113 lines
5.6 KiB
C++
113 lines
5.6 KiB
C++
/// @ref gtx_pca
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/// @file glm/gtx/pca.hpp
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///
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/// @see core (dependence)
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/// @see ext_scalar_relational (dependence)
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///
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/// @defgroup gtx_pca GLM_GTX_pca
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/// @ingroup gtx
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///
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/// Include <glm/gtx/pca.hpp> to use the features of this extension.
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///
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/// Implements functions required for fundamental 'princple component analysis' in 2D, 3D, and 4D:
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/// 1) Computing a covariance matrics from a list of _relative_ position vectors
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/// 2) Compute the eigenvalues and eigenvectors of the covariance matrics
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/// This is useful, e.g., to compute an object-aligned bounding box from vertices of an object.
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/// https://en.wikipedia.org/wiki/Principal_component_analysis
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///
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/// Example:
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/// ```
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/// std::vector<glm::dvec3> ptData;
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/// // ... fill ptData with some point data, e.g. vertices
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///
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/// glm::dvec3 center = computeCenter(ptData);
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///
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/// glm::dmat3 covarMat = glm::computeCovarianceMatrix(ptData.data(), ptData.size(), center);
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///
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/// glm::dvec3 evals;
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/// glm::dmat3 evecs;
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/// int evcnt = glm::findEigenvaluesSymReal(covarMat, evals, evecs);
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///
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/// if(evcnt != 3)
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/// // ... error handling
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///
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/// glm::sortEigenvalues(evals, evecs);
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///
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/// // ... now evecs[0] points in the direction (symmetric) of the largest spatial distribution within ptData
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/// ```
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#pragma once
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// Dependency:
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#include "../glm.hpp"
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#include "../ext/scalar_relational.hpp"
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#ifndef GLM_ENABLE_EXPERIMENTAL
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# error "GLM: GLM_GTX_pca is an experimental extension and may change in the future. Use #define GLM_ENABLE_EXPERIMENTAL before including it, if you really want to use it."
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#elif GLM_MESSAGES == GLM_ENABLE && !defined(GLM_EXT_INCLUDED)
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# pragma message("GLM: GLM_GTX_pca extension included")
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#endif
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namespace glm {
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/// @addtogroup gtx_pca
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/// @{
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/// Compute a covariance matrix form an array of relative coordinates `v` (e.g., relative to the center of gravity of the object)
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/// @param v Points to a memory holding `n` times vectors
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/// @param n Number of points in v
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template<length_t D, typename T, qualifier Q>
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GLM_INLINE mat<D, D, T, Q> computeCovarianceMatrix(vec<D, T, Q> const* v, size_t n);
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/// Compute a covariance matrix form an array of absolute coordinates `v` and a precomputed center of gravity `c`
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/// @param v Points to a memory holding `n` times vectors
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/// @param n Number of points in v
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/// @param c Precomputed center of gravity
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template<length_t D, typename T, qualifier Q>
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GLM_INLINE mat<D, D, T, Q> computeCovarianceMatrix(vec<D, T, Q> const* v, size_t n, vec<D, T, Q> const& c);
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/// Compute a covariance matrix form a pair of iterators `b` (begin) and `e` (end) of a container with relative coordinates (e.g., relative to the center of gravity of the object)
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/// Dereferencing an iterator of type I must yield a `vec<D, T, Q%gt;`
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template<length_t D, typename T, qualifier Q, typename I>
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GLM_FUNC_DECL mat<D, D, T, Q> computeCovarianceMatrix(I const& b, I const& e);
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/// Compute a covariance matrix form a pair of iterators `b` (begin) and `e` (end) of a container with absolute coordinates and a precomputed center of gravity `c`
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/// Dereferencing an iterator of type I must yield a `vec<D, T, Q%gt;`
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template<length_t D, typename T, qualifier Q, typename I>
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GLM_FUNC_DECL mat<D, D, T, Q> computeCovarianceMatrix(I const& b, I const& e, vec<D, T, Q> const& c);
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/// Assuming the provided covariance matrix `covarMat` is symmetric and real-valued, this function find the `D` Eigenvalues of the matrix, and also provides the corresponding Eigenvectors.
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/// Note: the data in `outEigenvalues` and `outEigenvectors` are in matching order, i.e. `outEigenvector[i]` is the Eigenvector of the Eigenvalue `outEigenvalue[i]`.
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/// This is a numeric implementation to find the Eigenvalues, using 'QL decomposition` (variant of QR decomposition: https://en.wikipedia.org/wiki/QR_decomposition).
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///
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/// @param[in] covarMat A symmetric, real-valued covariance matrix, e.g. computed from computeCovarianceMatrix
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/// @param[out] outEigenvalues Vector to receive the found eigenvalues
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/// @param[out] outEigenvectors Matrix to receive the found eigenvectors corresponding to the found eigenvalues, as column vectors
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/// @return The number of eigenvalues found, usually D if the precondition of the covariance matrix is met.
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template<length_t D, typename T, qualifier Q>
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GLM_FUNC_DECL unsigned int findEigenvaluesSymReal
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(
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mat<D, D, T, Q> const& covarMat,
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vec<D, T, Q>& outEigenvalues,
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mat<D, D, T, Q>& outEigenvectors
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);
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/// Sorts a group of Eigenvalues&Eigenvectors, for largest Eigenvalue to smallest Eigenvalue.
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/// The data in `outEigenvalues` and `outEigenvectors` are assumed to be matching order, i.e. `outEigenvector[i]` is the Eigenvector of the Eigenvalue `outEigenvalue[i]`.
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template<typename T, qualifier Q>
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GLM_FUNC_DECL void sortEigenvalues(vec<2, T, Q>& eigenvalues, mat<2, 2, T, Q>& eigenvectors);
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/// Sorts a group of Eigenvalues&Eigenvectors, for largest Eigenvalue to smallest Eigenvalue.
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/// The data in `outEigenvalues` and `outEigenvectors` are assumed to be matching order, i.e. `outEigenvector[i]` is the Eigenvector of the Eigenvalue `outEigenvalue[i]`.
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template<typename T, qualifier Q>
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GLM_FUNC_DECL void sortEigenvalues(vec<3, T, Q>& eigenvalues, mat<3, 3, T, Q>& eigenvectors);
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/// Sorts a group of Eigenvalues&Eigenvectors, for largest Eigenvalue to smallest Eigenvalue.
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/// The data in `outEigenvalues` and `outEigenvectors` are assumed to be matching order, i.e. `outEigenvector[i]` is the Eigenvector of the Eigenvalue `outEigenvalue[i]`.
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template<typename T, qualifier Q>
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GLM_FUNC_DECL void sortEigenvalues(vec<4, T, Q>& eigenvalues, mat<4, 4, T, Q>& eigenvectors);
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/// @}
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}//namespace glm
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#include "pca.inl"
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