eig Interface

public interface eig

This interface overloads the eig interface from stdlib_linalg to compute the eigenvalues and eigenvectors of a real-valued matrix whose type is Circulant.

Syntax

   call eig(A, lambda [, left] [, right])

Arguments

  • A : real-valued matrix of Circulant. It is an intent(in) argument.

  • lambda : Rank-1 real array returning the eigenvalues of A in increasing order. It is an intent(out) argument.

  • left (optional) : complex rank-2 array of the same kind as A returning the left eigenvectors of A. It is an intent(out) argument.

  • right (optional) : complex rank-2 array of the same kind as A returning the right eigenvectors of A. It is an intent(out) argument.

Note

Eigenvalues of a circulant matrix can be efficiently computed using the Fast Fourier Transform of the generating vector c. Likewise, its eigenvectors are simply the corresponding Fourier modes.


Subroutines

private module subroutine eig_rdp(A, lambda, left, right)

Utility function to compute the eigenvalues and eigenvectors of a Circulant matrix.

Arguments

Type IntentOptional Attributes Name
type(Circulant), intent(in) :: A

Input matrix.
complex(kind=dp), intent(out) :: lambda(:)

Eigenvalues.
complex(kind=dp), intent(out), optional :: left(:,:)

Eigenvectors.
complex(kind=dp), intent(out), optional :: right(:,:)

Eigenvectors.