stdlib_experimental_linalg.md

title
experimental_linalg

Linear Algebra

[TOC]

diag - Create a diagonal array or extract the diagonal elements of an array

Description

Create a diagonal array or extract the diagonal elements of an array

Syntax

d = diag(a [, k])

Arguments

a: Shall be a rank-1 or or rank-2 array. If a is a rank-1 array (i.e. a vector) then diag returns a rank-2 array with the elements of a on the diagonal. If a is a rank-2 array (i.e. a matrix) then diag returns a rank-1 array of the diagonal elements.

k (optional): Shall be a scalar of type integer and specifies the diagonal. The default k = 0 represents the main diagonal, k > 0 are diagonals above the main diagonal, k < 0 are diagonals below the main diagonal.

Return value

Returns a diagonal array or a vector with the extracted diagonal elements.

Example

program demo_diag1
    use stdlib_experimental_linalg, only: diag
    implicit none
    real, allocatable :: A(:,:)
    integer :: i
    A = diag([(1,i=1,10)]) ! creates a 10 by 10 identity matrix
end program demo_diag1

program demo_diag2
    use stdlib_experimental_linalg, only: diag
    implicit none
    real :: v(:)
    real, allocatable :: A(:,:)
    integer :: i
    v = [1,2,3,4,5]
    A = diag(v) ! creates a 5 by 5 matrix with elements of v on the diagonal
end program demo_diag2

program demo_diag3
    use stdlib_experimental_linalg, only: diag
    implicit none
    integer, parameter :: n = 10
    real :: c(n), ul(n-1)
    real :: A(n,n)
    integer :: i
    c = 2
    ul = -1
    A = diag(ul,-1) + diag(c) + diag(ul,1) ! Gil Strang's favorite matrix
end program demo_diag3

program demo_diag4
    use stdlib_experimental_linalg, only: diag
    implicit none
    integer, parameter :: n = 12
    real :: A(n,n)
    real :: v(n)
    integer :: i
    call random_number(A)
    v = diag(A) ! v contains diagonal elements of A
end program demo_diag4

program demo_diag5
    use stdlib_experimental_linalg, only: diag
    implicit none
    integer, parameter :: n = 3
    real :: A(n,n)
    real, allocatable :: v(:)
    integer :: i
    A = reshape([1,2,3,4,5,6,7,8,9],[n,n])
    v = diag(A,-1) ! v is [2,6]
    v = diag(A,1)  ! v is [4,8]
end program demo_diag5

eye - Construct the identity matrix

Description

Construct the identity matrix

Syntax

I = eye(n)

Arguments

n: Shall be a scalar of default type integer.

Return value

Returns the identity matrix, i.e. a square matrix with ones on the main diagonal and zeros elsewhere. The return value is of type integer(int8).

Example

program demo_eye1
    use stdlib_experimental_linalg, only: eye
    implicit none
    real :: a(3,3)
    A = eye(3)
end program demo_eye1

program demo_eye2
    use stdlib_experimental_linalg, only: eye, diag
    implicit none
    print *, all(eye(4) == diag([1,1,1,1])) ! prints .true.
end program demo_eye2

trace - Trace of a matrix

Description

Trace of a matrix (rank-2 array)

Syntax

result = trace(A)

Arguments

A: Shall be a rank-2 array. If A is not square, then trace(A) will return the sum of diagonal values from the square sub-section of A.

Return value

Returns the trace of the matrix, i.e. the sum of diagonal elements.

Example

program demo_trace
    use stdlib_experimental_linalg, only: trace
    implicit none
    real :: A(3,3)
    A = reshape([1,2,3,4,5,6,7,8,9],[3,3])
    print *, trace(A) ! 1 + 5 + 9
end program demo_trace