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**T   or   op( A ) = A**H.

SIDE

          SIDE is 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 ).

UPLO

          UPLO is 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.

TRANSA

          TRANSA is 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**T.


              TRANSA = 'C' or 'c'   op( A ) = A**H.

DIAG

          DIAG is 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.

M

          M is INTEGER


           On entry, M specifies the number of rows of B. M must be at


           least zero.

N

          N is INTEGER


           On entry, N specifies the number of columns of B.  N must be


           at least zero.

ALPHA

          ALPHA is 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.

A

          A is COMPLEX array, 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.

LDA

          LDA is 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 ).

B

          B is COMPLEX array, 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

          LDB is 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 ).

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

December 2016

  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.