-
Notifications
You must be signed in to change notification settings - Fork 14
/
Copy pathlp_scale.c
1075 lines (908 loc) · 28.7 KB
/
lp_scale.c
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
#include <string.h>
#include "commonlib.h"
#include "lp_lib.h"
#include "lp_report.h"
#include "lp_scale.h"
#ifdef FORTIFY
# include "lp_fortify.h"
#endif
/*
Scaling routines for lp_solve v5.0+
----------------------------------------------------------------------------------
Author: Kjell Eikland
Contact: [email protected]
License terms: LGPL.
Requires: lp_lib.h, lp_scale.h
Release notes:
v5.0.0 1 January 2004 Significantly expanded and repackaged scaling
routines.
v5.0.1 20 February 2004 Modified rounding behaviour in several areas.
v5.1.0 20 July 2004 Reworked with flexible matrix storage model.
v5.2.0 20 February 2005 Converted to matrix storage model without the OF.
----------------------------------------------------------------------------------
*/
/* First define scaling and unscaling primitives */
REAL scaled_value(lprec *lp, REAL value, int index)
{
if(fabs(value) < lp->infinite) {
if(lp->scaling_used) {
if(index > lp->rows)
value /= lp->scalars[index];
else
value *= lp->scalars[index];
}
}
else
value = my_sign(value)*lp->infinite;
return(value);
}
REAL unscaled_value(lprec *lp, REAL value, int index)
{
if(fabs(value) < lp->infinite) {
if(lp->scaling_used) {
if(index > lp->rows)
value *= lp->scalars[index];
else
value /= lp->scalars[index];
}
}
else
value = my_sign(value)*lp->infinite;
return(value);
}
STATIC REAL scaled_mat(lprec *lp, REAL value, int rownr, int colnr)
{
if(lp->scaling_used)
value *= lp->scalars[rownr] * lp->scalars[lp->rows + colnr];
return( value );
}
STATIC REAL unscaled_mat(lprec *lp, REAL value, int rownr, int colnr)
{
if(lp->scaling_used)
value /= lp->scalars[rownr] * lp->scalars[lp->rows + colnr];
return( value );
}
/* Compute the scale factor by the formulae:
FALSE: SUM (log |Aij|) ^ 2
TRUE: SUM (log |Aij| - RowScale[i] - ColScale[j]) ^ 2 */
REAL CurtisReidMeasure(lprec *lp, MYBOOL _Advanced, REAL *FRowScale, REAL *FColScale)
{
int i, nz;
REAL absvalue, logvalue;
register REAL result;
MATrec *mat = lp->matA;
REAL *value;
int *rownr, *colnr;
/* Do OF part */
result = 0;
for(i = 1; i <= lp->columns; i++) {
absvalue = fabs(lp->orig_obj[i]);
if(absvalue > 0) {
logvalue = log(absvalue);
if(_Advanced)
logvalue -= FRowScale[0] + FColScale[i];
result += logvalue*logvalue;
}
}
/* Do constraint matrix part */
mat_validate(mat);
value = &(COL_MAT_VALUE(0));
rownr = &(COL_MAT_ROWNR(0));
colnr = &(COL_MAT_COLNR(0));
nz = get_nonzeros(lp);
for(i = 0; i < nz;
i++, value += matValueStep, rownr += matRowColStep, colnr += matRowColStep) {
absvalue = fabs(*value);
if(absvalue > 0) {
logvalue = log(absvalue);
if(_Advanced)
logvalue -= FRowScale[*rownr] + FColScale[*colnr];
result += logvalue*logvalue;
}
}
return( result );
}
/* Implementation of the Curtis-Reid scaling based on the paper
"On the Automatic Scaling of Matrices for Gaussian
Elimination," Journal of the Institute of Mathematics and
Its Applications (1972) 10, 118-124.
Solve the system | M E | (r) (sigma)
| | ( ) = ( )
| E^T N | (c) ( tau )
by the conjugate gradient method (clever recurrences).
