netgen.py 44.5 KB
Newer Older
1
2
3
4
5
6
7
8
9
10
11
12
13
14
# generation and planar cutting of periodic pore networks
#
# Daniel W. Meyer
# Institute of Fluid Dynamics, ETH Zurich
# January 2019

from typing import List, Dict, Set, Tuple # for type hints in argument lists

LABELS = ('', 'in', 'out', 'cut') # don't change the order

class Pore:
    """Class of a pore connected to other pores via throats."""
    id = 0
    def __init__(self, pos: List[float], r: float, label: str = LABELS[0], \
sfritschi's avatar
sfritschi committed
15
        throats: Set = None, index: int = -1, id: int = -1):
16
17
18
19
20
21
22
23
24
        if id == -1: # no id given
            self.id = Pore.id; Pore.id = Pore.id+1
        else: # id provided
            self.id = id; Pore.id = max(id+1, Pore.id)
        self.pos = pos.copy() # position vector
        if throats is None: throats = set()
        self.throats = throats # throats set
        self.r = r # radius
        self.label = label # label string like '', 'in', or 'out'
sfritschi's avatar
sfritschi committed
25
26
        # Identifier for pores in list used in generate_dendrogram
        self.index = index
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
    def __repr__(self): return str(self.__class__) + ': ' + \
        str({k:self.__dict__[k] for k in self.__dict__ if k != 'throats'}) + \
        ' {0:d} throats'.format(len(self.throats)) # dont flush throat objects

class Throat:
    """Class of a throat connecting two pores.
    
    Periodic throats have a label 'X1 X2 X3' with Xc being element of {-1,0,1}.
    For Xc = 1, pore1 is at the right or upper domain bound in the c-direction
    and pore2 is at the left or lower bound. Vice versa for Xc = -1. With
    Xc = 0, the throat does not cross the bound periodically in c-direction.
    """
    id = 0
    def __init__(self, pore1: Pore, pore2: Pore, r: float, \
        label: str = LABELS[0], id: int = -1):
        if id == -1: # no id given
            self.id = Throat.id; Throat.id = Throat.id+1
        else: # id provided
            self.id = id; Throat.id = max(id+1, Throat.id)
        # pore objects
        self.pore1 = pore1
        self.pore2 = pore2
        # radius and label
        self.r = r
        self.label = label # label string like '' or periodicity label '1 0 -1'
    def __repr__(self): return str(self.__class__) + ': ' + str(self.__dict__)

class Network:
    """Network class with pore and throat lists.
    
    Lmax must be smaller than the smallest side length of the network ub-lb.
    """
    def __init__(self, lb: List[float] = [], ub: List[float] = [], \
        pores: List[Pore] = None, throats: List[Throat] = None, \
        Lmax: float = 0.0, label: str = None):
        # lower/upper bounds for network volume
        self.lb = lb.copy(); self.ub = ub.copy()
        # sets with pores and throats
        if pores is None: pores = set()
        if throats is None: throats = set()
        self.pores = pores.copy(); self.throats = throats.copy()
        # length of longest throat (distance between connected pores)
        self.Lmax = Lmax
        # network label or name
        from datetime import datetime
        if label is None:
            self.label = datetime.today().isoformat(sep=' ',timespec='seconds')
        else:
            self.label = label
    def __repr__(self):
        # count in/out resp. labelled pores
        k = sum([int(pore.label != LABELS[0]) for pore in self.pores])
        # report
        return 'Network \'' + self.label + '\' from ' + str(self.lb) + \
            ' to ' + str(self.ub) + \
            ' with {0:d}({1:d}) pores, {2:d} throats, Lmax = {3:e}'. \
            format(len(self.pores), k, len(self.throats), self.Lmax)
    def add_pore(self, pore: Pore):
        self.pores.add(pore)
    def remove_pore(self, pore: Pore):
        """Remove pore and all throats connected to it."""
        # disconnect throats from pores connected to pore
        for throat in pore.throats.copy():
            connected_pore = throat.pore1
            if (connected_pore == pore): connected_pore = throat.pore2
            connected_pore.throats.remove(throat)
            pore.throats.remove(throat)
            self.throats.remove(throat)
        # remove pore
        self.pores.remove(pore)
    def connect_pores(self, pore1: Pore, pore2: Pore, r: float, \
        throat_id: int = -1, label: str = LABELS[0]) -> Throat:
        """Establish a throat connection between two pores."""
        throat = Throat(pore1, pore2, r, label, throat_id)
        self.throats.add(throat)
        pore1.throats.add(throat); pore2.throats.add(throat)
        return throat

