Configuration structures and functions for the expert interface functions. More...

Data Structures
struct	starneig_hessenberg_conf
	Hessenberg reduction configuration structure. More...

struct	starneig_schur_conf
	Schur reduction configuration structure. More...

struct	starneig_reorder_conf
	Eigenvalue reordering configuration structure. More...

struct	starneig_eigenvectors_conf
	Eigenvector computation configuration structure. More...

Hessenberg reduction
void	starneig_hessenberg_init_conf (struct starneig_hessenberg_conf *conf)
	Initializes a Hessenberg reduction configuration structure with default parameters. More...

#define	STARNEIG_HESSENBERG_DEFAULT_TILE_SIZE -1
	Default tile size.

#define	STARNEIG_HESSENBERG_DEFAULT_PANEL_WIDTH -1
	Default panel width.

#define	STARNEIG_HESSENBERG_DEFAULT_PARALLEL_WORKER_SIZE -1
	Default parallel worker size.

Schur reduction
void	starneig_schur_init_conf (struct starneig_schur_conf *conf)
	Initializes a Schur reduction configuration structure with default parameters. More...

#define	STARNEIG_SCHUR_DEFAULT_INTERATION_LIMIT -1
	Default iteration limit.

#define	STARNEIG_SCHUR_DEFAULT_TILE_SIZE -1
	Default tile size.

#define	STARNEIG_SCHUR_DEFAULT_SMALL_LIMIT -1
	Default sequential QR limit.

#define	STARNEIG_SCHUR_DEFAULT_AED_WINDOW_SIZE -1
	Default AED window size.

#define	STARNEIG_SCHUR_DEFAULT_AED_NIBBLE -1
	Default nibble value.

#define	STARNEIG_SCHUR_DEFAULT_AED_PARALLEL_SOFT_LIMIT -1
	Default soft sequential AED limit.

#define	STARNEIG_SCHUR_DEFAULT_AED_PARALLEL_HARD_LIMIT -1
	Default hard sequential AED limit.

#define	STARNEIG_SCHUR_DEFAULT_SHIFT_COUNT -1
	Default shift count.

#define	STARNEIG_SCHUR_DEFAULT_WINDOW_SIZE -1
	Default bulge chasing window size.

#define	STARNEIG_SCHUR_ROUNDED_WINDOW_SIZE -2
	Rounded bulge chasing window.

#define	STARNEIG_SCHUR_DEFAULT_SHIFTS_PER_WINDOW -1
	Default number of shifts per bulge chasing window.

#define	STARNEIG_SCHUR_DEFAULT_UPDATE_WIDTH -1
	Default left-hand side update width.

#define	STARNEIG_SCHUR_DEFAULT_UPDATE_HEIGHT -1
	Default right-hand side update height.

#define	STARNEIG_SCHUR_DEFAULT_THRESHOLD -1
	Default deflation threshold.

#define	STARNEIG_SCHUR_NORM_STABLE_THRESHOLD -2
	Norm stable deflation threshold.

#define	STARNEIG_SCHUR_LAPACK_THRESHOLD -3
	LAPACK-style deflation threshold.

Eigenvalue reordering
enum	starneig_reorder_plan_t { STARNEIG_REORDER_DEFAULT_PLAN = 1, STARNEIG_REORDER_ONE_PART_PLAN = 2, STARNEIG_REORDER_MULTI_PART_PLAN = 3 }
	Reordering plan enumerator. More...

enum	starneig_reorder_blueprint_t { STARNEIG_REORDER_DEFAULT_BLUEPRINT = 1, STARNEIG_REORDER_DUMMY_INSERT_A = 2, STARNEIG_REORDER_DUMMY_INSERT_B = 3, STARNEIG_REORDER_CHAIN_INSERT_A = 4, STARNEIG_REORDER_CHAIN_INSERT_B = 5, STARNEIG_REORDER_CHAIN_INSERT_C = 6, STARNEIG_REORDER_CHAIN_INSERT_D = 7, STARNEIG_REORDER_CHAIN_INSERT_E = 8, STARNEIG_REORDER_CHAIN_INSERT_F = 9 }
	Task insertion blueprint. More...

void	starneig_reorder_init_conf (struct starneig_reorder_conf *conf)
	Initializes an eigenvalue reordering configuration structure with default parameters. More...

