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Several improvements in sparse module:

Browse Source 
* add a LDL^T factorization with solver using code from T. Davis's LDL
  library (LPGL2.1+)
* various bug fixes in trianfular solver, matrix product, etc.
* improve cmake files for the supported libraries
* split the sparse unit test
* etc.
This commit is contained in:
Gael Guennebaud
2008-11-05 13:47:55 +00:00
parent 9aba671cfc
commit 86ccd99d8d
16 changed files with 693 additions and 192 deletions
Download Patch File Download Diff File Expand all files Collapse all files

7
test/CMakeLists.txt
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@@ -158,18 +158,19 @@ ei_add_test(smallvectors)
ei_add_test(map)
ei_add_test(array)
ei_add_test(triangular)
ei_add_test(cholesky " " ${GSL_LIBRARIES})
ei_add_test(cholesky " " "${GSL_LIBRARIES}")
ei_add_test(lu ${EI_OFLAG})
ei_add_test(determinant)
ei_add_test(inverse)
ei_add_test(qr)
ei_add_test(eigensolver " " ${GSL_LIBRARIES})
ei_add_test(eigensolver " " "${GSL_LIBRARIES}")
ei_add_test(svd)
ei_add_test(geometry)
ei_add_test(hyperplane)
ei_add_test(parametrizedline)
ei_add_test(alignedbox)
ei_add_test(regression)
ei_add_test(sparse " " ${SPARSE_LIBS})
ei_add_test(sparse_basic " " "${SPARSE_LIBS}")
ei_add_test(sparse_solvers " " "${SPARSE_LIBS}")
endif(BUILD_TESTS)

92
test/sparse.h Normal file
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@@ -0,0 +1,92 @@
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra. Eigen itself is part of the KDE project.
//
// Copyright (C) 2008 Daniel Gomez Ferro <dgomezferro@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/>.
#ifndef EIGEN_TESTSPARSE_H
#ifdef __GNUC__
#include <ext/hash_map>
#endif
#ifdef EIGEN_GOOGLEHASH_SUPPORT
#include <google/sparse_hash_map>
#endif
#include "main.h"
#include <Eigen/Cholesky>
#include <Eigen/LU>
#include <Eigen/Sparse>
enum {
ForceNonZeroDiag = 1,
MakeLowerTriangular = 2,
MakeUpperTriangular = 4
};
/* Initializes both a sparse and dense matrix with same random values,
* and a ratio of \a density non zero entries.
* \param flags is a union of ForceNonZeroDiag, MakeLowerTriangular and MakeUpperTriangular
* allowing to control the shape of the matrix.
* \param zeroCoords and nonzeroCoords allows to get the coordinate lists of the non zero,
* and zero coefficients respectively.
*/
template<typename Scalar> void
initSparse(double density,
Matrix<Scalar,Dynamic,Dynamic>& refMat,
SparseMatrix<Scalar>& sparseMat,
int flags = 0,
std::vector<Vector2i>* zeroCoords = 0,
std::vector<Vector2i>* nonzeroCoords = 0)
{
sparseMat.startFill(refMat.rows()*refMat.cols()*density);
for(int j=0; j<refMat.cols(); j++)
{
for(int i=0; i<refMat.rows(); i++)
{
Scalar v = (ei_random<double>(0,1) < density) ? ei_random<Scalar>() : Scalar(0);
if ((flags&ForceNonZeroDiag) && (i==j))
{
v = ei_random<Scalar>()*Scalar(3.);
v = v*v + Scalar(5.);
}
if ((flags & MakeLowerTriangular) && j>i)
v = Scalar(0);
else if ((flags & MakeUpperTriangular) && j<i)
v = Scalar(0);
if (v!=Scalar(0))
{
sparseMat.fill(i,j) = v;
if (nonzeroCoords)
nonzeroCoords->push_back(Vector2i(i,j));
}
else if (zeroCoords)
{
zeroCoords->push_back(Vector2i(i,j));
}
refMat(i,j) = v;
}
}
sparseMat.endFill();
}
#endif // EIGEN_TESTSPARSE_H

187
test/sparse.cpp → test/sparse_basic.cpp
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@@ -22,63 +22,7 @@
// License and a copy of the GNU General Public License along with
// Eigen. If not, see <http://www.gnu.org/licenses/>.
