# sub2ind

Convert subscripts to linear indices

## Description

example

ind = sub2ind(sz,row,col) returns the linear indices ind corresponding to the row and column subscripts in row and col for a matrix of size sz. Here sz is a vector with two elements, where sz(1) specifies the number of rows and sz(2) specifies the number of columns.

example

ind = sub2ind(sz,I1,I2,...,In) returns the linear indices ind corresponding to multidimensional subscripts in n arrays I1,I2,...,In for a multidimensional array of size sz. Here sz is a vector with n elements that specifies the size of each array dimension.

## Examples

collapse all

The mapping from subscripts (indexing by position) to linear indices for a 3-by-3 matrix can be illustrated as in the following.

Specify the row and column subscripts in a 3-by-3 matrix. Convert the subscripts to linear indices.

row = [1 2 3 1];
col = [2 2 2 3];
sz = [3 3];
ind = sub2ind(sz,row,col)
ind = 1×4

4     5     6     7

The mapping from subscripts to linear indices for a 2-by-2-by-2 array can be illustrated as in the following.

Specify the row, column, and page subscripts in a 2-by-2-by-2 array. Convert the subscripts to linear indices.

I1 = [1 2 1 2];
I2 = [2 2 1 1];
I3 = [1 1 2 2];
sz = [2 2 2];
ind = sub2ind(sz,I1,I2,I3)
ind = 1×4

3     4     5     6

Convert a subscript index of a 3-D array to a single linear index.

Create an array, and find the linear index corresponding to the element in the (2,1,2) position.

A = rand(3,4,2);
linearInd = sub2ind(size(A),2,1,2)
linearInd = 14

Check that both index versions refer to the same element.

A(2,1,2)
ans = 0.4854
A(14)
ans = 0.4854

## Input Arguments

collapse all

Size of array, specified as a vector of positive integers. Each element of this vector indicates the size of the corresponding dimension. For example, [2 3 4] defines a 2-by-3-by-4 array.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Row subscripts, specified as a scalar, vector, matrix, or multidimensional array. row and col can be arrays of the same size, or either one can be scalar.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Column subscripts, specified as a scalar, vector, matrix, or multidimensional array. row and col can be arrays of the same size, or either one can be scalar.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Multidimensional subscripts, specified as a scalar, vector, matrix, or multidimensional array. I1,I2,…,In can be arrays of the same size, or any of them can be scalar.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

## Output Arguments

collapse all

Linear indices, returned as a scalar, vector, matrix, or multidimensional array.

• If the subscript inputs all have the same size, then ind is also that size.

• If the subscript inputs are a mix of scalars and arrays, then ind has the size of the nonscalar subscript inputs.

Data Types: double

## Algorithms

For an array A, if ind = sub2ind(size(A),I1,…,In), then A(ind(k)) = A(I1(k),…,In(k)) for all k.

## Version History

Introduced before R2006a

expand all