NAG Library Routine Document

F01CTF

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     $\mathrm{TRANSA}$ – CHARACTER(1)Input

2:     $\mathrm{TRANSB}$ – 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 $\mathbf{TRANSB}=\text{'T'}$ or $\text{'C'}$

The matrix will be transposed.

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

3:     $\mathrm{M}$ – 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:     $\mathrm{N}$ – 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:     $\mathrm{ALPHA}$ – REAL (KIND=nag_wp)Input

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

6:     $\mathrm{A}\left(\mathbf{LDA},*\right)$ – REAL (KIND=nag_wp) arrayInput

Note: the second dimension of the array A must be at least $\max \left(1,\mathbf{N}\right)$ if $\mathbf{TRANSA}=\text{'N'}$, and at least $\max \left(1,\mathbf{M}\right)$ otherwise.

On entry: if $\alpha =0.0$, the elements of array A need not be assigned. If $\alpha \ne 0.0$, then if $\mathbf{TRANSA}=\text{'N'}$, the leading $m$ by $n$ part of A must contain the matrix $A$, otherwise the leading $n$ by $m$ part of A must contain the matrix $A$.

7:     $\mathrm{LDA}$ – INTEGERInput

On entry: the first dimension of the array A as declared in the (sub)program from which F01CTF 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:     $\mathrm{BETA}$ – REAL (KIND=nag_wp)Input

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

9:     $\mathrm{B}\left(\mathbf{LDB},*\right)$ – REAL (KIND=nag_wp) arrayInput

Note: the second dimension of the array B must be at least $\max \left(1,\mathbf{N}\right)$ if $\mathbf{TRANSB}=\text{'N'}$, and at least $\max \left(1,\mathbf{M}\right)$ otherwise.

On entry: if $\beta =0.0$, the elements of array B need not be assigned. If $\beta \ne 0.0$, then if $\mathbf{TRANSA}=\text{'N'}$, the leading $m$ by $n$ part of B must contain the matrix $B$, otherwise the leading $n$ by $m$ part of B must contain the matrix $B$.

10:   $\mathrm{LDB}$ – INTEGERInput

On entry: the first dimension of the array B as declared in the (sub)program from which F01CTF 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:   $\mathrm{C}\left(\mathbf{LDC},*\right)$ – REAL (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:   $\mathrm{LDC}$ – INTEGERInput

On entry: the first dimension of the array C as declared in the (sub)program from which F01CTF is called.

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

13:   $\mathrm{IFAIL}$ – 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,

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,

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

$\mathbf{IFAIL}=-99$

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 (f01ctfe.f90)

10.2  Program Data

Program Data (f01ctfe.d)

10.3  Program Results

Program Results (f01ctfe.r)