105
class CellList:
sfritschi's avatar
sfritschi committed
106
107
108
109
    """CellList class dividing physical domain into equally-sized cells
    
    find_candidates() assumes pore is located in interior of domain (non-periodic)
    """
sfritschi's avatar
sfritschi committed
110
111
    def __init__(self, pores: List[Pore], domainSize: List[float], \
                         cellSize: float, Lmax: float):
sfritschi's avatar
sfritschi committed
112
        from math import ceil
113
114
115
        self.dim = len(domainSize)
        self.Lmax = Lmax
        # Number of cells in each dimension
sfritschi's avatar
sfritschi committed
116
        self.nCells = [max(1, ceil(domainSize[i] / cellSize)) for i in range(self.dim)]
117
118
119
120
        # Inverse of cell sizes in domain
        self.invCellSizes = [self.nCells[i] / domainSize[i] for i in range(self.dim)]
        # Total number of cells
        self.totalCells = prod(self.nCells)
sfritschi's avatar
sfritschi committed
121
122
123
124
125
        # Sort pores according to cell membership
        self.poresSorted = [set() for _ in range(self.totalCells)]
        for pore in pores:
            cellIdx = self.pore_to_index(pore)
            self.poresSorted[cellIdx].add(pore)
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
        
    # Helper for converting 3D index triple into 1D (flattened) index
    def flatten(self, i: int, j: int, k: int) -> int:
        return i + self.nCells[0] * (j + self.nCells[1] * k)
    
    def pore_to_triplet(self, pore: Pore) -> List[int]:
        from math import floor
        # Shift pore position to be positive first (buffer layer)
        return [floor( (pore.pos[i] + self.Lmax) * self.invCellSizes[i]) \
                        for i in range(self.dim)]
    # Compute index of given pore in cell list based on position
    def pore_to_index(self, pore: Pore) -> int:
        from math import floor
        # Shift pore position to be positive first (buffer layer)
        cellIdx = self.flatten(*[floor( (pore.pos[i] + self.Lmax) * self.invCellSizes[i]) \
                        for i in range(self.dim)])
        return cellIdx
    
sfritschi's avatar
sfritschi committed
144
    def is_valid_index(self, idx: int) -> bool:
145
146
        return 0 <= idx < self.totalCells
        
sfritschi's avatar
sfritschi committed
147
148
149
    # Compute dictionary of all nbor candidates of given pore
    def find_candidates(self, pore: Pore) -> Dict[Pore, float]:
        candidates  = {}
150
151
        cellIdxTrip = self.pore_to_triplet(pore)
        # Check all possible neighbor cells (27 in 3D)
sfritschi's avatar
sfritschi committed
152
        # TODO: Speed up finding of suitable candidates (e.g. multiprocessing)
153
154
155
        for i in range(-1, 2):
            for j in range(-1, 2):
                for k in range(-1, 2):
sfritschi's avatar
sfritschi committed
156
157
158
                    nborIdx = self.flatten(cellIdxTrip[0] + i, \
                                           cellIdxTrip[1] + j, \
                                           cellIdxTrip[2] + k)
159
                    # Check if valid cell index
sfritschi's avatar
sfritschi committed
160
161
162
163
164
165
166
167
168
169
                    #assert(self.is_valid_index(nborIdx))
                    
