After reading the docs about "stateEstimatorPF" I get a little confused about how to create the StateTransitionFcn for my case. In my case I have 10 sensors measurments that decay exponentially and I want to find the best parameters for my function model.
The function model is x = exp(B*deltaT)*x_1, where x are the hypotheses, deltaT is the constant time delta in my measurments and x_1 is the true previous state. I would like to use the particle filter to estimate the parameter B. If I guess right, B should be the particles and the weighted mean of this particles should be what I'm looking for.
How can I write the StateTransitionFcn and use the "stateEstimatorPF" to solve this problem?
The code below is what I get so far (and it does not work):
pf = robotics.ParticleFilter
pf.StateTransitionFcn = #stateTransitionFcn
pf.StateEstimationMethod = 'mean';
pf.ResamplingMethod = 'systematic';
initialize(pf,5000,[0.9],1);
measu = [1.0, 0.9351, 0.8512, 0.9028, 0.7754, 0.7114, 0.6830, 0.6147, 0.5628, 0.7090]
states = []
for i=1:10
[statePredicted,stateCov] = predict(pf);
[stateCorrected,stateCov] = correct(pf,measu(i));
states(i) = getStateEstimate(pf)
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function predictParticles = stateTransitionFcn(pf, prevParticles,x_1)
predictParticles = exp(prevParticles)*x_1 %how to properly use x_1?%;
end
Related
I am learning matlab GPU functions. My function myfun takes 2 input parameters delta, p. Eventually, I will apply myfun to many combinations of delta,p. For each combination of delta,p, 'myfun' will how many V's satisfies the condition delta*V-p>0, where V = [0:0.001:1]. Ideally, I want V to be a global variable. But it seems that matlab GPU has some restrictions on global variable. So I use another way to do this thing. The code is as the following:
function result = gpueg2()
dd = 0.1;
DELTA = [dd:dd:1];
dp = 0.001;
P = [0:dp:1];
[p,delta]=meshgrid(P,DELTA);
p = gpuArray(p(:));
delta = gpuArray(delta(:));
V = [0:0.001:1];
function [O] = myfun(delta,p)
O = sum((delta*V-p)>0);
end
result = arrayfun(#myfun,delta,p);
end
However, it through an error message
Function passed as first input argument contains unsupported or unknown function 'sum'.
But I believe sum is applicable in GPU.
Any advice and suggestions are highly appreciated.
The problem with sum is not with the GPU, it's with using arrayfun on a GPU. The list of functions that arrayfun on a GPU accepts is given here: https://www.mathworks.com/help/distcomp/run-element-wise-matlab-code-on-a-gpu.html. sum is not on the list on that page of documentation.
Your vectors are not so big (though I accept this may be a toy example of your real problem). I suggest the following alternative implementation:
function result = gpueg2()
dd = 0.1;
DELTA = dd:dd:1;
dp = 0.001;
P = 0:dp:1;
V = 0:0.001:1;
[p,delta,v] = meshgrid(P,DELTA,V);
p = gpuArray(p);
delta = gpuArray(delta);
v = gpuArray(v);
result = sum(delta.*v-p>0, 3);
end
Note the following differences:
I make 3D arrays of p,delta,v, rather than 2D. These three are only 24MB in total.
I do the calculation delta.*v-p>0 on the whole 3D array: this will be well split on the GPU.
I do the sum on the 3rd index, i.e. over V.
I have checked that your routine on the CPU and mine on the GPU give the same results.
I would like to calculate standard errors of contrasts in a linear mixed-effect model (fitlme) in MATLAB.
y = randn(100,1);
area = randi([1 3],100,1);
mea = randi([1 3],100,1);
sub = randi([1 5],100,1);
data = array2table([area mea sub y],'VariableNames',{'area','mea','sub','y'});
data.area = nominal(data.area,{'A','B','C'});
data.mea = nominal(data.mea,{'Baseline','+1h','+8h'});
data.sub = nominal(data.sub);
lme = fitlme(data,'y~area*mea+(1|sub)')
% Plot Area A on three measurements
coefv = table2array(dataset2table(lme.Coefficients(:,2)));
bar([coefv(1),sum(coefv([1 4])),sum(coefv([1 5]))])
Calculating the contrast means, e.g. area1-measurement1 vs area1-measurement2 vs area1-measurement3 can be done by summing the related coefficient parameters. However, does anyone know how to calculate the related standard errors?
I know a hypothesis test can be done by coefTest(lme,H), but only p values can be extracted.
An example for Area A is shown below:
I have resolved this issue!
