diff options
author | Gael Guennebaud <g.gael@free.fr> | 2016-04-14 15:11:33 +0200 |
---|---|---|
committer | Gael Guennebaud <g.gael@free.fr> | 2016-04-14 15:11:33 +0200 |
commit | ea7087ef319469cdb00f3c1c82aea8d2b1cc94ac (patch) | |
tree | 46c1375fe43665d5a70d8598d597f01718a8f6ea /test | |
parent | 36f5a10198a8bc745633121fc4e8794a00b559e7 (diff) | |
parent | 6498dadc2f3864dda73e8acd3bcd7edf795e8bf7 (diff) |
Merged in rmlarsen/eigen (pull request PR-174)
Add matrix condition number estimation module.
Diffstat (limited to 'test')
-rw-r--r-- | test/cholesky.cpp | 64 | ||||
-rw-r--r-- | test/lu.cpp | 23 |
2 files changed, 73 insertions, 14 deletions
diff --git a/test/cholesky.cpp b/test/cholesky.cpp index d652af5bf..b7abc230b 100644 --- a/test/cholesky.cpp +++ b/test/cholesky.cpp @@ -17,6 +17,12 @@ #include <Eigen/Cholesky> #include <Eigen/QR> +template<typename MatrixType, int UpLo> +typename MatrixType::RealScalar matrix_l1_norm(const MatrixType& m) { + MatrixType symm = m.template selfadjointView<UpLo>(); + return symm.cwiseAbs().colwise().sum().maxCoeff(); +} + template<typename MatrixType,template <typename,int> class CholType> void test_chol_update(const MatrixType& symm) { typedef typename MatrixType::Scalar Scalar; @@ -77,7 +83,7 @@ template<typename MatrixType> void cholesky(const MatrixType& m) { SquareMatrixType symmUp = symm.template triangularView<Upper>(); SquareMatrixType symmLo = symm.template triangularView<Lower>(); - + LLT<SquareMatrixType,Lower> chollo(symmLo); VERIFY_IS_APPROX(symm, chollo.reconstructedMatrix()); vecX = chollo.solve(vecB); @@ -85,6 +91,14 @@ template<typename MatrixType> void cholesky(const MatrixType& m) matX = chollo.solve(matB); VERIFY_IS_APPROX(symm * matX, matB); + const MatrixType symmLo_inverse = chollo.solve(MatrixType::Identity(rows,cols)); + RealScalar rcond = (RealScalar(1) / matrix_l1_norm<MatrixType, Lower>(symmLo)) / + matrix_l1_norm<MatrixType, Lower>(symmLo_inverse); + RealScalar rcond_est = chollo.rcond(); + // Verify that the estimated condition number is within a factor of 10 of the + // truth. + VERIFY(rcond_est > rcond / 10 && rcond_est < rcond * 10); + // test the upper mode LLT<SquareMatrixType,Upper> cholup(symmUp); VERIFY_IS_APPROX(symm, cholup.reconstructedMatrix()); @@ -93,6 +107,15 @@ template<typename MatrixType> void cholesky(const MatrixType& m) matX = cholup.solve(matB); VERIFY_IS_APPROX(symm * matX, matB); + // Verify that the estimated condition number is within a factor of 10 of the + // truth. + const MatrixType symmUp_inverse = cholup.solve(MatrixType::Identity(rows,cols)); + rcond = (RealScalar(1) / matrix_l1_norm<MatrixType, Upper>(symmUp)) / + matrix_l1_norm<MatrixType, Upper>(symmUp_inverse); + rcond_est = cholup.rcond(); + VERIFY(rcond_est > rcond / 10 && rcond_est < rcond * 10); + + MatrixType neg = -symmLo; chollo.compute(neg); VERIFY(chollo.info()==NumericalIssue); @@ -101,7 +124,7 @@ template<typename MatrixType> void cholesky(const