MATLAB: Converting equation to matlab

equationMATLAB

Hi, I am trying to convert the following equation to matlab code. I have a bunch of defined constants above this code but I am trying to figure out if my formatting is correct since I keep getting the wrong answer. I need to multiply the two functions and they are dependant on the variable E, everything else is a constant. Thanks!

Best Answer

% note .* to get element by element multiplication
% ./ for element by element division
g = 1.0/(2*pi^2*h^3)*(2*m)^(3/2)*sqrt(E-Ec) 
f = 1.0 ./(1+exp((E-Ef)/(k*T))) 
N = g.*f

Sorry I didn't notice you already had some code for N = g.*f at the bottom of your original post, I just saw the typeset equations. Maybe this is equivalent what you already have. If so I guess there is a problem in your definition of the constants. In any case you have some unecessary parenthesis and also the ./ in your first equation is not needed when the denominator is a scalar.

You also have some apparently unecessary parentheses in your definition of the constants. This is a good reference on Matlab's precedence rules https://www.mathworks.com/help/matlab/matlab_prog/operator-precedence.html

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MATLAB: Silly error somewhere in the code

This time a real answer: it's a math problem. If that's ok, I'll answer with some latex code.

Let f be the norm(0,1) pdf

Q5= \int (h_1 x^2+h_2 x +h_3) f(x) dx
  = h_1 E(X^2) + h_2 E(X) + h_3

Editing: the following was not correct (wrong definition of moment generating function)

*********************************

Now, the moment generating function M(t) gives:

M(0)=1
M(1)=1+E(X)
M(2)=1+E(X)+2E(X^2)

So Q6 would look like this:

Q6=h_1 M(2) + h_2 M(1) + h_3 M(0)
  =h_1 (1+E(X)+2E(X^2)) + h_2 (1+E(X)) + h_3
************************************
And is therefore not equal to Q5.

Convinced?

MATLAB: How to store output of looping integral in an array

I'm guessing you have some kind of units issue, such that something you are calculating is many orders of magnitude out of whack, or that you have something wrong in your formula.

You didn't tell us what all of those constants are (e.g. k), so I just set them all to 1, just to see if I could get your code to work at all.

I got what you did ... all the values the same. But I noticed that you are integrating over a tiny interval of something around 10^-18. So, it's not too surprising that your functions are all effectively equal over that tiny range, and give the same result.

When I integrate over [Ec, Ec+5000], I see variation in the output.

So, I would just carefully check all your units and the formula itself.

Best Answer

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MATLAB: Silly error somewhere in the code

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