Functions for solving non-symmetric standard eigenvalue problems on shared memory systems. More...

Computational functions
starneig_error_t	starneig_SEP_SM_Hessenberg (int n, double A[], int ldA, double Q[], int ldQ)
	Computes a Hessenberg decomposition of a general matrix. More...

starneig_error_t	starneig_SEP_SM_Schur (int n, double H[], int ldH, double Q[], int ldQ, double real[], double imag[])
	Computes a Schur decomposition given a Hessenberg decomposition. More...

starneig_error_t	starneig_SEP_SM_ReorderSchur (int n, int selected[], double S[], int ldS, double Q[], int ldQ, double real[], double imag[])
	Reorders selected eigenvalues to the top left corner of a Schur decomposition. More...

starneig_error_t	starneig_SEP_SM_Reduce (int n, double A[], int ldA, double Q[], int ldQ, double real[], double imag[], int(predicate)(double real, double imag, void arg), void arg, int selected[], int num_selected)
	Computes a (reordered) Schur decomposition of a general matrix. More...

starneig_error_t	starneig_SEP_SM_Eigenvectors (int n, int selected[], double S[], int ldS, double Q[], int ldQ, double X[], int ldX)
	Computes an eigenvector for each selected eigenvalue. More...

Helper functions
starneig_error_t	starneig_SEP_SM_Select (int n, double S[], int ldS, int(predicate)(double real, double imag, void arg), void arg, int selected[], int num_selected)
	Generates a selection array for a Schur matrix using a user-supplied predicate function. More...

Expert computational functions
starneig_error_t	starneig_SEP_SM_Hessenberg_expert (struct starneig_hessenberg_conf *conf, int n, int begin, int end, double A[], int ldA, double Q[], int ldQ)
	Computes a Hessenberg decomposition of a general matrix. More...

starneig_error_t	starneig_SEP_SM_Schur_expert (struct starneig_schur_conf *conf, int n, double H[], int ldH, double Q[], int ldQ, double real[], double imag[])
	Computes a Schur decomposition given a Hessenberg decomposition. More...

starneig_error_t	starneig_SEP_SM_ReorderSchur_expert (struct starneig_reorder_conf *conf, int n, int selected[], double S[], int ldS, double Q[], int ldQ, double real[], double imag[])
	Reorders selected eigenvalues to the top left corner of a Schur decomposition. More...

starneig_error_t	starneig_SEP_SM_Eigenvectors_expert (struct starneig_eigenvectors_conf *conf, int n, int selected[], double S[], int ldS, double Q[], int ldQ, double X[], int ldX)
	Computes an eigenvector for each selected eigenvalue. More...

Detailed Description

Functions for solving non-symmetric standard eigenvalue problems on shared memory systems.

Function Documentation

◆ starneig_SEP_SM_Hessenberg()

starneig_error_t starneig_SEP_SM_Hessenberg	(	int	n,
		double	A[],
		int	ldA,
		double	Q[],
		int	ldQ
	)

Computes a Hessenberg decomposition of a general matrix.

Parameters

[in]	n	The order of \(A\) and \(Q\).
[in,out]	A	On entry, the general matrix \(A\). On exit, the upper Hessenberg matrix \(H\).
[in]	ldA	The leading dimension of \(A\).
[in,out]	Q	On entry, the orthogonal matrix \(Q\). On exit, the product matrix \(Q * U\).
[in]	ldQ	The leading dimension of \(Q\).

Returns: STARNEIG_SUCCESS (0) on success. Negative integer -i when i'th argument is invalid. Positive error code otherwise.

Examples: sep_sm_full_chain.c.

◆ starneig_SEP_SM_Schur()

starneig_error_t starneig_SEP_SM_Schur	(	int	n,
		double	H[],
		int	ldH,
		double	Q[],
		int	ldQ,
		double	real[],
		double	imag[]
	)

Computes a Schur decomposition given a Hessenberg decomposition.

