File: ccealignmodule.c

package info (click to toggle)
python-biopython 1.85%2Bdfsg-4
  • links: PTS, VCS
  • area: main
  • in suites: forky, sid, trixie
  • size: 126,372 kB
  • sloc: xml: 1,047,995; python: 332,722; ansic: 16,944; sql: 1,208; makefile: 140; sh: 81
file content (763 lines) | stat: -rw-r--r-- 26,724 bytes parent folder | download
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
//
//  Original Code
//      Copyright (C) Jason Vertrees
//  Modifications
//      Copyright (C) Joao Rodrigues.
//      Modifications include removal of RMSD calculation code and associated
//      dependencies. Output of the module is now the best paths.
//
//  All rights reserved.
//  Redistribution and use in source and binary forms, with or without
//  modification, are permitted provided that the following conditions are
//  met:
//
//      * Redistributions of source code must retain the above copyright
//      notice, this list of conditions and the following disclaimer.
//
//      * Redistributions in binary form must reproduce the above copyright
//      notice, this list of conditions and the following disclaimer in
//      the documentation and/or other materials provided with the
//      distribution.
//
//  THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS
//  IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
//  TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A
//  PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER
//  OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
//  EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
//  PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
//  PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
//  LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
//  NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
//  SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

//  The following notice is provided since the code was adapted from
//  open-source Pymol.

//  Open-Source PyMOL Copyright Notice
//  ==================================

//  The Open-Source PyMOL source code is copyrighted, but you can freely
//  use and copy it as long as you don't change or remove any of the
//  Copyright notices. The Open-Source PyMOL product is made available
//  under the following open-source license terms:

//  ----------------------------------------------------------------------
//  Open-Source PyMOL is Copyright (C) Schrodinger, LLC.

//  All Rights Reserved

//  Permission to use, copy, modify, distribute, and distribute modified
//  versions of this software and its built-in documentation for any
//  purpose and without fee is hereby granted, provided that the above
//  copyright notice appears in all copies and that both the copyright
//  notice and this permission notice appear in supporting documentation,
//  and that the name of Schrodinger, LLC not be used in advertising or
//  publicity pertaining to distribution of the software without specific,
//  written prior permission.

//  SCHRODINGER, LLC DISCLAIMS ALL WARRANTIES WITH REGARD TO THIS SOFTWARE,
//  INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS. IN
//  NO EVENT SHALL SCHRODINGER, LLC BE LIABLE FOR ANY SPECIAL, INDIRECT OR
//  CONSEQUENTIAL DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS
//  OF USE, DATA OR PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE
//  OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE
//  USE OR PERFORMANCE OF THIS SOFTWARE.
//  ----------------------------------------------------------------------

//  PyMOL Trademark Notice
//  ======================

//  PyMOL(TM) is a trademark of Schrodinger, LLC. Derivative
//  software which contains PyMOL source code must be plainly
//  distinguished from any and all PyMOL products distributed by Schrodinger,
//  LLC in all publicity, advertising, and documentation.
//  The slogans, "Includes PyMOL(TM).", "Based on PyMOL(TM) technology.",
//  "Contains PyMOL(TM) source code.", and "Built using PyMOL(TM).", may
//  be used in advertising, publicity, and documentation of derivative
//  software provided that the notice, "PyMOL is a trademark of Schrodinger,
//  LLC.", is included in a footnote or at the end of the
//  document.

//  All other endorsements employing the PyMOL trademark require specific,
//  written prior permission.
//

#include "Python.h"

#define MAX_PATHS 20

// Typical XYZ point and array of points
typedef struct {
    double x;
    double y;
    double z;
} cePoint, *pcePoint;

// An AFP (aligned fragment pair), and list/pointer
typedef struct {
    int pA;
    int pB;
} afp, *path;