#define	STARNEIG_REORDER_DEFAULT_UPDATE_WIDTH -1
	Default left-hand side update task width.

#define	STARNEIG_REORDER_DEFAULT_UPDATE_HEIGHT -1
	Default right-hand side update task height.

#define	STARNEIG_REORDER_DEFAULT_TILE_SIZE -1
	Default tile size.

#define	STARNEIG_REORDER_DEFAULT_VALUES_PER_CHAIN -1
	Default number of selected eigenvalues per window.

#define	STARNEIG_REORDER_DEFAULT_WINDOW_SIZE -1
	Default default window size.

#define	STARNEIG_REORDER_ROUNDED_WINDOW_SIZE -2
	Default rounded window size.

#define	STARNEIG_REORDER_DEFAULT_SMALL_WINDOW_SIZE -1
	Default small window size.

#define	STARNEIG_REORDER_DEFAULT_SMALL_WINDOW_THRESHOLD -1
	Default small window threshold.

Eigenvectors
void	starneig_eigenvectors_init_conf (struct starneig_eigenvectors_conf *conf)
	Initializes an eigenvectors configuration structure with default parameters. More...

#define	STARNEIG_EIGENVECTORS_DEFAULT_TILE_SIZE -1
	Default tile size.

Detailed Description

Configuration structures and functions for the expert interface functions.

Data Structure Documentation

◆ starneig_hessenberg_conf

struct starneig_hessenberg_conf

Hessenberg reduction configuration structure.

Data Fields
int	tile_size	The matrices are divided into square tiles. This parameter defines the used tile size. If the parameter is set to STARNEIG_HESSENBERG_DEFAULT_TILE_SIZE, then the implementation will determine a suitable tile size automatically.
int	panel_width	The reduction is performed one panel at a time. This parameter defines the used panel width. If the parameter is set to STARNEIG_HESSENBERG_DEFAULT_PANEL_WIDTH, then the implementation will determine a suitable panel width automatically.
int	parallel_worker_size	The CPU variants of the panel reduction and trailing matrix update tasks are multithreaded. This parameter defines the number of cores allocated to these tasks. If the parameter is set to STARNEIG_HESSENBERG_DEFAULT_PARALLEL_WORKER_SIZE, then the implementation will determine a suitable CPU core count automatically.

◆ starneig_schur_conf

struct starneig_schur_conf

Schur reduction configuration structure.

