naginterfaces.library.sparse.direct_​real_​gen_​matmul

naginterfaces.library.sparse.direct_real_gen_matmul(trans, alpha, icolzp, irowix, a, b, beta, c=None)

direct_real_gen_matmul computes a matrix-matrix or transposed matrix-matrix product involving a real, square, sparse nonsymmetric matrix stored in compressed column (Harwell–Boeing) format.

For full information please refer to the NAG Library document for f11mk

https://support.nag.com/numeric/nl/nagdoc_30/flhtml/f11/f11mkf.html

Parameters

transstr, length 1

Specifies whether or not the matrix $A$ is transposed.

$trans=\text{'N'}$

$\alpha AB+\beta C$ is computed.

$trans=\text{'T'}$

$\alpha A^{T}B+\beta C$ is computed.

alphafloat

$\alpha$, the scalar factor in the matrix multiplication.

icolzpint, array-like, shape $(n+1)$

The new column index array of sparse matrix $A$. See the F11 Introduction.

irowixint, array-like, shape $\left(\text{asize}\right)$

The row index array of sparse matrix $A$. See the F11 Introduction.

afloat, array-like, shape $\left(\text{asize}\right)$

The array of nonzero values in the sparse matrix $A$.

bfloat, array-like, shape $(n,m)$

The $n\times m$ matrix $B$.

betafloat

The scalar factor $\beta$.

cNone or float, array-like, shape $(n,m)$, optional

The $n\times m$ matrix $C$.

Returns

cfloat, ndarray, shape $(n,m)$

$C$ is overwritten by $\alpha AB+\beta C$ or $\alpha A^{T}B+\beta C$ depending on the value of $trans$.

Raises

NagValueError

(errno $1$)

On entry, $m=⟨value⟩$.

Constraint: $m\ge 0$.

(errno $1$)

On entry, $n=⟨value⟩$.

Constraint: $n\ge 0$.

(errno $1$)

On entry, $trans=⟨value⟩$.

Constraint: $trans=\text{'N'}$ or $\text{'T'}$.

Notes

direct_real_gen_matmul computes either the matrix-matrix product $C\leftarrow \alpha AB+\beta C$, or the transposed matrix-matrix product $C\leftarrow \alpha A^{T}B+\beta C$, according to the value of the argument $trans$, where $A$ is a real $n\times n$ sparse nonsymmetric matrix, of arbitrary sparsity pattern with $\text{nnz}$ nonzero elements, $B$ and $C$ are $n\times m$ real dense matrices. The matrix $A$ is stored in compressed column (Harwell–Boeing) storage format. The array $a$ stores all nonzero elements of $A$, while arrays $icolzp$ and $irowix$ store the compressed column indices and row indices of $A$ respectively.