1c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// This file is part of Eigen, a lightweight C++ template library 2c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// for linear algebra. 3c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// 4c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr> 5c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// Copyright (C) 2010 Jitse Niesen <jitse@maths.leeds.ac.uk> 6c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// 7c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// This Source Code Form is subject to the terms of the Mozilla 8c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// Public License v. 2.0. If a copy of the MPL was not distributed 9c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. 10c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 11c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath#include "main.h" 12c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath#include <limits> 13c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath#include <Eigen/Eigenvalues> 14c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 15c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathtemplate<typename MatrixType> void selfadjointeigensolver(const MatrixType& m) 16c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath{ 17c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef typename MatrixType::Index Index; 18c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath /* this test covers the following files: 19c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath EigenSolver.h, SelfAdjointEigenSolver.h (and indirectly: Tridiagonalization.h) 20c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath */ 21c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Index rows = m.rows(); 22c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Index cols = m.cols(); 23c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 24c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef typename MatrixType::Scalar Scalar; 25c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef typename NumTraits<Scalar>::Real RealScalar; 26c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType; 27c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef Matrix<RealScalar, MatrixType::RowsAtCompileTime, 1> RealVectorType; 28c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef typename std::complex<typename NumTraits<typename MatrixType::Scalar>::Real> Complex; 29c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 30c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath RealScalar largerEps = 10*test_precision<RealScalar>(); 31c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 32c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath MatrixType a = MatrixType::Random(rows,cols); 33c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath MatrixType a1 = MatrixType::Random(rows,cols); 34c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath MatrixType symmA = a.adjoint() * a + a1.adjoint() * a1; 35c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath symmA.template triangularView<StrictlyUpper>().setZero(); 36c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 37c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath MatrixType b = MatrixType::Random(rows,cols); 38c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath MatrixType b1 = MatrixType::Random(rows,cols); 39c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath MatrixType symmB = b.adjoint() * b + b1.adjoint() * b1; 40c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath symmB.template triangularView<StrictlyUpper>().setZero(); 41c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 42c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath SelfAdjointEigenSolver<MatrixType> eiSymm(symmA); 43c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath SelfAdjointEigenSolver<MatrixType> eiDirect; 44c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath eiDirect.computeDirect(symmA); 45c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // generalized eigen pb 46c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath GeneralizedSelfAdjointEigenSolver<MatrixType> eiSymmGen(symmA, symmB); 47c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 48c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_EQUAL(eiSymm.info(), Success); 49c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY((symmA.template selfadjointView<Lower>() * eiSymm.eigenvectors()).isApprox( 50c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath eiSymm.eigenvectors() * eiSymm.eigenvalues().asDiagonal(), largerEps)); 51c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(symmA.template selfadjointView<Lower>().eigenvalues(), eiSymm.eigenvalues()); 52c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 53c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_EQUAL(eiDirect.info(), Success); 54c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY((symmA.template selfadjointView<Lower>() * eiDirect.eigenvectors()).isApprox( 55c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath eiDirect.eigenvectors() * eiDirect.eigenvalues().asDiagonal(), largerEps)); 56c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(symmA.template selfadjointView<Lower>().eigenvalues(), eiDirect.eigenvalues()); 57c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 58c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath SelfAdjointEigenSolver<MatrixType> eiSymmNoEivecs(symmA, false); 59c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_EQUAL(eiSymmNoEivecs.info(), Success); 60c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(eiSymm.eigenvalues(), eiSymmNoEivecs.eigenvalues()); 61c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 62c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // generalized eigen problem Ax = lBx 63c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath eiSymmGen.compute(symmA, symmB,Ax_lBx); 64c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_EQUAL(eiSymmGen.info(), Success); 65c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY((symmA.template selfadjointView<Lower>() * eiSymmGen.eigenvectors()).isApprox( 66c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath symmB.template selfadjointView<Lower>() * (eiSymmGen.eigenvectors() * eiSymmGen.eigenvalues().asDiagonal()), largerEps)); 67c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 68c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // generalized eigen problem BAx = lx 69c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath eiSymmGen.compute(symmA, symmB,BAx_lx); 70c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_EQUAL(eiSymmGen.info(), Success); 71c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY((symmB.template selfadjointView<Lower>() * (symmA.template selfadjointView<Lower>() * eiSymmGen.eigenvectors())).isApprox( 72c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath (eiSymmGen.eigenvectors() * eiSymmGen.eigenvalues().asDiagonal()), largerEps)); 