segment(st,sz).transpose().cwiseProduct(beta*mS.block(j,st,1,sz) - alpha*mT.block(j,st,1,sz)).sum() / (beta*mS.coeffRef(j,j) - alpha*mT.coeffRef(j,j));
|
||||
}
|
||||
}
|
||||
}
|
||||
m_eivec.col(i).real().noalias() = m_realQZ.matrixZ().transpose() * v;
|
||||
m_eivec.col(i).real().normalize();
|
||||
m_eivec.col(i).imag().setConstant(0);
|
||||
}
|
||||
++i;
|
||||
}
|
||||
else
|
||||
{
|
||||
// We need to extract the generalized eigenvalues of the pair of a general 2x2 block S and a positive diagonal 2x2 block T
|
||||
// Then taking beta=T_00*T_11, we can avoid any division, and alpha is the eigenvalues of A = (U^-1 * S * U) * diag(T_11,T_00):
|
||||
|
||||
// T = [a 0]
|
||||
// [0 b]
|
||||
RealScalar a = mT.diagonal().coeff(i),
|
||||
b = mT.diagonal().coeff(i+1);
|
||||
const RealScalar beta = m_betas.coeffRef(i) = m_betas.coeffRef(i+1) = a*b;
|
||||
|
||||
// ^^ NOTE: using diagonal()(i) instead of coeff(i,i) workarounds a MSVC bug.
|
||||
Matrix<RealScalar,2,2> S2 = mS.template block<2,2>(i,i) * Matrix<Scalar,2,1>(b,a).asDiagonal();
|
||||
|
||||
Scalar p = Scalar(0.5) * (S2.coeff(0,0) - S2.coeff(1,1));
|
||||
Scalar z = sqrt(abs(p * p + S2.coeff(1,0) * S2.coeff(0,1)));
|
||||
const ComplexScalar alpha = ComplexScalar(S2.coeff(1,1) + p, (beta > 0) ? z : -z);
|
||||
m_alphas.coeffRef(i) = conj(alpha);
|
||||
m_alphas.coeffRef(i+1) = alpha;
|
||||
|
||||
if (computeEigenvectors) {
|
||||
// Compute eigenvector in position (i+1) and then position (i) is just the conjugate
|
||||
cv.setZero();
|
||||
cv.coeffRef(i+1) = Scalar(1.0);
|
||||
// here, the "static_cast" workaound expression template issues.
|
||||
cv.coeffRef(i) = -(static_cast<Scalar>(beta*mS.coeffRef(i,i+1)) - alpha*mT.coeffRef(i,i+1))
|
||||
/ (static_cast<Scalar>(beta*mS.coeffRef(i,i)) - alpha*mT.coeffRef(i,i));
|
||||
for (Index j = i-1; j >= 0; j--)
|
||||
{
|
||||
const Index st = j+1;
|
||||
const Index sz = i+1-j;
|
||||
if (j > 0 && mS.coeff(j, j-1) != Scalar(0))
|
||||
{
|
||||
// 2x2 block
|
||||
Matrix<ComplexScalar, 2, 1> rhs = (alpha*mT.template block<2,Dynamic>(j-1,st,2,sz) - beta*mS.template block<2,Dynamic>(j-1,st,2,sz)) .lazyProduct( cv.segment(st,sz) );
|
||||
Matrix<ComplexScalar, 2, 2> lhs = beta * mS.template block<2,2>(j-1,j-1) - alpha * mT.template block<2,2>(j-1,j-1);
|
||||
cv.template segment<2>(j-1) = lhs.partialPivLu().solve(rhs);
|
||||
j--;
|
||||
} else {
|
||||
cv.coeffRef(j) = cv.segment(st,sz).transpose().cwiseProduct(beta*mS.block(j,st,1,sz) - alpha*mT.block(j,st,1,sz)).sum()
|
||||
/ (alpha*mT.coeffRef(j,j) - static_cast<Scalar>(beta*mS.coeffRef(j,j)));
|
||||
}
|
||||
}
|
||||
m_eivec.col(i+1).noalias() = (m_realQZ.matrixZ().transpose() * cv);
|
||||
m_eivec.col(i+1).normalize();
|
||||
m_eivec.col(i) = m_eivec.col(i+1).conjugate();
|
||||
}
|
||||
i += 2;
|
||||
}
|
||||
}
|
||||
|
||||
m_valuesOkay = true;
|
||||
m_vectorsOkay = computeEigenvectors;
|
||||
}
|
||||
return *this;
|
||||
}
|
||||
|
||||
} // end namespace Eigen
|
||||
|
||||
#endif // EIGEN_GENERALIZEDEIGENSOLVER_H
|
||||
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Reference in New Issue