const OpStringC MIME_DecodeCache_Storage::FileName(OpFileFolder &folder, BOOL get_original_body) const
{
if(get_original_body && source)
{
OpStringC rv0(source->FileName(folder, get_original_body));
return rv0;
}
OpStringC rv(DecodedMIME_Storage::FileName(folder, get_original_body));
return rv;
}
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;
typedef Matrix<Scalar,1,Dynamic> RowDenseVector;
typedef SparseVector<Scalar,0,Index> ColSpVector;
typedef SparseVector<Scalar,RowMajor,Index> RowSpVector;
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);
// sparse matrix * sparse vector
ColSpVector cv0(cols), cv1;
DenseVector dcv0(cols), dcv1;
initSparse(2*density,dcv0, cv0);
RowSpVector rv0(depth), rv1;
RowDenseVector drv0(depth), drv1(rv1);
initSparse(2*density,drv0, rv0);
VERIFY_IS_APPROX(cv1=rv0*m3, dcv1=drv0*refMat3);
VERIFY_IS_APPROX(rv1=rv0*m3, drv1=drv0*refMat3);
VERIFY_IS_APPROX(cv1=m3*cv0, dcv1=refMat3*dcv0);
VERIFY_IS_APPROX(cv1=m3t.adjoint()*cv0, dcv1=refMat3t.adjoint()*dcv0);
VERIFY_IS_APPROX(rv1=m3*cv0, drv1=refMat3*dcv0);
}
// 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());
// also check with a SparseWrapper:
DenseVector v1 = DenseVector::Random(cols);
DenseVector v2 = DenseVector::Random(rows);
VERIFY_IS_APPROX(m3=m2*v1.asDiagonal(), refM3=refM2*v1.asDiagonal());
VERIFY_IS_APPROX(m3=m2.transpose()*v2.asDiagonal(), refM3=refM2.transpose()*v2.asDiagonal());
VERIFY_IS_APPROX(m3=v2.asDiagonal()*m2, refM3=v2.asDiagonal()*refM2);
VERIFY_IS_APPROX(m3=v1.asDiagonal()*m2.transpose(), refM3=v1.asDiagonal()*refM2.transpose());
VERIFY_IS_APPROX(m3=v2.asDiagonal()*m2*v1.asDiagonal(), refM3=v2.asDiagonal()*refM2*v1.asDiagonal());
// 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);
// sparse selfadjointView * sparse
SparseMatrixType mSres(rows,rows);
VERIFY_IS_APPROX(mSres = mLo.template selfadjointView<Lower>()*mS,
refX = refLo.template selfadjointView<Lower>()*refS);
// sparse * sparse selfadjointview
VERIFY_IS_APPROX(mSres = mS * mLo.template selfadjointView<Lower>(),
refX = refS * refLo.template selfadjointView<Lower>());
}
}