73c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 74c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // generalized eigen problem ABx = lx 75c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath eiSymmGen.compute(symmA, symmB,ABx_lx); 76c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_EQUAL(eiSymmGen.info(), Success); 77c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY((symmA.template selfadjointView<Lower>() * (symmB.template selfadjointView<Lower>() * eiSymmGen.eigenvectors())).isApprox( 78c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath (eiSymmGen.eigenvectors() * eiSymmGen.eigenvalues().asDiagonal()), largerEps)); 79c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 80c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 81c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath MatrixType sqrtSymmA = eiSymm.operatorSqrt(); 82c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(MatrixType(symmA.template selfadjointView<Lower>()), sqrtSymmA*sqrtSymmA); 83c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(sqrtSymmA, symmA.template selfadjointView<Lower>()*eiSymm.operatorInverseSqrt()); 84c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 85c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath MatrixType id = MatrixType::Identity(rows, cols); 86c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(id.template selfadjointView<Lower>().operatorNorm(), RealScalar(1)); 87c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 88c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath SelfAdjointEigenSolver<MatrixType> eiSymmUninitialized; 89c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_RAISES_ASSERT(eiSymmUninitialized.info()); 90c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_RAISES_ASSERT(eiSymmUninitialized.eigenvalues()); 91c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_RAISES_ASSERT(eiSymmUninitialized.eigenvectors()); 92c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_RAISES_ASSERT(eiSymmUninitialized.operatorSqrt()); 93c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_RAISES_ASSERT(eiSymmUninitialized.operatorInverseSqrt()); 94c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 95c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath eiSymmUninitialized.compute(symmA, false); 96c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_RAISES_ASSERT(eiSymmUninitialized.eigenvectors()); 97c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_RAISES_ASSERT(eiSymmUninitialized.operatorSqrt()); 98c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_RAISES_ASSERT(eiSymmUninitialized.operatorInverseSqrt()); 99c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 100c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // test Tridiagonalization's methods 101c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Tridiagonalization<MatrixType> tridiag(symmA); 102c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // FIXME tridiag.matrixQ().adjoint() does not work 103c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(MatrixType(symmA.template selfadjointView<Lower>()), tridiag.matrixQ() * tridiag.matrixT().eval() * MatrixType(tridiag.matrixQ()).adjoint()); 104c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 105c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath if (rows > 1) 106c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath { 107c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // Test matrix with NaN 108c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath symmA(0,0) = std::numeric_limits<typename MatrixType::RealScalar>::quiet_NaN(); 109c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath SelfAdjointEigenSolver<MatrixType> eiSymmNaN(symmA); 110c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_EQUAL(eiSymmNaN.info(), NoConvergence); 111c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 112c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath} 113c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 114c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathvoid test_eigensolver_selfadjoint() 115c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath{ 116c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath int s; 117c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath for(int i = 0; i < g_repeat; i++) { 118c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // very important to test 3x3 and 2x2 matrices since we provide special paths for them 119c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath CALL_SUBTEST_1( selfadjointeigensolver(Matrix2d()) ); 120c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath CALL_SUBTEST_1( selfadjointeigensolver(Matrix3f()) ); 121c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath CALL_SUBTEST_2( selfadjointeigensolver(Matrix4d()) ); 122c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4); 123c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath CALL_SUBTEST_3( selfadjointeigensolver(MatrixXf(s,s)) ); 124c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4); 125c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath CALL_SUBTEST_4( selfadjointeigensolver(MatrixXd(s,s)) ); 126c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4); 127c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath CALL_SUBTEST_5( selfadjointeigensolver(MatrixXcd(s,s)) ); 128c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 129c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4); 130c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath CALL_SUBTEST_9( selfadjointeigensolver(Matrix<std::complex<double>,Dynamic,Dynamic,RowMajor>(s,s)) ); 131c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 132c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // some trivial but implementation-wise tricky cases 133c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath CALL_SUBTEST_4( selfadjointeigensolver(MatrixXd(1,1)) ); 134c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath CALL_SUBTEST_4( selfadjointeigensolver(MatrixXd(2,2)) ); 135c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath CALL_SUBTEST_6( selfadjointeigensolver(Matrix<double,1,1>()) ); 136c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath CALL_SUBTEST_7( selfadjointeigensolver(Matrix<double,2,2>()) ); 137c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 138c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 139c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // Test problem size constructors 140c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4); 141c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath CALL_SUBTEST_8(SelfAdjointEigenSolver<MatrixXf>(s)); 142c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath CALL_SUBTEST_8(Tridiagonalization<MatrixXf>(s)); 143c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 144c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath EIGEN_UNUSED_VARIABLE(s) 145c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath} 146c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 147