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1 /* ASCEND modelling environment
2 Copyright (C) 1990 Karl Michael Westerberg
3 Copyright (C) 1993 Joseph Zaher
4 Copyright (C) 1994 Boyd Safrit, Joseph Zaher, Benjamin Andrew Allan
5 Copyright (C) 1995 Benjamin Andrew Allan, Kirk Andre Abbott
6 Copyright (C) 2006 Carnegie Mellon University
7
8 This program is free software; you can redistribute it and/or modify
9 it under the terms of the GNU General Public License as published by
10 the Free Software Foundation; either version 2, or (at your option)
11 any later version.
12
13 This program is distributed in the hope that it will be useful,
14 but WITHOUT ANY WARRANTY; without even the implied warranty of
15 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
16 GNU General Public License for more details.
17
18 You should have received a copy of the GNU General Public License
19 along with this program; if not, write to the Free Software
20 Foundation, Inc., 59 Temple Place - Suite 330,
21 Boston, MA 02111-1307, USA.
22 *//** @file
23 * linsol II: Ascend Linear Equation Solver.
24 *
25 * A linear system consists of a coefficient matrix (A)
26 * and possibly several right-hand-sides (rhs). The
27 * solution vector x sought can be that of either
28 *<pre>
29 * T
30 * A x = rhs or A x = rhs
31 *</pre>
32 * depending on a specification inherent with rhs which
33 * dictates whether or not A should be transposed. If a
34 * rhs specifies transpose, then the vector itself is
35 * expected to be indexed by the original column numbers
36 * of the coefficient matrix and the solution vector shall
37 * be indexed by original row numbers. Otherwise, rhs
38 * is expected to be indexed by original row numbers while
39 * the solution can be referenced using original column
40 * numbers. The coefficient matrix and each rhs will be
41 * preserved throughout solving, except that the
42 * coefficient matrix may be permuted during reordering
43 * or (depending on the method) solving.
44 *
45 * The method of linear solution is an option new to
46 * linsolqr. Also, some of the data structures have been
47 * expanded as required. The factoring methods are
48 * enumerated and summarized below.
49 *
50 * Linsol is a general sparse solver. It uses mtx, though any
51 * proper sparse matrix package can be substituted. By
52 * proper, of course, we mean one with at least the
53 * functionality of mtx. If you find something with all
54 * the features of mtx that is faster than mtx, let us
55 * know, please. If you do any comparisons of linsol with
56 * other sparse codes (on sequential processors) also
57 * please let us know how you find its performance.
58 * You probably won't find algorithms for banded or
59 * symmetric matrices here. Why?
60 * The efficiency of most banded algorithms comes from
61 * the way they access memory with three assumptions:
62 * that all possible coefficient locations are known before
63 * a solution is attempted, that they are accessible
64 * in some ORDERED fashion, and that the matrix will not
65 * be reordered (except perhaps in very limited ways)
66 * during solution. Linsol is predicated on just
67 * the opposite assumptions at the moment.
68 * These assumptions would relieve the solver of
69 * memory allocation and a great deal of range checking.
70 * While we would do our flops efficiently with linsol/mtx
71 * on a banded matrix, the cost of accessing linear
72 * coefficients in an UNORDERED fashion is such that a good
73 * band, variable band, or symmetric skyline code making the
74 * ORDERED assumption will always beat linsol in speed,
75 * though perhaps not in robustness.
76 *
77 * Requires: #include <string.h>
78 * #include "utilities/ascConfig.h"
79 * #include "mtx.h"
80 *
81 * Each method is described here, including the unimplemented ones,
82 * however vaguely. By convention all methods assign unpivotable variables
83 * the value of 0.0 in the linear solution vector. This makes sense because
84 * the linear system usually arises from a nonlinear scheme wherein
85 * stepping in the unpivoted variables is left for a future iteration.
86 *
87 * The currently recommended methods are ranki_*2, in particular ba2.
88 *
89 * ranki_kw:
90 * Reordering method: SPK1, Stadtherr & Wood (1984), and like.
91 * The region used is confined to the main diagonal.
92 * The square region is reordered to lower triangular with spikes.
93 * Each spike is higher than or equal to all spikes to the left of it
94 * if the matrix is partitioned.
95 * Solution method: RANKI, Stadtherr & Wood
96 * Ref: Computers and Chemical Engineering (8)1 pp. 9-33 (1984)
97 * The square region is U/L factored with spikes dragged in to replace
98 * unacceptable pivots. Fill is in spike columns and
99 * dragged rows where it usually does take place.
100 * Numerically dependent rows and columns do not have dependencies
101 * automatically calculated. This is a change from linsol, so be
102 * careful in making comparisons.
103 * Authors: Karl Westerberg, Joe Zaher
104 * with some clean ups and restructuring by Ben Allan
105 *
106 * ranki_jz:
107 * As ranki_kw, except where ranki_kw looks only across the current row
108 * for pivots if the diagonal element is too small, ranki_jz also looks
109 * down the current column. This introduces additional spikes to the
110 * current block, but sometimes the overall effect is reduced fill. The
111 * main motivation is to broaden pivot choices on those problems
112 * where restricting the choice to the current row results in immediate
113 * explosions of fill due to a full subdiagonal and a moderately small
114 * pivot.