                    # Check all pores within current neighbor-cell
                    for nbor in self.poresSorted[nborIdx]:
                        if (nbor == pore): continue
                        l = distance(nbor.pos, pore.pos)
                        if (l < self.Lmax):
                            candidates[nbor] = l
        return candidates
    
sfritschi's avatar
sfritschi committed
170
171
172
173
174
175
176
177
178
179
180
181
182
    def find_best_candidate_in_cell(self, cellIdx: int, porePos: List[float],
                        poreIdx: int, throatLen: float) -> Tuple[int, float]:
        best_candidate_index = -1
        best_length = self.Lmax
        for nbor in self.poresSorted[cellIdx]:
            if (nbor.index == poreIdx): continue
            l = distance(nbor.pos, porePos)
            diff = abs(l - throatLen)
            if (l < self.Lmax and diff < abs(best_length - throatLen)):
                best_candidate_index = nbor.index
                best_length = l
        return (best_candidate_index, best_length)

sfritschi's avatar
sfritschi committed
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
    def cell_stats(self):
        cellCounts = [len(self.poresSorted[i]) for i in range(self.totalCells)]
        n    = sum(cellCounts)
        max_ = max(cellCounts)
        min_ = min(cellCounts)
        avg  = n / self.totalCells
        
        """
        print("Cell statistics:")
        print("Number of cells (%d, %d, %d)" % (self.nCells[0], self.nCells[1], self.nCells[2]))
        print("Max. pores per cell: %d (%f%%)" % (max_, max_ / n * 100.))
        print("Min. pores per cell: %d (%f%%)" % (min_, min_ / n * 100.))
        print("Avg. pores per cell: %.1f (%f%%)" % (avg, avg / n * 100.))
        """
        return (max_, min_, avg)

sfritschi's avatar
sfritschi committed
199
200
201
202
    # Remove pore from sorted pores
    def expel(self, pore: Pore):
        poreIdx = self.pore_to_index(pore)
        self.poresSorted[poreIdx].remove(pore)
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

def distance(p1: List[float], p2: List[float]):
    """Distance between points p1 and p2."""
    mag = 0.0
    for c1, c2 in zip(p1,p2): mag += (c1-c2)**2
    return mag**0.5


def prod(v):
    """Cumulative product of vector components."""
    from functools import reduce
    return(reduce(lambda a,b: a*b, v))


def random_direction(d: int) -> List[float]:
    """Unity vector with uniformly distributed orientation."""
    from math import pi, sin, cos, acos
    from random import random
    phi = 2*pi * random()
    if (d == 2):
        return([cos(phi), sin(phi)])
    elif (d == 3):
        theta = acos(2*random() - 1)
        return([sin(theta)*cos(phi), sin(theta)*sin(phi), cos(theta)])
    else:
        raise ValueError("random_direction supports d = 2 or 3")


def throat_ends(throat: Throat, L: List[float]) -> Tuple[List[float]]:
    """Provide the correct relative end points of a possibly periodic throat."""
    x1 = throat.pore1.pos.copy(); x2 = throat.pore2.pos.copy()
    # account for periodic throats
    if len(throat.label) != 0:
        direct = [int(k) for k in throat.label.split()] # periodicity
        x2 = [x2[k] + direct[k] * L[k] for k in range(len(L))]
    return (x1, x2)



def imperial_read(net_file_pref: str) -> Network:
    """Read network data in Imperial College format.
    
    For format specifics see PhD thesis of Taha Sochi from 2007 at Imperial.
    The names of the network files starts with the string net_file_pref.
    A Network object is returned.
    """
    # initialize network
    from os import sep
    network = Network(label = net_file_pref.split(sep)[-1])
    
    # read pore data
    with open(net_file_pref + '_node1.dat', 'r') as file:
        line = file.readline()
        size = [float(n) for n in line.replace('\t',' ').split()][1:]
        d = len(size) # dimensionality
        f = lambda words: (
            int(words[0]), # id
            [float(n) for n in words[1:(d+1)]], # pos
            [int(throat) for throat in words[(d+4+int(words[d+1])):]], # throats
            LABELS[int(words[d+2+int(words[d+1])]) + \
            2*int(words[d+3+int(words[d+1])])]) # label
        pores = [f(line.replace('\t',' ').split()) for line in file]
    pores.sort(key=lambda pore: pore[0])
    pores = [Pore(pore[1], 0.0, pore[3]) for pore in pores]
    # read pore radii
    with open(net_file_pref + '_node2.dat', 'r') as file:
        f = lambda words: (int(words[0]), float(words[2]))
        radii = [f(line.replace('\t',' ').split()) for line in file]
    radii.sort(key=lambda pore: pore[0])
    for k, pore in enumerate(pores): pore.r = radii[k][1]
    # add pores to network
    for pore in pores: network.add_pore(pore)

