I am working on maxima and minima of multi variables.getting multiple same errors "Variable appears to change size on every loop iteration. Consider preallocating for speed"

clc 
clear 
clear all
syms x y 
f(x,y) = input('Enter the function f(x,y):'); 
p = diff(f,x); q=diff(f,y); 
[ax,ay] = solve(p,q); 
ax = double(ax);ay=double(ay); %
r = diff(p,x); s = diff(q,x); t = diff(q,y); D = r*t-s^2; 
%figure 
fsurf(f); 
legstr={'Function Plot'}; % For legend
for i=1:size(ax) 
T1=D(ax(i),ay(i)); 
T2=r(ax(i),ay(i)); 
T3=f(ax(i),ay(i)); 
if(double(T1)==0) 
sprintf('At (%f,%f) further investigation is required',ax(i),ay(i)) 
legstr = [legstr,{'Case of Further investigation'}]; 
mkr ='ko'; 
elseif (double(T1)<0) 
sprintf('The point (%f,%f) is a saddle point', ax(i),ay(i)) 
legstr = [legstr,{'Saddle Point'}]; % updating Legend
mkr ='bv'; % marker
else
if (double(T2) > 0) 
sprintf('The maximum value of the function is f(%f,%f)=%f', ax(i),ay(i), T3) 
legstr = [legstr,{'Maximum value of the function'}];% updating Legend
mkr='g+';% marker
else
sprintf('The minimum value of the function is f(%f,%f)=%f', ax(i),ay(i), T3) 
legstr = [legstr,{'Minimum value of the function'}];% updating Legend 
mkr='r*'; % marker
end
end
hold on
plot3(ax(i),ay(i),T3,mkr,'Linewidth',4); 
end
legend(legstr,'Location','Best'); 

Answer 1

[Torsten]

It's just a warning, not an error, because you didn't preallocate an array somewhere - usually nothing to worry about. In your case, you didn't preallocate "legstr".

And I think your classification of the critical points is incorrect. Check here for the correct classification:

https://en.wikipedia.org/wiki/Second_partial_derivative_test

And you should use "Local Maximum" and "Local Minimum" instead of "Maximum value" and "Minimum value" in your legend.