diag

Create diagonal matrix or get diagonal elements of matrix

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Syntax

D = diag(v)

D = diag(v,k)

x = diag(A)

x = diag(A,k)

Description

example

D = diag(v) returns a square diagonal matrix with the elements of vector v on the main diagonal.

example

D = diag(v,k) places the elements of vector v on the kth diagonal. k=0 represents the main diagonal, k>0 is above the main diagonal, and k<0 is below the main diagonal.

example

x = diag(A) returns a column vector of the main diagonal elements of A.

example

x = diag(A,k) returns a column vector of the elements on the kth diagonal of A.

Examples

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Create Diagonal Matrices

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Create a 1-by-5 vector.

v = [2 1 -1 -2 -5];

Use diag to create a matrix with the elements of v on the main diagonal.

D = diag(v)

D = 5×5

     2     0     0     0     0
     0     1     0     0     0
     0     0    -1     0     0
     0     0     0    -2     0
     0     0     0     0    -5

Create a matrix with the elements of v on the first super diagonal (k=1).

D1 = diag(v,1)

D1 = 6×6

     0     2     0     0     0     0
     0     0     1     0     0     0
     0     0     0    -1     0     0
     0     0     0     0    -2     0
     0     0     0     0     0    -5
     0     0     0     0     0     0

The result is a 6-by-6 matrix. When you specify a vector of length n as an input, diag returns a square matrix of size n+abs(k).

Get Diagonal Elements

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Get the elements on the main diagonal of a random 6-by-6 matrix.

A = randi(10,6)

A = 6×6

     9     3    10     8     7     8
    10     6     5    10     8     1
     2    10     9     7     8     3
    10    10     2     1     4     1
     7     2     5     9     7     1
     1    10    10    10     2     9

x = diag(A)

Get the elements on the first subdiagonal (k=-1) of A. The result has one fewer element than the main diagonal.

x1 = diag(A,-1)

Calling diag twice returns a diagonal matrix composed of the diagonal elements of the original matrix.

A1 = diag(diag(A))

A1 = 6×6

     9     0     0     0     0     0
     0     6     0     0     0     0
     0     0     9     0     0     0
     0     0     0     1     0     0
     0     0     0     0     7     0
     0     0     0     0     0     9

Input Arguments

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`v` — Diagonal elements
vector

Diagonal elements, specified as a vector. If v is a vector with N elements, then diag(v,k) is a square matrix of order N+abs(k).

diag([]) returns an empty matrix, [].

`A` — Input matrix
matrix

Input matrix. diag returns an error if ndims(A) > 2.

diag([]) returns an empty matrix, [].

`k` — Diagonal number
integer

Diagonal number, specified as an integer. k=0 represents the main diagonal, k>0 is above the main diagonal, and k<0 is below the main diagonal.

For an m-by-n matrix, k is in the range $(- m + 1) \leq k \leq (n - 1) .$

Tips

The trace of a matrix is equal to sum(diag(A)).

Extended Capabilities

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

Usage notes and limitations:

If you supply k, then it must be a real and scalar integer value.
For variable-size inputs that are variable-length vectors (1-by-: or :-by-1), diag:
- Treats the input as a vector
- Returns a matrix with the input vector along the specified diagonal
For variable-size inputs that are not variable-length vectors, diag:
- Treats the input as a matrix
- Does not support inputs that are vectors at run time
- Returns a variable-length vector
If the input is variable-size (:m-by-:n) and has shape 0-by-0 at run time, then the output is 0-by-1, not 0-by-0. However, if the input is a constant size 0-by-0, then the output is [].
For variable-size inputs that are not variable-length vectors (1-by-: or :-by-1), diag treats the input as a matrix from which to extract a diagonal vector. This behavior occurs even if the input array is a vector at run time. To force diag to build a matrix from variable-size inputs that are not 1-by-: or :-by-1, use:
- diag(x(:)) instead of diag(x)
- diag(x(:),k) instead of diag(x,k)
See Variable-Sizing Restrictions for Code Generation of Toolbox Functions (MATLAB Coder).

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

Usage notes and limitations:

If you supply k, then it must be a real and scalar integer value.
For variable-size inputs that are variable-length vectors (1-by-: or :-by-1), diag:
- Treats the input as a vector
- Returns a matrix with the input vector along the specified diagonal
For variable-size inputs that are not variable-length vectors, diag:
- Treats the input as a matrix
- Does not support inputs that are vectors at run time
- Returns a variable-length vector
If the input is variable-size (:m-by-:n) and has shape 0-by-0 at run time, then the output is 0-by-1, not 0-by-0. However, if the input is a constant size 0-by-0, then the output is [].
For variable-size inputs that are not variable-length vectors (1-by-: or :-by-1), diag treats the input as a matrix from which to extract a diagonal vector. This behavior occurs even if the input array is a vector at run time. To force diag to build a matrix from variable-size inputs that are not 1-by-: or :-by-1, use:
- diag(x(:)) instead of diag(x)
- diag(x(:),k) instead of diag(x,k)

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).

Documentation

diag

Syntax

Description

Examples

Create Diagonal Matrices

Get Diagonal Elements

Input Arguments

`v` — Diagonal elements
vector

`A` — Input matrix
matrix

`k` — Diagonal number
integer

Tips

Extended Capabilities

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

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

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

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

See Also

MATLAB Documentation

Support

Documentation

diag

Syntax

Description

Examples

Create Diagonal Matrices

Get Diagonal Elements

Input Arguments

v — Diagonal elements vector

A — Input matrix matrix

k — Diagonal number integer

Tips

Extended Capabilities

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

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

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

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

See Also

MATLAB Documentation

Support

`v` — Diagonal elements
vector

`A` — Input matrix
matrix

`k` — Diagonal number
integer

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

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

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

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