How does logical indexing work?

Can I get a short primer on this?

Answer 1

[Doug Hull]

From the Getting Started book:

The logical vectors created from logical and relational operations can be used to reference subarrays. Suppose X is an ordinary matrix and L is a matrix of the same size that is the result of some logical operation. Then X(L) specifies the elements of X where the elements of L are nonzero.

Here's a short example of logical indexing to specify certain array elements:

m = magic(5)
% Get the logical matrix which is zero where
% m <= 20 and 1 where m >= 21
bigNumbersLocations = m > 20
% Extract those big numbers into an array
% Method #1:
bigNumbers = zeros(size(m));
bigNumbers(bigNumbersLocations) = m(bigNumbersLocations)
% Method #2:
bigNumbers2 = m;
bigNumbers2(~bigNumbersLocations) = 0
% Display the big numbers.  It will be a 1D vector.
m(bigNumbersLocations)

m =
    17    24     1     8    15
    23     5     7    14    16
     4     6    13    20    22
    10    12    19    21     3
    11    18    25     2     9

bigNumbersLocations =
     0     1     0     0     0
     1     0     0     0     0
     0     0     0     0     1
     0     0     0     1     0
     0     0     1     0     0

bigNumbers =
     0    24     0     0     0
    23     0     0     0     0
     0     0     0     0    22
     0     0     0    21     0
     0     0    25     0     0

bigNumbers2 =
     0    24     0     0     0
    23     0     0     0     0
     0     0     0     0    22
     0     0     0    21     0
     0     0    25     0     0

ans =
    23
    24
    25
    21
    22

[From the MATLAB FAQ of Ancient Times]

Answer 2

[Anish]

Assume A is a MxN matrix.

Let "tf" be a MxN logical matrix.

Then A(tf) extracts all elements of A corresponding to all true elements in tf

A = rand(5);    % Random 5x5 matrix
tf = A > .5     % Logical matrix of same size 5x5
A(tf)           % All values in A greater than .5 as a column

For more help, see Steve's excellent blog in this:

http://blogs.mathworks.com/steve/2008/01/28/logical-indexing/

Or good old MATLAB doc:

http://www.mathworks.com/help/techdoc/math/f1-85462.html#bq7egb6-1