F06ZJF (ZTRSM) (PDF version)
F06 Chapter Contents
F06 Chapter Introduction
NAG Library Manual

NAG Library Routine Document

F06ZJF (ZTRSM)

Note:  before using this routine, please read the Users' Note for your implementation to check the interpretation of bold italicised terms and other implementation-dependent details.

+ Contents

    1  Purpose
    7  Accuracy
    9  Example

1  Purpose

F06ZJF (ZTRSM) performs one of the matrix-matrix operations
BαA-1B , BαA-TB , BαA-HB , BαBA-1 , BαBA-T   or BαBA-H ,
where A is a complex triangular matrix, B is an m by n complex matrix, and α is a complex scalar. A-T  denotes AT-1  or equivalently A-1T ; A-H  denotes AH-1  or equivalently A-1H .
No test for singularity or near-singularity of A is included in this routine. Such tests must be performed before calling this routine.

2  Specification

SUBROUTINE F06ZJF ( SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
INTEGER  M, N, LDA, LDB
COMPLEX (KIND=nag_wp)  ALPHA, A(LDA,*), B(LDB,*)
CHARACTER(1)  SIDE, UPLO, TRANSA, DIAG
The routine may be called by its BLAS name ztrsm.

3  Description

None.

4  References

None.

5  Parameters

1:     SIDE – CHARACTER(1)Input
On entry: specifies whether B is operated on from the left or the right.
SIDE='L'
B is pre-multiplied from the left.
SIDE='R'
B is post-multiplied from the right.
Constraint: SIDE='L' or 'R'.
2:     UPLO – CHARACTER(1)Input
On entry: specifies whether A is upper or lower triangular.
UPLO='U'
A is upper triangular.
UPLO='L'
A is lower triangular.
Constraint: UPLO='U' or 'L'.
3:     TRANSA – CHARACTER(1)Input
On entry: specifies whether the operation involves A-1, A-T or A-H.
TRANSA='N'
The operation involves A-1.
TRANSA='T'
The operation involves A-T.
TRANSA='C'
The operation involves A-H.
Constraint: TRANSA='N', 'T' or 'C'.
4:     DIAG – CHARACTER(1)Input
On entry: specifies whether A has nonunit or unit diagonal elements.
DIAG='N'
The diagonal elements are stored explicitly.
DIAG='U'
The diagonal elements are assumed to be 1, and are not referenced.
Constraint: DIAG='N' or 'U'.
5:     M – INTEGERInput
On entry: m, the number of rows of the matrix B; the order of A if SIDE='L'.
Constraint: M0.
6:     N – INTEGERInput
On entry: n, the number of columns of the matrix B; the order of A if SIDE='R'.
Constraint: N0.
7:     ALPHA – COMPLEX (KIND=nag_wp)Input
On entry: the scalar α.
8:     A(LDA,*) – COMPLEX (KIND=nag_wp) arrayInput
Note: the second dimension of the array A must be at least max1,M if SIDE='L' and at least max1,N if SIDE='R'.
On entry: the triangular matrix A; A is m by m if SIDE='L', or n by n if SIDE='R'.
  • If UPLO='U', A is upper triangular and the elements of the array below the diagonal are not referenced.
  • If UPLO='L', A is lower triangular and the elements of the array above the diagonal are not referenced.
  • If DIAG='U', the diagonal elements of A are assumed to be 1, and are not referenced.
9:     LDA – INTEGERInput
On entry: the first dimension of the array A as declared in the (sub)program from which F06ZJF (ZTRSM) is called.
Constraints:
  • if SIDE='L', LDA max1,M ;
  • if SIDE='R', LDA max1,N .
10:   B(LDB,*) – COMPLEX (KIND=nag_wp) arrayInput/Output
Note: the second dimension of the array B must be at least max1,N.
On entry: the m by n matrix B.
If ALPHA=0, B need not be set.
On exit: the updated matrix B.
11:   LDB – INTEGERInput
On entry: the first dimension of the array B as declared in the (sub)program from which F06ZJF (ZTRSM) is called.
Constraint: LDB max1,M .

6  Error Indicators and Warnings

None.

7  Accuracy

Not applicable.

8  Further Comments

None.

9  Example

None.

F06ZJF (ZTRSM) (PDF version)
F06 Chapter Contents
F06 Chapter Introduction
NAG Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2011