This file is indexed.

/usr/include/ITK-4.5/sparse/spDefs.h is in libinsighttoolkit4-dev 4.5.0-3.

This file is owned by root:root, with mode 0o644.

The actual contents of the file can be viewed below.

  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
/*
 *  DATA STRUCTURE AND MACRO DEFINITIONS for Sparse.
 *
 *  Author:                     Advising professor:
 *      Kenneth S. Kundert          Alberto Sangiovanni-Vincentelli
 *      UC Berkeley
 *
 *  This file contains common type definitions and macros for the sparse
 *  matrix routines.  These definitions are of no interest to the user.
 */


/*
 *  Revision and copyright information.
 *
 *  Copyright (c) 1985-2003 by Kenneth S. Kundert
 *
 */


/*
 *  If running lint, change some of the compiler options to get a more
 *  complete inspection.
 */

#ifdef lint
#undef  REAL
#undef  spCOMPLEX
#undef  EXPANDABLE
#undef  TRANSLATE
#undef  INITIALIZE
#undef  DELETE
#undef  STRIP
#undef  MODIFIED_NODAL
#undef  QUAD_ELEMENT
#undef  TRANSPOSE
#undef  SCALING
#undef  DOCUMENTATION
#undef  MULTIPLICATION
#undef  DETERMINANT
#undef  CONDITION
#undef  PSEUDOCONDITION
#undef  FORTRAN
#undef  DEBUG

#define  REAL                           YES
#define  spCOMPLEX                      YES
#define  EXPANDABLE                     YES
#define  TRANSLATE                      YES
#define  INITIALIZE                     YES
#define  DELETE                         YES
#define  STRIP                          YES
#define  MODIFIED_NODAL                 YES
#define  QUAD_ELEMENT                   YES
#define  TRANSPOSE                      YES
#define  SCALING                        YES
#define  DOCUMENTATION                  YES
#define  MULTIPLICATION                 YES
#define  DETERMINANT                    YES
#define  CONDITION                      YES
#define  PSEUDOCONDITION                YES
#define  FORTRAN                        YES
#define  DEBUG                          YES

#define  LINT                           YES
#else /* not lint */
#define  LINT                           NO
#endif /* not lint */

/*
 *   MACRO DEFINITIONS
 *
 *   Macros are distinguished by using solely capital letters in their
 *   identifiers.  This contrasts with C defined identifiers which are strictly
 *   lower case, and program variable and procedure names which use both upper
 *   and lower case.
 */

/* Begin macros. */

/* Boolean data type */
#define  BOOLEAN        int
#define  NO             0
#define  YES            1
#define  NOT            !
#define  AND            &&
#define  OR             ||

/* NULL pointer */
#ifndef  NULL
#define  NULL           0
#endif

/* Define macros for validating matrix. */
#define  SPARSE_ID                      0xDeadBeef      /* Arbitrary. */
#define  IS_SPARSE(matrix)              (((matrix) != NULL) AND \
                                         ((matrix)->ID == SPARSE_ID))
#define  NO_ERRORS(matrix)              (((matrix)->Error >= spOKAY) AND \
                                         ((matrix)->Error < spFATAL))
#define  IS_FACTORED(matrix)            ((matrix)->Factored AND \
                                         NOT (matrix)->NeedsOrdering)

#define  ASSERT_IS_SPARSE(matrix)       vASSERT( IS_SPARSE(matrix), \
                                         spcMatrixIsNotValid )
#define  ASSERT_NO_ERRORS(matrix)       vASSERT( NO_ERRORS(matrix), \
                                         spcErrorsMustBeCleared )
#define  ASSERT_IS_FACTORED(matrix)     vASSERT( IS_FACTORED(matrix), \
                                         spcMatrixMustBeFactored )
#define  ASSERT_IS_NOT_FACTORED(matrix) vASSERT( NOT (matrix)->Factored, \
                                         spcMatrixMustNotBeFactored )

/* Macro commands */
/* Macro functions that return the maximum or minimum independent of type. */
#define  MAX(a,b)           ((a) > (b) ? (a) : (b))
#define  MIN(a,b)           ((a) < (b) ? (a) : (b))

/* Macro function that returns the absolute value of a floating point number. */
#define  ABS(a)             ((a) < 0 ? -(a) : (a))

/* Macro function that returns the square of a number. */
#define  SQR(a)             ((a)*(a))

/* Macro procedure that swaps two entities. */
#define  SWAP(type, a, b)   {type swapx; swapx = a; a = b; b = swapx;}


