Use Indexing for more than 1 dimension of array simultaneously

I have a 10 by 3 matrix:

matrix = rand(10, 3);

I have an indexing array which selects a column number for each row:

idx = [1; 2; 2; 3; 1; 2; 1; 2; 3; 3];

I want to produce a 10x1 array which uses the above index array to extract the respective column number element at each row. Without using a for loop.

I have tried:

output = matrix(1:10, idx)

output = 10×10

0.2039 0.6450 0.6450 0.8811 0.2039 0.6450 0.2039 0.6450 0.8811 0.8811 0.3955 0.0347 0.0347 0.1645 0.3955 0.0347 0.3955 0.0347 0.1645 0.1645 0.5710 0.9536 0.9536 0.9736 0.5710 0.9536 0.5710 0.9536 0.9736 0.9736 0.5103 0.9297 0.9297 0.2534 0.5103 0.9297 0.5103 0.9297 0.2534 0.2534 0.0723 0.4962 0.4962 0.0039 0.0723 0.4962 0.0723 0.4962 0.0039 0.0039 0.1273 0.1957 0.1957 0.3339 0.1273 0.1957 0.1273 0.1957 0.3339 0.3339 0.0603 0.7878 0.7878 0.9416 0.0603 0.7878 0.0603 0.7878 0.9416 0.9416 0.0832 0.5866 0.5866 0.9793 0.0832 0.5866 0.0832 0.5866 0.9793 0.9793 0.5630 0.3352 0.3352 0.9332 0.5630 0.3352 0.5630 0.3352 0.9332 0.9332 0.7188 0.8864 0.8864 0.6835 0.7188 0.8864 0.7188 0.8864 0.6835 0.6835

This produces a 10x10 matrix.

Answer 1

[Fangjun Jiang]

matrix(sub2ind(size(matrix),(1:10)',idx))

Answer 2

[the cyclist]

You can use linear indexing:

matrix = rand(10, 3);

idx = [1; 2; 2; 3; 1; 2; 1; 2; 3; 3];

linearIndex = sub2ind(size(matrix),1:10,idx');

matrix(linearIndex)

ans = 1×10

0.8064 0.6649 0.2393 0.9216 0.0166 0.3291 0.6957 0.8769 0.4766 0.2352

Answer 3

[James Tursa]

Yet another way using linear indexing (showing what sub2ind( ) does internally):

matrix = rand(10, 3);
idx = [1; 2; 2; 3; 1; 2; 1; 2; 3; 3];
m = size(matrix,1);
matrix( (1:m)' + m*(idx-1) )

ans = 10×1

0.8923 0.3166 0.8492 0.0101 0.2614 0.4642 0.7455 0.5160 0.9367 0.5664

And to show that it is the same as other solutions:

matrix(sub2ind(size(matrix),(1:m)',idx))

ans = 10×1

0.8923 0.3166 0.8492 0.0101 0.2614 0.4642 0.7455 0.5160 0.9367 0.5664

[Walter Roberson]

Note that linear indexing is what happens internally when you use sub2ind: sub2ind is a helper function to make it easier to calculate the correct linear indexing.