ctrmm

CTRMM(1)                         BLAS routine                         CTRMM(1)



NAME
       CTRMM - 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 one of   op( A ) = A or op( A ) = A' or op( A ) = conjg( A'
       )

SYNOPSIS
       SUBROUTINE CTRMM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB)

           COMPLEX                                                   ALPHA

           INTEGER                                                   LDA,LDB,M,N

           CHARACTER                                                 DIAG,SIDE,TRANSA,UPLO

           COMPLEX                                                   A(LDA,*),B(LDB,*)

PURPOSE
       CTRMM  performs one of the matrix-matrix operations


ARGUMENTS
       SIDE   - CHARACTER*1.
              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   - CHARACTER*1.
              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 - CHARACTER*1.  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 ) = conjg( A' ).

              Unchanged on exit.

       DIAG   - CHARACTER*1.
              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      - INTEGER.
              On entry, M specifies the number of rows of B. M must be at
              least zero.  Unchanged on exit.

       N      - INTEGER.
              On entry, N specifies the number of columns of B.  N must be at
              least zero.  Unchanged on exit.

       ALPHA  - COMPLEX         .
              On entry,  ALPHA specifies the scalar  alpha. When  alpha is
              zero then  A is not referenced and  B need not be set before
              entry.  Unchanged on exit.

       A      - COMPLEX          array of DIMENSION ( LDA, k ), where k is m
              when  SIDE = 'L' or 'l'  and is  n  when  SIDE = 'R' or 'r'.
              Before 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.  Before 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.  Note that when  DIAG =
              'U' or 'u',  the diagonal elements of A  are not referenced
              either,  but are assumed to be  unity.  Unchanged on exit.

       LDA    - INTEGER.
              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      - COMPLEX          array of DIMENSION ( LDB, n ).
              Before 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    - INTEGER.
              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.

FURTHER DETAILS
       Level 3 Blas routine.

       -- Written on 8-February-1989.
          Jack Dongarra, Argonne National Laboratory.
          Iain Duff, AERE Harwell.
          Jeremy Du Croz, Numerical Algorithms Group Ltd.
          Sven Hammarling, Numerical Algorithms Group Ltd.




BLAS routine                     November 2008                        CTRMM(1)