Parameters

[in]	n	The order of \(H\) and \(Q\).
[in,out]	H	On entry, the upper Hessenberg matrix \(H\). On exit, the Schur matrix \(S\).
[in]	ldH	The leading dimension of \(H\).
[in,out]	Q	On entry, the orthogonal matrix \(Q\). On exit, the product matrix \(Q * U\).
[in]	ldQ	The leading dimension of \(Q\).
[out]	real	An array of the same size as \(H\) containing the real parts of the computed eigenvalues.
[out]	imag	An array of the same size as \(H\) containing the imaginary parts of the computed eigenvalues.

Returns: STARNEIG_SUCCESS (0) on success. Negative integer -i when i'th argument is invalid. Positive error code otherwise. STARNEIG_DID_NOT_CONVERGE if the QR algorithm failed to converge.

Examples: sep_sm_full_chain.c.

◆ starneig_SEP_SM_ReorderSchur()

starneig_error_t starneig_SEP_SM_ReorderSchur	(	int	n,
		int	selected[],
		double	S[],
		int	ldS,
		double	Q[],
		int	ldQ,
		double	real[],
		double	imag[]
	)

Reorders selected eigenvalues to the top left corner of a Schur decomposition.

Parameters

[in]	n	The order of \(S\) and \(Q\).
[in,out]	selected	The selection array. On entry, the initial positions of the selected eigenvalues. On exit, the final positions of all correctly placed selected eigenvalues. In case of failure, the number of 1's in the output may be less than the number of 1's in the input.
[in,out]	S	On entry, the Schur matrix \(S\). On exit, the updated Schur matrix \(\hat{S}\).
[in]	ldS	The leading dimension of \(S\).
[in,out]	Q	On entry, the orthogonal matrix \(Q\). On exit, the product matrix \(Q * U\).
[in]	ldQ	The leading dimension of \(Q\).
[out]	real	An array of the same size as \(S\) containing the real parts of the computed eigenvalues.
[out]	imag	An array of the same size as \(S\) containing the imaginary parts of the computed eigenvalues.

Returns: STARNEIG_SUCCESS (0) on success. Negative integer -i when i'th argument is invalid. Positive error code otherwise. STARNEIG_PARTIAL_REORDERING if the Schur form is not fully reordered.

See also: starneig_SEP_SM_Select

Examples: sep_sm_full_chain.c.

◆ starneig_SEP_SM_Reduce()

starneig_error_t starneig_SEP_SM_Reduce	(	int	n,
		double	A[],
		int	ldA,
		double	Q[],
		int	ldQ,
		double	real[],
		double	imag[],
		int()(double real, double imag, void arg)	predicate,
		void *	arg,
		int	selected[],
		int *	num_selected
	)

Computes a (reordered) Schur decomposition of a general matrix.

Parameters

[in]	n	The order of \(A\) and \(Q\).
[in,out]	A	On entry, the general matrix \(A\). On exit, the Schur matrix \(S\).
[in]	ldA	The leading dimension of \(A\).
[in,out]	Q	On entry, the orthogonal matrix \(Q\). On exit, the product matrix \(Q * U\).
[in]	ldQ	The leading dimension of \(Q\).
[out]	real	An array of the same size as \(A\) containing the real parts of the computed eigenvalues.
[out]	imag	An array of the same size as \(A\) containing the imaginary parts of the computed eigenvalues.
[in]	predicate	A function that takes a (complex) eigenvalue as input and returns non-zero if it should be selected. For complex conjugate pairs of eigenvalues, the predicate is called only for the eigenvalue with positive imaginary part and the corresponding \(2 \times 2\) block is either selected or deselected. The reordering step is skipped if the argument is a NULL pointer.
[in]	arg	An optional argument for the predicate function.
[out]	selected	The final positions of all correctly placed selected eigenvalues.
[out]	num_selected	The number of selected eigenvalues (a complex conjugate pair is counted as two selected eigenvalues).

Returns: STARNEIG_SUCCESS (0) on success. Negative integer -i when i'th argument is invalid. Positive error code otherwise. STARNEIG_DID_NOT_CONVERGE if the QR algorithm failed to converge. STARNEIG_PARTIAL_REORDERING if the Schur form is not fully reordered.