E is the matrix A with all elements = 1
M is diagonal matrix of row counts (RowCount)
N is diagonal matrix of column counts (ColCount)
sigma is the vector of row logarithm sums (RowSum)
tau is the vector of column logarithm sums (ColSum)
r, c are resulting row and column scalings (RowScale, ColScale) */
int CurtisReidScales(lprec *lp, MYBOOL _Advanced, REAL *FRowScale, REAL *FColScale)
{
int i, row, col, ent, nz;
REAL *RowScalem2, *ColScalem2,
*RowSum, *ColSum,
*residual_even, *residual_odd;
REAL sk, qk, ek,
skm1, qkm1, ekm1,
qkm2, qkqkm1, ekm2, ekekm1,
absvalue, logvalue,
StopTolerance;
int *RowCount, *ColCount, colMax;
int Result;
MATrec *mat = lp->matA;
REAL *value;
int *rownr, *colnr;
if(CurtisReidMeasure(lp, _Advanced, FRowScale, FColScale)<0.1*get_nonzeros(lp))
return(0);
/* Allocate temporary memory and find RowSum and ColSum measures */
nz = get_nonzeros(lp);
colMax = lp->columns;
allocREAL(lp, &RowSum, lp->rows+1, TRUE);
allocINT(lp, &RowCount, lp->rows+1, TRUE);
allocREAL(lp, &residual_odd, lp->rows+1, TRUE);
allocREAL(lp, &ColSum, colMax+1, TRUE);
allocINT(lp, &ColCount, colMax+1, TRUE);
allocREAL(lp, &residual_even, colMax+1, TRUE);
allocREAL(lp, &RowScalem2, lp->rows+1, FALSE);
allocREAL(lp, &ColScalem2, colMax+1, FALSE);
/* Set origin for row scaling */
for(i = 1; i <= colMax; i++) {
absvalue=fabs(lp->orig_obj[i]);
if(absvalue>0) {
logvalue = log(absvalue);
ColSum[i] += logvalue;
RowSum[0] += logvalue;
ColCount[i]++;
RowCount[0]++;
}
}
value = &(COL_MAT_VALUE(0));
rownr = &(COL_MAT_ROWNR(0));
colnr = &(COL_MAT_COLNR(0));
for(i = 0; i < nz;
i++, value += matValueStep, rownr += matRowColStep, colnr += matRowColStep) {
absvalue=fabs(*value);
if(absvalue>0) {
logvalue = log(absvalue);
ColSum[*colnr] += logvalue;
RowSum[*rownr] += logvalue;
ColCount[*colnr]++;
RowCount[*rownr]++;
}
}
/* Make sure we dont't have division by zero errors */
for(row = 0; row <= lp->rows; row++)
if(RowCount[row] == 0)
RowCount[row] = 1;
for(col = 1; col <= colMax; col++)
if(ColCount[col] == 0)
ColCount[col] = 1;
/* Initialize to RowScale = RowCount-1 RowSum
ColScale = 0.0
residual = ColSum - ET RowCount-1 RowSum */
StopTolerance= MAX(lp->scalelimit-floor(lp->scalelimit), DEF_SCALINGEPS);
StopTolerance *= (REAL) nz;
for(row = 0; row <= lp->rows; row++) {
FRowScale[row] = RowSum[row] / (REAL) RowCount[row];
RowScalem2[row] = FRowScale[row];
}
/* Compute initial residual */
for(col = 1; col <= colMax; col++) {
FColScale[col] = 0;
ColScalem2[col] = 0;
residual_even[col] = ColSum[col];
if(lp->orig_obj[col] != 0)
residual_even[col] -= RowSum[0] / (REAL) RowCount[0];
i = mat->col_end[col-1];
rownr = &(COL_MAT_ROWNR(i));
ent = mat->col_end[col];
for(; i < ent;
i++, rownr += matRowColStep) {
residual_even[col] -= RowSum[*rownr] / (REAL) RowCount[*rownr];
}
}
/* Compute sk */
sk = 0;
skm1 = 0;
for(col = 1; col <= colMax; col++)
sk += (residual_even[col]*residual_even[col]) / (REAL) ColCount[col];