/*
 * COMPLEX OPERATION MACROS
 */

/* Macro function that returns the approx absolute value of a complex number. */
#if spCOMPLEX
#define  ELEMENT_MAG(ptr)   (ABS((ptr)->Real) + ABS((ptr)->Imag))
#else
#define  ELEMENT_MAG(ptr)   ((ptr)->Real < 0.0 ? -(ptr)->Real : (ptr)->Real)
#endif

/* Complex assignment statements. */
#define  CMPLX_ASSIGN(to,from)  \
{   (to).Real = (from).Real;    \
    (to).Imag = (from).Imag;    \
}
#define  CMPLX_CONJ_ASSIGN(to,from)     \
{   (to).Real = (from).Real;            \
    (to).Imag = -(from).Imag;           \
}
#define  CMPLX_NEGATE_ASSIGN(to,from)   \
{   (to).Real = -(from).Real;           \
    (to).Imag = -(from).Imag;           \
}
#define  CMPLX_CONJ_NEGATE_ASSIGN(to,from)      \
{   (to).Real = -(from).Real;                   \
    (to).Imag = (from).Imag;                    \
}
#define  CMPLX_CONJ(a)  (a).Imag = -(a).Imag
#define  CMPLX_NEGATE(a)        \
{   (a).Real = -(a).Real;       \
    (a).Imag = -(a).Imag;       \
}

/* Macro that returns the approx magnitude (L-1 norm) of a complex number. */
#define  CMPLX_1_NORM(a)        (ABS((a).Real) + ABS((a).Imag))

/* Macro that returns the approx magnitude (L-infinity norm) of a complex. */
#define  CMPLX_INF_NORM(a)      (MAX (ABS((a).Real),ABS((a).Imag)))

/* Macro function that returns the magnitude (L-2 norm) of a complex number. */
#define  CMPLX_2_NORM(a)        (sqrt((a).Real*(a).Real + (a).Imag*(a).Imag))

/* Macro function that performs complex addition. */
#define  CMPLX_ADD(to,from_a,from_b)            \
{   (to).Real = (from_a).Real + (from_b).Real;  \
    (to).Imag = (from_a).Imag + (from_b).Imag;  \
}

/* Macro function that performs complex subtraction. */
#define  CMPLX_SUBT(to,from_a,from_b)           \
{   (to).Real = (from_a).Real - (from_b).Real;  \
    (to).Imag = (from_a).Imag - (from_b).Imag;  \
}

/* Macro function that is equivalent to += operator for complex numbers. */
#define  CMPLX_ADD_ASSIGN(to,from)      \
{   (to).Real += (from).Real;           \
    (to).Imag += (from).Imag;           \
}

/* Macro function that is equivalent to -= operator for complex numbers. */
#define  CMPLX_SUBT_ASSIGN(to,from)     \
{   (to).Real -= (from).Real;           \
    (to).Imag -= (from).Imag;           \
}

/* Macro function that multiplies a complex number by a scalar. */
#define  SCLR_MULT(to,sclr,cmplx)       \
{   (to).Real = (sclr) * (cmplx).Real;  \
    (to).Imag = (sclr) * (cmplx).Imag;  \
}

/* Macro function that multiply-assigns a complex number by a scalar. */
#define  SCLR_MULT_ASSIGN(to,sclr)      \
{   (to).Real *= (sclr);                \
    (to).Imag *= (sclr);                \
}

/* Macro function that multiplies two complex numbers. */
#define  CMPLX_MULT(to,from_a,from_b)           \
{   (to).Real = (from_a).Real * (from_b).Real - \
                (from_a).Imag * (from_b).Imag;  \
    (to).Imag = (from_a).Real * (from_b).Imag + \
                (from_a).Imag * (from_b).Real;  \
}

/* Macro function that implements to *= from for complex numbers. */
#define  CMPLX_MULT_ASSIGN(to,from)             \
{   RealNumber to_real_ = (to).Real;            \
    (to).Real = to_real_ * (from).Real -        \
                (to).Imag * (from).Imag;        \
    (to).Imag = to_real_ * (from).Imag +        \
                (to).Imag * (from).Real;        \
}

/* Macro function that multiplies two complex numbers, the first of which is
 * conjugated. */
#define  CMPLX_CONJ_MULT(to,from_a,from_b)      \
{   (to).Real = (from_a).Real * (from_b).Real + \
                (from_a).Imag * (from_b).Imag;  \
    (to).Imag = (from_a).Real * (from_b).Imag - \
                (from_a).Imag * (from_b).Real;  \
}

