ZTRSM  -  solve  one of the matrix equations   op( A )*X =
       alpha*B, or X*op( A ) = alpha*B,


SYNOPSIS

       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, * )


PURPOSE

       ZTRSM  solves one of the matrix equations

       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 one  of

          op( A ) = A   or   op( A ) = A'   or   op( A ) = conjg(
       A' ).

       The matrix X is overwritten on B.


PARAMETERS

       SIDE   - CHARACTER*1.
              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   - 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 multi­
              plication as follows:


              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 trian­
              gular.

              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*16      .
              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*16       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


       B      - COMPLEX*16       array of DIMENSION ( LDB, n ).
              Before  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    - 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.

              Level 3 Blas routine.

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


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