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 27c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath RealScalar largerEps = 10*test_precision<RealScalar>(); 28c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 29c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath MatrixType a = MatrixType::Random(rows,cols); 30c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath MatrixType a1 = MatrixType::Random(rows,cols); 31c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath MatrixType symmA = a.adjoint() * a + a1.adjoint() * a1; 32615d816d068b4d0f5e8df601930b5f160bf7eda1Tim Murray MatrixType symmC = symmA; 33615d816d068b4d0f5e8df601930b5f160bf7eda1Tim Murray 34615d816d068b4d0f5e8df601930b5f160bf7eda1Tim Murray // randomly nullify some rows/columns 35615d816d068b4d0f5e8df601930b5f160bf7eda1Tim Murray { 36615d816d068b4d0f5e8df601930b5f160bf7eda1Tim Murray Index count = 1;//internal::random<Index>(-cols,cols); 37615d816d068b4d0f5e8df601930b5f160bf7eda1Tim Murray for(Index k=0; k<count; ++k) 38615d816d068b4d0f5e8df601930b5f160bf7eda1Tim Murray { 39615d816d068b4d0f5e8df601930b5f160bf7eda1Tim Murray Index i = internal::random<Index>(0,cols-1); 40615d816d068b4d0f5e8df601930b5f160bf7eda1Tim Murray symmA.row(i).setZero(); 41615d816d068b4d0f5e8df601930b5f160bf7eda1Tim Murray symmA.col(i).setZero(); 42615d816d068b4d0f5e8df601930b5f160bf7eda1Tim Murray } 43615d816d068b4d0f5e8df601930b5f160bf7eda1Tim Murray } 44615d816d068b4d0f5e8df601930b5f160bf7eda1Tim Murray 45c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath symmA.template triangularView<StrictlyUpper>().setZero(); 46615d816d068b4d0f5e8df601930b5f160bf7eda1Tim Murray symmC.template triangularView<StrictlyUpper>().setZero(); 47c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 48c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath MatrixType b = MatrixType::Random(rows,cols); 49c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath MatrixType b1 = MatrixType::Random(rows,cols); 50c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath MatrixType symmB = b.adjoint() * b + b1.adjoint() * b1; 51c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath symmB.template triangularView<StrictlyUpper>().setZero(); 52c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 53c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath SelfAdjointEigenSolver<MatrixType> eiSymm(symmA); 54c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath SelfAdjointEigenSolver<MatrixType> eiDirect; 55c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath eiDirect.computeDirect(symmA); 56c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // generalized eigen pb 57615d816d068b4d0f5e8df601930b5f160bf7eda1Tim Murray GeneralizedSelfAdjointEigenSolver<MatrixType> eiSymmGen(symmC, symmB); 58c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 59c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_EQUAL(eiSymm.info(), Success); 60c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY((symmA.template selfadjointView<Lower>() * eiSymm.eigenvectors()).isApprox( 61c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath eiSymm.eigenvectors() * eiSymm.eigenvalues().asDiagonal(), largerEps)); 62c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(symmA.template selfadjointView<Lower>().eigenvalues(), eiSymm.eigenvalues()); 63c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 64c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_EQUAL(eiDirect.info(), Success); 65c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY((symmA.template selfadjointView<Lower>() * eiDirect.eigenvectors()).isApprox( 66c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath eiDirect.eigenvectors() * eiDirect.eigenvalues().asDiagonal(), largerEps)); 67c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(symmA.template selfadjointView<Lower>().eigenvalues(), eiDirect.eigenvalues()); 68c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 69c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath SelfAdjointEigenSolver<MatrixType> eiSymmNoEivecs(symmA, false); 70c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_EQUAL(eiSymmNoEivecs.info(), Success); 71c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(eiSymm.eigenvalues(), eiSymmNoEivecs.eigenvalues()); 72c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 73c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // generalized eigen problem Ax = lBx 74615d816d068b4d0f5e8df601930b5f160bf7eda1Tim Murray eiSymmGen.compute(symmC, symmB,Ax_lBx); 75c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_EQUAL(eiSymmGen.info(), Success); 76615d816d068b4d0f5e8df601930b5f160bf7eda1Tim Murray VERIFY((symmC.template selfadjointView<Lower>() * eiSymmGen.eigenvectors()).isApprox( 77c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath symmB.template selfadjointView<Lower>() * (eiSymmGen.eigenvectors() * eiSymmGen.eigenvalues().asDiagonal()), largerEps)); 78c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 79c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // generalized eigen problem BAx = lx 80615d816d068b4d0f5e8df601930b5f160bf7eda1Tim Murray eiSymmGen.compute(symmC, symmB,BAx_lx); 81c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_EQUAL(eiSymmGen.info(), Success); 82615d816d068b4d0f5e8df601930b5f160bf7eda1Tim Murray VERIFY((symmB.template selfadjointView<Lower>() * (symmC.template selfadjointView<Lower>() * eiSymmGen.eigenvectors())).isApprox( 83c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath (eiSymmGen.eigenvectors() * eiSymmGen.eigenvalues().asDiagonal()), largerEps)); 84c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 85c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // generalized eigen problem ABx = lx 86615d816d068b4d0f5e8df601930b5f160bf7eda1Tim Murray eiSymmGen.compute(symmC, symmB,ABx_lx); 87c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_EQUAL(eiSymmGen.info(), Success); 88615d816d068b4d0f5e8df601930b5f160bf7eda1Tim Murray VERIFY((symmC.template selfadjointView<Lower>() * (symmB.template selfadjointView<Lower>() * eiSymmGen.eigenvectors())).isApprox( 89c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath (eiSymmGen.eigenvectors() * eiSymmGen.eigenvalues().asDiagonal()), largerEps)); 90c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 91c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 92615d816d068b4d0f5e8df601930b5f160bf7eda1Tim Murray eiSymm.compute(symmC); 93c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath