Find indices and values of nonzero elements (2024)

Find indices and values of nonzero elements

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Syntax

k = find(X)

k = find(X,n)

k = find(X,n,direction)

[row,col]= find(___)

[row,col,v]= find(___)

Description

example

k = find(X) returns a vector containing the linear indices of each nonzero element in array X.

  • If X is a vector, then find returns a vector with the same orientation as X.

  • If X is a multidimensional array, then find returns a column vector of the linear indices of the result.

example

k = find(X,n) returnsthe first n indices corresponding to the nonzeroelements in X.

example

k = find(X,n,direction),where direction is 'last', findsthe last n indices corresponding to nonzero elementsin X. The default for direction is 'first',which finds the first n indices corresponding tononzero elements.

example

[row,col]= find(___) returns the row and column subscriptsof each nonzero element in array X using any ofthe input arguments in previous syntaxes.

example

[row,col,v]= find(___) also returns vector v,which contains the nonzero elements of X.

Examples

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Zero and Nonzero Elements in Matrix

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Find the nonzero elements in a 3-by-3 matrix.

X = [1 0 2; 0 1 1; 0 0 4]
X = 3×3 1 0 2 0 1 1 0 0 4
k = find(X)
k = 5×1 1 5 7 8 9

Use the logical not operator on X to locate the zeros.

k2 = find(~X)
k2 = 4×1 2 3 4 6

Elements Satisfying a Condition

Open Live Script

Find the first five elements that are less than 10 in a 4-by-4 magic square matrix.

X = magic(4)
X = 4×4 16 2 3 13 5 11 10 8 9 7 6 12 4 14 15 1
k = 5×1 2 3 4 5 7

View the corresponding elements of X.

X(k)
ans = 5×1 5 9 4 2 7

Elements Equal to Specific Values

Open Live Script

To find a specific integer value, use the == operator. For instance, find the element equal to 13 in a 1-by-10 vector of odd integers.

x = 1:2:20
x = 1×10 1 3 5 7 9 11 13 15 17 19
k = find(x==13)
k = 7

To find a noninteger value, use a tolerance value based on your data. Otherwise, the result is sometimes an empty matrix due to floating-point roundoff error.

y = 0:0.1:1
y = 1×11 0 0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0.9000 1.0000
k = find(y==0.3)
k = 1x0 empty double row vector
k = find(abs(y-0.3) < 0.001)
k = 4

Last Several Nonzero Elements

Open Live Script

Create a 6-by-6 magic square matrix with all of the odd-indexed elements equal to zero.

X = magic(6);X(1:2:end) = 0
X = 6×6 0 0 0 0 0 0 3 32 7 21 23 25 0 0 0 0 0 0 8 28 33 17 10 15 0 0 0 0 0 0 4 36 29 13 18 11

Locate the last four nonzeros.

k = find(X,4,'last')
k = 4×1 30 32 34 36

Elements Satisfying Multiple Conditions

Open Live Script

Find the first three elements in a 4-by-4 matrix that are greater than 0 and less than 10. Specify two outputs to return the row and column subscripts to the elements.

X = [18 3 1 11; 8 10 11 3; 9 14 6 1; 4 3 15 21]
X = 4×4 18 3 1 11 8 10 11 3 9 14 6 1 4 3 15 21
[row,col] = find(X>0 & X<10,3)
row = 3×1 2 3 4
col = 3×1 1 1 1

The first instance is X(2,1), which is 8.

Subscripts and Values for Nonzero Elements

Open Live Script

Find the nonzero elements in a 3-by-3 matrix. Specify three outputs to return the row subscripts, column subscripts, and element values.

