SYNOPSIS
 SUBROUTINE DTPSV
 ( UPLO, TRANS, DIAG, N, AP, X, INCX )
 INTEGER INCX, N
 CHARACTER*1 DIAG, TRANS, UPLO
 DOUBLE PRECISION AP( * ), X( * )
PURPOSE
DTPSV solves one of the systems of equationswhere b and x are n element vectors and A is an n by n unit, or nonunit, upper or lower triangular matrix, supplied in packed form.
No test for singularity or nearsingularity 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 righthand 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 22October1986. Jack Dongarra, Argonne National Lab. Jeremy Du Croz, Nag Central Office. Sven Hammarling, Nag Central Office. Richard Hanson, Sandia National Labs.