I have a function f(x,y)= Exp(-x^2-y^-2)(x^2+y^2). I would like to look at the projection of this function onto the x-axis in MATLAB.
Any thoughts on the best way to do this?
something like this:
xs = [];
ys = [];
zs = [];
for x = -10:0.1:10
for y = -10:0.1:10
xs = [xs x];
ys = [ys y];
z = f(x,y);
zs = [zs z];
end
end
figure; plot3(xs,ys,zs); %plots the full function over both dimensions
figure; plot(xs,zs,'rx'); %plots the projection onto the x axis
figure; plot(ys,zs,'rx'); %plots the projection onto the y axis
that does it over the range -10 to 10 along both x and y but you can change that accordingly.
#Amro has a great solution, but you might also take a look at Scott Hirsch's awesome shadowplot from the MATLAB Central File Exchange. Check it out:
>> f = #(x,y) exp(-x.^2 -y.^(-2)).*(x.^2+y.^2);
>> [X,Y] = meshgrid(-10:0.5:10,-10:0.5:10);
>> surf(X,Y,f(X,Y))
>> xlim([-11,11])
>> ylim([-11,11])
>> shadowplot x
>> shadowplot y
You can manipulate the view to see the 2D-projection on the x-axis:
f = #(x,y) exp(-x.^2 -y.^(-2)).*(x.^2+y.^2);
[X,Y] = meshgrid(-10:0.5:10,-10:0.5:10);
surf(X,Y,f(X,Y))
view(90,0), shading interp
xlabel X, ylabel Y, zlabel Z
Related
How do I plot xyz In rectangular, polar, and 3-D?
for x = 0 to 35pi:
Y = x*sin(x)
Z = x*cos(x)
Using the the intervals of X which provides very smooth plots . Create three plots including tittle and labels .
This is the input I have put in so far. I'm not sure if this is correct:
x = pi*linspace(0,35);
y = pi*x,sin(pi*x);
z = pi*x,cos(pi*x);
plot3(x,y,z)
title('data analysis')
xlabel('independent x')
ylabel('dependent y')
zlabel('z')
I believe this solves the problem as you describe it:
x = linspace(0, 35*pi, 10000);
y = x .* sin(x);
z = x .* cos(x);
plot3(x, y, z);
title('data analysis');
xlabel('independent x');
ylabel('dependent y');
zlabel('z');
I would like to make a scattered stars and plot multiple spheres on top of it? I tried doing this:
x = rand(100,1); y = rand(100,1); z = rand(100,1);
scatter(x,y,z,'c*')
After this I tried plotting sphere but the sphere pushes the stars to the side. How do I fix this?
vec = [1;1;1]; rads = 1;
[x y z] = sphere;
x = rads*x+vec(1); y = rads*y+vec(2);
z = rads*z+vec(3);
surf(x, y, z, 'Edgecolor', 'none')
colormap colorcube
As you can see it pushed the stars to the side
Thank you.
Its pushing the scatter plot to the side because the range of the 'stars' is [0 1] because the command rand(...) generates values between 0 and 1. On the other hand, the sphere goes from 0 to 2 in all 3 directions.
To fix the problem, you can simply multiply the data used to generate the scatter plot by 2, so they will be in the range [0 2].
Doing so results in the following:
And the code. Note that I used scatter3 instead of scatter.
clear
clc
close all
xs = 2*rand(100,1); ys = 2*rand(100,1); zs = 2*rand(100,1);
hScatter = scatter3(xs,ys,zs,'c*')
hold on
vec = [1;1;1]; rads = 1;
[x y z] = sphere;
x = rads*x+vec(1); y = rads*y+vec(2);
z = rads*z+vec(3);
surf(x, y, z, 'Edgecolor', 'none')
colormap colorcube
rotate3d on
I'm having issues unterstanding the function fill in MATLAB , I have a PSD of a file the I want to change it background like :
[xPSD,f] = pwelch(x,hanning(4096),2048,4096*2 ,fs);
plot(f,10*log10(xPSD));
x= f(100:150);
y= 10*log10(xPSD(100:150))
fill(x,y,'y')
the result is in the right direction but not what I need :
I would like get the color tell x axis like :
is their a way to do this
A working solution is:
[xPSD,f] = pwelch(x,hanning(4096),2048,4096*2 ,fs);
plot(f,10*log10(xPSD));
hold on
x= f(100:150);
y= 10*log10(xPSD(100:150));
yMax = ylim;
yMax = yMax(2);
x = x'; % Use this line only in the case that the size(x, 1) > 1
X = [x fliplr(x)];
Y = [y' ones(1, length(y)) .* yMax];
fill(X, Y, 'y')
What you were missing is that fill method looks for an area to fill. In the above code the area is defined by pairs of points. That, for the first (i.e. lower part) of the area we have the x vector and the y points. The second area (i.e. the upper part) is defined by the reversed vector x (image your pencil to first starting drawing towards rights for the lower part and then for the upper going left) and the points of the upper limit of your axes.
