NAME

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

SYNOPSIS

       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, * )

PURPOSE

       DTRSM  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'.

       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
              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   - 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  - DOUBLE PRECISION.
              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      - DOUBLE PRECISION 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      - DOUBLE PRECISION 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
              Harwell.   Jeremy  Du Croz, Numerical Algorithms Group Ltd.  Sven Hammarling, Numerical Algorithms
              Group Ltd.