Data Fields
int	iteration_limit	The QR/QZ is an iterative algorithm. This parameter defines the maximum number of iterations the algorithm is allowed to perform. If the parameter is STARNEIG_SCHUR_DEFAULT_INTERATION_LIMIT, then the implementation will determine a suitable iteration limit automatically.
int	tile_size	The matrices are divided into square tiles. This parameter defines the used tile size. If the parameter is set to STARNEIG_SCHUR_DEFAULT_TILE_SIZE, then the implementation will determine a suitable tile size automatically.
int	small_limit	As the QR/QZ algorithm progresses, the size of the active region shrinks. Once the size of the active region is small enough, then the remaining problem is solved in a sequential manner. This parameter defines the transition point where the implementation switches to a sequential QR algorithm. If the parameter is set to STARNEIG_SCHUR_DEFAULT_SMALL_LIMIT, then the implementation will determine a suitable switching point automatically.
int	aed_window_size	The implementation relies on a so-called Aggressive Early Deflation (AED) technique to accelerate the convergence of the algorithm. Each AED is performed inside a small diagonal window. This parameter defines used AED window size. If the parameter is set to STARNEIG_SCHUR_DEFAULT_AED_WINDOW_SIZE, then the implementation will determine a suitable AED window size automatically.
int	aed_nibble	The implementation relies on a so-called Aggressive Early Deflation (AED) technique to accelerate the convergence of the algorithm. Each AED is performed inside a small diagonal window. If the number deflated (converged) eigenvalues is larger than `(aed_nibble / 100)` $\times$ `size of AED window`, then the next bulge chasing step is skipped. If the parameter is set to STARNEIG_SCHUR_DEFAULT_AED_NIBBLE, then the implementation will determine a suitable value automatically.
int	aed_parallel_soft_limit	The implementation relies on a so-called Aggressive Early Deflation (AED) technique to accelerate the convergence of the algorithm. Each AED is performed inside a small diagonal window. An AED can be performed sequentially or in parallel. This parameter defines the transition point where the implementation allowed to switch to a sequential AED algorithm. The decision is made based on the size of the AED window. If the parameter is set to STARNEIG_SCHUR_DEFAULT_AED_PARALLEL_SOFT_LIMIT, then the implementation will determine a suitable switching point automatically.
int	aed_parallel_hard_limit	The implementation relies on a so-called Aggressive Early Deflation (AED) technique to accelerate the convergence of the algorithm. Each AED is performed inside a small diagonal window. An AED can be performed sequentially or in parallel. This parameter defines the transition point where the implementation switches to a sequential AED algorithm. The decision is made based on the size of the AED window. If the parameter is set to STARNEIG_SCHUR_DEFAULT_AED_PARALLEL_HARD_LIMIT, then the implementation will determine a suitable switching point automatically.
int	shift_count	The QR/QZ algorithm chases a set of $3 \times 3$ bulges across the diagonal of the Hessenberg(-triangular) decomposition. Two shifts (eigenvalue estimates) are required to generate each bulge. This parameter defines the number of shifts to use. If the parameter is set to STARNEIG_SCHUR_DEFAULT_SHIFT_COUNT, then the implementation will determine a suitable shift count automatically.
int	window_size	The QR/QZ algorithm chases a set of $3 \times 3$ bulges across the diagonal of the Hessenberg(-triangular) decomposition. The bulges are chased in batches. The related similarity transformations are initially restricted to inside a small diagonal window and the accumulated transformation are applied only later as BLAS-3 updates. This parameter defines the used bulge chasing window size. If the parameter is set to STARNEIG_SCHUR_ROUNDED_WINDOW_SIZE, then maximum window size is set to 2 * tile_size and the windows are placed such that their lower right corners respect the boundaries of the underlying data tiles. If the parameter is set to STARNEIG_SCHUR_DEFAULT_WINDOW_SIZE, then the implementation will determine a suitable window size automatically.
int	shifts_per_window	The QR/QZ algorithm chases a set of $3 \times 3$ bulges across the diagonal of the Hessenberg(-triangular) decomposition. The bulges are chased in batches. This parameter defines the used batch size. If the parameter is set to STARNEIG_SCHUR_DEFAULT_SHIFTS_PER_WINDOW then the implementation will determine a suitable batch size automatically.
int	update_width	The similarity similarity transformations are initially restricted to inside a small diagonal window and the accumulated transformation are applied only later as BLAS-3 updates. This parameter defines the width of each left-hand side update task. The value should be multiple of the tile size. If the parameter is set to STARNEIG_SCHUR_DEFAULT_UPDATE_WIDTH, then the implementation will determine a suitable width automatically.
int	update_height	The similarity similarity transformations are initially restricted to inside a small diagonal window and the accumulated transformation are applied only later as BLAS-3 updates. This parameter defines the height of each right-hand side update task. The value should be multiple of the tile size. If the parameter is set to STARNEIG_SCHUR_DEFAULT_UPDATE_HEIGHT, then the implementation will determine a suitable height automatically.
double	left_threshold	The QR/QZ algorithm is allowed to set tiny matrix entires to zero as long as their magnitudes are smaller that a given threshold. This parameter defines the threshold for the left-hand side matrix ( ). If the parameter is set to STARNEIG_SCHUR_DEFAULT_THRESHOLD, then the implementation will determine a suitable threshold automatically. If the parameter is set to STARNEIG_SCHUR_NORM_STABLE_THRESHOLD, then the implementation will use the threshold , where is the unit roundoff and is the Frobenius norm of the matrix . If the parameter is set to STARNEIG_SCHUR_LAPACK_THRESHOLD, then the implementation will use a deflation threshold that is compatible with LAPACK.
double	right_threshold	The QZ algorithm is allowed to set tiny matrix entires to zero as long as their magnitudes are smaller that a given threshold. This parameter defines the threshold for the right-hand side matrix ( ) off-diagonal entires. If the parameter is set to STARNEIG_SCHUR_DEFAULT_THRESHOLD, then the implementation will determine a suitable threshold automatically. If the parameter is set to STARNEIG_SCHUR_NORM_STABLE_THRESHOLD, then the implementation will use the threshold , where is the unit roundoff and is the Frobenius norm of the matrix . If the parameter is set to STARNEIG_SCHUR_LAPACK_THRESHOLD, then the implementation will use a deflation threshold that is compatible with LAPACK.
double	inf_threshold	The QZ algorithm is allowed to set tiny matrix entires to zero as long as their magnitudes are smaller that a given threshold. This parameter defines the threshold for the right-hand side matrix ( ) diagonal entries. If the parameter is set to STARNEIG_SCHUR_DEFAULT_THRESHOLD, then the implementation will determine a suitable threshold automatically. If the parameter is set to STARNEIG_SCHUR_NORM_STABLE_THRESHOLD, then the implementation will use the threshold , where is the unit roundoff and is the Frobenius norm of the matrix .

