diff --git a/.gitignore b/.gitignore index ec55f0895..e5d044b72 100644 --- a/.gitignore +++ b/.gitignore @@ -52,3 +52,5 @@ Makefile # local build(s) build* +/.vs +/CMakeSettings.json diff --git a/glm/gtx/matrix_factorisation.hpp b/glm/gtx/matrix_factorisation.hpp new file mode 100644 index 000000000..9acc7f3ae --- /dev/null +++ b/glm/gtx/matrix_factorisation.hpp @@ -0,0 +1,64 @@ +/// @ref gtx_matrix_factorisation +/// @file glm/gtx/matrix_factorisation.hpp +/// +/// @see core (dependence) +/// +/// @defgroup gtx_matrix_factorisation GLM_GTX_matrix_factorisation +/// @ingroup gtx +/// +/// @brief Functions to factor matrices in various forms +/// +/// need to be included to use these functionalities. + +#pragma once + +// Dependency: +#include "../glm.hpp" + +#ifndef GLM_ENABLE_EXPERIMENTAL +# error "GLM: GLM_GTX_matrix_factorisation 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." +#endif + +#if GLM_MESSAGES == GLM_MESSAGES_ENABLED && !defined(GLM_EXT_INCLUDED) +# pragma message("GLM: GLM_GTX_matrix_factorisation extension included") +#endif + +/* +Suggestions: + - Move helper functions flipud and fliplr to another file: They may be helpful in more general circumstances. + - Implement other types of matrix factorisation, such as: QL and LQ, L(D)U, eigendecompositions, etc... +*/ + +namespace glm{ + /// @addtogroup gtx_matrix_factorisation + /// @{ + + /// Flips the matrix rows up and down. + /// From GLM_GTX_matrix_factorisation extension. + template class matType> + GLM_FUNC_DECL matType flipud(const matType& in); + + /// Flips the matrix columns right and left. + /// From GLM_GTX_matrix_factorisation extension. + template class matType> + GLM_FUNC_DECL matType fliplr(const matType& in); + + /// Performs QR factorisation of a matrix. + /// Returns 2 matrices, q and r, such that the columns of q are orthonormal and span the same subspace than those of the input matrix, r is an upper triangular matrix, and q*r=in. + /// Given an n-by-m input matrix, q has dimensions min(n,m)-by-m, and r has dimensions n-by-min(n,m). + /// From GLM_GTX_matrix_factorisation extension. + template class matType> + GLM_FUNC_DECL void qr_decompose(matType<(C < R ? C : R), R, T, P>& q, matType& r, const matType& in); + + /// Performs RQ factorisation of a matrix. + /// Returns 2 matrices, r and q, such that r is an upper triangular matrix, the rows of q are orthonormal and span the same subspace than those of the input matrix, and r*q=in. + /// Note that in the context of RQ factorisation, the diagonal is seen as starting in the lower-right corner of the matrix, instead of the usual upper-left. + /// Given an n-by-m input matrix, r has dimensions min(n,m)-by-m, and q has dimensions n-by-min(n,m). + /// From GLM_GTX_matrix_factorisation extension. + template class matType> + GLM_FUNC_DECL void rq_decompose(matType<(C < R ? C : R), R, T, P>& r, matType& q, const matType& in); + + /// @} +} + +#include "matrix_factorisation.inl" diff --git a/glm/gtx/matrix_factorisation.inl b/glm/gtx/matrix_factorisation.inl new file mode 100644 index 000000000..f165016f8 --- /dev/null +++ b/glm/gtx/matrix_factorisation.inl @@ -0,0 +1,76 @@ +/// @ref gtx_matrix_factorisation +/// @file glm/gtx/matrix_factorisation.inl + +namespace glm { + template class matType> + GLM_FUNC_QUALIFIER matType flipud(const matType& in) { + matType tin = transpose(in); + tin = fliplr(tin); + matType out = transpose(tin); + + return out; + } + + template class matType> + GLM_FUNC_QUALIFIER matType fliplr(const matType& in) { + matType out; + for (length_t i = 0; i < C; i++) { + out[i] = in[(C - i) - 1]; + } + + return out; + } + + template class matType> + GLM_FUNC_QUALIFIER void qr_decompose(matType<(C < R ? C : R), R, T, P>& q, matType& r, const matType& in) { + // Uses modified Gram-Schmidt method + // Source: https://en.wikipedia.org/wiki/Gram–Schmidt_process + // And https://en.wikipedia.org/wiki/QR_decomposition + + //For all the linearly independs columns of the input... + // (there can be no more linearly independents columns than there are rows.) + for (length_t i = 0; i < (C < R ? C : R); i++) { + //Copy in Q the input's i-th column. + q[i] = in[i]; + + //j = [0,i[ + // Make that column orthogonal to all the previous ones by substracting to it the non-orthogonal projection of all the previous columns. + // Also: Fill the zero elements of R + for (length_t j = 0; j < i; j++) { + q[i] -= dot(q[i], q[j])*q[j]; + r[j][i] = 