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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;
/* 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;
Scalar 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);
}
}
template<typename Scalar>
void inverse_zerosized()
{
Matrix<Scalar,Dynamic,Dynamic> A(0,0);
{
Matrix<Scalar,0,1> b, x;
x = A.inverse() * b;
}
{
Matrix<Scalar,Dynamic,Dynamic> b(0,1), x;
x = A.inverse() * b;
VERIFY_IS_EQUAL(x.rows(), 0);
VERIFY_IS_EQUAL(x.cols(), 1);
}
}
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)
CALL_SUBTEST_5( inverse_zerosized<float>() );
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>()) );
CALL_SUBTEST_8( inverse(Matrix4cd()) );
}
}