115 *
116 * ranki_kw2:
117 * ranki_jz2:
118 * As the ranki_XX factorizations, except uses drop tolerance and
119 * uses much faster bilevel matrices (master + slave matrix of mtx)
120 * to segregate the contents of U from L. Also, dependency information
121 * is not calculated automatically.
122 * Author: Ben Allan
123 *
124 * ranki_ba2:
125 * As the ranki_kw2 factorization, except pivot and row being eliminated
126 * are stored as linked lists/full org vectors (dual access) during
127 * elimination which removes the last significant quadratic effect from
128 * the ranki factorization.
129 *
130 * plain_qr:
131 * Reordering method: Transpose SPK1 (tspk1), LORA
132 * The region used may be rectangular, but will be modified
133 * if needed so that the upper left corner is on the diagonal.
134 * The region in sys->coef is not permuted in the solution process.
135 * Solution method:
136 * The rectangular region is QR factored with standard column pivoting
137 * modified by the pivot_tolerance. That is, at each step the column
138 * to factor in next is the leftmost col with norm alpha that satisfies
139 * alpha >= ptol * maxalpha.
140 * ptol = 1 --> Stewart's QRDC style pivoting.
141 * ptol = 0 --> no pivoting (Sometimes a dumb idea).
142 * plain_qr is to QRDC as ranki_kw is to LU factorization with strict
143 * partial pivoting.
144 * This implementation is best used on matrices where nrows about = ncols
145 * and data are not highly correlated.
146 * There are better QR methods (not available here) for vector processors,
147 * distributed processors, data fitting and so forth.
148 * Some care has been taken that the implementation here will scale up
149 * reasonably to larger matrices.
150 * Detailed references are given in the plain_qr section of the .c file.
151 * Author: Ben Allan
152 *
153 * cond_qr: (broken)
154 * Reordering method: Transpose SPK1 (tspk1)
155 * The region used is confined to the main diagonal.
156 * The square region is permuted in the solution process.
157 * Solution method:
158 * The square region is QR factored with pivoting by a local minimum
159 * fill criteria balanced against choosing pivots based on the
160 * incremental inverse R condition number.
161 * Ref:Incremental Condition Calculation and Column Selection,
162 * UMIACS TR 90-87, G.W.Stewart, July 1990)
163 * (Allan, Safrit, Westerberg, 1995)
164 * Authors: Ben Allan
165 *
166 * opt_qr:
167 * As cond_qr, except region may be underspecified (MxN, M < N)
168 * The region's upper left corner should be (or will be forced to be)
169 * on the main diagonal. The columns pivoted are expected to be a
170 * good basis. Solution is not a least squares solution of the
171 * transpose NxM problem; for this we need rowwise Householder
172 * transforms and spk1 reordering.
173 * Authors: Ben Allan
174 *
175 * ls_qr:
176 * As cond_qr, except region may be overspecified (MxN, M > N)
177 * Solves the system in a linear least squares sense.
178 * Authors: Ben Allan
179 *
180 * band_lu:
181 * symmetric_lu:
182 * (cholesky?)
183 * The best codes we can find already implemented to complement and/or
184 * verify our own. More detailed semantics unknown at this time.
185 *
186 * The parameters pivot_tolerance, condition_tolerance and drop_tolerance
187 * have semantics varying with the method.
188 * See the header of linsolqr_set_pivot_tolerance below for details.
