SHC_INNER_PRODUCT(3)

NAME

     shc_inner_product: The inner product of  an  array  of  data
     vectors  with an array of function value masks, specifically
     designed for estimation of spherical harmonic coefficients.

Syntax

     #include <soi_sds.h>
     #include <soi_error.h>

     int shc_inner_product (even_real, even_imag, odd_real, odd_imag, masks,
          l_min, l_max, delta_m, double d_m, ip_real, ip_imag)
     SDS *even_real, *even_imag, *odd_real, *odd_imag;
     SDS *masks;
     int l_min, l_max, delta_m;
     double d_m;
     SDS *ip_real, *ip_imag;

DESCRIPTION

     Input to the program are pointers to SDS  typedefs  for  the
     folded  data from a Fourier transform along rows of remapped
     data.  The folded data consist of  even  and  odd  "parity."
     This  parity  corresponds  to  that  of  l+m, where l is the
     degree and m the order of the spherical harmonic correspond-
     ing to the associated Legendre function mask data.  Real and
     imaginary components are used.  Also input in an SDS dataset
     are the mask elements.

     Outputs are SDS data members for the real and imaginary com-
     ponents of the resultant inner product.

     The input data are considered  K sets of vectors of length N
     the  inner  product  of  which with a set of  "masks" of the
     same length.

     For N elements, the equations for an inner product are
           2N-1
          ---
     z  = \      x  .  y  ,         j = 0, 1, ..., J-1
      j   /        nj    nj
          ---
          n = 0
     J < = K.
     j' = round(d_m . m)
     K is the number of columns of  data  and  J  the  number  of
     masks.

     Because the masks are either symmetric or antisymmetric  for
     spherical  harmonics,  the  equations implemented for N ele-
     ments each vector.
           N-1
          ---
     z  = \      x'  .  y ,         j = 0, 1, ..., J-1
      k   /        nj    nj
          ---
          n = 0

















































     x' = x  +  x            for use with symmetric spherical harmonics
      nj   nj    N-1-n j

     x' = x  -  x            for use with antisymmetric spherical harmonics
      nj   nj    N-1-n j

KEYWORDS

     Input parameters:
     data_cols      Width of input array
     masks_cols     Height of input array = columns in each mask.
     l_min          Minimum degree
     l_max          Maximum degree
     delta_m        Interval between values of order used
     d_m            The ratio of the data column to  be  used  to
     m.

RESTRICTIONS

     Every l from minimum to maximum is assumed to be used.  Max-
     imum m is assumed to be equal to maximum l.

BUGS

     The program was tested in another directory  using  the  old
     soi_sds.h.   It  compiles  with  the latest (1993 October 1)
     version of soi_sds.h.

HSITORY

     1993.11.24  lyle bacon        Created for SOI V.0.7.
     1993.02.08  lyle bacon        Verion 0.8