Integer, Intent (In)	::	m, n, lda, ldb, ldc
Integer, Intent (Inout)	::	ifail
Complex (Kind=nag_wp), Intent (In)	::	alpha, a(lda,), beta, b(ldb,)
Complex (Kind=nag_wp), Intent (Inout)	::	c(ldc,*)
Character (1), Intent (In)	::	transa, transb

C Header Interface

#include <nag.h>

void

f01cwf_ (const char *transa, const char *transb, const Integer *m, const Integer *n, const Complex *alpha, const Complex a[], const Integer *lda, const Complex *beta, const Complex b[], const Integer *ldb, Complex c[], const Integer *ldc, Integer *ifail, const Charlen length_transa, const Charlen length_transb)

The routine may be called by the names f01cwf or nagf_matop_complex_addsub.

3 Description

f01cwf performs one of the operations

$C ≔ α A + β B$ ,
$C ≔ α A^{T} + β B$ ,
$C ≔ α A^{H} + β B$ ,
$C ≔ α A + β B^{T}$ ,
$C ≔ α A^{T} + β B^{T}$ ,
$C ≔ α A^{H} + β B^{T}$ ,
$C ≔ α A + β B^{H}$ ,
$C ≔ α A^{T} + β B^{H}$ or
$C ≔ α A^{H} + β B^{H}$ ,

where

A

B

and

C

are matrices,

α

and

β

are scalars,

T

denotes transposition and

H

denotes conjugate transposition. For efficiency, the routine contains special code for the cases when one or both of

α

β

is equal to zero, unity or minus unity. The matrices, or their transposes, must be compatible for addition.

A

and

B

are either

m \times n

n \times m

matrices, depending on whether they are to be transposed before addition.

C

is an

m \times n

matrix.

4 References

None.

5 Arguments

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 $transb ='N'$: The matrix will not be transposed.
transa or $transb ='T'$: The matrix will be transposed.
transa or $transb ='C'$: The matrix will be transposed and conjugated.

Constraint:

transa ​ or ​ transb ='N'

'T'

'C'

3: $m$ – Integer Input

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:

m \geq 0

4: $n$ – Integer Input

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:

n \geq 0

5: $alpha$ – Complex (Kind=nag_wp) Input

On entry: the scalar

α

, by which matrix

A

is multiplied before addition.

6: $a (lda, *)$ – Complex (Kind=nag_wp) array Input

Note: the second dimension of the array a must be at least

\max (1, n)

alpha \neq 0

and

transa ='N'

\max (1, m)

alpha \neq 0

and

transa ='T'

'C'

and at least

1

alpha = 0

On entry: the matrix

A

. If

α = 0

, the array a is not referenced.

7: $lda$ – Integer Input

On entry: the first dimension of the array a as declared in the (sub)program from which f01cwf is called.

Constraints:

if $transa ='N'$ , $lda \geq \max (1, m)$ ;
otherwise $lda \geq \max (1, n)$ .

8: $beta$ – Complex (Kind=nag_wp) Input

On entry: the scalar

β

, by which matrix

B

is multiplied before addition.

9: $b (ldb, *)$ – Complex (Kind=nag_wp) array Input

Note: the second dimension of the array b must be at least

\max (1, n)

beta \neq 0

and

transb ='N'

\max (1, m)

beta \neq 0

and

transb ='T'

'C'

and at least

1

beta = 0

On entry: the matrix

B

. If

β = 0

, the array b is not referenced.

10: $ldb$ – Integer Input

On entry: the first dimension of the array b as declared in the (sub)program from which f01cwf is called.

Constraints:

if $transb ='N'$ , $ldb \geq \max (1, m)$ ;
otherwise $ldb \geq \max (1, n)$ .

11: $c (ldc, *)$ – Complex (Kind=nag_wp) array Output

Note: the second dimension of the array c must be at least

\max (1, n)

On exit: the elements of the

m \times n

matrix

C

12: $ldc$ – Integer Input

On entry: the first dimension of the array c as declared in the (sub)program from which f01cwf is called.

