Efficient way to delete multiple elements from a vector in matlab - matlab

I have looked around for an answer to this but could not see anything relevant.
I am timing some (Matlab) code and there is one part which takes up a large amount of time. I have a vector, V, of integers (that may contain repeats) and I have a much smaller vector, v, contain indices of elements that I wish to delete. I am currently implementing this as:
V(v) = [];
'V' is something that I am selecting indices from at random and without replacement. 'v' must not contain duplicates.
Any suggestions?

Related

MATLAB spending an incredible amount of time writing a relatively small matrix

I have a small MATLAB script (included below) for handling data read from a CSV file with two columns and hundreds of thousands of rows. Each entry is a natural number, with zeros only occurring in the second column. This code is taking a truly incredible amount of time (hours) to run what should be achievable in at most some seconds. The profiler identifies that approximately 100% of the run time is spent writing a matrix of zeros, whose size varies depending on input, but in all usage is smaller than 1000x1000.
The code is as follows
function [data] = DataHandler(D)
n = size(D,1);
s = max(D,1);
data = zeros(s,s);
for i = 1:n
data(D(i,1),D(i,2)+1) = data(D(i,1),D(i,2)+1) + 1;
end
It's the data = zeros(s,s); line that takes around 100% of the runtime. I can make the code run quickly by just changing out the s's in this line for 1000, which is a sufficient upper bound to ensure it won't run into errors for any of the data I'm looking at.
Obviously there're better ways to do this, but being that I just bashed the code together to quickly format some data I wasn't too concerned. As I said, I fixed it by just replacing s with 1000 for my purposes, but I'm perplexed as to why writing that matrix would bog MATLAB down for several hours. New code runs instantaneously.
I'd be very interested if anyone has seen this kind of behaviour before, or knows why this would be happening. Its a little disconcerting, and it would be good to be able to be confident that I can initialize matrices freely without killing MATLAB.
Your call to zeros is incorrect. Looking at your code, D looks like a D x 2 array. However, your call of s = max(D,1) would actually generate another D x 2 array. By consulting the documentation for max, this is what happens when you call max in the way you used:
C = max(A,B) returns an array the same size as A and B with the largest elements taken from A or B. Either the dimensions of A and B are the same, or one can be a scalar.
Therefore, because you used max(D,1), you are essentially comparing every value in D with the value of 1, so what you're actually getting is just a copy of D in the end. Using this as input into zeros has rather undefined behaviour. What will actually happen is that for each row of s, it will allocate a temporary zeros matrix of that size and toss the temporary result. Only the dimensions of the last row of s is what is recorded. Because you have a very large matrix D, this is probably why the profiler hangs here at 100% utilization. Therefore, each parameter to zeros must be scalar, yet your call to produce s would produce a matrix.
What I believe you intended should have been:
s = max(D(:));
This finds the overall maximum of the matrix D by unrolling D into a single vector and finding the overall maximum. If you do this, your code should run faster.
As a side note, this post may interest you:
Faster way to initialize arrays via empty matrix multiplication? (Matlab)
It was shown in this post that doing zeros(n,n) is in fact slow and there are several neat tricks to initializing an array of zeros. One way is to accomplish this by empty matrix multiplication:
data = zeros(n,0)*zeros(0,n);
One of my personal favourites is that if you assume that data was not declared / initialized, you can do:
data(n,n) = 0;
If I can also comment, that for loop is quite inefficient. What you are doing is calculating a 2D histogram / accumulation of data. You can replace that for loop with a more efficient accumarray call. This also avoids allocating an array of zeros and accumarray will do that under the hood for you.
As such, your code would basically become this:
function [data] = DataHandler(D)
data = accumarray([D(:,1) D(:,2)+1], 1);
accumarray in this case will take all pairs of row and column coordinates, stored in D(i,1) and D(i,2) + 1 for i = 1, 2, ..., size(D,1) and place all that match the same row and column coordinates into a separate 2D bin, we then add up all of the occurrences and the output at this 2D bin gives you the total tally of how many values at this 2D bin which corresponds to the row and column coordinate of interest mapped to this location.

Passing values to a sparse matrix in MATLAB

Might sound too simple to you but I need some help in regrad to do all folowings in one shot instead of defining redundant variables i.e. tmp_x, tmp_y:
X= sparse(numel(find(G==0)),2);
[tmp_x, temp_y] = ind2sub(size(G), find(G == 0));
X(:)=[tmp_x, tmp_y];
(More info: G is a sparse matrix)
I tried:
X(:)=ind2sub(size(G), find(G == 0));
but that threw an error.
How can I achieve this without defining tmp_x, tmp_y?
A couple of comments with your code:
numel(find(G == 0)) is probably one of the worst ways to determine how many entries that are zero in your matrix. I would personally do numel(G) - nnz(G). numel(G) determines how many elements are in G and nnz(G) determines how many non-zero values are in G. Subtracting these both would give you the total number of elements that are zero.
What you are doing is first declaring X to be sparse... then when you're doing the final assignment in the last line to X, it reconverts the matrix to double. As such, the first statement is totally redundant.
If I understand what you are doing, you want to find the row and column locations of what is zero in G and place these into a N x 2 matrix. Currently with what MATLAB has available, this cannot be done without intermediate variables. The functions that you'd typically use (find, ind2sub, etc.) require intermediate variables if you want to capture the row and column locations. Using one output variable will give you the column locations only.
You don't have a choice but to use intermediate variables. However, if you want to make this more efficient, you don't even need to use ind2sub. Just use find directly:
[I,J] = find(~G);
X = [I,J];

