How to build a cell-array or matrix of different dimension - matlab

I'm using the findpeaks method in Matlab to find peaks. I have a matrix(Peak) of 260x601 where its 260 different trials over 601 time points. I have a separate vector for the actual time (called TimeVec).
I'm using a for loop to loop over the trials.
for i = 1:size(Peak,1)
[pks(i),locs(i)]=findpeaks(Peak(i,:),timeVec,'MinPeakHeight',1);
end
The problem is that each trial could have a different number of peaks therefore it's trying to combine a different number of columns to each iteration. How can I get around this?

This is a short and not fully efficient method:
fp = #(k) findpeaks(Peak(k,:),timeVec,'MinPeakHeight',1);
[pks,locs] = arrayfun(fp,1:size(Peak,1),'UniformOutput',false);
it will be a bit faster with a for loop, but it worth changing this only if you have more data:
[pks,locs] = deal(cell(size(Peak,1),1));
for k = 1:size(Peak,1)
[pks{k},locs{k}] = findpeaks(Peak(k,:),timeVec,'MinPeakHeight',1);
end
for further manipulations on that, use #excaza advice and read the cell array docs.

Related

Improve code / remove for-loop when using accumarray MATLAB

I have the following piece of code that is quite slow to compute the percentiles from a data set ("DATA"), because the input matrices are large ("Data" is approx. 500.000 long with 10080 unique values assigned from "Indices").
Is there a possibility/suggestions to make this piece of code more efficient? For example, could I somehow omit the for-loop?
k = 1;
for i = 0:0.5:100; % in 0.5 fractile-steps
FRACTILE(:,k) = accumarray(Indices,Data,[], #(x) prctile(x,i));
k = k+1;
end
Calling prctile again and again with the same data is causing your performance issues. Call it once for each data set:
FRACTILE=cell2mat(accumarray(Indices,Data,[], #(x) {prctile(x,[0:0.5:100])}));
Letting prctile evaluate your 201 percentiles in one call costs roughly as much computation time as two iterations of your original code. First because prctile is faster this way and secondly because accumarray is called only once now.

Matlab vectorization of multiple embedded for loops

Suppose you have 5 vectors: v_1, v_2, v_3, v_4 and v_5. These vectors each contain a range of values from a minimum to a maximum. So for example:
v_1 = minimum_value:step:maximum_value;
Each of these vectors uses the same step size but has a different minimum and maximum value. Thus they are each of a different length.
A function F(v_1, v_2, v_3, v_4, v_5) is dependant on these vectors and can use any combination of the elements within them. (Apologies for the poor explanation). I am trying to find the maximum value of F and record the values which resulted in it. My current approach has been to use multiple embedded for loops as shown to work out the function for every combination of the vectors elements:
% Set the temp value to a small value
temp = 0;
% For every combination of the five vectors use the equation. If the result
% is greater than the one calculated previously, store it along with the values
% (postitions) of elements within the vectors
for a=1:length(v_1)
for b=1:length(v_2)
for c=1:length(v_3)
for d=1:length(v_4)
for e=1:length(v_5)
% The function is a combination of trigonometrics, summations,
% multiplications etc..
Result = F(v_1(a), v_2(b), v_3(c), v_4(d), v_5(e))
% If the value of Result is greater that the previous value,
% store it and record the values of 'a','b','c','d' and 'e'
if Result > temp;
temp = Result;
f = a;
g = b;
h = c;
i = d;
j = e;
end
end
end
end
end
end
This gets incredibly slow, for small step sizes. If there are around 100 elements in each vector the number of combinations is around 100*100*100*100*100. This is a problem as I need small step values to get a suitably converged answer.
I was wondering if it was possible to speed this up using Vectorization, or any other method. I was also looking at generating the combinations prior to the calculation but this seemed even slower than my current method. I haven't used Matlab for a long time but just looking at the number of embedded for loops makes me think that this can definitely be sped up. Thank you for the suggestions.
No matter how you generate your parameter combination, you will end up calling your function F 100^5 times. The easiest solution would be to use parfor instead in order to exploit multi-core calculation. If you do that, you should store the calculation results and find the maximum after the loop, because your current approach would not be thread-safe.
Having said that and not knowing anything about your actual problem, I would advise you to implement a more structured approach, like first finding a coarse solution with a bigger step size and narrowing it down successivley by reducing the min/max values of your parameter intervals. What you have currently is the absolute brute-force method which will never be very effective.