189 * </pre>
190 *//*
191 by Karl Westerberg
192 Created: 2/6/90
193 Last in CVS: $Revision: 1.13 $ $Date: 1997/07/25 17:23:49 $ $Author: ballan $
194 QR options by Ben Allan
195 C version based on sqr.pas v1.5, Boyd Safrit (1994)
196
197 Dates: 06/90 - original version (KW)
198 04/91 - removed output assignment and partitioning
199 (belong in structural analysis) (JZ)
200 08/92 - added transpose ability (JZ)
201 01/94 - broke out linsol_invert() and linsol_solve() (JZ)
202 10/94 - reorganized for multiple methods and QR (BA)
203 moved drag operator to mtx (BA,JZ)
204 11/94 - added linsolqr_get_factors/inverse for debugging.BA
205 09/95 - added factor_class to better manage families. BA
206 09/95 - added ranki_*2 methods (BA)
207 09/95 - added gauss (broken) (KA)
208 11/96 - added ranki_ba2 method (BA)
209
210 */
211
212 #ifndef ASC_LINSOLQR_H
213 #define ASC_LINSOLQR_H
214
215 /** @addtogroup linear
216 * @{
217 */
218
219 #define LINSOLMTX_DEBUG FALSE
220 /**< Debug mode. */
221 #define LINQR_DROP_TOLERANCE 1.0e-16
222 /**< This is the default for drop tolerances in methods which use a drop tol */
223
224 typedef struct linsolqr_header *linsolqr_system_t;
225 /**< linsolqr_system_t is the linear system handle. */
226
227 enum factor_class {
228 unknown_c, /**< error handling class */
229 ranki = 100, /**< all ranki (and gauss until broken out) methods */
230 s_qr = 200 /**< all sparse qr methods */
231 };
232
233 enum reorder_method {
234 unknown_r, /**< error handling method */
235 natural = 1000, /**< do nothing reorder */
236 spk1 = 2000, /**< Stadtherr's SPK1 reordering */
237 tspk1 = 3000 /**< transpose of Stadtherr's SPK1 reordering good for gauss */
238 /* future work:
239 invspk1, spk1 then diagonally inverted
240 invtspk1, tspk1 then diagonally inverted
241 widespk1, spk1 of an MxN region, N > M
242 */
243 };
244
245 enum factor_method {
246 unknown_f = 0, /**< error handling method */
247 ranki_kw = 1, /**< original linsol method */
248 ranki_jz = 2, /**< original linsol method with pseudo-complete pivoting */
249 ranki_kw2 = 3, /**< better data structure version of ranki_kw, w/drop tol */
250 ranki_jz2 = 4, /**< better data structure version of ranki_jz, w/drop tol */
251 ranki_ka = 12, /**< kirks hacked verion of the basic method. */
252 plain_qr = 5, /**< rectangular col pivoted qr variants */
253 cond_qr = 6, /**< stewart-based sparse QR method new Coke */
254 ranki_ba2 = 7, /**< proper linked list implementation of ranki (dragfree) */
255 opt_qr = 8, /**< coming soon */
256 ls_qr = 9, /**< anticipated */
257 gauss_ba2 = 10, /**< anticipated */
258 symmetric_lu = 11 /**< anticipated */
259 };
260
261 ASC_DLLSPEC(int ) g_linsolqr_timing;
262 /**<
263 * If nonzero and certain internal defines are set, factorization
264 * generates a fill and timing message.
265 */
266
267 /* KAA_DEBUG */
268 /* unimplemented function
269 extern boolean linsolqr_col_is_a_spike (mtx_matrix_t mtx, int32 col);
270 */
271 /* Returns true if the column in question is a spike. */
272
273
274 /* Functions for managing interfaces */
275
276 extern char *linsolqr_rmethods(void);
277 /**<
278 * Returns a comma-separated list of the names of reordering methods
279 * implemented. If you implement a new method, update this
280 * function. Do not free the pointer returned.<br><br>
281 *
282 * Not all reorderings are appropriate to all factorizations.
283 */
284
285 ASC_DLLSPEC(char *) linsolqr_fmethods(void);
286 /**<
287 * Returns a comma-separated list of the names of factorization methods
288 * implemented. If you implement a new method, update this
289 * function. Do not free the pointer returned. The string returned
290 * will contain no whitespace of any sort, tabs, blanks, or \n.
291 */
292
293 extern enum reorder_method linsolqr_rmethod_to_enum(char *s);
294 /**<
295 * Returns the enum of a reorder method with the name s.
296 * If you implement a new method, update this function.
297 */
298
299 extern enum factor_method linsolqr_fmethod_to_enum(char *s);
300 /**<
301 * Returns the enum of a factor method with the name s.
302 * If you implement a new method, update this function.
303 */
304
305 extern enum factor_class linsolqr_fmethod_to_fclass(enum factor_method fm);
306 /**<
307 * Returns the enum of the factor class containing the method given.
308 * If you implement a new method or class, update this function.
309 */
310
311 ASC_DLLSPEC(char *) linsolqr_enum_to_rmethod(enum reorder_method m);
312 /**<
313 * <!-- s=linsolqr_enum_to_rmethod(m); -->
314 *
315 * Returns the name of a reorder method with the enum m.
316 * If you implement a new method, update this function.
317 * Do not free the name.
318 */
319
320 extern char *linsolqr_enum_to_fmethod(enum factor_method m);
321 /**<
322 * Returns the name of a factor method with the enum m.
323 * If you implement a new method, update this function.
324 * Do not free the name.
325 */
326
327 ASC_DLLSPEC(char *) linsolqr_rmethod_description(enum reorder_method meth);
328 /**<
329 * Returns a string describing the method inquired on. Do not mess
330 * with the string: linsolqr owns it.
331 * If you implement a new method, update this function.
332 */
333
334 ASC_DLLSPEC(char *) linsolqr_fmethod_description(enum factor_method meth);
335 /**<
336 * Returns a string describing the method inquired on. Do not mess
337 * with the string: linsolqr owns it.
338 * If you implement a new method, update this function.
339 */
340
341 /* Functions for specifying problems and controlling them */
342
343 extern linsolqr_system_t linsolqr_create(void);
344 /**<
345 * Creates a linear system and returns a pointer to it. Initially the
346 * system has no coefficient matrix and no rhs.
347 */
348
349 extern void linsolqr_destroy(linsolqr_system_t sys);
350 /**<
351 * Destroys the linear system. The coefficient matrix and each rhs are
352 * not destroyed by this call.
