speye

Sparse identity matrix

Syntax

S = speye

S = speye(n)

S = speye(n,m)

S = speye(sz)

S = speye(___,typename)

Description

S = speye returns a sparse scalar 1.

S = speye(n) returns a sparse n-by-n identity matrix, with ones on the main diagonal and zeros elsewhere.

S = speye(n,m) returns a sparse n-by-m matrix, with ones on the main diagonal and zeros elsewhere.

S = speye(sz) returns a matrix with ones on the main diagonal and zeros elsewhere. The size vector sz defines size(S). For example, speye([2 3]) returns a 2-by-3 matrix.

S = speye(___,typename) returns a sparse matrix of the specified data type. Specify the data type in addition to any of the input argument combinations in previous syntaxes. (since R2025a)

Examples

Square Sparse Identity Matrix

Create a 1000-by-1000 square sparse identity matrix and view the sparsity pattern.

I = speye(1000);
spy(I)

The result is the same as sparse(eye(1000)), but this latter version requires temporary storage for the full representation before it is converted to sparse storage.

Rectangular Sparse Identity Matrix

Create a 400-by-800 sparse identity matrix and view the pattern of nonzeros.

S = speye(400,800);
spy(S)

This command is equivalent to speye([400 800]).

Input Arguments

n, m — Dimension sizes

nonnegative integer scalars

Dimension sizes, specified as nonnegative integer scalars.

• If n is the only input argument, then S is an n-by-n identity matrix.

• If n or m is 0, then S is an empty matrix.

• If n or m is negative, then it is treated as 0.

Example: speye(4) creates a 4-by-4 identity matrix.

Example: speye(3,6) creates a 3-by-6 identity matrix.

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

typename — Output data type

"double" (default) | "single" | "logical"

Since R2025a

Output data type, specified as "double", "single", or "logical".

sz — Dimension sizes

two-element row vector

Dimension sizes, specified as a two-element row vector. The row vector is of the form [numRows numCols].

• If an element of sz is 0, then S is an empty matrix.

• If an element of sz is negative, then the element is treated as 0.

Example: speye([4 5]) creates a 4-by-5 matrix and is equivalent to speye(4,5).

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

Output Arguments

S — Output matrix

sparse matrix

Output matrix, returned as a sparse identity matrix.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

Thread-Based Environment

Run code in the background using MATLAB® backgroundPool or accelerate code with Parallel Computing Toolbox™ ThreadPool.

This function fully supports thread-based environments. For more information, see Run MATLAB Functions in Thread-Based Environment.

GPU Arrays

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

The speye function supports GPU array input with these usage notes and limitations:

• To run this function on a GPU and obtain a gpuArray output, use any of these syntaxes:

  • S = gpuArray.speye.

  • S = gpuArray.speye(n).

  • S = gpuArray.speye(n,m).

  • S = gpuArray.speye(sz).

  • S = gpuArray.speye(___,typename), where typename specifies the data type in addition to the input argument combinations in any of the previous syntaxes. (since R2025a)

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).

Version History

Introduced before R2006a

R2025a: Create single-precision sparse matrix

You can specify the output data type by specifying the typename argument as "double", "single", or "logical".