I want to create the 3D plot of the probability density functions of my variable. I have a matrix with dimensions 189x10000, where rows correspond to the time and columns are results of the simulation. Can somebody help me to create a density plot over time? I want my plot to look like this:
A = [1:185]'; % substitute for date vector
K = linspace( -20, 20, 100);
f = zeros(185,100);
xi = zeros(185,100);
r = normrnd(0,1,[185,10000]);
for i=1:185
[f(i,:),xi(i,:)] = ksdensity(r(I,:));
end
a = figure;
meshc(A, K', f')
datetick('x', 'yyyy')
view(85, 50)
set(gca, 'YLim', [-15, 10])
set(gca, 'XLim', [A(1), A(end)])
xlabel('Time')
With this code I get this:
Replace random numbers with density distribution.
If you want a finer grid, then use more points. Your actual data has 10-times as much, right? Otherwise this is as good as it gets; "improving" your plot, e.g. smooth over your data, is more data-doctoring than science.
Solution provided by Adriaan.
Related
I'm trying to plot two lines (data and linear fit) in a single graph with logarithmic scale. My code:
Iots = I_An./Temp.^2; % I Over T Squared
Oot = 1./Temp; % One Over T
[p,~] = polyfit(Oot,Iots,1);
linfit = polyval(p,Oot);
figure('color','w','units','normalized','outerposition',[0 0 1 1]);
hold on
loglog(Oot,Iots,'.','LineWidth',2);
loglog(Oot,linfit,':r','LineWidth',2);
The result is not a logarithmic scale graph:
If I run just one of the plot lines, it works on its own. What should I do? Are there any contradicting commands?
You want to call hold on after creating your first loglog plot. Also, you only need to use loglog on the first plot to create the logarithmic axes. After than you can just call normal plot and it will use the logarithmic axes.
x = linspace(0, 100);
loglog(x, x, '.', 'LineWidth', 2);
hold on
plot(x, x.^2, '.r', 'LineWidth',2);
Matlab has a function spy for visualizing sparsity patterns of graph adjacency matrices.
Unfortunately it does not display the points by taking into account the magnitude of the values in the matrix. It uses a single color with same intensity to display all entries.
I wish to display the same spy plot but with the points "color-coded" like in a heatmap to indicate the magnitude of the entries. How can I do that?
spy function uses plot, which cannot have different marker colors in a lineseries object.
On the other hand, patch object can have different marker colors for different vertices. patch is originally for drawing polygons, but with no face color and no edge color, one can get similar result to plot with no line style.
S = bucky();
[m, n] = size(S);
[X, Y] = meshgrid(1:m, 1:n);
S = (X + Y) .* S;
nonzeroInd = find(S);
[x, y] = ind2sub([m n], nonzeroInd);
figure();
hp = patch(x, y, S(nonzeroInd), ...
'Marker', 's', 'MarkerFaceColor', 'flat', 'MarkerSize', 4, ...
'EdgeColor', 'none', 'FaceColor', 'none');
set(gca, 'XLim', [0, n + 1], 'YLim', [0, m + 1], 'YDir', 'reverse', ...
'PlotBoxAspectRatio', [n + 1, m + 1, 1]);
colorbar();
You can easily use different colormap, e.g., colormap(flipud(hot)).
If your matrix is not very large you could try to view it as an image using imagesc(). (Well you could use it for quite large matrices as well, but the pixels become very small.)
Here is an example of 20 random points in a 100x100 matrix, using colormap hot:
N = 100;
n = 20;
x = randi(N,1,n);
y = randi(N,1,n);
z = randi(N,1,n);
data = sparse(x,y,z);
imagesc(data)
axis square
colormap('hot')
This is the resulting image.
This can be compared to the plot we get using spy(data) where the markers are a bit larger.
If a white background is desired an easy way to achieve this is to flip the colormap:
figure
imagesc(data)
axis square
cmap = flipud(colormap('hot'));
colormap(cmap)
Hack solution redefining spy()
Googling a bit I found this thread at Matlab Central:
Spy with color for values?
