248 lines
9.3 KiB
C++
248 lines
9.3 KiB
C++
// This file is triangularView of Eigen, a lightweight C++ template library
|
|
// for linear algebra.
|
|
//
|
|
// Copyright (C) 2008-2009 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"
|
|
|
|
|
|
|
|
template<typename MatrixType> void triangular_square(const MatrixType& m)
|
|
{
|
|
typedef typename MatrixType::Scalar Scalar;
|
|
typedef typename NumTraits<Scalar>::Real RealScalar;
|
|
typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;
|
|
|
|
RealScalar largerEps = 10*test_precision<RealScalar>();
|
|
|
|
typename MatrixType::Index rows = m.rows();
|
|
typename MatrixType::Index cols = m.cols();
|
|
|
|
MatrixType m1 = MatrixType::Random(rows, cols),
|
|
m2 = MatrixType::Random(rows, cols),
|
|
m3(rows, cols),
|
|
m4(rows, cols),
|
|
r1(rows, cols),
|
|
r2(rows, cols);
|
|
VectorType v2 = VectorType::Random(rows);
|
|
|
|
MatrixType m1up = m1.template triangularView<Upper>();
|
|
MatrixType m2up = m2.template triangularView<Upper>();
|
|
|
|
if (rows*cols>1)
|
|
{
|
|
VERIFY(m1up.isUpperTriangular());
|
|
VERIFY(m2up.transpose().isLowerTriangular());
|
|
VERIFY(!m2.isLowerTriangular());
|
|
}
|
|
|
|
// VERIFY_IS_APPROX(m1up.transpose() * m2, m1.upper().transpose().lower() * m2);
|
|
|
|
// test overloaded operator+=
|
|
r1.setZero();
|
|
r2.setZero();
|
|
r1.template triangularView<Upper>() += m1;
|
|
r2 += m1up;
|
|
VERIFY_IS_APPROX(r1,r2);
|
|
|
|
// test overloaded operator=
|
|
m1.setZero();
|
|
m1.template triangularView<Upper>() = m2.transpose() + m2;
|
|
m3 = m2.transpose() + m2;
|
|
VERIFY_IS_APPROX(m3.template triangularView<Lower>().transpose().toDenseMatrix(), m1);
|
|
|
|
// test overloaded operator=
|
|
m1.setZero();
|
|
m1.template triangularView<Lower>() = m2.transpose() + m2;
|
|
VERIFY_IS_APPROX(m3.template triangularView<Lower>().toDenseMatrix(), m1);
|
|
|
|
VERIFY_IS_APPROX(m3.template triangularView<Lower>().conjugate().toDenseMatrix(),
|
|
m3.conjugate().template triangularView<Lower>().toDenseMatrix());
|
|
|
|
m1 = MatrixType::Random(rows, cols);
|
|
for (int i=0; i<rows; ++i)
|
|
while (numext::abs2(m1(i,i))<RealScalar(1e-1)) m1(i,i) = internal::random<Scalar>();
|
|
|
|
Transpose<MatrixType> trm4(m4);
|
|
// test back and forward subsitution with a vector as the rhs
|
|
m3 = m1.template triangularView<Upper>();
|
|
VERIFY(v2.isApprox(m3.adjoint() * (m1.adjoint().template triangularView<Lower>().solve(v2)), largerEps));
|
|
m3 = m1.template triangularView<Lower>();
|
|
VERIFY(v2.isApprox(m3.transpose() * (m1.transpose().template triangularView<Upper>().solve(v2)), largerEps));
|
|
m3 = m1.template triangularView<Upper>();
|
|
VERIFY(v2.isApprox(m3 * (m1.template triangularView<Upper>().solve(v2)), largerEps));
|
|
m3 = m1.template triangularView<Lower>();
|
|
VERIFY(v2.isApprox(m3.conjugate() * (m1.conjugate().template triangularView<Lower>().solve(v2)), largerEps));
|
|
|
|
// test back and forward substitution with a matrix as the rhs
|
|
m3 = m1.template triangularView<Upper>();
|
|
VERIFY(m2.isApprox(m3.adjoint() * (m1.adjoint().template triangularView<Lower>().solve(m2)), largerEps));
|
|
m3 = m1.template triangularView<Lower>();
|
|
