How to integrate a function inside the for loop ?
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I am trying to do integration inside a for loop. I am having problem with the matrix dimension or syntax maybe. Would anyone please help me fix it. Also It would like to plot the result of the integration.
clc
close all
clear all
Fs= 2.16*10^-5*pi; % Geometrical Factor for sun
Fa=pi; % Geometrical Factor for earth
Q=1.6*10^-16; % Electronic Charge
h= 4.136*10^-15; % Plancks Constant
c= 3*10^8; % Speed of light
K = 8.61*10^-5; % Boltzmanns Constant
Ts=5760; % Temparature of the sun
Ta=300; % Ambient Temparature
Eg=1.6; % BandGap Energy
A=((2*Fs)/(h^3*c^2));
B=(K*Ts);
C=((2*Fa)/(h^3*c^2));
D=(K*Ta);
vdata=0:0.01:1.6;
n=length(vdata);
q=zeros(1,n);
for i=1:n
V=vdata(i);
fun=@(E)((q.*E.^2).*((A/(exp(E./B)-1))-(C/(exp(E-(Q.*V))./B)-1)-(C/(exp(E./D)-1))));
q(i)=integral(fun,Eg,inf);
end
plot(V,q)
Accepted Answer
Your E will not be a scalar, so having something "/" a calculation involving E would be invoking the "matrix right divide" operator, not the element-by-element division operator.
However even if you fix that, you have the issue that your function involves multiplying by all of q where q is a vector, so the integral would have to result in a vector (one for each element of q). Because integral() passes in a non-scalar for the parameter, that is incompatible -- unless you use the 'vectorized', true option which would pass in a scalar for E and so allow a vector result the same size as q to be returned. But... your context expects a scalar result.
Each time you include all of q in your fun you are using a q that has at least some of the entries still as their zeros() . Each of those leads to a zero result because the 0 will be multiplying the entire result of the term. But.. that includes the first time, where q is all zero, so the first output would return all 0, and no matter which of those all-zero values you selected to store into q(i), you would be storing a zero, so q would not change. And that implies that all of your results are going to come out zero.
I think you need to reconsider using q inside fun . Perhaps it was intended to be Q ?
Fs= 2.16*10^-5*pi; % Geometrical Factor for sun
Fa=pi; % Geometrical Factor for earth
Q=1.6*10^-16; % Electronic Charge
h= 4.136*10^-15; % Plancks Constant
c= 3*10^8; % Speed of light
K = 8.61*10^-5; % Boltzmanns Constant
Ts=5760; % Temparature of the sun
Ta=300; % Ambient Temparature
Eg=1.6; % BandGap Energy
A=((2*Fs)/(h^3*c^2));
B=(K*Ts);
C=((2*Fa)/(h^3*c^2));
D=(K*Ta);
vdata=0:0.01:1.6;
n=length(vdata);
q=zeros(1,n);
for i=1:n
V=vdata(i);
fun=@(E)((q.*E.^2).*((A./(exp(E./B)-1))-(C./(exp(E-(Q.*V))./B)-1)-(C./(exp(E./D)-1))));
whos
q(i)=integral(fun,Eg,inf);
end
plot(V,q)
4 Comments
Md. Golam Zakaria
on 3 Feb 2022
Walter Roberson
on 3 Feb 2022
Edited: Walter Roberson
on 3 Feb 2022
Your function goes to infinity as E goes to infinity -- at least for positive V it does. So your integrals are always infinite.
Fs= 2.16*10^-5*pi; % Geometrical Factor for sun
Fa=pi; % Geometrical Factor for earth
Q=1.6*10^-16; % Electronic Charge
h= 4.136*10^-15; % Plancks Constant
c= 3*10^8; % Speed of light
K = 8.61*10^-5; % Boltzmanns Constant
Ts=5760; % Temparature of the sun
Ta=300; % Ambient Temparature
Eg=1.6; % BandGap Energy
A=((2*Fs)/(h^3*c^2));
B=(K*Ts);
C=((2*Fa)/(h^3*c^2));
D=(K*Ta);
vdata=0:0.01:1.6;
n=length(vdata);
q=zeros(1,n);
syms E V
F = ((Q.*E.^2).*((A./(exp(E./B)-1))-(C./(exp(E-(Q.*V))./B)-1)-(C./(exp(E./D)-1))))
string(F)
L0 = limit(limit(F, V, 0),E,inf)
L1 = limit(limit(F, V, 1),E,inf)
limit(F, E, inf)
Md. Golam Zakaria
on 3 Feb 2022
The following code gives a reasonable output. Would you take a look and confirm whether I can use the plot command as I used.
Fs= 2.16*10^-5*pi; % Geometrical Factor for sun
Fa=pi; % Geometrical Factor for earth
Q=1.6*10^-16; % Electronic Charge
h= 4.136*10^-15; % Plancks Constant
c= 3*10^8; % Speed of light
K = 8.61*10^-5; % Boltzmanns Constant
Ts=5760; % Temparature of the sun
Ta=300; % Ambient Temparature
Eg=1.6; % BandGap Energy
A=((2*Fs)/(h^3*c^2));
B=(K*Ts);
C=((2*Fa)/(h^3*c^2));
D=(K*Ta);
vdata=0:0.001:1.6;
n=length(vdata);
q=zeros(1,n);
for i=1:n
V=vdata(i);
fun=@(E) Q.*((E.^2).*((A./(exp(E./B)-1))-(C./(exp(E-(V))./B)-1)-(C./(exp(E./D)-1))));
q(i)=integral(fun,Eg,inf);
end
plot(vdata,q)
No. Your integral is properly infinite, but integrate() is giving up on integrating it after a while.
Fs= 2.16*10^-5*pi; % Geometrical Factor for sun
Fa=pi; % Geometrical Factor for earth
Q=1.6*10^-16; % Electronic Charge
h= 4.136*10^-15; % Plancks Constant
c= 3*10^8; % Speed of light
K = 8.61*10^-5; % Boltzmanns Constant
Ts=5760; % Temparature of the sun
Ta=300; % Ambient Temparature
Eg=1.6; % BandGap Energy
A=((2*Fs)/(h^3*c^2));
B=(K*Ts);
C=((2*Fa)/(h^3*c^2));
D=(K*Ta);
vdata=0:0.001:1.6;
n=length(vdata);
q=zeros(1,n);
syms V E
fun = Q.*((E.^2).*((A./(exp(E./B)-1))-(C./(exp(E-(V))./B)-1)-(C./(exp(E./D)-1))))
string(fun)
limit(fun, E, inf)
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