I have a wave simulation with values calculated like this: (pseudocode)
for(x):
for(y):
new_value = (current[x-1,y] + current[x+1,y] + current[x,y-1] + current[x,y+1]) / 2 - previous[x, y]
new_value -= new_value * damp
previous[x, y] = new_value
swap(current, previous)
Double the average of surrounding points minus previous value for that point.
Right now the change happens every frame so how fast it goes is dependent on the framerate. The problem is, I can't figure out how to scale this process by elapsed time. I tried getting the difference between old and new value and scaling it, but that doesn't work at all; probably something to do with board swapping but I'm not sure.
Can I make it work or do I need a completely different approach?
Ok I figured it out. My problem was based on the fact that I thought I have to run this algorithm every frame – I don't. If you just run it every few frames then obviously the resulting animation is not smooth; but I didn't consider that you can just do linear interpolation to get smooth transition from old state to new state which produces a result I'm happy with.
Related
Recently came across a simple issues that I could not solve on my own. I have a Simulink model that uses a matlab function for some calculations inside the model. The idea is that at some specified moment of time I need to change the voltage of an electric drive. And I need to change it until the rotor’s position reaches another specified value. For instance:
If control_signal == 1; (command to start the execution);
While Angle ~= 180 \\ desired angle is 180;
Control voltage = 5 - 0.1 (5V is the initial value, while the increment of
the voltage change is 0.1)
End
end
So technically what I was thinking will happen, is that the cycle will be executed until the angle of 180 is reached, at some value of the control voltage (for instance 4.6). But when I am running this code, Simulink can’t execute the model. So without any warning or errors, simulation freezes at some stage (when the main condition kicks in). So looks like it can’t process further when the cycle’s execution starts. Can somebody help me with the code? Because the described behaviour of the model during simulation is definitely caused by the above mentioned code.
Thank you in advance.
My guess is you convert the value of the angle expressed in radians to degrees, and you calculate the angle beforehand using trigonometry functions - it will never reach precisely 180 degrees. You should choose some epsilon such that 180 - epsilon is close enough to 180 for your application and use that value as your loop condition.
Also, based on your description of the problem you are trying to solve, sounds like you actually want to check whether the angle is not greater than 180, not if it equals 180.
Also, you are incrementing your voltage incorrectly. Everytime you enter the loop, your control_voltage variable equals 5 - 0.1, which means it's constant and will equal 4.9 no matter how many times you run that loop. This is the correct way:
control_voltage = 5; % initial value
if control_signal == 1; (command to start the execution);
while Angle ~= (180 - epsilon) % some epsilon of your choice
control_voltage = control_voltage - 0.1; % now it's smaller by 0.1 every time the loop is run
end
end
I am trying to avoid the for loops and I have been reading through all the old posts there are about it but I am not able to solve my problem. I am new in MATLAB, so apologies for my ignorance.
The thing is that I have a 300x2 cell and in each one I have a 128x128x256 matrix. Each one is an image with 128x128 pixels and 256 channels per pixel. In the first column of the 300x2 cell I have my parallel intensity values and in the second one my perpendicular intensity values.
What I want to do is to take every pixel of every image (for each component) and sum the intensity values channel by channel.
The code I have is the following:
Image_par_channels=zeros(128,128,256);
Image_per_channels=zeros(128,128,256);
Image_tot_channels=zeros(128,128,256);
for a=1:128
for b=1:128
for j=1:256
for i=1:numfiles
Image_par_channels(a,b,j)=Image_par_channels(a,b,j)+Image_cell_par_per{i,1}(a,b,j);
Image_per_channels(a,b,j)=Image_per_channels(a,b,j)+Image_cell_par_per{i,2}(a,b,j);
end
Image_tot_channels(a,b,j)=Image_par_channels(a,b,j)+2*G*Image_per_channels(a,b,j);
end
end
end
I think I could speed it up introducing (:,:,j) instead of specifying a and b. But still a for loop. I am trying to use cellfun without any success due to my lack of expertise. Could you please give me a hand?
I would really appreciate it.
Many thanks and have a nice day!
Y
I believe you could do something like
Image_par_channels=zeros(128,128,256);
Image_per_channels=zeros(128,128,256);
Image_tot_channels=zeros(128,128,256);
for i=1:numfiles
Image_par_channels = Image_par_channels + Image_cell_par_per{i,1};
Image_per_channels = Image_per_channels + Image_cell_par_per{i,2};
end
Image_tot_channels = Image_par_channels + 2*G*Image_per_channels;
I haven't work with matlab in a long time, but I seem to recall you can do something like this. g is a constant.
EDIT:
Removed the +=. Incremental assignment is not an operator available in matlab. You should also note that Image_tot_channels can be build directly in the loop, if you don't need the other two variables later.
I am trying to do a Monte Carlo simulation of a local volatility model, i.e.
dSt = sigma(St,t) * St dWt .
Unfortunately the Matlab package class sde can not be applied, as the function is rather complex.
