121 lines
5.1 KiB
C++
121 lines
5.1 KiB
C++
// This file is part of Eigen, a lightweight C++ template library
|
|
// for linear algebra.
|
|
//
|
|
// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
|
|
//
|
|
// 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 "sparse.h"
|
|
|
|
template <typename Scalar>
|
|
void initSPD(double density, Matrix<Scalar, Dynamic, Dynamic>& refMat, SparseMatrix<Scalar>& sparseMat) {
|
|
Matrix<Scalar, Dynamic, Dynamic> aux(refMat.rows(), refMat.cols());
|
|
initSparse(density, refMat, sparseMat);
|
|
refMat = refMat * refMat.adjoint();
|
|
for (int k = 0; k < 2; ++k) {
|
|
initSparse(density, aux, sparseMat, ForceNonZeroDiag);
|
|
refMat += aux * aux.adjoint();
|
|
}
|
|
sparseMat.setZero();
|
|
for (int j = 0; j < sparseMat.cols(); ++j)
|
|
for (int i = j; i < sparseMat.rows(); ++i)
|
|
if (refMat(i, j) != Scalar(0)) sparseMat.insert(i, j) = refMat(i, j);
|
|
sparseMat.finalize();
|
|
}
|
|
|
|
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 - dense
|
|
initSparse<Scalar>(density, refMat2, m2, ForceNonZeroDiag | MakeLowerTriangular, &zeroCoords, &nonzeroCoords);
|
|
VERIFY_IS_APPROX(refMat2.template triangularView<Lower>().solve(vec2),
|
|
m2.template triangularView<Lower>().solve(vec3));
|
|
|
|
// upper - dense
|
|
initSparse<Scalar>(density, refMat2, m2, ForceNonZeroDiag | MakeUpperTriangular, &zeroCoords, &nonzeroCoords);
|
|
VERIFY_IS_APPROX(refMat2.template triangularView<Upper>().solve(vec2),
|
|
m2.template triangularView<Upper>().solve(vec3));
|
|
VERIFY_IS_APPROX(refMat2.conjugate().template triangularView<Upper>().solve(vec2),
|
|
m2.conjugate().template triangularView<Upper>().solve(vec3));
|
|
{
|
|
SparseMatrix<Scalar> cm2(m2);
|
|
// Index rows, Index cols, Index nnz, Index* outerIndexPtr, Index* innerIndexPtr, Scalar* valuePtr
|
|
Map<SparseMatrix<Scalar> > mm2(rows, cols, cm2.nonZeros(), cm2.outerIndexPtr(), cm2.innerIndexPtr(),
|
|
cm2.valuePtr());
|
|
VERIFY_IS_APPROX(refMat2.conjugate().template triangularView<Upper>().solve(vec2),
|
|
mm2.conjugate().template triangularView<Upper>().solve(vec3));
|
|
}
|
|
|
|
// lower - transpose
|
|
initSparse<Scalar>(density, refMat2, m2, ForceNonZeroDiag | MakeLowerTriangular, &zeroCoords, &nonzeroCoords);
|
|
VERIFY_IS_APPROX(refMat2.transpose().template triangularView<Upper>().solve(vec2),
|
|
m2.transpose().template triangularView<Upper>().solve(vec3));
|
|
|
|
// upper - transpose
|
|
initSparse<Scalar>(density, refMat2, m2, ForceNonZeroDiag | MakeUpperTriangular, &zeroCoords, &nonzeroCoords);
|
|
VERIFY_IS_APPROX(refMat2.transpose().template triangularView<Lower>().solve(vec2),
|
|
m2.transpose().template triangularView<Lower>().solve(vec3));
|
|
|
|
SparseMatrix<Scalar> matB(rows, rows);
|
|
DenseMatrix refMatB = DenseMatrix::Zero(rows, rows);
|
|
|
|
// lower - sparse
|
|
initSparse<Scalar>(density, refMat2, m2, ForceNonZeroDiag | MakeLowerTriangular);
|
|
initSparse<Scalar>(density, refMatB, matB);
|
|
refMat2.template triangularView<Lower>().solveInPlace(refMatB);
|
|
m2.template triangularView<Lower>().solveInPlace(matB);
|
|
VERIFY_IS_APPROX(matB.toDense(), refMatB);
|
|
|
|
// upper - sparse
|
|
initSparse<Scalar>(density, refMat2, m2, ForceNonZeroDiag | MakeUpperTriangular);
|
|
initSparse<Scalar>(density, refMatB, matB);
|
|
refMat2.template triangularView<Upper>().solveInPlace(refMatB);
|
|
m2.template triangularView<Upper>().solveInPlace(matB);
|
|
VERIFY_IS_APPROX(matB, refMatB);
|
|
|
|
// test deprecated API
|
|
initSparse<Scalar>(density, refMat2, m2, ForceNonZeroDiag | MakeLowerTriangular, &zeroCoords, &nonzeroCoords);
|
|
VERIFY_IS_APPROX(refMat2.template triangularView<Lower>().solve(vec2),
|
|
m2.template triangularView<Lower>().solve(vec3));
|
|
|
|
// test empty triangular matrix
|
|
{
|
|
m2.resize(0, 0);
|
|
refMatB.resize(0, refMatB.cols());
|
|
DenseMatrix res = m2.template triangularView<Lower>().solve(refMatB);
|
|
VERIFY_IS_EQUAL(res.rows(), 0);
|
|
VERIFY_IS_EQUAL(res.cols(), refMatB.cols());
|
|
res = refMatB;
|
|
m2.template triangularView<Lower>().solveInPlace(res);
|
|
VERIFY_IS_EQUAL(res.rows(), 0);
|
|
VERIFY_IS_EQUAL(res.cols(), refMatB.cols());
|
|
}
|
|
}
|
|
}
|
|
|
|
EIGEN_DECLARE_TEST(sparse_solvers) {
|
|
for (int i = 0; i < g_repeat; i++) {
|
|
CALL_SUBTEST_1(sparse_solvers<double>(8, 8));
|
|
int s = internal::random<int>(1, 300);
|
|
CALL_SUBTEST_2(sparse_solvers<std::complex<double> >(s, s));
|
|
CALL_SUBTEST_1(sparse_solvers<double>(s, s));
|
|
}
|
|
}
|