Result = 0;
qk=1; qkm1=0; qkm2=0;
ek=0; ekm1=0; ekm2=0;
while(sk>StopTolerance) {
/* Given the values of residual and sk, construct
ColScale (when pass is even)
RowScale (when pass is odd) */
qkqkm1 = qk * qkm1;
ekekm1 = ek * ekm1;
if((Result % 2) == 0) { /* pass is even; construct RowScale[pass+1] */
if(Result != 0) {
for(row = 0; row <= lp->rows; row++)
RowScalem2[row] = FRowScale[row];
if(qkqkm1 != 0) {
for(row = 0; row <= lp->rows; row++)
FRowScale[row]*=(1 + ekekm1 / qkqkm1);
for(row = 0; row<=lp->rows; row++)
FRowScale[row]+=(residual_odd[row] / (qkqkm1 * (REAL) RowCount[row]) -
RowScalem2[row] * ekekm1 / qkqkm1);
}
}
}
else { /* pass is odd; construct ColScale[pass+1] */
for(col = 1; col <= colMax; col++)
ColScalem2[col] = FColScale[col];
if(qkqkm1 != 0) {
for(col = 1; col <= colMax; col++)
FColScale[col] *= (1 + ekekm1 / qkqkm1);
for(col = 1; col <= colMax; col++)
FColScale[col] += (residual_even[col] / ((REAL) ColCount[col] * qkqkm1) -
ColScalem2[col] * ekekm1 / qkqkm1);
}
}
/* update residual and sk (pass + 1) */
if((Result % 2) == 0) { /* even */
/* residual */
for(row = 0; row <= lp->rows; row++)
residual_odd[row] *= ek;
for(i = 1; i <= colMax; i++)
if(lp->orig_obj[i] != 0)
residual_odd[0] += (residual_even[i] / (REAL) ColCount[i]);
rownr = &(COL_MAT_ROWNR(0));
colnr = &(COL_MAT_COLNR(0));
for(i = 0; i < nz;
i++, rownr += matRowColStep, colnr += matRowColStep) {
residual_odd[*rownr] += (residual_even[*colnr] / (REAL) ColCount[*colnr]);
}
for(row = 0; row <= lp->rows; row++)
residual_odd[row] *= (-1 / qk);
/* sk */
skm1 = sk;
sk = 0;
for(row = 0; row <= lp->rows; row++)
sk += (residual_odd[row]*residual_odd[row]) / (REAL) RowCount[row];
}
else { /* odd */
/* residual */
for(col = 1; col <= colMax; col++)
residual_even[col] *= ek;
for(i = 1; i <= colMax; i++)
if(lp->orig_obj[i] != 0)
residual_even[i] += (residual_odd[0] / (REAL) RowCount[0]);
rownr = &(COL_MAT_ROWNR(0));
colnr = &(COL_MAT_COLNR(0));
for(i = 0; i < nz;
i++, rownr += matRowColStep, colnr += matRowColStep) {
residual_even[*colnr] += (residual_odd[*rownr] / (REAL) RowCount[*rownr]);
}
for(col = 1; col <= colMax; col++)
residual_even[col] *= (-1 / qk);
/* sk */
skm1 = sk;
sk = 0;
for(col = 1; col <= colMax; col++)
sk += (residual_even[col]*residual_even[col]) / (REAL) ColCount[col];
}
/* Compute ek and qk */
ekm2=ekm1;
ekm1=ek;
ek=qk * sk / skm1;
qkm2=qkm1;
qkm1=qk;
qk=1-ek;
Result++;
}
/* Synchronize the RowScale and ColScale vectors */
ekekm1 = ek * ekm1;
if(qkm1 != 0) {
if((Result % 2) == 0) { /* pass is even, compute RowScale */
for(row = 0; row<=lp->rows; row++)
FRowScale[row]*=(1.0 + ekekm1 / qkm1);
for(row = 0; row<=lp->rows; row++)
FRowScale[row]+=(residual_odd[row] / (qkm1 * (REAL) RowCount[row]) -
RowScalem2[row] * ekekm1 / qkm1);
}
else { /* pass is odd, compute ColScale */
for(col=1; col<=colMax; col++)
FColScale[col]*=(1 + ekekm1 / qkm1);