// Calculate distance matrix
static double **
calcDM(pcePoint coords, int len)
{
    double **dm = (double **)PyMem_RawMalloc(sizeof(double *) * len);

    for (int i = 0; i < len; i++) {
        dm[i] = (double *)PyMem_RawMalloc(sizeof(double) * len);
    }
    for (int row = 0; row < len; row++) {
        for (int col = row; col < len; col++) {
            double xd = coords[row].x - coords[col].x;
            double yd = coords[row].y - coords[col].y;
            double zd = coords[row].z - coords[col].z;
            double distance = sqrt(xd * xd + yd * yd + zd * zd);

            dm[row][col] = dm[col][row] = distance;
        }
    }

    return dm;
}

//
// This similarity corresponds to distance measure (i) or
// equation (6) in the paper.
//
static double
similarityI(
    double **dA,
    double **dB,
    const afp afpI,
    const afp afpJ,
    const int fragmentSize)
{
    const int iA = afpI.pA;
    const int iB = afpI.pB;
    const int jA = afpJ.pA;
    const int jB = afpJ.pB;
    const int m = fragmentSize;
    double similarity = fabs(dA[iA][jA] - dB[iB][jB]) +
        fabs(dA[iA + m-1][jA + m-1] - dB[iB + m-1][jB + m-1]);

    for (int k = 1; k < m - 1; k++) {
        similarity += fabs(dA[iA + k][jA + m-1 - k] -
            fabs(dB[iB + k][jB + m-1 - k]));
    }

    return -similarity / m;
}

//
// This similarity corresponds to distance measure (ii)
// or equation (7) in the paper.
//
static double
similarityII(
    double **dA,
    double **dB,
    const afp afpI,
    const int fragmentSize)
{
    const int iA = afpI.pA;
    const int iB = afpI.pB;
    double similarity = 0.0;
    // Term count is the number of terms in the summation
    const int termCount = (fragmentSize - 1) * (fragmentSize - 2) / 2;

    for (int k = 0; k < fragmentSize - 2; k++) {
        for (int l = k + 2; l < fragmentSize; l++) {
            similarity +=
                fabs(dA[iA + k][iA + l] - dB[iB + k][iB + l]);
        }
    }

    return -similarity / termCount;
}

// Calculate similarity matrix
static double **
calcS(
    double **dA,
    double **dB,
    const int lenA,
    const int lenB,
    const int fragmentSize)
{
    // Initialize the 2D similarity matrix
    const int rowCount = lenA - fragmentSize + 1;
    const int colCount = lenB - fragmentSize + 1;
    double **S = (double **)PyMem_RawMalloc(sizeof(double *) * rowCount);

    for (int i = 0; i < rowCount; i++) {
        S[i] = (double *)PyMem_RawMalloc(sizeof(double) * colCount);
    }

    //
    // This is where the magic of CE comes out. In the similarity matrix,
    // for each i and j, the value of S[i][j] is how well the fragment starting
    // at i in protein A matches the fragment starting at j in protein
    // B. A value of 0 means absolute match; a value << -3 means bad match.
    //
    for (int iA = 0; iA < rowCount; iA++) {
        for (int iB = 0; iB < colCount; iB++) {
            S[iA][iB] = similarityII(dA, dB, (afp) {iA, iB}, fragmentSize);
        }
    }

