Matrixwise subtraction yields vector - how to reshape to original logical matrix?

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Michaela Warnecke
Michaela Warnecke 2024-3-15
评论： Dyuman Joshi 2024-3-20
Hi,
I am working with a large dataset for which I need to do multiple substractions between vectors, then summing across logically indexed values. Currently, I index the vector subtraction in a for loop, but it takes forever as I have to run that loop ~ 1.5M, several times, so I would like to move to matrixwise calculations.
Below is a short version of the crux of my question. If I have a matrix A and a matrix B, and I index the values I am interested in using a logical matrix (cmpMatrix), then I subtract B from A and want to get the mean per column. However, the logical indexing always reshapes into a vector, not a matrix:
A = rand(3);
B = rand(3);
cmpMatrix = A>=0.5 %in my situation, there are always unequal numbers of 0s and 1s per column
cmpMatrix =
3×3 logical array
1 0 1
0 1 1
1 0 0
%Issue: ans for the following line is a vector.
A(cmpMatrix)
ans =
0.9612
0.7870
0.9437
0.9813
0.5702
I'd like to take the mean of all the values that are indexed per column, so I'd need to be able to backtrack where the values in the vector came from. Ideally, I'd be able to do something like:
mean(A(cmpMatrix) - B(cmpMatrix),2)
And receive a 1 x 3 vector where B was subtracted from A at each logical 1, and then the mean was taken across the matrix columns, so as to get a mean per column.
How do I achieve that?
Thank you for your help.

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采纳的回答

Stephen23
Stephen23 2024-3-15
Ran in:
A = rand(3);
B = rand(3);
X = A>=0.5;
[~,C] = find(X);
M = accumarray(C,A(X)-B(X),[],@mean).'
M = 1×3
0.6699 0.0500 0.5998
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显示 5更早的评论
Voss
Voss 2024-3-18
编辑：Voss 2024-3-18
Ran in:
They're equal up to round-off error:
A = rand(104,8193);
B = rand(104,8193);
max(abs(Stephen(A,B)-Voss(A,B)),[],'all')
ans = 1.6653e-16
function M = Stephen(A,B)
X = A>=0.5;
[~,C] = find(X);
M = accumarray(C,A(X)-B(X),[],@mean).';
end
function M = Dyuman(A,B)
[m,n] = size(A);
Y = repmat(1:n,m,1); % modification for non-square A
X = A>=0.5;
M = accumarray(Y(X),A(X)-B(X),[],@mean).';
end
function result = Walter1(A,B)
cmpMatrix = A>=0.5;
result = arrayfun(@(IDX) mean(A(cmpMatrix(:,IDX),IDX)-B(cmpMatrix(:,IDX),IDX)), 1:size(A,2));
end
function result = Walter2(A,B)
cmpMatrix = A>=0.5;
result = cellfun(@mean, mat2cell(A(cmpMatrix) - B(cmpMatrix), sum(cmpMatrix,1), 1)).'; % removing temp variable, and transposing for consistency with other methods
end
function result = Voss(A,B)
A_temp = A;
B_temp = B;
idx = A >= 0.5;
A_temp(~idx) = NaN;
B_temp(~idx) = NaN;
result = mean(A_temp-B_temp,1,'omitnan');
end
Dyuman Joshi
Dyuman Joshi 2024-3-20
I know and understand that they are round-off error; my point is why does it only occur in a single method and not in others, when all the methods use the same function (essentially the same operation)?

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更多回答（2 个）

Voss
Voss 2024-3-16
A_temp = A;
B_temp = B;
idx = A >= 0.5;
A_temp(~idx) = NaN;
B_temp(~idx) = NaN;
result = mean(A_temp-B_temp,1,'omitnan');
Walter Roberson
Walter Roberson 2024-3-15
One way:
result = arrayfun(@(IDX) mean(A(cmpMatrix(:,IDX),IDX)-B(cmpMatrix(:,IDX),IDX)), 1:size(A,2))
Chances are that this will be slower than looping.
Another way:
temp = A(cmpMatrix) - B(cmpMatrix);
result = cellfun(@mean, mat2cell(temp, sum(cmpMatrix,1), 1));
It would not surprise me if this is slower than looping.

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