Matlab uses the 'predict' function to estimate contrasts. To find confidence intervals for area A, at measurement +8h in this particular example use:
dsnew = dataset();
dsnew.area = nominal('A');
dsnew.mea = nominal('+8h');
dsnew.sub = nominal(1);
[yh yCI] = predict(lme,dsnew,'Conditional',false)
A result is shown below:
I'm writing a program in matlab to observe how a function evolves in time. I'd like to set up a matrix that fills its first row with the initial function, and progressively fills more rows based off of a time derivative (that's dependent on the spatial derivative). The function is arbitrary, the program just needs to 'evolve' it. This is what I have so far:
xleft = -10;
xright = 10;
xsampling = 1000;
tmax = 1000;
tsampling = 1000;
dt = tmax/tsampling;
x = linspace(xleft,xright,xsampling);
t = linspace(0,tmax,tsampling);
funset = [exp(-(x.^2)/100);cos(x)]; %Test functions.
funsetvel = zeros(size(funset)); %The functions velocities.
spacetimevalue1 = zeros(length(x), length(t));
spacetimevalue2 = zeros(length(x), length(t));
% Loop that fills the first functions spacetime matrix.
for j=1:length(t)
funsetvel(1,j) = diff(funset(1,:),x,2);
spacetimevalue1(:,j) = funsetvel(1,j)*dt + funset(1,j);
end
This outputs the error, Difference order N must be a positive integer scalar. I'm unsure what this means. I'm fairly new to Matlab. I will exchange the Euler-method for another algorithm once I can actually get some output along the proper expectation. Aside from the error associated with taking the spatial derivative, do you all have any suggestions on how to evaluate this sort of process? Thank you.
I would like to calibrate a interest rate tree using the optimization tool in matlab. Need some guidance on doing it.
The interest rate tree looks like this:
How it works:
3.73% = 2.5%*exp(2*0.2)
96.40453 = (0.5*100 + 0.5*100)/(1+3.73%)
94.15801 = (0.5*96.40453+ 0.5*97.56098)/(1+2.50%)
The value of 2.5% is arbitrary and the upper node is obtained by multiplying with an exponential of 2*volatility(here it is 20%).
I need to optimize the problem by varying different values for the lower node.
How do I do this optimization in Matlab?
What I have tried so far?
InterestTree{1}(1,1) = 0.03;
InterestTree{3-1}(1,3-1)= 2.5/100;
InterestTree{3}(2,:) = 100;
InterestTree{3-1}(1,3-2)= (2.5*exp(2*0.2))/100;
InterestTree{3-1}(2,3-1)=(0.5*InterestTree{3}(2,3)+0.5*InterestTree{3}(2,3-1))/(1+InterestTree{3-1}(1,3-1));
j = 3-2;
InterestTree{3-1}(2,3-2)=(0.5*InterestTree{3}(2,j+1)+0.5*InterestTree{3}(2,j))/(1+InterestTree{3-1}(1,j));
InterestTree{3-2}(2,3-2)=(0.5*InterestTree{3-1}(2,j+1)+0.5*InterestTree{3-1}(2,j))/(1+InterestTree{3-2}(1,j));
But I am not sure how to go about the optimization. Any suggestions to improve the code, do tell me..Need some guidance on this..
Are you expecting the tree to increase in size? Or are you just optimizing over the value of the "2.5%" parameter?
If it's the latter, there are two ways. The first is to model the tree using a closed form expression by replacing 2.5% with x, which is possible with the tree. There are nonlinear optimization toolboxes available in Matlab (e.g. more here), but it's been too long since I've done this to give you a more detailed answer.
The seconds is the approach I would immediately do. I'm interpreting the example you gave, so the equations I'm using may be incorrect - however, the principle of using the for loop is the same.
vol = 0.2;
maxival = 100;
val1 = zeros(1,maxival); %Preallocate
finalval = zeros(1,maxival);
for ival=1:maxival
val1(ival) = i/1000; %Use any scaling you want. This will go from 0.1% to 10%
val2=val1(ival)*exp(2*vol);
x1 = (0.5*100+0.5*100)/(1+val2); %Based on the equation you gave
x2 = (0.5*100+0.5*100)/(1+val1(ival)); %I'm assuming this is how you calculate the bottom node
finalval(ival) = x1*0.5+x2*0.5/(1+...); %The example you gave isn't clear, so replace this with whatever it should be
end
[maxval, indmaxval] = max(finalval);
The maximum value is in maxval, and the interest that maximized this is in val1(indmaxval).
