NAG Library Routine Document

F01CWF

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     TRANSA – CHARACTER(1)Input

2:     TRANSB – CHARACTER(1)Input

On entry: TRANSA and TRANSB must specify whether or not the matrix $A$ and the matrix $B$, respectively, are to be transposed before addition.

TRANSA or $\mathbf{TRANSB}=\text{'N'}$

The matrix will not be transposed.

TRANSA or $\mathbf{TRANSB}=\text{'T'}$

The matrix will be transposed.

TRANSA or $\mathbf{TRANSB}=\text{'C'}$

The matrix will be transposed and conjugated.

Constraint: $\mathbf{TRANSA}\text{ or }\mathbf{TRANSB}=\text{'N'}$, $\text{'T'}$ or $\text{'C'}$.

3:     M – INTEGERInput

On entry: $m$, the number of rows of the matrices $A$ and $B$ or their transposes. Also the number of rows of the matrix $C$.

Constraint: $\mathbf{M}\ge 0$.

4:     N – INTEGERInput

On entry: $n$, the number of columns of the matrices $A$ and $B$ or their transposes. Also the number of columns of the matrix $C$.

Constraint: $\mathbf{N}\ge 0$.

5:     ALPHA – COMPLEX (KIND=nag_wp)Input

On entry: the scalar $\alpha$, by which matrix $A$ is multiplied before addition.

6:     A(LDA,$*$) – COMPLEX (KIND=nag_wp) arrayInput

Note: the second dimension of the array A must be at least $\max \left(1,\mathbf{N}\right)$ if $\mathbf{ALPHA}\ne 0$ and $\mathbf{TRANSA}=\text{'N'}$, $\max \left(1,\mathbf{M}\right)$ if $\mathbf{ALPHA}\ne 0$ and $\mathbf{TRANSA}=\text{'T'}$ or $\text{'C'}$ and at least $1$ if $\mathbf{ALPHA}=0$.

On entry: the matrix $A$. If $\alpha =0$, the array A is not referenced.

7:     LDA – INTEGERInput

On entry: the first dimension of the array A as declared in the (sub)program from which F01CWF is called.

Constraints:

• if $\mathbf{TRANSA}=\text{'N'}$, $\mathbf{LDA}\ge \max \left(1,\mathbf{M}\right)$;
• otherwise $\mathbf{LDA}\ge \max \left(1,\mathbf{N}\right)$.

8:     BETA – COMPLEX (KIND=nag_wp)Input

On entry: the scalar $\beta$, by which matrix $B$ is multiplied before addition.

9:     B(LDB,$*$) – COMPLEX (KIND=nag_wp) arrayInput

Note: the second dimension of the array B must be at least $\max \left(1,\mathbf{N}\right)$ if $\mathbf{BETA}\ne 0$ and $\mathbf{TRANSB}=\text{'N'}$, $\max \left(1,\mathbf{M}\right)$ if $\mathbf{BETA}\ne 0$ and $\mathbf{TRANSB}=\text{'T'}$ or $\text{'C'}$ and at least $1$ if $\mathbf{BETA}=0$.

On entry: the matrix $B$. If $\beta =0$, the array B is not referenced.

10:   LDB – INTEGERInput

On entry: the first dimension of the array B as declared in the (sub)program from which F01CWF is called.

Constraints:

• if $\mathbf{TRANSB}=\text{'N'}$, $\mathbf{LDB}\ge \max \left(1,\mathbf{M}\right)$;
• otherwise $\mathbf{LDB}\ge \max \left(1,\mathbf{N}\right)$.

11:   C(LDC,$*$) – COMPLEX (KIND=nag_wp) arrayOutput

Note: the second dimension of the array C must be at least $\max \left(1,\mathbf{N}\right)$.

On exit: the elements of the $m$ by $n$ matrix $C$.

12:   LDC – INTEGERInput

On entry: the first dimension of the array C as declared in the (sub)program from which F01CWF is called.

Constraint: $\mathbf{LDC}\ge \max \left(1,\mathbf{M}\right)$.

13:   IFAIL – INTEGERInput/Output

On entry: IFAIL must be set to $0$, $-1\text{ or }1$. If you are unfamiliar with this parameter you should refer to Section 3.3 in the Essential Introduction for details.

For environments where it might be inappropriate to halt program execution when an error is detected, the value $-1\text{ or }1$ is recommended. If the output of error messages is undesirable, then the value $1$ is recommended. Otherwise, if you are not familiar with this parameter, the recommended value is $0$. When the value $-\mathbf{1}\text{ or }\mathbf{1}$ is used it is essential to test the value of IFAIL on exit.

On exit: $\mathbf{IFAIL}=\mathbf{0}$ unless the routine detects an error or a warning has been flagged (see Section 6).

6  Error Indicators and Warnings

$\mathbf{IFAIL}=1$

On entry,

one or both of TRANSA or TRANSB is not equal to 'N', 'T' or 'C'.

$\mathbf{IFAIL}=2$

On entry,

one or both of M or N is less than $0$.

$\mathbf{IFAIL}=3$

On entry,

$\mathbf{LDA}<\max \left(1,P\right)$, where $\mathrm{P}=\mathbf{M}$ if $\mathbf{TRANSA}=\text{'N'}$, and $\mathrm{P}=\mathbf{N}$ otherwise.

$\mathbf{IFAIL}=4$

On entry,

$\mathbf{LDB}<\max \left(1,P\right)$, where $\mathrm{P}=\mathbf{M}$ if $\mathbf{TRANSB}=\text{'N'}$, and $\mathrm{P}=\mathbf{N}$ otherwise.

$\mathbf{IFAIL}=5$

On entry,

$\mathbf{LDC}<\max \left(1,\mathbf{M}\right)$.

7  Accuracy

8  Further Comments

9  Example

9.1  Program Text

Program Text (f01cwfe.f90)

9.2  Program Data

Program Data (f01cwfe.d)

9.3  Program Results

Program Results (f01cwfe.r)