I have difficluties at understanding the Matlab documentation for the meshgrid, contour or surf functions. I simply do not understand how the matrix Z must be created to display values for x and y vectors.
Basically, I have loop that calculates x(n), y(n) and a value z(n) with n is the index. Now how do I map this into the meshgrid function to create a contour plot from this data?
for i = 1:n
x(n) = i;
y(n) = i;
z(n) = rand();
end
Now:
[X,Y] = meshgrid(x,y);
Z = ???;
contour(X,Y,Z)
Related
I have made a simple code for Lagrange interpolation of vectors of data x and y and , but I need some help with plotting and displaying errors.
I wish to plot the equidistant points together with the Lagrange Interpolated curve in the same plot, and display the error of the approximation. Plotting the points is trivial, but I struggle with plotting the interpolated polynomial curve on top of the (x,y) plot.
clear
clc
x = -1:0.25:1;
y = 1./(1+25.*x.^2);
N = 1:length(y);
M = zeros(length(y),length(x));
for n = 1:length(x)
for i = 1:length(y)
l = 1;
index = find(N ~= i);
for jj = 1:length(index)
l = l.*(x(n)-y(index(jj)))./(y(i)-y(index(jj)));
end
M(i,n) = l;
end
end
plot(x,y)
All help is appreciated
I am stuck with an apparently simple problem. I have to revolve of 360° a 2D curve around an axis, to obtain a 3D plot. Say, I want to do it with this sine function:
z = sin(r);
theta = 0:pi/20:2*pi;
xx = bsxfun(#times,r',cos(theta));
yy = bsxfun(#times,r',sin(theta));
zz = repmat(z',1,length(theta));
surf(xx,yy,zz)
axis equal
I now want to visualize the numerical values of the Z plane, stored in a matrix. I would normally do it this way:
ch=get(gca,'children')
X=get(ch,'Xdata')
Y=get(ch,'Ydata')
Z=get(ch,'Zdata')
If I visualize Z with
imagesc(Z)
I don't obtain the actual values of Z of the plot, but the "un-revolved" projection. I suspect that this is related to the way I generate the curve, and from the fact I don't have a function of the type
zz = f(xx,yy)
Is there any way I can obtain the grid values of xx and yy, as well as the values of zz at each gridpoint?
Thank you for your help.
Instead of bsxfun you can use meshgrid:
% The two parameters needed for the parametric equation
h = linspace(0,2) ;
th = 0:pi/20:2*pi ;
[R,T] = meshgrid(h,th) ;
% The parametric equation
% f(x) Rotation along Z
% ↓ ↓
X = sin(R) .* cos(T) ;
Y = sin(R) .* sin(T) ;
% Z = h
Z = R ;
surf(X,Y,Z,'EdgeColor',"none")
xlabel('X')
ylabel('Y')
zlabel('Z')
Which produce:
And if you want to extract the contour on the X plane (X = 0) you can use contour:
contour(Y,Z,X,[0,0])
Which produce:
I want to make a grid (Uniform Mapping) in matlab without Meshgrid.
I have make grid with meshgrid but now I just want to make it with a loop or any Second Method (without meshgrid)
This is my code using meshgrid:
figure(6)
[X,Y] = meshgrid(-1:0.1:1, -1:0.1:1)
plot(X,Y,'k-')
hold on
plot(Y,X,'k-');
use repmat, or multiply by ones vectors for even more basic functionality:
x = -1:0.1:1;
y = -1:0.1:1;
% with repmat
X1 = repmat(x(:)',[numel(y),1]);
Y1 = repmat(y(:),[1,numel(x)]);
% multiply with ones
X2 = ones(numel(y),1)*x(:)';
Y2 = y(:)*ones(1,numel(x));
% meshgrid
[X3,Y3] = meshgrid(x, y);
isequal(X1,X2,X3) && isequal(Y1,Y2,Y3) % true
plot(X1,Y1,'k');
hold on
plot(Y1,X1,'k');
I'm trying to practice curve fitting on a 2D Gaussian, but in order to do that I need to add random noise to my predefined Gaussian. My first instinct was to cycle through two for loops and create two matrices X and Y with random numbers, but when I tried that (I don't have the code anymore) Matlab wouldn't let me plot the Gaussian because I didn't generate my X and Y values using the meshgrid function. Since I seem to need to use meshgrid, can anyone help me figure out how to generate a random meshgrid so I can add some noise to my Gaussian?
