/* SOWaveFunction.h -- Functions defined in terms of waves */
/* Last edited on 2003-07-03 19:49:38 by ra014852 */

#ifndef SOWaveFunction_H
#define SOWaveFunction_H

#include <SOBasic.h>
#include <SOFunction.h>
#include <vec.h>
#include <js.h>

/* FUNCTIONS DEFINED IN TERMS OF WAVES */

/* An {SOWaveFunction} object describes a real-valued function
  {w_k} from {R^m} to {R}.  The function is characterized by 
  an integer /frequency vector/ {k[0..m-1]}, and is such that
    
    {w_k(x) =  sin(PI*x[0]) * ... * sin(PI*x[m-1]) * h_k(x) }
    
  where {h_k(x) is a Hartley wave with integer frequency {k}
  in the unit cube, i.e. 
  
    { h_k(x) = sin( PI/4 + 2 * PI * SUM { x[i]*k[i] : i=0..m } ) }
  
  For any frequency vector {k}, the function {w_k} has value zero on
  the boundary of the unit cube, and can be expressed as the sum of
  ordinary sine and cosine waves whose frequency vectors {r}
  are half-integers with {|r[i]| <= |k[i]| + 1/2}, for all {i}.
  
  */

typedef struct SOWaveFunction_Methods  /* Methods for SOWaveFunction: */
  { SOFunction_Methods fn;  
      /* Methods inherited from superclass, with some overrides.
        The {copy} method will also copy the frequency vector
        {f->d->freq}. */
      
    WriteMth *write;       
      /* Writes the function's def to {wr}, as an {SOWaveFunction}. */
        
  } SOWaveFunction_Methods;

typedef struct SOWaveFunction_Data  /* Data fields for SOWaveFunction: */
  { SOFunction_Data fn;   /* Data fields inherited from superclass. */
    int freq[MAX_PDIM];   /* Frequency vector. */
  } SOWaveFunction_Data;

typedef struct SOWaveFunction  /* Logically a subclass of SOFunction. */
  { char *type;                  /* Type identifier. */
    SOWaveFunction_Methods *m;   /* Function methods. */
    SOWaveFunction_Data *d;      /* Function parameters. */
  } SOWaveFunction;
  
#define SOWaveFunction_TypeId "SOF.Wave."

SOWaveFunction *SOWaveFunction_Cast(OBJ *f);
  /* If {f} (according to {f->type}) is a subclass of {SOWaveFunction},
    returns {f} cast to that type; otherwise returns NULL. */

/* ====================================================================== */

SOWaveFunction *SOWaveFunction_FromFreq(nat pDim, int *freq);
  /* Returns a wave function with frequency vector 
    {k[0..pDim-1] = freq[0..pDim-1]}. The function will have
    domain {R^pDim} and range {R} (i.e. {f->d->fDim = 1}). */

SOWaveFunction *SOWaveFunction_Read(FILE *rd, nat pDim);
  /* Reads a {SOWaveFunction} from {rd}. It must have been created by
    calling the {write} method of an {SOWaveFunction}. The domain
    dimension {pDim} must be provided by the caller, and must 
    be that of the original function that was written to the file. */

#endif