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266 lines
10 KiB
C++
266 lines
10 KiB
C++
// This file is triangularView of Eigen, a lightweight C++ template library
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// for linear algebra.
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//
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// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
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//
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// Eigen is free software; you can redistribute it and/or
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// modify it under the terms of the GNU Lesser General Public
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// License as published by the Free Software Foundation; either
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// version 3 of the License, or (at your option) any later version.
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//
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// Alternatively, you can redistribute it and/or
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// modify it under the terms of the GNU General Public License as
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// published by the Free Software Foundation; either version 2 of
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// the License, or (at your option) any later version.
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//
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// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
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// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
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// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
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// GNU General Public License for more details.
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//
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// You should have received a copy of the GNU Lesser General Public
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// License and a copy of the GNU General Public License along with
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// Eigen. If not, see <http://www.gnu.org/licenses/>.
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#include "main.h"
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template<typename MatrixType> void triangular_square(const MatrixType& m)
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{
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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<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;
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RealScalar largerEps = 10*test_precision<RealScalar>();
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typename MatrixType::Index rows = m.rows();
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typename MatrixType::Index cols = m.cols();
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MatrixType m1 = MatrixType::Random(rows, cols),
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m2 = MatrixType::Random(rows, cols),
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m3(rows, cols),
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m4(rows, cols),
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r1(rows, cols),
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r2(rows, cols),
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mzero = MatrixType::Zero(rows, cols),
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mones = MatrixType::Ones(rows, cols),
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identity = Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime>
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::Identity(rows, rows),
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square = Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime>
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::Random(rows, rows);
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VectorType v1 = VectorType::Random(rows),
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v2 = VectorType::Random(rows),
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vzero = VectorType::Zero(rows);
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MatrixType m1up = m1.template triangularView<Upper>();
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MatrixType m2up = m2.template triangularView<Upper>();
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if (rows*cols>1)
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{
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VERIFY(m1up.isUpperTriangular());
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VERIFY(m2up.transpose().isLowerTriangular());
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VERIFY(!m2.isLowerTriangular());
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}
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// VERIFY_IS_APPROX(m1up.transpose() * m2, m1.upper().transpose().lower() * m2);
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// test overloaded operator+=
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r1.setZero();
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r2.setZero();
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r1.template triangularView<Upper>() += m1;
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r2 += m1up;
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VERIFY_IS_APPROX(r1,r2);
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// test overloaded operator=
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m1.setZero();
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m1.template triangularView<Upper>() = m2.transpose() + m2;
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m3 = m2.transpose() + m2;
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VERIFY_IS_APPROX(m3.template triangularView<Lower>().transpose().toDenseMatrix(), m1);
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// test overloaded operator=
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m1.setZero();
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m1.template triangularView<Lower>() = m2.transpose() + m2;
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VERIFY_IS_APPROX(m3.template triangularView<Lower>().toDenseMatrix(), m1);
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VERIFY_IS_APPROX(m3.template triangularView<Lower>().conjugate().toDenseMatrix(),
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m3.conjugate().template triangularView<Lower>().toDenseMatrix());
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m1 = MatrixType::Random(rows, cols);
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for (int i=0; i<rows; ++i)
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while (internal::abs2(m1(i,i))<1e-1) m1(i,i) = internal::random<Scalar>();
