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');
Related
I made two 3D plots on the same axis. now I desire to give them different colors for easy identification. How do I do this coloring? The MATLAB code is shown below.
tic
Nx = 50;
Ny = 50;
x = linspace(0,1,Nx);
y = linspace(0,0.5,Ny);
[X,Y] = meshgrid(x,y);
[M,N] = size(X);
for m=1:M
for n=1:N
%get x,y coordinate
x_mn = X(m,n);
y_mn = Y(m,n);
%%% X=D2 and Y=D1
%Check if x_mn and y_mn satisfy requirement
if(x_mn >= y_mn)
%evaluate function 1
Z(m,n) = (x_mn^2 - 2*x_mn*y_mn + y_mn^2);
Z_1(m,n) = (x_mn^2);
elseif(x_mn < y_mn)
%evaluate function 2
Z(m,n) = 0;
Z_1(m,n) = (x_mn^2);
%% Z(m,n) = 2*(2*x_mn*y_mn + y_mn - y_mn^2 - 2*x_mn);
else
Z(m,n) = 0;
end
end
end
%Plot the surface
figure
surf(X,Y,Z) %first plot
surfc(X,Y,Z)
hold on
surf(X,Y,Z_1) %second plot
xlabel('Dm');
ylabel('D');
zlabel('pR');
grid on
shading interp
toc
disp('DONE!')
How can I create two differently colored surfaces?
figure
surf(X,Y,Z) %first plot
surfc(X,Y,Z)
hold on
surf(X,Y,Z_1)
Your surfc() call actually overwrites your surf() call, is this intended?
As to your colour: the documentation is a marvellous thing:
surfc(X,Y,Z,C) additionally specifies the surface color.
In other words: just specify the colour as you want it. C needs to be a matrix of size(Z) with the desired colours, i.e. set all of them equal to create an monocoloured surface:
x = 1:100;
y = 1:100;
z = rand(100);
figure;
surfc(x,y,z,ones(size(z)))
hold on
surfc(x,y,z+6,ones(size(z))+4)
Results in (MATLAB R2007b, but the syntax is the same nowadays)
I am trying to fit a 3D surface polynomial of n-degrees to some data points in 3D space. My system requires the surface to be monotonically increasing in the area of interest, that is the partial derivatives must be non-negative. This can be achieved using Matlab's built in lsqlin function.
So here's what I've done to try and achieve this:
I have a function that takes in four parameters;
x1 and x2 are my explanatory variables and y is my dependent variable. Finally, I can specify order of polynomial fit. First I build the design matrix A using data from x1 and x2 and the degree of fit I want. Next I build the matrix D that is my container for the partial derivatives of my datapoints. NOTE: the matrix D is double the length of matrix A since all datapoints must be differentiated with respect to both x1 and x2. I specify that Dx >= 0 by setting b to be zeroes.
Finally, I call lsqlin. I use "-D" since Matlab defines the function as Dx <= b.
function w_mono = monotone_surface_fit(x1, x2, y, order_fit)
% Initialize design matrix
A = zeros(length(x1), 2*order_fit+2);
% Adjusting for bias term
A(:,1) = ones(length(x1),1);
% Building design matrix
for i = 2:order_fit+1
A(:,(i-1)*2:(i-1)*2+1) = [x1.^(i-1), x2.^(i-1)];
end
% Initialize matrix containing derivative constraint.
% NOTE: Partial derivatives must be non-negative
D = zeros(2*length(y), 2*order_fit+1);
% Filling matrix that holds constraints for partial derivatives
% NOTE: Matrix D will be double length of A since all data points will have a partial derivative constraint in both x1 and x2 directions.
for i = 2:order_fit+1
D(:,(i-1)*2:(i-1)*2+1) = [(i-1)*x1.^(i-2), zeros(length(x2),1); ...
zeros(length(x1),1), (i-1)*x2.^(i-2)];
end
% Limit of derivatives
b = zeros(2*length(y), 1);
% Constrained LSQ fit
options = optimoptions('lsqlin','Algorithm','interior-point');
% Final weights of polynomial
w_mono = lsqlin(A,y,-D,b,[],[],[],[],[], options);
end
So now I get some weights out, but unfortunately they do not at all capture the structure of the data. I've attached an image so you can just how bad it looks. .
I'll give you my plotting script with some dummy data, so you can try it.
