NAG Library Routine Document

f06zff (ztrmm)

1
Purpose

f06zff (ztrmm) performs one of the matrix-matrix operations
BαAB, BαATB, BαAHB, BαBA, BαBAT  or BαBAH,  
where B is an m by n complex matrix, A is a complex triangular matrix, and α is a complex scalar.

2
Specification

Fortran Interface
Subroutine f06zff ( side, uplo, transa, diag, m, n, alpha, a, lda, b, ldb)
Integer, Intent (In):: m, n, lda, ldb
Complex (Kind=nag_wp), Intent (In):: alpha, a(lda,*)
Complex (Kind=nag_wp), Intent (Inout):: b(ldb,*)
Character (1), Intent (In):: side, uplo, transa, diag
C Header Interface
#include <nagmk26.h>
void  f06zff_ (const char *side, const char *uplo, const char *transa, const char *diag, const Integer *m, const Integer *n, const Complex *alpha, const Complex a[], const Integer *lda, Complex b[], const Integer *ldb, const Charlen length_side, const Charlen length_uplo, const Charlen length_transa, const Charlen length_diag)
The routine may be called by its BLAS name ztrmm.

3
Description

None.

4
References

None.

5
Arguments

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, AT or AH.
transa='N'
The operation involves A.
transa='T'
The operation involves AT.
transa='C'
The operation involves AH.
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:     alda* – 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 f06zff (ztrmm) is called.
Constraints:
  • if side='L', lda max1,m ;
  • if side='R', lda max1,n .
10:   bldb* – 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 f06zff (ztrmm) is called.
Constraint: ldb max1,m .

6
Error Indicators and Warnings

None.

7
Accuracy

Not applicable.

8
Parallelism and Performance

f06zff (ztrmm) 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

None.

10
Example

None.