MATLAB: How to properly use sum to sum up microstates

sum

Hey, I'm trying to use a function to sum up the microstates in an evenly split two configuration system but can't get my code to work. Here's what I have:

 function sumW = microstateSum(N)
 n1 = N:0;
 n2 = 0:N;
 sumW = sum(factorial(N)/(factorial(n1)*factorial(n2)));

I'm getting an error on line 5, the last line, with * telling me that matrix dimension must agree. I just want the n1 and n2 variables to decrement and increment respectively but not interpret it as matrix multiplication. I was working with a for loop but couldn't get that to work either. New to Matlab.

Best Answer

N:0 is length 0.

N:-1:0 would be length N+1

After that change the / to ./ and change the * to .*

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Have your vectors of weights be the same size as your vectors of locations, ordered so that corresponding weights and locations are in the same position:

%% parameters
a = -1; % lower bound
b = 1; % upper bound 
n = [-1/sqrt(3) 1/sqrt(3)]; %location values for n=2
n1 = [-0.86113 -0.33998 0.33998 0.86113]; %location values for n=4
n2 = [-0.93246 -0.66120 -0.23861 0.23861 0.66120 0.993246]; % location values for n=6
w = [1 1]; %weight for n=2
w1 = [0.34785 0.625214 0.625214 0.34785]; %weights for n=4
w2 = [0.17132 0.36076 0.6791 0.6791 0.36076 0.17132]; % weights for n=6
f = @(x) (1)./(x.^2 .* (sqrt(x.^2 +1)));%function 
%% Gauss_Legendre Quadrature 
% n=2
gaussleg = sum(w.*f(n));
%n=4
gaussleg1 = sum(w1.*f(n1));
%n=6
gaussleg2 = sum(w2.*f(n2));

Higher precision in your weights and locations will give more accurate results.

(edit) I also changed f slightly so that you could pass in the entire vector of locations at once.

MATLAB: Error using ==> rdivide

Use the bsxfun() function:

>> w = bsxfun(@rdivide,w,sum(w,1));

Best Answer

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