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351 lines
11 KiB
C++
351 lines
11 KiB
C++
// This file is part of Eigen, a lightweight C++ template library
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// for linear algebra.
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//
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// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
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//
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// This Source Code Form is subject to the terms of the Mozilla
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// Public License v. 2.0. If a copy of the MPL was not distributed
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// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
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#ifndef EIGEN_NO_ASSERTION_CHECKING
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#define EIGEN_NO_ASSERTION_CHECKING
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#endif
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static int nb_temporaries;
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#define EIGEN_DENSE_STORAGE_CTOR_PLUGIN { if(size!=0) nb_temporaries++; }
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#include "main.h"
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#include <Eigen/Cholesky>
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#include <Eigen/QR>
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#define VERIFY_EVALUATION_COUNT(XPR,N) {\
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nb_temporaries = 0; \
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XPR; \
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if(nb_temporaries!=N) std::cerr << "nb_temporaries == " << nb_temporaries << "\n"; \
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VERIFY( (#XPR) && nb_temporaries==N ); \
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}
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template<typename MatrixType,template <typename,int> class CholType> void test_chol_update(const MatrixType& symm)
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{
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typedef typename MatrixType::Scalar Scalar;
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typedef typename MatrixType::RealScalar RealScalar;
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typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;
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MatrixType symmLo = symm.template triangularView<Lower>();
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MatrixType symmUp = symm.template triangularView<Upper>();
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MatrixType symmCpy = symm;
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CholType<MatrixType,Lower> chollo(symmLo);
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CholType<MatrixType,Upper> cholup(symmUp);
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for (int k=0; k<10; ++k)
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{
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VectorType vec = VectorType::Random(symm.rows());
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RealScalar sigma = internal::random<RealScalar>();
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symmCpy += sigma * vec * vec.adjoint();
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// we are doing some downdates, so it might be the case that the matrix is not SPD anymore
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CholType<MatrixType,Lower> chol(symmCpy);
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if(chol.info()!=Success)
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break;
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chollo.rankUpdate(vec, sigma);
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VERIFY_IS_APPROX(symmCpy, chollo.reconstructedMatrix());
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cholup.rankUpdate(vec, sigma);
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VERIFY_IS_APPROX(symmCpy, cholup.reconstructedMatrix());
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}
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}
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template<typename MatrixType> void cholesky(const MatrixType& m)
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{
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typedef typename MatrixType::Index Index;
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/* this test covers the following files:
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LLT.h LDLT.h
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*/
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Index rows = m.rows();
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Index cols = m.cols();
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typedef typename MatrixType::Scalar Scalar;
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typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> SquareMatrixType;
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typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;
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MatrixType a0 = MatrixType::Random(rows,cols);
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VectorType vecB = VectorType::Random(rows), vecX(rows);
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MatrixType matB = MatrixType::Random(rows,cols), matX(rows,cols);
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SquareMatrixType symm = a0 * a0.adjoint();
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// let's make sure the matrix is not singular or near singular
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for (int k=0; k<3; ++k)
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{
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MatrixType a1 = MatrixType::Random(rows,cols);
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symm += a1 * a1.adjoint();
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}
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// to test if really Cholesky only uses the upper triangular part, uncomment the following
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// FIXME: currently that fails !!
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//symm.template part<StrictlyLower>().setZero();
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{
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SquareMatrixType symmUp = symm.template triangularView<Upper>();
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SquareMatrixType symmLo = symm.template triangularView<Lower>();
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LLT<SquareMatrixType,Lower> chollo(symmLo);
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VERIFY_IS_APPROX(symm, chollo.reconstructedMatrix());
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vecX = chollo.solve(vecB);
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VERIFY_IS_APPROX(symm * vecX, vecB);
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matX = chollo.solve(matB);
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VERIFY_IS_APPROX(symm * matX, matB);
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// test the upper mode
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LLT<SquareMatrixType,Upper> cholup(symmUp);
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VERIFY_IS_APPROX(symm, cholup.reconstructedMatrix());
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vecX = cholup.solve(vecB);
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VERIFY_IS_APPROX(symm * vecX, vecB);
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matX = cholup.solve(matB);
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VERIFY_IS_APPROX(symm * matX, matB);
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MatrixType neg = -symmLo;
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chollo.compute(neg);
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VERIFY(chollo.info()==NumericalIssue);
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VERIFY_IS_APPROX(MatrixType(chollo.matrixL().transpose().conjugate()), MatrixType(chollo.matrixU()));
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VERIFY_IS_APPROX(MatrixType(chollo.matrixU().transpose().conjugate()), MatrixType(chollo.matrixL()));
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VERIFY_IS_APPROX(MatrixType(cholup.matrixL().transpose().conjugate()), MatrixType(cholup.matrixU()));
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VERIFY_IS_APPROX(MatrixType(cholup.matrixU().transpose().conjugate()), MatrixType(cholup.matrixL()));
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// test some special use cases of SelfCwiseBinaryOp:
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MatrixType m1 = MatrixType::Random(rows,cols), m2(rows,cols);
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m2 = m1;
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m2 += symmLo.template selfadjointView<Lower>().llt().solve(matB);
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VERIFY_IS_APPROX(m2, m1 + symmLo.template selfadjointView<Lower>().llt().solve(matB));
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m2 = m1;
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m2 -= symmLo.template selfadjointView<Lower>().llt().solve(matB);
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VERIFY_IS_APPROX(m2, m1 - symmLo.template selfadjointView<Lower>().llt().solve(matB));
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m2 = m1;
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m2.noalias() += symmLo.template selfadjointView<Lower>().llt().solve(matB);
