eigh Interface
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- experimental
- 34 statements
- Source File
public interface eigh
Solves the eigendecomposition for a real symmetric or complex Hermitian square matrix. (Specification)
Summary
Subroutine interface for computing eigenvalues and eigenvectors of a real symmetric or complex Hermitian square matrix.
Description
This interface provides methods for computing the eigenvalues, and optionally eigenvectors,
of a real symmetric or complex Hermitian square matrix. Supported data types include real and complex.
The matrix must be symmetric (if real) or Hermitian (if complex). Only the lower or upper
half of the matrix is accessed, and the user can select which using the optional upper_a
flag (default: use lower half). The vectors are orthogonal, and may be returned as columns of an optional
matrix vectors with the same kind and size as A.
Preallocated space for both eigenvalues lambda and the eigenvector matrix must be user-provided.
Note
The solution is based on LAPACK's eigenproblem solvers *SYEV/*HEEV.
Note
BLAS/LAPACK backends do not currently support extended precision (xdp).
Subroutines
private module subroutine stdlib_linalg_eigh_c(a, lambda, vectors, upper_a, overwrite_a, err)
Eigendecomposition of a real symmetric or complex Hermitian matrix A returning an array lambda
of eigenvalues, and optionally right or left eigenvectors.
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| complex(kind=sp), | intent(inout), | target | :: | a(:,:) |
Input matrix A[m,n] |
|
| real(kind=sp), | intent(out) | :: | lambda(:) |
Array of eigenvalues |
||
| complex(kind=sp), | intent(out), | optional, | target | :: | vectors(:,:) |
The columns of vectors contain the orthonormal eigenvectors of A |
| logical(kind=lk), | intent(in), | optional | :: | upper_a |
[optional] Should the upper/lower half of A be used? Default: lower |
|
| logical(kind=lk), | intent(in), | optional | :: | overwrite_a |
[optional] Can A data be overwritten and destroyed? |
|
| type(linalg_state_type), | intent(out), | optional | :: | err |
[optional] state return flag. On error if not requested, the code will stop |
private module subroutine stdlib_linalg_eigh_d(a, lambda, vectors, upper_a, overwrite_a, err)
Eigendecomposition of a real symmetric or complex Hermitian matrix A returning an array lambda
of eigenvalues, and optionally right or left eigenvectors.
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| real(kind=dp), | intent(inout), | target | :: | a(:,:) |
Input matrix A[m,n] |
|
| real(kind=dp), | intent(out) | :: | lambda(:) |
Array of eigenvalues |
||
| real(kind=dp), | intent(out), | optional, | target | :: | vectors(:,:) |
The columns of vectors contain the orthonormal eigenvectors of A |
| logical(kind=lk), | intent(in), | optional | :: | upper_a |
[optional] Should the upper/lower half of A be used? Default: lower |
|
| logical(kind=lk), | intent(in), | optional | :: | overwrite_a |
[optional] Can A data be overwritten and destroyed? |
|
| type(linalg_state_type), | intent(out), | optional | :: | err |
[optional] state return flag. On error if not requested, the code will stop |
private module subroutine stdlib_linalg_eigh_s(a, lambda, vectors, upper_a, overwrite_a, err)
Eigendecomposition of a real symmetric or complex Hermitian matrix A returning an array lambda
of eigenvalues, and optionally right or left eigenvectors.
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| real(kind=sp), | intent(inout), | target | :: | a(:,:) |
Input matrix A[m,n] |
|
| real(kind=sp), | intent(out) | :: | lambda(:) |
Array of eigenvalues |
||
| real(kind=sp), | intent(out), | optional, | target | :: | vectors(:,:) |
The columns of vectors contain the orthonormal eigenvectors of A |
| logical(kind=lk), | intent(in), | optional | :: | upper_a |
[optional] Should the upper/lower half of A be used? Default: lower |
|
| logical(kind=lk), | intent(in), | optional | :: | overwrite_a |
[optional] Can A data be overwritten and destroyed? |
|
| type(linalg_state_type), | intent(out), | optional | :: | err |
[optional] state return flag. On error if not requested, the code will stop |
private module subroutine stdlib_linalg_eigh_z(a, lambda, vectors, upper_a, overwrite_a, err)
Eigendecomposition of a real symmetric or complex Hermitian matrix A returning an array lambda
of eigenvalues, and optionally right or left eigenvectors.
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| complex(kind=dp), | intent(inout), | target | :: | a(:,:) |
Input matrix A[m,n] |
|
| real(kind=dp), | intent(out) | :: | lambda(:) |
Array of eigenvalues |
||
| complex(kind=dp), | intent(out), | optional, | target | :: | vectors(:,:) |
The columns of vectors contain the orthonormal eigenvectors of A |
| logical(kind=lk), | intent(in), | optional | :: | upper_a |
[optional] Should the upper/lower half of A be used? Default: lower |
|
| logical(kind=lk), | intent(in), | optional | :: | overwrite_a |
[optional] Can A data be overwritten and destroyed? |
|
| type(linalg_state_type), | intent(out), | optional | :: | err |
[optional] state return flag. On error if not requested, the code will stop |