◆ starneig_reorder_conf

struct starneig_reorder_conf

Eigenvalue reordering configuration structure.

Data Fields
starneig_reorder_plan_t	plan	This parameter plan defines the used reordering plan. If the parameter is set to STARNEIG_REORDER_DEFAULT_PLAN, then the implementation will determine a suitable reordering plan automatically.
starneig_reorder_blueprint_t	blueprint	This parameter defines the used task insertion blueprint. If the parameter is set to STARNEIG_REORDER_DEFAULT_BLUEPRINT, then the implementation will determine a suitable task insertion blueprint automatically.
int	tile_size	The matrices are divided into square tiles. This parameter defines the used tile size. If the parameter is set to STARNEIG_REORDER_DEFAULT_TILE_SIZE, then the implementation will determine a suitable tile size automatically.
int	values_per_chain	The selected eigenvalues are processed in batches and each batch is assigned a window chain. This parameter defines the number of selected eigenvalues processed by each window chain. If the parameter is set to STARNEIG_REORDER_DEFAULT_VALUES_PER_CHAIN, then the implementation will determine a suitable value automatically.
int	window_size	The similarity similarity transformations are initially restricted to inside a small diagonal window and the accumulated transformation are applied only later as BLAS-3 updates. This parameter defines the size of the window. If the parameter is set to STARNEIG_REORDER_ROUNDED_WINDOW_SIZE, then maximum window size is set to 2 * tile_size, the windows are placed such that their upper left corners respect the boundaries of the underlying data tiles, and the parameter values_per_chain is ignored. If the parameter is set to STARNEIG_REORDER_DEFAULT_WINDOW_SIZE, then the implementation will determine a suitable window size automatically.
int	small_window_size	Larger diagonal window are processed using even smaller diagonal windows in a recursive manner. This parameter defines the used small window size. If the parameter is set to STARNEIG_REORDER_DEFAULT_SMALL_WINDOW_SIZE, then the implementation will determine a suitable small window size automatically.
int	small_window_threshold	Larger diagonal window are processed using even smaller diagonal windows in a recursive manner. This parameter defines the largest diagonal window that is processed in a scalar manner. If the parameter is set to STARNEIG_REORDER_DEFAULT_SMALL_WINDOW_THRESHOLD, then the implementation will determine a suitable threshold automatically.
int	update_width	The similarity similarity transformations are initially restricted to inside a small diagonal window and the accumulated transformation are applied only later as BLAS-3 updates. This parameter defines the width of each left-hand side update task. The value should be multiple of the tile size. If the parameter is set to STARNEIG_REORDER_DEFAULT_UPDATE_WIDTH, then the implementation will determine a suitable width automatically.
int	update_height	The similarity similarity transformations are initially restricted to inside a small diagonal window and the accumulated transformation are applied only later as BLAS-3 updates. This parameter defines the height of each right-hand side update task. The value should be multiple of the tile size. If the parameter is set to STARNEIG_REORDER_DEFAULT_UPDATE_HEIGHT, then the implementation will determine a suitable height automatically.

