I want to plot the surface of function f=((x1+1.5)^2+5*(x2-1.7)^2)*((x1-1.4)^2+0.6*(x2-0.5)^2);
with constraints:
-x1<0
-x2<0
3*x1-x1*x2+4*x2-7<0
2*x1+x2-3<0
3*x1-4*x2^2-4*x2<0
in MATLAB R2014b.
I only can plot f using ezsurf but I don't know to define the constraints. How to plot f with constraints?
syms x1 x2;
f=((x1+1.5)^2+5*(x2-1.7)^2)*((x1-1.4)^2+0.6*(x2-0.5)^2);
ezsurf(f);
hold on;
ADDENDUM:
As #Ander Biguri's comment, I have tried make the code as follows:
x=0:0.1:2;
y=0:0.1:2;
[X1,X2]=meshgrid(x,y);
constraint1 = -X1<=0;
constraint2 = -X2<=0;
constraint3 = 3*X1-X1*X2+4*X2-7<=0;
constraint4 = 2*X1+X2-3<=0;
constraint5 = 3*X1-4*X2^2-4*X2<=0;
X1(~constraint1) = NaN;
X2(~constraint1) = NaN;
X1(~constraint2) = NaN;
X2(~constraint2) = NaN;
X1(~constraint3) = NaN;
X2(~constraint3) = NaN;
X1(~constraint4) = NaN;
X2(~constraint4) = NaN;
X1(~constraint5) = NaN;
X2(~constraint5) = NaN;
f=((X1+1.5).^2+5*(X2-1.7).^2)*((X1-1.4).^2+0.6*(X2-0.5).^2);
surf(X1,X2,f);
But nothing appear in the figure.
What is my mistake?
The problem in your second version (numerical) is a typical one: use elementwise operations instead of matrix operations:
f=((X1+1.5).^2+5*(X2-1.7).^2).*((X1-1.4).^2+0.6*(X2-0.5).^2);
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)
The documentation online for this particular function is poor, and I was looking for an example on how to use it. It seems to take in 9+ arguments, but I'm not entirely sure what they even are. I am working on implementing function using the trapezoidal rule, however, I am missing the functions that compute the partial derivatives with respect to y and t. I believe that calculating one for t in MATLAB is another case, but here, I'm just trying to use MATLAB to compute it for y.
I'm using the following input initially:
func = #(t,y)(y.^2+y+t);
interval = [0 1];
y0 = 0;
[steps, derivY, derivJ, W, inverseW] = getTrapezoidalODEValues(func, interval, y0)
I set up the function like this:
function [h,J,T,W,iW] = getTrapezoidalODEValues(odefun,tspan,y0,options)
if (nargin==3)
options = odeset();
end
h = NaN; J(0) = NaN; T(0) = NaN; W(0) = NaN; iW = NaN;
[t,yy] = ode(odefun,tspan,y0,options);
[nstep,ndim] = size(yy);
d = 1/(2+sqrt(2));
for j=2:nsteps
h = t(j)-t(j-1);
I = eye(???,???); % identity matrix
quadpoly = ???; % the quadratic polynomial
J(j-1) = numjac(???); % <--partial derivative of odefun with respect to y
T(j-1) = ???; % partial derivative of odefun with respect to t
W(j-1) = I - h .* d .* J;
iW(j-1) = inv(W(j-1));
end
end
This is the link to the dataset. I have this contour plot which has a bit rough edges. My question is, how can I smooth these edges these edges correspond to Nan. I filled in the Z matrix with Nan so as to remove unwanted values.
I also wanted to ask that why shading flat and interp is not working on this contour.
I have set shading to flat and in Matlab2013b I get proper flat figure but in Matlab 2014b and 2015b I am getting this figure.
MATLAB 2015b:
MATLAB 2013b
How can I obtain perfectly meshed plot in Matlab 2015b, I checked for shading options in the documentation and there are only 3 faceted, interp and flat.
shading flat works in 2013b but not in subsequent versions. Can someone tell me why is it so?
This is the sample code which I am using right now:
clear all; close all; clc;
load temperature.txt;
time = temperature(:,1); % This column contains the time
x = temperature(:,2); % This column contains the x values.
temperature_system = temperature(:,3); % This column contains the temperatures.
