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

## STRSM, DTRSM, CTRSM, or ZTRSM Subroutine

### Purpose

Solves certain matrix equations.

### Library

BLAS Library (libblas.a)

### FORTRAN Syntax

`SUBROUTINE STRSM(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 DTRSM(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 CTRSM(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 ZTRSM(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 STRSM, DTRSM, CTRSM, or ZTRSM subroutine solves one of the matrix equations:

`op(`` A`` ) * X = alpha *`` B`
`X * op(`` A`` ) = alpha *`` B`

where alpha is a scalar, X and B are M by N matrices, A is a unit, or non-unit, upper or lower triangular matrix, and op( A ) is either op( A ) = A or op( A ) = A'. The matrix X is overwritten on B.

### Parameters

SIDE |
On entry, SIDE specifies whether op( A ) appears on the left or right of X as follows:
- SIDE = 'L' or 'l'
- op( A ) * X = alpha * B
- SIDE = 'R' or 'r'
- X * op( A ) = alpha * B
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, 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', LDA must be at least max( 1, M ); when SIDE = 'R' or 'r', 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 right-hand side matrix B, and on exit is overwritten by the solution matrix X. |

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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