353 */
354
355 extern void linsolqr_set_matrix(linsolqr_system_t sys, mtx_matrix_t mtx);
356 /**<
357 * Sets the coefficient matrix to mtx.
358 */
359
360 ASC_DLLSPEC(void ) linsolqr_set_region(linsolqr_system_t sys, mtx_region_t region);
361 /**<
362 * Sets the reg to region.
363 */
364
365 ASC_DLLSPEC(mtx_matrix_t ) linsolqr_get_matrix(linsolqr_system_t sys);
366 /**<
367 * Returns the coefficient matrix.
368 */
369
370 ASC_DLLSPEC(void ) linsolqr_add_rhs(linsolqr_system_t sys,
371 real64 *rhs,
372 boolean transpose);
373 /**<
374 * Adds the given rhs to the collection of rhs's already part of the
375 * system.
376 *
377 * You continue to be responsible for deallocating rhs. We do not take
378 * over management of that memory. Do not free the rhs you have given
379 * us without calling linsolqr_remove_rhs first.<br><br>
380 *
381 * Rhs should point to an array of reals indexed by original
382 * column number if the linear system is to be solved using the transpose
383 * of the matrix or by original row number if the matrix is not to be
384 * transposed. This is determined using the boolean transpose. The
385 * rhs should be refered to in the future by its pointer.
386 * <pre>
387 * For the mathematically impaired:
388 * M' denotes Transpose(M).
389 *
390 * transpose==FALSE --> rhs will be solved for x in A x = b.
391 * --> rhs b is an org row indexed column vector.
392 * --> x is an org col indexed column vector.
393 * --> yields dx = Newton direction in J.dx = -f
394 * if the b given is -f.
395 *
396 * transpose==TRUE --> rhs will be solved for y in A' y = d.
397 * --> rhs d is an org column indexed column vector.
398 * --> y is an org row indexed column vector.
399 * --> yields dx = Newton direction in J'.dx = -f.
400 * if the d given is -f and f,dx are properly indexed.
401 * This may be useful if A was created using
402 * mtx_transpose in order to improve factorization.
403 *
404 * Useful matrix identity: (M')^-1 == (M^-1)' for invertible M.
405 * </pre>
406 */
407
408 ASC_DLLSPEC(void ) linsolqr_remove_rhs(linsolqr_system_t sys, real64 *rhs);
409 /**<
410 * Removes the given rhs from the system. The rhs is not destroyed, just
411 * removed from the system.
412 */
413
414 extern int32 linsolqr_number_of_rhs(linsolqr_system_t sys);
415 /**<
416 * Returns the number of rhs's currently part of the system.
417 */
418
419 ASC_DLLSPEC(real64 *) linsolqr_get_rhs(linsolqr_system_t sys, int n);
420 /**<
421 * Returns the n-th rhs, where rhs's are indexed in the order they were
422 * added using linsolqr_add_rhs() from 0 to (# rhs's)-1. NULL is returned
423 * if the index is out of range.
424 */
425
426 ASC_DLLSPEC(void ) linsolqr_matrix_was_changed(linsolqr_system_t sys);
427 /**<
428 * Informs the solver that a numerical value of a non-zero was changed.
429 * This must be called whenever any numerical changes to the matrix are
430 * made.
431 */
432
433 ASC_DLLSPEC(void ) linsolqr_rhs_was_changed(linsolqr_system_t sys,
434 real64 *rhs);
435 /**<
436 * Informs the solver that the given rhs has been modified. This must be
437 * called whenever the rhs is modified.
438 */
439
440 extern void linsolqr_set_pivot_zero(linsolqr_system_t sys,
441 real64 pivot_zero);
442 /**<
443 * Sets the pivot zero for the system. Pivots less than or equal to
444 * this value are regarded as zero. linsolqr_set_pivot_zero() will
445 * automatically call linsolqr_matrix_was_changed().
446 */
447 extern real64 linsolqr_pivot_zero(linsolqr_system_t sys);
448 /**<
449 * Gets the pivot zero for the system. Pivots less than or equal to
450 * this value are regarded as zero.
451 */
452
453 extern void linsolqr_set_pivot_tolerance(linsolqr_system_t sys, real64 ptol);
454 /**< See discussion under linsolqr_drop_tolerance(). */
455 extern real64 linsolqr_pivot_tolerance(linsolqr_system_t sys);
456 /**< See discussion under linsolqr_drop_tolerance(). */
457 extern void linsolqr_set_condition_tolerance(linsolqr_system_t sys, real64 ctol);
458 /**< See discussion under linsolqr_drop_tolerance(). */
459 extern real64 linsolqr_condition_tolerance(linsolqr_system_t sys);
460 /**< See discussion under linsolqr_drop_tolerance(). */
461 extern void linsolqr_set_drop_tolerance(linsolqr_system_t sys, real64 dtol);
462 /**< See discussion under linsolqr_drop_tolerance(). */
463 extern real64 linsolqr_drop_tolerance(linsolqr_system_t sys);
464 /**<
465 * <pre>
466 * linsolqr_set_pivot_tolerance(sys,ptol)
467 * ptol = linsolqr_pivot_tolerance(sys)
468 *
469 * linsolqr_set_condition_tolerance(sys,ctol)
470 * ctol = linsolqr_condition_tolerance(sys)
471 *
472 * linsolqr_set_drop_tolerance(sys,dtol)
473 * dtol = linsolqr_drop_tolerance(sys)
474 *
475 * linsolqr_system_t sys;
476 * real64 ptol, ctol,dtol;
477 *
478 * Sets/gets the pivot/condition/drop tolerance for the system. Semantics of
479 * tolerances vary with method. Not to be confused with pivot zero, epsilon.
