/* Functions that implement various approximation bases. */
/* Last edited on 2007-12-26 15:19:29 by stolfi */

#ifndef basis1d_H
#define basis1d_H

/* Copyright © 2007 by the State University of Campinas (UNICAMP). */
/* See the copyright, authorship, and warranty notice at end of file. */
/* Last edited on 2007-04-16 17:30:29 by stolfi */

#include <interval.h>
#include <stdint.h>
#include <stdio.h>

#include <bool.h>

/* Created apr/2007 by Jorge Stolfi, UNICAMP */

typedef enum {
  b1d_kind_POLY = 0,  /* Polynomial. */
  b1d_kind_TRIG = 1,  /* Trigonometric. */
} b1d_kind_t;
  
#define b1d_kind_NUM 2
/* Number of distinct values in {b1d_kind_t}. */

char *b1d_kind_tag(b1d_kind_t bkind);
  /* Returns a fixed character string that identifies the basis
    kind {bkind}: "POLY", "TRIG", etc. */

typedef int8_t b1d_degree_t;
  /* Degree of a polynomial or spline, max order of a trig series, etc.. */
  
typedef int8_t b1d_cont_t;
  /* Continuity order of a spline. Value {-1} means discontinuous.. */

typedef struct b1d_family_t {
  b1d_kind_t bkind; /* Basis kind. */
  b1d_degree_t g;   /* Max degree or number of terms. */
  b1d_cont_t c;     /* Continuity order. */
} b1d_family_t;
  /* Describes a basis of mother functions with continuity {c},
    whose domain is the whole real line.  The parameter {g}
    is the maximum degree or order of the basis elements,
    depending on the {bkind}. */

void b1d_family_print(FILE *wr, b1d_family_t *fam);
  /* Prints out the description of mother basis {fam} to {wr}.  */

typedef int32_t b1d_mother_num_t;  
  /* Count of elements in a mother basis. */
  
typedef int32_t b1d_mother_index_t;  
  /* Identifies a mother element in a basis. */
  
b1d_mother_num_t b1d_family_num(b1d_family_t *fam);
  /* Number {num} of elements in the mother basis {fam}. 
    The elements are indexed {0..num-1}. */

typedef struct b1d_basis_t {
  b1d_family_t fam; /* Family of mother functions. */
  int gsz;          /* Number of intervals. */
  interval_t dom;   /* Argument domain. */
  bool_t wrap;      /* TRUE iff the domain is periodic. */
} b1d_basis_t;
  /* Describes a basis of functions defined over the domain {dom},
    whose elements are obtained by expanding and translating functions
    of mother basis {fam} over a regular grid.
    
    The domain {dom} is implicitly divided into {gsz} equal intervals
    (/cells/) of length {xstep}, starting at argument {xmin}. The
    generic basis element is {b(x) = F((x - xmin)/xstep - k)}, where
    {k} is an integer /displacement/ and {F} (the /mother element/) is
    an element of the basis {fam}.  
    
    If {wrap} is true, the domain {dom} is assumed to be circular,
    and the function {F} is wrapped-over and added to itself. */
  
char *b1d_basis_tag(b1d_basis_t *bas);
  /* Creates a new char string that identifies the basis {bas}. */

typedef int64_t b1d_grid_size_t;
  /* Size of a toroidal grid along an axis, in multiples of 
    the corresponding grid step. */
  
b1d_grid_size_t b1d_element_supp_count
  ( b1d_family_t *fam, 
    b1d_mother_index_t pix, 
    b1d_grid_size_t gsz,
    bool_t wrap
  );
  /* Number of cells where a basis element with mother element {fam,pix}
    may be nonzero, assuming a grid with {gsz} cells with
    periodicity flag {wrap}. 
    
    If {wrap} is FALSE, the result is simply the support count {msn}
    of the mother element. If {wrap} is TRUE, the result is the
    smallest of {gsz} and {msn}. */
  

typedef uint64_t b1d_cell_index_t;
  /* Identifies a cell in some (multi)grid. */

/* MULTISCALE BASES */

typedef int32_t b1d_rank_t;
  /* Identifies a layer in a multigrid, or the depth of a node
    in a binary tree, etc. It may also be a relative rank (i.e.
    difference of two ranks). */

#endif