I commonly need to summarize a time series with irregular timing with a given aggregation function (i.e., sum, average, etc.). However, the current solution that I have seems inefficient and slow.
Take the aggregation function:
function aggArray = aggregate(array, groupIndex, collapseFn)
groups = unique(groupIndex, 'rows');
aggArray = nan(size(groups, 1), size(array, 2));
for iGr = 1:size(groups,1)
grIdx = all(groupIndex == repmat(groups(iGr,:), [size(groupIndex,1), 1]), 2);
for iSer = 1:size(array, 2)
aggArray(iGr,iSer) = collapseFn(array(grIdx,iSer));
end
end
end
Note that both array and groupIndex can be 2D. Every column in array is an independent series to be aggregated, but the columns of groupIndex should be taken together (as a row) to specify a period.
Then when we bring an irregular time series to it (note the second period is one base period longer), the timing results are poor:
a = rand(20006,10);
b = transpose([ones(1,5) 2*ones(1,6) sort(repmat((3:4001), [1 5]))]);
tic; aggregate(a, b, #sum); toc
Elapsed time is 1.370001 seconds.
Using the profiler, we can find out that the grpIdx line takes about 1/4 of the execution time (.28 s) and the iSer loop takes about 3/4 (1.17 s) of the total (1.48 s).
Compare this with the period-indifferent case:
tic; cumsum(a); toc
Elapsed time is 0.000930 seconds.
Is there a more efficient way to aggregate this data?
Timing Results
Taking each response and putting it in a separate function, here are the timing results I get with timeit with Matlab 2015b on Windows 7 with an Intel i7:
original | 1.32451
felix1 | 0.35446
felix2 | 0.16432
divakar1 | 0.41905
divakar2 | 0.30509
divakar3 | 0.16738
matthewGunn1 | 0.02678
matthewGunn2 | 0.01977
Clarification on groupIndex
An example of a 2D groupIndex would be where both the year number and week number are specified for a set of daily data covering 1980-2015:
a2 = rand(36*52*5, 10);
b2 = [sort(repmat(1980:2015, [1 52*5]))' repmat(1:52, [1 36*5])'];
Thus a "year-week" period are uniquely identified by a row of groupIndex. This is effectively handled through calling unique(groupIndex, 'rows') and taking the third output, so feel free to disregard this portion of the question.
Method #1
You can create the mask corresponding to grIdx across all
groups in one go with bsxfun(#eq,..). Now, for collapseFn as #sum, you can bring in matrix-multiplication and thus have a completely vectorized approach, like so -
M = squeeze(all(bsxfun(#eq,groupIndex,permute(groups,[3 2 1])),2))
aggArray = M.'*array
For collapseFn as #mean, you need to do a bit more work, as shown here -
M = squeeze(all(bsxfun(#eq,groupIndex,permute(groups,[3 2 1])),2))
aggArray = bsxfun(#rdivide,M,sum(M,1)).'*array
Method #2
In case you are working with a generic collapseFn, you can use the 2D mask M created with the previous method to index into the rows of array, thus changing the complexity from O(n^2) to O(n). Some quick tests suggest this to give appreciable speedup over the original loopy code. Here's the implementation -
n = size(groups,1);
M = squeeze(all(bsxfun(#eq,groupIndex,permute(groups,[3 2 1])),2));
out = zeros(n,size(array,2));
for iGr = 1:n
out(iGr,:) = collapseFn(array(M(:,iGr),:),1);
end
Please note that the 1 in collapseFn(array(M(:,iGr),:),1) denotes the dimension along which collapseFn would be applied, so that 1 is essential there.
Bonus
By its name groupIndex seems like would hold integer values, which could be abused to have a more efficient M creation by considering each row of groupIndex as an indexing tuple and thus converting each row of groupIndex into a scalar and finally get a 1D array version of groupIndex. This must be more efficient as the datasize would be 0(n) now. This M could be fed to all the approaches listed in this post. So, we would have M like so -
dims = max(groupIndex,[],1);
agg_dims = cumprod([1 dims(end:-1:2)]);
[~,~,idx] = unique(groupIndex*agg_dims(end:-1:1).'); %//'
m = size(groupIndex,1);
M = false(m,max(idx));
M((idx-1)*m + [1:m]') = 1;
Mex Function 1
HAMMER TIME: Mex function to crush it:
The base case test with original code from the question took 1.334139 seconds on my machine. IMHO, the 2nd fastest answer from #Divakar is:
groups2 = unique(groupIndex);
aggArray2 = squeeze(all(bsxfun(#eq,groupIndex,permute(groups,[3 2 1])),2)).'*array;
Elapsed time is 0.589330 seconds.
