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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>
//
// 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>
template<typename MatrixType> void inverse(const MatrixType& m) { using std::abs; typedef typename MatrixType::Index Index; /* this test covers the following files:
Inverse.h */ Index rows = m.rows(); Index cols = m.cols();
typedef typename MatrixType::Scalar Scalar;
MatrixType m1(rows, cols), m2(rows, cols), identity = MatrixType::Identity(rows, rows); createRandomPIMatrixOfRank(rows,rows,rows,m1); m2 = m1.inverse(); VERIFY_IS_APPROX(m1, m2.inverse() );
VERIFY_IS_APPROX((Scalar(2)*m2).inverse(), m2.inverse()*Scalar(0.5));
VERIFY_IS_APPROX(identity, m1.inverse() * m1 ); VERIFY_IS_APPROX(identity, m1 * m1.inverse() );
VERIFY_IS_APPROX(m1, m1.inverse().inverse() );
// since for the general case we implement separately row-major and col-major, test that
VERIFY_IS_APPROX(MatrixType(m1.transpose().inverse()), MatrixType(m1.inverse().transpose()));
#if !defined(EIGEN_TEST_PART_5) && !defined(EIGEN_TEST_PART_6)
typedef typename NumTraits<Scalar>::Real RealScalar; typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, 1> VectorType; //computeInverseAndDetWithCheck tests
//First: an invertible matrix
bool invertible; RealScalar det;
m2.setZero(); m1.computeInverseAndDetWithCheck(m2, det, invertible); VERIFY(invertible); VERIFY_IS_APPROX(identity, m1*m2); VERIFY_IS_APPROX(det, m1.determinant());
m2.setZero(); m1.computeInverseWithCheck(m2, invertible); VERIFY(invertible); VERIFY_IS_APPROX(identity, m1*m2);
//Second: a rank one matrix (not invertible, except for 1x1 matrices)
VectorType v3 = VectorType::Random(rows); MatrixType m3 = v3*v3.transpose(), m4(rows,cols); m3.computeInverseAndDetWithCheck(m4, det, invertible); VERIFY( rows==1 ? invertible : !invertible ); VERIFY_IS_MUCH_SMALLER_THAN(abs(det-m3.determinant()), RealScalar(1)); m3.computeInverseWithCheck(m4, invertible); VERIFY( rows==1 ? invertible : !invertible ); // check with submatrices
{ Matrix<Scalar, MatrixType::RowsAtCompileTime+1, MatrixType::RowsAtCompileTime+1, MatrixType::Options> m5; m5.setRandom(); m5.topLeftCorner(rows,rows) = m1; m2 = m5.template topLeftCorner<MatrixType::RowsAtCompileTime,MatrixType::ColsAtCompileTime>().inverse(); VERIFY_IS_APPROX( (m5.template topLeftCorner<MatrixType::RowsAtCompileTime,MatrixType::ColsAtCompileTime>()), m2.inverse() ); } #endif
// check in-place inversion
if(MatrixType::RowsAtCompileTime>=2 && MatrixType::RowsAtCompileTime<=4) { // in-place is forbidden
VERIFY_RAISES_ASSERT(m1 = m1.inverse()); } else { m2 = m1.inverse(); m1 = m1.inverse(); VERIFY_IS_APPROX(m1,m2); } }
void test_inverse() { int s = 0; for(int i = 0; i < g_repeat; i++) { CALL_SUBTEST_1( inverse(Matrix<double,1,1>()) ); CALL_SUBTEST_2( inverse(Matrix2d()) ); CALL_SUBTEST_3( inverse(Matrix3f()) ); CALL_SUBTEST_4( inverse(Matrix4f()) ); CALL_SUBTEST_4( inverse(Matrix<float,4,4,DontAlign>()) ); s = internal::random<int>(50,320); CALL_SUBTEST_5( inverse(MatrixXf(s,s)) ); TEST_SET_BUT_UNUSED_VARIABLE(s) s = internal::random<int>(25,100); CALL_SUBTEST_6( inverse(MatrixXcd(s,s)) ); TEST_SET_BUT_UNUSED_VARIABLE(s) CALL_SUBTEST_7( inverse(Matrix4d()) ); CALL_SUBTEST_7( inverse(Matrix<double,4,4,DontAlign>()) ); } }
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