I’m currently a Physics student and for several weeks have been compiling data related to ‘Quantum Entanglement’. I’ve now got to a point where I have to plot my data (which should resemble a cos² graph - and does) to a sort of “best fit” cos² graph. The lab script says the following:
A more precise determination of the visibility V (this is basically how 'clean' the data is) follows from the best fit to the measured data using the function:
f(b) = A/2[1-Vsin(b-b(center)/P)]
Granted this probably doesn’t mean much out of context, but essentially A is the amplitude, b is an angle and P is the periodicity. Hence this is also a “wave” like the experimental data I have found.
From this I understand, as previously mentioned, I am making a “best fit” curve. However, I have been told that this isn’t possible with Excel and that the best approach is Matlab.
I know intermediate JavaScript but do not know Matlab and was hoping for some direction.
Is there a tutorial I can read for this? Is it possible for someone to go through it with me? I really have no idea what it entails, so any feed back would be greatly appreciated.
Thanks a lot!
Initial steps
I guess we should begin by getting a representation in Matlab of the function that you're trying to model. A direct translation of your formula looks like this:
function y = targetfunction(A,V,P,bc,b)
y = (A/2) * (1 - V * sin((b-bc) / P));
end
Getting hold of the data
My next step is going to be to generate some data to work with (you'll use your own data, naturally). So here's a function that generates some noisy data. Notice that I've supplied some values for the parameters.
function [y b] = generateData(npoints,noise)
A = 2;
V = 1;
P = 0.7;
bc = 0;
b = 2 * pi * rand(npoints,1);
y = targetfunction(A,V,P,bc,b) + noise * randn(npoints,1);
end
The function rand generates random points on the interval [0,1], and I multiplied those by 2*pi to get points randomly on the interval [0, 2*pi]. I then applied the target function at those points, and added a bit of noise (the function randn generates normally distributed random variables).
Fitting parameters
The most complicated function is the one that fits a model to your data. For this I use the function fminunc, which does unconstrained minimization. The routine looks like this:
function [A V P bc] = bestfit(y,b)
x0(1) = 1; %# A
x0(2) = 1; %# V
x0(3) = 0.5; %# P
x0(4) = 0; %# bc
f = #(x) norm(y - targetfunction(x(1),x(2),x(3),x(4),b));
x = fminunc(f,x0);
A = x(1);
V = x(2);
P = x(3);
bc = x(4);
end
Let's go through line by line. First, I define the function f that I want to minimize. This isn't too hard. To minimize a function in Matlab, it needs to take a single vector as a parameter. Therefore we have to pack our four parameters into a vector, which I do in the first four lines. I used values that are close, but not the same, as the ones that I used to generate the data.
Then I define the function I want to minimize. It takes a single argument x, which it unpacks and feeds to the targetfunction, along with the points b in our dataset. Hopefully these are close to y. We measure how far they are from y by subtracting from y and applying the function norm, which squares every component, adds them up and takes the square root (i.e. it computes the root mean square error).
Then I call fminunc with our function to be minimized, and the initial guess for the parameters. This uses an internal routine to find the closest match for each of the parameters, and returns them in the vector x.
Finally, I unpack the parameters from the vector x.
Putting it all together
We now have all the components we need, so we just want one final function to tie them together. Here it is:
function master
%# Generate some data (you should read in your own data here)
[f b] = generateData(1000,1);
%# Find the best fitting parameters
[A V P bc] = bestfit(f,b);
%# Print them to the screen
fprintf('A = %f\n',A)
fprintf('V = %f\n',V)
fprintf('P = %f\n',P)
fprintf('bc = %f\n',bc)
%# Make plots of the data and the function we have fitted
plot(b,f,'.');
hold on
plot(sort(b),targetfunction(A,V,P,bc,sort(b)),'r','LineWidth',2)
end
If I run this function, I see this being printed to the screen:
>> master
Local minimum found.
Optimization completed because the size of the gradient is less than
the default value of the function tolerance.
A = 1.991727
V = 0.979819
P = 0.695265
bc = 0.067431
And the following plot appears:
That fit looks good enough to me. Let me know if you have any questions about anything I've done here.
I am a bit surprised as you mention f(a) and your function does not contain an a, but in general, suppose you want to plot f(x) = cos(x)^2
First determine for which values of x you want to make a plot, for example
xmin = 0;
stepsize = 1/100;
xmax = 6.5;
x = xmin:stepsize:xmax;
y = cos(x).^2;
plot(x,y)
However, note that this approach works just as well in excel, you just have to do some work to get your x values and function in the right cells.