% Rejecting the outliers
pos = (temperature_system > prctile(temperature_system,97));
time(pos) = [];
x(pos) = [];
temperature_system(pos) = [];
X1 = [time x];
F = scatteredInterpolant(X1,temperature_system);
x1 = linspace(min(x),max(x),100);
x2 = linspace(min(time),max(time),100);
[X,Y] = meshgrid(x2,x1);
Z = F(X,Y);
% Is the data below the criteria for all points in space at a specific time
emptyTime = all(Z<10,1);
emptySpace = all(Z<10,2);
[emptyTime, emptySpace] = meshgrid(emptyTime, emptySpace);
Z(emptyTime | emptySpace) = nan;
% Replacing the remaining zeros with nan
pos = find(Z<1);
Z(pos) = nan;
f1 = figure(1);
%set(f1,'renderer','zbuffer');
%surf(X,Y,Z);
[C,h] = contourf(X,Y,Z, 'Linestyle', 'none');
shading flat;
colormap(jet);
q = colorbar;
set(q,'direction','reverse');
q.Label.String = 'Temperature';
xlabel('Time (ps)','FontSize', 16, 'FontWeight', 'bold',...
'FontName', 'Helvetica', 'Color', 'Black');
ylabel('Length of box (A)','FontSize', 16, 'FontWeight', 'bold',...
'FontName', 'Helvetica', 'Color', 'Black');
set(gca,'LineWidth',3,'TickLength',[0.02 0.02]);
set(gca,'XMinorTick','on');
set(gca,'YMinorTick','on','XTicksBetween', 5);
set(gca,'FontSize',12,'FontName','Helvetica');
It's difficult to test the issue without having your data. I got rid of the lines by means of the LineStyle property:
Code:
Z = peaks(20);
subplot(2,1,1);
contourf(Z,10);
colorbar;
subplot(2,1,2);
contourf(Z,10, 'LineStyle', 'none');
colorbar;
I have to create some draggable points on an axes. However, this seems to be a very slow process, on my machine taking a bit more than a second when done like so:
x = rand(100,1);
y = rand(100,1);
tic;
for i = 1:100
h(i) = impoint(gca, x(i), y(i));
end
toc;
Any ideas on speed up would be highly appreciated.
The idea is simply to provide the user with the possibility to correct positions in a figure that have been previously calculated by Matlab, here exemplified by the random numbers.
You can use the the ginput cursor within a while loop to mark all points you want to edit. Afterwards just click outside the axes to leave the loop, move the points and accept with any key.
f = figure(1);
scatter(x,y);
ax = gca;
i = 1;
while 1
[u,v] = ginput(1);
if ~inpolygon(u,v,ax.XLim,ax.YLim); break; end;
[~, ind] = min(hypot(x-u,y-v));
h(i).handle = impoint(gca, x(ind), y(ind));
h(i).index = ind;
i = i + 1;
end
Depending on how you're updating your plot you can gain a general speedup by using functions like clf (clear figure) and cla (clear axes) instead of always opening a new figure window as explained in this answer are may useful.
Alternatively the following is a very rough idea of what I meant in the comments. It throws various errors and I don't have the time to debug it right now. But maybe it helps as a starting point.
1) Conventional plotting of data and activating of datacursormode
x = rand(100,1);
y = rand(100,1);
xlim([0 1]); ylim([0 1])
f = figure(1)
scatter(x,y)
datacursormode on
dcm = datacursormode(f);
set(dcm,'DisplayStyle','datatip','Enable','on','UpdateFcn',#customUpdateFunction)
2) Custom update function evaluating the chosen datatip and creating an impoint
function txt = customUpdateFunction(empt,event_obj)
pos = get(event_obj,'Position');
ax = get(event_obj.Target,'parent');
sc = get(ax,'children');
x = sc.XData;
y = sc.YData;
mask = x == pos(1) & y == pos(2);
x(mask) = NaN;
y(mask) = NaN;
set(sc, 'XData', x, 'YData', y);
set(datacursormode(gcf),'Enable','off')
impoint(ax, pos(1),pos(2));
delete(findall(ax,'Type','hggroup','HandleVisibility','off'));
txt = {};
It works for the, if you'd just want to move one point. Reactivating the datacursormode and setting a second point fails:
Maybe you can find the error.
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.