Squashed 'third_party/eigen/' content from commit 61d72f6
Change-Id: Iccc90fa0b55ab44037f018046d2fcffd90d9d025
git-subtree-dir: third_party/eigen
git-subtree-split: 61d72f6383cfa842868c53e30e087b0258177257
diff --git a/test/eigensolver_selfadjoint.cpp b/test/eigensolver_selfadjoint.cpp
new file mode 100644
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--- /dev/null
+++ b/test/eigensolver_selfadjoint.cpp
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+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2010 Jitse Niesen <jitse@maths.leeds.ac.uk>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+#include <limits>
+#include <Eigen/Eigenvalues>
+
+template<typename MatrixType> void selfadjointeigensolver(const MatrixType& m)
+{
+ typedef typename MatrixType::Index Index;
+ /* this test covers the following files:
+ EigenSolver.h, SelfAdjointEigenSolver.h (and indirectly: Tridiagonalization.h)
+ */
+ Index rows = m.rows();
+ Index cols = m.cols();
+
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+
+ RealScalar largerEps = 10*test_precision<RealScalar>();
+
+ MatrixType a = MatrixType::Random(rows,cols);
+ MatrixType a1 = MatrixType::Random(rows,cols);
+ MatrixType symmA = a.adjoint() * a + a1.adjoint() * a1;
+ MatrixType symmC = symmA;
+
+ // randomly nullify some rows/columns
+ {
+ Index count = 1;//internal::random<Index>(-cols,cols);
+ for(Index k=0; k<count; ++k)
+ {
+ Index i = internal::random<Index>(0,cols-1);
+ symmA.row(i).setZero();
+ symmA.col(i).setZero();
+ }
+ }
+
+ symmA.template triangularView<StrictlyUpper>().setZero();
+ symmC.template triangularView<StrictlyUpper>().setZero();
+
+ MatrixType b = MatrixType::Random(rows,cols);
+ MatrixType b1 = MatrixType::Random(rows,cols);
+ MatrixType symmB = b.adjoint() * b + b1.adjoint() * b1;
+ symmB.template triangularView<StrictlyUpper>().setZero();
+
+ SelfAdjointEigenSolver<MatrixType> eiSymm(symmA);
+ SelfAdjointEigenSolver<MatrixType> eiDirect;
+ eiDirect.computeDirect(symmA);
+ // generalized eigen pb
+ GeneralizedSelfAdjointEigenSolver<MatrixType> eiSymmGen(symmC, symmB);
+
+ VERIFY_IS_EQUAL(eiSymm.info(), Success);
+ VERIFY((symmA.template selfadjointView<Lower>() * eiSymm.eigenvectors()).isApprox(
+ eiSymm.eigenvectors() * eiSymm.eigenvalues().asDiagonal(), largerEps));
+ VERIFY_IS_APPROX(symmA.template selfadjointView<Lower>().eigenvalues(), eiSymm.eigenvalues());
+
+ VERIFY_IS_EQUAL(eiDirect.info(), Success);
+ VERIFY((symmA.template selfadjointView<Lower>() * eiDirect.eigenvectors()).isApprox(
+ eiDirect.eigenvectors() * eiDirect.eigenvalues().asDiagonal(), largerEps));
+ VERIFY_IS_APPROX(symmA.template selfadjointView<Lower>().eigenvalues(), eiDirect.eigenvalues());
+
+ SelfAdjointEigenSolver<MatrixType> eiSymmNoEivecs(symmA, false);
+ VERIFY_IS_EQUAL(eiSymmNoEivecs.info(), Success);
+ VERIFY_IS_APPROX(eiSymm.eigenvalues(), eiSymmNoEivecs.eigenvalues());
+
+ // generalized eigen problem Ax = lBx
+ eiSymmGen.compute(symmC, symmB,Ax_lBx);
+ VERIFY_IS_EQUAL(eiSymmGen.info(), Success);
+ VERIFY((symmC.template selfadjointView<Lower>() * eiSymmGen.eigenvectors()).isApprox(
+ symmB.template selfadjointView<Lower>() * (eiSymmGen.eigenvectors() * eiSymmGen.eigenvalues().asDiagonal()), largerEps));
+
+ // generalized eigen problem BAx = lx
+ eiSymmGen.compute(symmC, symmB,BAx_lx);
+ VERIFY_IS_EQUAL(eiSymmGen.info(), Success);
+ VERIFY((symmB.template selfadjointView<Lower>() * (symmC.template selfadjointView<Lower>() * eiSymmGen.eigenvectors())).isApprox(