    return S;
}

static const double tableZtoP[] = {
    1.0, 9.20e-01, 8.41e-01, 7.64e-01, 6.89e-01, 6.17e-01, 5.49e-01, 4.84e-01, 4.24e-01, 3.68e-01,
    3.17e-01, 2.71e-01, 2.30e-01, 1.94e-01, 1.62e-01, 1.34e-01, 1.10e-01, 8.91e-02, 7.19e-02, 5.74e-02,
    4.55e-02, 3.57e-02, 2.78e-02, 2.14e-02, 1.64e-02, 1.24e-02, 9.32e-03, 6.93e-03, 5.11e-03, 3.73e-03,
    2.70e-03, 1.94e-03, 1.37e-03, 9.67e-04, 6.74e-04, 4.65e-04, 3.18e-04, 2.16e-04, 1.45e-04, 9.62e-05,
    6.33e-05, 4.13e-05, 2.67e-05, 1.71e-05, 1.08e-05, 6.80e-06, 4.22e-06, 2.60e-06, 1.59e-06, 9.58e-07,
    5.73e-07, 3.40e-07, 1.99e-07, 1.16e-07, 6.66e-08, 3.80e-08, 2.14e-08, 1.20e-08, 6.63e-09, 3.64e-09,
    1.97e-09, 1.06e-09, 5.65e-10, 2.98e-10, 1.55e-10, 8.03e-11, 4.11e-11, 2.08e-11, 1.05e-11, 5.20e-12,
    2.56e-12, 1.25e-12, 6.02e-13, 2.88e-13, 1.36e-13, 6.38e-14, 2.96e-14, 1.36e-14, 6.19e-15, 2.79e-15,
    1.24e-15, 5.50e-16, 2.40e-16, 1.04e-16, 4.46e-17, 1.90e-17, 7.97e-18, 3.32e-18, 1.37e-18, 5.58e-19,
    2.26e-19, 9.03e-20, 3.58e-20, 1.40e-20, 5.46e-21, 2.10e-21, 7.99e-22, 3.02e-22, 1.13e-22, 4.16e-23,
    1.52e-23, 5.52e-24, 1.98e-24, 7.05e-25, 2.48e-25, 8.64e-26, 2.98e-26, 1.02e-26, 3.44e-27, 1.15e-27,
    3.82e-28, 1.25e-28, 4.08e-29, 1.31e-29, 4.18e-30, 1.32e-30, 4.12e-31, 1.27e-31, 3.90e-32, 1.18e-32,
    3.55e-33, 1.06e-33, 3.11e-34, 9.06e-35, 2.61e-35, 7.47e-36, 2.11e-36, 5.91e-37, 1.64e-37, 4.50e-38,
    1.22e-38, 3.29e-39, 8.77e-40, 2.31e-40, 6.05e-41, 1.56e-41, 4.00e-42, 1.02e-42, 2.55e-43, 6.33e-44,
    1.56e-44, 3.80e-45, 9.16e-46, 2.19e-46, 5.17e-47, 1.21e-47, 2.81e-48, 6.45e-49, 1.46e-49, 3.30e-50};

static const double tablePtoZ[] = {
    0.00, 0.73, 1.24, 1.64, 1.99, 2.30, 2.58, 2.83, 3.07, 3.29,
    3.50, 3.70, 3.89, 4.07, 4.25, 4.42, 4.58, 4.74, 4.89, 5.04,
    5.19, 5.33, 5.46, 5.60, 5.73, 5.86, 5.99, 6.11, 6.23, 6.35,
    6.47, 6.58, 6.70, 6.81, 6.92, 7.02, 7.13, 7.24, 7.34, 7.44,
    7.54, 7.64, 7.74, 7.84, 7.93, 8.03, 8.12, 8.21, 8.30, 8.40,
    8.49, 8.57, 8.66, 8.75, 8.84, 8.92, 9.01, 9.09, 9.17, 9.25,
    9.34, 9.42, 9.50, 9.58, 9.66, 9.73, 9.81, 9.89, 9.97, 10.04,
    10.12, 10.19, 10.27, 10.34, 10.41, 10.49, 10.56, 10.63, 10.70, 10.77,
    10.84, 10.91, 10.98, 11.05, 11.12, 11.19, 11.26, 11.32, 11.39, 11.46,
    11.52, 11.59, 11.66, 11.72, 11.79, 11.85, 11.91, 11.98, 12.04, 12.10,
    12.17, 12.23, 12.29, 12.35, 12.42, 12.48, 12.54, 12.60, 12.66, 12.72,
    12.78, 12.84, 12.90, 12.96, 13.02, 13.07, 13.13, 13.19, 13.25, 13.31,
    13.36, 13.42, 13.48, 13.53, 13.59, 13.65, 13.70, 13.76, 13.81, 13.87,
    13.92, 13.98, 14.03, 14.09, 14.14, 14.19, 14.25, 14.30, 14.35, 14.41,
    14.46, 14.51, 14.57, 14.62, 14.67, 14.72, 14.77, 14.83, 14.88, 14.93};