480 *
481 * pivot_tolerance: Pivots less than this fraction of the maximum pivot
482 * value in the same row or column (depending on method) are disregarded.
483 *
484 * ranki_kw: pivot_tolerance applies to row. condition_tolerance ignored.
485 * ranki_jz: pivot_tolerance applies to row and col. condition ignored.
486 * ranki_ba2:
487 * ranki_kw2:
488 * ranki_jz2: as ranki_kw/ranki_jz except that matrix entries below
489 * dtol in magnitude are dropped.
490 * plain_qr: pivot_tolerance applies to cols. condition_tolerance used
491 * with a condition heuristic rather than actual condition.
492 *
493 * cond_qr and variants:
494 * Unpivoted columns are ordered by fill potential and then the first
495 * of these to meet the criterion CI*condition_tolerance <= min_CI
496 * is chosen as the next column to pivot with.
497 * Pivot_tolerance is applied to choose the pivot within the
498 * selected column.
499 *
500 * linsolqr_set_pivot/condition/drop_tolerance() will automatically call
501 * linsolqr_matrix_was_changed().
502 * </pre>
503 * @todo Separate documentation for these linsolqr functions?
504 */
505
506 /* Functions for analyzing and querying linear systems. */
507
508 extern enum factor_class linsolqr_fclass(linsolqr_system_t sys);
509 /**<
510 * Returns the most recently set factorization class of the system.
511 * The system should be previously prepped.
512 */
513
514 ASC_DLLSPEC(enum factor_method ) linsolqr_fmethod(linsolqr_system_t sys);
515 /**<
516 * Returns the most recently used factorization method of the system.
517 * The system should be previously prepped.
518 */
519
520 ASC_DLLSPEC(enum reorder_method ) linsolqr_rmethod(linsolqr_system_t sys);
521 /**<
522 * Returns the most recently set reorder method of the system.
523 * The system should be previously prepped.
524 */
525
526 extern int32 linsolqr_rank(linsolqr_system_t sys);
527 /**<
528 * Returns the rank of the system. The system must be previously
529 * factored.
530 */
531
532 extern real64 linsolqr_smallest_pivot(linsolqr_system_t sys);
533 /**<
534 * Returns the smallest pivot accepted in solving the system. The
535 * system must be previously factored. If no pivoting was performed,
536 * MAXDOUBLE is returned.
537 */
538
539 extern int linsolqr_prep(linsolqr_system_t sys,
540 enum factor_class fclass);
541 /**<
542 * This function is analogous to slv_select_solver. It
543 * takes care of allocations. The prep call should be done (once) at
544 * the beginning of any series of linear solutions being performed on
545 * on the same linsolqr system with the same factorization class.<br><br>
546 *
547 * You must prep before doing a reordering, factorization or solution
548 * as prep sets up the appropriate internal settings. You should set
549 * the matrix before you call prep.
550 * Prep (or subsequent preps) do not affect the right hand sides of
551 * the system.<br><br>
552 *
553 * If you wish to change from 1 factoring method to another and they
554 * are not part of the class of compatible methods, you should call
555 * prep again with the new class.
556 * After prep is called, reorder should be called before factorization.
557 * As most of the sparse routines depend for performance on the
558 * prior reordering.<br><br>
559 *
560 * Return 0 if ok, or 1 otherwise.
561 */
562
563 ASC_DLLSPEC(int ) linsolqr_reorder(linsolqr_system_t sys,
564 mtx_region_t *region,
565 enum reorder_method rmeth);
566 /**<
567 * The specified region of the coefficient matrix is reordered. This
568 * must be called before factoring the matrix. The specified region
569 * is assumed to contain only nonempty rows and columns and have a full
570 * diagonal.
571 * If the coefficient matrix in use is from a nonlinear system, the
572 * pattern in the coefficient matrix should be the structural one (as
573 * opposed to the numerically derived incidence which may be less.)<br><br>
574 *
575 * If you use the numerically derived incidence, you will need to reorder
576 * before every factorization. This is generally not cost effective.
577 * If region given is mtx_ENTIRE_MATRIX, a search will be done to find
578 * an appropriate bounding region in the coefficient mtx. This is
579 * not a particularly cheap search.<br><br>
580 *
581 * This function is analogous to slv_presolve. It
582 * takes care of any structural analysis necessary
583 * to the linear solution. The reorder call should be done (once) at
584 * the beginning of any series of linear solutions being performed on
585 * on structurally identical matrices.<br><br>
586 *
587 * The reordering done must be appropriate to the factorization class.