MatrixType& m) VERIFY_IS_APPROX(MatrixType(chollo.matrixU().transpose().conjugate()), MatrixType(chollo.matrixL())); VERIFY_IS_APPROX(MatrixType(cholup.matrixL().transpose().conjugate()), MatrixType(cholup.matrixU())); VERIFY_IS_APPROX(MatrixType(cholup.matrixU().transpose().conjugate()), MatrixType(cholup.matrixL())); - + // test some special use cases of SelfCwiseBinaryOp: MatrixType m1 = MatrixType::Random(rows,cols), m2(rows,cols); m2 = m1; @@ -137,6 +160,15 @@ template<typename MatrixType> void cholesky(const MatrixType& m) matX = ldltlo.solve(matB); VERIFY_IS_APPROX(symm * matX, matB); + const MatrixType symmLo_inverse = ldltlo.solve(MatrixType::Identity(rows,cols)); + RealScalar rcond = (RealScalar(1) / matrix_l1_norm<MatrixType, Lower>(symmLo)) / + matrix_l1_norm<MatrixType, Lower>(symmLo_inverse); + RealScalar rcond_est = ldltlo.rcond(); + // Verify that the estimated condition number is within a factor of 10 of the + // truth. + VERIFY(rcond_est > rcond / 10 && rcond_est < rcond * 10); + + LDLT<SquareMatrixType,Upper> ldltup(symmUp); VERIFY_IS_APPROX(symm, ldltup.reconstructedMatrix()); vecX = ldltup.solve(vecB); @@ -144,6 +176,14 @@ template<typename MatrixType> void cholesky(const MatrixType& m) matX = ldltup.solve(matB); VERIFY_IS_APPROX(symm * matX, matB); + // Verify that the estimated condition number is within a factor of 10 of the + // truth. + const MatrixType symmUp_inverse = ldltup.solve(MatrixType::Identity(rows,cols)); + rcond = (RealScalar(1) / matrix_l1_norm<MatrixType, Upper>(symmUp)) / + matrix_l1_norm<MatrixType, Upper>(symmUp_inverse); + rcond_est = ldltup.rcond(); + VERIFY(rcond_est > rcond / 10 && rcond_est < rcond * 10); + VERIFY_IS_APPROX(MatrixType(ldltlo.matrixL().transpose().conjugate()), MatrixType(ldltlo.matrixU())); VERIFY_IS_APPROX(MatrixType(ldltlo.matrixU().transpose().conjugate()), MatrixType(ldltlo.matrixL())); VERIFY_IS_APPROX(MatrixType(ldltup.matrixL().transpose().conjugate()), MatrixType(ldltup.matrixU())); @@ -167,7 +207,7 @@ template<typename MatrixType> void cholesky(const MatrixType& m) // restore if(sign == -1) symm = -symm; - + // check matrices coming from linear constraints with Lagrange multipliers if(rows>=3) { @@ -183,7 +223,7 @@ template<typename MatrixType> void cholesky(const MatrixType& m) vecX = ldltlo.solve(vecB); VERIFY_IS_APPROX(A * vecX, vecB); } - + // check non-full rank matrices if(rows>=3) { @@ -199,7 +239,7 @@ template<typename MatrixType> void cholesky(const MatrixType& m) vecX = ldltlo.solve(vecB); VERIFY_IS_APPROX(A * vecX, vecB); } - + // check matrices with a wide spectrum if(rows>=3) { @@ -225,7 +265,7 @@ template<typename MatrixType> void cholesky(const MatrixType& m) { RealScalar large_tol = std::sqrt(test_precision<RealScalar>()); VERIFY((A * vecX).isApprox(vecB, large_tol)); - + ++g_test_level; VERIFY_IS_APPROX(A * vecX,vecB); --g_test_level; @@ -314,14 +354,14 @@ template<typename MatrixType> void cholesky_bug241(const MatrixType& m) } // LDLT is not guaranteed to work for indefinite matrices, but happens to work fine if matrix is diagonal. -// This test checks that LDLT reports correctly that matrix is indefinite. +// This