/* Macro function that multiplies two complex numbers and then adds them
 * to another. to = add + mult_a * mult_b */
#define  CMPLX_MULT_ADD(to,mult_a,mult_b,add)                   \
{   (to).Real = (mult_a).Real * (mult_b).Real -                 \
                (mult_a).Imag * (mult_b).Imag + (add).Real;     \
    (to).Imag = (mult_a).Real * (mult_b).Imag +                 \
                (mult_a).Imag * (mult_b).Real + (add).Imag;     \
}

/* Macro function that subtracts the product of two complex numbers from
 * another.  to = subt - mult_a * mult_b */
#define  CMPLX_MULT_SUBT(to,mult_a,mult_b,subt)                 \
{   (to).Real = (subt).Real - (mult_a).Real * (mult_b).Real +   \
                              (mult_a).Imag * (mult_b).Imag;    \
    (to).Imag = (subt).Imag - (mult_a).Real * (mult_b).Imag -   \
                              (mult_a).Imag * (mult_b).Real;    \
}

/* Macro function that multiplies two complex numbers and then adds them
 * to another. to = add + mult_a* * mult_b where mult_a* represents mult_a
 * conjugate. */
#define  CMPLX_CONJ_MULT_ADD(to,mult_a,mult_b,add)              \
{   (to).Real = (mult_a).Real * (mult_b).Real +                 \
                (mult_a).Imag * (mult_b).Imag + (add).Real;     \
    (to).Imag = (mult_a).Real * (mult_b).Imag -                 \
                (mult_a).Imag * (mult_b).Real + (add).Imag;     \
}

/* Macro function that multiplies two complex numbers and then adds them
 * to another. to += mult_a * mult_b */
#define  CMPLX_MULT_ADD_ASSIGN(to,from_a,from_b)        \
{   (to).Real += (from_a).Real * (from_b).Real -        \
                 (from_a).Imag * (from_b).Imag;         \
    (to).Imag += (from_a).Real * (from_b).Imag +        \
                 (from_a).Imag * (from_b).Real;         \
}

/* Macro function that multiplies two complex numbers and then subtracts them
 * from another. */
#define  CMPLX_MULT_SUBT_ASSIGN(to,from_a,from_b)       \
{   (to).Real -= (from_a).Real * (from_b).Real -        \
                 (from_a).Imag * (from_b).Imag;         \
    (to).Imag -= (from_a).Real * (from_b).Imag +        \
                 (from_a).Imag * (from_b).Real;         \
}

/* Macro function that multiplies two complex numbers and then adds them
 * to the destination. to += from_a* * from_b where from_a* represents from_a
 * conjugate. */
#define  CMPLX_CONJ_MULT_ADD_ASSIGN(to,from_a,from_b)   \
{   (to).Real += (from_a).Real * (from_b).Real +        \
                 (from_a).Imag * (from_b).Imag;         \
    (to).Imag += (from_a).Real * (from_b).Imag -        \
                 (from_a).Imag * (from_b).Real;         \
}

/* Macro function that multiplies two complex numbers and then subtracts them
 * from the destination. to -= from_a* * from_b where from_a* represents from_a
 * conjugate. */
#define  CMPLX_CONJ_MULT_SUBT_ASSIGN(to,from_a,from_b)  \
{   (to).Real -= (from_a).Real * (from_b).Real +        \
                 (from_a).Imag * (from_b).Imag;         \
    (to).Imag -= (from_a).Real * (from_b).Imag -        \
                 (from_a).Imag * (from_b).Real;         \
}

/*
 * Macro functions that provide complex division.
 */

/* Complex division:  to = num / den */
#define CMPLX_DIV(to,num,den)                                           \
{   RealNumber  r_, s_;                                                 \
    if (((den).Real >= (den).Imag AND (den).Real > -(den).Imag) OR      \
        ((den).Real < (den).Imag AND (den).Real <= -(den).Imag))        \
    {   r_ = (den).Imag / (den).Real;                                   \
        s_ = (den).Real + r_*(den).Imag;                                \
        (to).Real = ((num).Real + r_*(num).Imag)/s_;                    \
        (to).Imag = ((num).Imag - r_*(num).Real)/s_;                    \
    }                                                                   \
    else                                                                \
    {   r_ = (den).Real / (den).Imag;                                   \
        s_ = (den).Imag + r_*(den).Real;                                \
        (to).Real = (r_*(num).Real + (num).Imag)/s_;                    \
        (to).Imag = (r_*(num).Imag - (num).Real)/s_;                    \
    }                                                                   \
}