X = [3 2 0; -5 0 7; 0 0 1]
X = 3×3 3 2 0 -5 0 7 0 0 1
[row,col,v] = find(X)
row = 5×1 1 2 1 2 3
col = 5×1 1 1 2 3 3
v = 5×1 3 -5 2 7 1

Subscripts of Multidimensional Array

Open Live Script

Find the nonzero elements in a 4-by-2-by-3 array. Specify two outputs, row and col, to return the row and column subscripts of the nonzero elements. When the input is a multidimensional array (N > 2), find returns col as a linear index over the N-1 trailing dimensions of X.

X = zeros(4,2,3);X([1 12 19 21]) = 1
X = X(:,:,1) = 1 0 0 0 0 0 0 0X(:,:,2) = 0 0 0 0 0 0 1 0X(:,:,3) = 0 1 0 0 1 0 0 0
[row,col] = find(X)
row = 4×1 1 4 3 1
col = 4×1 1 3 5 6

Input Arguments

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XInput array
scalar | vector | matrix | multidimensional array

Input array, specified as a scalar, vector, matrix, or multidimensional array.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | logical | char
Complex Number Support: Yes

nNumber of nonzeros to find
positive integer scalar

Number of nonzeros to find, specified as a positive integerscalar. By default, find(X,n) looks for the first n nonzeroelements in X.

directionSearch direction
'first' (default) | 'last'

Search direction, specified as the string 'first' or 'last'.Look for the last n nonzeroelements in X using find(X,n,'last').

Output Arguments

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k — Indices to nonzero elements
vector

Indices to nonzero elements, returned as a vector.

  • If X is a row vector, then k is also a row vector. Otherwise, k is a column vector.

  • k is an empty row vector or empty column vector when X is an empty array or has no nonzero elements.

  • find uses the convention that k is an empty matrix [] when X is an empty matrix [].

You can return the nonzero values in X using X(k).

row — Row subscripts
vector

Row subscripts, returned as a vector. Together, row and col specifythe X(row,col) subscripts corresponding to thenonzero elements in X.

col — Column subscripts
vector

Column subscripts, returned as a vector. Together, row and col specifythe X(row,col) subscripts corresponding to thenonzero elements in X.

If X is a multidimensional array with N> 2, then col is a linear index overthe N-1 trailing dimensions of X.This preserves the relation X(row(i),col(i)) == v(i).

v — Nonzero elements of X
vector

Nonzero elements of X, returned as a vector.

More About

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Linear Indices

A linear index allows use of a single subscriptto index into an array, such as A(k). MATLAB® treatsthe array as a single column vector with each column appended to thebottom of the previous column. Thus, linear indexing numbers the elementsin the columns from top to bottom, left to right.

For example, consider a 3-by-3 matrix. You can reference the A(2,2) elementwith A(5), and the A(2,3) elementwith A(8). The linear index changes depending onthe size of the array; A(5) returns a differentlylocated element for a 3-by-3 matrix than it does for a 4-by-4 matrix.

The sub2ind and ind2sub functionsare useful in converting between subscripts and linear indices.

Tips

  • To find array elements that meet a condition, use find inconjunction with a relational expression. For example, find(X<5) returnsthe linear indices to the elements in X that areless than 5.

  • To directly find the elements in X thatsatisfy the condition X<5, use X(X<5).Avoid function calls like X(find(X<5)), whichunnecessarily use find on a logical matrix.

  • When you execute find with a relationaloperation like X>1, it is important to rememberthat the result of the relational operation is a logical matrix ofones and zeros. For example, the command [row,col,v] = find(X>1) returnsa column vector of logical 1 (true)values for v.

  • The row and column subscripts, row and col,are related to the linear indices in k by k= sub2ind(size(X),row,col).

Extended Capabilities

This function fully supports GPU arrays. For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).

Version History

Introduced before R2006a

See Also

ind2sub | nonzeros | strfind | sub2ind | Short-Circuit AND | Short-Circuit OR | ismember

Topics

  • Find Array Elements That Meet a Condition
  • Array Indexing
  • Relational Operations
  • Sparse Matrices

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Find indices and values of nonzero elements (1)

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