◆ starneig_eigenvectors_conf

struct starneig_eigenvectors_conf

Eigenvector computation configuration structure.

Data Fields
int	tile_size	The matrices are divided into tiles. This parameter defines the used tile size. If the parameter is set to STARNEIG_EIGENVECTORS_DEFAULT_TILE_SIZE, then the implementation will determine a suitable tile size automatically.

Enumeration Type Documentation

◆ starneig_reorder_plan_t

enum starneig_reorder_plan_t

Reordering plan enumerator.

Eigenvalues that fall within a diagonal computation window are reordered such that all selected eigenvalues are moved to the upper left corner of the window. The corresponding orthogonal transformations are accumulated to separate accumulator matrix / matrices.

+---------+       +---------+
|¤ x x x x|       |$ x x x x|       $ selected eigenvalue
|  $ x x x|       |  $ x x x|       ¤ deselected eigenvalue
|    ¤ x x| ==> Q |    ¤ x x| Q^T   x non-zero entry
|      ¤ x|       |      ¤ x|
|        $|       |        ¤|
+---------+       +---------+

A window chain comprises from multiple overlapping diagonal computation windows that are intended to be processed in a particular order. More precisely, the windows are placed such that the overlap between two windows is big enough to accommodate all selected eigenvalues that fall within the preceding windows. In this way, the windows can be processed in sequential order, starting from the bottom window, such that the reordering that takes place in one window always moves the preceding selected eigenvalues to the lower right corner of the next window. In the end, all selected that fall within the combined computation area of the chain are moved to the upper left corner of the topmost window.

An example showing how an eigenvalue can be moved six entries upwards by using three diagonal windows:

+-------+         +-------+         +-------+         +-------+
| x x x |  ===>   | x x x |  ===>   | x x x |  ===>   | #<--+ |
|   x-x-+---+     |   x-x-+---+     |   x-x-+---+     |   ¤-|-+---+
|   | x x x |     |   | x x x |     |   | #<--+ |     |   | ¤ ¤ ¤ |
+---+---x-x-+---+ +---+---x-x-+---+ +---+---¤-|-+---+ +---+---¤-¤-+---+
    |   | x x x |     |   | #<--+ |     |   | ¤ ¤ ¤ |     |   | ¤ ¤ ¤ |
    +---+---x x |     +---+---¤ | |     +---+---¤ ¤ |     +---+---¤ ¤ |
        |     # |         |     ¤ |         |     ¤ |         |     ¤ |
        +-------+         +-------+         +-------+         +-------+

The number of selected eigenvalues that can be moved by a single window chain is limited by the windows size. Thus, the whole reordering procedure usually involves multiple chains that must be be processed in a particular order. A chain list describes a list of chains that are intended to be processed together. Window chains that belong to different chain lists are processed separately.

A plan consists from one or more chain lists that are intended to be processed in a particular order.

STARNEIG_REORDER_ONE_PART_PLAN :

The first chain is placed in the upper left corner of the matrix and its size is chosen such that it contains a desired number of selected eigenvalues (starneig_reorder_conf::values_per_chain parameter). The next chain is places such that its upper left corner is located one entry after the location where the last selected eigenvalue, that falls within the first chain, would be after the reordering. The chain is sized such that the part of the chain, that does not intersect the first chain, contain the desired number of selected eigenvalues. This same procedure is repeated until all selected eigenvalues have been accounted for. All chains belong to the same chain lists and are intended to be processed sequentially.