Find a Binary Data Sequence in a Signal

Here's my goal:
I'm trying to find a way to search through a data signal and find (index) locations where a known, repeating binary data sequence is located. Then, because the spreading code and demodulation is known, pull out the corresponding chip of data and read it. Currently, I believe xcorr will do the trick.
Here's my problem:
I can't seem to interpret my result from xcorr or xcorr2 to give me what I'm looking for. I'm either having a problem cross-referencing from the vector location of my xcorr function to my time vector, or a problem properly identifying my data sequence with xcorr, or both. Other possibilities may exist.
Where I am at/What I have:
I have created a random BPSK signal that consists of the data sequence of interest and garbage data over a repeating period. I have tried processing it using xcorr, which is where I am stuck.
Here's my code:
%% Clear Variables
clc;
clear all, close all;
%% Create random data
nbits = 2^10;
ngarbage = 3*nbits;
data = randi([0,1],1,nbits);
garbage = randi([0,1],1,ngarbage);
stream = horzcat(data,garbage);
%% Convert from Unipolar to Bipolar Encoding
stream_b = 2*stream - 1;
%% Define Parameters
%%% Variable Parameters
nsamples = 20*nbits;
nseq = 5 %# Iterate stream nseq times
T = 10; %# Number of periods
Ts = 1; %# Symbol Duration
Es = Ts/2; %# Energy per Symbol
fc = 1e9; %# Carrier frequency
%%% Dependent Parameters
A = sqrt(2*Es/Ts); %# Amplitude of Carrier
omega = 2*pi*fc %# Frequency in radians
t = linspace(0,T,nsamples) %# Discrete time from 0 to T periods with nsamples samples
nspb = nsamples/length(stream) %# Number of samples per bit
%% Creating the BPSK Modulation
%# First we have to stretch the stream to fit the time vector. We can quickly do this using _
%# simple matrix manipulation.
% Replicate each bit nspb/nseq times
repStream_b = repmat(stream_b',1,nspb/nseq);
% Tranpose and replicate nseq times to be able to fill to t
modSig_proto = repmat(repStream_b',1,nseq);
% Tranpose column by column, then rearrange into a row vector
modSig = modSig_proto(:)';
%% The Carrier Wave
carrier = A*cos(omega*t);
%% Modulated Signal
sig = modSig.*carrier;
Using XCORR
I use xcorr2() to eliminate the zero padding effect of xcorr on unequal vectors. See comments below for clarification.
corr = abs(xcorr2(data,sig); %# pull the absolute correlation between data and sig
[val,ind] = sort(corr(:),'descend') %# sort the correlation data and assign values and indices
ind_max = ind(1:nseq); %# pull the nseq highest valued indices and send to ind_max
Now, I think this should pull the five highest correlations between data and sig. These should correspond to the end bit of data in the stream for every iteration of stream, because I would think that is where the data would most strongly cross-correlate with sig, but they do not. Sometimes the maxes are not even one stream length apart. So I'm confused here.
Question
In a three part question:
Am I missing a certain step? How do I use xcorr in this case to find where data and sig are most strongly correlated?
Is my entire method wrong? Should I not be looking for the max correlations?
Or should I be attacking this problem from another angle, id est, not use xcorr and maybe use filter or another function?
Your overall method is great and makes a lot of sense. The problem you're having is that you're getting some actual correlation with your garbage data. I noticed that you shifted all of your sream to be zero-centered, but didn't do the same to your data. If you zero-center the data, your correlation peaks will be better defined (at least that worked when I tried it).
data = 2*data -1;
Also, I don't recommend using a simple sort to find your peaks. If you have a wide peak, which is especially possible with a noisy signal, you could have two high points right next to each other. Find a single maximum, and then zero that point and a few neighbors. Then just repeat however many times you like. Alternatively, if you know how long your epoch is, only do a correlation with one epoch's worth of data, and iterate through the signal as it arrives.
With #David K 's and #Patrick Mineault's help I manage to track down where I went wrong. First #Patrick Mineault suggested I flip the signals. The best way to see what you would expect from the result is to slide the small vector along the larger, searched vector. So
corr = xcorr2(sig,data);
Then I like to chop off the end there because it's just extra. I did this with a trim function I made that simply takes the signal you're sliding and trims it's irrelevant pieces off the end of the xcorr result.
trim = #(x,s2) x(1:end - (length(s2) - 1));
trim(corr,data);
Then, as #David K suggests, you need to have the data stream you're looking for encoded the same as your searched signal. So in this case
data = 2*data-1;
Second, if you just have your data at it's original bit length, and not at it's stretched, iterated length, it can be found in the signal but it will be VERY noisy. To reduce the noise, simply stretch the data to match it's stretched length in the iterated signal. So
rdata = repmat(data',1,nspb/nseq);
rdata = repmat(rdata',1,nseq);
data = rdata(:)';
Now finally, we should have crystal clear correlations for this case. And to pull out the maxes that should correspond to those correlations I wrote
[sortedValues sortIndex] = sort(corr(:),'descend');
c = 0 ;
for r = 1 : length(sortedValues)
if sortedValues(r,:) == max(corr)
c = c + 1;
maxIndex(1,c) = sortIndex(r,:);
else break % If you don't do this, you get loop lock
end
end
Now c should end up being nseq for this case and you should have 5 index times where the corrs should be! You can easily pull out the bits with another loop and c or length(maxIndex). I've also made this into a more "real world" toy script, where there is a data stream, doppler, fading, and it's over a time vector in seconds instead of samples.
Thanks for the help!
Try flipping the signal, i.e.:
corr = abs(xcorr2(data,sig(end:-1:1));
Is that any better?

