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();
}
void test_kronecker_product()
{
// DM = dense matrix; SM = sparse matrix
Matrix<double, 2, 3> DM_a;
SparseMatrix<double> SM_a(2,3);
SM_a.insert(0,0) = DM_a.coeffRef(0,0) = -0.4461540300782201;
SM_a.insert(0,1) = DM_a.coeffRef(0,1) = -0.8057364375283049;
SM_a.insert(0,2) = DM_a.coeffRef(0,2) = 0.3896572459516341;
SM_a.insert(1,0) = DM_a.coeffRef(1,0) = -0.9076572187376921;
SM_a.insert(1,1) = DM_a.coeffRef(1,1) = 0.6469156566545853;
SM_a.insert(1,2) = DM_a.coeffRef(1,2) = -0.3658010398782789;
MatrixXd DM_b(3,2);
SparseMatrix<double> SM_b(3,2);
SM_b.insert(0,0) = DM_b.coeffRef(0,0) = 0.9004440976767099;
SM_b.insert(0,1) = DM_b.coeffRef(0,1) = -0.2368830858139832;
SM_b.insert(1,0) = DM_b.coeffRef(1,0) = -0.9311078389941825;
SM_b.insert(1,1) = DM_b.coeffRef(1,1) = 0.5310335762980047;
SM_b.insert(2,0) = DM_b.coeffRef(2,0) = -0.1225112806872035;
SM_b.insert(2,1) = DM_b.coeffRef(2,1) = 0.5903998022741264;
SparseMatrix<double,RowMajor> SM_row_a(SM_a), SM_row_b(SM_b);
// test DM_fixedSize = kroneckerProduct(DM_block,DM)
Matrix<double, 6, 6> DM_fix_ab = kroneckerProduct(DM_a.topLeftCorner<2,3>(),DM_b);
CALL_SUBTEST(check_kronecker_product(DM_fix_ab));
CALL_SUBTEST(check_kronecker_product(kroneckerProduct(DM_a.topLeftCorner<2,3>(),DM_b)));
for(int i=0;i<DM_fix_ab.rows();++i)
for(int j=0;j<DM_fix_ab.cols();++j)
VERIFY_IS_APPROX(kroneckerProduct(DM_a,DM_b).coeff(i,j), DM_fix_ab(i,j));
// test DM_block = kroneckerProduct(DM,DM)
MatrixXd DM_block_ab(10,15);
DM_block_ab.block<6,6>(2,5) = kroneckerProduct(DM_a,DM_b);
CALL_SUBTEST(check_kronecker_product(DM_block_ab.block<6,6>(2,5)));
// test DM = kroneckerProduct(DM,DM)
MatrixXd DM_ab = kroneckerProduct(DM_a,DM_b);
CALL_SUBTEST(check_kronecker_product(DM_ab));
CALL_SUBTEST(check_kronecker_product(kroneckerProduct(DM_a,DM_b)));
// test SM = kroneckerProduct(SM,DM)
SparseMatrix<double> SM_ab = kroneckerProduct(SM_a,DM_b);
CALL_SUBTEST(check_kronecker_product(SM_ab));
SparseMatrix<double,RowMajor> SM_ab2 = kroneckerProduct(SM_a,DM_b);
CALL_SUBTEST(check_kronecker_product(SM_ab2));
CALL_SUBTEST(check_kronecker_product(kroneckerProduct(SM_a,DM_b)));
// test SM = kroneckerProduct(DM,SM)
SM_ab.setZero();
SM_ab.insert(0,0)=37.0;
SM_ab = kroneckerProduct(DM_a,SM_b);
CALL_SUBTEST(check_kronecker_product(SM_ab));
SM_ab2.setZero();
SM_ab2.insert(0,0)=37.0;
SM_ab2 = kroneckerProduct(DM_a,SM_b);
CALL_SUBTEST(check_kronecker_product(SM_ab2));
CALL_SUBTEST(check_kronecker_product(kroneckerProduct(DM_a,SM_b)));
// test SM = kroneckerProduct(SM,SM)
SM_ab.resize(2,33);
SM_ab.insert(0,0)=37.0;
SM_ab = kroneckerProduct(SM_a,SM_b);
CALL_SUBTEST(check_kronecker_product(SM_ab));
SM_ab2.resize(5,11);
SM_ab2.insert(0,0)=37.0;
SM_ab2 = kroneckerProduct(SM_a,SM_b);
CALL_SUBTEST(check_kronecker_product(SM_ab2));
CALL_SUBTEST(check_kronecker_product(kroneckerProduct(SM_a,SM_b)));
// test SM = kroneckerProduct(SM,SM) with sparse pattern
SM_a.resize(4,5);
SM_b.resize(3,2);
SM_a.resizeNonZeros(0);
SM_b.resizeNonZeros(0);
SM_a.insert(1,0) = -0.1;
SM_a.insert(0,3) = -0.2;
SM_a.insert(2,4) = 0.3;
SM_a.finalize();
SM_b.insert(0,0) = 0.4;
SM_b.insert(2,1) = -0.5;
SM_b.finalize();
SM_ab.resize(1,1);
SM_ab.insert(0,0)=37.0;
SM_ab = kroneckerProduct(SM_a,SM_b);
