How do you make multiple for loops into one for loop?

Hello,

I have a rough code that I want to fix/optimize. I have 5 for loops: all of them utilize the same given data but each loop builds off each other i.e. one loop creates a 10x1 matrix and the following loop uses those values to create a new set and so on. Each loop has a new equation which creates the values that uses the previous loop's value all to end in a final loop that uses all the found values to create a 10x10 matrix. I am struggling to get the final loop to work as well as optimizing the code to reduce the number of loops for the equations. Thank you!

clc; clear vars; clear all;

G=1367;%solar constant
phi=43.07;%lattitude of madison, wi
n=32;
delta = 23.45*sind(360*((284+n)/365));
w1=-75; w2=75; %hour angles from 7AM-5PM
w=15.* [-5 -4 -3 -2 -1 1 2 3 4 5]; %hour angles
t=[8 9 10 11 12 1 2 3 4 5]; %time 7AM-5PM
kT=[0.5 0.5 0.5 0.6 0.6 0.7 0.7 0.7 0.8 0.8]; %given values

A = ((12*3600*G)/pi); %simplified for eq
B = (1+(0.033*cosd((360*n)/365)));%simplified for eq
C = ((cosd(phi)*cosd(delta)*(sind(w2)-sind(w1))...%simplified for eq
    +((pi*(w2-w1)/180)*sind(phi)*sind(delta))));%simplified for eq
Io = A*B*C; %hourly radiation on horizontal surface MJ/m^2

N=length(kT);
O=length(w);
IT=zeros(N, length(w));%populated matrix that fills, used for graphing

for j=1:O %1st loop uses changing w values
    Rb(j,:)=(cosd(phi)*cosd(delta).*cosd(w(j)))+(sind(phi)*sind(delta));
 %this equation is needed for final IT equation
end

for i=1:N %2nd loop needed to find I for final IT equation w/changing kT vals
    I(i,:)=Io.*kT(i); %needed for following loops
end

for i=1:N %3rd loop needed to find Id for final IT equation w/changing kT vals
    Id(i,:)=(.9511-(.1604*kT(i))+(4.388*kT(i)^2)-(16.638*kT(i)^3)+(12.336*kT(i)^4)).*I(i); 
end

for i=1:N %4th loop needed to find Ib for final IT equation w/changing kT vals
    Ib(i,:)=(1-(Id(i)/I(i)))*I(i);
end

for i=1:N %final loop uses all values created by previous loops to create a 10x10 matrix
    %not exactly sure how to do the final loop, this is a rough guess
    for k=1:length(w)
        IT(i,k)=(Ib(i)*Rb(k))+(Id(i)*((1-cosd(beta))/2))+(I(i)*rho*((1-cosd(beta))/2));
        %not sure if this is possible
    end
end

[Manikanta Aditya]

Hey,

Looks like you are trying to calculate the values of 'Rb', 'I','Id','Ib' and 'IT' in seperate loops. You can actually calculate all these values in a single loop.

clc; clear vars; clear all;

G=1367; %solar constant
phi=43.07; %latitude of Madison, WI
n=32;
delta = 23.45*sind(360*((284+n)/365));
w1=-75; w2=75; %hour angles from 7AM-5PM
w=15.* [-5 -4 -3 -2 -1 1 2 3 4 5]; %hour angles
kT=[0.5 0.5 0.5 0.6 0.6 0.7 0.7 0.7 0.8 0.8]; %given values
A = ((12*3600*G)/pi); %simplified for eq
B = (1+(0.033*cosd((360*n)/365))); %simplified for eq
C = ((cosd(phi)*cosd(delta)*(sind(w2)-sind(w1))... %simplified for eq
    +((pi*(w2-w1)/180)*sind(phi)*sind(delta))); %simplified for eq
Io = A*B*C; %hourly radiation on horizontal surface MJ/m^2

N=length(kT);
O=length(w);
IT=zeros(N, length(w)); %populated matrix that fills, used for graphing

for i=1:N
    for j=1:O
        Rb=(cosd(phi)*cosd(delta).*cosd(w(j)))+(sind(phi)*sind(delta));
        I=Io.*kT(i);
        Id=(.9511-(.1604*kT(i))+(4.388*kT(i)^2)-(16.638*kT(i)^3)+(12.336*kT(i)^4)).*I;
        Ib=(1-(Id/I))*I;
        IT(i,j)=(Ib*Rb)+(Id*((1-cosd(beta))/2))+(I*rho*((1-cosd(beta))/2));
    end
end

Thanks.

[Fabian]

Thank you so much for the help, this solved my issue!

Answer 1

[Voss]

No loops required:

Rb = cosd(phi)*cosd(delta).*cosd(w)+(sind(phi)*sind(delta));      % row vector the same size as w

I = Io.*kT;                                                       % row vector the same size as kT

Id = (0.9511-0.1604*kT+4.388*kT.^2-16.638*kT.^3+12.336*kT.^4).*I; % row vector the same size as kT and I

Ib = (1-(Id./I)).*I;                                              % row vector the same size as kT, I, and Id

IT = Ib.'.*Rb+Id.'.*(1-cosd(beta))/2+I.'*rho*((1-cosd(beta))/2);  % matrix of size numel(kT)-by-numel(w)
                                                                  % because I, Id, and Ib are transposed
                                                                  % in this line and Rb is not

(Assuming beta and rho are scalars - they are not defined in the question.)

[Fabian]

Thank you for the help, this solved my issue!

[Voss]

You're welcome!