I am facing an issue with counting number of occurrences by date, suppose I have an excel file where the data is as follows:
1/1/2001 23
1/1/2001 29
1/1/2001 24
3/1/2001 22
3/1/2001 23
My desired output is:
1/1/2001 3
2/1/2001 0
3/1/2001 2
Though 2/1/2001 does't appear in the input, I want that included in the output with 0 counts. This is my current code:
[Value, Time] = xlsread('F:\1km\fire\2001- 02\2001_02.xlsx','Sheet1','A2:D159','',#convertSpreadsheetExcelDates);
tm=datenum(Time);
val=Value(:,4);
data=[tm val];
% a=(datestr(tm));
T1=datetime('9/23/2001');
T2=datetime('6/23/2002');
T = T1:T2;
tm_all=datenum(T);
[~, idx] = ismember(tm_all,data(:,1));
% idx=idx';
out = tm_all(idx);
The ismember function does not seem to work, because the length of tm_all is 274 and the size of data is 158x2
I suggest you to use datetime instead of datenum for converting your date strings into a serial representation, this can make (not only) the whole computation much easier:
tm = datetime({
'1/1/2001';
'1/1/2001';
'1/1/2001';
'3/1/2001';
'3/1/2001'
},'InputFormat','dd/MM/yyyy');
Once you have obtained your datetime vector, the calculation can be achieved as follows:
% Create a sequence of datetimes from the first date to the last date...
T = (min(tm):max(tm)).';
% Build an indexing of every occurrence to the regards of the sequence...
[~,idx] = ismember(tm,T);
% Count the occurrences for every occurrence...
C = accumarray(idx,1);
% Put unique dates and occurrences together into a single variable...
res = table(T,C)
Here is the output:
res =
T C
___________ _
01-Jan-2001 3
02-Jan-2001 0
03-Jan-2001 2
For more information about the functions used within the computation:
accumarray function
ismember function
On a side note, I didn't understand whether your dates are in dd/MM/yyyy or in MM/dd/yyyy format... because with the latter, you cannot have that output using my approach, and you should also implement an algorithm for detecting the current month and then splitting your data over a monthly (and eventually yearly, if your dates span over 2001) criterion instead:
tm = datetime({
'1/1/2001';
'1/1/2001';
'1/1/2001';
'3/1/2001';
'3/1/2001'
},'InputFormat','MM/dd/yyyy');
M = month(tm);
M_seq = (min(M):max(M)).';
[~,idx] = ismember(M,M_seq);
C = accumarray(idx,1);
res = table(datetime(2001,M_seq,1),C)
res =
Var1 C
___________ _
01-Jan-2001 3
01-Feb-2001 0
01-Mar-2001 2
I'll first give the code and then explain step by step.
code:
[Value, Time] = xlsread('stack','A1:D159','',#convertSpreadsheetExcelDates);
tm=datenum(Time);
val=Value(:,4);
data=[tm val];
a=(datestr(tm));
T1=datetime('1/1/2001');
T2=datetime('6/23/2002');
T = T1:T2;
tm_all=datenum(T);
[~, idx] = ismember(tm_all,data(:,1)); % get indices
[occurence,dates]= hist(data(:,1),unique(data(:,1))); % count occurences of dates from file
t = [0;data(:,1)]; % add 0 to dates (for later because MATLAB starts at 1
[~,idx] = ismember(t(idx+1),dates); % get incides
q = [0 occurence]; % add 0 to occurence (for later because MATLAB starts at 1
occ = q(idx+1); % make vector with occurences
out = [tm_all' occ']; % output
idx of ismember is an 1xlength(tm_all) vector that at position i contains the lowest index of where tm_all(i) is found in data(:,1). So take for example A = [1 2 3 4] and B = [1 1 2 4] then for [~,idx] = ismember(A,B) the result will be
idx = [1 3 0 4]
because A(1) = 1 and the first 1 in B is found at posistion 1. If a number in A doesn't occur in B, then the result will be 0.
