I am really trying to optimize calculus code on MATLAB.
This is a difficult calculation necessary to obtain material properties of a nonlinear material.
This calculation requires more than 240 million steps. It is quite simple in itself, since it consists of a huge amount sum. The only problem is that the numbers are stored in different arrays and lists, which are a bit confusing.
Here is the source code:
Tensor=zeros(3,3,3,3);
for m=1:3
for n=1:3
for o=1:3
for p=1:3
for x=1:16
for y=1:16
for z=1:16
for i=1:3
for j=1:3
for k=1:3
for l=1:3
for r=1:3
for s=1:3
sum=sum+(1/(8*(pi()^2))*P{x,y,z}(i,m)*P{x,y,z}(j,n)*P{x,y,z}(k,o)*P{x,y,z}(l,p)*(TensorC(i,j,k,l)-TensorC0(i,j,r,s))*TensorA(r,s,k,l)*sin(omega(x))*p_omega(x)*p_phi(y)*p_beta(z);
end
end
end
end
end
end
end
end
end
Tensor(m,n,o,p)=sum;
end
end
end
end
P{x,y,z}(i,m)- this is a change in the basic formula (the same for others): to i and mdetermine the type of formula, and the result is calculated using variables x, yand z.
All other numbers in the summation are real numbers collected in arrays and tensors.
, , :
Tensor=zeros(3,3,3,3);
CO1=1/(8*(pi()^2));
for m=1:3
for n=1:3
for o=1:3
for p=1:3
sum=C0_tensor(m,n,o,p);
for x=1:16
CO7=sin(omega(x));
CO8=p_omega(x);
for y=1:16
CO9=p_phi(y);
for z=1:16
CO10=p_beta(z);
for i=1:3
CO2=P{x,y,z}(i,m);
for j=1:3
CO3=P{x,y,z}(j,n);
for k=1:3
CO4=P{x,y,z}(k,o);
for l=1:3
CO5=P{x,y,z}(l,p);
CO6=TensorC(i,j,k,l);
for r=1:3
for s=1:3
CO11=TensorC0(i,j,r,s);
CO12=TensorA(r,s,k,l);
sum=sum+CO1*CO2*CO3*CO4*CO5*(CO6-CO11)*CO12*CO7*CO8*CO9*CO10;
end
end
end
end
end
end
end
end
end
Tensor(m,n,o,p)=sum;
end
end
end
end
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