    # read throat data
    with open(net_file_pref + '_link1.dat', 'r') as file:
        n = int(file.readline().strip('\n ')) # number of throats
        f = lambda words: (
            int(words[0]), int(words[1])-1, int(words[2])-1, float(words[3]))
        throats = [f(line.replace('\t',' ').split()) for line in file]
    throats.sort(key=lambda throat: throat[0])
    # connect pores
    for throat in throats:
        if (throat[1] >= 0) and (throat[2] >= 0): # no in-/outflow throats
            network.connect_pores(pores[throat[1]], pores[throat[2]], throat[3])

    # determine maximum throat length
    Lmax = 0.0
    for throat in network.throats:
        L = distance(throat.pore1.pos, throat.pore2.pos)
        Lmax = max(L,Lmax)
    network.Lmax = Lmax

    network.lb = [0 for i in range(len(size))]
    network.ub = size
    return network


def plot_network(network: Network, labels: bool = False):
    """Plot pore network.
    
    Returns a figure object. If labels == True, pore and throat ids are shown.
    Pores with label == '' are plotted in black. Pores with labels starting
    with 'in', 'out', 'cut' are plotted in red, blue, magenta, respectively.
    """
    # setup plot
    import matplotlib.pyplot as plt
    from mpl_toolkits.mplot3d import Axes3D
    plt.ion()
    fig = plt.figure()
    ax = fig.add_subplot(111, projection='3d')
    
    # plot throats
    for throat in network.throats:
        if throat.label == LABELS[0]: col = 'black'
        else: col = 'grey'
        p1 = throat.pore1.pos; p2 = throat.pore2.pos
        ax.plot([p1[0], p2[0]], [p1[1], p2[1]], [p1[2], p2[2]],
            linewidth=0.5, color=col)
        if labels:
            ax.text3D((p1[0]+p2[0])/2, (p1[1]+p2[1])/2, (p1[2]+p2[2])/2,
                str(throat.id), fontsize=5)

    # plotting function for pores
    def plot_pores(label, size, color):
        pnts = [pore.pos for pore in network.pores \
            if (pore.label[:max(1,len(label))] == label)]
        if len(pnts) == 0: return # in case of empty point list
        pnts = list(map(list, zip(*pnts))) # transpose double list
        ax.scatter(*pnts, s=size, marker='.', c=color)
        if labels:
            for pore in network.pores:
                if (pore.label[:max(1,len(label))] == label):
                    ax.text3D(*pore.pos, str(pore.id), fontsize=7, color=color)
    # plot ordinary pores
    plot_pores(LABELS[0], 4, 'black')
    # plot inflow pores
    plot_pores(LABELS[1], 7, 'red')
    # plot outflow pores
    plot_pores(LABELS[2], 7, 'blue')
    # plot cut pores
    plot_pores(LABELS[3], 7, 'magenta')

    #ax.axis('equal')
    return fig


def generate_simple_net(n_pores: int, targetsize: List[float], \
    r_pore: float, r_throat: float, coordinatnumb: int, Lmax: float, \
    sd: int = None) -> Network:
    """Generate a spatially periodic network with uniform pore distribution."""
    d = len(targetsize) # number of spatial dimensions
    density = n_pores / prod(targetsize)
    origin = [0.0 for k in range(d)]
    Lb = (1/density)**(1/d)
    basenet = Network(origin, [Lb for k in range(d)], \
        [Pore(origin, r_pore, throats = {k for k in range(coordinatnumb)})], \
        [Throat(None, None, r_throat)], Lmax)
    basenet.label = 'simplenet_' + basenet.label
    return generate_imperial(basenet, targetsize, sd, False)


def generate_imperial(basenet: Network, targetsize: List[float], \
    sd: int = None, correlated: bool = True) -> Network:
    """Generate a new spatially periodic network.

