From dd40903b740d1c86bd8f4a73a8978237587a48c2 Mon Sep 17 00:00:00 2001 From: SGrottel Date: Mon, 10 May 2021 13:14:29 +0200 Subject: [PATCH] Implemented 'principle component analysis' utility in gtx, including tests --- glm/gtx/pca.hpp | 111 +++++++ glm/gtx/pca.inl | 293 +++++++++++++++++ test/gtx/CMakeLists.txt | 1 + test/gtx/gtx_pca.cpp | 676 ++++++++++++++++++++++++++++++++++++++++ 4 files changed, 1081 insertions(+) create mode 100644 glm/gtx/pca.hpp create mode 100644 glm/gtx/pca.inl create mode 100644 test/gtx/gtx_pca.cpp diff --git a/glm/gtx/pca.hpp b/glm/gtx/pca.hpp new file mode 100644 index 00000000..93da745e --- /dev/null +++ b/glm/gtx/pca.hpp @@ -0,0 +1,111 @@ +/// @ref gtx_pca +/// @file glm/gtx/pca.hpp +/// +/// @see core (dependence) +/// @see ext_scalar_relational (dependence) +/// +/// @defgroup gtx_pca GLM_GTX_pca +/// @ingroup gtx +/// +/// Include to use the features of this extension. +/// +/// Implements functions required for fundamental 'princple component analysis' in 2D, 3D, and 4D: +/// 1) Computing a covariance matrics from a list of _relative_ position vectors +/// 2) Compute the eigenvalues and eigenvectors of the covariance matrics +/// This is useful, e.g., to compute an object-aligned bounding box from vertices of an object. +/// https://en.wikipedia.org/wiki/Principal_component_analysis +/// +/// Example: +/// ``` +/// std::vector ptData; +/// // ... fill ptData with some point data, e.g. vertices +/// +/// glm::dvec3 center = computeCenter(ptData); +/// +/// glm::dmat3 covarMat = glm::computeCovarianceMatrix(ptData.data(), ptData.size(), center); +/// +/// glm::dvec3 evals; +/// glm::dmat3 evecs; +/// int evcnt = glm::findEigenvaluesSymReal(covarMat, evals, evecs); +/// +/// if(evcnt != 3) +/// // ... error handling +/// +/// glm::sortEigenvalues(evals, evecs); +/// +/// // ... now evecs[0] points in the direction (symmetric) of the largest spatial distribuion within ptData +/// ``` + +#pragma once + +// Dependency: +#include "../glm.hpp" +#include "../ext/scalar_relational.hpp" + + +#if GLM_MESSAGES == GLM_ENABLE && !defined(GLM_EXT_INCLUDED) +# ifndef GLM_ENABLE_EXPERIMENTAL +# pragma message("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.") +# else +# pragma message("GLM: GLM_GTX_pca extension included") +# endif +#endif + +namespace glm { + /// @addtogroup gtx_pca + /// @{ + + /// Compute a covariance matrix form an array of relative coordinates `v` (e.g., relative to the center of gravity of the object) + /// @param v Points to a memory holding `n` times vectors + template + GLM_INLINE mat computeCovarianceMatrix(vec const* v, size_t n); + + /// Compute a covariance matrix form an array of absolute coordinates `v` and a precomputed center of gravity `c` + /// @param v Points to a memory holding `n` times vectors + template + GLM_INLINE mat computeCovarianceMatrix(vec const* v, size_t n, vec const& c); + + /// 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) + /// Dereferencing an iterator of type I must yield a `vec<D, T, Q%gt;` + template + GLM_FUNC_DECL mat computeCovarianceMatrix(I const& b, I const& e); + + /// 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` + /// Dereferencing an iterator of type I must yield a `vec<D, T, Q%gt;` + template + GLM_FUNC_DECL mat computeCovarianceMatrix(I const& b, I const& e, vec const& c); + + /// 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. + /// Note: the data in `outEigenvalues` and `outEigenvectors` are in matching order, i.e. `outEigenvector[i]` is the Eigenvector of the Eigenvalue `outEigenvalue[i]`. + /// This is a numeric implementation to find the Eigenvalues, using 'QL decomposition` (variant of QR decomposition: https://en.wikipedia.org/wiki/QR_decomposition). + /// @param covarMat A symmetric, real-valued covariance matrix, e.g. computed from `computeCovarianceMatrix`. + /// @param outEigenvalues Vector to receive the found eigenvalues + /// @param outEigenvectors Matrix to receive the found eigenvectors corresponding to the found eigenvalues, as column vectors + /// @return The number of eigenvalues found, usually D if the precondition of the covariance matrix is met. + template + GLM_FUNC_DECL