bell_utils.c File Reference

Bell handling utilities for local trigonomatric transforms. More...

#include "libftsh.h"

Defines
#define	ENTEREXIT   0
Functions
REAL	dualabell (REAL(*origbell)(int, int), int laplength, int t)
void	bell_1size_init (REAL *bellout, REAL(*whichbell)(int, int), int lapleft, int center, int lapright, int dual_flag)
void	fold_e_e_1s (REAL *coef, REAL *fcn, int numpts, REAL *left, int n_left, REAL *right, int n_right, REAL *bell, int dir)
void	fold_e_o_1s (REAL *coef, REAL *fcn, int numpts, REAL *left, int n_left, REAL *right, int n_right, REAL *bell, int dir)

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Detailed Description

Bell handling utilities for local trigonomatric transforms.

Summary:

• dualabell converts a bell to its dual bell
• bell_1size_init computes values for a given interval and overlap.
• fold_e_e_1s folds (or unfolds) a function (after belling) even on both sides.
• fold_e_o_1s folds (or unfolds) a function (after belling) even on left and odd on right.

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Function Documentation

void bell_1size_init	(	REAL *	bellout,
		REAL(*)(int, int)	whichbell,
		int	lapleft,
		int	center,
		int	lapright,
		int	dual_flag
	)

Computes bell values for a given size and overlap configuration.

INPUTS:

• whichbell -- a pointer to a bell function. The bells have the form bell(laplength,t) with
  • laplength -- the number of POINTS the bell spills out of the interval. It also spills in an equal number of points. Thus the bell takes 2*laplength points to rise from 0 to 1.
  • t -- Which point you want to evaluate the bell at. This should range from 0 to 2*laplength-1. bell(laplength,0)=~0 then it rises until bell(laplength,2*laplength-1)=~1 The edge of the interval is between points, at t=(laplength-1) +0.5 The bell function returns a REAL which is the bell's value at that point.
• lapleft -- the laplength to use at the left edge
• center -- the main interval length. must be at least lapleft+lapright. If it is longer than this, the bell is given value 1 on the extra portion
• lapright-- the laplength to use at the right edge
• dual_flag -- a flag for if we should make the dual of the input bell. Use for inverting bi-orthogonal bells
  • 0 (or !=1) -- normal, don't dual
  • 1 -- make the dual

OUTPUT: bellout --is written onto. The first lapleft+center+lapright entries are used.

Generally, the bell will look like

                               ---------------------\               
                         _____/                      -\______       
           _________/----                                    - ___  
    ___/---                                                        \-
/--                                                                 \
|---------------|--------------|--------------------|--------|--------|
   lapleft      | lapleft                            lapright|lapright
                |- - - - - - - - - center - - - - - - - - - -|      

NOTES:

• It is legal to have lapleft and or lapright equal to zero
• We could call memory internally, but we allow the user to try to localize memory.

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REAL dualabell	(	REAL(*)(int, int)	origbell,
		int	laplength,
		int	t
	)

Return the value of the dual to the given bell.

INPUTS:

• origbell - pointer to the original bell, e.g. bellmat5.
• laplength-- the number of POINTS the bell spills out of the interval. It also spills in an equal number of points. Thus the bell takes 2*laplength points to rise from 0 to 1.
• t -- Which point you want to evaluate the bell at. This should range from 0 to 2*laplength-1. bell(laplength,0)=~0 then it rises until bell(laplength,2*laplength-1)=~1. The edge of the interval is between points, at t=(laplength-1) +0.5

OUTPUT: return the REAL value at that point.

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void fold_e_e_1s	(	REAL *	coef,
		REAL *	fcn,
		int	numpts,
		REAL *	left,
		int	n_left,
		REAL *	right,
		int	n_right,
		REAL *	bell,
		int	dir
	)

Computes the folded version of a function, which is then usually DCTed also can unfold

INPUTS:

• coef -- a pointer to the left edge of the array for the folded function "coefficients"
• fcn -- a pointer to the left end of the main interval
• numpts -- the length of the main interval
• left -- a pointer to the right edge of the interval that sits to the left of the main interval left will be called with negative indices
• n_left-- the length of left to use. The bell spills this much into left, and the same amount into fcn.
• right -- a pointer to the left edge of the interval that sits to the right of the main interval
• n_right-- the length of right to use. The bell spills this much into right, and the same amount into fcn.
• bell --- an array containing the bell values
• dir -- which operation to do:
  • 1 : fold
  • -1 : unfold

OUTPUT:

• if dir==1: coef -- the folded version of the function. length numpts is written on
• if dir==-1: fcn,left,right -- the unfolded version of the function is ADDED to these arrays
• else : no action

NOTES:

• If all the data is contiguous, we will have right=fcn+numpts and left=fcn-1;
• We could incorporate a skip if the data is transposed.

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void fold_e_o_1s	(	REAL *	coef,
		REAL *	fcn,
		int	numpts,
		REAL *	left,
		int	n_left,
		REAL *	right,
		int	n_right,
		REAL *	bell,
		int	dir
	)

Computes the folded version of a function, which is then usually LCTed also can unfold.

INPUTS:

• coef -- a pointer to the left edge of the array for the folded function "coefficients"
• fcn -- a pointer to the left end of the main interval
• numpts -- the length of the main interval
• left -- a pointer to the right edge of the interval that sits to the left of the main interval. left will be called with negative indices.
• n_left-- the length of left to use. The bell spills this much into left, and the same amount into fcn.
• right -- a pointer to the left edge of the interval that sits to the right of the main interval
• n_right-- the length of right to use. The bell spills this much into right, and the same amount into fcn.
• bell --- an array containing the bell values
• dir -- which operation to do:
  • 1 : fold
  • -1 : unfold

OUTPUT:

• if dir==1: coef -- the folded version of the function. length numpts is written on
• if dir==-1: fcn,left,right -- the unfolded version of the function is ADDED to these arrays
• else : no action

NOTES:

• If all the data is contiguous, we will have right=fcn+numpts and left=fcn-1;
• We could incorporate a skip if the data is transposed

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