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* LU decomposition, supporting all rectangular matrices, with full

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pivoting for better numerical stability. For now the only application is
determinant.
* New determinant unit-test.
* Disable most of Swap.h for now as it makes LU fail (mysterious).
Anyway Swap needs a big overhaul as proposed on IRC.
* Remnants of old class Inverse removed.
* Some warnings fixed.
This commit is contained in:
Benoit Jacob
2008-08-04 04:45:59 +00:00
parent f81dfcf00b
commit c2f8ecf466
11 changed files with 237 additions and 50 deletions
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4
test/CMakeLists.txt
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@@ -2,7 +2,7 @@ IF(BUILD_TESTS)
IF(CMAKE_COMPILER_IS_GNUCXX)
IF(CMAKE_SYSTEM_NAME MATCHES Linux)
SET(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -O1 -g1")
SET(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -g2")
SET(CMAKE_CXX_FLAGS_RELWITHDEBINFO "${CMAKE_CXX_FLAGS_RELWITHDEBINFO} -O2 -g2")
SET(CMAKE_CXX_FLAGS_RELEASE "${CMAKE_CXX_FLAGS_RELEASE} -fno-inline-functions")
SET(CMAKE_CXX_FLAGS_DEBUG "${CMAKE_CXX_FLAGS_DEBUG} -O0 -g2")
@@ -95,7 +95,7 @@ EI_ADD_TEST(map)
EI_ADD_TEST(array)
EI_ADD_TEST(triangular)
EI_ADD_TEST(cholesky)
# EI_ADD_TEST(determinant)
EI_ADD_TEST(determinant)
EI_ADD_TEST(inverse)
EI_ADD_TEST(qr)
EI_ADD_TEST(eigensolver)

72
test/determinant.cpp
View File

@@ -25,54 +25,50 @@
#include "main.h"
#include <Eigen/LU>
template<typename MatrixType> void nullDeterminant(const MatrixType& m)
template<typename MatrixType> void determinant(const MatrixType& m)
{
/* this test covers the following files:
Determinant.h
*/
int rows = m.rows();
int cols = m.cols();
int size = m.rows();
MatrixType m1(size, size), m2(size, size);
m1.setRandom();
m2.setRandom();
typedef typename MatrixType::Scalar Scalar;
typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, MatrixType::ColsAtCompileTime> SquareMatrixType;
typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, 1> VectorType;
MatrixType dinv(rows, cols), dnotinv(rows, cols);
dinv.col(0).setOnes();
dinv.block(0,1, rows, cols-2).setRandom();
dnotinv.col(0).setOnes();
dnotinv.block(0,1, rows, cols-2).setRandom();
dnotinv.col(cols-1).setOnes();
for (int i=0 ; i<rows ; ++i)
{
dnotinv.row(i).block(0,1,1,cols-2) = ei_random<Scalar>(99.999999,100.00000001)*dnotinv.row(i).block(0,1,1,cols-2).normalized();
dnotinv(i,cols-1) = dnotinv.row(i).block(0,1,1,cols-2).norm2();
dinv(i,cols-1) = dinv.row(i).block(0,1,1,cols-2).norm2();
}
SquareMatrixType invertibleCovarianceMatrix = dinv.transpose() * dinv;
SquareMatrixType notInvertibleCovarianceMatrix = dnotinv.transpose() * dnotinv;
std::cout << notInvertibleCovarianceMatrix << "\n" << notInvertibleCovarianceMatrix.determinant() << "\n";
VERIFY_IS_MUCH_SMALLER_THAN(notInvertibleCovarianceMatrix.determinant(),
notInvertibleCovarianceMatrix.cwise().abs().maxCoeff());
VERIFY(invertibleCovarianceMatrix.inverse().exists());
VERIFY(!notInvertibleCovarianceMatrix.inverse().exists());
Scalar x = ei_random<Scalar>();
VERIFY(ei_isApprox(MatrixType::Identity(size, size).determinant(), Scalar(1)));
VERIFY(ei_isApprox((m1*m2).determinant(), m1.determinant() * m2.determinant()));
if(size==1) return;
int i = ei_random<int>(0, size-1);
int j;
do {
j = ei_random<int>(0, size-1);
} while(j==i);
m2 = m1;
m2.row(i).swap(m2.row(j));
VERIFY(ei_isApprox(m2.determinant(), -m1.determinant()));
m2 = m1;
m2.col(i).swap(m2.col(j));
VERIFY(ei_isApprox(m2.determinant(), -m1.determinant()));
VERIFY(ei_isApprox(m2.determinant(), m2.transpose().determinant()));
VERIFY(ei_isApprox(ei_conj(m2.determinant()), m2.adjoint().determinant()));
m2 = m1;
m2.row(i) += x*m2.row(j);
VERIFY(ei_isApprox(m2.determinant(), m1.determinant()));
m2 = m1;
m2.row(i) *= x;
VERIFY(ei_isApprox(m2.determinant(), m1.determinant() * x));
}
void test_determinant()
{
for(int i = 0; i < g_repeat; i++) {
CALL_SUBTEST( nullDeterminant(Matrix<float, 30, 3>()) );
CALL_SUBTEST( nullDeterminant(Matrix<double, 30, 3>()) );
CALL_SUBTEST( nullDeterminant(Matrix<float, 20, 4>()) );
CALL_SUBTEST( nullDeterminant(Matrix<double, 20, 4>()) );
// CALL_SUBTEST( nullDeterminant(MatrixXd(20,4));
CALL_SUBTEST( determinant(Matrix<float, 1, 1>()) );
CALL_SUBTEST( determinant(Matrix<double, 2, 2>()) );
CALL_SUBTEST( determinant(Matrix<double, 3, 3>()) );
CALL_SUBTEST( determinant(Matrix<double, 4, 4>()) );
CALL_SUBTEST( determinant(Matrix<std::complex<double>, 10, 10>()) );
CALL_SUBTEST( determinant(MatrixXd(20, 20)) );
}
}