CODEWITHSUNDEEP
matlabmatrix
bzak
bzak

Reputation: 563

Matlab: how to find row indices of a matrix satisfying certain requirements?

A is a matrix 40 x 10000. V1, V2 and V3 are 3 vectors with the same dimension 1 x 50.

I want to find 3 vectors W1, W2 and W3 with the same dimension 1 X p (p: the largest possible p<=40) satisfying the following conditions:

Wk is not a known vector! but Vk are predefined.

So the goal is to find row indices of A that contain Wk, with size(Wk) the largest possible.

example: (I used some character in the matrix to make the example clearer)

      95    45    92    41    13     1    84
       a     1     e    89     h    74    52
A=    60    82    17     5    19    44    20
      48    44    40    35    67    93    67
       b    61     f    81     m    46    83
       c    79     g    20     n    41     1

V1 = [51 a 23 11 b 5 c]

V2 = [e g 93 14 22 f 10]

V3 = [81 n 87 h 45 77 m]

for this example p=3 (the largest possible value) so:

W1 =[a b c]

W2 =[e f g]

W3 =[h m n]

The desired result: A(2,:), A(5,:) and A(6,:).

another example:

if:

      95    45    92    41    13     1    84
       a     1     e    89     h    74    52
A=    60    82    17     5    19    44    20
       b    44    40    35    67    93    67
      48    61     f    81     m    46    83
       c    79     g    20     n    41     1

V1 = [51 a 23 11 b 5 c]

V2 = [e g 93 14 22 f 10]

V3 = [81 n 87 h 45 77 m]

for this example p=2 (the largest possible value); because 48 does not belong to V1, and 40 and 67 do not belong to V2 and V3 respectively, so:

W1 =[a c]

W2 =[e g]

W3 =[h n]

The desired result: A(2,:) and A(6,:).

another example:

if: (if b in A is one column to the right)

      95    45    92    41    13     1    84
       a     1     e    89     h    74    52
A=    60    82    17     5    19    44    20
      77     b    40    35    67    93    67
      48    61     f    81     m    46    83
       c    79     g    20     n    41     1

V1 = [51 a 23 11 b 5 c]

V2 = [e g 93 14 22 f 10]

V3 = [81 n 87 h 45 77 m]

for this example p=2 (the largest possible value), so:

W1 =[a c]

W2 =[e g]

W3 =[h n]

The desired result: A(2,:) and A(6,:).

another example:

if: (if c in A is one column to the right)

      95    45    92    41    13     1    84
       a     1     e    89     h    74    52
A=    60    82    17     5    19    44    20
       b    44    40    35    67    93    67
      48    61     f    81     m    46    83
      88     c     g    20     n    41     1

V1 = [51 a 23 11 b 5 c]

V2 = [e g 93 14 22 f 10]

V3 = [81 n 87 h 45 77 m]

for this example p=1 (the largest possible value); so:

W1 =[a]

W2 =[e]

W3 =[h]

The desired result: A(2,:).

Upvotes: 2

Views: 253

Answers (1)

Luis Mendo
Luis Mendo

Reputation: 112769

The following seems to work. The variable result gives the set of selected rows (such as [2 5 6] or [2 6] in your examples). Of course, you could then take A(result,:), or obtain p as numel(result).

eq1 = any(bsxfun(@eq, A, permute(V1, [1 3 2])), 3); %// does entry of A match V1?
eq2 = any(bsxfun(@eq, A, permute(V2, [1 3 2])), 3); %// ...V2?
eq3 = any(bsxfun(@eq, A, permute(V3, [1 3 2])), 3); %// ...V3?
result = [];
for nr = 1:size(A,1) %// try all numbers of rows, in ascending order
    rows = nchoosek(1:size(A,1),nr).'; %'// all combinations of that nr rows
    for rr = rows %// try each combination of nr rows
        if any(all(eq1(rr,:),1)) & any(all(eq2(rr,:),1)) & any(all(eq3(rr,:),1))
            %// ",1" needed to make "all" by columns even if there's only one row
            result = rr; %// (overw)rite result (nr is larger now)
            break %// no need to keep trying combinations of rows for this nr
        end
    end
end

General Case: When you have more than 3 vectors, you can make these changes, so that your code looks concise -

%// Concatenate all V vectors into one
V = cat(1,V1,V2,V3,V4,V5,...)

%// Replace eq1, eq2 and eq3 calculations with this single calculation
eqa = squeeze(any(bsxfun(@eq,A,permute(V,[4 3 2 1])),3));

%// Replace the `IF` part with -
if all(any(all(eqa(rr,:,:),1)),3), result = rr, break, end ...

Upvotes: 3

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