[occurence,dates]= hist(data(:,1),unique(data(:,1))); gives the number of occurences for the dates.
t = [0;data(:,1)]; adds a zero in the beginning so tlooks like:
0
'date 1'
'date 2'
'date 3'
'date 4'
...
Why this is done, will be explained next.
t(idx+1) is a vector that is 1xlength(tm_all), and is kind of a copy of tm_all except that when a date doesn't occur in the file, the date is zero. How does this work? t(i) gives you the value of t at position i. So t( 1 5 4 2 9) is a vector with the values of t at positions 1, 5, 4, 2 and 9. Remember idx is the vector that contains the incides of the of the dates in data(:,1). Because Matlab indexing starts at 1, idx+1 is needed. The dates in data':,1) then must also be increased. That's done by adding the zero in the beginning.
[~,idx] = ismember(t(idx+1),dates); is the same as before, but idx now contains the indices of dates.
q = [0 occurence]; again adds a zero occ = q(idx+1); is the row of occurences of the dates.
Related
I am wondering if there is an efficient way of grouping/summing column values of a matrix based on a serial number date column (in years) in Matlab version 2013. To illustrate my point, assuming the data looks like:
737421 3
737106 -1
737222 4
736084 7
726105 -2
726442 4
`
One is expecting to get:
6
7
2
*PS:Using the aggregate function may solve this issue in a recent version of Matlab
Thanks in advance
This would be my approach:
x = [737421 3
737106 -1
737222 4
736084 7
726105 -2
726442 4]; % data
[~, ~, u] = unique(datestr(x(:,1), 'yyyy'), 'rows', 'stable'); % convert to years as
% a 2D char array, and then get unique labels of each year (row) preseving order
y = accumarray(u, x(:,2)); % compute sums grouped by those labels
You can just index the date and sum the values, which would be straight forward. The problem would be the size of the array to search. If it is very large you can make a tree out of the data for the date would be the Node and you can put the idx into the array as the value at that node. Then search the tree for the starting date and ending date, which will give the you index range in the array to sum. Building the tree and searching is easy and there are examples online.
x = [737421 3
737106 -1
737222 4
736084 7
726105 -2
726442 4]; % data
idx = x(:,1) >= 737421 & x(:,1) <= 737222;
out = sum(x(idx,2));
edit:
% Just updating to give one of the values to be correct.
% There would have to be a for loop to check every
% year range so #Luis Mendo is the best solution.
idx = x(:,1) >= 737106 & x(:,1) <= 737421; % index for each year
out = sum(x(idx,2));
I'm trying to elegantly split a vector. For example,
vec = [1 2 3 4 5 6 7 8 9 10]
According to another vector of 0's and 1's of the same length where the 1's indicate where the vector should be split - or rather cut:
cut = [0 0 0 1 0 0 0 0 1 0]
Giving us a cell output similar to the following:
[1 2 3] [5 6 7 8] [10]
Solution code
You can use cumsum & accumarray for an efficient solution -
%// Create ID/labels for use with accumarray later on
id = cumsum(cut)+1
%// Mask to get valid values from cut and vec corresponding to ones in cut
mask = cut==0
%// Finally get the output with accumarray using masked IDs and vec values
out = accumarray(id(mask).',vec(mask).',[],#(x) {x})
Benchmarking
Here are some performance numbers when using a large input on the three most popular approaches listed to solve this problem -
N = 100000; %// Input Datasize
vec = randi(100,1,N); %// Random inputs
cut = randi(2,1,N)-1;
disp('-------------------- With CUMSUM + ACCUMARRAY')
tic
id = cumsum(cut)+1;
mask = cut==0;
out = accumarray(id(mask).',vec(mask).',[],#(x) {x});
toc
disp('-------------------- With FIND + ARRAYFUN')
tic
N = numel(vec);
ind = find(cut);
ind_before = [ind-1 N]; ind_before(ind_before < 1) = 1;
ind_after = [1 ind+1]; ind_after(ind_after > N) = N;
out = arrayfun(#(x,y) vec(x:y), ind_after, ind_before, 'uni', 0);
toc
disp('-------------------- With CUMSUM + ARRAYFUN')
tic
cutsum = cumsum(cut);
cutsum(cut == 1) = NaN; %Don't include the cut indices themselves
sumvals = unique(cutsum); % Find the values to use in indexing vec for the output
sumvals(isnan(sumvals)) = []; %Remove NaN values from sumvals
output = arrayfun(#(val) vec(cutsum == val), sumvals, 'UniformOutput', 0);
toc
Runtimes
-------------------- With CUMSUM + ACCUMARRAY
Elapsed time is 0.068102 seconds.