#ifdef __GNUC__
#include <ext/hash_map>
#endif
#ifdef EIGEN_GOOGLEHASH_SUPPORT
#include <google/sparse_hash_map>
#endif
#include "main.h"
#include <Eigen/Cholesky>
#include <Eigen/LU>
#include <Eigen/Sparse>
enum {
ForceNonZeroDiag = 1,
MakeLowerTriangular = 2,
MakeUpperTriangular = 4
};
template<typename Scalar> void
initSparse(double density,
Matrix<Scalar,Dynamic,Dynamic>& refMat,
SparseMatrix<Scalar>& sparseMat,
int flags = 0,
std::vector<Vector2i>* zeroCoords = 0,
std::vector<Vector2i>* nonzeroCoords = 0)
{
sparseMat.startFill(refMat.rows()*refMat.cols()*density);
for(int j=0; j<refMat.cols(); j++)
{
for(int i=0; i<refMat.rows(); i++)
{
Scalar v = (ei_random<double>(0,1) < density) ? ei_random<Scalar>() : Scalar(0);
if ((flags&ForceNonZeroDiag) && (i==j))
{
v = ei_random<Scalar>()*Scalar(3.);
v = v*v + Scalar(5.);
}
if ((flags & MakeLowerTriangular) && j>i)
v = Scalar(0);
else if ((flags & MakeUpperTriangular) && j<i)
v = Scalar(0);
if (v!=Scalar(0))
{
sparseMat.fill(i,j) = v;
if (nonzeroCoords)
nonzeroCoords->push_back(Vector2i(i,j));
}
else if (zeroCoords)
{
zeroCoords->push_back(Vector2i(i,j));
}
refMat(i,j) = v;
}
}
sparseMat.endFill();
}
#include "sparse.h"
template<typename SetterType,typename DenseType, typename SparseType>
bool test_random_setter(SparseType& sm, const DenseType& ref, const std::vector<Vector2i>& nonzeroCoords)
@@ -98,7 +42,7 @@ bool test_random_setter(SparseType& sm, const DenseType& ref, const std::vector<
return sm.isApprox(ref);
}
template<typename Scalar> void sparse(int rows, int cols)
template<typename Scalar> void sparse_basic(int rows, int cols)
{
double density = std::max(8./(rows*cols), 0.01);
typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix;
@@ -113,8 +57,8 @@ template<typename Scalar> void sparse(int rows, int cols)
std::vector<Vector2i> nonzeroCoords;
initSparse<Scalar>(density, refMat, m, 0, &zeroCoords, &nonzeroCoords);
VERIFY(zeroCoords.size()>0 && "re-run the test");
VERIFY(nonzeroCoords.size()>0 && "re-run the test");
if (zeroCoords.size()==0 || nonzeroCoords.size()==0)
return;
// test coeff and coeffRef
for (int i=0; i<(int)zeroCoords.size(); ++i)
@@ -128,7 +72,7 @@ template<typename Scalar> void sparse(int rows, int cols)
refMat.coeffRef(nonzeroCoords[0].x(), nonzeroCoords[0].y()) = Scalar(5);
VERIFY_IS_APPROX(m, refMat);
/*
// test InnerIterators and Block expressions
for (int t=0; t<10; ++t)
{
@@ -167,6 +111,7 @@ template<typename Scalar> void sparse(int rows, int cols)
VERIFY_IS_APPROX(m.row(r) + m.row(r), (m + m).row(r));
VERIFY_IS_APPROX(m.row(r) + m.row(r), refMat.row(r) + refMat.row(r));
}
*/
// test SparseSetters
// coherent setter
@@ -234,7 +179,7 @@ template<typename Scalar> void sparse(int rows, int cols)
VERIFY_IS_APPROX(m2.transpose().eval(), refMat2.transpose().eval());
VERIFY_IS_APPROX(m2.transpose(), refMat2.transpose());
}
#if 0
// test matrix product
{
DenseMatrix refMat2 = DenseMatrix::Zero(rows, rows);
@@ -251,123 +196,13 @@ template<typename Scalar> void sparse(int rows, int cols)