unsigned int findEigenvaluesSymReal + ( + mat const& covarMat, + vec& outEigenvalues, + mat& outEigenvectors + ); + + /// Sorts a group of Eigenvalues&Eigenvectors, for largest Eigenvalue to smallest Eigenvalue. + /// The data in `outEigenvalues` and `outEigenvectors` are assumed to be matching order, i.e. `outEigenvector[i]` is the Eigenvector of the Eigenvalue `outEigenvalue[i]`. + template + GLM_INLINE void sortEigenvalues(vec<2, T, Q>& eigenvalues, mat<2, 2, T, Q>& eigenvectors); + + /// Sorts a group of Eigenvalues&Eigenvectors, for largest Eigenvalue to smallest Eigenvalue. + /// The data in `outEigenvalues` and `outEigenvectors` are assumed to be matching order, i.e. `outEigenvector[i]` is the Eigenvector of the Eigenvalue `outEigenvalue[i]`. + template + GLM_INLINE void sortEigenvalues(vec<3, T, Q>& eigenvalues, mat<3, 3, T, Q>& eigenvectors); + + /// Sorts a group of Eigenvalues&Eigenvectors, for largest Eigenvalue to smallest Eigenvalue. + /// The data in `outEigenvalues` and `outEigenvectors` are assumed to be matching order, i.e. `outEigenvector[i]` is the Eigenvector of the Eigenvalue `outEigenvalue[i]`. + template + GLM_INLINE void sortEigenvalues(vec<4, T, Q>& eigenvalues, mat<4, 4, T, Q>& eigenvectors); + + /// @} +}//namespace glm + +#include "pca.inl" diff --git a/glm/gtx/pca.inl b/glm/gtx/pca.inl new file mode 100644 index 00000000..db63772b --- /dev/null +++ b/glm/gtx/pca.inl @@ -0,0 +1,293 @@ +/// @ref gtx_pca + +namespace glm { + + + template + GLM_INLINE mat computeCovarianceMatrix(vec const* v, size_t n) + { + return std::move(computeCovarianceMatrix const*>(v, v + n)); + } + + + template + GLM_INLINE mat computeCovarianceMatrix(vec const* v, size_t n, vec const& c) + { + return std::move(computeCovarianceMatrix const*>(v, v + n, c)); + } + + + template + GLM_FUNC_DECL mat computeCovarianceMatrix(I const& b, I const& e) + { + glm::mat m{ 0 }; + + size_t cnt = 0; + for (I i = b; i != e; i++) + { + vec const& v = *i; + for (length_t x = 0; x < D; ++x) + for (length_t y = 0; y < D; ++y) + m[x][y] += static_cast(v[x] * v[y]); + cnt++; + } + if (cnt > 0) m /= static_cast(cnt); + + return std::move(m); + } + + + template + GLM_FUNC_DECL mat computeCovarianceMatrix(I const& b, I const& e, vec const& c) + { + glm::mat m{ 0 }; + glm::vec v; + + size_t cnt = 0; + for (I i = b; i != e; i++) + { + v = *i - c; + for (length_t x = 0; x < D; ++x) + for (length_t y = 0; y < D; ++y) + m[x][y] += static_cast(v[x] * v[y]); + cnt++; + } + if (cnt > 0) m /= static_cast(cnt); + + return std::move(m); + } + + + template + GLM_FUNC_DECL unsigned int findEigenvaluesSymReal + ( + mat const& covarMat, + vec& outEigenvalues, + mat& outEigenvectors + ) + { + T a[D * D]; // matrix -- input and workspace for algorithm (will be changed inplace) + auto A = [&](length_t const& r, length_t const& c) -> T& { return a[r * D + c]; }; + T d[D]; // diagonal elements + T e[D]; // off-diagonal elements + + for (length_t r = 0; r < D; r++) { + for (length_t c = 0; c < D; c++) { + A(r, c) = covarMat[c][r]; + } + } + + // 1. Householder reduction. + length_t l, k, j, i; + T scale, hh, h, g, f; + constexpr T epsilon = static_cast(0.0000001); + + for (i = D; i >= 2; i--) { + l = i - 1; + h = scale = 0; + if (l > 1) { + for (k = 1; k <= l; k++) { + scale += glm::abs(A(i - 1, k - 1)); + } + if (glm::equal(scale, 0, epsilon)) { + e[i - 1] = A(i - 1, l - 1); + } else { + for (k = 1; k <= l; k++) { + A(i - 1, k - 1) /= scale; + h += A(i - 1, k - 1) * A(i - 1, k - 1); + } + f = A(i - 1, l - 1); + g = ((f >= 0) ? -glm::sqrt(h) : glm::sqrt(h)); + e[i - 1] = scale * g; + h -= f * g; + A(i - 1, l - 1) = f - g; + f = 0; + for (j = 1; j <= l; j++) { + A(j - 1, i - 1) = A(i - 1, j - 1) / h; + g = 0; + for (k = 1; k <= j; k++) { + g += A(j - 1, k - 1) * A(i - 1, k - 1); + } + for (k = j + 1; k <= l; k++) { + g += A(k - 1, j - 1) * A(i - 1, k - 1); + } + e[j - 1] = g / h; + f += e[j - 1] * A(i - 1, j - 1); + } + hh = f / (h + h); + for (j = 1; j <= l; j++) { + f = A(i - 1, j - 1); + e[j - 1] = g = e[j - 1] - hh * f; + for (k = 1; k <= j; k++) { + A(j - 1, k - 1) -= (f * e[k - 1] + g * A(i - 1, k - 1)); + } + } + } + } else { + e[i - 1] = A(i - 1, l - 