588 * You must reorder before doing a factorization or solution as reorder
589 * sets up the appropriate internal settings. Even were the internals
590 * method independent, the reordering is critical to the performance of
591 * these methods.<br><br>
592 * Return 0 if ok, 1 if not.
593 * <pre>
594 * Brief notes on the reorderings available.
595 * SPK1: The region you give becomes the region for the problem,
596 * TSPK1: but for factorization purposes rows and columns that
597 * do not intersect the main diagonal within the region
598 * are considered structurally (therefore numerically) dependent.
599 * Natural: Blesses the system and does nothing.
600 * Again, the rows/cols not in the diagonal are dependent.
601 * </pre>
602 */
603
604 ASC_DLLSPEC(int ) linsolqr_factor(linsolqr_system_t sys,
605 enum factor_method fmethod);
606 /**<
607 * Decompose the reordered region of a copy of the coefficient matrix
608 * into upper and lower triangular factors (if necessary) which can be
609 * inverted easily when applied to any rhs. Matrix must be factored in
610 * order to perform any of the operations below. The numerical rank and
611 * the smallest pivot encountered during pivoting are computed in the
612 * process. Factorization method used is that given if it is compatible
613 * with the class set when the prep was done, otherwise the call fails.<br><br>
614 *
615 * If you are handed a linsolqr system and want to refactor it using the
616 * usual method, but don't know what that method is, call like:
617 * status = linsolqr_factor(sys,linsolqr_fmethod(sys));<br><br>
618 *
619 * Return 0 if ok, 1 if not.
620 */
621
622 extern int linsolqr_get_pivot_sets(linsolqr_system_t sys,
623 unsigned *org_rowpivots,
624 unsigned *org_colpivots);
625 /**<
626 * Returns the set of original row numbers / original column numbers which
627 * have been pivoted. org_rowpivots and org_colpivots are assumed to be
628 * sets created by (or at least for) the set module with sufficient size
629 * before calling this function. They must also be previously NULLed.
630 * The system must be previously factored.
631 * The sets input should be the result of set_create(neqn),set_create(nvar).
632 * There is no association of rows with columns here.<br><br>
633 *
634 * @return Status is 0 if not factored, 1 if factored. If 0, sets will not be
635 * changed.
636 * This bizarre piece of functionality should be done away with as soon
637 * as the equivalents below have been implemented.
638 */
639
640 ASC_DLLSPEC(mtx_sparse_t *) linsolqr_unpivoted_rows(linsolqr_system_t sys);
641 /**< See discussion under linsolqr_unpivoted_cols(). */
642 ASC_DLLSPEC(mtx_sparse_t *) linsolqr_unpivoted_cols(linsolqr_system_t sys);
643 /**<
644 * Returns the set of original row numbers / original column numbers which
645 * have NOT been pivoted and the rejected pivots in an mtx_sparse_t.
646 * Return is NULL if sys not factored or if no unpivoted rows/cols exist.
647 * E.g. singrows->idata[i] are the original rows that were not pivoted,
648 * singrows->data[i] is the pivot that was rejected,
649 * for i = 0 to singrows->len-1.
650 * If len is 0, the data and idata pointers may be NULL.
651 *
652 * The CALLER is responsible for deallocating the mtx_sparse_t returned;
653 * linsolqr wants nothing further to do with it.
654 * @bug Only deals with ranki based square systems at the moment.
655 * Then again, that's all we have at the moment (10/95).
656 * Returns NULL from non-ranki systems.
657 * @todo Separate documentation for these linsolqr functions?
658 */
659
660 extern mtx_sparse_t *linsolqr_pivoted_rows(linsolqr_system_t sys);
661 /**< See discussion under linsolqr_pivoted_cols(). */
662 extern mtx_sparse_t *linsolqr_pivoted_cols(linsolqr_system_t sys);
663 /**<
664 * Returns the set of original row numbers / original column numbers which
665 * have been pivoted and the pivots in an mtx_sparse_t.
666 * Return is NULL if sys not factored or if no pivoted rows/cols exist.
667 * E.g. pivrows->idata[i] are the original rows that were pivoted,
668 * pivrows->data[i] is the pivot,
669 * for i = 0 to pivrows->len-1.
670 * If len is 0, the data and idata pointers may be NULL.
671 *
672 * The CALLER is responsible for deallocating the mtx_sparse_t returned;
673 * linsolqr wants nothing further to do with it.
674 * @bug Only deals with ranki based square systems at the moment.
675 * Then again, that's all we have at the moment (10/95).
676 * Returns NULL from non-ranki systems.
677 * @todo Separate documentation for these linsolqr functions?
