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// 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 "main.h"
#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<Scalar>(0,1) < density) ? ei_random<Scalar>() : 0;
if ((flags&ForceNonZeroDiag) && (i==j))
while (ei_abs(v)<1e-2)
v = ei_random<Scalar>();
if ((flags & MakeLowerTriangular) && j>i)
v = 0;
else if ((flags & MakeUpperTriangular) && j<i)
v = 0;
if (v!=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();
}
template<typename Scalar> void sparse(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;
SparseMatrix<Scalar> m(rows, cols);
DenseMatrix refMat = DenseMatrix::Zero(rows, cols);
DenseVector vec1 = DenseVector::Random(rows);
std::vector<Vector2i> zeroCoords;
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");
// test coeff and coeffRef
for (int i=0; i<(int)zeroCoords.size(); ++i)
{
VERIFY_IS_MUCH_SMALLER_THAN( m.coeff(zeroCoords[i].x(),zeroCoords[i].y()), eps );
VERIFY_RAISES_ASSERT( m.coeffRef(zeroCoords[0].x(),zeroCoords[0].y()) = 5 );
}
VERIFY_IS_APPROX(m, refMat);
m.coeffRef(nonzeroCoords[0].x(), nonzeroCoords[0].y()) = Scalar(5);
refMat.coeffRef(nonzeroCoords[0].x(), nonzeroCoords[0].y()) = Scalar(5);
VERIFY_IS_APPROX(m, refMat);
// test InnerIterators and Block expressions
for(int j=0; j<cols; j++)
{
for(int i=0; i<rows; i++)
{
for(int w=1; w<cols-j; w++)
{
for(int h=1; h<rows-i; h++)
{
VERIFY_IS_APPROX(m.block(i,j,h,w), refMat.block(i,j,h,w));
for(int c=0; c<w; c++)
{
VERIFY_IS_APPROX(m.block(i,j,h,w).col(c), refMat.block(i,j,h,w).col(c));
for(int r=0; r<h; r++)
{
VERIFY_IS_APPROX(m.block(i,j,h,w).col(c).coeff(r), refMat.block(i,j,h,w).col(c).coeff(r));
}
}
for(int r=0; r<h; r++)
{
VERIFY_IS_APPROX(m.block(i,j,h,w).row(r), refMat.block(i,j,h,w).row(r));
for(int c=0; c<w; c++)
{
VERIFY_IS_APPROX(m.block(i,j,h,w).row(r).coeff(c), refMat.block(i,j,h,w).row(r).coeff(c));
}
}
}
}
}
}
for(int c=0; c<cols; c++)
{
VERIFY_IS_APPROX(m.col(c) + m.col(c), (m + m).col(c));
VERIFY_IS_APPROX(m.col(c) + m.col(c), refMat.col(c) + refMat.col(c));
}
for(int r=0; r<rows; r++)
{
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
// TODO extend the MatrixSetter
// {
// m.setZero();
// VERIFY_IS_NOT_APPROX(m, refMat);
// SparseSetter<SparseMatrix<Scalar>, FullyCoherentAccessPattern> w(m);
// for (int i=0; i<nonzeroCoords.size(); ++i)
// {
// w->coeffRef(nonzeroCoords[i].x(),nonzeroCoords[i].y()) = refMat.coeff(nonzeroCoords[i].x(),nonzeroCoords[i].y());
// }
// }
// VERIFY_IS_APPROX(m, refMat);
// random setter
{
m.setZero();
VERIFY_IS_NOT_APPROX(m, refMat);
SparseSetter<SparseMatrix<Scalar>, RandomAccessPattern> w(m);
std::vector<Vector2i> remaining = nonzeroCoords;
while(!remaining.empty())
{
int i = ei_random<int>(0,remaining.size()-1);
w->coeffRef(remaining[i].x(),remaining[i].y()) = refMat.coeff(remaining[i].x(),remaining[i].y());
remaining[i] = remaining.back();
remaining.pop_back();
}
}
VERIFY_IS_APPROX(m, refMat);
// test transpose
{
DenseMatrix refMat2 = DenseMatrix::Zero(rows, rows);
SparseMatrix<Scalar> m2(rows, rows);
initSparse<Scalar>(density, refMat2, m2);
VERIFY_IS_APPROX(m2.transpose().eval(), refMat2.transpose().eval());
VERIFY_IS_APPROX(m2.transpose(), refMat2.transpose());
}
// test matrix product
{
DenseMatrix refMat2 = DenseMatrix::Zero(rows, rows);
DenseMatrix refMat3 = DenseMatrix::Zero(rows, rows);
DenseMatrix refMat4 = DenseMatrix::Zero(rows, rows);
SparseMatrix<Scalar> m2(rows, rows);
SparseMatrix<Scalar> m3(rows, rows);
SparseMatrix<Scalar> m4(rows, rows);
initSparse<Scalar>(density, refMat2, m2);
initSparse<Scalar>(density, refMat3, m3);
initSparse<Scalar>(density, refMat4, m4);
VERIFY_IS_APPROX(m4=m2*m3, refMat4=refMat2*refMat3);
VERIFY_IS_APPROX(m4=m2.transpose()*m3, refMat4=refMat2.transpose()*refMat3);
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
{
}
}
void test_sparse()
{
sparse<double>(8, 8);
sparse<double>(16, 16);
sparse<double>(33, 33);
}
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