1); + } + d[i - 1] = h; + } + d[0] = 0; + e[0] = 0; + for (i = 1; i <= D; i++) { + l = i - 1; + if (!glm::equal(d[i - 1], 0, epsilon)) { + for (j = 1; j <= l; j++) { + g = 0; + for (k = 1; k <= l; k++) { + g += A(i - 1, k - 1) * A(k - 1, j - 1); + } + for (k = 1; k <= l; k++) { + A(k - 1, j - 1) -= g * A(k - 1, i - 1); + } + } + } + d[i - 1] = A(i - 1, i - 1); + A(i - 1, i - 1) = 1; + for (j = 1; j <= l; j++) { + A(j - 1, i - 1) = A(i - 1, j - 1) = 0; + } + } + + // 2. Calculation of eigenvalues and eigenvectors (QL algorithm) + length_t m, iter; + T s, r, p, dd, c, b; + const length_t MAX_ITER = 30; + auto transferSign = [](T const& v, T const& s) { return ((s) >= 0 ? glm::abs(v) : -glm::abs(v)); }; + auto pythag = [](T const& a, T const& b) { + constexpr T epsilon = static_cast(0.0000001); + T absa = glm::abs(a); + T absb = glm::abs(b); + if (absa > absb) { + absb /= absa; + absb *= absb; + return absa * glm::sqrt(static_cast(1) + absb); + } + if (glm::equal(absb, 0, epsilon)) return static_cast(0); + absa /= absb; + absa *= absa; + return absb * glm::sqrt(static_cast(1) + absa); + }; + + for (i = 2; i <= D; i++) { + e[i - 2] = e[i - 1]; + } + e[D - 1] = 0; + + for (l = 1; l <= D; l++) { + iter = 0; + do { + for (m = l; m <= D - 1; m++) { + dd = glm::abs(d[m - 1]) + glm::abs(d[m - 1 + 1]); + if (glm::equal(glm::abs(e[m - 1]) + dd, dd, epsilon)) break; + } + if (m != l) { + if (iter++ == MAX_ITER) { + return 0; // Too many iterations in FindEigenvalues + } + g = (d[l - 1 + 1] - d[l - 1]) / (2 * e[l - 1]); + r = pythag(g, 1); + g = d[m - 1] - d[l - 1] + e[l - 1] / (g + transferSign(r, g)); + s = c = 1; + p = 0; + for (i = m - 1; i >= l; i--) { + f = s * e[i - 1]; + b = c * e[i - 1]; + e[i - 1 + 1] = r = pythag(f, g); + if (glm::equal(r, 0, epsilon)) { + d[i - 1 + 1] -= p; + e[m - 1] = 0; + break; + } + s = f / r; + c = g / r; + g = d[i - 1 + 1] - p; + r = (d[i - 1] - g) * s + 2 * c * b; + d[i - 1 + 1] = g + (p = s * r); + g = c * r - b; + for (k = 1; k <= D; k++) { + f = A(k - 1, i - 1 + 1); + A(k - 1, i - 1 + 1) = s * A(k - 1, i - 1) + c * f; + A(k - 1, i - 1) = c * A(k - 1, i - 1) - s * f; + } + } + if (glm::equal(r, 0, epsilon) && (i >= l)) continue; + d[l - 1] -= p; + e[l - 1] = g; + e[m - 1] = 0; + } + } while (m != l); + } + + // 3. output + for(i = 0; i < D; i++) + outEigenvalues[i] = d[i]; + for(i = 0; i < D; i++) + for(j = 0; j < D; j++) + outEigenvectors[i][j] = A(j, i); + + return D; + } + + template + GLM_INLINE void sortEigenvalues(vec<2, T, Q>& eigenvalues, mat<2, 2, T, Q>& eigenvectors) + { + if (eigenvalues[0] < eigenvalues[1]) + { + std::swap(eigenvalues[0], eigenvalues[1]); + std::swap(eigenvectors[0], eigenvectors[1]); + } + } + + template + GLM_INLINE void sortEigenvalues(vec<3, T, Q>& eigenvalues, mat<3, 3, T, Q>& eigenvectors) + { + if (eigenvalues[0] < eigenvalues[1]) + { + std::swap(eigenvalues[0], eigenvalues[1]); + std::swap(eigenvectors[0], eigenvectors[1]); + } + if (eigenvalues[0] < eigenvalues[2]) + { + std::swap(eigenvalues[0], eigenvalues[2]); + std::swap(eigenvectors[0], eigenvectors[2]); + } + if (eigenvalues[1] < eigenvalues[2]) + { + std::swap(eigenvalues[1], eigenvalues[2]); + std::swap(eigenvectors[1], eigenvectors[2]); + } + } + + template + GLM_INLINE void sortEigenvalues(vec<4, T, Q>& eigenvalues, mat<4, 4, T, Q>& eigenvectors) + { + if (eigenvalues[0] < eigenvalues[2]) + { + std::swap(eigenvalues[0], eigenvalues[2]); + std::swap(eigenvectors[0], eigenvectors[2]); + } + if (eigenvalues[1] < eigenvalues[3]) + { + std::swap(eigenvalues[1], eigenvalues[3]); + std::swap(eigenvectors[1], eigenvectors[3]); + } + if (eigenvalues[0] < eigenvalues[1]) + { + std::swap(eigenvalues[0], eigenvalues[1]); + std::swap(eigenvectors[0], eigenvectors[1]); + } + if (eigenvalues[2] < eigenvalues[3]) + { + std::swap(eigenvalues[2], eigenvalues[3]); + std::swap(eigenvectors[2], eigenvectors[3]); + } + if (eigenvalues[1] < eigenvalues[2]) + { + std::swap(eigenvalues[1], eigenvalues[2]); + std::swap(eigenvectors[1], eigenvectors[2]); + } + } + +}//namespace glm diff --git a/test/gtx/CMakeLists.txt b/test/gtx/CMakeLists.txt index 5c8095cc..ad7bf492 100644 --- a/test/gtx/CMakeLists.txt +++ b/test/gtx/CMakeLists.txt @@ -37,6 +37,7 @@ glmCreateTestGTC(gtx_normalize_dot) glmCreateTestGTC(gtx_number_precision) glmCreateTestGTC(gtx_orthonormalize) glmCreateTestGTC(gtx_optimum_pow) +glmCreateTestGTC(gtx_pca) glmCreateTestGTC(gtx_perpendicular) glmCreateTestGTC(gtx_polar_coordinates) glmCreateTestGTC(gtx_projection) diff --git a/test/gtx/gtx_pca.cpp b/test/gtx/gtx_pca.cpp new file mode 100644 index 00000000..87673143 --- /dev/null +++ b/test/gtx/gtx_pca.cpp @@ -0,0 +1,676 @@ +#define GLM_ENABLE_EXPERIMENTAL +#include +#include + +#include +#include + +// Test data: 1AGA 'agarose double helix' +// https://www.rcsb.org/structure/1aga +// The fourth coordinate is randomized +namespace _1aga +{ + + // Fills `outTestData` with hard-coded atom positions from 1AGA + // The fourth coordinate is randomized + template + void fillTestData(std::vector& outTestData) + { + // x,y,z coordinates copied from RCSB PDB file of 1AGA + // w coordinate randomized with standard normal distribution + constexpr double _1aga[] = { + 3.219, -0.637, 19.462, 2.286, + 4.519, 0.024, 18.980, -0.828, + 4.163, 1.425, 18.481, -0.810, + 3.190, 1.341, 17.330, -0.170, + 1.962, 0.991, 18.165, 0.816, + 2.093, 1.952, 19.331, 0.276, + 5.119, -0.701, 17.908, -0.490, + 3.517, 2.147, 19.514, -0.207, + 2.970, 2.609, 16.719, 0.552, + 2.107, -0.398, 18.564, 0.403, + 2.847, 2.618, 15.335, 0.315, + 1.457, 3.124, 14.979, 0.683, + 1.316, 3.291, 13.473, 0.446, + 2.447, 4.155, 12.931, 1.324, + 3.795, 3.614, 13.394, 0.112, + 4.956, 4.494, 12.982, 0.253, + 0.483, 2.217, 15.479, 1.316, + 0.021, 3.962, 13.166, 1.522, + 2.311, 5.497, 13.395, 0.248, + 3.830, 3.522, 14.827, 0.591, + 5.150, 4.461, 11.576, 0.635, + -1.057, 3.106, 13.132, 0.191, + -2.280, 3.902, 12.650, 1.135, + -3.316, 2.893, 12.151, 0.794, + -2.756, 2.092, 11.000, 0.720, + -1.839, 1.204, 11.835, -1.172, + -2.737, 0.837, 13.001, -0.313, + -1.952, 4.784, 11.578, 2.082, + -3.617, 1.972, 13.184, 0.653, + -3.744, 1.267, 10.389, -0.413, + -0.709, 2.024, 12.234, -1.747, + -3.690, 1.156, 9.005, -1.275, + -3.434, -0.300, 8.649, 0.441, + -3.508, -0.506, 7.143, 0.237, + -4.822, 0.042, 6.601, -2.856, + -5.027, 1.480, 7.064, 0.985, + -6.370, 2.045, 6.652, 0.915, + -2.162, -0.690, 9.149, 1.100, + -3.442, -1.963, 6.836, -0.081, + -5.916, -0.747, 7.065, -2.345, + -4.965, 1.556, 8.497, 0.504, + -6.439, 2.230, 5.246, 1.451, + -2.161, -2.469, 6.802, -1.171, + -2.239, -3.925, 6.320, -1.434, + -0.847, -4.318, 5.821, 0.098, + -0.434, -3.433, 4.670, -1.446, + -0.123, -2.195, 5.505, 0.182, + 0.644, -2.789, 6.671, 0.865, + -3.167, -4.083, 5.248, -0.098, + 0.101, -4.119, 6.854, -0.001, + 0.775, -3.876, 4.059, 1.061, + -1.398, -1.625, 5.904, 0.230, + 0.844, -3.774, 2.675, 1.313, + 1.977, -2.824, 2.319, -0.112, + 2.192, -2.785, 0.813, -0.981, + 2.375, -4.197, 0.271, -0.355, + 1.232, -5.093, 0.734, 0.632, + 1.414, -6.539, 0.322, 0.576, + 1.678, -1.527, 2.819, -1.187, + 3.421, -1.999, 0.496, -1.770, + 3.605, -4.750, 0.735, 1.099, + 1.135, -5.078, 2.167, 0.854, + 1.289, -6.691, -1.084, -0.487, + -1.057, 3.106, 22.602, -1.297, + -2.280, 3.902, 22.120, 0.376, + -3.316, 2.893, 21.621, 0.932, + -2.756, 2.092, 20.470, 1.680, + -1.839, 1.204, 21.305, 0.615, + -2.737, 0.837, 22.471, 0.899, + -1.952, 4.784, 21.048, -0.521, + -3.617, 1.972, 22.654, 0.133, + -3.744, 1.267, 19.859, 0.081, + -0.709, 2.024, 21.704, 1.420, + -3.690, 1.156, 18.475, -0.850, + -3.434, -0.300, 18.119, -0.249, + -3.508, -0.506, 16.613, 1.434, + -4.822, 0.042, 16.071, -2.466, + -5.027, 1.480, 16.534, -1.045, + -6.370, 2.045, 16.122, 1.707, + -2.162, -0.690, 18.619, -2.023, + -3.442, -1.963, 16.336, -0.304, + -5.916, -0.747, 16.535, 0.979, + -4.965, 1.556, 17.967, -1.165, + -6.439, 2.230, 14.716, 0.929, + -2.161, -2.469, 16.302, -0.234, + -2.239, -3.925, 15.820, -0.228, + -0.847, -4.318, 15.321, 1.844, + -0.434, -3.433, 14.170, 1.132, + -0.123, -2.195, 15.005, 0.211, + 0.644, -2.789, 16.171, -0.632, + -3.167, -4.083, 14.748, -0.519, + 0.101, -4.119, 16.354, 0.173, + 0.775, -3.876, 13.559, 1.243, + -1.398, -1.625, 15.404, -0.187, + 0.844, -3.774, 12.175, -1.332, + 1.977, -2.824, 11.819, -1.616, + 2.192, -2.785, 10.313, 1.320, + 2.375, -4.197, 9.771, 0.237, + 1.232, -5.093, 10.234, 