Examples: sep_sm_eigenvectors.c.

◆ starneig_SEP_SM_Eigenvectors()

starneig_error_t starneig_SEP_SM_Eigenvectors	(	int	n,
		int	selected[],
		double	S[],
		int	ldS,
		double	Q[],
		int	ldQ,
		double	X[],
		int	ldX
	)

Computes an eigenvector for each selected eigenvalue.

Parameters

[in]	n	The order of \(S\) and \(Q\) and the number of rows of \(X\).
[in]	selected	The selection array specifying the locations of the selected eigenvalues. The number of 1's in the array is the same as the number of columns in \(X\).
[in]	S	The Schur matrix \(S\).
[in]	ldS	The leading dimension of \(S\).
[in]	Q	The orthogonal matrix \(Q\).
[in]	ldQ	The The leading dimension of \(Q\).
[out]	X	A matrix with \(n\) rows and one column for each selected eigenvalue. The columns represent the computed eigenvectors as previously described.
[in]	ldX	The leading dimension of \(X\).

Returns: STARNEIG_SUCCESS (0) on success. Negative integer -i when i'th argument is invalid. Positive error code otherwise.

See also: starneig_SEP_SM_Select

Examples: sep_sm_eigenvectors.c.

◆ starneig_SEP_SM_Select()

starneig_error_t starneig_SEP_SM_Select	(	int	n,
		double	S[],
		int	ldS,
		int()(double real, double imag, void arg)	predicate,
		void *	arg,
		int	selected[],
		int *	num_selected
	)

Generates a selection array for a Schur matrix using a user-supplied predicate function.

Parameters

[in]	n	The order of \(S\).
[in]	S	The Schur matrix \(S\).
[in]	ldS	The leading dimension of \(S\).
[in]	predicate	A function that takes a (complex) eigenvalue as input and returns non-zero if it should be selected. For complex conjugate pairs of eigenvalues, the predicate is called only for the eigenvalue with positive imaginary part and the corresponding \(2 \times 2\) block is either selected or deselected.
[in]	arg	An optional argument for the predicate function.
[out]	selected	The selection array. Both elements of a selected complex conjugate pair are set to 1.
[out]	num_selected	The number of selected eigenvalues (a complex conjugate pair is counted as two selected eigenvalues).

Returns: STARNEIG_SUCCESS (0) on success. Negative integer -i when i'th argument is invalid. Positive error code otherwise.

Examples: sep_sm_eigenvectors.c, and sep_sm_full_chain.c.

◆ starneig_SEP_SM_Hessenberg_expert()

starneig_error_t starneig_SEP_SM_Hessenberg_expert	(	struct starneig_hessenberg_conf *	conf,
		int	n,
		int	begin,
		int	end,
		double	A[],
		int	ldA,
		double	Q[],
		int	ldQ
	)

Computes a Hessenberg decomposition of a general matrix.

Parameters

[in]	conf	Configuration structure.
[in]	n	The order of \(A\) and \(Q\).
[in]	begin	First column to be reduced.
[in]	end	Last column to be reduced + 1.
[in,out]	A	On entry, the general matrix \(A\). On exit, the upper Hessenberg matrix \(H\).
[in]	ldA	The leading dimension of \(A\).
[in,out]	Q	On entry, the orthogonal matrix \(Q\). On exit, the product matrix \(Q * U\).
[in]	ldQ	The leading dimension of \(Q\).

Returns: STARNEIG_SUCCESS (0) on success. Negative integer -i when i'th argument is invalid. Positive error code otherwise.

See also: starneig_SEP_SM_Hessenberg; starneig_hessenberg_conf; starneig_hessenberg_init_conf

◆ starneig_SEP_SM_Schur_expert()

starneig_error_t starneig_SEP_SM_Schur_expert	(	struct starneig_schur_conf *	conf,
		int	n,
		double	H[],
		int	ldH,
		double	Q[],
		int	ldQ,
		double	real[],
		double	imag[]
	)

Computes a Schur decomposition given a Hessenberg decomposition.