There a solution is suggested that redefines spy(). It's however worth noting that (further down in the thread) this solution can also cause Matlab to crash for larger matrices.
I submitted a file on matlab exchange that also performs the spy task with points colored according to their value. Please see here.
I need to write a script that load some data file which contains variables x and y and fit first, second, third, fourth, and fifth degree polynomials to it. Plot the data as blue dots on a figure, and plot all five polynomial fits using lines of different colors on the same axes. This is how it should be:
Instead I get my polynomials separated from the data. The Data axis are([100 200 -0.2 0.2]), while my polinoms are at axis ([0 100 -0.2 0.2]).
My script:
%Fitting Polynomials
Dat=load('randomData.mat');
[p1,S1,mu] = polyfit(x,y,1)
[Y1,delta]= polyval(p1,x,S1,mu)
[p2,S2,mu] = polyfit(x,y,2)
[Y2,delta]= polyval(p2,x,S2,mu)
[p3,S3,mu] = polyfit(x,y,3)
[Y3,delta]= polyval(p3,x,S3,mu)
[p4,S4,mu] = polyfit(x,y,4)
[Y4,delta]= polyval(p4,x,S4,mu)
[p5,S5,mu] = polyfit(x,y,5)
[Y5,delta]= polyval(p5,x,S5,mu)
figure;
plot(x,y,'b.','MarkerSize',10)
hold on
plot(Y1,'r')
plot(Y2,'g')
plot(Y3,'m')
plot(Y4,'c')
plot(Y5,'k')
xlabel('X');
ylabel('Y');
title('Polynomial fitting to noisy data');
legend('Data','order 1','order 2','order 3','order 4','order 5')
hold off
plot(Y1,'r')
should be
plot(x, Y1,'r');
and so on
Remember that Y1 doesn't actually represent a polynomial relationship, it is just a vector of samples of the polynomial p1 evaluated (via polyval) at the points x.
Assume y is a vector with random numbers following the distribution f(x)=sqrt(4-x^2)/(2*pi). At the moment I use the command hist(y,30). How can I plot the distribution function f(x)=sqrt(4-x^2)/(2*pi) into the same histogram?
Instead of normalizing numerically, you could also do it by finding a theoretical scaling factor as follows.
nbins = 30;
nsamples = max(size(y));
binsize = (max(y)-min(y)) / nsamples
hist(y,nbins)
hold on
x1=linspace(min(y),max(y),100);
scalefactor = nsamples * binsize
y1=scalefactor * sqrt(4-x^2)/(2*pi)
plot(x1,y1)
Update: How it works.
For any dataset that is large enough to give a good approximation to the pdf (call it f(x)), the integral of f(x) over this domain will be approximately unity. However we know that the area under any histogram is precisely equal to the total number of samples times the bin-width.
So a very simple scale factor to bring the pdf into line with the histogram is Ns*Wb, the total number of sample point times the width of the bins.
Let's take an example of another distribution function, the standard normal. To do exactly what you say you want, you do this:
nRand = 10000;
y = randn(1,nRand);
[myHist, bins] = hist(y,30);
pdf = normpdf(bins);
figure, bar(bins, myHist,1); hold on; plot(bins,pdf,'rx-'); hold off;
This is probably NOT what you actually want though. Why? You'll notice that your density function looks like a thin line at the bottom of your histogram plot. This is because a histogram is counts of numbers in bins, while a density function is normalized to integrate to one. If you have hundreds of items in a bin, there is no way that the density function will match that in scale, so you have a scaling or normalization problem. Either you have to normalize the histogram, or plot a scaled distribution function. I prefer to scale the distribution function so that my counts are sensical when I look at the histogram:
normalizedpdf = pdf/sum(pdf)*sum(myHist);
figure, bar(bins, myHist,1); hold on; plot(bins,normalizedpdf,'rx-'); hold off;
Your case is the same, except you'll use the function f(x) you specified instead of the normpdf command.