Then my MEX function:
[groups3, aggArray3] = mg_aggregate(array, groupIndex, #(x) sum(x, 1));
Elapsed time is 0.079725 seconds.
Testing that we get the same answer: norm(groups2-groups3) returns 0 and norm(aggArray2 - aggArray3) returns 2.3959e-15. Results also match original code.
Code to generate the test conditions:
array = rand(20006,10);
groupIndex = transpose([ones(1,5) 2*ones(1,6) sort(repmat((3:4001), [1 5]))]);
For pure speed, go mex. If the thought of compiling c++ code / complexity is too much of a pain, go with Divakar's answer. Another disclaimer: I haven't subject my function to robust testing.
Mex Approach 2
Somewhat surprising to me, this code appears even faster than the full Mex version in some cases (eg. in this test took about .05 seconds). It uses a mex function mg_getRowsWithKey to figure out the indices of groups. I think it may be because my array copying in the full mex function isn't as fast as it could be and/or overhead from calling 'feval'. It's basically the same algorithmic complexity as the other version.
[unique_groups, map] = mg_getRowsWithKey(groupIndex);
results = zeros(length(unique_groups), size(array,2));
for iGr = 1:length(unique_groups)
array_subset = array(map{iGr},:);
%// do your collapse function on array_subset. eg.
results(iGr,:) = sum(array_subset, 1);
end
When you do array(groups(1)==groupIndex,:) to pull out array entries associated with the full group, you're searching through the ENTIRE length of groupIndex. If you have millions of row entries, this will totally suck. array(map{1},:) is far more efficient.
There's still unnecessary copying of memory and other overhead associated with calling 'feval' on the collapse function. If you implement the aggregator function efficiently in c++ in such a way to avoid copying of memory, probably another 2x speedup can be achieved.
A little late to the party, but a single loop using accumarray makes a huge difference:
function aggArray = aggregate_gnovice(array, groupIndex, collapseFn)
[groups, ~, index] = unique(groupIndex, 'rows');
numCols = size(array, 2);
aggArray = nan(numel(groups), numCols);
for col = 1:numCols
aggArray(:, col) = accumarray(index, array(:, col), [], collapseFn);
end
end
Timing this using timeit in MATLAB R2016b for the sample data in the question gives the following:
original | 1.127141
gnovice | 0.002205
Over a 500x speedup!
Doing away with the inner loop, i.e.
function aggArray = aggregate(array, groupIndex, collapseFn)
groups = unique(groupIndex, 'rows');
aggArray = nan(size(groups, 1), size(array, 2));
for iGr = 1:size(groups,1)
grIdx = all(groupIndex == repmat(groups(iGr,:), [size(groupIndex,1), 1]), 2);
aggArray(iGr,:) = collapseFn(array(grIdx,:));
end
and calling the collapse function with a dimension parameter
res=aggregate(a, b, #(x)sum(x,1));
gives some speedup (3x on my machine) already and avoids the errors e.g. sum or mean produce, when they encounter a single row of data without a dimension parameter and then collapse across columns rather than labels.
If you had just one group label vector, i.e. same group labels for all columns of data, you could speed further up:
function aggArray = aggregate(array, groupIndex, collapseFn)
ng=max(groupIndex);
aggArray = nan(ng, size(array, 2));
for iGr = 1:ng
aggArray(iGr,:) = collapseFn(array(groupIndex==iGr,:));
end
The latter functions gives identical results for your example, with a 6x speedup, but cannot handle different group labels per data column.