/* Complex division and assignment:  num /= den */
#define CMPLX_DIV_ASSIGN(num,den)                                       \
{   RealNumber  r_, s_, t_;                                             \
    if (((den).Real >= (den).Imag AND (den).Real > -(den).Imag) OR      \
        ((den).Real < (den).Imag AND (den).Real <= -(den).Imag))        \
    {   r_ = (den).Imag / (den).Real;                                   \
        s_ = (den).Real + r_*(den).Imag;                                \
        t_ = ((num).Real + r_*(num).Imag)/s_;                           \
        (num).Imag = ((num).Imag - r_*(num).Real)/s_;                   \
        (num).Real = t_;                                                \
    }                                                                   \
    else                                                                \
    {   r_ = (den).Real / (den).Imag;                                   \
        s_ = (den).Imag + r_*(den).Real;                                \
        t_ = (r_*(num).Real + (num).Imag)/s_;                           \
        (num).Imag = (r_*(num).Imag - (num).Real)/s_;                   \
        (num).Real = t_;                                                \
    }                                                                   \
}

/* Complex reciprocation:  to = 1.0 / den */
#define CMPLX_RECIPROCAL(to,den)                                        \
{   RealNumber  r_;                                                     \
    if (((den).Real >= (den).Imag AND (den).Real > -(den).Imag) OR      \
        ((den).Real < (den).Imag AND (den).Real <= -(den).Imag))        \
    {   r_ = (den).Imag / (den).Real;                                   \
        (to).Imag = -r_*((to).Real = 1.0/((den).Real + r_*(den).Imag)); \
    }                                                                   \
    else                                                                \
    {   r_ = (den).Real / (den).Imag;                                   \
        (to).Real = -r_*((to).Imag = -1.0/((den).Imag + r_*(den).Real));\
    }                                                                   \
}


/*
 *  ASSERT and ABORT
 *
 *  Macro used to assert that if the code is working correctly, then
 *  a condition must be true.  If not, then execution is terminated
 *  and an error message is issued stating that there is an internal
 *  error and giving the file and line number.  These assertions are
 *  not evaluated unless the DEBUG flag is true.
 */

#if DEBUG
#define ASSERT(condition)       \
{   if (NOT(condition))         \
    {   (void)fflush(stdout);   \
        (void)fprintf(stderr, "sparse: internal error detected in file `%s' at line %d.\n    assertion `%s' failed.\n",\
        __FILE__, __LINE__, spcQUOTE(condition) ); \
        (void)fflush(stderr);   \
        abort();                \
    }                           \
}
#else
#define ASSERT(condition)
#endif

#if DEBUG
#define vASSERT(condition,message)      \
{   if (NOT(condition))                 \
        vABORT(message);                \
}
#else
#define vASSERT(condition,message)
#endif

#if DEBUG
#define  vABORT(message)        \
{   (void)fflush(stdout);       \
    (void)fprintf(stderr, "sparse: internal error detected in file `%s' at line %d.\n    %s.\n", __FILE__, __LINE__, message );\
    (void)fflush(stderr);       \
    abort();                    \
}

#define  ABORT()                \
{   (void)fflush(stdout);       \
    (void)fprintf(stderr, "sparse: internal error detected in file `%s' at line %d.\n", __FILE__, __LINE__ );   \
    (void)fflush(stderr);       \
    abort();                    \
}
#else
#define  vABORT(message)        abort()
#define  ABORT()                abort()
#endif


/*
 *  IMAGINARY VECTORS
 *
 *  The imaginary vectors iRHS and iSolution are only needed when the
 *  options spCOMPLEX and spSEPARATED_COMPLEX_VECTORS are set.  The following
 *  macro makes it easy to include or exclude these vectors as needed.
 */

#if spCOMPLEX AND spSEPARATED_COMPLEX_VECTORS
#define IMAG_VECTORS    , iRHS, iSolution
#define IMAG_RHS        , iRHS
#define IMAG_RHS_DECL   , RealVector iRHS
#define IMAG_VECT_DECL  , RealVector iRHS, RealVector iSolution
#else
#define IMAG_VECTORS
#define IMAG_RHS
#define IMAG_RHS_DECL
#define IMAG_VECT_DECL
#endif


/*
 * MEMORY ALLOCATION
 */

spcEXTERN void *malloc(size_t size);
spcEXTERN void *calloc(size_t nmemb, size_t size);
spcEXTERN void *realloc(void *ptr, size_t size);
spcEXTERN void free(void *ptr);
spcEXTERN void abort(void);

