ground/gcs/src/libs/eigen/test/eigensolver_selfadjoint.cpp

   1 // This file is part of Eigen, a lightweight C++ template library
   2 // for linear algebra.
   3 //
   4 // Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
   5 // Copyright (C) 2010 Jitse Niesen <jitse@maths.leeds.ac.uk>
   6 //
   7 // This Source Code Form is subject to the terms of the Mozilla
   8 // Public License v. 2.0. If a copy of the MPL was not distributed
   9 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
  10
  11 #include "main.h"
  12 #include <limits>
  13 #include <Eigen/Eigenvalues>
  14
  15 template<typename MatrixType> void selfadjointeigensolver(const MatrixType& m)
  16 {
  17   typedef typename MatrixType::Index Index;
  18   /* this test covers the following files:
  19      EigenSolver.h, SelfAdjointEigenSolver.h (and indirectly: Tridiagonalization.h)
  20   */
  21   Index rows = m.rows();
  22   Index cols = m.cols();
  23
  24   typedef typename MatrixType::Scalar Scalar;
  25   typedef typename NumTraits<Scalar>::Real RealScalar;
  26
  27   RealScalar largerEps = 10*test_precision<RealScalar>();
  28
  29   MatrixType a = MatrixType::Random(rows,cols);
  30   MatrixType a1 = MatrixType::Random(rows,cols);
  31   MatrixType symmA =  a.adjoint() * a + a1.adjoint() * a1;
  32   MatrixType symmC = symmA;
  33
  34   // randomly nullify some rows/columns
  35   {
  36     Index count = 1;//internal::random<Index>(-cols,cols);
  37     for(Index k=0; k<count; ++k)
  38     {
  39       Index i = internal::random<Index>(0,cols-1);
  40       symmA.row(i).setZero();
  41       symmA.col(i).setZero();
  42     }
  43   }
  44
  45   symmA.template triangularView<StrictlyUpper>().setZero();
  46   symmC.template triangularView<StrictlyUpper>().setZero();
  47
  48   MatrixType b = MatrixType::Random(rows,cols);
  49   MatrixType b1 = MatrixType::Random(rows,cols);
  50   MatrixType symmB = b.adjoint() * b + b1.adjoint() * b1;
  51   symmB.template triangularView<StrictlyUpper>().setZero();
  52
  53   SelfAdjointEigenSolver<MatrixType> eiSymm(symmA);
  54   SelfAdjointEigenSolver<MatrixType> eiDirect;
  55   eiDirect.computeDirect(symmA);
  56   // generalized eigen pb
  57   GeneralizedSelfAdjointEigenSolver<MatrixType> eiSymmGen(symmC, symmB);
  58
  59   VERIFY_IS_EQUAL(eiSymm.info(), Success);
  60   VERIFY((symmA.template selfadjointView<Lower>() * eiSymm.eigenvectors()).isApprox(
  61           eiSymm.eigenvectors() * eiSymm.eigenvalues().asDiagonal(), largerEps));
  62   VERIFY_IS_APPROX(symmA.template selfadjointView<Lower>().eigenvalues(), eiSymm.eigenvalues());
  63
  64   VERIFY_IS_EQUAL(eiDirect.info(), Success);
  65   VERIFY((symmA.template selfadjointView<Lower>() * eiDirect.eigenvectors()).isApprox(
  66           eiDirect.eigenvectors() * eiDirect.eigenvalues().asDiagonal(), largerEps));
  67   VERIFY_IS_APPROX(symmA.template selfadjointView<Lower>().eigenvalues(), eiDirect.eigenvalues());
  68
  69   SelfAdjointEigenSolver<MatrixType> eiSymmNoEivecs(symmA, false);
  70   VERIFY_IS_EQUAL(eiSymmNoEivecs.info(), Success);
  71   VERIFY_IS_APPROX(eiSymm.eigenvalues(), eiSymmNoEivecs.eigenvalues());
  72
  73   // generalized eigen problem Ax = lBx
  74   eiSymmGen.compute(symmC, symmB,Ax_lBx);
  75   VERIFY_IS_EQUAL(eiSymmGen.info(), Success);
  76   VERIFY((symmC.template selfadjointView<Lower>() * eiSymmGen.eigenvectors()).isApprox(
  77           symmB.template selfadjointView<Lower>() * (eiSymmGen.eigenvectors() * eiSymmGen.eigenvalues().asDiagonal()), largerEps));
  78
  79   // generalized eigen problem BAx = lx
  80   eiSymmGen.compute(symmC, symmB,BAx_lx);
  81   VERIFY_IS_EQUAL(eiSymmGen.info(), Success);
  82   VERIFY((symmB.template selfadjointView<Lower>() * (symmC.template selfadjointView<Lower>() * eiSymmGen.eigenvectors())).isApprox(
  83          (eiSymmGen.eigenvectors() * eiSymmGen.eigenvalues().asDiagonal()), largerEps));
