schur Interface
-
- experimental
- 74 statements
- Source File
public interface schur
Computes the Schur decomposition of matrix . (Specification)
Summary
Compute the Schur decomposition of a real or complex matrix: , where is
orthonormal/unitary and is upper-triangular or quasi-upper-triangular. Matrix has size [m,m].
Description
This interface provides methods for computing the Schur decomposition of a matrix.
Supported data types include real and complex. If a pre-allocated workspace is provided, no internal
memory allocations take place when using this interface.
The output matrix is upper-triangular for complex input matrices and quasi-upper-triangular
for real input matrices (with possible blocks on the diagonal).
Note
The solution is based on LAPACK's Schur decomposition routines (*GEES).
Subroutines
private module subroutine stdlib_linalg_c_schur(a, t, z, eigvals, overwrite_a, storage, err)
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| complex(kind=sp), | intent(inout), | target | :: | a(:,:) |
Input matrix a[m,m] |
|
| complex(kind=sp), | intent(out), | contiguous, target | :: | t(:,:) |
Schur form of A: upper-triangular or quasi-upper-triangular matrix T |
|
| complex(kind=sp), | intent(out), | optional, | contiguous, target | :: | z(:,:) |
Unitary/orthonormal transformation matrix Z |
| complex(kind=sp), | intent(out), | optional, | contiguous, target | :: | eigvals(:) |
[optional] Output eigenvalues that appear on the diagonal of T |
| logical(kind=lk), | intent(in), | optional | :: | overwrite_a |
[optional] Can A data be overwritten and destroyed? |
|
| complex(kind=sp), | intent(inout), | optional, | target | :: | storage(:) |
[optional] Provide pre-allocated workspace, size to be checked with schur_space |
| 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_d_schur(a, t, z, eigvals, overwrite_a, storage, err)
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| real(kind=dp), | intent(inout), | target | :: | a(:,:) |
Input matrix a[m,m] |
|
| real(kind=dp), | intent(out), | contiguous, target | :: | t(:,:) |
Schur form of A: upper-triangular or quasi-upper-triangular matrix T |
|
| real(kind=dp), | intent(out), | optional, | contiguous, target | :: | z(:,:) |
Unitary/orthonormal transformation matrix Z |
| complex(kind=dp), | intent(out), | optional, | contiguous, target | :: | eigvals(:) |
[optional] Output eigenvalues that appear on the diagonal of T |
| logical(kind=lk), | intent(in), | optional | :: | overwrite_a |
[optional] Can A data be overwritten and destroyed? |
|
| real(kind=dp), | intent(inout), | optional, | target | :: | storage(:) |
[optional] Provide pre-allocated workspace, size to be checked with schur_space |
| 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_real_eig_c_schur(a, t, z, eigvals, overwrite_a, storage, err)
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| complex(kind=sp), | intent(inout), | target | :: | a(:,:) |
Input matrix a[m,m] |
|
| complex(kind=sp), | intent(out), | contiguous, target | :: | t(:,:) |
Schur form of A: upper-triangular or quasi-upper-triangular matrix T |
|
| complex(kind=sp), | intent(out), | optional, | contiguous, target | :: | z(:,:) |
Unitary/orthonormal transformation matrix Z |
| real(kind=sp), | intent(out), | contiguous, target | :: | eigvals(:) |
Output real eigenvalues that appear on the diagonal of T |
|
| logical(kind=lk), | intent(in), | optional | :: | overwrite_a |
[optional] Can A data be overwritten and destroyed? |
|
| complex(kind=sp), | intent(inout), | optional, | target | :: | storage(:) |
[optional] Provide pre-allocated workspace, size to be checked with schur_space |
| 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_real_eig_d_schur(a, t, z, eigvals, overwrite_a, storage, err)
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| real(kind=dp), | intent(inout), | target | :: | a(:,:) |
Input matrix a[m,m] |
|
| real(kind=dp), | intent(out), | contiguous, target | :: | t(:,:) |
Schur form of A: upper-triangular or quasi-upper-triangular matrix T |
|
| real(kind=dp), | intent(out), | optional, | contiguous, target | :: | z(:,:) |
Unitary/orthonormal transformation matrix Z |
| real(kind=dp), | intent(out), | contiguous, target | :: | eigvals(:) |
