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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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