for(col=1; col<=colMax; col++)
FColScale[col]+=(residual_even[col] / ((REAL) ColCount[col] * qkm1) -
ColScalem2[col] * ekekm1 / qkm1);
}
}
/* Do validation, if indicated */
if(FALSE && mat_validate(mat)){
double check, error;
/* CHECK: M RowScale + E ColScale = RowSum */
error = 0;
for(row = 0; row <= lp->rows; row++) {
check = (REAL) RowCount[row] * FRowScale[row];
if(row == 0) {
for(i = 1; i <= colMax; i++) {
if(lp->orig_obj[i] != 0)
check += FColScale[i];
}
}
else {
i = mat->row_end[row-1];
ent = mat->row_end[row];
for(; i < ent; i++) {
col = ROW_MAT_COLNR(i);
check += FColScale[col];
}
}
check -= RowSum[row];
error += check*check;
}
/* CHECK: E^T RowScale + N ColScale = ColSum */
error = 0;
for(col = 1; col <= colMax; col++) {
check = (REAL) ColCount[col] * FColScale[col];
if(lp->orig_obj[col] != 0)
check += FRowScale[0];
i = mat->col_end[col-1];
ent = mat->col_end[col];
rownr = &(COL_MAT_ROWNR(i));
for(; i < ent;
i++, rownr += matRowColStep) {
check += FRowScale[*rownr];
}
check -= ColSum[col];
error += check*check;
}
}
/* Convert to scaling factors (rounding to nearest power
of 2 can optionally be done as a separate step later) */
for(col = 1; col <= colMax; col++) {
absvalue = exp(-FColScale[col]);
if(absvalue < MIN_SCALAR) absvalue = MIN_SCALAR;
if(absvalue > MAX_SCALAR) absvalue = MAX_SCALAR;
if(!is_int(lp,col) || is_integerscaling(lp))
FColScale[col] = absvalue;
else
FColScale[col] = 1;
}
for(row = 0; row <= lp->rows; row++) {
absvalue = exp(-FRowScale[row]);
if(absvalue < MIN_SCALAR) absvalue = MIN_SCALAR;
if(absvalue > MAX_SCALAR) absvalue = MAX_SCALAR;
FRowScale[row] = absvalue;
}
/* free temporary memory */
FREE(RowSum);
FREE(ColSum);
FREE(RowCount);
FREE(ColCount);
FREE(residual_even);
FREE(residual_odd);
FREE(RowScalem2);
FREE(ColScalem2);
return(Result);
}
STATIC MYBOOL scaleCR(lprec *lp, REAL *scaledelta)
{
REAL *scalechange = NULL;
int Result;
if(!lp->scaling_used) {
allocREAL(lp, &lp->scalars, lp->sum_alloc + 1, FALSE);
for(Result = 0; Result <= lp->sum; Result++)
lp->scalars[Result] = 1;
lp->scaling_used = TRUE;
}
if(scaledelta == NULL)
allocREAL(lp, &scalechange, lp->sum + 1, FALSE);
else
scalechange = scaledelta;
Result=CurtisReidScales(lp, FALSE, scalechange, &scalechange[lp->rows]);
if(Result>0) {
/* Do the scaling*/
if(scale_updaterows(lp, scalechange, TRUE) ||
scale_updatecolumns(lp, &scalechange[lp->rows], TRUE))
lp->scalemode |= SCALE_CURTISREID;
set_action(&lp->spx_action, ACTION_REBASE | ACTION_REINVERT | ACTION_RECOMPUTE);
}
if(scaledelta == NULL)
FREE(scalechange);
return((MYBOOL) (Result > 0));
}
STATIC MYBOOL transform_for_scale(lprec *lp, REAL *value)
{
MYBOOL Accept = TRUE;
*value = fabs(*value);
#ifdef Paranoia
if(*value < lp->epsmachine) {
Accept = FALSE;
report(lp, SEVERE, "transform_for_scale: A zero-valued entry was passed\n");
}
else
#endif
if(is_scalemode(lp, SCALE_LOGARITHMIC))
*value = log(*value);