%% Plot different order polynomials to data with constraints
x1 = [-5;12;4;9;18;-1;-8;13;0;7;-5;-8;-6;14;-1;1;9;14;12;1;-5;9;-10;-2;9;7;-1;19;-7;12;-6;3;14;0;-8;6;-2;-7;10;4;-5;-7;-4;-6;-1;18;5;-3;3;10];
x2 = [81.25;61;73;61.75;54.5;72.25;80;56.75;78;64.25;85.25;86;80.5;61.5;79.25;76.75;60.75;54.5;62;75.75;80.25;67.75;86.5;81.5;62.75;66.25;78.25;49.25;82.75;56;84.5;71.25;58.5;77;82;70.5;81.5;80.75;64.5;68;78.25;79.75;81;82.5;79.25;49.5;64.75;77.75;70.25;64.5];
y = [-6.52857142857143;-1.04736842105263;-5.18750000000000;-3.33157894736842;-0.117894736842105;-3.58571428571429;-5.61428571428572;0;-4.47142857142857;-1.75438596491228;-7.30555555555556;-8.82222222222222;-5.50000000000000;-2.95438596491228;-5.78571428571429;-5.15714285714286;-1.22631578947368;-0.340350877192983;-0.142105263157895;-2.98571428571429;-4.35714285714286;-0.963157894736842;-9.06666666666667;-4.27142857142857;-3.43684210526316;-3.97894736842105;-6.61428571428572;0;-4.98571428571429;-0.573684210526316;-8.22500000000000;-3.01428571428571;-0.691228070175439;-6.30000000000000;-6.95714285714286;-2.57232142857143;-5.27142857142857;-7.64285714285714;-2.54035087719298;-3.45438596491228;-5.01428571428571;-7.47142857142857;-5.38571428571429;-4.84285714285714;-6.78571428571429;0;-0.973684210526316;-4.72857142857143;-2.84285714285714;-2.54035087719298];
% Used to plot the surface in all points in the grid
X1 = meshgrid(-10:1:20);
X2 = flipud(meshgrid(30:2:90).');
figure;
for i = 1:4
w_mono = monotone_surface_fit(x1, x2, y, i);
y_nr = w_mono(1)*ones(size(X1)) + w_mono(2)*ones(size(X2));
for j = 1:i
y_nr = w_mono(j*2)*X1.^j + w_mono(j*2+1)*X2.^j;
end
subplot(2,2,i);
scatter3(x1, x2, y); hold on;
axis tight;
mesh(X1, X2, y_nr);
set(gca, 'ZDir','reverse');
xlabel('x1'); ylabel('x2');
zlabel('y');
% zlim([-10 0])
end
I think it may have something to do with the fact that I haven't specified anything about the region of interest, but really I don't know. Thanks in advance for any help.
Alright I figured it out.
The main problem was simply an error in the plotting script. The value of y_nr should be updated and not overwritten in the loop.
Also I figured out that the second derivative should be monotonically decreasing. Here's the updated code if anybody is interested.
%% Plot different order polynomials to data with constraints
x1 = [-5;12;4;9;18;-1;-8;13;0;7;-5;-8;-6;14;-1;1;9;14;12;1;-5;9;-10;-2;9;7;-1;19;-7;12;-6;3;14;0;-8;6;-2;-7;10;4;-5;-7;-4;-6;-1;18;5;-3;3;10];
x2 = [81.25;61;73;61.75;54.5;72.25;80;56.75;78;64.25;85.25;86;80.5;61.5;79.25;76.75;60.75;54.5;62;75.75;80.25;67.75;86.5;81.5;62.75;66.25;78.25;49.25;82.75;56;84.5;71.25;58.5;77;82;70.5;81.5;80.75;64.5;68;78.25;79.75;81;82.5;79.25;49.5;64.75;77.75;70.25;64.5];
y = [-6.52857142857143;-1.04736842105263;-5.18750000000000;-3.33157894736842;-0.117894736842105;-3.58571428571429;-5.61428571428572;0;-4.47142857142857;-1.75438596491228;-7.30555555555556;-8.82222222222222;-5.50000000000000;-2.95438596491228;-5.78571428571429;-5.15714285714286;-1.22631578947368;-0.340350877192983;-0.142105263157895;-2.98571428571429;-4.35714285714286;-0.963157894736842;-9.06666666666667;-4.27142857142857;-3.43684210526316;-3.97894736842105;-6.61428571428572;0;-4.98571428571429;-0.573684210526316;-8.22500000000000;-3.01428571428571;-0.691228070175439;-6.30000000000000;-6.95714285714286;-2.57232142857143;-5.27142857142857;-7.64285714285714;-2.54035087719298;-3.45438596491228;-5.01428571428571;-7.47142857142857;-5.38571428571429;-4.84285714285714;-6.78571428571429;0;-0.973684210526316;-4.72857142857143;-2.84285714285714;-2.54035087719298];
% Used to plot the surface in all points in the grid
X1 = meshgrid(-10:1:20);
X2 = flipud(meshgrid(30:2:90).');
figure;
for i = 1:4
w_mono = monotone_surface_fit(x1, x2, y, i);
% NOTE: Should only have 1 bias term
y_nr = w_mono(1)*ones(size(X1));
for j = 1:i
y_nr = y_nr + w_mono(j*2)*X1.^j + w_mono(j*2+1)*X2.^j;
end
subplot(2,2,i);
scatter3(x1, x2, y); hold on;
axis tight;
mesh(X1, X2, y_nr);
set(gca, 'ZDir','reverse');
xlabel('x1'); ylabel('x2');
zlabel('y');
% zlim([-10 0])
end
And here's the updated function
function [w_mono, w] = monotone_surface_fit(x1, x2, y, order_fit)
% Initialize design matrix
A = zeros(length(x1), 2*order_fit+1);
% Adjusting for bias term
A(:,1) = ones(length(x1),1);
% Building design matrix
for i = 2:order_fit+1
A(:,(i-1)*2:(i-1)*2+1) = [x1.^(i-1), x2.^(i-1)];
end
% Initialize matrix containing derivative constraint.