#define ALLOC(type,number)  ((type *)malloc((unsigned)(sizeof(type)*(number))))
#define REALLOC(ptr,type,number)  \
           ptr = (type *)realloc((char *)ptr,(unsigned)(sizeof(type)*(number)))
#define FREE(ptr) { if ((ptr) != NULL) free((char *)(ptr)); (ptr) = NULL; }


/* Calloc that properly handles allocating a cleared vector. */
#define CALLOC(ptr,type,number)                         \
{   int i; ptr = ALLOC(type, number);                   \
    if (ptr != (type *)NULL)                            \
        for (i=(number)-1;i>=0; i--) ptr[i] = (type) 0;  \
}

/*
 * Utility Functions
 */
/*
 * Compute the product of two intergers while avoiding overflow.
 * Used when computing Markowitz products.
 */

#define spcMarkoProd(product, op1, op2) \
        if (( (op1) > LARGEST_SHORT_INTEGER AND (op2) != 0) OR \
            ( (op2) > LARGEST_SHORT_INTEGER AND (op1) != 0)) \
        {   double fProduct = (double)(op1) * (double)(op2); \
            if (fProduct >= LARGEST_LONG_INTEGER) \
                (product) = LARGEST_LONG_INTEGER; \
            else \
                (product) = (long)fProduct; \
        } \
        else (product) = (op1)*(op2);

/*
 *  REAL NUMBER
 */

/* Begin `RealNumber'. */

typedef  spREAL  RealNumber, *RealVector;

/*
 *  COMPLEX NUMBER DATA STRUCTURE
 *
 *  >>> Structure fields:
 *  Real  (RealNumber)
 *      The real portion of the number.  Real must be the first
 *      field in this structure.
 *  Imag  (RealNumber)
 *      The imaginary portion of the number. This field must follow
 *      immediately after Real.
 */

/* Begin `ComplexNumber'. */

typedef  struct
{   RealNumber  Real;
    RealNumber  Imag;
} ComplexNumber, *ComplexVector;

/*
 *  MATRIX ELEMENT DATA STRUCTURE
 *
 *  Every nonzero element in the matrix is stored in a dynamically allocated
 *  MatrixElement structure.  These structures are linked together in an
 *  orthogonal linked list.  Two different MatrixElement structures exist.
 *  One is used when only real matrices are expected, it is missing an entry
 *  for imaginary data.  The other is used if complex matrices are expected.
 *  It contains an entry for imaginary data.
 *
 *  >>> Structure fields:
 *  Real  (RealNumber)
 *      The real portion of the value of the element.  Real must be the first
 *      field in this structure.
 *  Imag  (RealNumber)
 *      The imaginary portion of the value of the element. If the matrix
 *      routines are not compiled to handle complex matrices, then this
 *      field does not exist.  If it exists, it must follow immediately after
 *      Real.
 *  Row  (int)
 *      The row number of the element.
 *  Col  (int)
 *      The column number of the element.
 *  NextInRow  (struct MatrixElement *)
 *      NextInRow contains a pointer to the next element in the row to the
 *      right of this element.  If this element is the last nonzero in the
 *      row then NextInRow contains NULL.
 *  NextInCol  (struct MatrixElement *)
 *      NextInCol contains a pointer to the next element in the column below
 *      this element.  If this element is the last nonzero in the column then
 *      NextInCol contains NULL.
 *  pInitInfo  (spGenericPtr)
 *      Pointer to user data used for initialization of the matrix element.
 *      Initialized to NULL.
 *
 *  >>> Type definitions:
 *  ElementPtr
 *      A pointer to a MatrixElement.
 *  ArrayOfElementPtrs
 *      An array of ElementPtrs.  Used for FirstInRow, FirstInCol and
 *      Diag pointer arrays.
 */

/* Begin `MatrixElement'. */

struct  MatrixElement
{   RealNumber   Real;
#if spCOMPLEX
    RealNumber   Imag;
#endif
    int          Row;
    int          Col;
    struct MatrixElement  *NextInRow;
    struct MatrixElement  *NextInCol;
#if INITIALIZE
    spGenericPtr pInitInfo;
#endif
};

typedef  struct MatrixElement  *ElementPtr;
typedef  ElementPtr  *ArrayOfElementPtrs;

/*
 *  ALLOCATION DATA STRUCTURE
 *
 *  The sparse matrix routines keep track of all memory that is allocated by
 *  the operating system so the memory can later be freed.  This is done by
 *  saving the pointers to all the chunks of memory that are allocated to a
 *  particular matrix in an allocation list.  That list is organized as a
 *  linked list so that it can grow without a priori bounds.
 *
 *  >>> Structure fields:
 *  AllocatedPtr  (void *)
 *      Pointer to chunk of memory that has been allocated for the matrix.
 *  NextRecord  (struct  AllocationRecord *)
 *      Pointer to the next allocation record.
 */

