inplace_decomposition.cpp

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2016 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// 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 <Eigen/LU>
#include <Eigen/Cholesky>
#include <Eigen/QR>

// This file test inplace decomposition through Ref<>, as supported by Cholesky, LU, and QR decompositions.

template<typename DecType,typename MatrixType> void inplace(bool square = false, bool SPD = false)
{
  typedef typename MatrixType::Scalar Scalar;
  typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> RhsType;
  typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, 1> ResType;

  Index rows = MatrixType::RowsAtCompileTime==Dynamic ? internal::random<Index>(2,EIGEN_TEST_MAX_SIZE/2) : Index(MatrixType::RowsAtCompileTime);
  Index cols = MatrixType::ColsAtCompileTime==Dynamic ? (square?rows:internal::random<Index>(2,rows))    : Index(MatrixType::ColsAtCompileTime);

  MatrixType A = MatrixType::Random(rows,cols);
  RhsType b = RhsType::Random(rows);
  ResType x(cols);

  if(SPD)
  {
    assert(square);
    A.topRows(cols) = A.topRows(cols).adjoint() * A.topRows(cols);
    A.diagonal().array() += 1e-3;
  }

  MatrixType A0 = A;
  MatrixType A1 = A;

  DecType dec(A);

  // Check that the content of A has been modified
  VERIFY_IS_NOT_APPROX( A, A0 );

  // Check that the decomposition is correct:
  if(rows==cols)
  {
    VERIFY_IS_APPROX( A0 * (x = dec.solve(b)), b );
  }
  else
  {
    VERIFY_IS_APPROX( A0.transpose() * A0 * (x = dec.solve(b)), A0.transpose() * b );
  }

  // Check that modifying A breaks the current dec:
  A.setRandom();
  if(rows==cols)
  {
    VERIFY_IS_NOT_APPROX( A0 * (x = dec.solve(b)), b );
  }
  else
  {
    VERIFY_IS_NOT_APPROX( A0.transpose() * A0 * (x = dec.solve(b)), A0.transpose() * b );
  }

  // Check that calling compute(A1) does not modify A1:
  A = A0;
  dec.compute(A1);
  VERIFY_IS_EQUAL(A0,A1);
  VERIFY_IS_NOT_APPROX( A, A0 );
  if(rows==cols)
  {
    VERIFY_IS_APPROX( A0 * (x = dec.solve(b)), b );
  }
  else
  {
    VERIFY_IS_APPROX( A0.transpose() * A0 * (x = dec.solve(b)), A0.transpose() * b );
  }
}


void test_inplace_decomposition()
{
  EIGEN_UNUSED typedef Matrix<double,4,3> Matrix43d;
  for(int i = 0; i < g_repeat; i++) {
    CALL_SUBTEST_1(( inplace<LLT<Ref<MatrixXd> >, MatrixXd>(true,true) ));
    CALL_SUBTEST_1(( inplace<LLT<Ref<Matrix4d> >, Matrix4d>(true,true) ));

    CALL_SUBTEST_2(( inplace<LDLT<Ref<MatrixXd> >, MatrixXd>(true,true) ));
    CALL_SUBTEST_2(( inplace<LDLT<Ref<Matrix4d> >, Matrix4d>(true,true) ));

    CALL_SUBTEST_3(( inplace<PartialPivLU<Ref<MatrixXd> >, MatrixXd>(true,false) ));
    CALL_SUBTEST_3(( inplace<PartialPivLU<Ref<Matrix4d> >, Matrix4d>(true,false) ));

    CALL_SUBTEST_4(( inplace<FullPivLU<Ref<MatrixXd> >, MatrixXd>(true,false) ));
    CALL_SUBTEST_4(( inplace<FullPivLU<Ref<Matrix4d> >, Matrix4d>(true,false) ));

    CALL_SUBTEST_5(( inplace<HouseholderQR<Ref<MatrixXd> >, MatrixXd>(false,false) ));
    CALL_SUBTEST_5(( inplace<HouseholderQR<Ref<Matrix43d> >, Matrix43d>(false,false) ));

    CALL_SUBTEST_6(( inplace<ColPivHouseholderQR<Ref<MatrixXd> >, MatrixXd>(false,false) ));
    CALL_SUBTEST_6(( inplace<ColPivHouseholderQR<Ref<Matrix43d> >, Matrix43d>(false,false) ));

    CALL_SUBTEST_7(( inplace<FullPivHouseholderQR<Ref<MatrixXd> >, MatrixXd>(false,false) ));
    CALL_SUBTEST_7(( inplace<FullPivHouseholderQR<Ref<Matrix43d> >, Matrix43d>(false,false) ));

    CALL_SUBTEST_8(( inplace<CompleteOrthogonalDecomposition<Ref<MatrixXd> >, MatrixXd>(false,false) ));
    CALL_SUBTEST_8(( inplace<CompleteOrthogonalDecomposition<Ref<Matrix43d> >, Matrix43d>(false,false) ));
  }
}