linalg_eigen – LINALG

private pure subroutine eigen_symm(a, vals, vecs)

Computes the eigenvalues, and optionally the eigenvectors, of a matrix by solving the eigenvalue problem $A \vec{v} = \lambda \vec{v}$ when $A$ is a symmetric matrix.

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=real64),	intent(in),		dimension(:,:)	::	a	The N-by-N symmetric matrix on which to operate.
real(kind=real64),	intent(out),		dimension(:)	::	vals	An N-element array that will contain the eigenvalues sorted into ascending order.
real(kind=real64),	intent(out),	optional,	dimension(:,:)	::	vecs	If present, the eigenvectors will be computed and this matrix will contain the eigenvectors (one per column) corresponding to each eigenvalue in vals.

private pure subroutine eigen_asymm(a, vals, rvecs, lvecs)

Computes the eigenvalues, and optionally the eigenvectors, of a matrix by solving the eigenvalue problem $A \vec{v} = \lambda \vec{v}$ when $A$ is square, but not necessarily symmetric.

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=real64),	intent(in),		dimension(:,:)	::	a	On input, the N-by-N matrix on which to operate. On output, the contents of this matrix are overwritten.
complex(kind=real64),	intent(out),		dimension(:)	::	vals	An N-element array containing the eigenvalues of the matrix. The eigenvalues are not sorted.
complex(kind=real64),	intent(out),	optional,	dimension(:,:)	::	rvecs	An optional N-by-N matrix, that if supplied, signals to compute the right eigenvectors (one per column).
complex(kind=real64),	intent(out),	optional,	dimension(:,:)	::	lvecs	An optional N-by-N matrix, that if supplied, signals to compute the left eigenvectors (one per column).

private pure subroutine eigen_gen(a, b, alpha, beta, rvecs, lvecs)

Computes the eigenvalues, and optionally the eigenvectors, by solving the eigenvalue problem: $A X = \lambda B X$ .

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=real64),	intent(in),		dimension(:,:)	::	a	The N-by-N matrix $A$ .
real(kind=real64),	intent(in),		dimension(:,:)	::	b	The N-by-N matrix $B$ .
complex(kind=real64),	intent(out),		dimension(:)	::	alpha	An N-element array that, if beta is not supplied, contains the eigenvalues. If beta is supplied however, the eigenvalues must be computed as $\lambda = \alpha / \beta$ . This however, is not as trivial as it seems as it is entirely possible, and likely, that $\alpha / \beta$ can overflow or underflow. With that said, the values in $\alpha$ will always be less than and usually comparable with the NORM( $A$ ).
real(kind=real64),	intent(out),	optional,	dimension(:)	::	beta	An optional N-element array that if provided forces alpha to return the numerator, and this array contains the denominator used to determine the eigenvalues as $\lambda = \alpha / \beta$ . If used, the values in this array will always be less than and usually comparable with the NORM( $B$ ).
complex(kind=real64),	intent(out),	optional,	dimension(:,:)	::	rvecs	An optional N-by-N matrix, that if supplied, signals to compute the right eigenvectors (one per column).
complex(kind=real64),	intent(out),	optional,	dimension(:,:)	::	lvecs	An optional N-by-N matrix, that if supplied, signals to compute the left eigenvectors (one per column).

private pure subroutine eigen_cmplx(a, vals, rvecs, lvecs)

Computes the eigenvalues, and optionally the eigenvectors, of a matrix by solving the eigenvalue problem $A \vec{v} = \lambda \vec{v}$ when $A$ is square, but not necessarily symmetric.

Arguments

Type	Intent	Optional	Attributes		Name
complex(kind=real64),	intent(in),		dimension(:,:)	::	a	The N-by-N matrix on which to operate.
complex(kind=real64),	intent(out),		dimension(:)	::	vals	An N-element array containing the eigenvalues of the matrix. The eigenvalues are not sorted.
complex(kind=real64),	intent(out),	optional,	dimension(:,:)	::	rvecs	An optional N-by-N matrix, that if supplied, signals to compute the right eigenvectors (one per column).
complex(kind=real64),	intent(out),	optional,	dimension(:,:)	::	lvecs	An optional N-by-N matrix, that if supplied, signals to compute the left eigenvectors (one per column).

linalg_eigen Module

Contents

Interfaces

Uses

Interfaces

public interface eigen

private pure subroutine eigen_symm(a, vals, vecs)

Arguments

private pure subroutine eigen_asymm(a, vals, rvecs, lvecs)

Arguments

private pure subroutine eigen_gen(a, b, alpha, beta, rvecs, lvecs)

Arguments

private pure subroutine eigen_cmplx(a, vals, rvecs, lvecs)

Arguments