-------------------- With FIND + ARRAYFUN
Elapsed time is 0.117953 seconds.
-------------------- With CUMSUM + ARRAYFUN
Elapsed time is 12.560973 seconds.
Special case scenario: In cases where you might have runs of 1's, you need to modify few things as listed next -
%// Mask to get valid values from cut and vec corresponding to ones in cut
mask = cut==0
%// Setup IDs differently this time. The idea is to have successive IDs.
id = cumsum(cut)+1
[~,~,id] = unique(id(mask))
%// Finally get the output with accumarray using masked IDs and vec values
out = accumarray(id(:),vec(mask).',[],#(x) {x})
Sample run with such a case -
>> vec
vec =
1 2 3 4 5 6 7 8 9 10
>> cut
cut =
1 0 0 1 1 0 0 0 1 0
>> celldisp(out)
out{1} =
2
3
out{2} =
6
7
8
out{3} =
10
For this problem, a handy function is cumsum, which can create a cumulative sum of the cut array. The code that produces an output cell array is as follows:
vec = [1 2 3 4 5 6 7 8 9 10];
cut = [0 0 0 1 0 0 0 0 1 0];
cutsum = cumsum(cut);
cutsum(cut == 1) = NaN; %Don't include the cut indices themselves
sumvals = unique(cutsum); % Find the values to use in indexing vec for the output
sumvals(isnan(sumvals)) = []; %Remove NaN values from sumvals
output = {};
for i=1:numel(sumvals)
output{i} = vec(cutsum == sumvals(i)); %#ok<SAGROW>
end
As another answer shows, you can use arrayfun to create a cell array with the results. To apply that here, you'd replace the for loop (and the initialization of output) with the following line:
output = arrayfun(#(val) vec(cutsum == val), sumvals, 'UniformOutput', 0);
That's nice because it doesn't end up growing the output cell array.
The key feature of this routine is the variable cutsum, which ends up looking like this:
cutsum =
0 0 0 NaN 1 1 1 1 NaN 2
Then all we need to do is use it to create indices to pull the data out of the original vec array. We loop from zero to max and pull matching values. Notice that this routine handles some situations that may arise. For instance, it handles 1 values at the very beginning and very end of the cut array, and it gracefully handles repeated ones in the cut array without creating empty arrays in the output. This is because of the use of unique to create the set of values to search for in cutsum, and the fact that we throw out the NaN values in the sumvals array.
You could use -1 instead of NaN as the signal flag for the cut locations to not use, but I like NaN for readability. The -1 value would probably be more efficient, as all you'd have to do is truncate the first element from the sumvals array. It's just my preference to use NaN as a signal flag.
