NAG Library Routine Document

F01CWF

+− Contents

1 Purpose

2 Specification

3 Description

4 References

5 Parameters

6 Error Indicators and Warnings

7 Accuracy

8 Further Comments

+− 9 Example

9.1 Program Text

9.2 Program Data

9.3 Program Results

1 Purpose

F01CWF adds two complex matrices, each one optionally transposed and multiplied by a scalar.

2 Specification

SUBROUTINE F01CWF (	TRANSA, TRANSB, M, N, ALPHA, A, LDA, BETA, B, LDB, C, LDC, IFAIL)
INTEGER	M, N, LDA, LDB, LDC, IFAIL
**complex16***	ALPHA, A(LDA,), BETA, B(LDB,), C(LDC,*)
CHARACTER*1	TRANSA, TRANSB

3 Description

F01CWF performs one of the operations

C:=αA+βB,
C:=αAT+βB,
C:=αAH+βB,
C:=αA+βBT,
C:=αAT+βBT,
C:=αAH+βBT,
C:=αA+βBH,
C:=αAT+βBH or
C:=αAH+βBH,

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 by n or n by m matrices, depending on whether they are to be transposed before addition. C is an m by n matrix.

5 Parameters

1: TRANSA – CHARACTER*1Input

2: TRANSB – CHARACTER*1Input

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 and TRANSB must be one of 'N', 'T' or '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: M≥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: N≥0.

5: ALPHA – complex*16Input

On entry: the scalar α, by which matrix A is multiplied before addition.

6: A(LDA,*) – complex*16 arrayInput

Note: the second dimension of the array A must be at least max1,N if ALPHA≠0 and TRANSA='N', max1,M if ALPHA≠0 and TRANSA='T' or 'C' and at least 1 if ALPHA=0.

On entry: the matrix A. If α=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 TRANSA='N', LDA≥max1,M;
otherwise LDA≥max1,N.

8: BETA – complex*16Input

On entry: the scalar β, by which matrix B is multiplied before addition.

9: B(LDB,*) – complex*16 arrayInput

Note: the second dimension of the array B must be at least max1,N if BETA≠0 and TRANSB='N', max1,M if BETA≠0 and TRANSB='T' or 'C' and at least 1 if ALPHA=0.

On entry: the matrix B. If β=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 TRANSB='N', LDB≥max1,M;
otherwise LDB≥max1,N.

11: C(LDC,*) – complex*16 arrayOutput

Note: the second dimension of the array C must be at least max1,N.

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: LDC≥max1,M.

13: IFAIL – INTEGERInput/Output

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

On exit: IFAIL=0 unless the routine detects an error (see Section 6).

For environments where it might be inappropriate to halt program execution when an error is detected, the value -1 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 -1 or 1 is used it is essential to test the value of IFAIL on exit.