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NAME

       STRSV - solve one of the systems of equations   A*x = b, or A’*x = b,

SYNOPSIS

       SUBROUTINE STRSV ( UPLO, TRANS, DIAG, N, A, LDA, X, INCX )

           INTEGER      INCX, LDA, N

           CHARACTER*1  DIAG, TRANS, UPLO

           REAL         A( LDA, * ), X( * )

PURPOSE

       STRSV  solves one of the systems of equations

       where  b  and  x are n element vectors and A is an n by n unit, or non-
       unit, upper or lower triangular matrix.

       No test  for  singularity  or  near-singularity  is  included  in  this
       routine. Such tests must be performed before calling this routine.

PARAMETERS

       UPLO   - CHARACTER*1.
              On entry, UPLO specifies whether the matrix 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.

       TRANS  - CHARACTER*1.
              On entry, TRANS specifies the equations to be solved as follows:

              TRANS = ’N’ or ’n’   A*x = b.

              TRANS = ’T’ or ’t’   A’*x = b.

              TRANS = ’C’ or ’c’   A’*x = b.

              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.

       N      - INTEGER.
              On entry, N specifies the order of the matrix A.  N must  be  at
              least zero.  Unchanged on exit.

       A      - REAL             array of DIMENSION ( LDA, n ).
              Before  entry  with  UPLO = ’U’ or ’u’, the leading n by n 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  n
              by n 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. LDA must be at least  max(  1,  n  ).
              Unchanged on exit.

       X      - REAL             array of dimension at least
              (  1  +  ( n - 1 )*abs( INCX ) ).  Before entry, the incremented
              array X must contain the n element right-hand side vector b.  On
              exit, X is overwritten with the solution vector x.

       INCX   - INTEGER.
              On  entry,  INCX  specifies the increment for the elements of X.
              INCX must not be zero.  Unchanged on exit.

              Level 2 Blas routine.

              -- Written on 22-October-1986.  Jack Dongarra, Argonne  National
              Lab.   Jeremy Du Croz, Nag Central Office.  Sven Hammarling, Nag
              Central Office.  Richard Hanson, Sandia National Labs.