The output of this is a cell array with the results:
output{1} =
1 2 3
output{2} =
5 6 7 8
output{3} =
10
There are some odd conditions we need to handle. Consider the situation:
vec = [1 2 3 4 5 6 7 8 9 10 11 12 13 14];
cut = [1 0 0 1 1 0 0 0 0 1 0 0 0 1];
There are repeated 1's in there, as well as a 1 at the beginning and end. This routine properly handles all this without any empty sets:
output{1} =
2 3
output{2} =
6 7 8 9
output{3} =
11 12 13
You can do this with a combination of find and arrayfun:
vec = [1 2 3 4 5 6 7 8 9 10];
N = numel(vec);
cut = [0 0 0 1 0 0 0 0 1 0];
ind = find(cut);
ind_before = [ind-1 N]; ind_before(ind_before < 1) = 1;
ind_after = [1 ind+1]; ind_after(ind_after > N) = N;
out = arrayfun(#(x,y) vec(x:y), ind_after, ind_before, 'uni', 0);
We thus get:
>> celldisp(out)
out{1} =
1 2 3
out{2} =
5 6 7 8
out{3} =
10
So how does this work? Well, the first line defines your input vector, the second line finds how many elements are in this vector and the third line denotes your cut vector which defines where we need to cut in our vector. Next, we use find to determine the locations that are non-zero in cut which correspond to the split points in the vector. If you notice, the split points determine where we need to stop collecting elements and begin collecting elements.
However, we need to account for the beginning of the vector as well as the end. ind_after tells us the locations of where we need to start collecting values and ind_before tells us the locations of where we need to stop collecting values. To calculate these starting and ending positions, you simply take the result of find and add and subtract 1 respectively.
Each corresponding position in ind_after and ind_before tell us where we need to start and stop collecting values together. In order to accommodate for the beginning of the vector, ind_after needs to have the index of 1 inserted at the beginning because index 1 is where we should start collecting values at the beginning. Similarly, N needs to be inserted at the end of ind_before because this is where we need to stop collecting values at the end of the array.
Now for ind_after and ind_before, there is a degenerate case where the cut point may be at the end or beginning of the vector. If this is the case, then subtracting or adding by 1 will generate a start and stopping position that's out of bounds. We check for this in the 4th and 5th line of code and simply set these to 1 or N depending on whether we're at the beginning or end of the array.
The last line of code uses arrayfun and iterates through each pair of ind_after and ind_before to slice into our vector. Each result is placed into a cell array, and our output follows.
We can check for the degenerate case by placing a 1 at the beginning and end of cut and some values in between:
vec = [1 2 3 4 5 6 7 8 9 10];
cut = [1 0 0 1 0 0 0 1 0 1];
Using this example and the above code, we get:
>> celldisp(out)
out{1} =
1
out{2} =
2 3
out{3} =
5 6 7
out{4} =
9
out{5} =
10
Yet another way, but this time without any loops or accumulating at all...
lengths = diff(find([1 cut 1])) - 1; % assuming a row vector
lengths = lengths(lengths > 0);
data = vec(~cut);
result = mat2cell(data, 1, lengths); % also assuming a row vector
The diff(find(...)) construct gives us the distance from each marker to the next - we append boundary markers with [1 cut 1] to catch any runs of zeros which touch the ends. Each length is inclusive of its marker, though, so we subtract 1 to account for that, and remove any which just cover consecutive markers, so that we won't get any undesired empty cells in the output.
For the data, we mask out any elements corresponding to markers, so we just have the valid parts we want to partition up. Finally, with the data ready to split and the lengths into which to split it, that's precisely what mat2cell is for.
Also, using #Divakar's benchmark code;
-------------------- With CUMSUM + ACCUMARRAY
Elapsed time is 0.272810 seconds.
-------------------- With FIND + ARRAYFUN
Elapsed time is 0.436276 seconds.
-------------------- With CUMSUM + ARRAYFUN
Elapsed time is 17.112259 seconds.
-------------------- With mat2cell
Elapsed time is 0.084207 seconds.