  84
  85   // generalized eigen problem ABx = lx
  86   eiSymmGen.compute(symmC, symmB,ABx_lx);
  87   VERIFY_IS_EQUAL(eiSymmGen.info(), Success);
  88   VERIFY((symmC.template selfadjointView<Lower>() * (symmB.template selfadjointView<Lower>() * eiSymmGen.eigenvectors())).isApprox(
  89          (eiSymmGen.eigenvectors() * eiSymmGen.eigenvalues().asDiagonal()), largerEps));
  90
  91
  92   eiSymm.compute(symmC);
  93   MatrixType sqrtSymmA = eiSymm.operatorSqrt();
  94   VERIFY_IS_APPROX(MatrixType(symmC.template selfadjointView<Lower>()), sqrtSymmA*sqrtSymmA);
  95   VERIFY_IS_APPROX(sqrtSymmA, symmC.template selfadjointView<Lower>()*eiSymm.operatorInverseSqrt());
  96
  97   MatrixType id = MatrixType::Identity(rows, cols);
  98   VERIFY_IS_APPROX(id.template selfadjointView<Lower>().operatorNorm(), RealScalar(1));
  99
 100   SelfAdjointEigenSolver<MatrixType> eiSymmUninitialized;
 101   VERIFY_RAISES_ASSERT(eiSymmUninitialized.info());
 102   VERIFY_RAISES_ASSERT(eiSymmUninitialized.eigenvalues());
 103   VERIFY_RAISES_ASSERT(eiSymmUninitialized.eigenvectors());
 104   VERIFY_RAISES_ASSERT(eiSymmUninitialized.operatorSqrt());
 105   VERIFY_RAISES_ASSERT(eiSymmUninitialized.operatorInverseSqrt());
 106
 107   eiSymmUninitialized.compute(symmA, false);
 108   VERIFY_RAISES_ASSERT(eiSymmUninitialized.eigenvectors());
 109   VERIFY_RAISES_ASSERT(eiSymmUninitialized.operatorSqrt());
 110   VERIFY_RAISES_ASSERT(eiSymmUninitialized.operatorInverseSqrt());
 111
 112   // test Tridiagonalization's methods
 113   Tridiagonalization<MatrixType> tridiag(symmC);
 114   // FIXME tridiag.matrixQ().adjoint() does not work
 115   VERIFY_IS_APPROX(MatrixType(symmC.template selfadjointView<Lower>()), tridiag.matrixQ() * tridiag.matrixT().eval() * MatrixType(tridiag.matrixQ()).adjoint());
 116
 117   if (rows > 1)
 118   {
 119     // Test matrix with NaN
 120     symmC(0,0) = std::numeric_limits<typename MatrixType::RealScalar>::quiet_NaN();
 121     SelfAdjointEigenSolver<MatrixType> eiSymmNaN(symmC);
 122     VERIFY_IS_EQUAL(eiSymmNaN.info(), NoConvergence);
 123   }
 124 }
 125
 126 void test_eigensolver_selfadjoint()
 127 {
 128   int s = 0;
 129   for(int i = 0; i < g_repeat; i++) {
 130     // very important to test 3x3 and 2x2 matrices since we provide special paths for them
 131     CALL_SUBTEST_1( selfadjointeigensolver(Matrix2f()) );
 132     CALL_SUBTEST_1( selfadjointeigensolver(Matrix2d()) );
 133     CALL_SUBTEST_1( selfadjointeigensolver(Matrix3f()) );
 134     CALL_SUBTEST_1( selfadjointeigensolver(Matrix3d()) );
 135     CALL_SUBTEST_2( selfadjointeigensolver(Matrix4d()) );
 136     s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4);
 137     CALL_SUBTEST_3( selfadjointeigensolver(MatrixXf(s,s)) );
 138     s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4);
 139     CALL_SUBTEST_4( selfadjointeigensolver(MatrixXd(s,s)) );
 140     s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4);
 141     CALL_SUBTEST_5( selfadjointeigensolver(MatrixXcd(s,s)) );
 142
 143     s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4);
 144     CALL_SUBTEST_9( selfadjointeigensolver(Matrix<std::complex<double>,Dynamic,Dynamic,RowMajor>(s,s)) );
 145
 146     // some trivial but implementation-wise tricky cases
 147     CALL_SUBTEST_4( selfadjointeigensolver(MatrixXd(1,1)) );
 148     CALL_SUBTEST_4( selfadjointeigensolver(MatrixXd(2,2)) );
 149     CALL_SUBTEST_6( selfadjointeigensolver(Matrix<double,1,1>()) );
 150     CALL_SUBTEST_7( selfadjointeigensolver(Matrix<double,2,2>()) );
 151   }
 152
 153   // Test problem size constructors
 154   s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4);
 155   CALL_SUBTEST_8(SelfAdjointEigenSolver<MatrixXf> tmp1(s));
 156   CALL_SUBTEST_8(Tridiagonalization<MatrixXf> tmp2(s));
 157
 158   TEST_SET_BUT_UNUSED_VARIABLE(s)
 159 }
 160