0.851, + 1.414, -6.539, 9.822, 1.816, + 1.678, -1.527, 12.319, -1.657, + 3.421, -1.999, 10.036, 1.559, + 3.605, -4.750, 10.235, 0.831, + 1.135, -5.078, 11.667, 0.060, + 1.289, -6.691, 8.416, 1.066, + 3.219, -0.637, 10.002, 2.111, + 4.519, 0.024, 9.520, -0.874, + 4.163, 1.425, 9.021, -1.012, + 3.190, 1.341, 7.870, -0.250, + 1.962, 0.991, 8.705, -1.359, + 2.093, 1.952, 9.871, -0.126, + 5.119, -0.701, 8.448, 0.995, + 3.517, 2.147, 10.054, 0.941, + 2.970, 2.609, 7.259, -0.562, + 2.107, -0.398, 9.104, -0.038, + 2.847, 2.618, 5.875, 0.398, + 1.457, 3.124, 5.519, 0.481, + 1.316, 3.291, 4.013, -0.187, + 2.447, 4.155, 3.471, -0.429, + 3.795, 3.614, 3.934, -0.432, + 4.956, 4.494, 3.522, -0.788, + 0.483, 2.217, 6.019, -0.923, + 0.021, 3.962, 3.636, -0.316, + 2.311, 5.497, 3.935, -1.917, + 3.830, 3.522, 5.367, -0.302, + 5.150, 4.461, 2.116, -1.615 + }; + constexpr size_t _1agaSize = sizeof(_1aga) / (4 * sizeof(double)); + + outTestData.resize(_1agaSize); + for(size_t i = 0; i < _1agaSize; ++i) + for(size_t d = 0; d < vec::length(); ++d) + outTestData[i][d] = static_cast(_1aga[i * 4 + d]); + } + + void getExpectedCovarDataPtr(const double*& ptr) + { + static constexpr double _1agaCovar4x4d[] = { + 9.624340680272107, -0.000066573696146, -4.293213765684049, 0.018793741874528, + -0.000066573696146, 9.624439378684805, 5.351138726379443, -0.115692591458806, + -4.293213765684049, 5.351138726379443, 35.628485496346691, 0.908742392542202, + 0.018793741874528, -0.115692591458806, 0.908742392542202, 1.097059718568909 + }; + ptr = _1agaCovar4x4d; + } + void getExpectedCovarDataPtr(const float*& ptr) + { + // note: the value difference to `_1agaCovar4x4d` is due to the numeric error propagation during computation of the covariance matrix. + static constexpr float _1agaCovar4x4f[] = { + 9.624336242675781f, -0.000066711785621f, -4.293214797973633f, 0.018793795257807f, + -0.000066711785621f, 9.624438285827637f, 5.351140022277832f, -0.115692682564259f, + -4.293214797973633f, 5.351140022277832f, 35.628479003906250f, 0.908742427825928f, + 0.018793795257807f, -0.115692682564259f, 0.908742427825928f, 1.097059369087219f + }; + ptr = _1agaCovar4x4f; + } + + template + int checkCovarMat(glm::mat const& covarMat) + { + const T* expectedCovarData = nullptr; + getExpectedCovarDataPtr(expectedCovarData); + for(size_t x = 0; x < D; ++x) + for(size_t y = 0; y < D; ++y) + if(!glm::equal(covarMat[y][x], expectedCovarData[x * 4 + y], static_cast(0.000001))) + return 1; + return 0; + } + + template void getExpectedEigenvaluesEigenvectorsDataPtr(const T*& evals, const T*& evecs); + template<> void getExpectedEigenvaluesEigenvectorsDataPtr<2, float>(const float*& evals, const float*& evecs) + { + static constexpr float expectedEvals[] = { + 9.624471664428711f, 9.624302864074707f + }; + static constexpr float expectedEvecs[] = { + -0.443000972270966f, 0.896521151065826f, + 0.896521151065826f, 0.443000972270966f + }; + evals = expectedEvals; + evecs = expectedEvecs; + } + template<> void getExpectedEigenvaluesEigenvectorsDataPtr<2, double>(const double*& evals, const double*& evecs) + { + static constexpr double expectedEvals[] = { + 9.624472899262972, 9.624307159693940 + }; + static constexpr double expectedEvecs[] = { + -0.449720461624363, 0.893169360421846, + 0.893169360421846, 0.449720461624363 + }; + evals = expectedEvals; + evecs = expectedEvecs; + } + template<> void getExpectedEigenvaluesEigenvectorsDataPtr<3, float>(const float*& evals, const float*& evecs) + { + static constexpr float expectedEvals[] = { + 37.327442169189453f, 9.624311447143555f, 7.925499439239502f + }; + static constexpr float expectedEvecs[] = { + -0.150428697466850f, 0.187497511506081f, 0.970678031444550f, + 0.779980957508087f, 0.625803351402283f, -0.000005212802080f, + 0.607454538345337f, -0.757109522819519f, 0.240383237600327f + }; + evals = expectedEvals; + evecs = expectedEvecs; + } + template<> void getExpectedEigenvaluesEigenvectorsDataPtr<3, double>(const double*& evals, const double*& evecs) + { + static constexpr double expectedEvals[] = { + 37.327449427468345, 9.624314341614987, 7.925501786220276 + }; + static constexpr double expectedEvecs[] = { + -0.150428640509585, 