...just sayin' ;)
Here's what you need:
function spl = Splitting(vec,cut)
n=1;
j=1;
for i=1:1:length(b)
if cut(i)==0
spl{n}(j)=vec(i);
j=j+1;
else
n=n+1;
j=1;
end
end
end
Despite how simple my method is, it's in 2nd place for performance:
-------------------- With CUMSUM + ACCUMARRAY
Elapsed time is 0.264428 seconds.
-------------------- With FIND + ARRAYFUN
Elapsed time is 0.407963 seconds.
-------------------- With CUMSUM + ARRAYFUN
Elapsed time is 18.337940 seconds.
-------------------- SIMPLE
Elapsed time is 0.271942 seconds.
Unfortunately there is no 'inverse concatenate' in MATLAB. If you wish to solve a question like this you can try the below code. It will give you what you looking for in the case where you have two split point to produce three vectors at the end. If you want more splits you will need to modify the code after the loop.
The results are in n vector form. To make them into cells, use num2cell on the results.
pos_of_one = 0;
% The loop finds the split points and puts their positions into a vector.
for kk = 1 : length(cut)
if cut(1,kk) == 1
pos_of_one = pos_of_one + 1;
A(1,one_pos) = kk;
end
end
F = vec(1 : A(1,1) - 1);
G = vec(A(1,1) + 1 : A(1,2) - 1);
H = vec(A(1,2) + 1 : end);
I have a matrix with constant consecutive values randomly distributed throughout the matrix. I want the indices of the consecutive values, and further, I want a matrix of the same size as the original matrix, where the number of consecutive values are stored in the indices of the consecutive values. For Example
original_matrix = [1 1 1;2 2 3; 1 2 3];
output_matrix = [3 3 3;2 2 0;0 0 0];
I have struggled mightily to find a solution to this problem. It has relevance for meteorological data quality control. For example, if I have a matrix of temperature data from a number of sensors, and I want to know what days had constant consecutive values, and how many days were constant, so I can then flag the data as possibly faulty.
temperature matrix is number of days x number of stations and I want an output matrix that is also number of days x number of stations, where the consecutive values are flagged as described above.
If you have a solution to that, please provide! Thank you.
For this kind of problems, I made my own utility function runlength:
function RL = runlength(M)
% calculates length of runs of consecutive equal items along columns of M
% work along columns, so that you can use linear indexing
% find locations where items change along column
jumps = diff(M) ~= 0;
% add implicit jumps at start and end
ncol = size(jumps, 2);
jumps = [true(1, ncol); jumps; true(1, ncol)];
% find linear indices of starts and stops of runs
ijump = find(jumps);
nrow = size(jumps, 1);
istart = ijump(rem(ijump, nrow) ~= 0); % remove fake starts in last row
istop = ijump(rem(ijump, nrow) ~= 1); % remove fake stops in first row
rl = istop - istart;
assert(sum(rl) == numel(M))
% make matrix of 'derivative' of runlength
% don't need last row, but needs same size as jumps for indices to be valid
dRL = zeros(size(jumps));
dRL(istart) = rl;
dRL(istop) = dRL(istop) - rl;
% remove last row and 'integrate' to get runlength
RL = cumsum(dRL(1:end-1,:));
It only works along columns since it uses linear indexing. Since you want do something similar along rows, you need to transpose back and forth, so you could use it for your case like so:
>> original = [1 1 1;2 2 3; 1 2 3];
>> original = original.'; % transpose, since runlength works along columns
>> output = runlength(original);
>> output = output.'; % transpose back
>> output(output == 1) = 0; % see hitzg's comment
>> output
output =
3 3 3
2 2 0
0 0 0
so I have a matrix Data in this format:
Data = [Date Time Price]
Now what I want to do is plot the Price against the Time, but my data is very large and has lines where there are multiple Prices for the same Date/Time, e.g. 1st, 2nd lines
29 733575.459548611 40.0500000000000
29 733575.459548611 40.0600000000000
29 733575.459548612 40.1200000000000
29 733575.45954862 40.0500000000000
I want to take an average of the prices with the same Date/Time and get rid of any extra lines. My goal is to do linear intrapolation on the values which is why I must have only one Time to one Price value.