vector of variable length vectors in MATLAB

I want to sum up several vectors of different size in an array. Each time one of the vectors drops out of my program, I want to append it to my array. Like this:
array = [array, vector];
In the end I want to let this array be the output of a function. But it gives me wrong results. Is this possible with MATLAB?
Thanks and kind regards,
Damian
Okay, given that we're dealing with column vectors of different size, you can't put them all in a numerical array, since a numerical array has to be rectangular. If you really wanted to put them in the numerical array, then the column length of the array will need to be the length of the longest vector, and you'll have to pad out the shorter vectors with NaNs.
Given this, a better solution would be, as chaohuang hinted at in the comments, to use a cell array, and store one vector in each cell. The problem is that you don't know beforehand how many vectors there will be. The usual approach that I'm aware of for this problem is as follows (but if someone has a better idea, I'm keen to learn!):
UpperBound = SomeLargeNumber;
Array = cell(1, UpperBound);
Counter = 0;
while SomeCondition
Counter = Counter + 1;
if Counter > UpperBound
error('You did not choose a large enough upper bound!');
end
%#Create your vector here
Array{1, Counter} = YourVectorHere;
end
Array = Array(1, 1:Counter);
In other words, choose some upper bound beforehand that you are sure you won't go above in the loop, and then cut your cell array down to size once the loop is finished. Also, I've put in an error trap in case you're choice of upper bound turns out to be too small!
Oh, by the way, I just noted in your question the words "sum up several vectors". Was this a figure of speech or did you actually want to perform a sum operation somewhere?

MATLAB: apply a function to every n items in a vector

This related question How can I apply a function to every row/column of a matrix in MATLAB? seems to indicate one way to do this is using num2cell, which I kind of want to stay away from.
Here's what I want to do. I've got an index list for a triangle mesh, the indices index the vertex list.
I want to run func(a,b,c) on the first 3 indices, then the next three indices, and so on.
So I could reshape(idxs,3,[]) so now i've got my data into triplets as column vectors. But arrayfun does not do what I want it to do.
Looking for something like a column-map operator.
First, get your func properly vectorized, if necessary, such that the arguments can be lists of equal length:
vec_func = #(a,b,c)(arrayfun(#func,a,b,c))
Then, you can directly access every third element of idxs:
vec_func( idxs(1:3:end), idxs(2:3:end), idxs(3:3:end) )

Compact MATLAB matrix indexing notation

I've got an n-by-k sized matrix, containing k numbers per row. I want to use these k numbers as indexes into a k-dimensional matrix. Is there any compact way of doing so in MATLAB or must I use a for loop?
This is what I want to do (in MATLAB pseudo code), but in a more MATLAB-ish way:
for row=1:1:n
finalTable(row) = kDimensionalMatrix(indexmatrix(row, 1),...
indexmatrix(row, 2),...,indexmatrix(row, k))
end
If you want to avoid having to use a for loop, this is probably the cleanest way to do it:
indexCell = num2cell(indexmatrix, 1);
linearIndexMatrix = sub2ind(size(kDimensionalMatrix), indexCell{:});
finalTable = kDimensionalMatrix(linearIndexMatrix);
The first line puts each column of indexmatrix into separate cells of a cell array using num2cell. This allows us to pass all k columns as a comma-separated list into sub2ind, a function that converts subscripted indices (row, column, etc.) into linear indices (each matrix element is numbered from 1 to N, N being the total number of elements in the matrix). The last line uses these linear indices to replace your for loop. A good discussion about matrix indexing (subscript, linear, and logical) can be found here.
Some more food for thought...
The tendency to shy away from for loops in favor of vectorized solutions is something many MATLAB users (myself included) have become accustomed to. However, newer versions of MATLAB handle looping much more efficiently. As discussed in this answer to another SO question, using for loops can sometimes result in faster-running code than you would get with a vectorized solution.
I'm certainly NOT saying you shouldn't try to vectorize your code anymore, only that every problem is unique. Vectorizing will often be more efficient, but not always. For your problem, the execution speed of for loops versus vectorized code will probably depend on how big the values n and k are.
To treat the elements of the vector indexmatrix(row, :) as separate subscripts, you need the elements as a cell array. So, you could do something like this
subsCell = num2cell( indexmatrix( row, : ) );
finalTable( row ) = kDimensionalMatrix( subsCell{:} );
To expand subsCell as a comma-separated-list, unfortunately you do need the two separate lines. However, this code is independent of k.
Convert your sub-indices into linear indices in a hacky way
ksz = size(kDimensionalMatrix);
cksz = cumprod([ 1 ksz(1:end-1)] );
lidx = ( indexmatrix - 1 ) * cksz' + 1; #'
% lindx is now (n)x1 linear indices into kDimensionalMatrix, one index per row of indexmatrix
% access all n values:
selectedValues = kDimensionalMatrix( lindx );
Cheers!