NAG Library Routine Document

F01CKF

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     $\mathrm{A}\left(\mathbf{N},\mathbf{P}\right)$ – REAL (KIND=nag_wp) arrayOutput

On exit: if $\mathbf{OPT}=1$, A contains the result of the matrix multiplication.

2:     $\mathrm{B}\left(\mathbf{N},\mathbf{M}\right)$ – REAL (KIND=nag_wp) arrayInput/Output

On entry: the $n$ by $m$ matrix $B$.

On exit: if $\mathbf{OPT}=2$, B contains the result of the multiplication.

3:     $\mathrm{C}\left(\mathbf{M},\mathbf{P}\right)$ – REAL (KIND=nag_wp) arrayInput/Output

On entry: the $m$ by $p$ matrix $C$.

On exit: if $\mathbf{OPT}=3$, C contains the result of the multiplication.

4:     $\mathrm{N}$ – INTEGERInput

On entry: $n$, the number of rows of the array $A$ and of the array $B$.

Constraints:

• if $\mathbf{OPT}=3$, $\mathbf{N}=\mathbf{M}$;
• otherwise $\mathbf{N}\ge 1$.

5:     $\mathrm{P}$ – INTEGERInput

On entry: $p$, the number of columns of the array $A$ and of the array $C$.

Constraints:

• if $\mathbf{OPT}=2$, $\mathbf{P}=\mathbf{M}$;
• otherwise $\mathbf{P}\ge 1$.

6:     $\mathrm{M}$ – INTEGERInput

On entry: $m$, the number of columns of the array $B$ and rows of the array $C$.

Constraints:

• if $\mathbf{OPT}=2$, $\mathbf{M}=\mathbf{P}$;
• if $\mathbf{OPT}=3$, $\mathbf{M}=\mathbf{N}$;
• if $\mathbf{OPT}\ne 1$, $\mathbf{M}\le \mathbf{IZ}$;
• otherwise $\mathbf{M}\ge 1$.

7:     $\mathrm{Z}\left(\mathbf{IZ}\right)$ – REAL (KIND=nag_wp) arrayWorkspace

8:     $\mathrm{IZ}$ – INTEGERInput

On entry: the dimension of the array Z as declared in the (sub)program from which F01CKF is called.

Constraints:

• if $\mathbf{OPT}=1$, $\mathbf{IZ}\ge 1$;
• if $\mathbf{OPT}\ne 1$, $\mathbf{IZ}\ge \mathbf{M}$.

9:     $\mathrm{OPT}$ – INTEGERInput

On entry: the value of OPT determines which array is to contain the final result.

$\mathbf{OPT}=1$

A must be distinct from B and C and, on exit, contains the result. B and C need not be distinct in this case.

$\mathbf{OPT}=2$

B must be distinct from C and on exit, contains the result. A is not used in this case and need not be distinct from B or C.

$\mathbf{OPT}=3$

C must be distinct from B and on exit, contains the result. A is not used in this case and need not be distinct from B or C.

Constraint: $1\le \mathbf{OPT}\le 3$.

10:   $\mathrm{IFAIL}$ – 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, M or P or $\mathbf{N}\le 0$.

$\mathbf{IFAIL}=2$

$\mathbf{OPT}=2$ and $\mathbf{M}\ne \mathbf{P}$.

$\mathbf{IFAIL}=3$

$\mathbf{OPT}=3$ and $\mathbf{N}\ne \mathbf{M}$.

$\mathbf{IFAIL}=4$

$\mathbf{OPT}\ne 1$ and $\mathbf{IZ}<\mathbf{M}$.

$\mathbf{IFAIL}=-99$

An unexpected error has been triggered by this routine. Please contact NAG.

See Section 3.8 in the Essential Introduction for further information.

$\mathbf{IFAIL}=-399$

Your licence key may have expired or may not have been installed correctly.

See Section 3.7 in the Essential Introduction for further information.

$\mathbf{IFAIL}=-999$

Dynamic memory allocation failed.

See Section 3.6 in the Essential Introduction for further information.

7  Accuracy

8  Parallelism and Performance

9  Further Comments

10  Example

10.1  Program Text

Program Text (f01ckfe.f90)

10.2  Program Data

Program Data (f01ckfe.d)

10.3  Program Results

Program Results (f01ckfe.r)