From octave-sources-request at bevo dot che dot wisc dot edu  Fri May 19 03:57:19 2000
Subject: 'zigf.m' and 'recf.m' : FAST zigzag and rectangle wave functions
From: Rolf Fabian <fabian at tu-cottbus dot de>
To: "'octave-sources UWISC'" <octave-sources at bevo dot che dot wisc dot edu>
Date: Fri, 19 May 2000 10:54:05 +0200

Hi,

I've developped two  algorithms depending on tricky combinations
of octaves ,abs' and ,floor'  builtin funtions to calculate 
trigonometric - like zigzag and rectangle wave functions in a very 
FAST way, because **NO LOOPS of  IF STATEMENTS ** are needed !!

Attached, please  find

*  zigzag (sewsaw) - function            -- /\/\/\/\ --              ,zigf(x,MODE,PERIOD)'
*  rectangle wave    -function     --  ``|_| ``|_|``|_|`` --      ;recf(x,MODE,PERIOD)'
*  a graphical demo   ,recf_zigf_X( N )'
   NOTE: Have a closer look at demo number N=3, to
               get an impression  about interesting combinations of these two functions

Any feedback welcome!
Bye Rolf

--------------------------------------------------------------------------------------------

##USAGE	y = zigf( x {,m=0 {,p=2*pi}} )
##
##	zigzag-function     -- /\/\/\ --
##
##INPUT
##m     mode of phase   x: 0 p/4 p/2 3/4p
##      0 : cosine         1  0  -1   0
##      1 :   sine         0  1   0  -1
##p	(scalar) period
##
##NOTES	* works elementwise  on matrices x
##	* very FAST algorithm (no if-loops)
##	* zigf(x,1)./zigf(x) follows tan(x)
##
##ASSOC	recf
##AUTHOR (C) 2000 Rolf Fabian <fabian at tu-cottbus dot de> 0519

#EXA	N=501; t=linspace(-5,5,N)'; 
#	plot(t,[zigf(t),cos(t),zigf(t,1),sin(t)])
#	plot(t,[zigf(t,1)./zigf(t),tan(t)])


#990404 * argument number reduced
#	* intro fast calculation using 'abs' and 'floor'
#000519   minor changes

function y=zigf(x,m,p)

	if	(nargin>3||nargin<1) fprintf(stderr,\
		"USAGE y=zigf(x {,m=0 ,p=2*pi}} ) .. quit");
		y=[]; return;
	endif
	if	(nargin<3) p=2*pi; endif
	if	(nargin<2) m   =0; endif

	if	(m) x=x-p/4;	   endif	# define sine-phase

	y = 4*(abs(x/p-floor(x/p)-1/2)-1/4);

endfunction
--------------------------------------------------------------------------------------------

##USAGE	y = recf( x {,m=0 {,p=2*pi}} )
##				 _   _ 
##	rectangle-function -- |_| |_| |_| --
##
##INPUT
##m     mode of phase	   x: 0 p/4 p/2 3/4p
##      0 : cosine - like     1  0  -1   0
##      1 :   sine - like     0  1   0  -1
##p	(scalar) period
##
##NOTES	* works elementwise  on matrices x
##	* very FAST algorithm (no if-loops)
##
##ASSOC	zigf
##AUTHOR (C) 2000 Rolf Fabian <fabian at tu-cottbus dot de> 0519

#EXA	N=501; t=linspace(-5,5,N)'; 
#	plot(t,[recf(t),cos(t),recf(t,1),sin(t)])

#990404 * argument number reduced
#	* intro fast calculation using 'floor'
#000519   minor changes

function y=recf(x,m,p)

	if	(nargin>3||nargin<1) fprintf(stderr,\
		"USAGE y=recf( x {,m=0 {,p=2*pi}} ) .. quit.");
		y=[]; return;
	endif
	if	(nargin<3) p=2*pi; endif
	if	(nargin<2) m=0;    endif

	if	(!m) x=x+p/4;	   endif	# define cos-phase

	y = -2*(floor(2*x/p)-2*floor(x/p)-1/2);

endfunction

--------------------------------------------------------------------------------------------

##USAGE	recf_zigf_X( { N=3 } )
##	select N=1 or N=2 or N=3
##	recf_zigf - demo
##AUTHOR (C) 2000 Rolf Fabian <fabian at tu-cottbus dot de> 0519

function recf_zigf_X(N)

	if	nargin<1 N=3; end

	M=501; t=linspace(-4,4,M)'; 

	gset key;
	gset grid;
	xlabel('x');
	ylabel('y');

	if	(N==1)
		title('recf example')
		gset yrange [-2:2];
		plot(	t,recf(t)  ,';cos phase (M=0);',t,cos(t),';;',\
			t,recf(t,1),';sin phase (M=1);',t,sin(t),';;')
	elseif	(N==2)
		gset yrange [-2:2];
		title('zigf example')
		plot(	t,zigf(t)  ,';cos phase (M=0);',t,cos(t),';;',\
			t,zigf(t,1),';sin phase (M=1);',t,sin(t),';;')
	elseif	(N==3)
		gset yrange [-4:4];
		plot(	t,tan(t),';tan(t);',\
			t,zigf(t,1)./zigf(t),';zigf(t,1) / zigf(t);',\
			t,zigf(t,1)./recf(t),';zigf(t,1) / recf(t);',\
			t,recf(t,1)./zigf(t),';recf(t,1) / zigf(t);',\
			t,recf(t,1)./recf(t),';recf(t,1) / recf(t);');
	else
		disp('unknown example tag .. select N=1 -or- N=2 -or- N=3')
	end




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