% NOTE: Partial derivatives must be non-negative
D = zeros(2*length(y), 2*order_fit+1);
for i = 2:order_fit+1
D(:,(i-1)*2:(i-1)*2+1) = [(i-1)*x1.^(i-2), zeros(length(x2),1); ...
zeros(length(x1),1), -(i-1)*x2.^(i-2)];
end
% Limit of derivatives
b = zeros(2*length(y), 1);
% Constrained LSQ fit
options = optimoptions('lsqlin','Algorithm','active-set');
w_mono = lsqlin(A,y,-D,b,[],[],[],[],[], options);
w = lsqlin(A,y);
end
Finally a plot of the fitting (Have used a new simulation, but fit also works on given dummy data).
How to do the same but without contour and meshgrid functions? I need an alternative code using plot function.
[x,y]=meshgrid(linspace(-3,3,1000));
contour(x,y,x.^2 + y.^2-2.*x,'LevelList',0,'LineColor','r','LineWidth',2);
hold on
contour(x,y,x.^2 - y.^2-y,'LevelList',0,'LineColor','b','LineWidth',2);
What you can do is create the matrices x and y "by hand", create a logical image that represents the sign of your function and use bwboundaries to extract the line of "sign changes":
t=linspace(-3,3,100); % set up matrices
o = ones(size(t));
x = o'*t;
y = x';
image = x.^2 + y.^2-2.*x > 0; % generate image
BW = bwboundaries(image); % extract paths from image
hold on
for k=1:numel(BW);
path = BW{k};
x = t(path(:,1));
y = t(path(:,2));
plot(x,y); % plot paths
end
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.
I have a matlab function that contain some constant parameter, I want to draw that function, on say same figure, using hold on (probably) while changing the value of that constant.
This my code:
close all
clear all
clc
m = 5;
x = 1:1:10;
y = m*x + 10;
h1 = figure;
plot(x,y)
m = 10;
figure(h1);
hold on
plot(x,y,': r')
When I tried using this code, I got two lines coincident on each others; and it looks matlab just used last value for the parameter m how can I make it use different values.
I found some stuff here, but doesn't fulfill my needs.
Any suggestions?
You need to recalculate y as well:
m = 5;
x = 1:1:10;
y = m*x + 10;
h1 = figure;
plot(x,y); hold on;
m = 10;
y = m*x + 10;
figure(h1);
plot(x,y,': r')
Or create an anonymous function:
x = 1:1:10;
f = #(m) m*x + 10;
%// and then:
h1 = figure;
plot(x,f(5) ); hold on;
plot(x,f(10),': r');
Currently, you're only updating m but you also have to calculate y again. This is why it plots exactly the same y (i.e. m is still 5) function when you issue the second plot.
You might want to use a simple for loop for that, like:
m = 5;
x = 1:1:10;
figure;
hold on;
for m=1:1:10
y = m*x + 10;
plot(x,y,': r')
end
In addition to the short answer - improving the plot..
%% Data Preparations
x = 1:10;
ms = 3; % number of different slopes
%% Graph Preparations
hold on;
% Prepare the string cell array
s = cell(1, ms);
% Handle storage
h = zeros(1, ms);
% Plot graphs
for m=1:ms
y = m*x + 10;
h(m)= plot(x,y,'Color',[1/m rand() rand()]);
s{m} = sprintf('Plot of y(m=%d)', m);
end
% Plot all or select the plots to include in the legend
ind = [ms:-1:1] .* ones(1,ms); % plot all
%ind = [ 1 3 4 ]; % plot selected
% Create legend for the selected plots
legend(h(ind), s{ind});
Additional advice: When working with MATLAB and you try to improve the performance of your code, you shoud try to avoid using for-loops since MATLAB is MATrix manipulation and that's what it can do best. Ones you've taken this philosophy in, you'll create the most beautiful code one-liners! ;)
This script is an adoption of Steve Lord's post.