VERIFY_IS_APPROX(m4=m2.transpose()*m3.transpose(), refMat4=refMat2.transpose()*refMat3.transpose());
VERIFY_IS_APPROX(m4=m2*m3.transpose(), refMat4=refMat2*refMat3.transpose());
}
// test triangular solver
{
DenseVector vec2 = vec1, vec3 = vec1;
SparseMatrix<Scalar> m2(rows, cols);
DenseMatrix refMat2 = DenseMatrix::Zero(rows, cols);
// lower
initSparse<Scalar>(density, refMat2, m2, ForceNonZeroDiag|MakeLowerTriangular, &zeroCoords, &nonzeroCoords);
VERIFY_IS_APPROX(refMat2.template marked<Lower>().solveTriangular(vec2),
m2.template marked<Lower>().solveTriangular(vec3));
// upper
initSparse<Scalar>(density, refMat2, m2, ForceNonZeroDiag|MakeUpperTriangular, &zeroCoords, &nonzeroCoords);
VERIFY_IS_APPROX(refMat2.template marked<Upper>().solveTriangular(vec2),
m2.template marked<Upper>().solveTriangular(vec3));
// TODO test row major
}
// test LLT
if (!NumTraits<Scalar>::IsComplex)
{
// TODO fix the issue with complex (see SparseLLT::solveInPlace)
SparseMatrix<Scalar> m2(rows, cols);
DenseMatrix refMat2(rows, cols);
DenseVector b = DenseVector::Random(cols);
DenseVector refX(cols), x(cols);
initSparse<Scalar>(density, refMat2, m2, ForceNonZeroDiag|MakeLowerTriangular, &zeroCoords, &nonzeroCoords);
refMat2 += refMat2.adjoint();
refMat2.diagonal() *= 0.5;
refMat2.llt().solve(b, &refX);
typedef SparseMatrix<Scalar,Lower|SelfAdjoint> SparseSelfAdjointMatrix;
x = b;
SparseLLT<SparseSelfAdjointMatrix> (m2).solveInPlace(x);
//VERIFY(refX.isApprox(x,test_precision<Scalar>()) && "LLT: default");
#ifdef EIGEN_CHOLMOD_SUPPORT
x = b;
SparseLLT<SparseSelfAdjointMatrix,Cholmod>(m2).solveInPlace(x);
VERIFY(refX.isApprox(x,test_precision<Scalar>()) && "LLT: cholmod");
#endif
#ifdef EIGEN_TAUCS_SUPPORT
x = b;
SparseLLT<SparseSelfAdjointMatrix,Taucs>(m2,IncompleteFactorization).solveInPlace(x);
VERIFY(refX.isApprox(x,test_precision<Scalar>()) && "LLT: taucs (IncompleteFactorization)");
x = b;
SparseLLT<SparseSelfAdjointMatrix,Taucs>(m2,SupernodalMultifrontal).solveInPlace(x);
VERIFY(refX.isApprox(x,test_precision<Scalar>()) && "LLT: taucs (SupernodalMultifrontal)");
x = b;
SparseLLT<SparseSelfAdjointMatrix,Taucs>(m2,SupernodalLeftLooking).solveInPlace(x);
VERIFY(refX.isApprox(x,test_precision<Scalar>()) && "LLT: taucs (SupernodalLeftLooking)");
#endif
}
// test LU
{
static int count = 0;
SparseMatrix<Scalar> m2(rows, cols);
DenseMatrix refMat2(rows, cols);
DenseVector b = DenseVector::Random(cols);
DenseVector refX(cols), x(cols);
initSparse<Scalar>(density, refMat2, m2, ForceNonZeroDiag, &zeroCoords, &nonzeroCoords);
LU<DenseMatrix> refLu(refMat2);
refLu.solve(b, &refX);
Scalar refDet = refLu.determinant();
x.setZero();
// // SparseLU<SparseMatrix<Scalar> > (m2).solve(b,&x);
// // VERIFY(refX.isApprox(x,test_precision<Scalar>()) && "LU: default");
#ifdef EIGEN_SUPERLU_SUPPORT
{
x.setZero();
SparseLU<SparseMatrix<Scalar>,SuperLU> slu(m2);
if (slu.succeeded())
{
if (slu.solve(b,&x)) {
VERIFY(refX.isApprox(x,test_precision<Scalar>()) && "LU: SuperLU");
}