678 */
679
680 extern int32 linsolqr_org_row_to_org_col(linsolqr_system_t sys,
681 int32 org_row);
682 /**< See discussion under linsolqr_org_col_to_org_row(). */
683 extern int32 linsolqr_org_col_to_org_row(linsolqr_system_t sys,
684 int32 org_col);
685 /**<
686 * Pivoted original columns and pivoted original rows can be associated
687 * with one another via the pivot sequence. These functions returned the
688 * org_col/org_row associated with the given org_row/org_col. If the given
689 * org_row/org_col is not pivoted, a meaningless value is returned. The
690 * system must be previously factored. If not factored, these functions
691 * will return a value, but linsolqr may reorder making the value wrong.
692 * @todo Separate documentation for these linsolqr functions?
693 */
694
695 ASC_DLLSPEC(void) linsolqr_calc_row_dependencies(linsolqr_system_t sys);
696 /**< See discussion under linsolqr_calc_col_dependencies(). */
697
698 ASC_DLLSPEC(void) linsolqr_calc_col_dependencies(linsolqr_system_t sys);
699 /**<
700 * Given a factored system for which dependencies are not yet
701 * calculated, calculates row/column dependencies. This must be
702 * called before either linsolqr_org_row/col_dependency
703 * or linsolqr_row/col_dependence_coefs can be called.
704 * All rows/columns in the region specified to reorder
705 * and not part of the final factorization have their dependencies
706 * calculated.
707 *
708 * The calculation method is fairly standard.
709 * We will give the version for LU column dependency. Transpose it
710 * for row dependency. Similar things can be done for QR.
711 * Given a matrix region A, factor it and arrive at
712 * A11 | A12 where A11 = L U and columns of A12 are dependent,
713 * --------- that is A12 = A11 . Y. (The row A2 need not exist,
714 * A21 | eps but if it does, A22 must be small or we could have
715 * factored further.) Solve for Y. The Yi are the coefficients of the
716 * linear combination of columns in A11 which sum to A12.
717 * And, note that since the columns of A12 were treated during
718 * factoring as if they were ultimately going to be pivoted in,
719 * we only need to substitute on the other triangle factor, half the
720 * work of a regular solve.
721 * @todo Separate documentation for these linsolqr functions?
722 */
723
724 ASC_DLLSPEC(mtx_sparse_t *) linsolqr_row_dependence_coefs(
725 linsolqr_system_t sys, int32 orgrow);
726 /**< See discussion under linsolqr_col_dependence_coefs(). */
727
728 ASC_DLLSPEC(mtx_sparse_t *) linsolqr_col_dependence_coefs(
729 linsolqr_system_t sys, int32 orgcol
730 );
731 /**<
732 * Given an org row/col and a factored system, returns a mtx_sparse_t
733 * containing the org row/col indices and linear combination coefficients
734 * contributing to the given dependent row/col. If the orgrow/orgcol
735 * given is not dependent or dependencies have not been calculated,
736 * return is NULL.
737 * E.g. rowcoefs->idata[i] is the org row index of a contributing row,
738 * rowcoefs->data[i] is the dependency coefficient,
739 * for i = 0 to rowcoefs->len-1.
740 * Numeric dependency calculation is a numeric process with lots of room
741 * for interpretation of the results. Not everything that claims to
742 * contribute to a singularity really does so. We leave this interpre-
743 * tation to the the caller.
744 *
745 * The CALLER is responsible for deallocating the mtx_sparse_t returned;
746 * linsol wants nothing further to do with it.
747 *
748 * @todo Separate documentation for these linsolqr functions?
749 */
750
751 extern real64 linsolqr_org_row_dependency(linsolqr_system_t sys,
752 int32 dep, int32 ind);
753 /**< See discussion under linsolqr_org_col_dependency(). */
754 extern real64 linsolqr_org_col_dependency(linsolqr_system_t sys,
755 int32 dep, int32 ind);
756 /**<
757 * Any original row / column of the coefficient matrix which when submitted
758 * to the linear solver is not pivoted, is called dependent and can be
759 * written as a linear combination of the independent (pivoted) original
760 * rows / columns. These functions return the previously computed
761 * coefficients of the linear combination. The system must be previously
762 * factored and the independent row / column must be a member of the
763 * set of row / column pivots obtained by linsolqr_get_pivot_sets.
764 * This is a slow and clunky way to retrieve dependency info.
765 * This ought to be done away with when the above function is done.
766 *
767 * @todo Separate documentation for these linsolqr functions?
768 */
769
770 ASC_DLLSPEC(int ) linsolqr_solve(linsolqr_system_t sys, real64 *rhs);
771 /**<
772 * Solves the system of linear equations (if necessary) utilizing the
773 * specified rhs along with the previously factored matrix. The rhs
774 * is automatically checked if the matrix factors need to be transposed
775 * or not (see linsolqr_add_rhs.)
776 * Solution method will be appropriate to the factorization method used
777 * in linsolqr_factor.
778 * @return 0 if ok, 1 if not.
779 */
780
781 extern real64 linsolqr_var_value(linsolqr_system_t sys,
782 real64 *rhs, int32 var);
783 /**<
784 * Returns the value of the variable in the solution vector associated
785 * with the given rhs and either the matrix or its transpose. The rhs
786 * must be solved for first. If rhs specifies transpose, then var is
787 * expected to be an original row number, otherwise it should be an
788 * original column number.
