eye

Identity matrix

Syntax

I = eye

I = eye(n)

I = eye(n,m)

I = eye(sz)

I = eye(___,typename)

I = eye(___,like=p)

Description

I = eye returns the scalar 1.

I = eye(n) returns an n-by-n identity matrix with ones on the main diagonal and zeros elsewhere.

I = eye(n,m) returns an n-by-m matrix with ones on the main diagonal and zeros elsewhere.

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

I = eye(___,typename) also specifies the data type (class) of I for any of the previous syntaxes. For example, eye(5,"int8") returns a 5-by-5 identity matrix consisting of 8-bit integers.

I = eye(___,like=p) specifies that I has the same data type, sparsity, and complexity (real or complex) as the numeric variable p.

Examples

Square Identity Matrix

Create a 4-by-4 identity matrix.

I = eye(4)

I = 4×4

     1     0     0     0
     0     1     0     0
     0     0     1     0
     0     0     0     1

Rectangular Matrix

Create a 2-by-3 identity matrix.

I = eye(2,3)

I = 2×3

     1     0     0
     0     1     0

Identity Vector

Create a 3-by-1 identity vector.

sz = [3,1];
I = eye(sz)

I = 3×1

     1
     0
     0

Nondefault Numeric Data Type

Create a 3-by-3 identity matrix whose elements are 32-bit unsigned integers.

I = eye(3,"uint32")

I = 3×3 uint32 matrix

   1   0   0
   0   1   0
   0   0   1

class(I)

ans = 
'uint32'

Complex Identity Matrix

Create a 2-by-2 identity matrix that is not real valued, but instead is complex like an existing array.

Define a complex vector.

p = [1+2i 3i];

Create an identity matrix that is complex like p.

I = eye(2,like=p)

I = 2×2 complex

   1.0000 + 0.0000i   0.0000 + 0.0000i
   0.0000 + 0.0000i   1.0000 + 0.0000i

Sparse Identity Matrix

Define a 5-by-5 sparse matrix.

p = sparse(5,5,pi);

Create a 5-by-5 identity matrix that is sparse like P.

I = eye(5,like=p)

I = 5×5 sparse double matrix (5 nonzeros)
   (1,1)        1
   (2,2)        1
   (3,3)        1
   (4,4)        1
   (5,5)        1

Size and Numeric Data Type Defined by Existing Array

Define a 2-by-2 matrix of single precision.

p = single([1 3; 2 4]);

Create an identity matrix that is the same size and data type as p.

I = eye(size(p),like=p)

I = 2×2 single matrix

     1     0
     0     1

class(I)

ans = 
'single'

Input Arguments

n — Size of first dimension of I

integer value

Size of first dimension of I, specified as an integer value.

• If n is the only integer input argument, then I is a square n-by-n identity matrix.

• If n is 0, then I is an empty matrix.

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

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

m — Size of second dimension of I

integer value

Size of second dimension of I, specified as an integer value.

• If m is 0, then I is an empty matrix.

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

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

sz — Size of I

row vector of no more than two integer values

Size of I, specified as a row vector of no more than two integer values.

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

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

Example: sz = [2 3] defines I as a 2-by-3 matrix.

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

typename — Output class

"double" (default) | "single" | "logical" | "int8" | "uint8" | ...

Output class, specified as "double", "single", "logical", "int8", "uint8", "int16", "uint16", "int32", "uint32", "int64", or "uint64".

p — Prototype

numeric variable

Prototype, specified as a numeric variable.

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

Output Arguments

I — Identity matrix

scalar | matrix

Identity matrix, returned as a scalar or matrix.

Extended Capabilities

C/C++ Code Generation

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

Usage notes and limitations:

• typename must be a built-in MATLAB^® numeric type. Does not invoke the static eye method for other classes. For example, eye(m, n, 'myclass') does not invoke myclass.eye(m,n).

• Size arguments must have a fixed size.

GPU Code Generation

Generate CUDA® code for NVIDIA® GPUs using GPU Coder™.

Usage notes and limitations:

• typename must be a built-in MATLAB numeric type. Does not invoke the static eye method for other classes. For example, eye(m, n, 'myclass') does not invoke myclass.eye(m,n).

• Size arguments must have a fixed size.

Thread-Based Environment

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

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

• You can specify typename as 'gpuArray'. If you specify typename as 'gpuArray', the default underlying type of the array is double.

  To create a GPU array with underlying type datatype, specify the underlying type as an additional argument before typename. For example, I = eye(3,datatype,'gpuArray') creates a 3-by-3 GPU identity matrix with underlying type datatype.

  You can specify the underlying type datatype as one of these options:

  • 'double'

  • 'single'

  • 'logical'

  • 'int8'

  • 'uint8'

  • 'int16'

  • 'uint16'

  • 'int32'

  • 'uint32'

  • 'int64'

  • 'uint64'

• You can also specify the numeric variable p as a gpuArray.

  If you specify p as a gpuArray, the underlying type of the returned array is the same as p.

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™.

The eye function supports distributed arrays with these usage notes and limitations:

• You can specify typename as 'codistributed' or 'distributed'. If you specify typename as 'codistributed' or 'distributed', the default underlying type of the returned array is double.

  To create a distributed or codistributed array with underlying type datatype, specify the underlying type as an additional argument before typename. For example, I = eye(3,datatype,'distributed') creates a 3-by-3 distributed identity matrix with underlying type datatype.

  You can specify the underlying type datatype as one of these options:

  • 'double'

  • 'single'

  • 'logical'

  • 'int8'

  • 'uint8'

  • 'int16'

  • 'uint16'

  • 'int32'

  • 'uint32'

  • 'int64'

  • 'uint64'

• You can also specify p as a codistributed or distributed array.

  If you specify p as a codistributed or distributed array, the underlying type of the returned array is the same as p.

• For additional codistributed syntaxes, see eye (codistributed) (Parallel Computing Toolbox).

For more information, see Run MATLAB Functions with Distributed Arrays (Parallel Computing Toolbox).

Version History

Introduced before R2006a