amp = 1;
x0 = 0;
y0 = 0;
sigmaX = 1;
sigmaY = 1;
%X = 1:1:100;
%Y = 1:1:100;
[X,Y] = meshgrid(-3:.1:3);
%Z = X .* exp(-X.^2 - Y.^2);
Z = amp*exp(-((X-x0).^2/(2*sigmaX^2)+(Y-y0).^2/(2*sigmaY^2)));
surf(X, Y, Z);
%Add noise now
EDIT: So I found out that rand can return a random matrix which will work with the surf function (for some reason it wasn't working for me earlier though). The result looks something like this: noisy 2D gaussian
amp = 1;
x0 = 0;
y0 = 0;
sigmaX = 1;
sigmaY = 1;
[X,Y] = meshgrid(-3:.1:3);
%Z = X .* exp(-X.^2 - Y.^2);
Z = amp*exp(-((X-x0).^2/(2*sigmaX^2)+(Y-y0).^2/(2*sigmaY^2)));
surf(X, Y, Z);
%Make some noise
[xRows, xColumns] = size(X);
[yRows, yColumns] = size(Y);
figure(2)
X = -.1 + (.1+.1)*rand(61,61);
Y = -.1 + (.1+.1)*rand(61,61);
Z = amp*exp(-((X-x0).^2/(2*sigmaX^2)+(Y-y0).^2/(2*sigmaY^2)));
surf(X, Y, Z)
But I feel like the Gaussian has largely lost it's typical bell shape and looks more like a slope field than anything. I'm going to try and refine it but I would love any input.
That's what i would do.
amp=1;
x0=0;
y0=0;
sigmaX=1;
sigmaY=1;
noiseAmp=.1;
x=[-2:.1:2];
y=[-2:.1:2];
%Create two Noise Vectors
noisez1=noiseAmp.*rand(1,length(x));
noisez2=noiseAmp.*rand(1,length(x));
% Make an meshgrid out of the two Vectors
[noiseZ1,noiseZ2]=meshgrid(noisez1,noisez2);
% Add the Meshgrids togehter
Noise=noiseZ1+noiseZ2;
[X,Y]=meshgrid(x,y);
% Add the Noise to the result of Z
Z=amp*exp(-((X-x0).^2/(2*sigmaX^2)+(Y-y0).^2/(2*sigmaY^2)))+Noise;
surf(X,Y,Z);
if you just want a 2D plot you can try this
amp=1;
noiseAmp=0.01;
x0=0;
y0=0;
sigmaX=1;
sigmaY=1;
x=[-5:.01:5];
noiseY=noiseAmp*rand(1,length(x));
y=noiseY+amp*exp(-((x-x0).^2/(2*sigmaX^2)));
plot(x,y);
where noiseAmp is the Amplitude of the noise.
But if you still want to create a 3D plot with the surf() function, you have to add a random meshgrid to the Z result.
Given a system of the form y' = A*y(t) with solution y(t) = e^(tA)*y(0), where e^A is the matrix exponential (i.e. sum from n=0 to infinity of A^n/n!), how would I use matlab to compute the solution given the values of matrix A and the initial values for y?
That is, given A = [-2.1, 1.6; -3.1, 2.6], y(0) = [1;2], how would I solve for y(t) = [y1; y2] on t = [0:5] in matlab?
I try to use something like
t = 0:5
[y1; y2] = expm(A.*t).*[1;2]
and I'm finding errors in computing the multiplication due to dimensions not agreeing.
Please note that matrix exponential is defined for square matrices. Your attempt to multiply the attenuation coefs with the time vector doesn't give you what you'd want (which should be a 3D matrix that should be exponentiated slice by slice).
One of the simple ways would be this:
A = [-2.1, 1.6; -3.1, 2.6];
t = 0:5;
n = numel(t); %'number of samples'
y = NaN(2, n);
y(:,1) = [1;2];
for k =2:n
y(:,k) = expm(t(k)*A) * y(:,1);
end;
figure();
plot(t, y(1,:), t, y(2,:));
Please note that in MATLAB array are indexed from 1.