// Convert a z-score into a probability
static double zToP(const double z)
{
    int index = (int)(z / 0.1);

    if (index < 0) {
        index = 0;
    }
    if (index > 149) {
        index = 149;
    }

    return tableZtoP[index];
}

// Convert a probability into a z-score
static double pToZ(const double p)
{
    int index = (int)(-log10(p) * 3.0);

    if (index < 0) {
        index = 0;
    }
    if (index > 149) {
        index = 149;
    }

    return tablePtoZ[index];
}

// These empirical data are reproduced from the original CE source code.
static const double similarityAvgs[] =
    {2.54, 2.51, 2.72, 3.01, 3.31, 3.61, 3.90, 4.19, 4.47, 4.74,
        4.99, 5.22, 5.46, 5.70, 5.94, 6.13, 6.36, 6.52, 6.68, 6.91};
static const double similaritySDs[] =
    {1.33, 0.88, 0.73, 0.71, 0.74, 0.80, 0.86, 0.92, 0.98, 1.04,
        1.08, 1.10, 1.15, 1.19, 1.23, 1.25, 1.32, 1.34, 1.36, 1.45};

static double zScoreSimilarity(
    const int pathLength,
    const double similarity)
{
    // This method only works for the default fragment size
    if (pathLength < 1) {
        return 0.0;
    }

    double similarityAvg, similaritySD;

    // 20 is the number of stored statistics (averages and standard deviations)
    // in the arrays above.
    if (pathLength <= 20) {
        similarityAvg = similarityAvgs[pathLength - 1];
        similaritySD = similaritySDs[pathLength - 1];
    }
    else {
        similarityAvg = 0.209874 * pathLength + 2.944714;
        similaritySD = 0.039487 * pathLength + 0.675735;
    }
    if (similarity > similarityAvg) {
        return 0.0;
    }

    return (similarityAvg - similarity) / similaritySD;
}

static const double gapCountAvgs[] =
    {0.00, 11.50, 23.32, 35.95, 49.02, 62.44, 76.28, 90.26,
        104.86, 119.97, 134.86, 150.54, 164.86, 179.57, 194.39,
        209.38, 224.74, 238.96, 253.72, 270.79};
static const double gapCountSDs[] =
    {0.00, 9.88, 14.34, 17.99, 21.10, 23.89, 26.55, 29.00, 31.11,
        33.10, 35.02, 36.03, 37.19, 38.82, 41.04, 43.35, 45.45,
        48.41, 50.87, 52.27};

static double zScoreGapCount(
    const int pathLength,
    const int gapCount)
{
    if (pathLength < 1) {
        return 0.0;
    }

    double gapCountAvg, gapCountSD;

    // 20 is the number of stored statistics (averages and standard deviations)
    // in the arrays above.
    if (pathLength <= 20) {
        gapCountAvg = gapCountAvgs[pathLength - 1];
        gapCountSD = gapCountSDs[pathLength - 1];
    }
    else {
        gapCountAvg = 14.949173 * pathLength - 14.581193;
        gapCountSD = 2.045067 * pathLength + 13.191095;
    }
    if (gapCount > gapCountAvg) {
        return 0.0;
    }

    return (gapCountAvg - gapCount) / gapCountSD;
}

// The z-score calculation is adapted from the code in
// https://github.com/kad-ecoli/CE.
static double calcZScore(
    const int fragmentSize,
    const int pathLength,
    const double pathSimilarity,
    const int gapCount)
{
    if (fragmentSize != 8) {
        // Z-score calculation is only supported for the default fragment size.
        return 0.0;
    }

    const double z1 = zScoreSimilarity(pathLength, pathSimilarity);
    const double z2 = zScoreGapCount(pathLength, gapCount);

    return pToZ(zToP(z1) * zToP(z2));
}

static pcePoint
getCoords(PyObject *L, int length)
{
    // Make space for the current coords
    pcePoint coords = (pcePoint)PyMem_RawMalloc(sizeof(cePoint) * length);

    if (!coords)
        return NULL;

    // loop through the arguments, pulling out the
    // XYZ coordinates.
    for (int i = 0; i < length; i++) {
        PyObject *curCoord = PyList_GetItem(L, i);
        Py_INCREF(curCoord);