// std::cerr << refDet << " == " << slu.determinant() << "\n";
if (count==0) {
VERIFY_IS_APPROX(refDet,slu.determinant()); // FIXME det is not very stable for complex
}
}
}
#endif
#ifdef EIGEN_UMFPACK_SUPPORT
{
// check solve
x.setZero();
SparseLU<SparseMatrix<Scalar>,UmfPack> slu(m2);
if (slu.succeeded()) {
if (slu.solve(b,&x)) {
if (count==0) {
VERIFY(refX.isApprox(x,test_precision<Scalar>()) && "LU: umfpack"); // FIXME solve is not very stable for complex
}
}
VERIFY_IS_APPROX(refDet,slu.determinant());
// TODO check the extracted data
//std::cerr << slu.matrixL() << "\n";
}
}
#endif
count++;
}
#endif
}
void test_sparse()
void test_sparse_basic()
{
for(int i = 0; i < g_repeat; i++) {
CALL_SUBTEST( sparse<double>(8, 8) );
CALL_SUBTEST( sparse<std::complex<double> >(16, 16) );
CALL_SUBTEST( sparse<double>(33, 33) );
CALL_SUBTEST( sparse_basic<double>(8, 8) );
CALL_SUBTEST( sparse_basic<std::complex<double> >(16, 16) );
CALL_SUBTEST( sparse_basic<double>(33, 33) );
}
}

180
test/sparse_solvers.cpp Normal file
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@@ -0,0 +1,180 @@
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra. Eigen itself is part of the KDE project.
//
// Copyright (C) 2008 Daniel Gomez Ferro <dgomezferro@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 "sparse.h"
template<typename Scalar> void sparse_solvers(int rows, int cols)
{
double density = std::max(8./(rows*cols), 0.01);
typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix;
typedef Matrix<Scalar,Dynamic,1> DenseVector;
Scalar eps = 1e-6;
DenseVector vec1 = DenseVector::Random(rows);
std::vector<Vector2i> zeroCoords;
std::vector<Vector2i> nonzeroCoords;
// test triangular solver
{
DenseVector vec2 = vec1, vec3 = vec1;
SparseMatrix<Scalar> m2(rows, cols);
DenseMatrix refMat2 = DenseMatrix::Zero(rows, cols);
// lower
initSparse<Scalar>(density, refMat2, m2, ForceNonZeroDiag|MakeLowerTriangular, &zeroCoords, &nonzeroCoords);
VERIFY_IS_APPROX(refMat2.template marked<Lower>().solveTriangular(vec2),
m2.template marked<Lower>().solveTriangular(vec3));
// upper
initSparse<Scalar>(density, refMat2, m2, ForceNonZeroDiag|MakeUpperTriangular, &zeroCoords, &nonzeroCoords);
VERIFY_IS_APPROX(refMat2.template marked<Upper>().solveTriangular(vec2),
m2.template marked<Upper>().solveTriangular(vec3));
// TODO test row major
}
// test LLT
if (!NumTraits<Scalar>::IsComplex)
{
// TODO fix the issue with complex (see SparseLLT::solveInPlace)
SparseMatrix<Scalar> m2(rows, cols);
DenseMatrix refMat2(rows, cols);
DenseVector b = DenseVector::Random(cols);
DenseVector refX(cols), x(cols);
initSparse<Scalar>(density, refMat2, m2, ForceNonZeroDiag|MakeLowerTriangular, &zeroCoords, &nonzeroCoords);
refMat2 += refMat2.adjoint();
refMat2.diagonal() *= 0.5;
refMat2.llt().solve(b, &refX);
typedef SparseMatrix<Scalar,Lower|SelfAdjoint> SparseSelfAdjointMatrix;
x = b;
SparseLLT<SparseSelfAdjointMatrix> (m2).solveInPlace(x);
//VERIFY(refX.isApprox(x,test_precision<Scalar>()) && "LLT: default");
