DTPMV  performs one of the matrix-vector operations


    x := A*x,   or   x := A**T*x,


 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.

UPLO

          UPLO is 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.

TRANS

          TRANS is 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**T*x.


              TRANS = 'C' or 'c'   x := A**T*x.

DIAG

          DIAG is 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.

N

          N is INTEGER


           On entry, N specifies the order of the matrix A.


           N must be at least zero.

AP

          AP is DOUBLE PRECISION array, 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.

X

          X is DOUBLE PRECISION array, 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


           transformed vector x.

INCX

          INCX is INTEGER


           On entry, INCX specifies the increment for the elements of


           X. INCX must not be zero.

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

December 2016

  Level 2 Blas routine.


  The vector and matrix arguments are not referenced when N = 0, or M = 0


  -- 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.