Compute the Schur decomposition of a matrix. More...

Public Member Functions
subroutine	la_s_schur (a, t, z, eigvals, overwrite_a, storage, err)

	la_real_eig_s_schur

subroutine	la_d_schur (a, t, z, eigvals, overwrite_a, storage, err)

	la_real_eig_d_schur

subroutine	la_q_schur (a, t, z, eigvals, overwrite_a, storage, err)

	la_real_eig_q_schur

subroutine	la_c_schur (a, t, z, eigvals, overwrite_a, storage, err)

	la_real_eig_c_schur

subroutine	la_z_schur (a, t, z, eigvals, overwrite_a, storage, err)

subroutine	la_real_eig_z_schur (a, t, z, eigvals, overwrite_a, storage, err)

subroutine	la_w_schur (a, t, z, eigvals, overwrite_a, storage, err)

	la_real_eig_w_schur

Detailed Description

Compute the Schur decomposition of a matrix.

This function computes the Schur decomposition of a real or complex matrix \( A \):

\( A = Z T Z^H \)

where \( Z \) is an orthonormal/unitary matrix and \( T \) is upper-triangular or quasi-upper-triangular. The input matrix \( A \) has size \( [m, m] \).

The decomposition is available for both real and complex matrices:

For real matrices, the Schur form \( T \) may contain 2x2 blocks for complex eigenvalues.
For complex matrices, \( T \) is always upper-triangular.

Parameters

[in,out]	A	The input matrix of size \( [m, m] \). Can be overwritten if `overwrite_a` is set.
[out]	T	The upper-triangular or quasi-upper-triangular matrix of size \( [m, m] \).
[out]	Z	(Optional) The unitary/orthonormal transformation matrix of size \( [m, m] \).
[out]	eigvals	(Optional) The eigenvalues that appear on the diagonal of \( T \). For real matrices, this is a real-valued array. For complex matrices, this is a complex-valued array.
[in,out]	storage	(Optional) Pre-allocated workspace array. If provided, no internal allocations occur.
[in]	overwrite_a	(Optional) Logical flag indicating whether \( A \) can be overwritten.
[out]	err	(Optional) State return flag. If not provided, the function will stop on error.

Note: The computation is based on LAPACK's Schur decomposition routines (GEES).

Warning: Ensure that overwrite_a is set correctly to avoid unintended modification of \( A \).

Member Function/Subroutine Documentation

◆ la_c_schur()

subroutine la_schur::schur::la_c_schur	(	complex(sp), dimension(:,:), intent(inout), target	a,
		complex(sp), dimension(:,:), intent(out), target, contiguous	t,
		complex(sp), dimension(:,:), intent(out), optional, target, contiguous	z,
		complex(sp), dimension(:), intent(out), optional, target, contiguous	eigvals,
		logical(lk), intent(in), optional	overwrite_a,
		complex(sp), dimension(:), intent(inout), optional, target	storage,
		type(la_state), intent(out), optional	err )

Parameters

[in,out]	a	Input matrix a[m,m]
[out]	t	Schur form of A: upper-triangular or quasi-upper-triangular matrix T
[out]	z	Unitary/orthonormal transformation matrix Z
[out]	eigvals	[optional] Output eigenvalues that appear on the diagonal of T
[in,out]	storage	[optional] Provide pre-allocated workspace, size to be checked with schur_space
[in]	overwrite_a	[optional] Can A data be overwritten and destroyed?
[out]	err	[optional] State return flag. On error if not requested, the code will stop

◆ la_d_schur()

subroutine la_schur::schur::la_d_schur	(	real(dp), dimension(:,:), intent(inout), target	a,
		real(dp), dimension(:,:), intent(out), target, contiguous	t,
		real(dp), dimension(:,:), intent(out), optional, target, contiguous	z,
		complex(dp), dimension(:), intent(out), optional, target, contiguous	eigvals,
		logical(lk), intent(in), optional	overwrite_a,
		real(dp), dimension(:), intent(inout), optional, target	storage,
		type(la_state), intent(out), optional	err )

Parameters

[in,out]	a	Input matrix a[m,m]
[out]	t	Schur form of A: upper-triangular or quasi-upper-triangular matrix T
[out]	z	Unitary/orthonormal transformation matrix Z
[out]	eigvals	[optional] Output eigenvalues that appear on the diagonal of T
[in,out]	storage	[optional] Provide pre-allocated workspace, size to be checked with schur_space
[in]	overwrite_a	[optional] Can A data be overwritten and destroyed?
[out]	err	[optional] State return flag. On error if not requested, the code will stop

◆ la_q_schur()

subroutine la_schur::schur::la_q_schur	(	real(qp), dimension(:,:), intent(inout), target	a,
		real(qp), dimension(:,:), intent(out), target, contiguous	t,
		real(qp), dimension(:,:), intent(out), optional, target, contiguous	z,
		complex(qp), dimension(:), intent(out), optional, target, contiguous	eigvals,
		logical(lk), intent(in), optional	overwrite_a,
		real(qp), dimension(:), intent(inout), optional, target	storage,
		type(la_state), intent(out), optional	err )

Parameters

[in,out]	a	Input matrix a[m,m]
[out]	t	Schur form of A: upper-triangular or quasi-upper-triangular matrix T
[out]	z	Unitary/orthonormal transformation matrix Z
[out]	eigvals	[optional] Output eigenvalues that appear on the diagonal of T
[in,out]	storage	[optional] Provide pre-allocated workspace, size to be checked with schur_space
[in]	overwrite_a	[optional] Can A data be overwritten and destroyed?
[out]	err	[optional] State return flag. On error if not requested, the code will stop