Output real eigenvalues that appear on the diagonal of T |
|
| logical(kind=lk), | intent(in), | optional | :: | overwrite_a |
[optional] Can A data be overwritten and destroyed? |
|
| real(kind=dp), | intent(inout), | optional, | target | :: | storage(:) |
[optional] Provide pre-allocated workspace, size to be checked with schur_space |
| 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_real_eig_s_schur(a, t, z, eigvals, overwrite_a, storage, err)
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| real(kind=sp), | intent(inout), | target | :: | a(:,:) |
Input matrix a[m,m] |
|
| real(kind=sp), | intent(out), | contiguous, target | :: | t(:,:) |
Schur form of A: upper-triangular or quasi-upper-triangular matrix T |
|
| real(kind=sp), | intent(out), | optional, | contiguous, target | :: | z(:,:) |
Unitary/orthonormal transformation matrix Z |
| real(kind=sp), | intent(out), | contiguous, target | :: | eigvals(:) |
Output real eigenvalues that appear on the diagonal of T |
|
| logical(kind=lk), | intent(in), | optional | :: | overwrite_a |
[optional] Can A data be overwritten and destroyed? |
|
| real(kind=sp), | intent(inout), | optional, | target | :: | storage(:) |
[optional] Provide pre-allocated workspace, size to be checked with schur_space |
| 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_real_eig_z_schur(a, t, z, eigvals, overwrite_a, storage, err)
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| complex(kind=dp), | intent(inout), | target | :: | a(:,:) |
Input matrix a[m,m] |
|
| complex(kind=dp), | intent(out), | contiguous, target | :: | t(:,:) |
Schur form of A: upper-triangular or quasi-upper-triangular matrix T |
|
| complex(kind=dp), | intent(out), | optional, | contiguous, target | :: | z(:,:) |
Unitary/orthonormal transformation matrix Z |
| real(kind=dp), | intent(out), | contiguous, target | :: | eigvals(:) |
Output real eigenvalues that appear on the diagonal of T |
|
| logical(kind=lk), | intent(in), | optional | :: | overwrite_a |
[optional] Can A data be overwritten and destroyed? |
|
| complex(kind=dp), | intent(inout), | optional, | target | :: | storage(:) |
[optional] Provide pre-allocated workspace, size to be checked with schur_space |
| 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_s_schur(a, t, z, eigvals, overwrite_a, storage, err)
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| real(kind=sp), | intent(inout), | target | :: | a(:,:) |
Input matrix a[m,m] |
|
| real(kind=sp), | intent(out), | contiguous, target | :: | t(:,:) |
Schur form of A: upper-triangular or quasi-upper-triangular matrix T |
|
| real(kind=sp), | intent(out), | optional, | contiguous, target | :: | z(:,:) |
Unitary/orthonormal transformation matrix Z |
| complex(kind=sp), | intent(out), | optional, | contiguous, target | :: | eigvals(:) |
[optional] Output eigenvalues that appear on the diagonal of T |
| logical(kind=lk), | intent(in), | optional | :: | overwrite_a |
[optional] Can A data be overwritten and destroyed? |
|
| real(kind=sp), | intent(inout), | optional, | target | :: | storage(:) |
[optional] Provide pre-allocated workspace, size to be checked with schur_space |
| 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_z_schur(a, t, z, eigvals, overwrite_a, storage, err)
Arguments
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| complex(kind=dp), | intent(inout), | target | :: | a(:,:) |
Input matrix a[m,m] |
|
| complex(kind=dp), | intent(out), | contiguous, target | :: | t(:,:) |
Schur form of A: upper-triangular or quasi-upper-triangular matrix T |
|
| complex(kind=dp), | intent(out), | optional, | contiguous, target | :: | z(:,:) |
Unitary/orthonormal transformation matrix Z |
| complex(kind=dp), | intent(out), | optional, | contiguous, target | :: | eigvals(:) |
[optional] Output eigenvalues that appear on the diagonal of T |
| logical(kind=lk), | intent(in), | optional | :: | overwrite_a |
[optional] Can A data be overwritten and destroyed? |
|
| complex(kind=dp), | intent(inout), | optional, | target | :: | storage(:) |
[optional] Provide pre-allocated workspace, size to be checked with schur_space |
| type(linalg_state_type), | intent(out), | optional | :: | err |
[optional] State return flag. On error if not requested, the code will stop |