DTPSV  -  solve one of the systems of equations   A*x = b,
       or A'*x = b,


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 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, sup­
       plied 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


              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 ) respec­
              tively, 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 ele­
              ments 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.


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