0.187497426513576, 0.970678082149394, + 0.779981605126846, 0.625802441381904, -0.000004919018357, + 0.607453635908278, -0.757110308615089, 0.240383154173870 + }; + evals = expectedEvals; + evecs = expectedEvecs; + } + template<> void getExpectedEigenvaluesEigenvectorsDataPtr<4, float>(const float*& evals, const float*& evecs) + { + static constexpr float expectedEvals[] = { + 37.347740173339844f, 9.624703407287598f, 7.940164566040039f, 1.061712265014648f + }; + static constexpr float expectedEvecs[] = { + -0.150269940495491f, 0.187220811843872f, 0.970467865467072f, 0.023652425035834f, + 0.779159665107727f, 0.626788496971130f, -0.000105984276161f, -0.006797631736845f, + 0.608242213726044f, -0.755563497543335f, 0.238818943500519f, 0.046158745884895f, + -0.019251370802522f, 0.034755907952785f, -0.034024771302938f, 0.998630762100220f, + }; + evals = expectedEvals; + evecs = expectedEvecs; + } + template<> void getExpectedEigenvaluesEigenvectorsDataPtr<4, double>(const double*& evals, const double*& evecs) + { + static constexpr double expectedEvals[] = { + 37.347738991879226, 9.624706889211053, 7.940170752816341, 1.061708639965897 + }; + static constexpr double expectedEvecs[] = { + -0.150269954805403, 0.187220917596058, 0.970467838469868, 0.023652551509145, + 0.779159831346545, 0.626788431871120, -0.000105940250315, -0.006797622027466, + 0.608241962267880, -0.755563776664248, 0.238818902950296, 0.046158707986616, + -0.019251317755512, 0.034755849578017, -0.034024915369495, 0.998630924225204, + }; + evals = expectedEvals; + evecs = expectedEvecs; + } + + template + int checkEigenvaluesEigenvectors( + glm::vec const& evals, + glm::mat const& evecs) + { + const T* expectedEvals = nullptr; + const T* expectedEvecs = nullptr; + getExpectedEigenvaluesEigenvectorsDataPtr(expectedEvals, expectedEvecs); + + for(int i = 0; i < D; ++i) + if(!glm::equal(evals[i], expectedEvals[i], static_cast(0.000001))) + return 1; + + for (int i = 0; i < D; ++i) + for (int d = 0; d < D; ++d) + if (!glm::equal(evecs[i][d], expectedEvecs[i * D + d], static_cast(0.000001))) + return 1; + + return 0; + } + +} // namespace _1aga + +// Compute center of gravity +template +vec computeCenter(const std::vector& testData) +{ + double c[vec::length()]; + std::fill(c, c + vec::length(), 0.0); + + for(vec const& v : testData) + for(size_t d = 0; d < vec::length(); ++d) + c[d] += static_cast(v[d]); + + vec cVec; + for(size_t d = 0; d < vec::length(); ++d) + cVec[d] = static_cast(c[d] / static_cast(testData.size())); + return std::move(cVec); +} + +// Test sorting of Eigenvalue&Eigenvector lists. Use exhaustive search. +template +int testEigenvalueSort() +{ + // Test input data: four arbitrary values + constexpr glm::vec refVal + { + glm::vec<4, T, Q> + { + 10, 8, 6, 4 + } + }; + // Test input data: four arbitrary vectors, which can be matched to the above values + constexpr glm::mat refVec + { + glm::mat<4, 4, T, Q> + { + 10, 20, 5, 40, + 8, 16, 4, 32, + 6, 12, 3, 24, + 4, 8, 2, 16 + } + }; + // Permutations of test input data for exhaustive check, based on `D` (1 <= D <= 4) + constexpr int permutationCount[] + { + 0, + 1, + 2, + 6, + 24 + }; + // The permutations t perform, based on `D` (1 <= D <= 4) + constexpr glm::ivec4 permutation[] + { + { 0, 1, 2, 3 }, + { 1, 0, 2, 3 }, // last for D = 2 + { 0, 2, 1, 3 }, + { 1, 2, 0, 3 }, + { 2, 0, 1, 3 }, + { 2, 1, 0, 3 }, // last for D = 3 + { 0, 1, 3, 2 }, + { 1, 0, 3, 2 }, + { 0, 2, 3, 1 }, + { 1, 2, 3, 0 }, + { 2, 0, 3, 1 }, + { 2, 1, 3, 0 }, + { 0, 3, 1, 2 }, + { 1, 3, 0, 2 }, + { 0, 3, 2, 1 }, + { 1, 3, 2, 0 }, + { 2, 3, 0, 1 }, + { 2, 3, 1, 0 }, + { 3, 0, 1, 2 }, + { 3, 1, 0, 2 }, + { 3, 0, 2, 1 }, + { 3, 1, 2, 0 }, + { 3, 2, 0, 1 }, + { 3, 2, 1, 0 } // last for D = 4 + }; + // Lambda utility to check the result + auto checkResult = [&refVal,&refVec](glm::vec const& value, glm::mat const& vector) + { + constexpr T epsilon = static_cast(0.0000001); + // check that values are ordered ascending + for(int i = 1; i < D; ++i) + { + if(value[0] < value[1]) + return false; + } + // check that values and vectors are equal to the reference values + for(int i = 0; i < D; ++i) + { + if(!glm::equal(refVal[i], value[i], epsilon)) + return