Parameters

[in]	conf	Configuration structure.
[in]	n	The order of \(H\) and \(Q\).
[in,out]	H	On entry, the upper Hessenberg matrix \(H\). On exit, the Schur matrix \(S\).
[in]	ldH	The leading dimension of \(H\).
[in,out]	Q	On entry, the orthogonal matrix \(Q\). On exit, the product matrix \(Q * U\).
[in]	ldQ	The leading dimension of \(Q\).
[out]	real	An array of the same size as \(H\) containing the real parts of the computed eigenvalues.
[out]	imag	An array of the same size as \(H\) containing the imaginary parts of the computed eigenvalues.

Returns: STARNEIG_SUCCESS (0) on success. Negative integer -i when i'th argument is invalid. Positive error code otherwise.

See also: starneig_SEP_SM_Schur; starneig_schur_conf; starneig_schur_init_conf

◆ starneig_SEP_SM_ReorderSchur_expert()

starneig_error_t starneig_SEP_SM_ReorderSchur_expert	(	struct starneig_reorder_conf *	conf,
		int	n,
		int	selected[],
		double	S[],
		int	ldS,
		double	Q[],
		int	ldQ,
		double	real[],
		double	imag[]
	)

Reorders selected eigenvalues to the top left corner of a Schur decomposition.

Parameters

[in]	conf	Configuration structure.
[in]	n	The order of \(S\) and \(Q\).
[in,out]	selected	The selection array.
[in,out]	S	On entry, the Schur matrix \(S\). On exit, the updated Schur matrix \(\hat{S}\).
[in]	ldS	The leading dimension of \(S\).
[in,out]	Q	On entry, the orthogonal matrix \(Q\). On exit, the product matrix \(Q * U\).
[in]	ldQ	The leading dimension of \(Q\).
[out]	real	An array of the same size as \(S\) containing the real parts of the computed eigenvalues.
[out]	imag	An array of the same size as \(S\) containing the imaginary parts of the computed eigenvalues.

Returns: STARNEIG_SUCCESS (0) on success. Negative integer -i when i'th argument is invalid. Positive error code otherwise.

See also: starneig_SEP_SM_ReorderSchur; starneig_SEP_SM_Select; starneig_reorder_conf; starneig_reorder_init_conf

◆ starneig_SEP_SM_Eigenvectors_expert()

starneig_error_t starneig_SEP_SM_Eigenvectors_expert	(	struct starneig_eigenvectors_conf *	conf,
		int	n,
		int	selected[],
		double	S[],
		int	ldS,
		double	Q[],
		int	ldQ,
		double	X[],
		int	ldX
	)

Computes an eigenvector for each selected eigenvalue.

Parameters

[in]	conf	Configuration structure.
[in]	n	The order of \(S\) and \(Q\) and the number of rows of \(X\).
[in]	selected	The selection array specifying the locations of the selected eigenvalues. The number of 1's in the array is the same as the number of columns in \(X\).
[in]	S	The Schur matrix \(S\).
[in]	ldS	The leading dimension of \(S\).
[in]	Q	The orthogonal matrix \(Q\).
[in]	ldQ	The The leading dimension of \(Q\).
[out]	X	A matrix with \(n\) rows and one column for each selected eigenvalue. The columns represent the computed eigenvectors as previously described.
[in]	ldX	The leading dimension of \(X\).

Returns: STARNEIG_SUCCESS (0) on success. Negative integer -i when i'th argument is invalid. Positive error code otherwise.

See also: starneig_SEP_SM_Select

Computational functions

Helper functions

Expert computational functions

Detailed Description

Function Documentation

◆ starneig_SEP_SM_Hessenberg()

◆ starneig_SEP_SM_Schur()

◆ starneig_SEP_SM_ReorderSchur()

◆ starneig_SEP_SM_Reduce()

◆ starneig_SEP_SM_Eigenvectors()

◆ starneig_SEP_SM_Select()

◆ starneig_SEP_SM_Hessenberg_expert()

◆ starneig_SEP_SM_Schur_expert()

◆ starneig_SEP_SM_ReorderSchur_expert()

◆ starneig_SEP_SM_Eigenvectors_expert()