What is the optimal way to get selected elements from a matrix?

Question

I have a 2x2 matrix "M", and a list "ind" containing pairs of indices.

M = {{a, b, c}, {d, f, g}, {h, i, j}};
ind = {{1, 2}, {1, 1}, {3, 1}};

I would like to get the elements of the matrix given by the indices in "ind", in this case:

{b,a,h}

The only way I've found to do this is with MapThread:

MapThread[M[[#1, #2]] &, ind\[Transpose]]

However, the matrices and lists I am using are quite large, and this takes considerable time. Is there a more efficient way to do this? Can this be parallelized (maybe by using ParallelMap, instead of MapThread)?

Answer 1

One way is the following

M = {{a, b, c}, {d, f, g}, {h, i, j}};
ind = {{1, 2}, {1, 1}, {3, 1}};

Now

 Extract[M, ind]

Look up Extract

Also Position is designed to return index location which can be used by Extract which makes it easy. You can use Position and then pass the result directly to Extract without having to worry if it will work or not and this works for lists of different dimensions.

The position specifications used by Extract have the same form as those returned by Position, and used in functions such as MapAt and ReplacePart. »