The function called DicePlot simulates rolling 10 dice 5000 times.
The function calculates the sum of values of the 10 dice of each roll, which will be a 1 ⇥ 5000 vector, and plot relative frequency histogram with edges of bins being selected in where each bin in the histogram represents a possible value of for the sum of the dice.
The mean and standard deviation of the 1 ⇥ 5000 sums of dice values will be computed, and the probability density function of normal distribution (with the mean and standard deviation computed) on top of the relative frequency histogram will be plotted.
Below is my code so far - What am I doing wrong? The graph shows up but not the extra red line on top? I looked at answers like this, and I don't think I'll be plotting anything like the Gaussian function.
% function[]= DicePlot()
for roll=1:5000
diceValues = randi(6,[1, 10]);
SumDice(roll) = sum(diceValues);
end
distr=zeros(1,6*10);
for i = 10:60
distr(i)=histc(SumDice,i);
end
bar(distr,1)
Y = normpdf(X)
xlabel('sum of dice values')
ylabel('relative frequency')
title(['NumDice = ',num2str(NumDice),' , NumRolls = ',num2str(NumRolls)]);
end
It is supposed to look like
But it looks like
The red line is not there because you aren't plotting it. Look at the documentation for normpdf. It computes the pdf, it doesn't plot it. So you problem is how do you add this line to the plot. The answer to that problem is to google "matlab hold on".
Here's some code to get you going in the right direction:
% Normalize your distribution
normalizedDist = distr/sum(distr);
bar(normalizedDist ,1);
hold on
% Setup your density function using the mean and std of your sample data
mu = mean(SumDice);
stdv = std(SumDice);
yy = normpdf(xx,mu,stdv);
xx = linspace(0,60);
% Plot pdf
h = plot(xx,yy,'r'); set(h,'linewidth',1.5);
Related
I am trying to fit a distribution curve to the histogram of some data. (I have used some model data here instead because it is difficult to upload the actual data. I have included the complete code after my question.)
Because the histogram looks normally distributed when I plotted the x-axis in logscale, I transform the data first before fitting a normal distribution to it and I got the following results:
>>pdn=fitdist(log(data),'Normal')
pdn =
Normal distribution
mu = -0.334458 [-0.34704, -0.321876]
sigma = 0.351478 [0.342804, 0.360605]
When I plotted out the pdf with the histogram, I got this:
The result seems reasonable to me. Then I discovered that in the Matlab fitdist(), it already has a 'Lognormal' option and I don't really need the transform my data first and this is what I got:
>>pdln = fitdist(data,'Lognormal')
pdln =
Lognormal distribution
mu = -0.334458 [-0.34704, -0.321876]
sigma = 0.351478 [0.342804, 0.360605]
Exactly the same mean and standard deviation as I have got before. However, when I plotted it out with the histogram, I got a different curve:
This curve fits better to the data but the positions of the mean and the mean+/-std points are not as I have expected (i.e. mean at the peak and the mean+/-std at the same levels).
Which come to my question, why would fitdist(data,'Lognormal') give the same result as fitdist(log(data),'Normal') but a different plot? I have looked through the Matlab help pages and I still could not understand why, or where are my mistakes, please help.
My aim for all this is to get some numerical parameters about the distributions of my data under different conditions and compare them to see if there is any difference. At the moment, I am not certain which way would give me reliable estimates of the means and standard deviations.
