Need to test all permutations

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CD
CD 2019-4-6
评论： Star Strider 2019-4-6
Say I have the following:
A = [1 2 3], B = [1 2], C = [4],
D = C + B*A
I need D to contain all permutations of C+B*A:
D1 = 4+1*1
D2 = 4+1*2
D3 = 4+1*3
D4 = 4+2*1
D5 = 4+2*2
D6 = 4+2*3
What is this called and what tools are available to perform this on bigger equations?

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Star Strider
Star Strider 2019-4-6
One approach is to use the ndgrid (link) function:
A = [1 2 3];
B = [1 2];
C = [4];
[p1,p2,p3] = ndgrid(A,B,C);
P = [p3(:),p2(:),p1(:)]; % Components
D = p3(:) + p2(:).*p1(:)
The ‘P’ assignment simply displays the components used in the ‘D’ calculation. It is not otherwise necessary for the code.
I cannot guarantee that this will easily scale to other problems. It works here.
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Star Strider
Star Strider 2019-4-6
编辑：Star Strider 2019-4-6
Craig Dekker’s Answer moved to this Comment:
Thank you.
I'll try breaking the equation into several nested loops.
Star Strider
Star Strider 2019-4-6
As always, my pleasure.
That may not be absolutely necessary.
I simply don’t understand your notation well enough to figure out how to use the ndgrid approach with it.
Experiment with something like this:
Dv1 = [1 2];
M2v1 = [3 4 5];
M1v1 = [6 7 8 9 10 11];
Fmv1 = (12:12+17);
Rv1 = [30 31];
[p1,p2,p3,p4,p5] = ndgrid(Dv1,M2v1,M1v1,Fmv1,Rv1);
Rv = p5(:);
Fmv = p4(:);
M1v = p3(:);
M2v = p2(:);
Dv = p1(:);
It seems that it might work, although I can’t guarantee it. I may also have missed something, since this code produces a series of (1296x1) vectors, while:
veclen = 2*3*6*3*18*2*2;
would have 7776 elements.
If the ndgrid approach works, it would definitely be faster than nested for loops. The challenge then comes in reshaping the output vector into a matrix that is meaningful in terms of the argument vectors. Appropriately indexing the result is the principal reason I would err on the side of the loops.

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