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VERIFY_IS_APPROX(m2, m1 + symmLo.template selfadjointView<Lower>().llt().solve(matB));
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m2 = m1;
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m2.noalias() -= symmLo.template selfadjointView<Lower>().llt().solve(matB);
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VERIFY_IS_APPROX(m2, m1 - symmLo.template selfadjointView<Lower>().llt().solve(matB));
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}
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// LDLT
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{
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int sign = internal::random<int>()%2 ? 1 : -1;
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if(sign == -1)
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{
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symm = -symm; // test a negative matrix
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}
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SquareMatrixType symmUp = symm.template triangularView<Upper>();
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SquareMatrixType symmLo = symm.template triangularView<Lower>();
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LDLT<SquareMatrixType,Lower> ldltlo(symmLo);
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VERIFY_IS_APPROX(symm, ldltlo.reconstructedMatrix());
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vecX = ldltlo.solve(vecB);
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VERIFY_IS_APPROX(symm * vecX, vecB);
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matX = ldltlo.solve(matB);
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VERIFY_IS_APPROX(symm * matX, matB);
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LDLT<SquareMatrixType,Upper> ldltup(symmUp);
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VERIFY_IS_APPROX(symm, ldltup.reconstructedMatrix());
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vecX = ldltup.solve(vecB);
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VERIFY_IS_APPROX(symm * vecX, vecB);
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matX = ldltup.solve(matB);
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VERIFY_IS_APPROX(symm * matX, matB);
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VERIFY_IS_APPROX(MatrixType(ldltlo.matrixL().transpose().conjugate()), MatrixType(ldltlo.matrixU()));
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VERIFY_IS_APPROX(MatrixType(ldltlo.matrixU().transpose().conjugate()), MatrixType(ldltlo.matrixL()));
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VERIFY_IS_APPROX(MatrixType(ldltup.matrixL().transpose().conjugate()), MatrixType(ldltup.matrixU()));
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VERIFY_IS_APPROX(MatrixType(ldltup.matrixU().transpose().conjugate()), MatrixType(ldltup.matrixL()));
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if(MatrixType::RowsAtCompileTime==Dynamic)
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{
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// note : each inplace permutation requires a small temporary vector (mask)
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// check inplace solve
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matX = matB;
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VERIFY_EVALUATION_COUNT(matX = ldltlo.solve(matX), 0);
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VERIFY_IS_APPROX(matX, ldltlo.solve(matB).eval());
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matX = matB;
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VERIFY_EVALUATION_COUNT(matX = ldltup.solve(matX), 0);
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VERIFY_IS_APPROX(matX, ldltup.solve(matB).eval());
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}
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// restore
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if(sign == -1)
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symm = -symm;
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}
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// update/downdate
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CALL_SUBTEST(( test_chol_update<SquareMatrixType,LLT>(symm) ));
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CALL_SUBTEST(( test_chol_update<SquareMatrixType,LDLT>(symm) ));
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}
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template<typename MatrixType> void cholesky_cplx(const MatrixType& m)
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{
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// classic test
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cholesky(m);
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// test mixing real/scalar types
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typedef typename MatrixType::Index Index;
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Index rows = m.rows();
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Index cols = m.cols();
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typedef typename MatrixType::Scalar Scalar;
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typedef typename NumTraits<Scalar>::Real RealScalar;
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typedef Matrix<RealScalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> RealMatrixType;
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typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;
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RealMatrixType a0 = RealMatrixType::Random(rows,cols);
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VectorType vecB = VectorType::Random(rows), vecX(rows);
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MatrixType matB = MatrixType::Random(rows,cols), matX(rows,cols);
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RealMatrixType symm = a0 * a0.adjoint();
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// let's make sure the matrix is not singular or near singular
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for (int k=0; k<3; ++k)
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{
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RealMatrixType a1 = RealMatrixType::Random(rows,cols);
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symm += a1 * a1.adjoint();
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}
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{
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RealMatrixType symmLo = symm.template triangularView<Lower>();
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LLT<RealMatrixType,Lower> chollo(symmLo);
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VERIFY_IS_APPROX(symm, chollo.reconstructedMatrix());
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vecX = chollo.solve(vecB);
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VERIFY_IS_APPROX(symm * vecX, vecB);
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// matX = chollo.solve(matB);
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// VERIFY_IS_APPROX(symm * matX, matB);
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}
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// LDLT
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{
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int sign = internal::random<int>()%2 ? 1 : -1;
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if(sign == -1)
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{
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symm = -symm; // test a negative matrix
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}
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RealMatrixType symmLo = symm.template triangularView<Lower>();
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LDLT<RealMatrixType,Lower> ldltlo(symmLo);
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VERIFY_IS_APPROX(symm, ldltlo.reconstructedMatrix());
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vecX = ldltlo.solve(vecB);
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VERIFY_IS_APPROX(symm * vecX, vecB);
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// matX = ldltlo.solve(matB);
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// VERIFY_IS_APPROX(symm * matX, matB);
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}
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}
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// regression test for bug 241
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template<typename MatrixType> void cholesky_bug241(const MatrixType& m)
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{
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eigen_assert(m.rows() == 2 && m.cols() == 2);
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typedef typename MatrixType::Scalar Scalar;
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typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;
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MatrixType matA;
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matA << 1, 1, 1, 1;
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VectorType vecB;
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vecB << 1, 1;
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VectorType vecX = matA.ldlt().solve(vecB);
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VERIFY_IS_APPROX(matA * vecX, vecB);
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}
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// LDLT is not guaranteed to work for indefinite matrices, but happens to work fine if matrix is diagonal.