The code for the graphs is below:
%random data in lognormal distribution
mu=-0.335742;
sigma=0.35228;
data=lognrnd(mu,sigma,[3000 1]);
%make histogram
interval=0.1;
svalue=sort(data);
bx(1)=interval/2;
i=2;
while bx(i-1)<=max(svalue)
bx(i)=bx(i-1)+interval;
i=i+1;
end
by=hist(svalue,bx);
subplot(211)
h = bar(bx,by,'hist');
set(h,'FaceColor',[.9 .9 .9]);
set(gca,'xlim',[0.05 10]);
xticks=[0.05 0.1 0.2 0.5 1 2 5 10];
set(gca,'xscale','log','xminortick','on')
set(gca,'xtick',xticks)
ylabel('counts')
subplot(212)
h = bar(bx,by,'hist');
set(h,'FaceColor',[.9 .9 .9]);
set(gca,'xlim',[0.05 10]);
xticks=[0.05 0.1 0.2 0.5 1 2 5 10];
set(gca,'xscale','log','xminortick','on')
set(gca,'xtick',xticks)
ylabel('counts')
% fit distribution curves
pdf_x = 0:0.01:max(data);
max_by=max(by); % for scaling the pdf to the histogram
% case 1 - PDF fitted using fitdist(log(data),'Normal')
subplot(211)
hold on
pdn = fitdist(log(data),'Normal')
pdf_y = pdf(pdn,log(pdf_x));
h1=plot(pdf_x,pdf_y./max(pdf_y).*max_by,'-k');
range=[exp(pdn.mu-pdn.sigma) exp(pdn.mu+pdn.sigma)];
h2=plot(exp(pdn.mu),pdf(pdn,(pdn.mu))./max(pdf_y).*max_by,'sk') ;
h3=plot(range,pdf(pdn,log(range))./max(pdf_y).*max_by,'ok') ;
title('PDF fitted using fitdist(log(data),''Normal'')');
legend([h1 h2 h3],'pdf','mean','meam+/-std');
% case 2 - PDF fitted using fitdist(data,'Lognormal')
subplot(212)
hold on
pdln = fitdist(data,'Lognormal')
pdf_y = pdf(pdln,pdf_x);
h1=plot(pdf_x,pdf_y./max(pdf_y).*max_by,'-b');
range=[exp(pdln.mu-pdln.sigma) exp(pdln.mu+pdln.sigma)];
h2=plot(exp(pdln.mu),pdf(pdln,exp(pdln.mu))./max(pdf_y).*max_by,'sb');
h3=plot(range,pdf(pdln,range)./max(pdf_y).*max_by,'ob') ;
title('PDF fitted using fitdist(data,''Lognormal'')');
legend([h1 h2 h3],'pdf','mean','meam+/-std');
I have two different functions of time x(t) and y(t). I want to plot x(t) vs y(t) in Matlab . The plot needs to be divided into a 40x40 grid stretching from min and max values of signal in each direction. I then need to calculate the number of grid boxes occupied in the plot. Please suggest a convenient way to implement this in Matlab.
I've tried the following code (neglect the upper and lower limits of axis):
NrGrid = 20; % Number Of Grids
x = linspace(0, 100, NrGrid+1);
[X,Y] = meshgrid(x);
figure(1)
plot(X,Y,'k')
hold on
plot(Y,X,'k')
hold off
set(gca, 'Box','off', 'XTick',[], 'YTick',[])
axis square
In my understanding, the code only divides the plot into grids. how do I count the number of grids that are occupied?
Reference: I basically need to implement the algorithm in this paper:
http://www.fhv.at/media/pdf/forschung/prozess-und-produktengineering/working-papers/working-papers-2005/detecting-ventricular
Sounds like you want to create a 40x40 matrix and then use a Bresenham line drawing algorithm to connect each of the points (after appropriate scaling) in x(t)/y(t) correspondence in that matrix.
You can then use nnz to count the number of non-zero elements in the matrix.
I managed to get a much simpler solution than the one mentioned by Dave Durbin by quantizing the signal into 40 levels and then comparing it with its shifted region. The code is attached for reference:
function TD=TimeDelay(val,fs)
n=40;
jump=( max(val) + abs(min(val)))/40;
level=zeros(n,1);
level(1)=min(val) + jump;
for i=2:n
level(i)=level(i-1)+jump;
end
level(n)=level(n)+1;
ScaledECG=zeros(size(val));
ScaledECG(val <= level(1))=1;
for j=2:n
ScaledECG( val<=level(j) & val>level(j-1))=j;
end
tau=fs*.5;
N=zeros(n,n);
for k=tau+1:1:length(val)
N(ScaledECG(k-tau),ScaledECG(k))=N(ScaledECG(k-tau),ScaledECG(k)) + 1;
end
N(N>5)=0;
N(N<=5)=1;
TD=sum(sum(N));
I haven't used MATLAB in a while and I am stuck on a small detail. I would really appreciate it if someone could help me out!
So I am trying to plot a transfer function using a specific function called freqs but I can't figure out how I can label specific points on the graph.
b = [0 0 10.0455]; % Numerator coefficients
a = [(1/139344) (1/183.75) 1]; % Denominator coefficients
w = logspace(-3,5); % Frequency vector
freqs(b,a,w)
grid on
I want to mark values at points x=600 Hz and 7500 Hz with a marker or to be more specific, points (600,20) and (7500,-71), both of which should lie on the curve. For some reason, freqs doesn't let me do that.
freqs is very limited when you want to rely on it plotting the frequency response for you. Basically, you have no control on how to modify the graph on top of what MATLAB generates for you.
Instead, generate the output response in a vector yourself, then plot the magnitude and phase of the output yourself so that you have full control. If you specify an output when calling freqs, you will get the response of the system.