else if(is_scalemode(lp, SCALE_QUADRATIC))
(*value) *= (*value);
return( Accept );
}
STATIC void accumulate_for_scale(lprec *lp, REAL *min, REAL *max, REAL value)
{
if(transform_for_scale(lp, &value)) {
if(is_scaletype(lp, SCALE_MEAN)) {
*max += value;
*min += 1;
}
else {
SETMAX(*max, value);
SETMIN(*min, value);
}
}
}
STATIC REAL minmax_to_scale(lprec *lp, REAL min, REAL max, int itemcount)
{
REAL scale;
/* Initialize according to transformation / weighting model */
if(is_scalemode(lp, SCALE_LOGARITHMIC))
scale = 0;
else
scale = 1;
if(itemcount <= 0)
return(scale);
/* Compute base scalar according to chosen scaling type */
if(is_scaletype(lp, SCALE_MEAN)) {
if(min > 0)
scale = max / min;
}
else if(is_scaletype(lp, SCALE_RANGE))
scale = (max + min) / 2;
else if(is_scaletype(lp, SCALE_GEOMETRIC))
scale = sqrt(min*max);
else if(is_scaletype(lp, SCALE_EXTREME))
scale = max;
/* Compute final scalar according to transformation / weighting model */
if(is_scalemode(lp, SCALE_LOGARITHMIC))
scale = exp(-scale);
else if(is_scalemode(lp, SCALE_QUADRATIC)) {
if(scale == 0)
scale = 1;
else
scale = 1 / sqrt(scale);
}
else {
if(scale == 0)
scale = 1;
else
scale = 1 / scale;
}
/* Make sure we are within acceptable scaling ranges */
SETMAX(scale, MIN_SCALAR);
SETMIN(scale, MAX_SCALAR);
return(scale);
}
STATIC REAL roundPower2(REAL scale)
/* Purpose is to round a number to it nearest power of 2; in a system
with binary number representation, this avoids rounding errors when
scale is used to normalize another value */
{
long int power2;
MYBOOL isSmall = FALSE;
if(scale == 1)
return( scale );
/* Obtain the fractional power of 2 */
if(scale < 2) {
scale = 2 / scale;
isSmall = TRUE;
}
else
scale /= 2;
scale = log(scale)/log(2.0);
/* Find the desired nearest power of two and compute the associated scalar */
power2 = (long) ceil(scale-0.5);
scale = 1 << power2;
if(isSmall)
scale = 1.0 / scale;
return( scale );
}
STATIC MYBOOL scale_updatecolumns(lprec *lp, REAL *scalechange, MYBOOL updateonly)
{
int i, j;
/* Verify that the scale change is significant (different from the unit) */
for(i = lp->columns; i > 0; i--)
if(fabs(scalechange[i]-1) > lp->epsprimal)
break;
if(i <= 0)
return( FALSE );
/* Update the pre-existing column scalar */
if(updateonly)
for(i = 1, j = lp->rows + 1; j <= lp->sum; i++, j++)
lp->scalars[j] *= scalechange[i];
else
for(i = 1, j = lp->rows + 1; j <= lp->sum; i++, j++)
lp->scalars[j] = scalechange[i];
return( TRUE );
}
STATIC MYBOOL scale_updaterows(lprec *lp, REAL *scalechange, MYBOOL updateonly)
{
int i;
/* Verify that the scale change is significant (different from the unit) */
for(i = lp->rows; i >= 0; i--) {
if(fabs(scalechange[i]-1) > lp->epsprimal)
break;
}
if(i < 0)
return( FALSE );
/* Update the pre-existing row scalar */
if(updateonly)
for(i = 0; i <= lp->rows; i++)
lp->scalars[i] *= scalechange[i];
else
for(i = 0; i <= lp->rows; i++)
lp->scalars[i] = scalechange[i];
