ind2sub

Convert linear indices to subscripts

Syntax

[row,col] = ind2sub(sz,ind)

[I1,I2,...,In] = ind2sub(sz,ind)

Description

[row,col] = ind2sub(sz,ind) returns the arrays row and col containing the equivalent row and column subscripts corresponding to the linear indices ind 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.

[I1,I2,...,In] = ind2sub(sz,ind) returns n arrays I1,I2,...,In containing the equivalent multidimensional subscripts corresponding to the linear indices ind for a multidimensional array of size sz. Here sz is a vector with n elements that specifies the size of each array dimension.

Examples

Convert Linear Indices to Subscripts for Matrix

Convert the linear indices [3 4 5 6] to row and column subscripts in a 3-by-3 matrix. The mapping from linear indices to subscripts (indexing by position) is illustrated in the following.

Create input vectors and perform the conversion.

ind = [3 4 5 6];
sz = [3 3];
[row,col] = ind2sub(sz,ind)

row = 1×4

     3     1     2     3

col = 1×4

     1     2     2     2

Convert Linear Indices to Subscripts for Three-Dimensional Array

Convert the linear indices [3 4 5 6] to subscripts in a 2-by-2-by-2 array. The mapping from linear indices to subscripts (indexing by position) for a 2-by-2-by-2 array can be illustrated as in the following.

Create input vectors and perform the conversion.

ind = [3 4 5 6];
sz = [2 2 2];
[I1,I2,I3] = ind2sub(sz,ind)

I1 = 1×4

     1     2     1     2

I2 = 1×4

     2     2     1     1

I3 = 1×4

     1     1     2     2

Access Element of 3-D Array

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

Create an array, and find the subscript index corresponding to the 14 th element of the array.

A = rand(3,4,2);
[row,col,page] = ind2sub(size(A),14)

row = 2

col = 1

page = 2

Check that both index versions refer to the same element of the array.

A(14)

ans = 0.4854

A(row,col,page)

ans = 0.4854

Use ind2sub with Fewer Output Arguments

When using ind2sub for an N-dimensional array, you would typically supply N output arguments for each dimension of the matrix. This example shows the different results when you return fewer output arguments for a 3-dimensional array.

Create the input arguments needed to convert the linear indices 1 through 8 for a 3-dimensional array with size 2-by-2-by-2.

ind = 1:8;
sz = [2 2 2];

Specify three output arguments when using ind2sub to return the row, column, and page subscripts for the 2-by-2-by-2 array.

[row,col,page] = ind2sub(sz,ind)

row = 1×8

     1     2     1     2     1     2     1     2

col = 1×8

     1     1     2     2     1     1     2     2

page = 1×8

     1     1     1     1     2     2     2     2

If you specify only two output arguments, ind2sub ignores the third dimension of the array and returns subscripts for a 2-dimensional array with size 2-by-4 instead.

[row,col] = ind2sub(sz,ind)

row = 1×8

     1     2     1     2     1     2     1     2

col = 1×8

     1     1     2     2     3     3     4     4

If you specify only one output argument, ind2sub ignores the second and third dimensions of the array and returns subscripts for a 1-dimensional array with size 1-by-8 instead.

row = ind2sub(sz,ind)

row = 1×8

     1     2     3     4     5     6     7     8

Input Arguments

sz — Size of array

vector of positive integers

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

ind — Linear indices

scalar | vector | matrix | multidimensional array

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

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

Output Arguments

row — Row subscripts

scalar | vector | matrix | multidimensional array

Row subscripts, returned as a scalar, vector, matrix, or multidimensional array. The size of row is the same as the size of the input ind.

Data Types: double

col — Column subscripts

scalar | vector | matrix | multidimensional array

Column subscripts, returned as a scalar, vector, matrix, or multidimensional array. The size of col is the same as the size of the input ind.

Data Types: double

I1,I2,...,In — Multidimensional subscripts

scalar | vector | matrix | multidimensional array

Multidimensional subscripts, returned as a scalar, vector, matrix, or multidimensional array. The size of each array I1,I2,…,In is the same as the size of the input ind.

Data Types: double

Tips

• To get the linear indices of matrix elements that satisfy a specific condition for matrix A, you can use the find function with one output argument. To get the subscript indices, use the find function with two output arguments. For example, [row,col] = ind2sub(size(A),find(A>5)) gives the same result as [row,col] = find(A>5).

Algorithms

For an array A, if [I1,…,In] = ind2sub(size(A),ind), then A(I1(k),…,In(k)) = A(ind(k)) for all k.

Extended Capabilities

Tall Arrays

Calculate with arrays that have more rows than fit in memory.

This function fully supports tall arrays. For more information, see Tall Arrays.

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

• The first argument must be a valid size vector. Size vectors for arrays with more than intmax elements are not supported.

• The generated code treats NaN inputs as out of range and throws a run-time error.

• See Variable-Sizing Restrictions for Code Generation of Toolbox Functions (MATLAB Coder).

GPU Arrays

Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

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

Distributed Arrays

Partition large arrays across the combined memory of your cluster using Parallel Computing Toolbox™.

This function fully supports distributed arrays. For more information, see Run MATLAB Functions with Distributed Arrays (Parallel Computing Toolbox).