MatrixType sqrtSymmA = eiSymm.operatorSqrt(); 94615d816d068b4d0f5e8df601930b5f160bf7eda1Tim Murray VERIFY_IS_APPROX(MatrixType(symmC.template selfadjointView<Lower>()), sqrtSymmA*sqrtSymmA); 95615d816d068b4d0f5e8df601930b5f160bf7eda1Tim Murray VERIFY_IS_APPROX(sqrtSymmA, symmC.template selfadjointView<Lower>()*eiSymm.operatorInverseSqrt()); 96c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 97c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath MatrixType id = MatrixType::Identity(rows, cols); 98c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(id.template selfadjointView<Lower>().operatorNorm(), RealScalar(1)); 99c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 100c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath SelfAdjointEigenSolver<MatrixType> eiSymmUninitialized; 101c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_RAISES_ASSERT(eiSymmUninitialized.info()); 102c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_RAISES_ASSERT(eiSymmUninitialized.eigenvalues()); 103c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_RAISES_ASSERT(eiSymmUninitialized.eigenvectors()); 104c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_RAISES_ASSERT(eiSymmUninitialized.operatorSqrt()); 105c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_RAISES_ASSERT(eiSymmUninitialized.operatorInverseSqrt()); 106c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 107c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath eiSymmUninitialized.compute(symmA, false); 108c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_RAISES_ASSERT(eiSymmUninitialized.eigenvectors()); 109c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_RAISES_ASSERT(eiSymmUninitialized.operatorSqrt()); 110c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_RAISES_ASSERT(eiSymmUninitialized.operatorInverseSqrt()); 111c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 112c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // test Tridiagonalization's methods 113615d816d068b4d0f5e8df601930b5f160bf7eda1Tim Murray Tridiagonalization<MatrixType> tridiag(symmC); 114c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // FIXME tridiag.matrixQ().adjoint() does not work 115615d816d068b4d0f5e8df601930b5f160bf7eda1Tim Murray VERIFY_IS_APPROX(MatrixType(symmC.template selfadjointView<Lower>()), tridiag.matrixQ() * tridiag.matrixT().eval() * MatrixType(tridiag.matrixQ()).adjoint()); 116c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 117c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath if (rows > 1) 118c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath { 119c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // Test matrix with NaN 120615d816d068b4d0f5e8df601930b5f160bf7eda1Tim Murray symmC(0,0) = std::numeric_limits<typename MatrixType::RealScalar>::quiet_NaN(); 121615d816d068b4d0f5e8df601930b5f160bf7eda1Tim Murray SelfAdjointEigenSolver<MatrixType> eiSymmNaN(symmC); 122c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_EQUAL(eiSymmNaN.info(), NoConvergence); 123c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 124c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath} 125c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 126c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathvoid test_eigensolver_selfadjoint() 127c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath{ 1287faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez int s = 0; 129c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath for(int i = 0; i < g_repeat; i++) { 130c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // very important to test 3x3 and 2x2 matrices since we provide special paths for them 131615d816d068b4d0f5e8df601930b5f160bf7eda1Tim Murray CALL_SUBTEST_1( selfadjointeigensolver(Matrix2f()) ); 132c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath CALL_SUBTEST_1( selfadjointeigensolver(Matrix2d()) ); 133c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath CALL_SUBTEST_1( selfadjointeigensolver(Matrix3f()) ); 134615d816d068b4d0f5e8df601930b5f160bf7eda1Tim Murray CALL_SUBTEST_1( selfadjointeigensolver(Matrix3d()) ); 135c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath CALL_SUBTEST_2( selfadjointeigensolver(Matrix4d()) ); 136c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4); 137c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath CALL_SUBTEST_3( selfadjointeigensolver(MatrixXf(s,s)) ); 138c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4); 139c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath CALL_SUBTEST_4( selfadjointeigensolver(MatrixXd(s,s)) ); 140c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4); 141c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath CALL_SUBTEST_5( selfadjointeigensolver(MatrixXcd(s,s)) ); 142c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 143c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4); 144c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath CALL_SUBTEST_9( selfadjointeigensolver(Matrix<std::complex<double>,Dynamic,Dynamic,RowMajor>(s,s)) ); 145c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 146c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // some trivial but implementation-wise tricky cases 147c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath CALL_SUBTEST_4( selfadjointeigensolver(MatrixXd(1,1)) ); 148c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath CALL_SUBTEST_4( selfadjointeigensolver(MatrixXd(2,2)) ); 149c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath CALL_SUBTEST_6( selfadjointeigensolver(Matrix<double,1,1>()) ); 150c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath CALL_SUBTEST_7( selfadjointeigensolver(Matrix<double,2,2>()) ); 151c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 152c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 153c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // Test problem size constructors 154c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4); 1557faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez CALL_SUBTEST_8(SelfAdjointEigenSolver<MatrixXf> tmp1(s)); 1567faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez CALL_SUBTEST_8(Tridiagonalization<MatrixXf> tmp2(s)); 157c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 1587faaa9f3f0df9d23790277834d426c3d992ac3baCarlos Hernandez TEST_SET_BUT_UNUSED_VARIABLE(s) 159c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath} 160c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 161