VERIFY(m2.isApprox(m3.transpose() * (m1.transpose().template triangularView<Upper>().solve(m2)), largerEps));
|
|
m3 = m1.template triangularView<Upper>();
|
|
VERIFY(m2.isApprox(m3 * (m1.template triangularView<Upper>().solve(m2)), largerEps));
|
|
m3 = m1.template triangularView<Lower>();
|
|
VERIFY(m2.isApprox(m3.conjugate() * (m1.conjugate().template triangularView<Lower>().solve(m2)), largerEps));
|
|
|
|
// check M * inv(L) using in place API
|
|
m4 = m3;
|
|
m1.transpose().template triangularView<Eigen::Upper>().solveInPlace(trm4);
|
|
VERIFY_IS_APPROX(m4 * m1.template triangularView<Eigen::Lower>(), m3);
|
|
|
|
// check M * inv(U) using in place API
|
|
m3 = m1.template triangularView<Upper>();
|
|
m4 = m3;
|
|
m3.transpose().template triangularView<Eigen::Lower>().solveInPlace(trm4);
|
|
VERIFY_IS_APPROX(m4 * m1.template triangularView<Eigen::Upper>(), m3);
|
|
|
|
// check solve with unit diagonal
|
|
m3 = m1.template triangularView<UnitUpper>();
|
|
VERIFY(m2.isApprox(m3 * (m1.template triangularView<UnitUpper>().solve(m2)), largerEps));
|
|
|
|
// VERIFY(( m1.template triangularView<Upper>()
|
|
// * m2.template triangularView<Upper>()).isUpperTriangular());
|
|
|
|
// test swap
|
|
m1.setOnes();
|
|
m2.setZero();
|
|
m2.template triangularView<Upper>().swap(m1);
|
|
m3.setZero();
|
|
m3.template triangularView<Upper>().setOnes();
|
|
VERIFY_IS_APPROX(m2,m3);
|
|
|
|
m1.setRandom();
|
|
m3 = m1.template triangularView<Upper>();
|
|
Matrix<Scalar, MatrixType::ColsAtCompileTime, Dynamic> m5(cols, internal::random<int>(1,20)); m5.setRandom();
|
|
Matrix<Scalar, Dynamic, MatrixType::RowsAtCompileTime> m6(internal::random<int>(1,20), rows); m6.setRandom();
|
|
VERIFY_IS_APPROX(m1.template triangularView<Upper>() * m5, m3*m5);
|
|
VERIFY_IS_APPROX(m6*m1.template triangularView<Upper>(), m6*m3);
|
|
|
|
m1up = m1.template triangularView<Upper>();
|
|
VERIFY_IS_APPROX(m1.template selfadjointView<Upper>().template triangularView<Upper>().toDenseMatrix(), m1up);
|
|
VERIFY_IS_APPROX(m1up.template selfadjointView<Upper>().template triangularView<Upper>().toDenseMatrix(), m1up);
|
|
VERIFY_IS_APPROX(m1.template selfadjointView<Upper>().template triangularView<Lower>().toDenseMatrix(), m1up.adjoint());
|
|
VERIFY_IS_APPROX(m1up.template selfadjointView<Upper>().template triangularView<Lower>().toDenseMatrix(), m1up.adjoint());
|
|
|
|
VERIFY_IS_APPROX(m1.template selfadjointView<Upper>().diagonal(), m1.diagonal());
|
|
|
|
}
|
|
|
|
|
|
template<typename MatrixType> void triangular_rect(const MatrixType& m)
|
|
{
|
|
typedef const typename MatrixType::Index Index;
|
|
typedef typename MatrixType::Scalar Scalar;
|
|
typedef typename NumTraits<Scalar>::Real RealScalar;
|
|
enum { Rows = MatrixType::RowsAtCompileTime, Cols = MatrixType::ColsAtCompileTime };
|
|
|
|
Index rows = m.rows();
|
|
Index cols = m.cols();
|
|
|
|
MatrixType m1 = MatrixType::Random(rows, cols),
|
|
m2 = MatrixType::Random(rows, cols),
|
|
m3(rows, cols),
|
|
m4(rows, cols),
|
|
r1(rows, cols),
|
|
r2(rows, cols);
|
|
|
|
MatrixType m1up = m1.template triangularView<Upper>();
|
|
MatrixType m2up = m2.template triangularView<Upper>();
|
|
|
|
if (rows>1 && cols>1)
|
|
{
|
|
VERIFY(m1up.isUpperTriangular());
|
|
VERIFY(m2up.transpose().isLowerTriangular());
|