return( TRUE );
}
STATIC MYBOOL scale_columns(lprec *lp, REAL *scaledelta)
{
int i,j, colMax, nz;
REAL *scalechange;
REAL *value;
int *colnr;
MATrec *mat = lp->matA;
/* Check that columns are in fact targeted */
if((lp->scalemode & SCALE_ROWSONLY) != 0)
return( TRUE );
if(scaledelta == NULL)
scalechange = &lp->scalars[lp->rows];
else
scalechange = &scaledelta[lp->rows];
colMax = lp->columns;
/* Scale matrix entries (including any Lagrangean constraints) */
for(i = 1; i <= lp->columns; i++) {
lp->orig_obj[i] *= scalechange[i];
}
mat_validate(lp->matA);
nz = get_nonzeros(lp);
value = &(COL_MAT_VALUE(0));
colnr = &(COL_MAT_COLNR(0));
for(i = 0; i < nz;
i++, value += matValueStep, colnr += matRowColStep) {
(*value) *= scalechange[*colnr];
}
/* Scale variable bounds as well */
for(i = 1, j = lp->rows + 1; j <= lp->sum; i++, j++) {
if(lp->orig_lowbo[j] > -lp->infinite)
lp->orig_lowbo[j] /= scalechange[i];
if(lp->orig_upbo[j] < lp->infinite)
lp->orig_upbo[j] /= scalechange[i];
if(lp->sc_lobound[i] != 0)
lp->sc_lobound[i] /= scalechange[i];
}
lp->columns_scaled = TRUE;
set_action(&lp->spx_action, ACTION_REBASE | ACTION_REINVERT | ACTION_RECOMPUTE);
return( TRUE );
}
STATIC MYBOOL scale_rows(lprec *lp, REAL *scaledelta)
{
int i, j, nz, colMax;
REAL *scalechange;
REAL *value;
int *rownr;
MATrec *mat = lp->matA;
/* Check that rows are in fact targeted */
if((lp->scalemode & SCALE_COLSONLY) != 0)
return( TRUE );
if(scaledelta == NULL)
scalechange = lp->scalars;
else
scalechange = scaledelta;
colMax = lp->columns;
/* First row-scale the matrix (including the objective function) */
for(i = 1; i <= colMax; i++) {
lp->orig_obj[i] *= scalechange[0];
}
nz = get_nonzeros(lp);
value = &(COL_MAT_VALUE(0));
rownr = &(COL_MAT_ROWNR(0));
for(i = 0; i < nz;
i++, value += matValueStep, rownr += matRowColStep) {
(*value) *= scalechange[*rownr];
}
/* ...and scale the rhs and the row bounds (RANGES in MPS!!) */
for(i = 0; i <= lp->rows; i++) {
if(fabs(lp->orig_rhs[i]) < lp->infinite)
lp->orig_rhs[i] *= scalechange[i];
j = lp->presolve_undo->var_to_orig[i];
if(j != 0)
lp->presolve_undo->fixed_rhs[j] *= scalechange[i];
if(lp->orig_upbo[i] < lp->infinite) /* This is the range */
lp->orig_upbo[i] *= scalechange[i];
if((lp->orig_lowbo[i] != 0) && (fabs(lp->orig_lowbo[i]) < lp->infinite))
lp->orig_lowbo[i] *= scalechange[i];
}
set_action(&lp->spx_action, ACTION_REBASE | ACTION_REINVERT | ACTION_RECOMPUTE);
return( TRUE );
}
STATIC REAL scale(lprec *lp, REAL *scaledelta)
{
int i, j, nz, row_count, nzOF = 0;
REAL *row_max, *row_min, *scalechange = NULL, absval;
REAL col_max, col_min;
MYBOOL rowscaled, colscaled;
MATrec *mat = lp->matA;
REAL *value;
int *rownr;
if(is_scaletype(lp, SCALE_NONE))
return(0.0);
if(!lp->scaling_used) {
allocREAL(lp, &lp->scalars, lp->sum_alloc + 1, FALSE);
for(i = 0; i <= lp->sum; i++) {
lp->scalars[i] = 1;
}
lp->scaling_used = TRUE;
}
#ifdef Paranoia
else
