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NAME

       DTPMV - perform one of the matrix-vector operations   x := A*x, or x :=
       A’*x,

SYNOPSIS

       SUBROUTINE DTPMV ( UPLO, TRANS, DIAG, N, AP, X, INCX )

           INTEGER      INCX, N

           CHARACTER*1  DIAG, TRANS, UPLO

           DOUBLE       PRECISION AP( * ), X( * )

PURPOSE

       DTPMV  performs one of the matrix-vector operations

       where x is an n element vector and  A is an n by n unit,  or  non-unit,
       upper or lower triangular matrix, supplied in packed form.

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  operation  to  be  performed  as
              follows:

              TRANS = ’N’ or ’n’   x := A*x.

              TRANS = ’T’ or ’t’   x := A’*x.

              TRANS = ’C’ or ’c’   x := A’*x.

              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  vector  x.  On  exit,  X  is
              overwritten with the tranformed 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.