|
VERIFY(!m2.isLowerTriangular());
|
|
}
|
|
|
|
// test overloaded operator+=
|
|
r1.setZero();
|
|
r2.setZero();
|
|
r1.template triangularView<Upper>() += m1;
|
|
r2 += m1up;
|
|
VERIFY_IS_APPROX(r1,r2);
|
|
|
|
// test overloaded operator=
|
|
m1.setZero();
|
|
m1.template triangularView<Upper>() = 3 * m2;
|
|
m3 = 3 * m2;
|
|
VERIFY_IS_APPROX(m3.template triangularView<Upper>().toDenseMatrix(), m1);
|
|
|
|
|
|
m1.setZero();
|
|
m1.template triangularView<Lower>() = 3 * m2;
|
|
VERIFY_IS_APPROX(m3.template triangularView<Lower>().toDenseMatrix(), m1);
|
|
|
|
m1.setZero();
|
|
m1.template triangularView<StrictlyUpper>() = 3 * m2;
|
|
VERIFY_IS_APPROX(m3.template triangularView<StrictlyUpper>().toDenseMatrix(), m1);
|
|
|
|
|
|
m1.setZero();
|
|
m1.template triangularView<StrictlyLower>() = 3 * m2;
|
|
VERIFY_IS_APPROX(m3.template triangularView<StrictlyLower>().toDenseMatrix(), m1);
|
|
m1.setRandom();
|
|
m2 = m1.template triangularView<Upper>();
|
|
VERIFY(m2.isUpperTriangular());
|
|
VERIFY(!m2.isLowerTriangular());
|
|
m2 = m1.template triangularView<StrictlyUpper>();
|
|
VERIFY(m2.isUpperTriangular());
|
|
VERIFY(m2.diagonal().isMuchSmallerThan(RealScalar(1)));
|
|
m2 = m1.template triangularView<UnitUpper>();
|
|
VERIFY(m2.isUpperTriangular());
|
|
m2.diagonal().array() -= Scalar(1);
|
|
VERIFY(m2.diagonal().isMuchSmallerThan(RealScalar(1)));
|
|
m2 = m1.template triangularView<Lower>();
|
|
VERIFY(m2.isLowerTriangular());
|
|
VERIFY(!m2.isUpperTriangular());
|
|
m2 = m1.template triangularView<StrictlyLower>();
|
|
VERIFY(m2.isLowerTriangular());
|
|
VERIFY(m2.diagonal().isMuchSmallerThan(RealScalar(1)));
|
|
m2 = m1.template triangularView<UnitLower>();
|
|
VERIFY(m2.isLowerTriangular());
|
|
m2.diagonal().array() -= Scalar(1);
|
|
VERIFY(m2.diagonal().isMuchSmallerThan(RealScalar(1)));
|
|
// test swap
|
|
m1.setOnes();
|
|
m2.setZero();
|
|
m2.template triangularView<Upper>().swap(m1);
|
|
m3.setZero();
|
|
m3.template triangularView<Upper>().setOnes();
|
|
VERIFY_IS_APPROX(m2,m3);
|
|
}
|
|
|
|
void bug_159()
|
|
{
|
|
Matrix3d m = Matrix3d::Random().triangularView<Lower>();
|
|
EIGEN_UNUSED_VARIABLE(m)
|
|
}
|
|
|
|
void test_triangular()
|
|
{
|
|
int maxsize = (std::min)(EIGEN_TEST_MAX_SIZE,20);
|
|
for(int i = 0; i < g_repeat ; i++)
|
|
{
|
|
int r = internal::random<int>(2,maxsize); TEST_SET_BUT_UNUSED_VARIABLE(r)
|
|
int c = internal::random<int>(2,maxsize); TEST_SET_BUT_UNUSED_VARIABLE(c)
|
|
|
|
CALL_SUBTEST_1( triangular_square(Matrix<float, 1, 1>()) );
|
|
CALL_SUBTEST_2( triangular_square(Matrix<float, 2, 2>()) );
|
|
CALL_SUBTEST_3( triangular_square(Matrix3d()) );
|
|
CALL_SUBTEST_4( triangular_square(Matrix<std::complex<float>,8, 8>()) );
|
|
CALL_SUBTEST_5( triangular_square(MatrixXcd(r,r)) );
|
|
CALL_SUBTEST_6( triangular_square(Matrix<float,Dynamic,Dynamic,RowMajor>(r, r)) );
|
|
|
|
CALL_SUBTEST_7( triangular_rect(Matrix<float, 4, 5>()) );
|
|
CALL_SUBTEST_8( triangular_rect(Matrix<double, 6, 2>()) );
|
|
CALL_SUBTEST_9( triangular_rect(MatrixXcf(r, c)) );
|
|
CALL_SUBTEST_5( triangular_rect(MatrixXcd(r, c)) );
|
|
CALL_SUBTEST_6( triangular_rect(Matrix<float,Dynamic,Dynamic,RowMajor>(r, c)) );
|
|
}
|
|
|
|
CALL_SUBTEST_1( bug_159() );
|
|
}
|