test checks that LDLT reports correctly that matrix is indefinite. // See http://forum.kde.org/viewtopic.php?f=74&t=106942 and bug 736 template<typename MatrixType> void cholesky_definiteness(const MatrixType& m) { eigen_assert(m.rows() == 2 && m.cols() == 2); MatrixType mat; LDLT<MatrixType> ldlt(2); - + { mat << 1, 0, 0, -1; ldlt.compute(mat); @@ -384,11 +424,11 @@ void test_cholesky() CALL_SUBTEST_3( cholesky_definiteness(Matrix2d()) ); CALL_SUBTEST_4( cholesky(Matrix3f()) ); CALL_SUBTEST_5( cholesky(Matrix4d()) ); - - s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE); + + s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE); CALL_SUBTEST_2( cholesky(MatrixXd(s,s)) ); TEST_SET_BUT_UNUSED_VARIABLE(s) - + s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/2); CALL_SUBTEST_6( cholesky_cplx(MatrixXcd(s,s)) ); TEST_SET_BUT_UNUSED_VARIABLE(s) @@ -402,6 +442,6 @@ void test_cholesky() // Test problem size constructors CALL_SUBTEST_9( LLT<MatrixXf>(10) ); CALL_SUBTEST_9( LDLT<MatrixXf>(10) ); - + TEST_SET_BUT_UNUSED_VARIABLE(nb_temporaries) } diff --git a/test/lu.cpp b/test/lu.cpp index f14435114..9787f4d86 100644 --- a/test/lu.cpp +++ b/test/lu.cpp @@ -11,6 +11,11 @@ #include <Eigen/LU> using namespace std; +template<typename MatrixType> +typename MatrixType::RealScalar matrix_l1_norm(const MatrixType& m) { + return m.cwiseAbs().colwise().sum().maxCoeff(); +} + template<typename MatrixType> void lu_non_invertible() { typedef typename MatrixType::Index Index; @@ -143,7 +148,14 @@ template<typename MatrixType> void lu_invertible() m3 = MatrixType::Random(size,size); m2 = lu.solve(m3); VERIFY_IS_APPROX(m3, m1*m2); - VERIFY_IS_APPROX(m2, lu.inverse()*m3); + MatrixType m1_inverse = lu.inverse(); + VERIFY_IS_APPROX(m2, m1_inverse*m3); + + RealScalar rcond = (RealScalar(1) / matrix_l1_norm(m1)) / matrix_l1_norm(m1_inverse); + const RealScalar rcond_est = lu.rcond(); + // Verify that the estimated condition number is within a factor of 10 of the + // truth. + VERIFY(rcond_est > rcond / 10 && rcond_est < rcond * 10); // test solve with transposed lu.template _solve_impl_transposed<false>(m3, m2); @@ -170,6 +182,7 @@ template<typename MatrixType> void lu_partial_piv() PartialPivLU.h */ typedef typename MatrixType::Index Index; + typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar; Index size = internal::random<Index>(1,4); MatrixType m1(size, size), m2(size, size), m3(size, size); @@ -181,7 +194,13 @@ template<typename MatrixType> void lu_partial_piv() m3 = MatrixType::Random(size,size); m2 = plu.solve(m3); VERIFY_IS_APPROX(m3, m1*m2); - VERIFY_IS_APPROX(m2, plu.inverse()*m3); + MatrixType m1_inverse = plu.inverse(); + VERIFY_IS_APPROX(m2, m1_inverse*m3); + + RealScalar rcond = (RealScalar(1) / matrix_l1_norm(m1)) / matrix_l1_norm(m1_inverse); + const RealScalar rcond_est = plu.rcond(); + // Verify that the estimate is within a factor of 10 of the truth. + VERIFY(rcond_est > rcond / 10 && rcond_est < rcond * 10); // test solve with transposed plu.template _solve_impl_transposed<false>(m3, m2); |