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NAME

       STPSV - solve one of the systems of equations   A*x = b, or A'*x = b,

SYNOPSIS

       SUBROUTINE STPSV ( UPLO, TRANS, DIAG, N, AP, X, INCX )

           INTEGER      INCX, N

           CHARACTER*1  DIAG, TRANS, UPLO

           REAL         AP( * ), X( * )

PURPOSE

       STPSV  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, supplied in packed form.

       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.

       AP     - REAL             array of DIMENSION at least
              (  (  n*(  n  + 1 ) )/2 ).  Before entry with  UPLO = 'U' or 'u', the array AP must
              contain the upper triangular matrix packed sequentially, column by column, so  that
              AP(  1  )  contains  a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 )
              respectively, and so on.  Before entry with UPLO = 'L' or 'l', the  array  AP  must
              contain  the lower triangular matrix packed sequentially, column by column, so that
              AP( 1 ) contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and  a(  3,  1  )
              respectively,  and so on.  Note that when  DIAG = 'U' or 'u', the diagonal elements
              of A are not referenced, but are assumed to be unity.  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.