Octave efficient way to repeat an array - octave

Hi I have a 2D array in Octave, called Sig in the code, and I want to replicate this repeatedly to form a certain number of cycles of this array. The way I've written is working but very slow, am I missing a trick to speed this up?
Cycles=262800
Sig_1=Sig
for i=1:1:Cycles-1;
Sig_1=[Sig_1;Sig];
endfor

You can use repmat:
Sig_1 = repmat(Sig, [Cycles, 1])

Related

1D fft on 2nd dim on Armadillo complex matrix

I need to compute the 1D fft of a cx_mat in it's second dimension. So say I have this matrix:
cx_mat A(randu(5,10),randu(5,10));
The MATLAB version would look like:
A_fft=fft(A,[],2);
How would I go about this in Armadillo?
I'm trying to keep this as fast as possible so I figure a for loop running through the columns would not be the best option.
I then saw the .each_col attribute and tried
cx_mat A_fft=A.each_col([](vec& a){fft(a);});
But that would not compile. Maybe that is correct but my syntax is wrong
Any help would be greatly appreciated.
You need to have a complex vector as argument in the lambda function:
cx_mat A_fft=A.each_col([](cx_vec& a){fft(a);});

Octave: How to solve a one order differential equation with variable coefficients

I'm trying to solve a one order differential equation with variable coefficients of the following form:
xdot(1)=a(t)*x(1)+b;
where b=a constant and where a(t) = a time dependent function. I know that I can solve this equation by hand butt a(t) is a quite complex function.
So, my problem is the following. a(t) is a function which I know its values from an experiment (I've got all the results in a file) --> a(t) is a vector (n x 1) which is a problem because x(1)= xdot(1)=a scalar. So, how could I solve this equation, with lsode ?
Possibly I have underestimated your problem, but the way I read it, you are asking to integrate a first order ODE. In general there are two ways to proceed,, implicit methods and explicit methods. Here is the crudest, but easiest to understand, method I can come up with:
nt=101;a=-ones(1,nt);b=1/2;x=NaN*ones(1,nt);x(1)=pi;dt=0.01;
for kt=2:nt
dxdt=a(kt-1)*x(kt-1)+b;
x(kt)=x(kt-1)+dxdt*dt;
endfor
plot(x)
I have assumed a<0 so there is no tendency to blow up. You will want to set it equal to your observed values.

Making sense of soundMixer.computeSpectrum

All examples that I can find on the Internet just visualize the result array of the function computeSpectrum, but I am tasked with something else.
I generate a music note and I need by analyzing the result array to be able to say what note is playing. I figured out that I need to set the second parameter of the function call 'FFTMode' to true and then it returns sound frequencies. I thought that really it should return only one non-zero value which I could use to determine what note I generated using Math.sin function, but it is not the case.
Can somebody suggest a way how I can accomplish the task? Using the soundMixer.computeSpectrum is a requirement because I am going to analyze more complex sounds later.
FFT will transform your signal window into set of Nyquist sine waves so unless 440Hz is one of them you will obtain more than just one nonzero value! For a single sine wave you would obtain 2 frequencies due to aliasing. Here an example:
As you can see for exact Nyquist frequency the FFT response is single peak but for nearby frequencies there are more peaks.
Due to shape of the signal you can obtain continuous spectrum with peaks instead of discrete values.
Frequency of i-th sample is f(i)=i*samplerate/N where i={0,1,2,3,4,...(N/2)-1} is sample index (first one is DC offset so not frequency for 0) and N is the count of samples passed to FFT.
So in case you want to detect some harmonics (multiples of single fundamental frequency) then set the samplerate and N so samplerate/N is that fundamental frequency or divider of it. That way you would obtain just one peak for harmonics sinwaves. Easing up the computations.

