Derivative Operator Picture Code

The figure in Derivative Matrix for a Function Vector was generated with the following code:

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% -__-, \\,/ \\ |/ \\ \\ ( \_, | \/\\ \\/\\/ \\,\ \\ \\ \\ ,-_-

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% John Hawkins

% LNA

% Derivative Matrix Example

% 2 Feb 2010

function DerivativeExample

x=linspace(0,4*pi,500)';

y=sin(x);

dydx=cos(x);

h.fig=figure('color','w','units','normalized','position',[.2 .2 .6 .6]);

plot(x,y,'color',[.8 .8 .8]);

hold on;

plot(x,dydx,'color',[.8 .8 .8]);

numStartPoints=10;

x=linspace(0,4*pi,numStartPoints)';

y=sin(x);

dydx=DERIV(x,y);

h.y=plot(x,y,'b.');

h.construct=plot(0,0,'r');

h.dydx=plot(0,0,'r.');

legend([h.y,h.construct,h.dydx],'y','Construction Line','dy/dx');

xlabel('x'); ylabel('y');

axis equal;

title('Taking the Derivative of a Finite Function Vector for y=sin x',...

   'fontname','times','fontsize',20);

set([h.construct,h.dydx],'visible','off');

fig = getframe(h.fig);

[im,map] = rgb2ind(fig.cdata,256,'nodither');

set(h.construct,'visible','on','xdata',x([1,2]),'ydata',y([1,2]));

im=CAPTUREFIG(im,map,h);

set(h.dydx,'visible','on','xdata',x(1),'ydata',dydx(1));

im=CAPTUREFIG(im,map,h);

for n=2:numStartPoints-1

   set(h.construct,'xdata',x([n-1,n+1]),'ydata',y([n-1,n+1]));

   im=CAPTUREFIG(im,map,h);

   set(h.dydx,'xdata',x(1:n),'ydata',dydx(1:n));

   im=CAPTUREFIG(im,map,h);

end

set(h.construct,'xdata',x([numStartPoints-1,numStartPoints]),...

   'ydata',y([numStartPoints-1,numStartPoints]));

im=CAPTUREFIG(im,map,h);

set(h.dydx,'xdata',x,'ydata',dydx);

im=CAPTUREFIG(im,map,h);

set(h.construct,'visible','off');

im=CAPTUREFIG(im,map,h);

for k=1:5

   im=CAPTUREFIG(im,map,h);

end

for n=[15 20 30 50 100 200 500]

   x=linspace(0,4*pi,n)';

   y=sin(x);

   dydx=DERIV(x,y);

   set(h.y,'xdata',x,'ydata',y);

   set(h.dydx,'xdata',x,'ydata',dydx);

   im=CAPTUREFIG(im,map,h);

end

for k=1:5

   im=CAPTUREFIG(im,map,h);

end

imwrite(im,map,'Derivative.gif','DelayTime',.5,'LoopCount',inf)

function dydx=DERIV(x,y)

num=numel(y);

deltax=x(2)-x(1);

operator=zeros(num);

operator(1,1)=-2;

operator(1,2)=2;

for k=2:num-1

   operator(k,k+1)=1;

   operator(k,k-1)=-1;

end

operator(num,num-1)=-2;

operator(num,num)=2;

operator=operator/(2*deltax);

dydx=operator*y;

function im=CAPTUREFIG(im,map,h)

fig = getframe(h.fig);

im(:,:,1,size(im,4)+1) = rgb2ind(fig.cdata,map,'nodither');

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