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dtrsm

 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 multiplica-
             tion 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 triangu-
             lar.

             DIAG = 'N' or 'n'   A is not assumed to be unit tri-
             angular.

             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.

 is m
      A      -
              DOUBLE PRECISION array of DIMENSION ( LDA, k ), where k
             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 refer-
             enced.  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 refer-
             enced.  Note that when  DIAG = 'U' or 'u',  the diag-
             onal 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.