◆ la_real_eig_c_schur()

la_schur::schur::la_real_eig_c_schur

◆ la_real_eig_d_schur()

la_schur::schur::la_real_eig_d_schur

◆ la_real_eig_q_schur()

la_schur::schur::la_real_eig_q_schur

◆ la_real_eig_s_schur()

la_schur::schur::la_real_eig_s_schur

◆ la_real_eig_w_schur()

la_schur::schur::la_real_eig_w_schur

◆ la_real_eig_z_schur()

subroutine la_schur::schur::la_real_eig_z_schur	(	complex(dp), dimension(:,:), intent(inout), target	a,
		complex(dp), dimension(:,:), intent(out), target, contiguous	t,
		complex(dp), dimension(:,:), intent(out), optional, target, contiguous	z,
		real(dp), dimension(:), intent(out), target, contiguous	eigvals,
		logical(lk), intent(in), optional	overwrite_a,
		complex(dp), dimension(:), intent(inout), optional, target	storage,
		type(la_state), intent(out), optional	err )

Parameters

[in,out]	a	Input matrix a[m,m]
[out]	t	Schur form of A: upper-triangular or quasi-upper-triangular matrix T
[out]	z	Unitary/orthonormal transformation matrix Z
[out]	eigvals	Output eigenvalues that appear on the diagonal of T
[in,out]	storage	[optional] Provide pre-allocated workspace, size to be checked with schur_space
[in]	overwrite_a	[optional] Can A data be overwritten and destroyed?
[out]	err	[optional] State return flag. On error if not requested, the code will stop

◆ la_s_schur()

subroutine la_schur::schur::la_s_schur	(	real(sp), dimension(:,:), intent(inout), target	a,
		real(sp), dimension(:,:), intent(out), target, contiguous	t,
		real(sp), dimension(:,:), intent(out), optional, target, contiguous	z,
		complex(sp), dimension(:), intent(out), optional, target, contiguous	eigvals,
		logical(lk), intent(in), optional	overwrite_a,
		real(sp), dimension(:), intent(inout), optional, target	storage,
		type(la_state), intent(out), optional	err )

Parameters

[in,out]	a	Input matrix a[m,m]
[out]	t	Schur form of A: upper-triangular or quasi-upper-triangular matrix T
[out]	z	Unitary/orthonormal transformation matrix Z
[out]	eigvals	[optional] Output eigenvalues that appear on the diagonal of T
[in,out]	storage	[optional] Provide pre-allocated workspace, size to be checked with schur_space
[in]	overwrite_a	[optional] Can A data be overwritten and destroyed?
[out]	err	[optional] State return flag. On error if not requested, the code will stop

◆ la_w_schur()

subroutine la_schur::schur::la_w_schur	(	complex(qp), dimension(:,:), intent(inout), target	a,
		complex(qp), dimension(:,:), intent(out), target, contiguous	t,
		complex(qp), dimension(:,:), intent(out), optional, target, contiguous	z,
		complex(qp), dimension(:), intent(out), optional, target, contiguous	eigvals,
		logical(lk), intent(in), optional	overwrite_a,
		complex(qp), dimension(:), intent(inout), optional, target	storage,
		type(la_state), intent(out), optional	err )

Parameters

[in,out]	a	Input matrix a[m,m]
[out]	t	Schur form of A: upper-triangular or quasi-upper-triangular matrix T
[out]	z	Unitary/orthonormal transformation matrix Z
[out]	eigvals	[optional] Output eigenvalues that appear on the diagonal of T
[in,out]	storage	[optional] Provide pre-allocated workspace, size to be checked with schur_space
[in]	overwrite_a	[optional] Can A data be overwritten and destroyed?
[out]	err	[optional] State return flag. On error if not requested, the code will stop

◆ la_z_schur()

subroutine la_schur::schur::la_z_schur	(	complex(dp), dimension(:,:), intent(inout), target	a,
		complex(dp), dimension(:,:), intent(out), target, contiguous	t,
		complex(dp), dimension(:,:), intent(out), optional, target, contiguous	z,
		complex(dp), dimension(:), intent(out), optional, target, contiguous	eigvals,
		logical(lk), intent(in), optional	overwrite_a,
		complex(dp), dimension(:), intent(inout), optional, target	storage,
		type(la_state), intent(out), optional	err )

Parameters

[in,out]	a	Input matrix a[m,m]
[out]	t	Schur form of A: upper-triangular or quasi-upper-triangular matrix T
[out]	z	Unitary/orthonormal transformation matrix Z
[out]	eigvals	[optional] Output eigenvalues that appear on the diagonal of T
[in,out]	storage	[optional] Provide pre-allocated workspace, size to be checked with schur_space
[in]	overwrite_a	[optional] Can A data be overwritten and destroyed?
[out]	err	[optional] State return flag. On error if not requested, the code will stop

The documentation for this interface was generated from the following file:

la_schur.f90

Public Member Functions

Detailed Description

Member Function/Subroutine Documentation

◆ la_c_schur()

◆ la_d_schur()

◆ la_q_schur()

◆ la_real_eig_c_schur()

◆ la_real_eig_d_schur()

◆ la_real_eig_q_schur()

◆ la_real_eig_s_schur()

◆ la_real_eig_w_schur()

◆ la_real_eig_z_schur()

◆ la_s_schur()

◆ la_w_schur()

◆ la_z_schur()