/* Begin `AllocationRecord'. */
struct AllocationRecord
{   void  *AllocatedPtr;
    struct  AllocationRecord  *NextRecord;
};

typedef  struct  AllocationRecord  *AllocationListPtr;

/*
 *  FILL-IN LIST DATA STRUCTURE
 *
 *  The sparse matrix routines keep track of all fill-ins separately from
 *  user specified elements so they may be removed by spStripFills().  Fill-ins
 *  are allocated in bunched in what is called a fill-in lists.  The data
 *  structure defined below is used to organize these fill-in lists into a
 *  linked-list.
 *
 *  >>> Structure fields:
 *  pFillinList  (ElementPtr)
 *      Pointer to a fill-in list, or a bunch of fill-ins arranged contiguously
 *      in memory.
 *  NumberOfFillinsInList  (int)
 *      Seems pretty self explanatory to me.
 *  Next  (struct  FillinListNodeStruct *)
 *      Pointer to the next fill-in list structures.
 */

/* Begin `FillinListNodeStruct'. */
struct FillinListNodeStruct
{   ElementPtr  pFillinList;
    int         NumberOfFillinsInList;
    struct      FillinListNodeStruct  *Next;
};

/*
 *  MATRIX FRAME DATA STRUCTURE
 *
 *  This structure contains all the pointers that support the orthogonal
 *  linked list that contains the matrix elements.  Also included in this
 *  structure are other numbers and pointers that are used globally by the
 *  sparse matrix routines and are associated with one particular matrix.
 *
 *  >>> Type definitions:
 *  MatrixPtr
 *      A pointer to MatrixFrame.  Essentially, a pointer to the matrix.
 *
 *  >>> Structure fields:
 *  AbsThreshold  (RealNumber)
 *      The absolute magnitude an element must have to be considered as a
 *      pivot candidate, except as a last resort.
 *  AllocatedExtSize  (int)
 *      The allocated size of the arrays used to translate external row and
 *      column numbers to their internal values.
 *  AllocatedSize  (int)
 *      The currently allocated size of the matrix; the size the matrix can
 *      grow to when EXPANDABLE is set true and AllocatedSize is the largest
 *      the matrix can get without requiring that the matrix frame be
 *      reallocated.
 *  Complex  (BOOLEAN)
 *      The flag which indicates whether the matrix is complex (true) or
 *      real.
 *  CurrentSize  (int)
 *      This number is used during the building of the matrix when the
 *      TRANSLATE option is set true.  It indicates the number of internal
 *      rows and columns that have elements in them.
 *  Diag  (ArrayOfElementPtrs)
 *      Array of pointers that points to the diagonal elements.
 *  DoCmplxDirect  (BOOLEAN *)
 *      Array of flags, one for each column in matrix.  If a flag is true
 *      then corresponding column in a complex matrix should be eliminated
 *      in spFactor() using direct addressing (rather than indirect
 *      addressing).
 *  DoRealDirect  (BOOLEAN *)
 *      Array of flags, one for each column in matrix.  If a flag is true
 *      then corresponding column in a real matrix should be eliminated
 *      in spFactor() using direct addressing (rather than indirect
 *      addressing).
 *  Elements  (int)
 *      The number of original elements (total elements minus fill ins)
 *      present in matrix.
 *  Error  (int)
 *      The error status of the sparse matrix package.
 *  ExtSize  (int)
 *      The value of the largest external row or column number encountered.
 *  ExtToIntColMap  (int [])
 *      An array that is used to convert external columns number to internal
 *      external column numbers.  Present only if TRANSLATE option is set true.
 *  ExtToIntRowMap  (int [])
 *      An array that is used to convert external row numbers to internal
 *      external row numbers.  Present only if TRANSLATE option is set true.
 *  Factored  (BOOLEAN)
 *      Indicates if matrix has been factored.  This flag is set true in
 *      spFactor() and spOrderAndFactor() and set false in spCreate()
 *      and spClear().
 *  Fillins  (int)
 *      The number of fill-ins created during the factorization the matrix.
 *  FirstInCol  (ArrayOfElementPtrs)
 *      Array of pointers that point to the first nonzero element of the
 *      column corresponding to the index.
 *  FirstInRow  (ArrayOfElementPtrs)
 *      Array of pointers that point to the first nonzero element of the row
 *      corresponding to the index.
 *  ID  (unsigned long int)
 *      A constant that provides the sparse data structure with a signature.
 *      When DEBUG is true, all externally available sparse routines check
 *      this signature to assure they are operating on a valid matrix.
 *  Intermediate  (RealVector)
 *      Temporary storage used in the spSolve routines. Intermediate is an
 *      array used during forward and backward substitution.  It is
 *      commonly called y when the forward and backward substitution process is
 *      denoted  Ax = b => Ly = b and Ux = y.
 *  InternalVectorsAllocated  (BOOLEAN)
 *      A flag that indicates whether theMmarkowitz vectors and the
 *      Intermediate vector have been created.
 *      These vectors are created in spcCreateInternalVectors().
 *  IntToExtColMap  (int [])
 *      An array that is used to convert internal column numbers to external
 *      external column numbers.
 *  IntToExtRowMap  (int [])
 *      An array that is used to convert internal row numbers to external
 *      external row numbers.
 *  MarkowitzCol  (int [])
