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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@gmail.com>
//
// Eigen is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
// License as published by the Free Software Foundation; either
// version 3 of the License, or (at your option) any later version.
//
// Alternatively, you can redistribute it and/or
// modify it under the terms of the GNU General Public License as
// published by the Free Software Foundation; either version 2 of
// the License, or (at your option) any later version.
//
// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public
// License and a copy of the GNU General Public License along with
// Eigen. If not, see <http://www.gnu.org/licenses/>.
#include "main.h"
template<typename MatrixType> void product_selfadjoint(const MatrixType& m)
{
typedef typename MatrixType::Scalar Scalar;
typedef typename NumTraits<Scalar>::Real RealScalar;
typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;
typedef Matrix<Scalar, 1, MatrixType::RowsAtCompileTime> RowVectorType;
int rows = m.rows();
int cols = m.cols();
MatrixType m1 = MatrixType::Random(rows, cols),
m2 = MatrixType::Random(rows, cols),
m3;
VectorType v1 = VectorType::Random(rows),
v2 = VectorType::Random(rows);
RowVectorType r1 = RowVectorType::Random(rows),
r2 = RowVectorType::Random(rows);
Scalar s1 = ei_random<Scalar>(),
s2 = ei_random<Scalar>(),
s3 = ei_random<Scalar>();
m1 = m1.adjoint()*m1;
// lower
m2.setZero();
m2.template triangularView<LowerTriangular>() = m1;
ei_product_selfadjoint_vector<Scalar,MatrixType::Flags&RowMajorBit,LowerTriangularBit>
(cols,m2.data(),cols, v1.data(), v2.data());
VERIFY_IS_APPROX(v2, m1 * v1);
VERIFY_IS_APPROX((m2.template selfadjointView<LowerTriangular>() * v1).eval(), m1 * v1);
// upper
m2.setZero();
m2.template triangularView<UpperTriangular>() = m1;
ei_product_selfadjoint_vector<Scalar,MatrixType::Flags&RowMajorBit,UpperTriangularBit>(cols,m2.data(),cols, v1.data(), v2.data());
VERIFY_IS_APPROX(v2, m1 * v1);
VERIFY_IS_APPROX((m2.template selfadjointView<UpperTriangular>() * v1).eval(), m1 * v1);
// rank2 update
m2 = m1.template triangularView<LowerTriangular>();
m2.template selfadjointView<LowerTriangular>().rank2update(v1,v2);
VERIFY_IS_APPROX(m2, (m1 + v1 * v2.adjoint()+ v2 * v1.adjoint()).template triangularView<LowerTriangular>().toDense());
m2 = m1.template triangularView<UpperTriangular>();
m2.template selfadjointView<UpperTriangular>().rank2update(-v1,s2*v2,s3);
VERIFY_IS_APPROX(m2, (m1 + (-s2*s3) * (v1 * v2.adjoint()+ v2 * v1.adjoint())).template triangularView<UpperTriangular>().toDense());
m2 = m1.template triangularView<UpperTriangular>();
m2.template selfadjointView<UpperTriangular>().rank2update(-r1.adjoint(),r2.adjoint()*s3,s1);
VERIFY_IS_APPROX(m2, (m1 + (-s3*s1) * (r1.adjoint() * r2 + r2.adjoint() * r1)).template triangularView<UpperTriangular>().toDense());
if (rows>1)
{
m2 = m1.template triangularView<LowerTriangular>();
m2.block(1,1,rows-1,cols-1).template selfadjointView<LowerTriangular>().rank2update(v1.end(rows-1),v2.start(cols-1));
m3 = m1;
m3.block(1,1,rows-1,cols-1) += v1.end(rows-1) * v2.start(cols-1).adjoint()+ v2.start(cols-1) * v1.end(rows-1).adjoint();
VERIFY_IS_APPROX(m2, m3.template triangularView<LowerTriangular>().toDense());
}