For this reason I am simulating this SDE manually with the Euler-Mayurama method. More specifically I used Ito's formula to get an SDE for the log-process Xt=log(St)
dXt = -1/2 sigma^2(exp(Xt),t) dt + sigma(exp(Xt),t) dWt
The code for this is the following:
function [S]=geom_bb(sigma,T,N,m)
% T.. Time horizon, sigma.. standard deviation, N.. timesteps, m.. dimensions
X=zeros(N+1,m);
dt=T/N;
t=(0:N)'*dt;
dW=randn(N,m);
for j=1:N
X(j+1,:)=X(j,:) - 1/2* sigma(exp(X(j,:)),t(j))^2 * sqrt(dt) + sigma(exp(X(j,:)),t(j))*dW(j,:);
end
S=exp(X*sqrt(dt));
end
This code works rather good for small sigma, however for sigma around 10 the process S always tends to zero. This should not happen as S is a martingale, and therefore has expectation =1 (at least for constant sigma).
However X should be simulated correctly, as the mean is exact.
Can anyone help me with this issue? Is this only due to numerical rounding errors? Is there another simulation method that should be preferred to solve this problem?
First are you sure S=exp(X*sqrt(dt)) outside the loop is doing what you want ? Why not have it inside the loop to start with ? You're using the exp(X) for sigma() inside the loop in any case, which is now missing the sqrt(dt).
Beyond that, suggested ways to improve behavior: use the Milstein scheme instead, increase the number of timesteps, make sure your sigma() value is commensurate with your timestep. Sigma of 10 means 1000% volatility, i.e. moves of 60% per day. Assuming dt is more than a few minutes, this simply can't be good.
I find examples the best way to demonstrate my question. I generate some data, add some random noise, and fit it to get back my chosen "generator" value...
x = linspace(0.01,1,50);
value = 3.82;
y = exp(-value.*x);
y = awgn(y,30);
options = optimset('MaxFunEvals',1000,'MaxIter',1000,'TolFun',1e-10,'Display','off');
model = #(p,x) exp(-p(1).*x);
startingVals = [5];
lb = [1];
ub = [10];
[fittedValue] = lsqcurvefit(model,startingVals,x,y,lb,ub,options)
fittedGraph = exp(-fittedValue.*x);
plot(x,y,'o');
hold on
plot(x,fittedGraph,'r-');
In this new example, I have generated the same data but this time added much more noise to the first 15 points. Because it is random sometimes it works out okay, but after a few runs I get a good example that illustrates my problem. Same code, except for these lines added under value = 3.82
y = exp(-value.*x);
y(1:15) = awgn(y(1:15),5);
y(15:end) = awgn(y(15:end),30);
As you can see, it has clearly not given a good fit to where the data seems reliable, because it is fitting from points 1-50. What I want to do is say, okay MATLAB, I can see we have some noisy data but it seems decent over a range, only fit your exponential from points 15 to the end. I could go back to my code and update it to do this, but I will be batch fitting graphs like this where each one will have different ranges of 'good' data.
So what I am after is a GUI callback mechanisms that allows me to click on two circles from the data and have them change color or something, which indicates the lsqcurvefit will only fit over that range. Internally all it has to change is inside the lsqcurvefit call e.g.
x(16:end),y(16:end)
But the range should update depending on the starting and ending circles I have clicked.
I hope my question is clear. Thanks.
You could use ginput to select the two points for your min and max in the plot.
[x,y]=ginput(2);
%this returns you the x and y coordinates of two points clicked after each other
%the min point is assumed to be clicked first
min=[x(1) y(1)];
max=[x(2) y(2)];
then you could fit your curve with the coordinates for min and max I guess.
You could also switch between a rightclick for the min and a leftclick for the max etc.
Hope this helps you.
In Matlab, is it possible to measure local variation of a signal across an entire signal without using for loops? I.e., can I implement the following:
window_length = <something>
for n = 1:(length_of_signal - window_length/2)
global_variance(n) = var(my_signal(1:window_length))
end
in a vectorized format?
If you have the image processing toolbox, you can use STDFILT:
global_std = stdfilt(my_signal(:),ones(window_length,1));
% square to get the variance
global_variance = global_std.^2;
You could create a 2D array where each row is shifted one w.r.t. to the row above, and with the number of rows equal to the window width; then computing the variance is trivial. This doesn't require any toolboxes. Not sure if it's much faster than the for loop though:
longSignal = repmat(mySignal(:), [1 window_length+1]);
longSignal = reshape(longSignal(1:((length_of_signal+1)*window_length)), [length_of_signal+1, window_length])';
global_variance = sum(longSignal.*longSignal, 2);
global_variance = global_variance(1:length_of_signal-window_length));
Note that the second column is shifted down by one relative to the one above - this means that when we have the blocks of data on which we want to operate in rows, so I take the transpose. After that, the sum operator will sum over the first dimension, which gives you a row vector with the results you want. However, there is a bit of wrapping of data going on, so we have to limit to the number of "good" values.
I don't have matlab handy right now (I'm at home), so I was unable to test the above - but I think the general idea should work. It's vectorized - I can't guarantee it's fast...
Check the "moving window standard deviation" function at Matlab Central. Your code would be:
movingstd(my_signal, window_length, 'forward').^2
There's also moving variance code, but it seems to be broken.
The idea is to use filter function.