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Transpose<MatrixType> trm4(m4);
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// test back and forward subsitution with a vector as the rhs
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m3 = m1.template triangularView<Upper>();
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VERIFY(v2.isApprox(m3.adjoint() * (m1.adjoint().template triangularView<Lower>().solve(v2)), largerEps));
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m3 = m1.template triangularView<Lower>();
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VERIFY(v2.isApprox(m3.transpose() * (m1.transpose().template triangularView<Upper>().solve(v2)), largerEps));
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m3 = m1.template triangularView<Upper>();
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VERIFY(v2.isApprox(m3 * (m1.template triangularView<Upper>().solve(v2)), largerEps));
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m3 = m1.template triangularView<Lower>();
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VERIFY(v2.isApprox(m3.conjugate() * (m1.conjugate().template triangularView<Lower>().solve(v2)), largerEps));
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// test back and forward subsitution with a matrix as the rhs
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m3 = m1.template triangularView<Upper>();
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VERIFY(m2.isApprox(m3.adjoint() * (m1.adjoint().template triangularView<Lower>().solve(m2)), largerEps));
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m3 = m1.template triangularView<Lower>();
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VERIFY(m2.isApprox(m3.transpose() * (m1.transpose().template triangularView<Upper>().solve(m2)), largerEps));
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m3 = m1.template triangularView<Upper>();
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VERIFY(m2.isApprox(m3 * (m1.template triangularView<Upper>().solve(m2)), largerEps));
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m3 = m1.template triangularView<Lower>();
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VERIFY(m2.isApprox(m3.conjugate() * (m1.conjugate().template triangularView<Lower>().solve(m2)), largerEps));
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// check M * inv(L) using in place API
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m4 = m3;
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m3.transpose().template triangularView<Eigen::Upper>().solveInPlace(trm4);
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VERIFY(m4.cwiseAbs().isIdentity(test_precision<RealScalar>()));
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// check M * inv(U) using in place API
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m3 = m1.template triangularView<Upper>();
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m4 = m3;
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m3.transpose().template triangularView<Eigen::Lower>().solveInPlace(trm4);
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VERIFY(m4.cwiseAbs().isIdentity(test_precision<RealScalar>()));
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// check solve with unit diagonal
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m3 = m1.template triangularView<UnitUpper>();
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VERIFY(m2.isApprox(m3 * (m1.template triangularView<UnitUpper>().solve(m2)), largerEps));
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// VERIFY(( m1.template triangularView<Upper>()
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// * m2.template triangularView<Upper>()).isUpperTriangular());
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// test swap
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m1.setOnes();
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m2.setZero();
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m2.template triangularView<Upper>().swap(m1);
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m3.setZero();
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m3.template triangularView<Upper>().setOnes();
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VERIFY_IS_APPROX(m2,m3);
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}
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template<typename MatrixType> void triangular_rect(const MatrixType& m)
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{
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typedef const typename MatrixType::Index Index;
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typedef typename MatrixType::Scalar Scalar;
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typedef typename NumTraits<Scalar>::Real RealScalar;
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enum { Rows = MatrixType::RowsAtCompileTime, Cols = MatrixType::ColsAtCompileTime };
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typedef Matrix<Scalar, Rows, 1> VectorType;
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typedef Matrix<Scalar, Rows, Rows> RMatrixType;
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Index rows = m.rows();
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Index cols = m.cols();
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MatrixType m1 = MatrixType::Random(rows, cols),
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m2 = MatrixType::Random(rows, cols),
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m3(rows, cols),
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m4(rows, cols),
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r1(rows, cols),
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r2(rows, cols),
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mzero = MatrixType::Zero(rows, cols),
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mones = MatrixType::Ones(rows, cols);
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RMatrixType identity = Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime>
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::Identity(rows, rows),
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square = Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime>
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::Random(rows, rows);
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VectorType v1 = VectorType::Random(rows),
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v2 = VectorType::Random(rows),
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vzero = VectorType::Zero(rows);
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MatrixType m1up = m1.template triangularView<Upper>();
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MatrixType m2up = m2.template triangularView<Upper>();
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if (rows*cols>1)
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{