}
template<typename MatrixType> void symm(const MatrixType& m)
{
typedef typename MatrixType::Scalar Scalar;
typedef typename NumTraits<Scalar>::Real RealScalar;
typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, Dynamic> Rhs1;
typedef Matrix<Scalar, Dynamic, MatrixType::RowsAtCompileTime> Rhs2;
typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, Dynamic,RowMajor> Rhs3;
int rows = m.rows();
int cols = m.cols();
MatrixType m1 = MatrixType::Random(rows, cols),
m2 = MatrixType::Random(rows, cols);
m1 = (m1+m1.adjoint()).eval();
Rhs1 rhs1 = Rhs1::Random(cols, ei_random<int>(1,320)), rhs12, rhs13;
Rhs2 rhs2 = Rhs2::Random(ei_random<int>(1,320), rows), rhs22, rhs23;
Rhs3 rhs3 = Rhs3::Random(cols, ei_random<int>(1,320)), rhs32, rhs33;
Scalar s1 = ei_random<Scalar>(),
s2 = ei_random<Scalar>();
m2 = m1.template triangularView<LowerTriangular>();
VERIFY_IS_APPROX(rhs12 = (s1*m2).template selfadjointView<LowerTriangular>() * (s2*rhs1),
rhs13 = (s1*m1) * (s2*rhs1));
m2 = m1.template triangularView<UpperTriangular>();
VERIFY_IS_APPROX(rhs12 = (s1*m2).template selfadjointView<UpperTriangular>() * (s2*rhs1),
rhs13 = (s1*m1) * (s2*rhs1));
m2 = m1.template triangularView<LowerTriangular>();
VERIFY_IS_APPROX(rhs22 = (s1*m2).template selfadjointView<LowerTriangular>() * (s2*rhs2.adjoint()),
rhs23 = (s1*m1) * (s2*rhs2.adjoint()));
m2 = m1.template triangularView<UpperTriangular>();
VERIFY_IS_APPROX(rhs22 = (s1*m2).template selfadjointView<UpperTriangular>() * (s2*rhs2.adjoint()),
rhs23 = (s1*m1) * (s2*rhs2.adjoint()));
m2 = m1.template triangularView<UpperTriangular>();
VERIFY_IS_APPROX(rhs22 = (s1*m2.adjoint()).template selfadjointView<LowerTriangular>() * (s2*rhs2.adjoint()),
rhs23 = (s1*m1.adjoint()) * (s2*rhs2.adjoint()));
// test row major = <...>
m2 = m1.template triangularView<LowerTriangular>();
VERIFY_IS_APPROX(rhs32 = (s1*m2).template selfadjointView<LowerTriangular>() * (s2*rhs3),
rhs33 = (s1*m1) * (s2 * rhs3));
m2 = m1.template triangularView<UpperTriangular>();
VERIFY_IS_APPROX(rhs32 = (s1*m2.adjoint()).template selfadjointView<LowerTriangular>() * (s2*rhs3).conjugate(),
rhs33 = (s1*m1.adjoint()) * (s2*rhs3).conjugate());
// test matrix * selfadjoint
m2 = m1.template triangularView<LowerTriangular>();
VERIFY_IS_APPROX(rhs22 = (rhs2) * (m2).template selfadjointView<LowerTriangular>(),
rhs23 = (rhs2) * (m1));
VERIFY_IS_APPROX(rhs22 = (s2*rhs2) * (s1*m2).template selfadjointView<LowerTriangular>(),
rhs23 = (s2*rhs2) * (s1*m1));
}
void test_product_selfadjoint()
{
for(int i = 0; i < g_repeat ; i++) {
CALL_SUBTEST( product_selfadjoint(Matrix<float, 1, 1>()) );
CALL_SUBTEST( product_selfadjoint(Matrix<float, 2, 2>()) );
CALL_SUBTEST( product_selfadjoint(Matrix3d()) );
CALL_SUBTEST( product_selfadjoint(MatrixXcf(4, 4)) );
CALL_SUBTEST( product_selfadjoint(MatrixXcd(21,21)) );
CALL_SUBTEST( product_selfadjoint(MatrixXd(14,14)) );
CALL_SUBTEST( product_selfadjoint(Matrix<float,Dynamic,Dynamic,RowMajor>(17,17)) );
CALL_SUBTEST( product_selfadjoint(Matrix<std::complex<double>,Dynamic,Dynamic,RowMajor>(19, 19)) );
}
for(int i = 0; i < g_repeat ; i++)
{
int s;
s = ei_random<int>(10,320);
CALL_SUBTEST( symm(MatrixXf(s, s)) );
s = ei_random<int>(10,320);
CALL_SUBTEST( symm(MatrixXcd(s, s)) );
}
}
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