0; + } + + //Now, Q i-th column is orthogonal to all the previous columns. Normalize it. + q[i] = normalize(q[i]); + + //j = [i,C[ + //Finally, compute the corresponding coefficients of R by computing the projection of the resulting column on the other columns of the input. + for (length_t j = i; j < C; j++) { + r[j][i] = dot(in[j], q[i]); + } + } + } + + template class matType> + GLM_FUNC_QUALIFIER void rq_decompose(matType<(C < R ? C : R), R, T, P>& r, matType& q, const matType& in) { + // From https://en.wikipedia.org/wiki/QR_decomposition: + // The RQ decomposition transforms a matrix A into the product of an upper triangular matrix R (also known as right-triangular) and an orthogonal matrix Q. The only difference from QR decomposition is the order of these matrices. + // QR decomposition is Gram–Schmidt orthogonalization of columns of A, started from the first column. + // RQ decomposition is Gram–Schmidt orthogonalization of rows of A, started from the last row. + + matType tin = transpose(in); + tin = fliplr(tin); + + matType tr; + matType<(C < R ? C : R), C, T, P> tq; + qr_decompose(tq, tr, tin); + + tr = fliplr(tr); + r = transpose(tr); + r = fliplr(r); + + tq = fliplr(tq); + q = transpose(tq); + } +} //namespace glm diff --git a/test/gtx/CMakeLists.txt b/test/gtx/CMakeLists.txt index 6fe2fc27e..6b3202943 100644 --- a/test/gtx/CMakeLists.txt +++ b/test/gtx/CMakeLists.txt @@ -21,6 +21,7 @@ glmCreateTestGTC(gtx_io) glmCreateTestGTC(gtx_log_base) glmCreateTestGTC(gtx_matrix_cross_product) glmCreateTestGTC(gtx_matrix_decompose) +glmCreateTestGTC(gtx_matrix_factorisation) glmCreateTestGTC(gtx_matrix_interpolation) glmCreateTestGTC(gtx_matrix_major_storage) glmCreateTestGTC(gtx_matrix_operation) diff --git a/test/gtx/gtx_matrix_factorisation.cpp b/test/gtx/gtx_matrix_factorisation.cpp new file mode 100644 index 000000000..7d32078f6 --- /dev/null +++ b/test/gtx/gtx_matrix_factorisation.cpp @@ -0,0 +1,103 @@ +#define GLM_ENABLE_EXPERIMENTAL +#include + +const double epsilon = 1e-10f; + +template class matType> +int test_qr(matType m) { + matType<(C < R ? C : R), R, T, P> q(-999); + matType r(-999); + + glm::qr_decompose(q, r, m); + + //Test if q*r really equals the input matrix + matType tm = q*r; + matType err = tm - m; + + for (glm::length_t i = 0; i < C; i++) { + for (glm::length_t j = 0; j < R; j++) { + if (std::abs(err[i][j]) > epsilon) return 1; + } + } + + //Test if the columns of q are orthonormal + for (glm::length_t i = 0; i < (C < R ? C : R); i++) { + if ((length(q[i]) - 1) > epsilon) return 2; + + for (glm::length_t j = 0; j epsilon) return 3; + } + } + + //Test if the matrix r is upper triangular + for (glm::length_t i = 0; i < C; i++) { + for (glm::length_t j = i + 1; j < (C < R ? C : R); j++) { + if (r[i][j] != 0) return 4; + } + } + + return 0; +} + +template class matType> +int test_rq(matType m) { + matType q(-999); + matType<(C < R ? C : R), R, T, P> r(-999); + + glm::rq_decompose(r, q, m); + + //Test if q*r really equals the input matrix + matType tm = r*q; + matType err = tm - m; + + for (glm::length_t i = 0; i < C; i++) { + for (glm::length_t j = 0; j < R; j++) { + if (std::abs(err[i][j]) > epsilon) return 1; + } + } + + + //Test if the rows of q are orthonormal + matType<(C < R ? C : R), C, T, P> tq = transpose(q); + + for (glm::length_t i = 0; i < (C < R ? C : R); i++) { + if ((length(tq[i]) - 1) > epsilon) return 2; + + for (glm::length_t j = 0; j epsilon) return 3; + } + } + + //Test if the matrix r is upper triangular + for (glm::length_t i = 0; i < (C < R ? C : R); i++) { + for (glm::length_t j = R - (C < R ? C : R) + i + 1; j < R; j++) { + if (r[i][j] != 0) return 4; + } + } + + return 0; +} + +int main() +{ + + //Test QR square + if(test_qr(glm::dmat3(12, 6, -4, -51, 167, 24, 4, -68, -41))) return 1; + + //Test RQ square + if (test_rq(glm::dmat3(12, 6, -4, -51, 167, 24, 4, -68, -41))) return 2; + + //Test QR triangular 1 + if (test_qr(glm::dmat3x4(12, 6, -4, -51, 167, 24, 4, -68, -41, 7, 2, 15))) return 3; + + //Test QR triangular 2 + if (test_qr(glm::dmat4x3(12, 6, -4, -51, 167, 24, 4, -68, -41, 7, 2, 15))) return 4; + + //Test RQ triangular 1 : Fails at the triangular test + if (test_rq(glm::dmat3x4(12, 6, -4, -51, 167, 24, 4, -68, -41, 7, 2, 15))) return 5; + + //Test QR triangular 2 + if (test_rq(glm::dmat4x3(12, 6, -4, -51, 167, 24, 4, -68, -41, 7, 2, 15))) return 6; + + return 0; +}