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VERIFY(m1up.isUpperTriangular());
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VERIFY(m2up.transpose().isLowerTriangular());
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VERIFY(!m2.isLowerTriangular());
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}
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// test overloaded operator+=
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r1.setZero();
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r2.setZero();
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r1.template triangularView<Upper>() += m1;
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r2 += m1up;
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VERIFY_IS_APPROX(r1,r2);
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// test overloaded operator=
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m1.setZero();
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m1.template triangularView<Upper>() = 3 * m2;
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m3 = 3 * m2;
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VERIFY_IS_APPROX(m3.template triangularView<Upper>().toDenseMatrix(), m1);
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m1.setZero();
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m1.template triangularView<Lower>() = 3 * m2;
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VERIFY_IS_APPROX(m3.template triangularView<Lower>().toDenseMatrix(), m1);
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m1.setZero();
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m1.template triangularView<StrictlyUpper>() = 3 * m2;
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VERIFY_IS_APPROX(m3.template triangularView<StrictlyUpper>().toDenseMatrix(), m1);
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m1.setZero();
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m1.template triangularView<StrictlyLower>() = 3 * m2;
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VERIFY_IS_APPROX(m3.template triangularView<StrictlyLower>().toDenseMatrix(), m1);
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m1.setRandom();
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m2 = m1.template triangularView<Upper>();
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VERIFY(m2.isUpperTriangular());
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VERIFY(!m2.isLowerTriangular());
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m2 = m1.template triangularView<StrictlyUpper>();
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VERIFY(m2.isUpperTriangular());
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VERIFY(m2.diagonal().isMuchSmallerThan(RealScalar(1)));
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m2 = m1.template triangularView<UnitUpper>();
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VERIFY(m2.isUpperTriangular());
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m2.diagonal().array() -= Scalar(1);
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VERIFY(m2.diagonal().isMuchSmallerThan(RealScalar(1)));
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m2 = m1.template triangularView<Lower>();
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VERIFY(m2.isLowerTriangular());
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VERIFY(!m2.isUpperTriangular());
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m2 = m1.template triangularView<StrictlyLower>();
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VERIFY(m2.isLowerTriangular());
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VERIFY(m2.diagonal().isMuchSmallerThan(RealScalar(1)));
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m2 = m1.template triangularView<UnitLower>();
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VERIFY(m2.isLowerTriangular());
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m2.diagonal().array() -= Scalar(1);
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VERIFY(m2.diagonal().isMuchSmallerThan(RealScalar(1)));
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// test swap
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m1.setOnes();
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m2.setZero();
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m2.template triangularView<Upper>().swap(m1);
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m3.setZero();
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m3.template triangularView<Upper>().setOnes();
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VERIFY_IS_APPROX(m2,m3);
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}
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void bug_159()
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{
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Matrix3d m = Matrix3d::Random().triangularView<Lower>();
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}
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void test_triangular()
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{
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for(int i = 0; i < g_repeat ; i++)
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{
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int r = internal::random<int>(2,20); EIGEN_UNUSED_VARIABLE(r);
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int c = internal::random<int>(2,20); EIGEN_UNUSED_VARIABLE(c);
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CALL_SUBTEST_1( triangular_square(Matrix<float, 1, 1>()) );
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CALL_SUBTEST_2( triangular_square(Matrix<float, 2, 2>()) );
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CALL_SUBTEST_3( triangular_square(Matrix3d()) );
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CALL_SUBTEST_4( triangular_square(Matrix<std::complex<float>,8, 8>()) );
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CALL_SUBTEST_5( triangular_square(MatrixXcd(r,r)) );
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CALL_SUBTEST_6( triangular_square(Matrix<float,Dynamic,Dynamic,RowMajor>(r, r)) );
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CALL_SUBTEST_7( triangular_rect(Matrix<float, 4, 5>()) );
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CALL_SUBTEST_8( triangular_rect(Matrix<double, 6, 2>()) );
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CALL_SUBTEST_9( triangular_rect(MatrixXcf(r, c)) );
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CALL_SUBTEST_5( triangular_rect(MatrixXcd(r, c)) );
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CALL_SUBTEST_6( triangular_rect(Matrix<float,Dynamic,Dynamic,RowMajor>(r, c)) );
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}
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CALL_SUBTEST_1( bug_159() );
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}
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