How to normalize plot?

How to normalize the plot to one?

clc;clear all;close all;
syms x y 
x0 = -.02:0.001:.02;lambda=532*10^-9;
y0 = -.02:0.001:.02;w0 = 0.002;
omegax=1;omegay=2;zr=pi*w0^2/lambda;

m = 2;
s=1;k=0.0002;Rx=zr;Ry=Rx;
[X0,Y0] = meshgrid(x0,y0);
f = @(x0,y0)sinh((omegax*x0+omegay*y0)/w0).*exp(-(x0.^2+y0.^2)/w0^2).*(x0+(1i*s.*y0)).^m.*exp((1i*k/2)*((x0^2/Rx)+(y0^2/Ry)));

I_numerical = real(abs(vpa(f)));
figure
fcontour(real(I_numerical),  [-1 1  -1 1]*1E-2, 'Fill','on', 'MeshDensity',150)
colormap('hot');
colorbar('vert');
axis('equal')

Answer 1

[Torsten]

x0 = -.02:0.001:.02;lambda=532*10^-9;
y0 = -.02:0.001:.02;w0 = 0.002;
omegax=1;omegay=2;zr=pi*w0^2/lambda;
m = 2;
s=1;k=0.0002;Rx=zr;Ry=Rx;
[X0,Y0] = meshgrid(x0,y0);
f = @(x0,y0)sinh((omegax*x0+omegay*y0)/w0).*exp(-(x0.^2+y0.^2)/w0^2).*(x0+(1i*s.*y0)).^m.*exp((1i*k/2)*((x0^2/Rx)+(y0^2/Ry)));
Z0 = arrayfun(@(x,y)f(x,y),X0,Y0);
contourf(X0,Y0,real(abs(Z0))/max(real(abs(Z0(:)))))
colormap('hot');
colorbar('vert');
axis('equal')

[Athira T Das]

How to remove these blacks lines from the plot?

[Star Strider]

Try this —

contourf(X0,Y0,real(abs(Z0))/max(real(abs(Z0(:)))), 'EdgeColor','none')

.

[Athira T Das]

I tried this code for my function and showing some error

clc;clear all;close all;
z=100;
y=linspace(-.1,.1,500);x=y;
[X0,Y0] = meshgrid(x,y);
m =1;
lambda=532*10^(-9);
wo = 0.02;
Omega = 30;
k = (2.*pi)./(lambda); 
Pho=0.05;sgm=1;

Gamma = ((1i.*k)./(2.*z)) + (1./(Pho.^2)) + (1./(wo.^2));
Gamma_star = subs(Gamma, 1i, -1i);
alpha = (Gamma_star) - 1./((Gamma.*Pho.^4));
C = (1./(4.*(lambda.^2).*(z.^2))).*((pi.^2)./(alpha.*Gamma)).*(1./(2.*1i.*sqrt(Gamma)).^m);

fx = ((Omega.^2)./(4.*Gamma)) + ((1i.*k.*x.*Omega)./(2.*z.*Gamma)) - ((k.^2.*x.^2)./(4.*z.^2.*Gamma));
fy = ((Omega.^2)./(4.*Gamma)) + ((1i.*k.*y.*Omega)./(2.*z.*Gamma)) - ((k.^2.*y.^2)./(4.*z.^2.*Gamma));
gx = ((Omega.^2)./(4.*Gamma)) - ((1i.*k.*x.*Omega)./(2.*z.*Gamma)) - ((k.^2.*x.^2)./(4.*z.^2.*Gamma));
gy = ((Omega.^2)./(4.*Gamma)) - ((1i.*k.*y.*Omega)./(2.*z.*Gamma)) - ((k.^2.*y.^2)./(4.*z.^2.*Gamma));
Bx_p = ((-1i.*k.*x)./(2.*z)) + ((1i.*k.*x)./(2.*z.*Gamma.*Pho.^2)) + (Omega)./(2.*Gamma.*Pho.^2) + (Omega./2);
Bx_n = ((-1i.*k.*x)./(2.*z)) + ((1i.*k.*x)./(2.*z.*Gamma.*Pho.^2)) + (Omega)./(2.*Gamma.*Pho.^2) - (Omega./2);
By_p = ((-1i.*k.*y)./(2.*z)) + ((1i.*k.*y)./(2.*z.*Gamma.*Pho.^2)) + (Omega)./(2.*Gamma.*Pho.^2) + (Omega./2);
By_n = ((-1i.*k.*y)./(2.*z)) + ((1i.*k.*y)./(2.*z.*Gamma.*Pho.^2)) + (Omega)./(2.*Gamma.*Pho.^2) - (Omega./2);
Kx_p = ((-1i.*k.*x)./(2.*z)) + ((1i.*k.*x)./(2.*z.*Gamma.*Pho.^2)) - (Omega)./(2.*Gamma.*Pho.^2) + (Omega./2);
Kx_n = ((-1i.*k.*x)./(2.*z)) + ((1i.*k.*x)./(2.*z.*Gamma.*Pho.^2)) - (Omega)./(2.*Gamma.*Pho.^2) - (Omega./2);
Ky_p = ((-1i.*k.*y)./(2.*z)) + ((1i.*k.*y)./(2.*z.*Gamma.*Pho.^2)) - (Omega)./(2.*Gamma.*Pho.^2) + (Omega./2);
Ky_n = ((-1i.*k.*y)./(2.*z)) + ((1i.*k.*y)./(2.*z.*Gamma.*Pho.^2)) - (Omega)./(2.*Gamma.*Pho.^2) - (Omega./2);