An example showing the placement of the chains in a case where each chain wields two selected eigenvalues:

                                                      before:      after:
.-------+                                             .            0
| 0     | <-- chain 0                                 0 _          1_
|   .-----------+                                     . .   ====>  2
|   | . |       | <-- chain 1                         . . _        3_
+---|---1---------------+ . . . . . . . . . . . . . . 1_. .        4
    |   | .     |       | <-- chain 2                   . . _      5_
    |   |   2-------------------+                       2 . .      6
    |   |   | . |       |       | <-- chain 3           . . . _    7_
    +---|---|---3-----------------------+ . . . . . . . 3_. . .    8
        |   |   | 4     |       |       | <-- chain 4     4 . .    9
        |   |   |   .   |       |       |                 . . .    .
        |   |   |     . |       |       |                 . . .    .
        +---|---|-------5       |       | . . . . . . . . 5_. .    .
            |   |         6     |       |                   6 .    .
            |   |           .   |       |                   . .    .
            |   |             . |       |                   . .    .
            +---|---------------7       | . . . . . . . . . 7_.    .
                |                 .     |                     .    .
                |                   .   |                     .    .
                |                     8 |                     8    .
                +-----------------------9 . . . . . . . . . . 9    .

An example showing what happens when the first three chains are processed:

.-------+                        >0<------+
| 0     |                         |>1<    |
|   .-----------+                 |   #-----------+
|   | . |       |                 |   | # |       |
+---|---1---------------+         +---|---#---------------+
    |   | .     |       |             |   | .     |       |
    |   |   2   |       |  ===>       |   |   2   |       |  ===>
    |   |     . |       |             |   |     . |       |
    +---|-------3       |             +---|-------3       |
        |         4     |                 |         4     |
        |           .   |                 |           .   |
        |             . |                 |             . |
        +---------------5                 +---------------5
0-------+                         0-------+
| 1     |                         | 1     |
|  >2<----------+                 |   2-----------+
|   |>3<|       |                 |   | 3 |       |
+---|---#---------------+         +---|-->4<--------------+
    |   | #     |       |             |   |>5<    |       |
    |   |   #   |       |   ===>      |   |   #   |       |
    |   |     # |       |             |   |     # |       |
    +---|-------#       |             +---|-------#       |
        |         4     |                 |         #     |
        |           .   |                 |           #   |
        |             . |                 |             # |
        +---------------5                 +---------------#

If necessary, each chain is re-sized to avoid splitting any $2 \times 2$ tiles.

Windows are placed such that the first window is located in the lower right corner of the computation area of the window chain. The last window is correspondingly placed in the upper left corner of the computation area.

If necessary, each window is re-sized to avoid splitting any $2 \times 2$ tiles.

STARNEIG_REORDER_MULTI_PART_PLAN :

A multi-part reordering plan is derived from an one-part reordering plan by splitting the chains into sub-chains as shown below:

Initial one-part plan:
  Chain 0: aaaaaa
  Chain 1:  bbbbbbbbbb               a,b,c,d,e diagonal computation window
  Chain 2:   cccccccccccccc
  Chain 3:    dddddddddddddddddd
  Chain 4:     eeeeeeeeeeeeeeeeeeeeee
Resulting multi-part plan:
  Chain 0: aaaaaa
  Chain 1:  ......bbbb
  Chain 2:   ..........cccc               chain list 0
  Chain 3:    ..............dddd
  Chain 4:     ..................eeee
  -----------------------------------------------------
  Chain 0:  bbbbbb....
  Chain 1:   ......cccc....               chain list 1
  Chain 2:    ..........dddd....
  Chain 3:     ..............eeee....
  -----------------------------------------------------
  Chain 0:   cccccc........
  Chain 1:    ......dddd........          chain list 2
  Chain 2:     ..........eeee........
  -----------------------------------------------------
  Chain 0:    dddddd............          chain list 3
  Chain 1:     ......eeee............
  -----------------------------------------------------
  Chain 0:     eeeeee................     chain list 4

Note that the chains that belong to the same chain list are independent from each other and can therefore be processed in an arbitrary order.

Enumerator
STARNEIG_REORDER_DEFAULT_PLAN	Default plan.
STARNEIG_REORDER_ONE_PART_PLAN	One part plan.
STARNEIG_REORDER_MULTI_PART_PLAN	Multi part plan.

◆ starneig_reorder_blueprint_t

enum starneig_reorder_blueprint_t

Task insertion blueprint.

A task insertion blueprint defines how a reordering plan is carried out.

