How to plot the surface $z= f(x,y)=\sum_{n=0}^100 x^{2-n}y^{n/2}$ for $0
Check this link: https://in.mathworks.com/help/matlab/ref/meshgrid.html
Alternatively, PFA a crude code (debugging required). Use the above method as a better practice.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
clear all
clc
x = 0.1:1/10:10;
y = 0.1:1/10:10;
lenX = length(x);
lenY = length(y);
[X,Y] = meshgrid(x,y);
z = zeros(lenX,lenY);
for i = 1:length(x)
for j = 1:length(y)
temp = 0;
for n = 0:100
temp = temp + (x(i).^(2-n))*(y(j).^(n/2));
end
z(i,j) = temp;
end
end
surf(X,Y,z);
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Here is a (numerical) solution of your problem:
n = 0:1:100;
x = 0:0.1:10; % generate x coordinates
y = 0:0.1:10; % generate y coordinates
[X,Y] = meshgrid(x,y); % generate mesh
temp = zeros(length(y), length(x), length(n)); % preallocate array for temporary results
for i = 1:length(n)
temp(:, :, i) = X.^(2-n(i)).*Y.^(n(i)/2); % evaluate values at given n
end
fxy = sum(temp, 3); % summation along the 3rd dimension
surf(X, Y, fxy);
The two previous answers are a great start, BUT ...not sure we can assume that the variation for n from 0 to 100 is the same as over the grid of x and y ?? clarification please
x=linspace(0,10,50);
y=linspace(0,10,100);
n = 0:1:100;
z=zeros(size(x,2),size(y,2));
for i=1:size(n,2)
z= z + (x.^(2-n(i)))'*(y.^(n(i)/2));
end
surf(y,x,z)
my solution.
Dear Prof. Samanta and Somolik,
Thank you for your kind suggestions. Comparing the both your suggestions the idea diverges each other. Although, the shape of the of plots are converging but the directions are opposite to each other.
Let me do a quick check of an arbitrary function of a known shape.
Let me choose the following function:
f(x,y) = \sum_(n=0)^4 (x - 10)^n + y^n, where 0
My previous concern was based on an erroneous reading -- I see now what the function looks like, and that it is to be evaluated at a grid of X,Y values.
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