false; + for(int j = 0; j < D; ++j) + { + if(!glm::equal(refVec[i][j], vector[i][j], epsilon)) + return false; + } + } + return true; // all matched + }; + + // initial sanity check + if(!checkResult(refVal, refVec)) + return 1; + + // Exhaustive search through all permutations + for(int p = 0; p < permutationCount[D]; ++p) + { + glm::vec testVal; + glm::mat testVec; + for(int i = 0; i < D; ++i) + { + testVal[i] = refVal[permutation[p][i]]; + testVec[i] = refVec[permutation[p][i]]; + } + + glm::sortEigenvalues(testVal, testVec); + + if(!checkResult(testVal, testVec)) + return 2 + p; + } + + return 0; +} + +// Test covariance matrix creation functions +template +int testCovar(unsigned int dataSize, unsigned int randomEngineSeed) +{ + typedef glm::vec vec; + typedef glm::mat mat; + + // #1: test expected result with fixed data set + std::vector testData; + _1aga::fillTestData(testData); + + // compute center of gravity + vec center = computeCenter(testData); + + mat covarMat = glm::computeCovarianceMatrix(testData.data(), testData.size(), center); + if(_1aga::checkCovarMat(covarMat)) + return 1; + + // #2: test function variant consitency with random data + std::default_random_engine rndEng{ randomEngineSeed }; + std::normal_distribution normalDist; + testData.resize(dataSize); + // some common offset of all data + T offset[D]; + for(size_t d = 0; d < D; ++d) + offset[d] = normalDist(rndEng); + // init data + for(size_t i = 0; i < dataSize; ++i) + for(size_t d = 0; d < D; ++d) + testData[i][d] = offset[d] + normalDist(rndEng); + center = computeCenter(testData); + + std::vector centeredTestData; + centeredTestData.reserve(testData.size()); + for(vec const& v : testData) + centeredTestData.push_back(v - center); + + mat c1 = glm::computeCovarianceMatrix(centeredTestData.data(), centeredTestData.size()); + mat c2 = glm::computeCovarianceMatrix(centeredTestData.begin(), centeredTestData.end()); + mat c3 = glm::computeCovarianceMatrix(testData.data(), testData.size(), center); + mat c4 = glm::computeCovarianceMatrix(testData.rbegin(), testData.rend(), center); + + if(c1 != c2) + return 1; + if(c1 != c3) + return 1; + if(c1 != c4) + return 1; + + return 0; +} + +template +int testEigenvectors() +{ + typedef glm::vec vec; + typedef glm::mat mat; + + // test expected result with fixed data set + std::vector testData; + _1aga::fillTestData(testData); + vec center = computeCenter(testData); + mat covarMat = glm::computeCovarianceMatrix(testData.data(), testData.size(), center); + vec eigenvalues; + mat eigenvectors; + unsigned int c = glm::findEigenvaluesSymReal(covarMat, eigenvalues, eigenvectors); + if(c != D) + return 1; + glm::sortEigenvalues(eigenvalues, eigenvectors); + + if(_1aga::checkEigenvaluesEigenvectors(eigenvalues, eigenvectors) != 0) + return 1; + + return 0; +} + +/// A simple small smoke test: +/// - a uniformly sampled block +/// - reconstruct main axes +/// - check order of eigenvalues equals order of extends of block in direction of main axes +int smokeTest() +{ + using glm::vec3; + using glm::mat3; + std::vector pts; + pts.reserve(11 * 15 * 7); + + for(int x = -5; x <= 5; ++x) + for(int y = -7; y <= 7; ++y) + for(int z = -3; z <= 3; ++z) + pts.push_back(vec3{ x, y, z }); + + mat3 covar = glm::computeCovarianceMatrix(pts.data(), pts.size()); + mat3 eVec; + vec3 eVal; + int eCnt = glm::findEigenvaluesSymReal(covar, eVal, eVec); + if(eCnt != 3) + return 1; + + // sort eVec by decending eVal + if(eVal[0] < eVal[1]) + { + std::swap(eVal[0], eVal[1]); + std::swap(eVec[0], eVec[1]); + } + if(eVal[0] < eVal[2]) + { + std::swap(eVal[0], eVal[2]); + std::swap(eVec[0], eVec[2]); + } + if(eVal[1] < eVal[2]) + { + std::swap(eVal[1], eVal[2]); + std::swap(eVec[1], eVec[2]); + } + + if(!glm::all(glm::equal(glm::abs(eVec[0]), vec3{ 0, 1, 0 }))) + return 2; + if(!glm::all(glm::equal(glm::abs(eVec[1]), vec3{ 1, 0, 0 }))) + return 3; + if(!glm::all(glm::equal(glm::abs(eVec[2]), vec3{ 0, 0, 1 }))) + return 4; + + return 0; +} + +int rndTest(unsigned int randomEngineSeed) +{ + std::default_random_engine rndEng{ randomEngineSeed }; + std::normal_distribution normalDist; + + // construct orthonormal system + glm::dvec3 