# find

## Purpose

Find indices and values of nonzero elements.

## Synopsis

    k = find(X)
    [i,j] = find(X)
    [i,j,s] = find(X)

## Description

`k = find(X)` returns the indices of the vector `X` that point to nonzero elements. If none is found, `find` returns an empty matrix. If `X` is a matrix, `find` regards `X` as `X(:)`, which is the long column vector formed by concatenating the columns of `X`.

`[i,j] = find(X)` returns the row and column indices of the nonzero entries in the matrix `X`. This is often used with sparse matrices.

`[i,j,s] = find(X)` also returns a column vector of the nonzero entries in `X`. Note that `find(X)` and `find(X ~= 0)` produce the same `i` and `j`, but the latter produces an `s` with all 1s.

## Examples

Some operations on a vector

    x = [11  0  33  0  55]';

    find(x) =
        1
        3
        5

    find(x == 0) =
        2
        4

    find(0 < x & x < 10*pi) =
        1

And on a matrix

    M = magic(3)

    M =
        8    1    6
        3    5    7
        4    9    2
    [i,j,m] = find(M > 6)

    i =
        1
        3
        2

    j =
        1
        2
        3

    m =
        1
        1
        1

## See Also

    <, <=,>,>=,==, ~=, isempty, nonzeros, sparse

(c) Copyright 1994 by The MathWorks, Inc.