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CTPSV(l)				   BLAS routine 				 CTPSV(l)

NAME
       CTPSV  -  solve one of the systems of equations	 A*x = b, or A'*x = b, or conjg( A' )*x =
       b,

SYNOPSIS
       SUBROUTINE CTPSV ( UPLO, TRANS, DIAG, N, AP, X, INCX )

	   INTEGER	INCX, N

	   CHARACTER*1	DIAG, TRANS, UPLO

	   COMPLEX	AP( * ), X( * )

PURPOSE
       CTPSV  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'   conjg( 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     - COMPLEX 	 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      - COMPLEX 	 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.

BLAS routine				 16 October 1992				 CTPSV(l)
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