        PyObject *curVal = PyList_GetItem(curCoord, 0);
        Py_INCREF(curVal);
        coords[i].x = PyFloat_AsDouble(curVal);
        Py_DECREF(curVal);

        curVal = PyList_GetItem(curCoord, 1);
        Py_INCREF(curVal);
        coords[i].y = PyFloat_AsDouble(curVal);
        Py_DECREF(curVal);

        curVal = PyList_GetItem(curCoord, 2);
        Py_INCREF(curVal);
        coords[i].z = PyFloat_AsDouble(curVal);

        Py_DECREF(curVal);
        Py_DECREF(curCoord);
    }

    return coords;
}

// Find the best N alignment paths
static PyObject *
findPath(
    double **S,
    double **dA,
    double **dB,
    const int lenA,
    const int lenB,
    const int fragmentSize,
    const int gapMax)
{
    const double D0 = -3.0;
    const double D1 = -4.0;

    // Length of longest possible alignment
    const int smaller = (lenA < lenB) ? lenA : lenB;

    // For storing the best N paths
    int bufferSize = 0;
    int lenBuffer[MAX_PATHS];
    double similarityBuffer[MAX_PATHS];
    path pathBuffer[MAX_PATHS];

    for (int i = 0; i < MAX_PATHS; i++) {
        // Initialize the paths
        similarityBuffer[i] = -1e6;
        lenBuffer[i] = 0;
        pathBuffer[i] = 0;
    }

    //======================================================================
    // Start the search through the similarity matrix.
    //
    for (int iA = 0; iA <= lenA - fragmentSize; iA++) {
        if (bufferSize > 0 &&
            iA > lenA - fragmentSize * (lenBuffer[bufferSize - 1] - 1))
            break;

        for (int iB = 0; iB <= lenB - fragmentSize; iB++) {
            if (S[iA][iB] <= D0)
                continue;
            if (bufferSize > 0 &&
                iB > lenB - fragmentSize * (lenBuffer[bufferSize - 1] - 1))
                break;

            // Initialize current path
            path curPath = (path)PyMem_RawMalloc(sizeof(afp) * smaller);
            int curPathLength = 1;
            double curPathSimilarity = S[iA][iB];

            curPath[0] = (afp) {iA, iB};

            for (int i = 1; i < smaller; i++) {
                curPath[i] = (afp) {-1, -1};
            }

            //
            // Build the best path starting from iA, iB
            //
            while (1) {
                double gapBestSimilarity = -1e6;
                int gapBestIndex = -1;

                //
                // Check all possible gaps from here
                //
                for (int g = 0; g < (gapMax * 2) + 1; g++) {
                    int jA = curPath[curPathLength - 1].pA + fragmentSize;
                    int jB = curPath[curPathLength - 1].pB + fragmentSize;

                    if ((g + 1) % 2 == 0) {
                        jA += (g + 1) / 2;
                    } else { // ( g odd )
                        jB += (g + 1) / 2;
                    }

                    // Following are three heuristics to ensure high quality
                    // long paths and make sure we don't run over the end of
                    // the S, matrix.

                    // 1st: If jA or jB is at the end of the similarity matrix
                    if (jA > lenA - fragmentSize || jB > lenB - fragmentSize)
                        continue;
                    // 2nd: If this candidate AFP is bad, ignore it.
                    if (S[jA][jB] <= D0)
                        continue;

                    const afp afpJ = (afp) {jA, jB};
                    double curSimilarity = 0.0;

                    for (int s = 0; s < curPathLength; s++) {
                        curSimilarity +=
                            similarityI(
                                dA,
                                dB,
                                curPath[s],
                                afpJ,
                                fragmentSize);
                    }

                    curSimilarity /= curPathLength;

                    // store GAPPED best
                    if (curSimilarity > D1 &&
                        curSimilarity > gapBestSimilarity) {
                        curPath[curPathLength] = afpJ;
                        gapBestSimilarity = curSimilarity;
                        gapBestIndex = g;
                    }
                } /// ROF -- END GAP SEARCHING

                if (gapBestIndex == -1) {
                    // if here, then there was no good candidate AFP,
                    // so quit and restart from starting point
                    break;
                }