for(i = 0; i <= lp->sum; i++) {
if(lp->scalars[i] == 0)
report(lp, SEVERE, "scale: Zero-valued scalar found at index %d\n", i);
}
#endif
if(scaledelta == NULL)
allocREAL(lp, &scalechange, lp->sum + 1, FALSE);
else
scalechange = scaledelta;
/* Must initialize due to computation of scaling statistic - KE */
for(i = 0; i <= lp->sum; i++)
scalechange[i] = 1;
row_count = lp->rows;
allocREAL(lp, &row_max, row_count + 1, TRUE);
allocREAL(lp, &row_min, row_count + 1, FALSE);
/* Initialise min and max values of rows */
for(i = 0; i <= row_count; i++) {
if(is_scaletype(lp, SCALE_MEAN))
row_min[i] = 0; /* Carries the count of elements */
else
row_min[i] = lp->infinite; /* Carries the minimum element */
}
/* Calculate row scaling data */
for(j = 1; j <= lp->columns; j++) {
absval = lp->orig_obj[j];
if(absval != 0) {
absval = scaled_mat(lp, absval, 0, j);
accumulate_for_scale(lp, &row_min[0], &row_max[0], absval);
nzOF++;
}
i = mat->col_end[j - 1];
value = &(COL_MAT_VALUE(i));
rownr = &(COL_MAT_ROWNR(i));
nz = mat->col_end[j];
for(; i < nz;
i++, value += matValueStep, rownr += matRowColStep) {
absval = scaled_mat(lp, *value, *rownr, j);
accumulate_for_scale(lp, &row_min[*rownr], &row_max[*rownr], absval);
}
}
/* Calculate scale factors for rows */
i = 0;
for(; i <= lp->rows; i++) {
if(i == 0)
nz = nzOF;
else
nz = mat_rowlength(lp->matA, i);
absval = minmax_to_scale(lp, row_min[i], row_max[i], nz); /* nz instead of nzOF KJEI 20/05/2010 */
if(absval == 0)
absval = 1;
scalechange[i] = absval;
}
FREE(row_max);
FREE(row_min);
/* Row-scale the matrix (including the objective function and Lagrangean constraints) */
rowscaled = scale_updaterows(lp, scalechange, TRUE);
/* Calculate column scales */
i = 1;
for(j = 1; j <= lp->columns; j++) {
if(is_int(lp,j) && !is_integerscaling(lp)) { /* do not scale integer columns */
scalechange[lp->rows + j] = 1;
}
else {
col_max = 0;
if(is_scaletype(lp, SCALE_MEAN))
col_min = 0;
else
col_min = lp->infinite;
absval = lp->orig_obj[j];
if(absval != 0) {
absval = scaled_mat(lp, absval, 0, j);
accumulate_for_scale(lp, &col_min, &col_max, absval);
}
i = mat->col_end[j - 1];
value = &(COL_MAT_VALUE(i));
rownr = &(COL_MAT_ROWNR(i));
nz = mat->col_end[j];
for(; i < nz;
i++, value += matValueStep, rownr += matRowColStep) {
absval = scaled_mat(lp, *value, *rownr, j);
accumulate_for_scale(lp, &col_min, &col_max, absval);
}
nz = mat_collength(lp->matA, j);
if(fabs(lp->orig_obj[j]) > 0)
nz++;
scalechange[lp->rows + j] = minmax_to_scale(lp, col_min, col_max, nz);
}
}
/* ... and then column-scale the already row-scaled matrix */
colscaled = scale_updatecolumns(lp, &scalechange[lp->rows], TRUE);
/* Create a geometric mean-type measure of the extent of scaling performed; */
/* ideally, upon successive calls to scale() the value should converge to 0 */
if(rowscaled || colscaled) {
col_max = 0;
for(j = 1; j <= lp->columns; j++)
col_max += log(scalechange[lp->rows + j]);
