How can i improve my code

syms E Eg V g;
z=[ ];
y=[ ];

c=3 .*(10.^8); 
h=4.1361e-015; 
k=8.62E-5;
Tc=300;

for Ei=0.5:0.05:1.3;
         z=[ ];
for Eg=1.4:0.01:3.2;

Ec=Eg-Ei;
a = quad( @(E)(E.^2) ./ (exp(E./0.5172)-1), Eg , 100);
aa= quad( @(E)(E.^2) ./ (exp(E./0.5172)-1), Ec , Eg);

for Ucv=Eg-.2:0.005:Eg-.01;
for Uiv=Ei-.1:.005:Ei-.01;
Pin = 1.4458e+026 ;  
Uci=Ucv-Uiv;                                                        

b = quad(@(E)(E.^2) ./ (exp(( E-Ucv )./0.0259)-1),Eg,100);
bb= quad(@(E)(E.^2) ./ (exp(( E-Uci )./0.0259)-1),Ec,Eg);

if abs(quad( @(E)(E.^2) ./ (exp(E./0.5172)-1), Ei , Ec)- quad(@(E)(E.^2) ./ (exp(( E-Uiv )./0.0259)-1),Ei,Ec)-...
        aa+bb)  <=  10^-3

P = ( 2.*Ucv./6.3682e-027 ) .* ( a + aa - b - bb ) ./ Pin  

z = [z P]  
m = max(z) 
  end

end
end
end
y=[y m]
end

Ei=0.5:0.05:1.3;
plot(Ei,y,'b')
xlabel('Ei');
ylabel('η[%]');

it have to spend 4~5 hours , how can i improve so that more efficiency ?

Answer 1

[Jan]

I did not work with symbolic math in Matlab yet. Therefore I have a silly question:

syms E Eg 
...
for Eg=1.4:0.01:3.2
  ...
  b = quad(@(E)(E.^2) ./ (exp(( E-Ucv )./0.0259)-1),Eg,100)

1. Is is the symbolic type for Eg useful, when it is a counter in a FOR loop? Or is the type ignored and Eg is a double?
2. When quad operates on an anonymous function, which contains a symbolic variable, is the quadrature computed symbolically?
3. Isn't it possible and much faster to solve the integral over an exponential function manually?
4. The repeated growing of z and y is a bad idea, look for "pre-allocation" in this forum. Even MLint should display a corresponding warning, which should be considered carefully. But I assume, that profile will show, that this is not the bottleneck, but the symbolic (?) quad s are more expensive.

[Walter Roberson]

When a name is used in an anonymous function dummy argument, the situation is equivalent to using it as an input argument name in a "real" function -- that is, whatever value or type the name has in the surrounding expression is ignored.

When a name has been declared through syms and then that same name is used as the loop index variable in a "for" loop, the names existence as a symbolic variable is forgotten (except that if any constraints had been put on the name, the constraints might be properly erased.)

Answer 2

[Walter Roberson]

One kind of thing to look for:

The code line

b = quad(@(E)(E.^2) ./ (exp(( E-Ucv )./0.0259)-1),Eg,100);

does not depend upon the value of Uiv, so you can calculate the value before you start the "for Uiv" loop.

[Tai-i]

it doesn't have significant work ...

Answer 3

[Rahul Kashyap]

try to make the divisions smaller. you have the following statements:

for Ei=0.5:0.05:1.3;

for Eg=1.4:0.01:3.2;

for Ucv=Eg-.2:0.005:Eg-.01;

for Uiv=Ei-.1:.005:Ei-.01;

replace the above lines with:

for Ei=0.5:0.5:1.3;

for Eg=1.4:0.1:3.2;

for Ucv=Eg-.2:0.5:Eg-.01;

for Uiv=Ei-.1:.5:Ei-.01;

this will decrease the iterations. although, its a trade off between accuracy but you should give it a try. if we use your code, the loop will run 17x181x39x19 times, but if you try my statements it will run for 19x2 times. give it a try :)

[Tai-i]

thx ^^.

[Rahul Kashyap]

did it worked?