Efficiency and alternatives for for loops

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Good afternoon,
Recently I have been trying to plot multiple 2D plots of a yield surface equation, the goal was to be able to show the multiple parameters. The problem I am having is the enormous amount of for loops I am having to run, which im now finding our very expensive (Im relatively new). Could someone help me find an alternative? would declaring a matrix of data points rather then running a for loop be faster?
Heres a sample of the code, for refrence I would have to repeat this around 5 times for 1 surface.
Is there a way to have everything within the first 3 for loops? I have tried to puzzle my way around this but nothing seems to work.
Thank you for the time!
Kevin
clc; clear; close all;
tic;
Yieldstr = 1000; %KPa
f = 0.8; g = 0.6; h = 0.4;
f1 = 0.2; g1 = 0.4; h1 = 0.6;
f2 = 0.8; g2 = 0.4; h2 = 0.2;
l = 0.5; m = 0.6; n = 0.4;
l1 = 0.4; m1 = 0.2; n1 = 0.7;
l2 = 0.8; m2 = 0.1; n2 = 1.0;
PStress = zeros(134343,3);
PStress12 = zeros(134343,2);
PStress23 = zeros(134343,2);
Shear12 = zeros(42334,2);
Shear23 = zeros(42334,2);
minValue = -4*Yieldstr;
maxValue = 4*Yieldstr;
fidelity = Yieldstr/125;
i=1;
j=1;
k=1;
for sigx = minValue:fidelity:maxValue
for sigy = minValue:fidelity:maxValue
for sigz = 0:0
Hill12 = sqrt(((1/2).*((g+h).*sigx.^2)) + ((1/2).*((f+h).*sigy.^2)) - h.*sigx.*sigy);
if Hill12 < Yieldstr
if (sigx==sigy)
%stops code
else
PStress12(i,1) = sigx;
PStress12(i,2) = sigy;
i = i + 1;
end
end
end
end
end
for sigx = minValue:fidelity:maxValue
for sigy = minValue:fidelity:maxValue
for sigz = 0:0
Hill121 = sqrt(((1/2).*((g1+h1).*sigx.^2)) + ((1/2).*((f1+h1).*sigy.^2)) - h1.*sigx.*sigy);
Hill122 = sqrt(((1/2).*((g2+h2).*sigx.^2)) + ((1/2).*((f2+h2).*sigy.^2)) - h2.*sigx.*sigy);
if Hill121 < Yieldstr
if (sigx==sigy)
%stops code
else
PStress121(j,1) = sigx;
PStress121(j,2) = sigy;
j = j + 1;
end
end
end
end
end
for sigx = minValue:fidelity:maxValue
for sigy = minValue:fidelity:maxValue
for sigz = 0:0
Hill122 = sqrt(((1/2).*((g2+h2).*sigx.^2)) + ((1/2).*((f2+h2).*sigy.^2)) - h2.*sigx.*sigy);
if Hill122 < Yieldstr
if (sigx==sigy)
%stops code
else
PStress122(k,1) = sigx;
PStress122(k,2) = sigy;
k = k + 1;
end
end
end
end
end
G = boundary(PStress12,0);
plot(PStress12(G,1),PStress12(G,2),'LineWidth',1.75);
hold on
G1 = boundary(PStress121,0);
plot(PStress121(G1,1),PStress121(G1,2),'LineWidth',1.75);
G2 = boundary(PStress122,0);
plot(PStress122(G2,1),PStress122(G2,2),'LineWidth',1.75);
hold off
axis('tight')
title('\sigma_y vs \sigma_x')
legend('f = 0.8, g = 0.6, h = 0.4','f = 0.2, g = 0.4, h = 0.6','f = 0.8, g = 0.4, h = 0.2','Location',"best")
xlabel('\sigma_x (KPa)');
ylabel('\sigma_y (KPa)');

Accepted Answer

DGM
DGM on 30 Sep 2021
Edited: DGM on 30 Sep 2021
I'm not sure if this is going to give you exactly what you want. The following simplified example will produce the same boundary curve, but the output arrays will be shorter, since they only include the points within the ROI. I'm only doing the first loop for sake of clarity, but the other should be very similar.
clc; clf; clearvars
Yieldstr = 1000; %KPa
f = 0.8; g = 0.6; h = 0.4;
f1 = 0.2; g1 = 0.4; h1 = 0.6;
f2 = 0.8; g2 = 0.4; h2 = 0.2;
l = 0.5; m = 0.6; n = 0.4;
l1 = 0.4; m1 = 0.2; n1 = 0.7;
l2 = 0.8; m2 = 0.1; n2 = 1.0;
kw = 4; % 4
kf = 125; % 125
minValue = -kw*Yieldstr;
maxValue = kw*Yieldstr;
fidelity = Yieldstr/kf;
% OLD METHOD
tic
PStress12 = zeros(134343,2);
i=1;
for sigx = minValue:fidelity:maxValue
for sigy = minValue:fidelity:maxValue
for sigz = 0:0
Hill12 = sqrt(((1/2).*((g+h).*sigx.^2)) + ((1/2).*((f+h).*sigy.^2)) - h.*sigx.*sigy);
if Hill12 < Yieldstr
if (sigx==sigy)
%stops code
else
PStress12(i,1) = sigx;
PStress12(i,2) = sigy;
i = i + 1;
end
end
end
end
end
toc
Elapsed time is 0.040100 seconds.
G_orig = boundary(PStress12,0);
% ALT METHOD
tic
sigx = minValue:fidelity:maxValue;
sigy = sigx.'; % if sigx,sigy are never unique, this may simplify further
Hill12 = sqrt(((1/2).*((g+h).*sigx.^2)) + ((1/2).*((f+h).*sigy.^2)) - h.*sigx.*sigy);
[m,n,~] = find(Hill12 < Yieldstr);
PStress12 = [sigx(n).' sigy(m)]; % note we don't need to preallocate this array anymore
PStress12 = PStress12(PStress12(:,1)~=PStress12(:,2),:); % idk why this is necessary
toc
Elapsed time is 0.026506 seconds.
G = boundary(PStress12,0);
plot(PStress12(G,1),PStress12(G,2),'LineWidth',1.75);
immse(G_orig,G) % show that the two boundary curves are identical
ans = 0
I imagine there are yet ways to expedite things.
  2 Comments
Kevin Hanekom
Kevin Hanekom on 30 Sep 2021
That contourf plot looks amazing, thank you both for these amazing ideas!! I think doing it your way @DGM will allow me to write each equation in "one loop" rather then the 3 for loops i needed for each equation resulting in a final 15 for loops (old way).
Thank you again!

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