col_max = exp(col_max/lp->columns);
i = 0;
col_min = 0;
for(; i <= lp->rows; i++)
col_min += log(scalechange[i]);
col_min = exp(col_min/row_count);
}
else {
col_max = 1;
col_min = 1;
}
if(scaledelta == NULL)
FREE(scalechange);
return(1 - sqrt(col_max*col_min));
}
STATIC MYBOOL finalize_scaling(lprec *lp, REAL *scaledelta)
{
int i;
/* Check if we should equilibrate */
if(is_scalemode(lp, SCALE_EQUILIBRATE) && !is_scaletype(lp, SCALE_CURTISREID)) {
int oldmode;
oldmode = lp->scalemode;
lp->scalemode = SCALE_LINEAR + SCALE_EXTREME;
scale(lp, scaledelta);
lp->scalemode = oldmode;
}
/* Check if we should prevent rounding errors */
if(is_scalemode(lp, SCALE_POWER2)) {
REAL *scalars;
if(scaledelta == NULL)
scalars = lp->scalars;
else
scalars = scaledelta;
for(i = 0; i <= lp->sum; i++)
scalars[i] = roundPower2(scalars[i]);
}
/* Then transfer the scalars to the model's data */
return( scale_rows(lp, scaledelta) && scale_columns(lp, scaledelta) );
}
STATIC REAL auto_scale(lprec *lp)
{
int n = 1;
REAL scalingmetric = 0, *scalenew = NULL;
if(lp->scaling_used &&
((((lp->scalemode & SCALE_DYNUPDATE) == 0)) || (lp->bb_level > 0)))
return( scalingmetric);
if(lp->scalemode != SCALE_NONE) {
/* Allocate array for incremental scaling if appropriate */
if((lp->solvecount > 1) && (lp->bb_level < 1) &&
((lp->scalemode & SCALE_DYNUPDATE) != 0))
allocREAL(lp, &scalenew, lp->sum + 1, FALSE);
if(is_scaletype(lp, SCALE_CURTISREID)) {
scalingmetric = scaleCR(lp, scalenew);
}
else {
REAL scalinglimit, scalingdelta;
int count;
/* Integer value of scalelimit holds the maximum number of iterations; default to 1 */
count = (int) floor(lp->scalelimit);
scalinglimit = lp->scalelimit;
if((count == 0) || (scalinglimit == 0)) {
if(scalinglimit > 0)
count = DEF_SCALINGLIMIT; /* A non-zero convergence has been given, default to max 5 iterations */
else
count = 1;
}
else
scalinglimit -= count;
/* Scale to desired relative convergence or iteration limit */
n = 0;
scalingdelta = 1.0;
scalingmetric = 1.0;
while((n < count) && (fabs(scalingdelta) > scalinglimit)) {
n++;
scalingdelta = scale(lp, scalenew);
scalingmetric = scalingmetric*(1+scalingdelta);
}
scalingmetric -= 1;
}
}
/* Update the inf norm of the elements of the matrix (excluding the OF) */
mat_computemax(lp->matA);
/* Check if we really have to do scaling */
if(lp->scaling_used && (fabs(scalingmetric) >= lp->epsprimal))
/* Ok, do it */
finalize_scaling(lp, scalenew);
else {
/* Otherwise reset scaling variables */
if(lp->scalars != NULL) {
FREE(lp->scalars);
}
lp->scaling_used = FALSE;
lp->columns_scaled = FALSE;
}
if(scalenew != NULL)
FREE(scalenew);
return(scalingmetric);
}
STATIC void unscale_columns(lprec *lp)
{
int i, j, nz;
MATrec *mat = lp->matA;
REAL *value;
int *rownr, *colnr;
if(!lp->columns_scaled)
return;
/* Unscale OF */
for(j = 1; j <= lp->columns; j++) {
lp->orig_obj[j] = unscaled_mat(lp, lp->orig_obj[j], 0, j);
}