Cuda Kernel with different array sizes

I am working on a fluid dynamic problem in cuda and discovered a problem like this
if I have an array e.g debug_array with the length 600 and an array
value_array with the length 100 and I wanna do sth like
for(int i=0;i<6;i++)
{
debug_array[6*(bx*block_size+tx)+i] = value_array[bx*block_size+tx];
}
block_size would in this example be based on the 100 element array, e.g
4 blocks block_size 25
if value_array contains e.g 10;20;30;.....
I would expect debug_array to have groups of 6 similar values like
10;10;10;10;10;10;20;20;20;20;20;20;30......
The problem is that it is not picking up all values from the values array, any idea
why this isn't working or a good workaround.
What will work is if I define float val = value_array[bx*block_size+tx]; outside the for loop and keep this inside the loop debug_array[bx*block_size+tx+i] = val;
But I would like to avoid that as my kernels have between 5 and 10 device function inside the loop and it makes it just hard to read.
thanks in advance any advice will be appriciated
Markus
There seems to be an error in computing the index:
Let's assume bx = 0 and tx = 0
The first 6 elements in debug_array will be filled with data.
Next thread: tx = 1: Elements 1 to 7 will be filled with data (overwriting existing data).
Due to the threads working in parallel it is not determined which thread will be scheduled first and therefore which values will be written into the debug_array.
You should have written:
debug_array[6*(bx*block_size+tx)+i] = value_array[bx*block_size+tx];
If changing the code to move the value_array expression out of the loop and into a temp variable makes the code work - and that is the only code change you made - then this smells like a compiler bug.
Try changing your nvcc compiler options to reduce or disable optimizations and see if the value_array expression inside the loop changes behavior. Also, make sure you're using the latest CUDA tools.
Optimizing compilers will often attempt to move expressions that aren't dependent on the loop index variable out of the loop, exactly like your manual workaround. It's called "invariant code motion" and it makes loops faster by reducing the amount of code that executes in each iteration of the loop. If manually extracting the invariant code from the loop works, but letting the compiler figure it out on its own doesn't, that casts doubt on the compiler.

matlab function which is a function of an intergral

I need to write my own function which has the form f(x,y)=Integrate(g(x,y,z),z from 0 to inf). so the code I used was:
function y=f(x,y)
g=#(z)exp(-z.^2)./(z.^x).*(z.^2+y.^2).^(x/2);% as a function of x,y and z
y=quadgk(g,0,inf)
and if I call it for a single value like f(x0,y0), it works but if I try to calculate something like f([1:10],y0), then the error message says that there is something wrong with the times and dimension. In principle I can use for loops but then my code slows down and takes forever. Is there any help I can get from you guys? or references?
I'm trying to avoid the for loop since in matlab it's much faster to use matrix computation than to use for loop. I wonder if there is any trick that I can take advantage of this feature.
Thanks for any help in advance,
Lynn
Perhaps you can try to transpose the interval, creating row based values instead of column based f([1:10]',y0). Otherwise something in your function might be wrong, for example to get x^y to work with lists as input, you have to prefix with a dot x.^y. The same for mulitply and division I think..
If loop is no problem for you, you should do something like:
function y2=f(x,y)
y2=zeros(size(x));
for n=1:numel(x)
g=#(z)exp(-z.^2)./(z.^x(n)).*(z.^2+y.^2).^(x(n)/2);% as a function of x,y and z
y2(n)=quadgk(g,0,inf)
end
The problem here is that quadk itself uses vectors as argument for g. Then you have in g somethink like z.^x, which is the power of two vectors that is only defined if z and x have the same dimension. But this is not what you want.
I assume that you want to evaluate the function for all arguments in x and that the output vector has the same dimension as x. But this does not seem to be possible since even this simple example
g=#(x)[x;x.^2]
quad(g,0,1)
does not work:
Error using quad (line 79)
The integrand function must return an output vector of the same length as the
input vector.
A similar error shows when using quadgk. The documentation also says that this routine works only for scalar functions and this is not surprising since an adaptive quadrature rule would in general use different points for each function to evaluate the integral.
You have to use quadvinstead, which can integrate vector valued functions. But this gives wrong results since your function is integrated in the interval [0,\infty).