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4x4 inverse:

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* change block selection threshold from 1e-2 to 1e-1
* add rigorous precision test
This commit is contained in:
Benoit Jacob 2009-11-23 10:13:21 -05:00
parent 06f11f3379
commit 44d0d667cd
5 changed files with 100 additions and 14 deletions
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7
Eigen/src/LU/Inverse.h
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@ -235,8 +235,11 @@ struct ei_compute_inverse<MatrixType, ResultType, 4>
int good_row0, good_row1, good_i;
Matrix<RealScalar,6,1> absdet;
// any 2x2 block with determinant above this threshold will be considered good enough
RealScalar d = (matrix.col(0).squaredNorm()+matrix.col(1).squaredNorm()) * RealScalar(1e-2);
// any 2x2 block with determinant above this threshold will be considered good enough.
// The magic value 1e-1 here comes from experimentation. The bigger it is, the higher the precision,
// the slower the computation. This value 1e-1 gives precision almost as good as the brutal cofactors
// algorithm, both in average and in worst-case precision.
RealScalar d = (matrix.col(0).squaredNorm()+matrix.col(1).squaredNorm()) * RealScalar(1e-1);
#define ei_inv_size4_helper_macro(i,row0,row1) \
absdet[i] = ei_abs(matrix.coeff(row0,0)*matrix.coeff(row1,1) \
- matrix.coeff(row0,1)*matrix.coeff(row1,0)); \

2
test/CMakeLists.txt
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@ -160,6 +160,8 @@ ei_add_test(swap)
ei_add_test(conservative_resize)
ei_add_test(permutationmatrices)
ei_add_test(prec_inverse_4x4)
ei_add_property(EIGEN_TESTING_SUMMARY "CXX: ${CMAKE_CXX_COMPILER}\n")
if(CMAKE_COMPILER_IS_GNUCXX)
execute_process(COMMAND ${CMAKE_CXX_COMPILER} --version COMMAND head -n 1 OUTPUT_VARIABLE EIGEN_CXX_VERSION_STRING OUTPUT_STRIP_TRAILING_WHITESPACE)

8
test/inverse.cpp
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@ -104,12 +104,4 @@ void test_inverse()
s = ei_random<int>(25,100);
CALL_SUBTEST_6( inverse(MatrixXcd(s,s)) );
}
#ifdef EIGEN_TEST_PART_4
// test some tricky cases for 4x4 matrices
VERIFY_IS_APPROX((Matrix4f() << 0,0,1,0, 1,0,0,0, 0,1,0,0, 0,0,0,1).finished().inverse(),
(Matrix4f() << 0,1,0,0, 0,0,1,0, 1,0,0,0, 0,0,0,1).finished());
VERIFY_IS_APPROX((Matrix4f() << 1,0,0,0, 0,0,1,0, 0,0,0,1, 0,1,0,0).finished().inverse(),
(Matrix4f() << 1,0,0,0, 0,0,0,1, 0,1,0,0, 0,0,1,0).finished());
#endif
}

11
test/main.h
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@ -372,6 +372,14 @@ template<> struct GetDifferentType<double> { typedef float type; };
template<typename T> struct GetDifferentType<std::complex<T> >
{ typedef std::complex<typename GetDifferentType<T>::type> type; };
template<typename T> std::string type_name() { return "other"; }
template<> std::string type_name<float>() { return "float"; }
template<> std::string type_name<double>() { return "double"; }
template<> std::string type_name<int>() { return "int"; }
template<> std::string type_name<std::complex<float> >() { return "complex<float>"; }
template<> std::string type_name<std::complex<double> >() { return "complex<double>"; }
template<> std::string type_name<std::complex<int> >() { return "complex<int>"; }
// forward declaration of the main test function
void EIGEN_CAT(test_,EIGEN_TEST_FUNC)();
@ -445,6 +453,3 @@ int main(int argc, char *argv[])
EIGEN_CAT(test_,EIGEN_TEST_FUNC)();
return 0;
}

84
test/prec_inverse_4x4.cpp Normal file
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@ -0,0 +1,84 @@
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@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"
#include <Eigen/LU>
#include <algorithm>
template<typename MatrixType> void inverse_permutation_4x4()
{
typedef typename MatrixType::Scalar Scalar;
typedef typename MatrixType::RealScalar RealScalar;
double error_max = 0.;
Vector4i indices(0,1,2,3);
for(int i = 0; i < 24; ++i)
{
MatrixType m = PermutationMatrix<4>(indices);
MatrixType inv = m.inverse();
double error = double( (m*inv-MatrixType::Identity()).norm() / epsilon<Scalar>() );
error_max = std::max(error_max, error);
std::next_permutation(indices.data(),indices.data()+4);
}
std::cerr << "inverse_permutation_4x4, Scalar = " << type_name<Scalar>() << std::endl;
EIGEN_DEBUG_VAR(error_max);
VERIFY(error_max < (NumTraits<Scalar>::IsComplex ? 150.0 : 60.) );
}
template<typename MatrixType> void inverse_general_4x4(int repeat)
{
typedef typename MatrixType::Scalar Scalar;
typedef typename MatrixType::RealScalar RealScalar;
double error_sum = 0., error_max = 0.;
for(int i = 0; i < repeat; ++i)
{
MatrixType m;
RealScalar absdet;
do {
m = MatrixType::Random();
absdet = ei_abs(m.determinant());
} while(absdet == RealScalar(0));
MatrixType inv = m.inverse();
double error = double( (m*inv-MatrixType::Identity()).norm() * absdet / epsilon<Scalar>() );
error_sum += error;
error_max = std::max(error_max, error);
}
std::cerr << "inverse_general_4x4, Scalar = " << type_name<Scalar>() << std::endl;
double error_avg = error_sum / repeat;
EIGEN_DEBUG_VAR(error_avg);
EIGEN_DEBUG_VAR(error_max);
VERIFY(error_avg < (NumTraits<Scalar>::IsComplex ? 8.4 : 1.4) );
VERIFY(error_max < (NumTraits<Scalar>::IsComplex ? 150.0 : 60.) );
}
void test_prec_inverse_4x4()
{
CALL_SUBTEST_1((inverse_permutation_4x4<Matrix4f>()));
CALL_SUBTEST_1(( inverse_general_4x4<Matrix4f>(200000 * g_repeat) ));
CALL_SUBTEST_2((inverse_permutation_4x4<Matrix<double,4,4,RowMajor> >()));
CALL_SUBTEST_2(( inverse_general_4x4<Matrix<double,4,4,RowMajor> >(200000 * g_repeat) ));
CALL_SUBTEST_3((inverse_permutation_4x4<Matrix4cf>()));
CALL_SUBTEST_3((inverse_general_4x4<Matrix4cf>(50000 * g_repeat)));
}