+ (eiSymmGen.eigenvectors() * eiSymmGen.eigenvalues().asDiagonal()), largerEps));
+
+ // generalized eigen problem ABx = lx
+ eiSymmGen.compute(symmC, symmB,ABx_lx);
+ VERIFY_IS_EQUAL(eiSymmGen.info(), Success);
+ VERIFY((symmC.template selfadjointView<Lower>() * (symmB.template selfadjointView<Lower>() * eiSymmGen.eigenvectors())).isApprox(
+ (eiSymmGen.eigenvectors() * eiSymmGen.eigenvalues().asDiagonal()), largerEps));
+
+
+ eiSymm.compute(symmC);
+ MatrixType sqrtSymmA = eiSymm.operatorSqrt();
+ VERIFY_IS_APPROX(MatrixType(symmC.template selfadjointView<Lower>()), sqrtSymmA*sqrtSymmA);
+ VERIFY_IS_APPROX(sqrtSymmA, symmC.template selfadjointView<Lower>()*eiSymm.operatorInverseSqrt());
+
+ MatrixType id = MatrixType::Identity(rows, cols);
+ VERIFY_IS_APPROX(id.template selfadjointView<Lower>().operatorNorm(), RealScalar(1));
+
+ SelfAdjointEigenSolver<MatrixType> eiSymmUninitialized;
+ VERIFY_RAISES_ASSERT(eiSymmUninitialized.info());
+ VERIFY_RAISES_ASSERT(eiSymmUninitialized.eigenvalues());
+ VERIFY_RAISES_ASSERT(eiSymmUninitialized.eigenvectors());
+ VERIFY_RAISES_ASSERT(eiSymmUninitialized.operatorSqrt());
+ VERIFY_RAISES_ASSERT(eiSymmUninitialized.operatorInverseSqrt());
+
+ eiSymmUninitialized.compute(symmA, false);
+ VERIFY_RAISES_ASSERT(eiSymmUninitialized.eigenvectors());
+ VERIFY_RAISES_ASSERT(eiSymmUninitialized.operatorSqrt());
+ VERIFY_RAISES_ASSERT(eiSymmUninitialized.operatorInverseSqrt());
+
+ // test Tridiagonalization's methods
+ Tridiagonalization<MatrixType> tridiag(symmC);
+ // FIXME tridiag.matrixQ().adjoint() does not work
+ VERIFY_IS_APPROX(MatrixType(symmC.template selfadjointView<Lower>()), tridiag.matrixQ() * tridiag.matrixT().eval() * MatrixType(tridiag.matrixQ()).adjoint());
+
+ if (rows > 1)
+ {
+ // Test matrix with NaN
+ symmC(0,0) = std::numeric_limits<typename MatrixType::RealScalar>::quiet_NaN();
+ SelfAdjointEigenSolver<MatrixType> eiSymmNaN(symmC);
+ VERIFY_IS_EQUAL(eiSymmNaN.info(), NoConvergence);
+ }
+}
+
+void test_eigensolver_selfadjoint()
+{
+ int s = 0;
+ for(int i = 0; i < g_repeat; i++) {
+ // very important to test 3x3 and 2x2 matrices since we provide special paths for them
+ CALL_SUBTEST_1( selfadjointeigensolver(Matrix2f()) );
+ CALL_SUBTEST_1( selfadjointeigensolver(Matrix2d()) );
+ CALL_SUBTEST_1( selfadjointeigensolver(Matrix3f()) );
+ CALL_SUBTEST_1( selfadjointeigensolver(Matrix3d()) );
+ CALL_SUBTEST_2( selfadjointeigensolver(Matrix4d()) );
+ s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4);
+ CALL_SUBTEST_3( selfadjointeigensolver(MatrixXf(s,s)) );
+ s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4);
+ CALL_SUBTEST_4( selfadjointeigensolver(MatrixXd(s,s)) );
+ s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4);
+ CALL_SUBTEST_5( selfadjointeigensolver(MatrixXcd(s,s)) );
+
+ s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4);
+ CALL_SUBTEST_9( selfadjointeigensolver(Matrix<std::complex<double>,Dynamic,Dynamic,RowMajor>(s,s)) );
+
+ // some trivial but implementation-wise tricky cases
+ CALL_SUBTEST_4( selfadjointeigensolver(MatrixXd(1,1)) );
+ CALL_SUBTEST_4( selfadjointeigensolver(MatrixXd(2,2)) );
+ CALL_SUBTEST_6( selfadjointeigensolver(Matrix<double,1,1>()) );
+ CALL_SUBTEST_7( selfadjointeigensolver(Matrix<double,2,2>()) );
+ }
+
+ // Test problem size constructors
+ s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4);
+ CALL_SUBTEST_8(SelfAdjointEigenSolver<MatrixXf> tmp1(s));
+ CALL_SUBTEST_8(Tridiagonalization<MatrixXf> tmp2(s));
+
+ TEST_SET_BUT_UNUSED_VARIABLE(s)
+}
+