Edit:
Minimal example with the handel data from MATLAB:
load handel;
x = y; % Just to be consistent with the OP
fs = Fs; % Just to be consistent with the OP
[xPSD,f] = pwelch(x,hanning(4096),2048,4096*2 ,fs);
plot(f,10*log10(xPSD));
hold on
x= f(100:150);
y= 10*log10(xPSD(100:150));
yMax = ylim;
yMax = yMax(2);
x = x'; % Use this line only in the case that the size(x, 1) > 1
X = [x fliplr(x)];
Y = [y' ones(1, length(y)) .* yMax];
fill(X, Y, 'y')
xlim([0 200]) % To focus on the result
The result is:
Yes, there is always a way ;)
In your case, you simply need to add two points in x and y that go to the top boudary of the plot:
x = f(100:150);
y = 10*log10(xPSD(100:150))
% Add two points
Y = ylim;
x = [x(1) ; x(:) ; x(end)];
y = [Y(2) ; y(:) ; Y(2)];
% Display filled area
fill(x,y,'y')
Best,
I try to use contour to plot this function
3y + y^3 - x^3 = 5
I try contour(3*y+y^3-x^3-5) but it doesn't work.
How can I use contour to plot this function?
Are x and y properly defined as 2x2 matrices? If so then the "power" operator needs to be done on a component-wise basis (.^3 instead of ^3).
This works:
[x,y] = meshgrid(-2:.2:2,-2:.2:2);
contour(3*y+y.^3-x.^3-5)
Maybe you can try fcontour, which plots the contour lines of the function z = f(x,y) for constant levels of z over the default interval [-5 5] for x and y.
f = #(x,y) 3*y + y.^3 - x.^3 - 5;
fcontour(f)
Output:
I'm not convinced this addresses all parts of your question but it's a start. If you absolutely want contour to call a function, you can adjust my example to contour(X,Y,fh(X,Y)).
Better Approach
fh=#(x,y) 3*y + y.^3 - x.^3 -5; % <--- This is your function
x = (-4:.25:4)';
y = (-2:.25:2)';
[X,Y] = meshgrid(x,y);
Z = fh(X,Y);
contour(X,Y,fh(X,Y))
The Direct Approach (not preferred but works)
Notice the Z is transposed to make this work.
fh=#(x,y) 3*y + y.^3 - x.^3 -5; % <----this is your function
X = (-4:.25:4)';
Y = (-2:.25:2)';
Z = zeros(length(X),length(Y));
for i = 1:length(X)
for j = 1:length(Y)
xi = X(i);
yj = Y(j);
Z(i,j) = fh(xi,yj);
end
end
contour(X,Y,Z','LevelList',-60:10:60,'ShowText','on','LineWidth',1.4) % Fancied it up a bit
I would like to plot the gradient of the following function in MATLAB.
g(x,y) = [(x^2)-1; -y]
My code is:
x = linspace(-3,3);
y = linspace(-3,3);
[xx, yy] = meshgrid(x,y);
z = [xx.^2-1;-yy];
[dx,dy] = gradient(z,.3,.3);
contour(x,y,z)
hold on
quiver(x,y,dx,dy)
But I'm just getting this error:
The size of Y must match the size of Z or the number of rows
of Z.
I've no idea how I could make the size of both match. y is a 1x100 matrix and z a 200x100. To match them I would need y to be a 1x200 or z to be 100x100, but would I be able to plot it then?
Instead of
z = [xx.^2-1;-yy];
try each component separately:
z1 = [xx.^2-1];
z2 = [-yy];
[dx,dy] = gradient(z1,.3,.3);
contour(x,y,z1)
%etc.
Use hold on again if you really want them in the same plot.