789 * If sys, rhs, and var are not proper, the value returned is 0.0
790 * and a warning is issued to stderr.
791 */
792
793 ASC_DLLSPEC(boolean ) linsolqr_copy_solution(linsolqr_system_t sys,
794 real64 *rhs, real64 *vector);
795 /**<
796 * Once a sys has been factored and rhs solved, this
797 * fills in a copy of the solution vector associated with rhs. Caller
798 * must provide vector and vector must be of length at least as long
799 * as the order of the matrix that was solved. The vector entries
800 * will be in org_col order if the rhs is normal or in org_row order
801 * if the rhs is a transpose.
802 *
803 * @return TRUE if something is amiss, FALSE otherwise.
804 *
805 */
806
807 extern real64 linsolqr_eqn_residual(linsolqr_system_t sys,
808 real64 *rhs, int32 eqn);
809 /**<
810 * Returns the equation residual using the solution vector associated
811 * with the given rhs and either the matrix or its transpose.
812 * <pre>
813 * T
814 * residual = A x - b or residual = A x - b
815 * </pre>
816 * The rhs must be solved for first. If rhs specifies transpose, then
817 * eqn is expected to be an original column number, otherwise it should
818 * be an original row number.
819 * If the system and rhs and eqn are not properly solved, the return
820 * value is MAXDOUBLE.
821 */
822
823 extern boolean linsolqr_calc_residual(linsolqr_system_t sys,
824 real64 *rhs, real64 *vector);
825 /**<
826 * Returns the residuals using the solution associated
827 * with the given rhs and either the matrix or its transpose.
828 * <pre>
829 * T
830 * residual = A x - b or residual = A x - b
831 * </pre>
832 * The rhs must be solved for first. Caller
833 * must provide vector and vector must be of length at least as long
834 * as the order of the matrix that was solved. The vector entries
835 * will be in org_row order if the rhs is normal or in org_col order
836 * if the rhs is a transpose. Entries of the vector which do not
837 * correspond to rows/cols of factored system solved will not be modified.<br><br>
838 *
839 * @return If the system and rhs are not properly solved, or other is amiss
840 * return value is TRUE, else FALSE.
841 */
842
843 /* miscellaneous functions for C programmers wanting to know things. */
844
845 extern size_t linsolqr_size(linsolqr_system_t sys);
846 /**<
847 * Returns the amount of memory in use by a system and all its
848 * bits and pieces. User supplied RHS vectors and coefficient
849 * matrix are NOT included in the size calculation. The user
850 * must do accounting for those.
851 */
852
853 extern void linsolqr_free_reused_mem(void);
854 /**<
855 * Deallocates any memory that linsolqr may be squirrelling away for
856 * internal reuse. Calling this while any slv_system_t using linsolqr exists
857 * is likely to be fatal: handle with care.
858 * There isn't a way to query how many bytes this is.
859 */
860
861 /*-----------------------------------------------------------------------------
862 * The following calls exist to facilitate debugging of the linear
863 * solver when it is being tested on large systems. Do not use them
864 * in routine coding. If you need access to the factor/inverse matrices
865 * for computational purpose, you should probably consider adding that
866 * functionality to linsol.
867 */
868
869 ASC_DLLSPEC(mtx_matrix_t ) linsolqr_get_factors(linsolqr_system_t sys);
870 /**< See discussion under linsolqr_get_inverse(). */
871 extern mtx_matrix_t linsolqr_get_inverse(linsolqr_system_t sys);
872 /**<
873 * Returns the handle of the factor (L\U, Q\R) or inverse matrix.
874 * The handle may be NULL, and should be checked before use.
875 * The matrix should not be tampered (other than to look at it)
876 * with if any other mathematical operations will take place with
877 * sys. Linsol expects to deallocate both factors and inverse; do
878 * not do so yourself.
879 *
880 * @NOTE All the factorization methods use some sort of dense vectors
881 * for storing pivots and whatnot. As with a FORTRAN factorization,
882 * there's not much you can do with a factorization without
883 * also understanding in detail the factorization routine and getting
884 * your hands on the dense vectors.
885 *
886 * @todo Separate documentation of linsolqr_get_factors()
887 * and linsolqr_get_inverse()?
888 */
889
890 extern mtx_region_t *linsolqr_get_region(linsolqr_system_t sys);
891 /**<
892 * Returns a pointer to the current linsolqr region.
893 * This is being created for use in the check numeric dependency
894 * routine and may be removed once the new "problem manager" window
895 * is created to take over this functionality (and others).
896 */
897
898 extern int linsolqr_setup_ngslv(linsolqr_system_t sys,
899 real64 *rhs,
900 mtx_range_t *un_p_rng,
901 real64 *tmpvec);
902 /**< Sets up the NGSlv solver. */
903 extern real64 *linsolqr_get_varvalue(linsolqr_system_t sys, int n);
904 /**< Returns the value of the nth variable in sys. */
905
906 /** @} */
907
908 #endif /* ASC_LINSOLQR_H */

john.pye@anu.edu.au
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