 *      An array that contains the count of the non-zero elements excluding
 *      the pivots for each column. Used to generate and update MarkowitzProd.
 *  MarkowitzProd  (long [])
 *      The array of the products of the Markowitz row and column counts. The
 *      element with the smallest product is the best pivot to use to maintain
 *      sparsity.
 *  MarkowitzRow  (int [])
 *      An array that contains the count of the non-zero elements excluding
 *      the pivots for each row. Used to generate and update MarkowitzProd.
 *  MaxRowCountInLowerTri  (int)
 *      The maximum number of off-diagonal element in the rows of L, the
 *      lower triangular matrix.  This quantity is used when computing an
 *      estimate of the roundoff error in the matrix.
 *  NeedsOrdering  (BOOLEAN)
 *      This is a flag that signifies that the matrix needs to be ordered
 *      or reordered.  NeedsOrdering is set true in spCreate() and
 *      spGetElement() or spGetAdmittance() if new elements are added to the
 *      matrix after it has been previously factored.  It is set false in
 *      spOrderAndFactor().
 *  NumberOfInterchangesIsOdd  (BOOLEAN)
 *      Flag that indicates the sum of row and column interchange counts
 *      is an odd number.  Used when determining the sign of the determinant.
 *  Partitioned  (BOOLEAN)
 *      This flag indicates that the columns of the matrix have been
 *      partitioned into two groups.  Those that will be addressed directly
 *      and those that will be addressed indirectly in spFactor().
 *  PivotsOriginalCol  (int)
 *      Column pivot was chosen from.
 *  PivotsOriginalRow  (int)
 *      Row pivot was chosen from.
 *  PivotSelectionMethod  (char)
 *      Character that indicates which pivot search method was successful.
 *  PreviousMatrixWasComplex  (BOOLEAN)
 *      This flag in needed to determine how to clear the matrix.  When
 *      dealing with real matrices, it is important that the imaginary terms
 *      in the matrix elements be zero.  Thus, if the previous matrix was
 *      complex, then the current matrix will be cleared as if it were complex
 *      even if it is real.
 *  RelThreshold  (RealNumber)
 *      The magnitude an element must have relative to others in its row
 *      to be considered as a pivot candidate, except as a last resort.
 *  Reordered  (BOOLEAN)
 *      This flag signifies that the matrix has been reordered.  It
 *      is cleared in spCreate(), set in spMNA_Preorder() and
 *      spOrderAndFactor() and is used in spPrint().
 *  RowsLinked  (BOOLEAN)
 *      A flag that indicates whether the row pointers exist.  The AddByIndex
 *      routines do not generate the row pointers, which are needed by some
 *      of the other routines, such as spOrderAndFactor() and spScale().
 *      The row pointers are generated in the function spcLinkRows().
 *  SingularCol  (int)
 *      Normally zero, but if matrix is found to be singular, SingularCol is
 *      assigned the external column number of pivot that was zero.
 *  SingularRow  (int)
 *      Normally zero, but if matrix is found to be singular, SingularRow is
 *      assigned the external row number of pivot that was zero.
 *  Singletons  (int)
 *      The number of singletons available for pivoting.  Note that if row I
 *      and column I both contain singletons, only one of them is counted.
 *  Size  (int)
 *      Number of rows and columns in the matrix.  Does not change as matrix
 *      is factored.
 *  TrashCan  (MatrixElement)
 *      This is a dummy MatrixElement that is used to by the user to stuff
 *      data related to the zero row or column.  In other words, when the user
 *      adds an element in row zero or column zero, then the matrix returns
 *      a pointer to TrashCan.  In this way the user can have a uniform way
 *      data into the matrix independent of whether a component is connected
 *      to ground.
 *
 *  >>> The remaining fields are related to memory allocation.
 *  TopOfAllocationList  (AllocationListPtr)
 *      Pointer which points to the top entry in a list. The list contains
 *      all the pointers to the segments of memory that have been allocated
 *      to this matrix. This is used when the memory is to be freed on
 *      deallocation of the matrix.
 *  RecordsRemaining  (int)
 *      Number of slots left in the list of allocations.
 *  NextAvailElement  (ElementPtr)
 *      Pointer to the next available element which has been allocated but as
 *      yet is unused. Matrix elements are allocated in groups of
 *      ELEMENTS_PER_ALLOCATION in order to speed element allocation and
 *      freeing.
 *  ElementsRemaining  (int)
 *      Number of unused elements left in last block of elements allocated.
 *  NextAvailFillin  (ElementPtr)
 *      Pointer to the next available fill-in which has been allocated but
 *      as yet is unused.  Fill-ins are allocated in a group in order to keep
 *      them physically close in memory to the rest of the matrix.
 *  FillinsRemaining  (int)
 *      Number of unused fill-ins left in the last block of fill-ins
 *      allocated.
 *  FirstFillinListNode  (FillinListNodeStruct *)
 *      A pointer to the head of the linked-list that keeps track of the
 *      lists of fill-ins.
 *  LastFillinListNode  (FillinListNodeStruct *)
 *      A pointer to the tail of the linked-list that keeps track of the
 *      lists of fill-ins.
 */