How can I do this? I did this (this reduces the matrix so that it only takes the first line for the lines with repeated date/times) but I don't know how to take the average
function [ C ] = test( DN )
[Qrows, cols] = size(DN);
C = DN(1,:);
for i = 1:(Qrows-1)
if DN(i,2) == DN(i+1,2)
%n = 1;
%while DN(i,2) == DN(i+n,2) && i+n<Qrows
% n = n + 1;
%end
% somehow take average;
else
C = [C;DN(i+1,:)];
end
end
[C,ia,ic] = unique(A,'rows') also returns index vectors ia and ic
such that C = A(ia,:) and A = C(ic,:)
If you use as input A only the columns you do not want to average over (here: date & time), ic with one value for every row where rows you want to combine have the same value.
Getting from there to the means you want is for MATLAB beginners probably more intuitive with a for loop: Use logical indexing, e.g. DN(ic==n,3) you get a vector of all values you want to average (where n is the index of the date-time-row it belongs to). This you need to do for all different date-time-combinations.
A more vector-oriented way would be to use accumarray, which leads to a solution of your problem in two lines:
[DateAndTime,~,idx] = unique(DN(:,1:2),'rows');
Price = accumarray(idx,DN(:,3),[],#mean);
I'm not quite sure how you want the result to look like, but [DataAndTime Price] gives you the three-row format of the input again.
Note that if your input contains something like:
1 0.1 23
1 0.2 47
1 0.1 42
1 0.1 23
then the result of applying unique(...,'rows') to the input before the above lines will give a different result for 1 0.1 than using the above directly, as the latter would calculate the mean of 23, 23 and 42, while in the former case one 23 would be eliminates as duplicate before and the differing row with 42 would have a greater weight in the average.
Try the following:
[Qrows, cols] = size(DN);
% C is your result matrix
C = DN;
% this will give you the indexes where DN(i,:)==DN(i+1)
i = find(diff(DN(:,2)==0);
% replace C(i,:) with the average
C(i,:) = (DN(i,:)+DN(i+1,:))/2;
% delete the C(i+1,:) rows
C(i,:) = [];
Hope this works.
This should work if the repeated time values come in pairs (the average is calculated between i and i+1). Should you have time repeats of 3 or more then try to rethink how to change these steps.
Something like this would work, but I did not run the code so I can't promise there's no bugs.
newX = unique(DN(:,2));
newY = zeros(1,length(newX));
for ix = 1:length(newX)
allOcurrences = find(DN(:,2)==DN(i,2));
% If there's duplicates, take their mean
if numel(allOcurrences)>1
newY(ix) = mean(DN(allOcurrences,3));
else
% If not, use the only Y value
newY(ix) = DN(ix,3);
end
end
I'm quite new to matlab, and I'm curious how to do this:
I have a rather large (27000x11) matrix, and the 8th column contains a number which changes sometimes but is constant for like 2000 rows (not necessarily consecutive).
I would like to calculate the mean of the entries in the 3rd column for those rows where the 8th column has the same value. This for each value of the 8th column.
I would also like to plot the 3rd column's means as a function of the 8th column's value but that I can do if I can get a new matrix (2x2) containing [mean_of_3rd,8th].
Ex: (smaller matrix for convenience)
1 2 3 4 5
3 7 5 3 2
1 3 2 5 3
4 5 7 5 8
2 4 7 4 4
Since the 4th column has the same value in row 1 and 5 I'd like to calculate the mean of 2 and 4 (the corresponding elements of column 2, italic bold) and put it in another matrix together with the 4th column's value. The same for 3 and 5 (bold) since the 4th column has the same value for these two.
3 4
4 5
and so on... is this possible in an easy way?