Assuming a 2D test case for the group index (provided here as well with 10 different columns for groupIndex:
a = rand(20006,10);
B=[]; % make random length periods for each of the 10 signals
for i=1:size(a,2)
n0=randi(10);
b=transpose([ones(1,n0) 2*ones(1,11-n0) sort(repmat((3:4001), [1 5]))]);
B=[B b];
end
tic; erg0=aggregate(a, B, #sum); toc % original method
tic; erg1=aggregate2(a, B, #(x)sum(x,1)); toc %just remove the inner loop
tic; erg2=aggregate3(a, B, #(x)sum(x,1)); toc %use function below
Elapsed time is 2.646297 seconds.
Elapsed time is 1.214365 seconds.
Elapsed time is 0.039678 seconds (!!!!).
function aggArray = aggregate3(array, groupIndex, collapseFn)
[groups,ix1,jx] = unique(groupIndex, 'rows','first');
[groups,ix2,jx] = unique(groupIndex, 'rows','last');
ng=size(groups,1);
aggArray = nan(ng, size(array, 2));
for iGr = 1:ng
aggArray(iGr,:) = collapseFn(array(ix1(iGr):ix2(iGr),:));
end
I think this is as fast as it gets without using MEX. Thanks to the suggestion of Matthew Gunn!
Profiling shows that 'unique' is really cheap here and getting out just the first and last index of the repeating rows in groupIndex speeds things up considerably. I get 88x speedup with this iteration of the aggregation.
Well I have a solution that is almost as quick as the mex but only using matlab.
The logic is the same as most of the above, creating a dummy 2D matrix but instead of using #eq I initialize a logical array from the start.
Elapsed time for mine is 0.172975 seconds.
Elapsed time for Divakar 0.289122 seconds.
function aggArray = aggregate(array, group, collapseFn)
[m,~] = size(array);
n = max(group);
D = false(m,n);
row = (1:m)';
idx = m*(group(:) - 1) + row;
D(idx) = true;
out = zeros(m,size(array,2));
for ii = 1:n
out(ii,:) = collapseFn(array(D(:,ii),:),1);
end
end
I store some functions in cell, e.g. f = {#sin, #cos, #(x)x+4}.
Is it possible to call all those functions at the same time (with the same input). I mean something more efficient than using a loop.
As constructed, the *fun family of functions exists for this purpose (e.g., cellfun is the pertinent one here). They are other questions on the use and performance of these functions.
However, if you construct f as a function that constructs a cell array as
f = #(x) {sin(x), cos(x), x+4};
then you can call the function more naturally: f([1,2,3]) for example.
This method also avoids the need for the ('UniformOutput',false) option pair needed by cellfun for non-scalar argument.
You can also use regular double arrays, but then you need to be wary of input shape for concatenation purposes: #(x) [sin(x), cos(x), x+4] vs. #(x) [sin(x); cos(x); x+4].
I'm just posting these benchmarking results here, just to illustrate that loops not necessarily are slower than other approaches:
f = {#sin, #cos, #(x)x+4};
x = 1:100;
tic
for ii = 1:1000
for jj = 1:numel(f)
res{jj} = f{jj}(x);
end
end
toc
tic
for ii = 1:1000
res = cellfun(#(arg) arg(x),functions,'uni',0);
end
toc
Elapsed time is 0.042201 seconds.
Elapsed time is 0.179229 seconds.
Troy's answer is almost twice as fast as the loop approach:
tic
for ii = 1:1000
res = f((1:100).');
end
toc
Elapsed time is 0.025378 seconds.
This might do the trick
functions = {#(arg) sin(arg),#(arg) sqrt(arg)}
x = 5;
cellfun(#(arg) arg(x),functions)
hope this helps.
Adrien.
yesterday I implemented my first bootstrap in MATLab. (and yes, I know, for loops are evil.):
%data is an mxn matrix where the data should be sampled per column but there
can be a NaNs Elements
%from the array (a column of data) n values are sampled nReps times
function result = bootstrap_std(data, n, nReps,quantil)
result = zeros(1,size(data,2));
for i=1:size(data,2)
bootstrap_data = zeros(n,nReps);
values = find(~isnan(data(:,i)));
if isempty(values)
bootstrap_data(:,:) = NaN;
else
for k=1:nReps
bootstrap_data(:,k) = datasample(data(values,i),n);
end
end
stat = zeros(1,nReps);
for k=1:nReps
stat(k) = nanstd(bootstrap_data(:,k));
end
sort(stat);
result(i) = quantile(stat,quantil);
end
end
As one can see, this version works columnwise. The algorithm does what it should but is really slow when the data size increaes. My question is now: Is it possible to implement this logic without using for loops? My problem is here that I could not find a version of datasample which does the sampling columnwise. Or is there a better function to use?