Let me add another example to the mix:
%# some normally distributed random data
data = randn(1e3,1);
%# histogram
numbins = 30;
hist(data, numbins);
h(1) = get(gca,'Children');
set(h(1), 'FaceColor',[.8 .8 1])
%# figure out how to scale the pdf (with area = 1), to the area of the histogram
[bincounts,binpos] = hist(data, numbins);
binwidth = binpos(2) - binpos(1);
histarea = binwidth*sum(bincounts);
%# fit a gaussian
[muhat,sigmahat] = normfit(data);
x = linspace(binpos(1),binpos(end),100);
y = normpdf(x, muhat, sigmahat);
h(2) = line(x, y*histarea, 'Color','b', 'LineWidth',2);
%# kernel estimator
[f,x,u] = ksdensity( data );
h(3) = line(x, f*histarea, 'Color','r', 'LineWidth',2);
legend(h, {'freq hist','fitted Gaussian','kernel estimator'})
I have a problem dealing with 3rd dimension plot for three variables.
I have three matrices: Temperature, Humidity and Power. During one year, at every hour, each one of the above were measured. So, we have for each matrix 365*24 = 8760 points. Then, one average point is taken every day. So,
Tavg = 365 X 1
Havg = 365 X 1
Pavg = 365 X 1
In electrical point of veiw, the power depends on the temperature and humidity. I want to discover this relation using a three dimensional plot.
I tried using mesh, meshz, surf, plot3, and many other commands in MATLAB but unfortunately I couldn't get what I want. For example, let us take first 10 days. Here, every day is represented by average temperature, average humidity and average power.
Tavg = [18.6275
17.7386
15.4330
15.4404
16.4487
17.4735
19.4582
20.6670
19.8246
16.4810];
Havg = [75.7105
65.0892
40.7025
45.5119
47.9225
62.8814
48.1127
62.1248
73.0119
60.4168];
Pavg = [13.0921
13.7083
13.4703
13.7500
13.7023
10.6311
13.5000
12.6250
13.7083
12.9286];
How do I represent these matrices by three dimension plot?
The challenge is that the 3-D surface plotting functions (mesh, surf, etc.) are looking for a 2-D matrix of z values. So to use them you need to construct such a matrix from the data.
Currently the data is sea of points in 3-D space, so, you have to map these points to a surface. A simple approach to this is to divide up the X-Y (temperature-humidity) plane into bins and then take the average of all of the Z (power) data. Here is some sample code for this that uses accumarray() to compute the averages for each bin:
% Specify bin sizes
Tbin = 3;
Hbin = 20;
% Create binned average array
% First create a two column array of bin indexes to use as subscripts
subs = [round(Havg/Hbin)+1, round(Tavg/Tbin)+1];
% Now create the Z (power) estimate as the average value in each bin
Pest = accumarray(subs,Pavg,[],#mean);
% And the corresponding X (temp) & Y (humidity) vectors
Tval = Tbin/2:Tbin:size(Pest,2)*Tbin;
Hval = Hbin/2:Hbin:size(Pest,1)*Hbin;
% And create the plot
figure(1)
surf(Tval, Hval, Pest)
xlabel('Temperature')
ylabel('Humidity')
zlabel('Power')
title('Simple binned average')
xlim([14 24])
ylim([40 80])
The graph is a bit coarse (can't post image yet, since I am new) because we only have a few data points. We can enhance the visualization by removing any empty bins by setting their value to NaN. Also the binning approach hides any variation in the Z (power) data so we can also overlay the orgional point cloud using plot3 without drawing connecting lines. (Again no image b/c I am new)
Additional code for the final plot:
%% Expanded Plot
% Remove zeros (useful with enough valid data)
%Pest(Pest == 0) = NaN;
% First the original points
figure(2)
plot3(Tavg, Havg, Pavg, '.')