x{ normalDist(rndEng), normalDist(rndEng), normalDist(rndEng) }; + double l = glm::length(x); + while(l < 0.000001) + x = glm::dvec3{ normalDist(rndEng), normalDist(rndEng), normalDist(rndEng) }; + x = glm::normalize(x); + glm::dvec3 y{ normalDist(rndEng), normalDist(rndEng), normalDist(rndEng) }; + l = glm::length(y); + while(l < 0.000001) + y = glm::dvec3{ normalDist(rndEng), normalDist(rndEng), normalDist(rndEng) }; + while(glm::abs(glm::dot(x, y)) < 0.000001) + { + y = glm::dvec3{ normalDist(rndEng), normalDist(rndEng), normalDist(rndEng) }; + while(l < 0.000001) + y = glm::dvec3{ normalDist(rndEng), normalDist(rndEng), normalDist(rndEng) }; + } + y = glm::normalize(y); + glm::dvec3 z = glm::normalize(glm::cross(x, y)); + y = glm::normalize(glm::cross(z, x)); + + //printf("\n"); + //printf("x: %.10lf, %.10lf, %.10lf\n", x.x, x.y, x.z); + //printf("y: %.10lf, %.10lf, %.10lf\n", y.x, y.y, y.z); + //printf("z: %.10lf, %.10lf, %.10lf\n", z.x, z.y, z.z); + + // generate input point data + std::vector ptData; + constexpr int patters[] = { + 8, 0, 0, + 4, 1, 2, + 0, 2, 0, + 0, 0, 4 + }; + glm::dvec3 offset{ normalDist(rndEng), normalDist(rndEng), normalDist(rndEng) }; + for(int p = 0; p < 4; ++p) + for(int xs = 1; xs >= -1; xs -= 2) + for(int ys = 1; ys >= -1; ys -= 2) + for(int zs = 1; zs >= -1; zs -= 2) + ptData.push_back( + offset + + x * static_cast(patters[p * 3 + 0] * xs) + + y * static_cast(patters[p * 3 + 1] * ys) + + z * static_cast(patters[p * 3 + 2] * zs)); + + // perform PCA: + glm::dvec3 center = computeCenter(ptData); + glm::dmat3 covarMat = glm::computeCovarianceMatrix(ptData.data(), ptData.size(), center); + glm::dvec3 evals; + glm::dmat3 evecs; + int evcnt = glm::findEigenvaluesSymReal(covarMat, evals, evecs); + if(evcnt != 3) + return 1; + glm::sortEigenvalues(evals, evecs); + + //printf("\n"); + //printf("evec0: %.10lf, %.10lf, %.10lf\n", evecs[0].x, evecs[0].y, evecs[0].z); + //printf("evec2: %.10lf, %.10lf, %.10lf\n", evecs[2].x, evecs[2].y, evecs[2].z); + //printf("evec1: %.10lf, %.10lf, %.10lf\n", evecs[1].x, evecs[1].y, evecs[1].z); + + if(glm::length(glm::abs(x) - glm::abs(evecs[0])) > 0.000001) + return 1; + if(glm::length(glm::abs(y) - glm::abs(evecs[2])) > 0.000001) + return 1; + if(glm::length(glm::abs(z) - glm::abs(evecs[1])) > 0.000001) + return 1; + + return 0; +} + +int main() +{ + + // A small smoke test to fail early with most problems + if(smokeTest()) + return __LINE__; + + // test sorting utility. + if(testEigenvalueSort<2, float, glm::defaultp>() != 0) + return __LINE__; + if(testEigenvalueSort<2, double, glm::defaultp>() != 0) + return __LINE__; + if(testEigenvalueSort<3, float, glm::defaultp>() != 0) + return __LINE__; + if(testEigenvalueSort<3, double, glm::defaultp>() != 0) + return __LINE__; + if(testEigenvalueSort<4, float, glm::defaultp>() != 0) + return __LINE__; + if(testEigenvalueSort<4, double, glm::defaultp>() != 0) + return __LINE__; + + // Note: the random engine uses a fixed seed to create consistent and reproducible test data + // test covariance matrix computation from different data sources + if(testCovar<2, float, glm::defaultp>(100, 12345) != 0) + return __LINE__; + if(testCovar<2, double, glm::defaultp>(100, 42) != 0) + return __LINE__; + if(testCovar<3, float, glm::defaultp>(100, 2021) != 0) + return __LINE__; + if(testCovar<3, double, glm::defaultp>(100, 815) != 0) + return __LINE__; + if(testCovar<4, float, glm::defaultp>(100, 3141) != 0) + return __LINE__; + if(testCovar<4, double, glm::defaultp>(100, 174) != 0) + return __LINE__; + + // test PCA eigen vector reconstruction + if(testEigenvectors<2, float, glm::defaultp>() != 0) + return __LINE__; + if(testEigenvectors<2, double, glm::defaultp>() != 0) + return __LINE__; + if(testEigenvectors<3, float, glm::defaultp>() != 0) + return __LINE__; + if(testEigenvectors<3, double, glm::defaultp>() != 0) + return __LINE__; + if (testEigenvectors<4, float, glm::defaultp>() != 0) + return __LINE__; + if (testEigenvectors<4, double, glm::defaultp>() != 0) + return __LINE__; + + // Final tests with randomized data + if(rndTest(12345) != 0) + return __LINE__; + if(rndTest(42) != 0) + return __LINE__; + + return 0; +}