ZTPSV(3)        BLAS routine of NEC Numeric Library Collection        ZTPSV(3)



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

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

           INTEGER      INCX, N

           CHARACTER*1  DIAG, TRANS, UPLO

           COMPLEX*16   AP( * ), X( * )

PURPOSE
       ZTPSV  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 rou-
       tine. 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*16       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 ) respec-
              tively, and so on.  Before entry with UPLO =  'L'  or  'l',  the
              array AP must contain the lower triangular matrix packed sequen-
              tially, column by column, so that AP( 1 ) contains a(  1,  1  ),
              AP(  2  )  and  AP(  3 ) contain a( 2, 1 ) and a( 3, 1 ) respec-
              tively, and so on.  Note that when  DIAG = 'U' or 'u', the diag-
              onal  elements  of  A  are not referenced, but are assumed to be
              unity.  Unchanged on exit.

       X      - COMPLEX*16       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                       ZTPSV(3)