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// This test checks that LDLT reports correctly that matrix is indefinite.
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// See http://forum.kde.org/viewtopic.php?f=74&t=106942 and bug 736
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template<typename MatrixType> void cholesky_definiteness(const MatrixType& m)
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{
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eigen_assert(m.rows() == 2 && m.cols() == 2);
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MatrixType mat;
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{
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mat << 1, 0, 0, -1;
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LDLT<MatrixType> ldlt(mat);
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VERIFY(!ldlt.isNegative());
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VERIFY(!ldlt.isPositive());
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}
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{
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mat << 1, 2, 2, 1;
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LDLT<MatrixType> ldlt(mat);
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VERIFY(!ldlt.isNegative());
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VERIFY(!ldlt.isPositive());
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}
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{
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mat << 0, 0, 0, 0;
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LDLT<MatrixType> ldlt(mat);
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VERIFY(ldlt.isNegative());
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VERIFY(ldlt.isPositive());
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}
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{
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mat << 0, 0, 0, 1;
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LDLT<MatrixType> ldlt(mat);
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VERIFY(!ldlt.isNegative());
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VERIFY(ldlt.isPositive());
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}
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{
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mat << -1, 0, 0, 0;
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LDLT<MatrixType> ldlt(mat);
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VERIFY(ldlt.isNegative());
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VERIFY(!ldlt.isPositive());
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}
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}
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template<typename MatrixType> void cholesky_verify_assert()
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{
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MatrixType tmp;
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LLT<MatrixType> llt;
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VERIFY_RAISES_ASSERT(llt.matrixL())
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VERIFY_RAISES_ASSERT(llt.matrixU())
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VERIFY_RAISES_ASSERT(llt.solve(tmp))
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VERIFY_RAISES_ASSERT(llt.solveInPlace(&tmp))
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LDLT<MatrixType> ldlt;
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VERIFY_RAISES_ASSERT(ldlt.matrixL())
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VERIFY_RAISES_ASSERT(ldlt.permutationP())
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VERIFY_RAISES_ASSERT(ldlt.vectorD())
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VERIFY_RAISES_ASSERT(ldlt.isPositive())
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VERIFY_RAISES_ASSERT(ldlt.isNegative())
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VERIFY_RAISES_ASSERT(ldlt.solve(tmp))
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VERIFY_RAISES_ASSERT(ldlt.solveInPlace(&tmp))
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}
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void test_cholesky()
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{
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int s = 0;
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for(int i = 0; i < g_repeat; i++) {
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CALL_SUBTEST_1( cholesky(Matrix<double,1,1>()) );
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CALL_SUBTEST_3( cholesky(Matrix2d()) );
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CALL_SUBTEST_3( cholesky_bug241(Matrix2d()) );
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CALL_SUBTEST_3( cholesky_definiteness(Matrix2d()) );
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CALL_SUBTEST_4( cholesky(Matrix3f()) );
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CALL_SUBTEST_5( cholesky(Matrix4d()) );
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s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE);
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CALL_SUBTEST_2( cholesky(MatrixXd(s,s)) );
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s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/2);
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CALL_SUBTEST_6( cholesky_cplx(MatrixXcd(s,s)) );
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}
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CALL_SUBTEST_4( cholesky_verify_assert<Matrix3f>() );
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CALL_SUBTEST_7( cholesky_verify_assert<Matrix3d>() );
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CALL_SUBTEST_8( cholesky_verify_assert<MatrixXf>() );
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CALL_SUBTEST_2( cholesky_verify_assert<MatrixXd>() );
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// Test problem size constructors
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CALL_SUBTEST_9( LLT<MatrixXf>(10) );
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CALL_SUBTEST_9( LDLT<MatrixXf>(10) );
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TEST_SET_BUT_UNUSED_VARIABLE(s)
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TEST_SET_BUT_UNUSED_VARIABLE(nb_temporaries)
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}
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