Addressing multiple ranges via indices in a vector

To begin, this problem is easily solvable with a for-loop. However, I'm trying to force/teach myself to think vector-wise to take advantage of what Matlab does best.
Simplified, here is the problem explanation:
I have a vector with data in it.
I have a 2xN array of start/stop indices that represent ranges of interesting data in the vector.
I want to perform calculations on each of those ranges, resulting in a number (N results, corresponding to each start/stop range.)
In code, here's a pseudoexample of what I'd like to have at the end:
A = 1:10000;
startIndicies = [5 100 1000];
stopIndicies = [10 200 5000];
...
calculatedResults = [func(A(5:10)) func(A(100:200)) func(A(1000:5000))]
The length of A, and of the start/stop index array is variable.
Like I said, I can easily solve this with a for loop. However since could be used with a large data set, I'd like to know if there's a good solution without a for loop.
Here is one possible solution, although, I won't call it a fully vectorized solution, rather a one liner one.
out = cellfun(#(i,j) fun(A(i:j)), num2cell(startIndicies), num2cell(stopIndicies) );
or, if you plan to have homogeneous outputs,
out = arrayfun(#(i,j) fun(A(i:j)), startIndicies, stopIndicies);

Parallelize or vectorize all-against-all operation on a large number of matrices?

I have approximately 5,000 matrices with the same number of rows and varying numbers of columns (20 x ~200). Each of these matrices must be compared against every other in a dynamic programming algorithm.
In this question, I asked how to perform the comparison quickly and was given an excellent answer involving a 2D convolution. Serially, iteratively applying that method, like so
list = who('data_matrix_prefix*')
H = cell(numel(list),numel(list));
for i=1:numel(list)
for j=1:numel(list)
if i ~= j
eval([ 'H{i,j} = compare(' char(list(i)) ',' char(list(j)) ');']);
end
end
end
is fast for small subsets of the data (e.g. for 9 matrices, 9*9 - 9 = 72 calls are made in ~1 s, 870 calls in ~2.5 s).
However, operating on all the data requires almost 25 million calls.
I have also tried using deal() to make a cell array composed entirely of the next element in data, so I could use cellfun() in a single loop:
# who(), load() and struct2cell() calls place k data matrices in a 1D cell array called data.
nextData = cell(k,1);
for i=1:k
[nextData{:}] = deal(data{i});
H{:,i} = cellfun(#compare,data,nextData,'UniformOutput',false);
end
Unfortunately, this is not really any faster, because all the time is in compare(). Both of these code examples seem ill-suited for parallelization. I'm having trouble figuring out how to make my variables sliced.
compare() is totally vectorized; it uses matrix multiplication and conv2() exclusively (I am under the impression that all of these operations, including the cellfun(), should be multithreaded in MATLAB?).
Does anyone see a (explicitly) parallelized solution or better vectorization of the problem?
Note
I realize both my examples are inefficient - the first would be twice as fast if it calculated a triangular cell array, and the second is still calculating the self comparisons, as well. But the time savings for a good parallelization are more like a factor of 16 (or 72 if I install MATLAB on everyone's machines).
Aside
There is also a memory issue. I used a couple of evals to append each column of H into a file, with names like H1, H2, etc. and then clear Hi. Unfortunately, the saves are very slow...
Does
compare(a,b) == compare(b,a)
and
compare(a,a) == 1
If so, change your loop
for i=1:numel(list)
for j=1:numel(list)
...
end
end
to
for i=1:numel(list)
for j= i+1 : numel(list)
...
end
end
and deal with the symmetry and identity case. This will cut your calculation time by half.
The second example can be easily sliced for use with the Parallel Processing Toolbox. This toolbox distributes iterations of your code among up to 8 different local processors. If you want to run the code on a cluster, you also need the Distributed Computing Toolbox.
%# who(), load() and struct2cell() calls place k data matrices in a 1D cell array called data.
parfor i=1:k-1 %# this will run the loop in parallel with the parallel processing toolbox
%# only make the necessary comparisons
H{i+1:k,i} = cellfun(#compare,data(i+1:k),repmat(data(i),k-i,1),'UniformOutput',false);
%# if the above doesn't work, try this
hSlice = cell(k,1);
hSlice{i+1:k} = cellfun(#compare,data(i+1:k),repmat(data(i),k-i,1),'UniformOutput',false);
H{:,i} = hSlice;
end
If I understand correctly you have to perform 5000^2 matrix comparisons ? Rather than try to parallelise the compare function, perhaps you should think of your problem being composed of 5000^2 tasks ? The Matlab Parallel Compute Toolbox supports task-based parallelism. Unfortunately my experience with PCT is with parallelisation of large linear algebra type problems so I can't really tell you much more than that. The documentation will undoubtedly help you more.