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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( * )



     #include <sunperf.h>

     void ctpsv(char uplo, char trans, char diag, int n,  complex
               *cap, complex *cx, int incx) ;

PURPOSE
     CTPSV  solves one of the systems of equations A*x  =  b,  or
     A'*x  =  b, or conjg( 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'   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  tri-
               angular.

               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  overwrit-
               ten 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.

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