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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>
//
// 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 SparseMatrixType> void sparse_product(const SparseMatrixType& ref)
{
const int rows = ref.rows();
const int cols = ref.cols();
typedef typename SparseMatrixType::Scalar Scalar;
enum { Flags = SparseMatrixType::Flags };
double density = std::max(8./(rows*cols), 0.01);
typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix;
typedef Matrix<Scalar,Dynamic,1> DenseVector;
// test matrix-matrix product
{
DenseMatrix refMat2 = DenseMatrix::Zero(rows, rows);
DenseMatrix refMat3 = DenseMatrix::Zero(rows, rows);
DenseMatrix refMat4 = DenseMatrix::Zero(rows, rows);
DenseMatrix dm4 = DenseMatrix::Zero(rows, rows);
SparseMatrixType m2(rows, rows);
SparseMatrixType m3(rows, rows);
SparseMatrixType 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());
// sparse * dense
VERIFY_IS_APPROX(dm4=m2*refMat3, refMat4=refMat2*refMat3);
VERIFY_IS_APPROX(dm4=m2*refMat3.transpose(), refMat4=refMat2*refMat3.transpose());
VERIFY_IS_APPROX(dm4=m2.transpose()*refMat3, refMat4=refMat2.transpose()*refMat3);
VERIFY_IS_APPROX(dm4=m2.transpose()*refMat3.transpose(), refMat4=refMat2.transpose()*refMat3.transpose());
// dense * sparse
VERIFY_IS_APPROX(dm4=refMat2*m3, refMat4=refMat2*refMat3);
VERIFY_IS_APPROX(dm4=refMat2*m3.transpose(), refMat4=refMat2*refMat3.transpose());
VERIFY_IS_APPROX(dm4=refMat2.transpose()*m3, refMat4=refMat2.transpose()*refMat3);
VERIFY_IS_APPROX(dm4=refMat2.transpose()*m3.transpose(), refMat4=refMat2.transpose()*refMat3.transpose());
VERIFY_IS_APPROX(m3=m3*m3, refMat3=refMat3*refMat3);
}
// test matrix - diagonal product
if(false) // it compiles, but the precision is terrible. probably doesn't matter in this branch....
{
DenseMatrix refM2 = DenseMatrix::Zero(rows, rows);
DenseMatrix refM3 = DenseMatrix::Zero(rows, rows);
DiagonalMatrix<DenseVector> d1(DenseVector::Random(rows));
SparseMatrixType m2(rows, rows);
SparseMatrixType m3(rows, rows);
initSparse<Scalar>(density, refM2, m2);
initSparse<Scalar>(density, refM3, m3);
VERIFY_IS_APPROX(m3=m2*d1, refM3=refM2*d1);
VERIFY_IS_APPROX(m3=m2.transpose()*d1, refM3=refM2.transpose()*d1);
VERIFY_IS_APPROX(m3=d1*m2, refM3=d1*refM2);
VERIFY_IS_APPROX(m3=d1*m2.transpose(), refM3=d1 * refM2.transpose());
}
// test self adjoint products
{
DenseMatrix b = DenseMatrix::Random(rows, rows);
DenseMatrix x = DenseMatrix::Random(rows, rows);
DenseMatrix refX = DenseMatrix::Random(rows, rows);
DenseMatrix refUp = DenseMatrix::Zero(rows, rows);
DenseMatrix refLo = DenseMatrix::Zero(rows, rows);
DenseMatrix refS = DenseMatrix::Zero(rows, rows);
SparseMatrixType mUp(rows, rows);
SparseMatrixType mLo(rows, rows);
SparseMatrixType mS(rows, rows);
do {
initSparse<Scalar>(density, refUp, mUp, ForceRealDiag|/*ForceNonZeroDiag|*/MakeUpperTriangular);
} while (refUp.isZero());
refLo = refUp.transpose().conjugate();
mLo = mUp.transpose().conjugate();
refS = refUp + refLo;
refS.diagonal() *= 0.5;
mS = mUp + mLo;
for (int k=0; k<mS.outerSize(); ++k)
for (typename SparseMatrixType::InnerIterator it(mS,k); it; ++it)
if (it.index() == k)
it.valueRef() *= 0.5;
VERIFY_IS_APPROX(refS.adjoint(), refS);
VERIFY_IS_APPROX(mS.transpose().conjugate(), mS);
VERIFY_IS_APPROX(mS, refS);
VERIFY_IS_APPROX(x=mS*b, refX=refS*b);
VERIFY_IS_APPROX(x=mUp.template marked<UpperTriangular|SelfAdjoint>()*b, refX=refS*b);
VERIFY_IS_APPROX(x=mLo.template marked<LowerTriangular|SelfAdjoint>()*b, refX=refS*b);
VERIFY_IS_APPROX(x=mS.template marked<SelfAdjoint>()*b, refX=refS*b);
}
}
void test_eigen2_sparse_product()
{
for(int i = 0; i < g_repeat; i++) {
CALL_SUBTEST_1( sparse_product(SparseMatrix<double>(8, 8)) );
CALL_SUBTEST_2( sparse_product(SparseMatrix<std::complex<double> >(16, 16)) );
CALL_SUBTEST_1( sparse_product(SparseMatrix<double>(33, 33)) );
CALL_SUBTEST_3( sparse_product(DynamicSparseMatrix<double>(8, 8)) );
}
}
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