Computing terms of a sequence generated by a nonlinear difference equation
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I would like to compute the first 19 terms of a sequence. I find it takes a very long time. Is there something I am missing? Anyway to speed it up?
It takes 78 secs. Using Excel would be instantaneous.
tic
syms alpha
T=19;
X = sym(1:T);
X(1)=0.1;
for i=2:T
X(i)=(1-alpha - X(i-1)).*X(i-1);
end
disp(X)
toc
采纳的回答
Alan Stevens
2020-10-13
Must be the fact that you are using symbolic maths. Without that it's fast (as long as you specify a value for alpha of course):
tic
T=19;
alpha = 0.1;
X = zeros(1,T);
X(1) = 0.1;
for i = 2:T
X(i) = (1-alpha-X(i-1)).*X(i-1);
end
disp(X);
toc
3 个评论
Hassan Benchekroun
2020-10-13
Alan Stevens
2020-10-13
You could still just make X a function of alpha along the following lines:
tic
T = 19;
% Example calculating X rapidly for many values of alpha.
alpha = 0.01:0.01:1;
X = zeros(numel(alpha),T);
for k = 1:numel(alpha)
X(k,:) = fn(alpha(k),T);
end
toc
function x = fn(alpha,T)
x=zeros(1,T);
x(1) = 0.1;
for i = 2:T
x(i)=(1-alpha-x(i-1))*x(i-1);
end
end
The above calculates 100 sets of 19 values of X in about 0.002 seconds on my laptop.
Hassan Benchekroun
2020-10-13
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