Constraint:

ldc \geq \max (1, m)

13: $ifail$ – Integer Input/Output

On entry: ifail must be set to

0

−1

1

to set behaviour on detection of an error; these values have no effect when no error is detected.

A value of

0

causes the printing of an error message and program execution will be halted; otherwise program execution continues. A value of

−1

means that an error message is printed while a value of

1

means that it is not.

If halting is not appropriate, the value

−1

1

is recommended. If message printing is undesirable, then the value

1

is recommended. Otherwise, the value

0

is recommended. When the value $- 1$ or $1$ is used it is essential to test the value of ifail on exit.

On exit:

ifail = 0

unless the routine detects an error or a warning has been flagged (see Section 6).

6 Error Indicators and Warnings

If on entry

ifail = 0

−1

, explanatory error messages are output on the current error message unit (as defined by x04aaf).

Errors or warnings detected by the routine:

$ifail = 1$: On entry, $transa = ⟨ value ⟩$ .
Constraint: $transa ='N'$ , $'T'$ or $'C'$ .

On entry, $transb = ⟨ value ⟩$ .
Constraint: $transb ='N'$ , $'T'$ or $'C'$ .

$ifail = 2$: On entry, $m = ⟨ value ⟩$ and $n = ⟨ value ⟩$ .
Constraint: $m \geq 0$ and $n \geq 0$ .

$ifail = 3$: On entry, $lda = ⟨ value ⟩$ and $m = ⟨ value ⟩$ .
Constraint: if $transa = ⟨ value ⟩$ , $lda \geq \max (1, m)$ .

On entry, $lda = ⟨ value ⟩$ and $n = ⟨ value ⟩$ .
Constraint: if $transa = ⟨ value ⟩$ , $lda \geq \max (1, n)$ .

$ifail = 4$: On entry, $ldb = ⟨ value ⟩$ and $m = ⟨ value ⟩$ .
Constraint: if $transb = ⟨ value ⟩$ , $ldb \geq \max (1, m)$ .

On entry, $ldb = ⟨ value ⟩$ and $n = ⟨ value ⟩$ .
Constraint: if $transb = ⟨ value ⟩$ , $ldb \geq \max (1, n)$ .

$ifail = 5$: On entry, $ldc = ⟨ value ⟩$ and $m = ⟨ value ⟩$ .
Constraint: $ldc \geq \max (1, m)$ .

$ifail = - 99$: An unexpected error has been triggered by this routine. Please contact NAG.
See Section 7 in the Introduction to the NAG Library FL Interface for further information.

$ifail = - 399$: Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library FL Interface for further information.

$ifail = - 999$: Dynamic memory allocation failed.
See Section 9 in the Introduction to the NAG Library FL Interface for further information.

7 Accuracy

The results returned by f01cwf are accurate to machine precision.

8 Parallelism and Performance

Background information to multithreading can be found in the Multithreading documentation.

f01cwf is threaded by NAG for parallel execution in multithreaded implementations of the NAG Library.

Please consult the X06 Chapter Introduction for information on how to control and interrogate the OpenMP environment used within this routine. Please also consult the Users' Note for your implementation for any additional implementation-specific information.

9 Further Comments

The time taken for a call of f01cwf varies with m, n and the values of

α

and

β

. The routine is quickest if either or both of

α

and

β

are equal to zero, or plus or minus unity.

10 Example

The following program reads in a pair of matrices

A

and

b

, along with values for transa, transb, alpha and beta, and adds them together, printing the result matrix

C

. The process is continued until the end of the input stream is reached.

f01cw: FL CL CPP AD PY MB

NAG FL Interfacef01cwf (complex_​addsub)

▸▿ Contents

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

6 Error Indicators and Warnings

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results

NAG FL Interface
f01cwf (complex_addsub)