How to minimize a function without using a loop

2016 7 26
1 个回答
更新时间：2016 7 26
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I have an equation with 3 constant (Nug & Sill, Lag) and 2 variable (R[ranges from 1 to 4000], alpha[ranges from 1 to 2, step of 0.1]). I need to find the value R and alpha that minimizes the function. Is there any Matlab function or any way i can do it without having to do a doublé for loop.
%q = 4000
for i=1:q
Theoritical(i,1) = Nug+Sill*(1-exp(-(Lag(i,1)/R)^alpha));
end
Thank you. Darl.

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回答（1 个）

Guillaume
Guillaume 2016-7-26

1 个投票

It doesn't look like your Lag is much of a constant if there's 4000 values for it. Does Lag changes with R (since there's also 4000 R values)?
You can use fminsearch or fminbnd but if there's only 4000 values for R and 11 for alpha, you could simply calculate the result for all of them at once and get the minimum :
[R, alpha] = ndgrid(1:4000, 1:0.1:2); %get all combinations of R and alpha
result = Nug + Sill * (1 - exp(-bsxfun(@rdivide, Lag, R) .^ alpha)); %assumes Lag is a column vector with 4000 elements
[minvalue, location] = min(result(:));
minR = R(location)
minalpha = alpha(location)

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Darlington Mensah
Darlington Mensah 2016-7-26
编辑：Darlington Mensah 2016-7-26
Thank you @Guillaume. Lag is vector with 11 elements ranging from 0 to 4000.
Guillaume
Guillaume 2016-7-26
Oh! I'm not sure why you accepted the answer then as it's not going to work.
What is your equation then? In your question you're indexing Lag with i, i goes from 1 to q and q is said to be 4000. That's in direct contradiction with your statement above.
How do these 11 different values figure in the equation?
Darlington Mensah
Darlington Mensah 2016-7-26
编辑：Darlington Mensah 2016-7-26
%q = 11
for i=1:q
Theoritical(i,1) = Nug+Sill*(1-exp(-(Lag(i,1)/R)^alpha));
end
I made a mistake in my initial question. I apologize.
Per the equation, i consider each element of Lag in the computation. Omitting the q for now and assuming Lag is a constant, with variables being only alpha and R.
Guillaume
Guillaume 2016-7-26
So, for a given R and alpha, you've 11 different theoritical (theoretical?) values. What is it you want to minimise?
Darlington Mensah
Darlington Mensah 2016-7-26
编辑：Darlington Mensah 2016-7-26
I have a function (ExpSemivariance) that creates a vector of 11 elements. This elements are then represented on a graph in a scattered diagram and I intend finding the curve (Theoretical) that best fit 'ExpSemivariance' by using mimimum residual
Step = 10;
q = 11;
for i=1:q
Theoretical(i,1) = Nug+Sill*(1-exp(-(Lag(i,1)/R)^alpha));
end
Error = sum(abs(Theoretical-ExpSemivariance));
while Step > 1
R = R + Step;
for i=1:q
Theoretical(i,1) = Nug+Sill*(1-exp(-(Lag(i,1)/R)^alpha));
end
error = sum(abs(Theoretical-ExpSemivariance));
if error > Error
R = R - Step;
Step = Step/2;
else
Error = error;
end
end
The variables are R and alpha. Initially, i made alpha constant and used the code above to calculate min®. My problem is how to calculate both min® and min(alpha) for each i of the fun(Theoretical) such that Theoretical would be the best function that minimizes the error (between ExpSemivariance and Theoretical)

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