# How to substitute x and y with X and Y respectively and get the same result as Test1(last line of my code)

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WLL on 8 Jun 2021
Edited: WLL on 8 Jun 2021
Below is my code. About the last line of my code, I would like to know how to substitute x and y with X and Y respectively and get the same result as Test1. Test1 is the output of "combine_wxx=vpa(combine_wxx)"
Thank you very much!!
clc
clear
format long
E=209e+3;
q=-1;
h=15;
D=6.459478021978022e+07;
I=2.8125e+02;
a=600;b=2400;
% change the value of mn
n =3;
[T1, T2] = meshgrid(1:2:n);
mn = [T1(:), T2(:)]
syms x y
x_value=0:100:600;
y_value=0:100:2400;
[X,Y]=meshgrid(x_value,y_value) ;
% Fine the amn
len=length(mn);
amn=zeros(1,len);
for i=1:len
m=mn(i,1);
n=mn(i,2);
amn(i)=(16*q/(m*n*D*pi^6))*(1/((m/a)^2+(n/b)^2)^2);
end
% Fine the wmn
for i=1:len
m=mn(i,1);
n=mn(i,2);
wmn(i)=amn(i).*((sin(m.*pi.*x./a)).*(sin(n.*pi.*y./b)));
wxx(i)=diff(wmn(i),x,2);
wyy(i)=diff(wmn(i),y,2);
end
combine_wxx=sum(wxx);
combine_wxx=vpa(combine_wxx)
% Test1 is the output of "combine_wxx=vpa(combine_wxx)" and I substitute x and y with X and Y respectively.
Test1=0.000010011120098275262104647981847237*sin(0.015707963267948966192313216916398.*X).*sin(0.0039269908169872415480783042290994.*Y) + 0.000033438807664284280352743957795044*sin(0.015707963267948966192313216916398.*X).*sin(0.0013089969389957471826927680763665.*Y) + 0.00012498683220294698455252916478176.*sin(0.0039269908169872415480783042290994.*Y).*sin(0.0052359877559829887307710723054658.*X) + 0.00081090072796029611652649055794769.*sin(0.0052359877559829887307710723054658.*X).*sin(0.0013089969389957471826927680763665.*Y)
% How should I use "subs" function or other function which you suggest to substitute x and y with X and Y respectively and get the same result as Test1
% I have tried "wxx_value=subs(combine_wxx,[x,y],[X,Y])" but it showed "Inconsistency between sizes of second and third arguments."

Sambit Supriya Dash on 8 Jun 2021
Just before your major calculations (where you are willing to use the variables X & Y), you can add a line,
x = X; y = Y;
Then, whatever you write in terms of further calculations, you can use x & y as the replaced variables of X & Y.
WLL on 8 Jun 2021
But it seems the variables x and y do not transfer to X and Y.
I would like to transfer the variables X and Y from x and y for the the calculation of "combine_wxx=sum(wxx)". So I add the "x = X; y = Y;" And I got the combine_wxx =
0.000010011120098275262104647981847237*sin(0.015707963267948966192313216916398*x)*sin(0.0039269908169872415480783042290994*y) + 0.000033438807664284280352743957795044*sin(0.015707963267948966192313216916398*x)*sin(0.0013089969389957471826927680763665*y) + 0.00012498683220294698455252916478176*sin(0.0039269908169872415480783042290994*y)*sin(0.0052359877559829887307710723054658*x) + 0.00081090072796029611652649055794769*sin(0.0052359877559829887307710723054658*x)*sin(0.0013089969389957471826927680763665*y)
Also, the X and Y is 25 x 7 matrix, so the combine_wxx should also be 25 x 7 matrix.
Then I will try to use the funtion mesh(X,Y,combine_wxx) to plot the result.
Below is my code
clc
clear
format long
E=209e+3;
q=-1;
h=15;
D=6.459478021978022e+07;
I=2.8125e+02;
a=600;b=2400;
% change the value of mn
n =3;
[T1, T2] = meshgrid(1:2:n);
mn = [T1(:), T2(:)]
syms x y
x_value=0:100:600;
y_value=0:100:2400;
[X,Y]=meshgrid(x_value,y_value) ;
% Fine the amn
len=length(mn);
amn=zeros(1,len);
for i=1:len
m=mn(i,1);
n=mn(i,2);
amn(i)=(16*q/(m*n*D*pi^6))*(1/((m/a)^2+(n/b)^2)^2); % amn(i) storage the array
end
% Fine the wmn
for i=1:len
m=mn(i,1);
n=mn(i,2);
wmn(i)=amn(i).*((sin(m.*pi.*x./a)).*(sin(n.*pi.*y./b)));
wxx(i)=diff(wmn(i),x,2);
wyy(i)=diff(wmn(i),y,2);
end
x = X; y = Y;
combine_wxx=sum(wxx);
combine_wxx=vpa(combine_wxx)
% Test1 is the output of "combine_wxx=vpa(combine_wxx)" and I substitute x and y with X and Y respectively.
%Test1=0.000010011120098275262104647981847237*sin(0.015707963267948966192313216916398.*X).*sin(0.0039269908169872415480783042290994.*Y) + 0.000033438807664284280352743957795044*sin(0.015707963267948966192313216916398.*X).*sin(0.0013089969389957471826927680763665.*Y) + 0.00012498683220294698455252916478176.*sin(0.0039269908169872415480783042290994.*Y).*sin(0.0052359877559829887307710723054658.*X) + 0.00081090072796029611652649055794769.*sin(0.0052359877559829887307710723054658.*X).*sin(0.0013089969389957471826927680763665.*Y)
% How should I use "subs" function or other function which you suggest to substitute x and y with X and Y respectively and get the same result as Test1
% I have tried "wxx_value=subs(combine_wxx,[x,y],[X,Y])" but it showed "Inconsistency between sizes of second and third arguments."

R2021a

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