subroutine dtpsv ( uplo, trans, diag, n, ap, x, incx )
*     .. scalar arguments ..
      integer            incx, n
      character*1        diag, trans, uplo
*     .. array arguments ..
      double precision   ap( * ), x( * )
*     ..
*
*  purpose
*  =======
*
*  dtpsv  solves one of the systems of equations
*
*     a*x = b,   or   a'*x = b,
*
*  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     - double precision 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      - double precision 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.
*