CALL_SUBTEST(check_sparse_kronecker_product(SM_ab));
// test dimension of result of DM = kroneckerProduct(DM,DM)
MatrixXd DM_a2(2,1);
MatrixXd DM_b2(5,4);
MatrixXd DM_ab2 = kroneckerProduct(DM_a2,DM_b2);
CALL_SUBTEST(check_dimension(DM_ab2,2*5,1*4));
DM_a2.resize(10,9);
DM_b2.resize(4,8);
DM_ab2 = kroneckerProduct(DM_a2,DM_b2);
CALL_SUBTEST(check_dimension(DM_ab2,10*4,9*8));
for(int i = 0; i < g_repeat; i++)
{
double density = Eigen::internal::random<double>(0.01,0.5);
int ra = Eigen::internal::random<int>(1,50);
int ca = Eigen::internal::random<int>(1,50);
int rb = Eigen::internal::random<int>(1,50);
int cb = Eigen::internal::random<int>(1,50);
SparseMatrix<float,ColMajor> sA(ra,ca), sB(rb,cb), sC;
SparseMatrix<float,RowMajor> sC2;
MatrixXf dA(ra,ca), dB(rb,cb), dC;
initSparse(density, dA, sA);
initSparse(density, dB, sB);
sC = kroneckerProduct(sA,sB);
dC = kroneckerProduct(dA,dB);
VERIFY_IS_APPROX(MatrixXf(sC),dC);
sC = kroneckerProduct(sA.transpose(),sB);
dC = kroneckerProduct(dA.transpose(),dB);
VERIFY_IS_APPROX(MatrixXf(sC),dC);
sC = kroneckerProduct(sA.transpose(),sB.transpose());
dC = kroneckerProduct(dA.transpose(),dB.transpose());
VERIFY_IS_APPROX(MatrixXf(sC),dC);
sC = kroneckerProduct(sA,sB.transpose());
dC = kroneckerProduct(dA,dB.transpose());
VERIFY_IS_APPROX(MatrixXf(sC),dC);
sC2 = kroneckerProduct(sA,sB);
dC = kroneckerProduct(dA,dB);
VERIFY_IS_APPROX(MatrixXf(sC2),dC);
}
}
template<typename SparseMatrixType> void sparse_product()
{
typedef typename SparseMatrixType::Index Index;
Index n = 100;
const Index rows = internal::random<int>(1,n);
const Index cols = internal::random<int>(1,n);
const Index depth = internal::random<int>(1,n);
typedef typename SparseMatrixType::Scalar Scalar;
enum { Flags = SparseMatrixType::Flags };
double density = (std::max)(8./(rows*cols), 0.1);
typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix;
typedef Matrix<Scalar,Dynamic,1> DenseVector;
Scalar s1 = internal::random<Scalar>();
Scalar s2 = internal::random<Scalar>();
// test matrix-matrix product
{
DenseMatrix refMat2 = DenseMatrix::Zero(rows, depth);
DenseMatrix refMat2t = DenseMatrix::Zero(depth, rows);
DenseMatrix refMat3 = DenseMatrix::Zero(depth, cols);
DenseMatrix refMat3t = DenseMatrix::Zero(cols, depth);
DenseMatrix refMat4 = DenseMatrix::Zero(rows, cols);
DenseMatrix refMat4t = DenseMatrix::Zero(cols, rows);
DenseMatrix refMat5 = DenseMatrix::Random(depth, cols);
DenseMatrix refMat6 = DenseMatrix::Random(rows, rows);
DenseMatrix dm4 = DenseMatrix::Zero(rows, rows);
// DenseVector dv1 = DenseVector::Random(rows);
SparseMatrixType m2 (rows, depth);
SparseMatrixType m2t(depth, rows);
SparseMatrixType m3 (depth, cols);
SparseMatrixType m3t(cols, depth);
SparseMatrixType m4 (rows, cols);
SparseMatrixType m4t(cols, rows);
SparseMatrixType m6(rows, rows);
initSparse(density, refMat2, m2);
initSparse(density, refMat2t, m2t);
initSparse(density, refMat3, m3);
initSparse(density, refMat3t, m3t);
initSparse(density, refMat4, m4);
initSparse(density, refMat4t, m4t);
initSparse(density, refMat6, m6);
// int c = internal::random<int>(0,depth-1);
// sparse * sparse
VERIFY_IS_APPROX(m4=m2*m3, refMat4=refMat2*refMat3);
VERIFY_IS_APPROX(m4=m2t.transpose()*m3, refMat4=refMat2t.transpose()*refMat3);
