sdoti, ddoti, cdotui, zdotui, cdotci, zdotci 

Inner product of a vector and a sparse vector

FORMAT

  {S,D}DOTI ( nz, x, indx, y )
  {C,Z}DOT{U,C}I ( nz, x, indx, y )

Function Value

  dotpr               real*4 | real*8 | complex*8 | complex*16
                      The inner product of the sparse vector x and the full
                      vector y.

Arguments

  nz                  integer*4
                      On entry, the number of elements in the vector in the
                      compressed form.
                      On exit, nz is unchanged.

  x                   real*4 | real*8 | complex*8 | complex*16
                      On entry, an array of the elements of vector x in
                      compressed form.
                      On exit, x is unchanged.

  indx                integer*4
                      On entry, an array containing the indices of the
                      compressed form.
                      On exit, indx is unchanged.

  y                   real*4 | real*8 | complex*8 | complex*16
                      On entry, an array of the elements of vector y stored
                      in full form.
                      On exit, y is unchanged.  Only the elements in the
                      vector y corresponding to the indices in the INDX array
                      are accessed.

Description

  These routines compute the vector inner product of a sparse vector x stored
  in compressed form with a vector y stored in full form.  If nz <=0, dotpr
  is set equal to zero.

  SDOTI and DDOTI multiply a real vector by a sparse vector of real values
  stored in compressed form.  CDOTUI and ZDOTUI multiply a complex vector by
  an unconjugated sparse vector of complex values stored in compressed form.
  CDOTCI and ZDOTCI multiply a complex vector by a conjugated sparse vector
  of complex values stored in compressed form.

  CDOTUI and ZDOTUI operate on the vector x in the unconjugated form; CDOTCI
  and ZDOTCI operate on the vector x in conjugated form.

  (Unconjugated  form:)

       dotpr = SUM(i=1...nz,x(i) * y(indx(i))

  (Conjugated  form:)

       dotpr = SUM(i=1...nz,conjugate(x(i)) * y(indx(i))

  The order of operations for the evaluation of dotpr may be different from
  the sequential order of operations.  The results obtained from these two
  evaluations may not be identical.

Example

  INTEGER NZ, INDX(15)
  COMPLEX*8 Y(50), X(15)
  NZ = 10
  CINNER = CDOTUI(NZ, X, INDX, Y)

  This FORTRAN code produces the inner product of two vectors, x and y. y is
  stored in full form and x is stored in compressed form. The elements of
  vector x are used in unconjugated form.