saxpyi, daxpyi, caxpyi, zaxpyi 

Vector plus the product of a scalar and a sparse vector

FORMAT

  {S,D,C,Z}AXPYI ( nz, alpha, x, indx, y )

Arguments

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

  alpha               real*4 | real*8 | complex*8 | complex*16
                      On entry, the scalar multiplier for the elements of
                      vector x.
                      On exit, alpha 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.  The values in the INDX array must be
                      distinct for consistent vector or parallel execution.
                      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, if nz <= 0 or if alpha = 0, y is unchanged. If
                      nz > 0, the elements in the vector y corresponding to
                      the indices in the INDX array are overwritten.

Description

  The _AXPYI subprograms compute the product of a scalar alpha and a sparse
  vector x stored in compressed form. The product is then added to a vector y
  and the result is stored as an updated vector y in full form.  Only the
  elements of vector y whose indices are listed in INDX are updated. For i
  =1, ..., nz:

      y(indx(i)) =  y(indx(i)) + alpha * x(i)

  If nz <= 0 or alpha = 0.0, y is unchanged.

  SAXPYI and DAXPYI compute the product of a real scalar and a real sparse
  vector stored in compressed form, and  add the product to a real vector in
  full form. CAXPYI and ZAXPYI compute the product of a complex scalar and a
  complex sparse vector stored in compressed form, and add the product to a
  complex vector stored in full form.

Example

  INTEGER NZ, INDX(10)
  REAL*4 Y(40), X(10), ALPHA
  NZ = 10
  ALPHA = 2.0
  CALL SAXPYI(NZ, ALPHA, X, INDX, Y)

  This FORTRAN code shows how the nz elements in y, corresponding to the
  indices  in the INDX array, are updated  by the addition of a scalar
  multiple of the corresponding element of the compressed vector, x.