VERIFY_IS_APPROX(m4=m2t.transpose()*m3t.transpose(), refMat4=refMat2t.transpose()*refMat3t.transpose());
VERIFY_IS_APPROX(m4=m2*m3t.transpose(), refMat4=refMat2*refMat3t.transpose());
VERIFY_IS_APPROX(m4 = m2*m3/s1, refMat4 = refMat2*refMat3/s1);
VERIFY_IS_APPROX(m4 = m2*m3*s1, refMat4 = refMat2*refMat3*s1);
VERIFY_IS_APPROX(m4 = s2*m2*m3*s1, refMat4 = s2*refMat2*refMat3*s1);
VERIFY_IS_APPROX(m4=(m2*m3).pruned(0), refMat4=refMat2*refMat3);
VERIFY_IS_APPROX(m4=(m2t.transpose()*m3).pruned(0), refMat4=refMat2t.transpose()*refMat3);
VERIFY_IS_APPROX(m4=(m2t.transpose()*m3t.transpose()).pruned(0), refMat4=refMat2t.transpose()*refMat3t.transpose());
VERIFY_IS_APPROX(m4=(m2*m3t.transpose()).pruned(0), refMat4=refMat2*refMat3t.transpose());
// test aliasing
m4 = m2; refMat4 = refMat2;
VERIFY_IS_APPROX(m4=m4*m3, refMat4=refMat4*refMat3);
// sparse * dense
VERIFY_IS_APPROX(dm4=m2*refMat3, refMat4=refMat2*refMat3);
VERIFY_IS_APPROX(dm4=m2*refMat3t.transpose(), refMat4=refMat2*refMat3t.transpose());
VERIFY_IS_APPROX(dm4=m2t.transpose()*refMat3, refMat4=refMat2t.transpose()*refMat3);
VERIFY_IS_APPROX(dm4=m2t.transpose()*refMat3t.transpose(), refMat4=refMat2t.transpose()*refMat3t.transpose());
VERIFY_IS_APPROX(dm4=m2*(refMat3+refMat3), refMat4=refMat2*(refMat3+refMat3));
VERIFY_IS_APPROX(dm4=m2t.transpose()*(refMat3+refMat5)*0.5, refMat4=refMat2t.transpose()*(refMat3+refMat5)*0.5);
// dense * sparse
VERIFY_IS_APPROX(dm4=refMat2*m3, refMat4=refMat2*refMat3);
VERIFY_IS_APPROX(dm4=refMat2*m3t.transpose(), refMat4=refMat2*refMat3t.transpose());
VERIFY_IS_APPROX(dm4=refMat2t.transpose()*m3, refMat4=refMat2t.transpose()*refMat3);
VERIFY_IS_APPROX(dm4=refMat2t.transpose()*m3t.transpose(), refMat4=refMat2t.transpose()*refMat3t.transpose());
// sparse * dense and dense * sparse outer product
test_outer<SparseMatrixType,DenseMatrix>::run(m2,m4,refMat2,refMat4);
VERIFY_IS_APPROX(m6=m6*m6, refMat6=refMat6*refMat6);
}
// test matrix - diagonal product
{
DenseMatrix refM2 = DenseMatrix::Zero(rows, cols);
DenseMatrix refM3 = DenseMatrix::Zero(rows, cols);
DenseMatrix d3 = DenseMatrix::Zero(rows, cols);
DiagonalMatrix<Scalar,Dynamic> d1(DenseVector::Random(cols));
DiagonalMatrix<Scalar,Dynamic> d2(DenseVector::Random(rows));
SparseMatrixType m2(rows, cols);
SparseMatrixType m3(rows, cols);
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()*d2, refM3=refM2.transpose()*d2);
VERIFY_IS_APPROX(m3=d2*m2, refM3=d2*refM2);
VERIFY_IS_APPROX(m3=d1*m2.transpose(), refM3=d1*refM2.transpose());
// evaluate to a dense matrix to check the .row() and .col() iterator functions
VERIFY_IS_APPROX(d3=m2*d1, refM3=refM2*d1);
VERIFY_IS_APPROX(d3=m2.transpose()*d2, refM3=refM2.transpose()*d2);
VERIFY_IS_APPROX(d3=d2*m2, refM3=d2*refM2);
VERIFY_IS_APPROX(d3=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.adjoint();
mLo = mUp.adjoint();
refS = refUp + refLo;
refS.diagonal() *= 0.5;
mS = mUp + mLo;
// TODO be able to address the diagonal....
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.adjoint(), mS);
VERIFY_IS_APPROX(mS, refS);
VERIFY_IS_APPROX(x=mS*b, refX=refS*b);
VERIFY_IS_APPROX(x=mUp.template selfadjointView<Upper>()*b, refX=refS*b);
VERIFY_IS_APPROX(x=mLo.template selfadjointView<Lower>()*b, refX=refS*b);
VERIFY_IS_APPROX(x=mS.template selfadjointView<Upper|Lower>()*b, refX=refS*b);
}
}