                // The current path has n AFPs, and we are considering adding
                // the (n+1)-th AFP.
                // Imagine a matrix where entry ij is D_ij of the i-th and j-th
                // AFPs in the path.
                // The path similarity is the average of the upper triangle of
                // this matrix.
                const afp afpJ = curPath[curPathLength];
                const double n = (double) curPathLength;
                const double curTermCount = n + n * (n - 1) / 2;
                const double newTermCount = n + 1 + n * (n + 1) / 2;
                // Notice that the new term count is
                // the current term count plus n + 1.
                const double newSimilarity =
                        (curTermCount * curPathSimilarity +
                        n * gapBestSimilarity +
                        S[afpJ.pA][afpJ.pB]) / newTermCount;

                if (newSimilarity > D1) {
                    curPathSimilarity = newSimilarity;
                    curPathLength++;
                }
                else {
                    // Heuristic -- path is getting sloppy, stop looking
                    break;
                }
            } /// END WHILE

            //
            // At this point, we've found the best path starting at iA, iB.
            //
            for (int i = 0; i < bufferSize; i++) {
                if (curPathLength > lenBuffer[i] ||
                    (curPathLength == lenBuffer[i] &&
                     curPathSimilarity > similarityBuffer[i])) {
                     // Swap the current path with the path in the buffer
                     int tempLength = lenBuffer[i];
                     double tempSimilarity = similarityBuffer[i];
                     path tempPath = pathBuffer[i];

                     lenBuffer[i] = curPathLength;
                     similarityBuffer[i] = curPathSimilarity;
                     pathBuffer[i] = curPath;

                     curPathLength = tempLength;
                     curPathSimilarity = tempSimilarity;
                     curPath = tempPath;
                }
            }

            if (bufferSize < MAX_PATHS) {
                lenBuffer[bufferSize] = curPathLength;
                similarityBuffer[bufferSize] = curPathSimilarity;
                pathBuffer[bufferSize] = curPath;
                bufferSize += 1;
            }
            else {
                PyMem_RawFree(curPath);
            }
        } // ROF -- end for iB
    }     // ROF -- end for iA

    double zScoreBuffer[MAX_PATHS];

    for (int i = 0; i < bufferSize; i++) {
        const int pathLength = lenBuffer[i];
        const double pathSimilarity = similarityBuffer[i];
        int gapCount = 0;

        for (int j = 1; j < pathLength; j++) {
            gapCount += pathBuffer[i][j].pA - pathBuffer[i][j - 1].pA - 1;
            gapCount += pathBuffer[i][j].pB - pathBuffer[i][j - 1].pB - 1;
        }

        zScoreBuffer[i] = calcZScore(fragmentSize, pathLength, pathSimilarity, gapCount);
    }

    // To make it simpler to use this code and more portable, we are decoupling
    // the path finding (the actual CEAlign innovation) from the RMSD
    // calculation.
    //
    // As such, we return the N best paths to Python-land. Since the paths are
    // encoded as structs, it's simpler to return the each path as a list of
    // lists with the corresponding atom indices. e.g. [path1, path2, path3,
    // ..., pathN], where pathN is defined as,
    // [[Ai, Aj, Ak, ...], [Bi, Bj, Bk, ...], where An and Bn are equivalent
    // coordinates for structures A and B.

    // List to store all paths
    PyObject *result = PyList_New(bufferSize);
    Py_INCREF(result);

    for (int o = 0; o < bufferSize; o++) {
        // Make a new list to store this path
        PyObject *pathAList = PyList_New(0);
        PyObject *pathBList = PyList_New(0);
        Py_INCREF(pathAList);
        Py_INCREF(pathBList);

        for (int j = 0; j < lenBuffer[o]; j++) {
            const int pA = pathBuffer[o][j].pA;
            const int pB = pathBuffer[o][j].pB;

            for (int k = 0; k < fragmentSize; k++) {
                PyObject *v = Py_BuildValue("i", pA + k);
                PyList_Append(pathAList, v);
                Py_DECREF(v);
                v = Py_BuildValue("i", pB + k);
                PyList_Append(pathBList, v);
                Py_DECREF(v);
            }
        }

        const double zScore = zScoreBuffer[o];
        const int length = lenBuffer[o];
        PyObject *pairList = Py_BuildValue("[NN]", pathAList, pathBList);
        Py_INCREF(pairList);