hold on
% And now our estimate
% The use of 'FaceColor' 'Interp' uses colors that "bleed" down the face
% rather than only coloring the faces away from the origin
surfc(Tval, Hval, Pest, 'FaceColor', 'Interp')
% Make this plot semi-transparent to see the original dots anb back side
alpha(0.5)
xlabel('Temperature')
ylabel('Humidity')
zlabel('Power')
grid on
title('Nicer binned average')
xlim([14 24])
ylim([40 80])
I think you're asking for a surface fit for your data. The Curve Fitting Toolbox handles this nicely:
% Fit model to data.
ft = fittype( 'poly11' );
fitresult = fit( [Tavg, Havg], Pavg, ft);
% Plot fit with data.
plot( fitresult, [xData, yData], zData );
legend( 'fit 1', 'Pavg vs. Tavg, Havg', 'Location', 'NorthEast' );
xlabel( 'Tavg' );
ylabel( 'Havg' );
zlabel( 'Pavg' );
grid on
If you don't have the Curve Fitting Toolbox, you can use the backslash operator:
% Find the coefficients.
const = ones(size(Tavg));
coeff = [Tavg Havg const] \ Pavg;
% Plot the original data points
clf
plot3(Tavg,Havg,Pavg,'r.','MarkerSize',20);
hold on
% Plot the surface.
[xx, yy] = meshgrid( ...
linspace(min(Tavg),max(Tavg)) , ...
linspace(min(Havg),max(Havg)) );
zz = coeff(1) * xx + coeff(2) * yy + coeff(3);
surf(xx,yy,zz)
title(sprintf('z=(%f)*x+(%f)*y+(%f)',coeff))
grid on
axis tight
Both of these fit a linear polynomial surface, i.e. a plane, but you'll probably want to use something more complicated. Both of these techniques can be adapted to this situation. There's more information on this subject at mathworks.com: How can I determine the equation of the best-fit line, plane, or N-D surface using MATLAB?.
You might want to look at Delaunay triangulation:
tri = delaunay(Tavg, Havg);
trisurf(tri, Tavg, Havg, Pavg);
Using your example data, this code generates an interesting 'surface'. But I believe this is another way of doing what you want.
You might also try the GridFit tool by John D'Errico from MATLAB Central. This tool produces a surface similar to interpolating between the data points (as is done by MATLAB's griddata) but with cleaner results because it smooths the resulting surface. Conceptually multiple datapoints for nearby or overlapping X,Y coordinates are averaged to produce a smooth result rather than noisy "ripples." The tool also allows for some extrapolation beyond the data points. Here is a code example (assuming the GridFit Tool has already been installed):
%Establish points for surface
num_points = 20;
Tval = linspace(min(Tavg),max(Tavg),num_points);
Hval = linspace(min(Havg),max(Havg),num_points);
%Do the fancy fitting with smoothing
Pest = gridfit(Tavg, Havg, Pavg, Tval, Hval);
%Plot results
figure(5)
surfc(XI,YI,Pest, 'FaceColor', 'Interp')
To produce an even nicer plot, you can add labels, some transparancy and overlay the original points:
alpha(0.5)
hold on
plot3(Tavg,Havg,Pavg,'.')
xlabel('Temperature')
ylabel('Humidity')
zlabel('Power')
grid on
title('GridFit')
PS: #upperBound: Thanks for the Delaunay triangulation tip. That seems like the way to go if you want to go through each of the points. I am a newbie so can't comment yet.
Below is your solution:
Save/write the Myplot3D function
function [x,y,V]=Myplot3D(X,Y,Z)
x=linspace(X(1),X(end),100);
y=linspace(Y(1),Y(end),100);
[Xt,Yt]=meshgrid(x,y);
V=griddata(X,Y,Z,Xt,Yt);
Call the following from your command line (or script)
[Tavg_new,Pavg_new,V]=Myplot3D(Tavg,Pavg,Havg);
surf(Tavg_new,Pavg_new,V)
colormap jet;
xlabel('Temperature')
ylabel('Power/Pressure')
zlabel('Humidity')