X = 0;
for l = 0:m
  L = (((1i).*sgm).^(m-l)).*nchoosek(m,l);
  sum_j = 0;
  for j = 0:m
      J= (((-1i).*sgm).^(m-j)).*nchoosek(m,j);  
      
      sum1 = 0.0;
      for p = 0:1/2:l/2
            faktor1_P = (((-1).^p).*factorial(l))./(gamma(p+1).*factorial(l-(2.*p))).*(((2.*1i)./(sqrt(Gamma))).^(l-(2.*p))).*exp(fx).*exp(fy);
            for s1 = 0:l-2*p
                faktor1_s1 =  nchoosek((l-(2.*p)),s1).*((1./(Pho.^2)).^s1).*((((1i.*k.*x)./(2.*z))+(Omega./2)).^(l-(2.*p)-s1)).*(1./(((2.*1i.*sqrt(alpha))).^(j+s1)));
                for q = 0:1/2:(m-l)/2
                    faktor1_Q = (((-1).^q).*factorial(m-l))./(gamma(q+1).*factorial(m-l-(2.*q))).*(((2.*1i)./(sqrt(Gamma))).^(m-l-(2.*q)));
                   sum_inner_1=0;
                    for s2 = 0:m-l-2*q
                        E1 = (exp(((Bx_p).^2)./alpha).*hermiteH(j+s1,((1i.*Bx_p)./(sqrt(alpha)))).*exp(((By_p).^2)./alpha).*hermiteH(m-j+s2,((1i.*By_p)./(sqrt(alpha))))) - (exp(((Bx_n).^2)./alpha).*hermiteH(j+s1,((1i.*Bx_n)./(sqrt(alpha)))).*exp(((By_n).^2)./alpha).*hermiteH(m-j+s2,((1i.*By_n)./(sqrt(alpha)))));
                        sum_inner_1 =sum_inner_1+ nchoosek((m-l-(2.*q)),s2).*((1./(Pho.^2)).^s2).*((((1i.*k.*y)./(2.*z))+(Omega./2)).^(m-l-(2.*q)-s2)).*(1./(((2.*1i.*sqrt(alpha))).^(m-j+s2))).*E1;
                    end
                end
            end
            sum1 = sum1 + faktor1_P.*faktor1_s1.*faktor1_Q.*sum_inner_1;
       end

   sum_j= sum_j + J.*(sum1);
  end
 X = X + (L.*sum_j);
end  

X = subs(real(C.*X));
I_numerical = real(abs(vpa(X)));
f = @(x,y) I_numerical;
Z0 = arrayfun(@(x1,y1)f(x1,y1),X0,Y0);

Error using arrayfun
Non-scalar in Uniform output, at index 1, output 1.
Set 'UniformOutput' to false.

contourf(X0,Y0,real(abs(Z0))/max(real(abs(Z0(:)))))
colormap('hot');
colorbar('vert');
axis('equal')

[Torsten]

I_numerical is an array of numerical values of size 1x500, not a function.

So setting

f = @(x,y) I_numerical;

makes no sense since f(x,y) will return this 1x500 array for each value pair (x,y).

I don't know against which independent variable(s) you intend I_numerical to plot.

[Athira T Das]

I need to plot I_numerical w.r.t x and y

[Torsten]

Then arrange your code such that I_numerical has size 500x500 since x has 500 elements and y has 500 elements.

At the moment, I_numerical has size 1x500.