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.

2 Specification

#include "f11/nagcpp_f11mk.hpp"

template <typename ICOLZP, typename IROWIX, typename A, typename B, typename C>

void function direct_real_gen_matmul(const string trans, const double alpha, const ICOLZP &icolzp, const IROWIX &irowix, const A &a, const B &b, const double beta, C &&c, OptionalF11MK opt)

template <typename ICOLZP, typename IROWIX, typename A, typename B, typename C>

void function direct_real_gen_matmul(const string trans, const double alpha, const ICOLZP &icolzp, const IROWIX &irowix, const A &a, const B &b, const double beta, C &&c)

3 Description

direct_real_gen_matmul computes either the matrix-matrix product

C \leftarrow α A B + β C

, or the transposed matrix-matrix product

C \leftarrow α A^{T} B + β 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

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.

4 References

None.

5 Arguments

1: $trans$ – string Input

On entry: specifies whether or not the matrix

A

is transposed.

$trans ='N'$: $α A B + β C$ is computed.
$trans ='T'$: $α A^{T} B + β C$ is computed.

Constraint:

trans ='N'

'T'

2: $alpha$ – double Input

On entry:

α

, the scalar factor in the matrix multiplication.

3: $icolzp (n + 1)$ – types::f77_integer array Input

On entry: the new column index array of sparse matrix

A

. See Section 2.1.3 in the F11 Chapter Introduction.

4: $irowix (vl_asize)$ – types::f77_integer array Input

On entry: the row index array of sparse matrix

A

. See Section 2.1.3 in the F11 Chapter Introduction.

5: $a (vl_asize)$ – double array Input

On entry: the array of nonzero values in the sparse matrix

A

6: $b (n, m)$ – double array Input

On entry: the

n \times m

matrix

B

7: $beta$ – double Input

On entry: the scalar factor

β

8: $c (n, m)$ – double array Input/Output

On entry: the

n \times m

matrix

C

On exit:

C

is overwritten by

α A B + β C

α A^{T} B + β C

depending on the value of trans.

9: $opt$ – OptionalF11MK Input/Output

Optional parameter container, derived from Optional.

5.1Additional Quantities

1: $n$: $n$ , the order of the matrix $A$
2: $m$: $m$ , the number of columns of matrices $B$ and $C$

6 Exceptions and Warnings

Errors or warnings detected by the function:

All errors and warnings have an associated numeric error code field, errorid, stored either as a member of the thrown exception object (see errorid), or as a member of opt.ifail, depending on how errors and warnings are being handled (see Error Handling for more details).

Raises: ErrorException

$errorid = 1$: On entry, $m = ⟨ value ⟩$ .
Constraint: $m \geq 0$ .

$errorid = 1$: On entry, $n = ⟨ value ⟩$ .
Constraint: $n \geq 0$ .

$errorid = 1$: On entry, $trans = ⟨ value ⟩$ .
Constraint: $trans = "N" or "T"$ .

$errorid = 10601$: On entry, argument $⟨ value ⟩$ must be a vector of size $⟨ value ⟩$ array.
Supplied argument has $⟨ value ⟩$ dimensions.

$errorid = 10601$: On entry, argument $⟨ value ⟩$ must be a vector of size $⟨ value ⟩$ array.
Supplied argument was a vector of size $⟨ value ⟩$ .

$errorid = 10601$: On entry, argument $⟨ value ⟩$ must be a vector of size $⟨ value ⟩$ array.
The size for the supplied array could not be ascertained.

$errorid = 10601$: On entry, argument $⟨ value ⟩$ must be a $⟨ value ⟩$ x $⟨ value ⟩$ array.
Supplied argument has $⟨ value ⟩$ dimensions.

$errorid = 10601$: On entry, argument $⟨ value ⟩$ must be a $⟨ value ⟩$ x $⟨ value ⟩$ array.
Supplied argument was a $⟨ value ⟩$ x $⟨ value ⟩$ array.

$errorid = 10601$: On entry, argument $⟨ value ⟩$ must be a $⟨ value ⟩$ x $⟨ value ⟩$ array.
Not all of the sizes for the supplied array could be ascertained.

$errorid = 10602$: On entry, the raw data component of $⟨ value ⟩$ is null.

$errorid = 10603$: On entry, unable to ascertain a value for $⟨ value ⟩$ .

$errorid = 10604$: On entry, the data in $⟨ value ⟩$ is stored in $⟨ value ⟩$ Major Order.
The data was expected to be in $⟨ value ⟩$ Major Order.