        PyStructSequence_Field namedtupleFields[] = {
            (PyStructSequence_Field) {
                "path",
                NULL,
            },
            (PyStructSequence_Field) {
                "z_score",
                NULL,
            },
            (PyStructSequence_Field) {
                "length",
                NULL,
            },
            {NULL},
        };
        PyStructSequence_Desc namedtupleDesc = (PyStructSequence_Desc) {
            "ccealign.CEAlignment",
            NULL,
            namedtupleFields,
            3,
        };
        PyTypeObject *namedtupleType =
            PyStructSequence_NewType(&namedtupleDesc);
        PyObject *namedtuple = PyStructSequence_New(namedtupleType);

        PyStructSequence_SetItem(namedtuple, 0, pairList);
        PyStructSequence_SetItem(namedtuple, 1, PyFloat_FromDouble(zScore));
        PyStructSequence_SetItem(namedtuple, 2, PyLong_FromLong(length * fragmentSize));

        PyList_SET_ITEM(result, o, namedtuple);
        Py_DECREF(namedtupleType);
    }

    return result;
}

// Main Function
PyObject *
PyCealign(PyObject *Py_UNUSED(self), PyObject *args)
{
    int fragmentSize = 8;
    int gapMax = 30;

    PyObject *listA, *listB, *result;

    /* Unpack the arguments from Python */
    PyArg_ParseTuple(args, "OO|ii", &listA, &listB, &fragmentSize, &gapMax);

    /* Get the list lengths */
    const int lenA = (int)PyList_Size(listA);
    const int lenB = (int)PyList_Size(listB);

    /* get the coodinates from the Python objects */
    pcePoint coordsA = (pcePoint)getCoords(listA, lenA);
    pcePoint coordsB = (pcePoint)getCoords(listB, lenB);

    /* calculate the distance matrix for each protein */
    double **dA = (double **)calcDM(coordsA, lenA);
    double **dB = (double **)calcDM(coordsB, lenB);

    /* calculate the CE Similarity matrix */
    double **S = (double **)calcS(dA, dB, lenA, lenB, fragmentSize);

    // Calculate Top N Paths
    result = (PyObject *)findPath(S, dA, dB, lenA, lenB, fragmentSize, gapMax);

    /* release memory */
    PyMem_RawFree(coordsA);
    PyMem_RawFree(coordsB);

    /* distance matrices	 */
    for (int i = 0; i < lenA; i++)
        PyMem_RawFree(dA[i]);
    PyMem_RawFree(dA);

    for (int i = 0; i < lenB; i++)
        PyMem_RawFree(dB[i]);
    PyMem_RawFree(dB);

    // Similarity matrix
    for (int i = 0; i <= lenA - fragmentSize; i++)
        PyMem_RawFree(S[i]);
    PyMem_RawFree(S);

    return result;
}

//
// Python Interface
//
PyDoc_STRVAR(method_doc,
"run_cealign(coordsA, coordsB, fragmentSize, gapMax) -> list\
\n\n\
Find the optimal alignments between two structures, using CEAlign.\
\n\n\
Arguments:\n\
- listA: List of lists with coordinates for structure A.\n\
- listB: List of lists with coordinates for structure B.\n\
- fragmentSize: Size of fragments to be used in alignment.\n\
- gapMax: Maximum gap allowed between two aligned fragment pairs.");

static PyMethodDef CEAlignMethods[] = {
    {"run_cealign", PyCealign, METH_VARARGS, method_doc},
    {NULL, NULL, 0, NULL}
};

PyDoc_STRVAR(module_doc,
"Pairwise structure alignment of 3D structures using combinatorial extension.\
\n\n\
This module implements a single function: run_cealign. \
Refer to its docstring for more documentation on usage and implementation.");

PyObject *PyInit_ccealign(void)
{
    static struct PyModuleDef moduledef = {PyModuleDef_HEAD_INIT,
                                           "ccealign",
                                           module_doc,
                                           -1,
                                           CEAlignMethods,
                                           NULL,
                                           NULL,
                                           NULL,
                                           NULL};
    return PyModule_Create(&moduledef);
}