Im new to matlab and I want to plot a ContourPlot together with two inequalities but I dont know how. The function that I want to plot its ContourPlot is something like this:
Z = (X-2).^2 + (Y-1).^2;
and here are the two inequalities:
ineq1 = X.^2 - Y <= 2;
ineq2 = X + Y <= 2;
this is what I have dodne so far:
[X,Y] = meshgrid(-4:.2:4,-4:.2:4);
Z = (X-2).^2 + (Y-1).^2;
[C,h] = contour(X,Y,Z);
clabel(C,h)
ineq1 = X.^2 - Y <= 2;
ineq2 = X + Y <= 2;
range = (-4:.2:4);
hold on
plot(range,ineq1, range, ineq2)
hold off
but this does not feel right.
What I want to do is to visualize an optimization problem. First I want to plot the ContourPlot of the function and then the possible areas in that same plot, It would be great if I could show the intersection areas too.
If you want to draw the boundaries of the inequalities onto the contour plot, you can do this with line.
[X,Y] = meshgrid(-4:.2:4,-4:.2:4);
Z = (X-2).^2 + (Y-1).^2;
[C,h] = contour(X,Y,Z);
clabel(C,h)
x_vect = (-4:.05:4);
y_ineq1 = x_vect.^2 - 2;
y_ineq2 = 2 - x_vect;
line(x_vect, y_ineq1);
line(x_vect, y_ineq2);
Coloring the intersection area is a bit more tricky, and I'm not sure if it's exactly what you want to do, but you could look into using patch, something like
% Indexes of x_vect, y_ineq1 and y_ineq2 for region where both satisfied:
region_indexes = find(y_ineq1<y_ineq2);
region_indexes_rev = region_indexes(end:-1:1);
% To plot this area need to enclose it
% (forward along y_ineq1 then back along y_ineq2)
patch([x_vect(region_indexes),x_vect(region_indexes_rev)],...
[y_ineq1(region_indexes),y_ineq2(region_indexes_rev)],...
[1 0.8 1]) % <- Color as [r g b]
% May or may not need following line depending on MATLAB version to set the yaxes
ylim([-4 4])
% Get the original plot over the top
hold on
[C,h] = contour(X,Y,Z);
clabel(C,h)
hold off
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 have two contour maps in Matlab and each of the two maps has a single curve specifying a single Z-value. I want to super impose the two contour maps so that I can find the single solution where the two z-value curves intersect. How could I go about super imposing the two contour maps?
% the two contour maps are coded the exact same way, but with different z-values
x = 0.05:0.05:1;
y = 0.0:0.05:1;
[X, Y] = meshgrid(x, y);
% Z-value data is copied from excel and pasted into an array
Z = [data]
contourf(X, Y, Z);
pcolor(X, Y, Z); hold on
shading interp
title();
xlabel();
ylabel();
colorbar
val = %z-value to plot onto colormap
tol = %tolerance
idxZval = (Z <= val+tol) & (Z >= val-tol);
plot(X(idxZval), Y(idxZval))[enter image description here][1]
The end result you seek is possible using contourc or using contour specifying the same contours (isolines).
This answer extends this answer in Approach 1 using contourc and provides a simple solution with contour in Approach 2.
You might ask "Why Approach 1 when Approach 2 is so simple?"
Approach 1 provides a way to directly access the individual isolines in the event you require a numerical approach to searching for intersections.
Approach 1
Example Data:
% MATLAB R2018b
x = 0:0.01:1;
y = 0:0.01:1;
[X,Y] = meshgrid(x,y);
Z = sqrt(X.^3+Y); % Placeholder 1
W = sqrt(X.*Y + X.^2 + Y.^(2/3)); % Placeholder 2
Overlay Single Isoline from 2 Contour Plots
Mimicking this answer and using
v = [.5 0.75 .85 1]; % Values of Z to plot isolines
we can visualize these two functions, Z, and W, respectively.
We can overlay the isolines since they share the same (x,y) domain. For example, they both equal 0.8 as displayed below.
val = 0.8; % Isoline value to plot (for Z & W)
Ck = contourc(x,y,Z,[val val]);
Ck2 = contourc(x,y,W,[val val]);
figure, hold on, box on
plot(Ck(1,2:end),Ck(2,2:end),'k-','LineWidth',2,'DisplayName',['Z = ' num2str(val)])
plot(Ck2(1,2:end),Ck2(2,2:end),'b-','LineWidth',2,'DisplayName',['W = ' num2str(val)])
legend('show')
Overlay Multiple Isolines from 2 Contour Plots
We can also do this for more isolines at a time.
v = [1 0.5]; % Isoline values to plot (for Z & W)
figure, hold on, box on
for k = 1:length(v)
Ck = contourc(x,y,Z,[v(k) v(k)]);
Ck2 = contourc(x,y,W,[v(k) v(k)]);
p(k) = plot(Ck(1,2:end),Ck(2,2:end),'k-','LineWidth',2,'DisplayName',['Z = ' num2str(v(k))]);
p2(k) = plot(Ck2(1,2:end),Ck2(2,2:end),'b-','LineWidth',2,'DisplayName',['W = ' num2str(v(k))]);
end
p(2).LineStyle = '--';
p2(2).LineStyle = '--';
legend('show')
Approach 2
Without making it pretty...
% Single Isoline
val = 1.2;
contour(X,Y,Z,val), hold on
contour(X,Y,W,val)
% Multiple Isolines
v = [.5 0.75 .85 1];
contour(X,Y,Z,v), hold on
contour(X,Y,W,v)
It is straightforward to clean these up for presentation. If val is a scalar (single number), then c1 = contour(X,Y,Z,val); and c2 = contour(X,Y,W,val) gives access to the isoline for each contour plot.
I have the function:
f(z) = conj(z) + 0.4*z^2,
Going from a polar grid where 0 < theta < 2pi and between 0.5 < |z| < 2.5 for its two radii. I have no idea where to start as I'm new to MATLAB but I'm trying to make 2 subplots each with two parametric equations for each curve but I've had no success.
Try this code. Swap the definition of f to switch between the polar grid and the transformed grid. I also answered a similar question here.
clear
clc
N = 41;
t = linspace(0, 2*pi, N);
r = linspace(0.5, 2.5, N);
[R,T] = meshgrid(r,t);
Z = R.*exp(T*1i);
% f = Z; %Original mesh
f = conj(Z) + 0.4*Z.^2; %Transformed mesh
U = real(f);
V = imag(f);
%Plot mesh
hold off
plot(U,V,'b-');
hold on
plot(U',V','r-');
xlim([-5,5]);
ylim([-5,5]);
axis equal
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.
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,