Enumerator
STARNEIG_REORDER_DEFAULT_BLUEPRINT	Default blueprint.
STARNEIG_REORDER_DUMMY_INSERT_A	One-pass forward dummy blueprint. Processes the window chains in order starting from the topmost chain. All update tasks are inserted right after each window reordering task.
STARNEIG_REORDER_DUMMY_INSERT_B	Two-pass backward dummy blueprint. Processes the window chains in two phases starting from the bottommost chain. The window reordering tasks and the right-hand side update tasks are inserted during the first phase. Other update tasks are inserted during the second phase.
STARNEIG_REORDER_CHAIN_INSERT_A	One-pass forward chain blueprint. Processes the window chains in order starting from the topmost chain. The window reordering tasks and high priority right-hand side update tasks are inserted first. Other update tasks are inserted after them.
STARNEIG_REORDER_CHAIN_INSERT_B	Two-pass forward chain blueprint. Processes the window chains in two phases starting from the topmost chain. The window reordering tasks and high priority right-hand side update tasks are inserted first. The left- hand side updates are inserted after them. Other updates are inserted during the second phase.
STARNEIG_REORDER_CHAIN_INSERT_C	One-pass backward chain blueprint. Processes the window chains in order starting from the bottommost chain. The window reordering tasks and high priority right-hand side update tasks are inserted first. Other update tasks are inserted later.
STARNEIG_REORDER_CHAIN_INSERT_D	Two-pass backward chain blueprint. Processes the window chains in two phases starting from the bottommost chain. The window reordering tasks and high priority right-hand side update tasks are inserted first. Update tasks that are related to the Schur matrix are inserted later. Update tasks that are related to the orthogonal matrices are inserted during the second phase.
STARNEIG_REORDER_CHAIN_INSERT_E	Two-pass delayed backward chain blueprint. Processes the window chains in order starting from the bottommost chain. The window reordering tasks and high priority right-hand side update tasks are inserted first. Update tasks that are related to the Schur matrix are inserted later. Update tasks that are related to the orthogonal matrices are inserted only after all chain list have been processed.
STARNEIG_REORDER_CHAIN_INSERT_F	Three-pass delayed backward chain blueprint. Processes the window chains in two phases starting from the bottommost chain. The window reordering tasks and high priority right-hand side update tasks are inserted during the first phase. Update tasks that are related to the Schur matrix are inserted during the second phase. Update tasks that are related to the orthogonal matrices are inserted only after all chain list have been processed.

Function Documentation

◆ starneig_hessenberg_init_conf()

void starneig_hessenberg_init_conf ( struct starneig_hessenberg_conf * conf )

Initializes a Hessenberg reduction configuration structure with default parameters.

Parameters

[out] conf The Hessenberg reduction configuration structure.

◆ starneig_schur_init_conf()

void starneig_schur_init_conf ( struct starneig_schur_conf * conf )

Initializes a Schur reduction configuration structure with default parameters.

Parameters

[out] conf The Schur reduction configuration structure.

◆ starneig_reorder_init_conf()

void starneig_reorder_init_conf ( struct starneig_reorder_conf * conf )

Initializes an eigenvalue reordering configuration structure with default parameters.

Parameters

[out] conf The eigenvalue reordering configuration structure.

◆ starneig_eigenvectors_init_conf()

void starneig_eigenvectors_init_conf ( struct starneig_eigenvectors_conf * conf )

Initializes an eigenvectors configuration structure with default parameters.

Parameters

[out] conf The eigenvectors configuration structure.

Data Structures

Hessenberg reduction

Schur reduction

Eigenvalue reordering

Eigenvectors

Detailed Description

Data Structure Documentation

◆ starneig_hessenberg_conf

◆ starneig_schur_conf

◆ starneig_reorder_conf

◆ starneig_eigenvectors_conf

Enumeration Type Documentation

◆ starneig_reorder_plan_t

◆ starneig_reorder_blueprint_t

Function Documentation

◆ starneig_hessenberg_init_conf()

◆ starneig_schur_init_conf()

◆ starneig_reorder_init_conf()

◆ starneig_eigenvectors_init_conf()