Use the all-mighty, underused accumarray :
This line gives you mean values of 4th column accumulated by 2nd column:
means = accumarray( A(:,4) ,A(:,2),[],#mean)
This line gives you number of element in each set:
count = accumarray( A(:,4) ,ones(size(A(:,4))))
Now if you want to filter only those that have at least one occurence:
>> filtered = means(count>1)
filtered =
3
4
This will work only for positive integers in the 4th column.
Another possibility for counting amount of elements in each set:
count = accumarray( A(:,4) ,A(:,4),[],#numel)
A slightly refined approach based on the ideas of Andrey and Rody. We can not use accumarray directly, since the data is real, not integer. But, we can use unique to find the indices of the repeating entries. Then we operate on integers.
% get unique entries in 4th column
[R, I, J] = unique(A(:,4));
% count the repeating entries: now we have integer indices!
counts = accumarray(J, 1, size(R));
% sum the 2nd column for all entries
sums = accumarray(J, A(:,2), size(R));
% compute means
means = sums./counts;
% choose only the entries that show more than once in 4th column
inds = counts>1;
result = [means(inds) R(inds)];
Time comparison for the following synthetic data:
A=randi(100, 1000000, 5);
% Rody's solution
Elapsed time is 0.448222 seconds.
% The above code
Elapsed time is 0.148304 seconds.
My official answer:
A4 = A(:,4);
R = unique(A4);
means = zeros(size(R));
inds = false(size(R));
for jj = 1:numel(R)
I = A4==R(jj);
sumI = sum(I);
inds(jj) = sumI>1;
means(jj) = sum(A(I,2))/sumI;
end
result = [means(inds) R(inds)];
This is because of the following. Here's all of the alternatives we've come up with, in profiling form:
%# sample data
A = [
1 2 3 4 5
3 7 5 3 2
1 3 2 5 3
4 5 7 5 8
2 4 7 4 4];
%# accumarray
%# works only on positive integers in A(:,4)
tic
for ii = 1:1e4
means = accumarray( A(:,4) ,A(:,2),[],#mean);
count = accumarray( A(:,4) ,ones(size(A(:,4))));
filtered = means(count>1);
end
toc
%# arrayfun
%# works only on integers in A(:,4)
tic
for ii = 1:1e4
B = arrayfun(#(x) A(A(:,4)==x, 2), min(A(:,4)):max(A(:,4)), 'uniformoutput', false);
filtered = cellfun(#mean, B(cellfun(#(x) numel(x)>1, B)) );
end
toc
%# ordinary loop
%# works only on integers in A(:,4)
tic
for ii = 1:1e4
A4 = A(:,4);
R = min(A4):max(A4);
means = zeros(size(R));
inds = false(size(R));
for jj = 1:numel(R)
I = A4==R(jj);
sumI = sum(I);
inds(jj) = sumI>1;
means(jj) = sum(A(I,2))/sumI;
end
filtered = means(inds);
end
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Results:
Elapsed time is 1.238352 seconds. %# (accumarray)
Elapsed time is 7.208585 seconds. %# (arrayfun + cellfun)
Elapsed time is 0.225792 seconds. %# (for loop)
The ordinary loop is clearly the way to go here.
Note the absence of mean in the inner loop. This is because mean is not a Matlab builtin function (at least, on R2010), so that using it inside the loop makes the loop unqualified for JIT compilation, which slows it down by a factor of over 10. Using the form above accelerates the loop to almost 5.5 times the speed of the accumarray solution.
Judging on your comment, it is almost trivial to change the loop to work on all entries in A(:,4) (not just the integers):
A4 = A(:,4);
R = unique(A4);
means = zeros(size(R));
inds = false(size(R));
for jj = 1:numel(A4)
I = A4==R(jj);
sumI = sum(I);
inds(jj) = sumI>1;
means(jj) = sum(A(I,2))/sumI;
end
filtered = means(inds);
Which I will copy-paste to the top as my official answer :)