Elements processing in array

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Lee Lee
Lee Lee 2017-4-10
编辑： Jan 2017-4-11
If array A=[ b c ], I want to create value [b+c -b+c b-c -b-c]
or A=[ b c d ], then output should be [ b+c+d b+c-d b-c+d b-c-d -b+c+d -b+c-d -b-c+d -b-c-d ]
Is there any function in MATLAB that can easily solve my problem ? Thanks.

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Guillaume
Guillaume 2017-4-10
You basically want the sum of the n-ary product of the +/- sets of each element of your array. That can be done easily with ndgrid:
A = [1 3 8 2]; %demo data;
sets = num2cell([A; -A], 1); %split into sets of +/- values
nprod = cell(1, numel(A)); %create destination for n-ary product
[nprod{:}] = ndgrid(sets{:}); %calculate n-ary product
nprod = reshape(cat(numel(A)+1, nprod{:}), [], numel(A)); %concatenate into one matrix and reshape. Each row is one of the possible combination
sumnprod = sum(nprod, 2) %wanted result
  2 个评论
Jan
Jan 2017-4-11
+1: This is efficient for larg inputs - and as usual for code concerning permutations, "large" means 20 elements already.

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更多回答（2 个）

Jan
Jan 2017-4-11
编辑：Jan 2017-4-11
With http://www.mathworks.com/matlabcentral/fileexchange/26242-vchoosekro:
n = numel(A);
M = VChooseKRO([-1, 1], n) * A(:);
Timings: See comment.
And if single precision is enough, this is 33% faster for an [1 x 20] input:
n = numel(A);
M = VChooseKRO(single([-1, 1]), n) * A(:);
Jan
Jan 2017-4-10
编辑：Jan 2017-4-11
n = numel(A);
M = (1 - 2 * (dec2bin(0:2^n-1) - '0')) * A(:);
[EDITED, parenthesis inserted]
  2 个评论
Guillaume
Guillaume 2017-4-11
That is indeed shorter than my answer and possibly will fall over later than ndgrid on larger arrays. However, it's probably slower due to number - string conversions.
Jan
Jan 2017-4-11
编辑：Jan 2017-4-11
@Guillaume: I know, I detest dec2bin in my code and use it in the forum only. I productive codes I'd use:
n = numel(A);
s = rem(floor((0:2^n-1).' * pow2((1-n):0)), 2);
M = (1 - 2 * s) * A(:));
Before speculating about speed, let's measure it:
A = 1:5;
rep = 10000; % Repetitions for accurate timings
tic;
for k = 1:rep
sets = num2cell([A; -A], 1);
nprod = cell(1, numel(A));
[nprod{:}] = ndgrid(sets{:});
nprod = reshape(cat(numel(A)+1, nprod{:}), [], numel(A));
sumnprod = sum(nprod, 2);
end
toc
tic;
for k = 1:rep
n = numel(A);
M = (1 - 2 * (dec2bin(0:2^n-1) - '0')) * A(:);
end
toc
tic;
for k = 1:rep
n = numel(A);
s = rem(floor((0:2^n-1).' * pow2((1-n):0)), 2);
M = (1 - 2 * s) * A(:);
end
toc
tic;
for k = 1:rep
M = VChooseKRO([-1, 1], numel(A)) * A(:);
end
toc
R2016b/64, Win7:
Elapsed time is 1.799392 seconds. Guillaume
Elapsed time is 0.355071 seconds. DEC2BIN
Elapsed time is 0.278210 seconds. my_DEC2BIN
Elapsed time is 0.078271 seconds. VChooseKRO
And now with a larger input:
A = 1:20;
rep = 2;
Elapsed time is 1.007342 seconds. Guillaume
Elapsed time is 3.261605 seconds. DEC2BIN
Elapsed time is 2.929411 seconds. my_DEC2BIN
Elapsed time is 0.468315 seconds. VChooseKRO
Conclusion: The multiplication with the binary matrix is fast for small arrays and slow for large arrays. The conversion to CHAR and back has some overhead. Creating large temporary array in a DEC2BIN style is a bad idea. But with an efficient creation of the [1, -1] matrix the computations are faster than the cell approach. But therefore it is required to compile a C-Mex function. Therefore is pure Matlab is wanted, Guillaume's method is better - except a user needs millions of results for short input vectors.

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