Forward, Backwawrd, Central, and Perfect Difference
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Bailey Smith
am 14 Jun. 2018
Bearbeitet: Jan
am 18 Jun. 2018
Could someone please explain how to use the differences, especially with vectors? I would like to make a chart of the values of the four differences types, along with the corresponding x value. Say x=[0:0.2:0.6], y=sin(x), and yperfect=cos(x), how would I go about this?
UPDATE: This is the code I have to take the forward difference (first order).
function [out] = forwarddiff(x,y)
n=1;
L=length(x);
while n < L
out(n,1)=x(n);
out(n,2)=(y(n+1)-y(n))/(x(n+1)-x(n));
n=n+1;
end
out(L,1)=x(L);
out(L,2)=NaN;
end
X and Y values can be input by the user. My new question is: Would the second order forward difference look something like this?
function [out] = forwarddiff(x,y)
n=1;
L=length(x);
while n < L
out(n,1)=x(n);
out(n,2)=(y(n+2)-2*y(n+1)+y(n))/(x(n+1)-x(n))^2;
n=n+1;
end
out(L,1)=x(L);
out(L,2)=NaN;
end
I get an error about exceeding matrix dimensions when I run this.
3 Kommentare
Jan
am 15 Jun. 2018
I agree with John. Please try it, post the code and ask a specific question. It is unlikely that the forum will do your work in exactly the way you need it.
Is this your homework?
Bailey Smith
am 15 Jun. 2018
An old homework, but no Matlab required. I've been wanting to take my old homeworks and code them into Matlab so that I can better understand the program before I take any advanced computing class. If I have time, I will try to get a code posted tonight or tomorrow.
Akzeptierte Antwort
Ankita Bansal
am 18 Jun. 2018
Hi, in line
out(n,2)=(y(n+2)-2*y(n+1)+y(n))/(x(n+1)-x(n))^2;
you are getting error because you are trying to access y(n+2) at n=L-1.
Change your code to
function [out] = forwarddiff(x,y)
n=1;
L=length(x);
while n < L-1
out(n,1)=x(n);
out(n,2)=(y(n+2)-2*y(n+1)+y(n))/(x(n+1)-x(n))^2;
n=n+1;
end
out(L-1,1)=x(L-1);
out(L-1,2)=NaN;
end
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Jan
am 18 Jun. 2018
Bearbeitet: Jan
am 18 Jun. 2018
A shorter form of your 1st order forward difference:
function [out] = forwarddiff(x,y)
x = x(:); % Consider row vectors
y = y(:);
dy = (y(2:end) - y(1:end-1)) / (x(2:end) - x(1:end-1));
out = [x, [dy; NaN]];
end
If you really want to do this with a loop, care for a pre-allocation. Letting the output grow iteratively wastes a lot of resources.
See also the diff command and gradient.
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