/* Begin `MatrixFrame'. */
struct  MatrixFrame
{   RealNumber                   AbsThreshold;
    int                          AllocatedSize;
    int                          AllocatedExtSize;
    BOOLEAN                      Complex;
    int                          CurrentSize;
    ArrayOfElementPtrs           Diag;
    BOOLEAN                     *DoCmplxDirect;
    BOOLEAN                     *DoRealDirect;
    int                          Elements;
    int                          Error;
    int                          ExtSize;
    int                         *ExtToIntColMap;
    int                         *ExtToIntRowMap;
    BOOLEAN                      Factored;
    int                          Fillins;
    ArrayOfElementPtrs           FirstInCol;
    ArrayOfElementPtrs           FirstInRow;
    unsigned long                ID;
    RealVector                   Intermediate;
    BOOLEAN                      InternalVectorsAllocated;
    int                         *IntToExtColMap;
    int                         *IntToExtRowMap;
    int                         *MarkowitzRow;
    int                         *MarkowitzCol;
    long                        *MarkowitzProd;
    int                          MaxRowCountInLowerTri;
    BOOLEAN                      NeedsOrdering;
    BOOLEAN                      NumberOfInterchangesIsOdd;
    BOOLEAN                      Partitioned;
    int                          PivotsOriginalCol;
    int                          PivotsOriginalRow;
    char                         PivotSelectionMethod;
    BOOLEAN                      PreviousMatrixWasComplex;
    RealNumber                   RelThreshold;
    BOOLEAN                      Reordered;
    BOOLEAN                      RowsLinked;
    int                          SingularCol;
    int                          SingularRow;
    int                          Singletons;
    int                          Size;
    struct MatrixElement         TrashCan;

    AllocationListPtr            TopOfAllocationList;
    int                          RecordsRemaining;
    ElementPtr                   NextAvailElement;
    int                          ElementsRemaining;
    ElementPtr                   NextAvailFillin;
    int                          FillinsRemaining;
    struct FillinListNodeStruct *FirstFillinListNode;
    struct FillinListNodeStruct *LastFillinListNode;
};
typedef  struct MatrixFrame  *MatrixPtr;


/*
 *  Declarations
 */

spcEXTERN ElementPtr spcGetElement( MatrixPtr );
spcEXTERN ElementPtr spcGetFillin( MatrixPtr );
spcEXTERN ElementPtr spcFindDiag( MatrixPtr, int );
spcEXTERN ElementPtr spcCreateElement( MatrixPtr, int, int,
                                ElementPtr*, ElementPtr*, int );
spcEXTERN void spcCreateInternalVectors( MatrixPtr );
spcEXTERN void spcLinkRows( MatrixPtr );
spcEXTERN void spcColExchange( MatrixPtr, int, int );
spcEXTERN void spcRowExchange( MatrixPtr, int, int );

spcEXTERN char spcMatrixIsNotValid[];
spcEXTERN char spcErrorsMustBeCleared[];
spcEXTERN char spcMatrixMustBeFactored[];
spcEXTERN char spcMatrixMustNotBeFactored[];