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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008-2010 Gael Guennebaud <g.gael@free.fr>
//
// 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"
#include <Eigen/SparseExtra>
#ifdef EIGEN_CHOLMOD_SUPPORT
#include <Eigen/CholmodSupport>
#endif
template<typename Scalar,typename Index> void sparse_ldlt(int rows, int cols)
{
static bool odd = true;
odd = !odd;
double density = (std::max)(8./(rows*cols), 0.01);
typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix;
typedef Matrix<Scalar,Dynamic,1> DenseVector;
typedef SparseMatrix<Scalar,ColMajor,Index> SparseMatrixType;
SparseMatrixType m2(rows, cols);
DenseMatrix refMat2(rows, cols);
DenseVector b = DenseVector::Random(cols);
DenseVector refX(cols), x(cols);
initSparse<Scalar>(density, refMat2, m2, ForceNonZeroDiag|MakeUpperTriangular, 0, 0);
SparseMatrixType m3 = m2 * m2.adjoint(), m3_lo(rows,rows), m3_up(rows,rows);
DenseMatrix refMat3 = refMat2 * refMat2.adjoint();
refX = refMat3.template selfadjointView<Upper>().ldlt().solve(b);
typedef SparseMatrix<Scalar,Upper|SelfAdjoint,Index> SparseSelfAdjointMatrix;
x = b;
SparseLDLT<SparseSelfAdjointMatrix> ldlt(m3);
if (ldlt.succeeded())
ldlt.solveInPlace(x);
else
std::cerr << "warning LDLT failed\n";
VERIFY_IS_APPROX(refMat3.template selfadjointView<Upper>() * x, b);
VERIFY(refX.isApprox(x,test_precision<Scalar>()) && "LDLT: default");
#ifdef EIGEN_CHOLMOD_SUPPORT
{
x = b;
SparseLDLT<SparseSelfAdjointMatrix, Cholmod> ldlt2(m3);
if (ldlt2.succeeded())
{
ldlt2.solveInPlace(x);
VERIFY_IS_APPROX(refMat3.template selfadjointView<Upper>() * x, b);
VERIFY(refX.isApprox(x,test_precision<Scalar>()) && "LDLT: cholmod solveInPlace");
x = ldlt2.solve(b);
VERIFY_IS_APPROX(refMat3.template selfadjointView<Upper>() * x, b);
VERIFY(refX.isApprox(x,test_precision<Scalar>()) && "LDLT: cholmod solve");
}
else
std::cerr << "warning LDLT failed\n";
}
#endif
// new Simplicial LLT
// new API
{
SparseMatrixType m2(rows, cols);
DenseMatrix refMat2(rows, cols);
DenseVector b = DenseVector::Random(cols);
DenseVector ref_x(cols), x(cols);
DenseMatrix B = DenseMatrix::Random(rows,cols);
DenseMatrix ref_X(rows,cols), X(rows,cols);
initSparse<Scalar>(density, refMat2, m2, ForceNonZeroDiag|MakeLowerTriangular, 0, 0);
for(int i=0; i<rows; ++i)
m2.coeffRef(i,i) = refMat2(i,i) = internal::abs(internal::real(refMat2(i,i)));
SparseMatrixType m3 = m2 * m2.adjoint(), m3_lo(rows,rows), m3_up(rows,rows);
DenseMatrix refMat3 = refMat2 * refMat2.adjoint();
m3_lo.template selfadjointView<Lower>().rankUpdate(m2,0);
m3_up.template selfadjointView<Upper>().rankUpdate(m2,0);
// with a single vector as the rhs
ref_x = refMat3.template selfadjointView<Lower>().llt().solve(b);
x = SimplicialCholesky<SparseMatrixType, Lower>().setMode(odd ? SimplicialCholeskyLLt : SimplicialCholeskyLDLt).compute(m3).solve(b);
VERIFY(ref_x.isApprox(x,test_precision<Scalar>()) && "SimplicialCholesky: solve, full storage, lower, single dense rhs");
x = SimplicialCholesky<SparseMatrixType, Upper>().setMode(odd ? SimplicialCholeskyLLt : SimplicialCholeskyLDLt).compute(m3).solve(b);
VERIFY(ref_x.isApprox(x,test_precision<Scalar>()) && "SimplicialCholesky: solve, full storage, upper, single dense rhs");
x = SimplicialCholesky<SparseMatrixType, Lower>(m3_lo).solve(b);
VERIFY(ref_x.isApprox(x,test_precision<Scalar>()) && "SimplicialCholesky: solve, lower only, single dense rhs");
x = SimplicialCholesky<SparseMatrixType, Upper>(m3_up).solve(b);
VERIFY(ref_x.isApprox(x,test_precision<Scalar>()) && "SimplicialCholesky: solve, upper only, single dense rhs");
// with multiple rhs
ref_X = refMat3.template selfadjointView<Lower>().llt().solve(B);
X = SimplicialCholesky<SparseMatrixType, Lower>().setMode(odd ? SimplicialCholeskyLLt : SimplicialCholeskyLDLt).compute(m3).solve(B);
VERIFY(ref_X.isApprox(X,test_precision<Scalar>()) && "SimplicialCholesky: solve, full storage, lower, multiple dense rhs");
X = SimplicialCholesky<SparseMatrixType, Upper>().setMode(odd ? SimplicialCholeskyLLt : SimplicialCholeskyLDLt).compute(m3).solve(B);
VERIFY(ref_X.isApprox(X,test_precision<Scalar>()) && "SimplicialCholesky: solve, full storage, upper, multiple dense rhs");
// with a sparse rhs
SparseMatrixType spB(rows,cols), spX(rows,cols);
B.diagonal().array() += 1;
spB = B.sparseView(0.5,1);
ref_X = refMat3.template selfadjointView<Lower>().llt().solve(DenseMatrix(spB));
spX = SimplicialCholesky<SparseMatrixType, Lower>(m3).solve(spB);
VERIFY(ref_X.isApprox(spX.toDense(),test_precision<Scalar>()) && "LLT: SimplicialCholesky solve, multiple sparse rhs");
//
spX = SimplicialCholesky<SparseMatrixType, Upper>(m3).solve(spB);
VERIFY(ref_X.isApprox(spX.toDense(),test_precision<Scalar>()) && "LLT: SimplicialCholesky solve, multiple sparse rhs");
}
// for(int i=0; i<rows; ++i)
// m2.coeffRef(i,i) = refMat2(i,i) = internal::abs(internal::real(refMat2(i,i)));
//
// refX = refMat2.template selfadjointView<Upper>().ldlt().solve(b);
// typedef SparseMatrix<Scalar,Upper|SelfAdjoint> SparseSelfAdjointMatrix;
// x = b;
// SparseLDLT<SparseSelfAdjointMatrix> ldlt(m2);
// if (ldlt.succeeded())
// ldlt.solveInPlace(x);
// else
// std::cerr << "warning LDLT failed\n";
//
// VERIFY_IS_APPROX(refMat2.template selfadjointView<Upper>() * x, b);
// VERIFY(refX.isApprox(x,test_precision<Scalar>()) && "LDLT: default");
}
void test_sparse_ldlt()
{
for(int i = 0; i < g_repeat; i++) {
CALL_SUBTEST_1( (sparse_ldlt<double,int>(8, 8)) );
CALL_SUBTEST_1( (sparse_ldlt<double,long int>(8, 8)) );
int s = internal::random<int>(1,300);
CALL_SUBTEST_2( (sparse_ldlt<std::complex<double>,int>(s,s)) );
CALL_SUBTEST_1( (sparse_ldlt<double,int>(s,s)) );
}
}
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