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# Technical Reference: Base Operating System and Extensions , Volume 2

## STRMM, DTRMM, CTRMM, or ZTRMM Subroutine

### Purpose

Performs matrix-matrix operations on triangular matrices.

### Library

BLAS Library (libblas.a)

### FORTRAN Syntax

SUBROUTINE STRMM(SIDE, UPLO, TRANSA, DIAG,
M, N, ALPHA, A, LDA, B, LDB)
CHARACTER*1 SIDE, UPLO, TRANSA, DIAG
INTEGER M, N, LDA, LDB
REAL ALPHA
REAL A(LDA,*), B(LDB,*)

```SUBROUTINE DTRMM(SIDE, UPLO, TRANSA, DIAG,
M, N, ALPHA, A, LDA, B, LDB)
CHARACTER*1
SIDE,UPLO,TRANSA,DIAG
INTEGER M,N,LDA,LDB
DOUBLE PRECISION ALPHA
DOUBLE PRECISION A(LDA,*), B(LDB,*)
```

```SUBROUTINE CTRMM(SIDE, UPLO, TRANSA, DIAG,
M, N, ALPHA, A, LDA, B, LDB)
CHARACTER*1
SIDE,UPLO,TRANSA,DIAG
INTEGER M,N,LDA,LDB
COMPLEX ALPHA
COMPLEX A(LDA,*), B(LDB,*)
```

```SUBROUTINE ZTRMM(SIDE, UPLO, TRANSA, DIAG,
M, N, ALPHA, A, LDA, B, LDB)
CHARACTER*1
SIDE,UPLO,TRANSA,DIAG
INTEGER M,N,LDA,LDB
COMPLEX*16 ALPHA
COMPLEX*16 A(LDA,*), B(LDB,*)
```

### Description

The STRMM, DTRMM, CTRMM, or ZTRMM subroutine performs one of the matrix-matrix operations:

B := alpha * op( A ) * B

OR

B := alpha * B * op( A )

where alpha is a scalar, B is an M by N matrix, A is a unit, or non-unit, upper or lower triangular matrix, and op( A ) is either op( A ) = A or op( A ) = A'.

### Parameters

 SIDE On entry, SIDE specifies whether op( A ) multiplies B from the left or right as follows: SIDE = 'L' or 'l' B := alpha * op( A ) * B SIDE = 'R' or 'r' B := alpha * B * op( A ) Unchanged on exit. UPLO On entry, UPLO specifies whether the matrix A is an upper or lower triangular matrix as follows: UPLO = 'U' or 'u' A is an upper triangular matrix. UPLO = 'L' or 'l' A is a lower triangular matrix. Unchanged on exit. TRANSA On entry, TRANSA specifies the form of op( A ) to be used in the matrix multiplication as follows: TRANSA = 'N' or 'n' op( A ) = A TRANSA = 'T' or 't' op( A ) = A' TRANSA = 'C' or 'c' op( A ) = A' Unchanged on exit. DIAG On entry, DIAG specifies whether or not A is unit triangular as follows: DIAG = 'U' or 'u' A is assumed to be unit triangular. DIAG = 'N' or 'n' A is not assumed to be unit triangular. Unchanged on exit. M On entry, M specifies the number of rows of B; M must be at least 0; unchanged on exit. N On entry, N specifies the number of columns of B; N must be at least 0; unchanged on exit. ALPHA On entry, ALPHA specifies the scalar alpha. When alpha is 0 then A is not referenced and B need not be set before entry; unchanged on exit. A An array of dimension ( LDA, k ), where k is M when SIDE = 'L' or 'l' and is N when SIDE = 'R' or 'r'; on entry with UPLO = 'U' or 'u', the leading k by k upper triangular part of the array A must contain the upper triangular matrix and the strictly lower triangular part of A is not referenced; on entry with UPLO = 'L' or 'l', the leading k by k lower triangular part of the array A must contain the lower triangular matrix and the strictly upper triangular part of A is not referenced. When DIAG = 'U' or 'u', the diagonal elements of A are not referenced either, but are assumed to be unity; unchanged on exit. LDA On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. When SIDE = 'L' or 'l' then LDA must be at least max( 1, M ), when SIDE = 'R' or 'r' then LDA must be at least max( 1, N ); unchanged on exit. B An array of dimension ( LDB, N ); on entry, the leading M by N part of the array B must contain the matrix B, and on exit is overwritten by the transformed matrix. LDB On entry, LDB specifies the first dimension of B as declared in the calling (sub) program; LDB must be at least max( 1, M ); unchanged on exit.

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