#ifdef EIGEN_CHOLMOD_SUPPORT
x = b;
SparseLLT<SparseSelfAdjointMatrix,Cholmod>(m2).solveInPlace(x);
VERIFY(refX.isApprox(x,test_precision<Scalar>()) && "LLT: cholmod");
#endif
#ifdef EIGEN_TAUCS_SUPPORT
x = b;
SparseLLT<SparseSelfAdjointMatrix,Taucs>(m2,IncompleteFactorization).solveInPlace(x);
VERIFY(refX.isApprox(x,test_precision<Scalar>()) && "LLT: taucs (IncompleteFactorization)");
x = b;
SparseLLT<SparseSelfAdjointMatrix,Taucs>(m2,SupernodalMultifrontal).solveInPlace(x);
VERIFY(refX.isApprox(x,test_precision<Scalar>()) && "LLT: taucs (SupernodalMultifrontal)");
x = b;
SparseLLT<SparseSelfAdjointMatrix,Taucs>(m2,SupernodalLeftLooking).solveInPlace(x);
VERIFY(refX.isApprox(x,test_precision<Scalar>()) && "LLT: taucs (SupernodalLeftLooking)");
#endif
}
// test LDLT
if (!NumTraits<Scalar>::IsComplex)
{
// TODO fix the issue with complex (see SparseLDT::solveInPlace)
SparseMatrix<Scalar> m2(rows, cols);
DenseMatrix refMat2(rows, cols);
DenseVector b = DenseVector::Random(cols);
DenseVector refX(cols), x(cols);
initSparse<Scalar>(density, refMat2, m2, ForceNonZeroDiag|MakeUpperTriangular, &zeroCoords, &nonzeroCoords);
refMat2 += refMat2.adjoint();
refMat2.diagonal() *= 0.5;
refMat2.ldlt().solve(b, &refX);
typedef SparseMatrix<Scalar,Lower|SelfAdjoint> SparseSelfAdjointMatrix;
x = b;
SparseLDLT<SparseSelfAdjointMatrix> ldlt(m2);
if (ldlt.succeeded())
ldlt.solveInPlace(x);
VERIFY(refX.isApprox(x,test_precision<Scalar>()) && "LDLT: default");
}
// test LU
{
static int count = 0;
SparseMatrix<Scalar> m2(rows, cols);
DenseMatrix refMat2(rows, cols);
DenseVector b = DenseVector::Random(cols);
DenseVector refX(cols), x(cols);
initSparse<Scalar>(density, refMat2, m2, ForceNonZeroDiag, &zeroCoords, &nonzeroCoords);
LU<DenseMatrix> refLu(refMat2);
refLu.solve(b, &refX);
Scalar refDet = refLu.determinant();
x.setZero();
// // SparseLU<SparseMatrix<Scalar> > (m2).solve(b,&x);
// // VERIFY(refX.isApprox(x,test_precision<Scalar>()) && "LU: default");
#ifdef EIGEN_SUPERLU_SUPPORT
{
x.setZero();
SparseLU<SparseMatrix<Scalar>,SuperLU> slu(m2);
if (slu.succeeded())
{
if (slu.solve(b,&x)) {
VERIFY(refX.isApprox(x,test_precision<Scalar>()) && "LU: SuperLU");
}
// std::cerr << refDet << " == " << slu.determinant() << "\n";
if (count==0) {
VERIFY_IS_APPROX(refDet,slu.determinant()); // FIXME det is not very stable for complex
}
}
}
#endif
#ifdef EIGEN_UMFPACK_SUPPORT
{
// check solve
x.setZero();
SparseLU<SparseMatrix<Scalar>,UmfPack> slu(m2);
if (slu.succeeded()) {
if (slu.solve(b,&x)) {
if (count==0) {
VERIFY(refX.isApprox(x,test_precision<Scalar>()) && "LU: umfpack"); // FIXME solve is not very stable for complex
}
}
VERIFY_IS_APPROX(refDet,slu.determinant());
// TODO check the extracted data
//std::cerr << slu.matrixL() << "\n";
}
}
#endif
count++;
}
}
void test_sparse_solvers()
{
for(int i = 0; i < g_repeat; i++) {
CALL_SUBTEST( sparse_solvers<double>(8, 8) );
CALL_SUBTEST( sparse_solvers<std::complex<double> >(16, 16) );
CALL_SUBTEST( sparse_solvers<double>(33, 33) );
}
}