With this, you can find the magnitude of the output by abs and the phase by angle. BTW, (600,20) and (7500,-71) make absolutely no sense unless you're talking about magnitude in dB.... which I will assume is the case for the moment.
As such, we can reproduce the plot that freqs gives by the following. The key is to use semilogx to get a semi-logarithmic graph on the x-axis. On top of this, declare those points that you want to mark on the magnitude, so (600,20) and (7500,-71):
%// Your code:
b = [0 0 10.0455]; % Numerator coefficients
a = [(1/139344) (1/183.75) 1]; % Denominator coefficients
w = logspace(-3,5); % Frequency vector
%// New code
h = freqs(b,a,w); %// Output of freqs
mag = 20*log10(abs(h)); %// Magnitude in dB
pha = (180/pi)*angle(h); %// Phase in degrees
%// Declare points
wpt = [600, 7500];
mpt = [20, -71];
%// Plot the magnitude as well as markers
figure;
subplot(2,1,1);
semilogx(w, mag, wpt, mpt, 'r.');
xlabel('Frequency');
ylabel('Magnitude (dB)');
grid;
%// Plot phase
subplot(2,1,2);
semilogx(w, pha);
xlabel('Frequency');
ylabel('Phase (Degrees)');
grid;
We get this:
If you check what freqs generates for you, you'll see that we get the same thing, but the magnitude is in gain (V/V) instead of dB. If you want it in V/V, then just plot the magnitude without the 20*log10() call. Using your data, the markers I plotted are not on the graph (wpt and mpt), so adjust the points to whatever you see fit.
There are a couple issues before we attempt to answer your question. First, there is no data-point at 600Hz or 7500Hz. These frequencies fall between data-points when graphed using the freqs command. See the image below, with datatips added interactively. I copy-pasted your code to generate this data.
Second, it does not appear that either (600,20) or (7500,-71) lie on the curves, at least with the data as you entered above.
One solution is to use plot a marker on the desired position, and use a "text" object to add a string describing the point. I put together a script using your data, to generate this figure:
The code is as follows:
b = [0 0 10.0455];
a = [(1/139344) (1/183.75) 1];
w = logspace(-3,5);
freqs(b,a,w)
grid on
figureHandle = gcf;
figureChildren = get ( figureHandle , 'children' ); % The children this returns may vary.
axes1Handle = figureChildren(1);
axes2Handle = figureChildren(2);
axes1Children = get(axes1Handle,'children'); % This should be a "line" object.
axes2Children = get(axes2Handle,'children'); % This should be a "line" object.
axes1XData = get(axes1Children,'xdata');
axes1YData = get(axes1Children,'ydata');
axes2XData = get(axes2Children,'xdata');
axes2YData = get(axes2Children,'ydata');
hold(axes1Handle,'on');
plot(axes1Handle,axes1XData(40),axes1YData(40),'m*');
pointString1 = ['(',num2str(axes1XData(40)),',',num2str(axes1YData(40)),')'];
handleText1 = text(axes1XData(40),axes1YData(40),pointString1,'parent',axes1Handle);
hold(axes2Handle,'on');
plot(axes2Handle,axes2XData(40),axes2YData(40),'m*');
pointString2 = ['(',num2str(axes2XData(40)),',',num2str(axes2YData(40)),')'];
handleText2 = text(axes2XData(40),axes2YData(40),pointString2,'parent',axes2Handle);
I'm using the Matlab function "hist" to estimate the probability density function of a realization of a random process I have.
I'm actually:
1) taking the histogram of h0
2) normalizing its area in order to get 1
3) plotting the normalized curve.
The problem is that, no matter how many bins I use, the histogram never start from 0 and never go back to 0 whereas I would really like that kind of behavior.
The code I use is the following:
Nbin = 36;
[n,x0] = hist(h0,Nbin);
edge = find(n~=0,1,'last');
Step = x0(edge)/Nbin;
Scale_factor = sum(Step*n);
PDF_h0 = n/Scale_factor;
hist(h0 ,Nbin) %plot the histogram
figure;
plot(a1,p_rice); %plot the theoretical curve in blue
hold on;
plot(x0, PDF_h0,'red'); %plot the normalized curve obtained from the histogram
And the plots I get are:
If your problem is that the plotted red curve does not go to zero: you can solve that adding initial and final points with y-axis value 0. It seems from your code that the x-axis separation is Step, so it would be:
plot([x0(1)-Step x0 x0(end)+Step], [0 PDF_h0 0], 'red')
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')