I am happy for any hint or idea how I can speed up this implementation.
Thanks and best regards!
stephan
The bottlenecks in your implementation are
The function spends a lot of time inside nanstd which is unnecessary since you exclude NaN values from your sample anyway.
There are a lot of functions that operate column-wise, but you spend time looping over the columns and calling them many times.
You make many calls to datasample which is a relatively slow function. It's much faster to create a random vector of indices using randi and use that instead.
Here's how I would write the function (actually I probably wouldn't put in this many comments, and I wouldn't use so many temp variables, but I'm doing it now so you can see what all the steps of the computation are).
function result = bootstrap_std_new(data, n, nRep, quantil)
result = zeros(1, size(data,2));
for i = 1:size(data,2)
isbad = isnan(data(:,i)); %// Vector of NaN values
if all(isbad)
result(i) = NaN;
else
data0 = data(~isbad, i); %// Temp copy of this column for indexing
index = randi(size(data0,1), n, nRep); %// Create the indexing vector
bootstrapdata = data0(index); %// Sample the data
stdevs = std(bootstrapdata); %// Stdev of sampled data
result(i) = quantile(stdevs, quantil); %// Find the correct quantile
end
end
end
Here are some timings
>> data = randn(100,10);
>> data(randi(1000, 50, 1)) = NaN;
>> tic, bootstrap_std(data, 50, 1000, 0.5); toc
Elapsed time is 1.359529 seconds.
>> tic, bootstrap_std_new(data, 50, 1000, 0.5); toc
Elapsed time is 0.038558 seconds.
So this gives you about a 35x speedup.
Your main issue seems to be that you may have varying numbers/positions of NaN in each column, so can't work on the full matrix unless you're okay with also sampling NaNs. However, some of the inner loops could be simplified.
for k=1:nReps
bootstrap_data(:,k) = datasample(data(values,i),n);
end
Since you're sampling with replacement, you should be able to just do:
bootstrap_data = datasample(data(values,i), n*nReps);
bootstrap_data = reshape(bootstrap_data, [n nReps]);
Also nanstd can work on a full matrix so no need to loop:
stat = nanstd(bootstrap_data); % or nanstd(x,0,2) to change dimension
It would also be worth just looking over your code with profile to see where the bottlenecks are.
I have the problem when I compute in a matrix. This problem is about the speed of computation.
I have a matrix of binary image (f), I find conected component by bwlabel in matlab. [L num]=bwlabel(f);
after that base on some property I found a vector p that include some value of L that I need to remove. this is my code and explanation
function [f,L] = clear_nontext(f,L,nontext)
% p is a vector include a lot of value we need to remove
p=find(nontext(:)~=0);
% example p= [1 2 9 10 100...] that mean we need to find in L matrix where get the value =1,2,9,10,100..] and remove it
[a b]=size(L);
g=zeros(a,b);
for u=1:length(p)
for i=1:a
for j=1:b
if L(i,j)==p(u)
g(i,j)=1;
%L(i,j)=500000;
f(i,j)=0;
end
end
end
end
end
When I use this way, program run but it is so slow, because with one value of p we need to check all value in matrix f (or L) again. So I need another way to run it faster. Could you help me?
Thank you so much
Generally, MATLAB performs matrix operations (or index operations) faster then loops.
You can try the following:
g(ismember(L,p)) = 1;
f(ismember(L,p)) = 1;
EDIT:
I was curious so I ran a little test:
L = round(20*randn(10000,10000));
f = L;
p = 1:5;
[a b]=size(L);
g=zeros(a,b);
tic;
for u=1:length(p)
for i=1:a
for j=1:b
if L(i,j)==p(u)
g(i,j)=1;
f(i,j)=0;
end
end
end
end
toc
for which I got:
Elapsed time is 38.960842 seconds.
When I tried the following:
tic;
g(ismember(L,p)) = 1;
f(ismember(L,p)) = 0;
toc
I got
Elapsed time is 5.735137 seconds.