An interface to the eigenvalue and eigenvector routines.
Computes the eigenvalues, and optionally the eigenvectors, of a matrix by solving the eigenvalue problem when is a symmetric matrix.
| 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. |
Computes the eigenvalues, and optionally the eigenvectors, of a matrix by solving the eigenvalue problem when is square, but not necessarily symmetric.
| 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). |
Computes the eigenvalues, and optionally the eigenvectors, by solving the eigenvalue problem: .
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| real(kind=real64), | intent(in), | dimension(:,:) | :: | a |
The N-by-N matrix . |
|
| real(kind=real64), | intent(in), | dimension(:,:) | :: | b |
The N-by-N matrix . |
|
| 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 . This however, is not as trivial as it seems as it is entirely possible, and likely, that can overflow or underflow. With that said, the values in will always be less than and usually comparable with the NORM(). |
|
| 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 . If used, the values in this array will always be less than and usually comparable with the NORM(). |
| 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). |
Computes the eigenvalues, and optionally the eigenvectors, of a matrix by solving the eigenvalue problem when is square, but not necessarily symmetric.
| 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). |