    Based on an existing network basenet, generate a new network of size
    targetsize by using the algorithm outlined on p.54 of the PhD thesis of
    Nasiru Abiodun Idowu from 2009 at Imperial College.
    Pores are uniformly distribute with pore number density as in basenet.
    Pore radii and number of throat connections are sampled from basenet.
    Closest pores are connected. Throat radii are taken from basenet such
    that throat radius and radius-sum of the connected pores are correlated.
    Periodic throats are marked with a periodicity label, e.g., '1 0 -1' in 3d.
    """
    from random import seed, random, randint
    seed(sd)
    d = len(targetsize) # number of spatial dimensions
    # check target size (must be > basenet.Lmax)
    if any([L < basenet.Lmax for L in targetsize]):
        raise NameError('targetsize must be > Lmax of basenet!')

    # pores, uniformly distributed
    # number of pores in new network
    import math
    basesize = list(map(lambda a,b: a-b, basenet.ub, basenet.lb))
    n = math.ceil(prod(targetsize) * len(basenet.pores) / prod(basesize))
    # distribute pores uniformly
    basepores = [pore for pore in basenet.pores] # make indexable
    pores = [Pore(pos=[random()*L for L in targetsize], # pos
        # radius, label, number of throat connections
        r=basepores[idx].r, label=LABELS[0],
        throats=len(basepores[idx].throats)) for j, idx in \
        enumerate([randint(0,len(basepores)-1) for k in range(n)])]

    # add pore buffer layers for spatial periodicity
    n = len(pores)
    _ = __add_buffer_layers(pores, targetsize, basenet.Lmax)

    # throats, connect pores
    # triangulation
    import numpy as np
    from scipy.spatial import Delaunay
    points = np.array([pore.pos for pore in pores])
    tri = Delaunay(points) # possibility for missing (coplanar) points!
    # return neighbors of point pnt based on triangulation tri
    def neighbors_of(pnt, tri):
        return tri.vertex_neighbor_vertices[1][ \
            tri.vertex_neighbor_vertices[0][pnt]: \
            tri.vertex_neighbor_vertices[0][pnt+1]]
    # connect pores
    throats = []
    for k, pore in enumerate(pores[:n]):
        # initialize neighbor lists
        nbors = neighbors_of(k, tri)
        nbors = dict(zip(nbors,
            [distance(pore.pos, pores[j].pos) for j in nbors]))
        oldies = {k:0.0}
        # establish throat connections between pore and its neighbors
        while (pore.throats > 0) \
            and (len(nbors) > 0) and (min(nbors.values()) <= basenet.Lmax):
            # find closest neighbor
            for nbor in nbors:
                if nbors[nbor] == min(nbors.values()): break
            # if nbor is periodic copy, get original pore and periodicity label
            if (pores[nbor].label != LABELS[0]):
                nbor_o, lbl = pores[nbor].label.split(' ',1)
                nbor_o = int(nbor_o)
            else:
                nbor_o = nbor; lbl = LABELS[0]
            # is nbor a valid pore to connect to?
            if not ((nbor_o <= k) or (nbor in oldies) or \
                (pores[nbor_o].throats == 0)):
                # yes -> add connection to pore nbor_o
                throats.append([k, nbor_o, lbl])
                pore.throats = pore.throats - 1
                pores[nbor_o].throats = pores[nbor_o].throats - 1
            # nbor has been dealt with
            oldies[nbor] = nbors[nbor]
            # expand search neighborhood
            for j in neighbors_of(nbor, tri):
                nbors[j] = distance(pores[k].pos, pores[j].pos)
            for oldie in oldies.keys():
                if oldie in nbors: del nbors[oldie]
    
    # initialize throat sets of pores
    k = 0 # count of unrealised throats
    for pore in pores[:n]:
        k = k + pore.throats
        pore.throats = set() # initialize throats set

    # set throat radii
    # sort branch weights (branch weight is prop. to sum of pore radii)
    bw = [pores[throat[0]].r + pores[throat[1]].r for throat in throats]
    bw = list(enumerate(bw))
    bw.sort(key=lambda w: w[1])
    # sample throat radii from basenet
    basethroats = [throat for throat in basenet.throats] # make indexable
    r = [randint(0,len(basethroats)-1) for k in range(len(bw))]
    r = [basethroats[k].r for k in r]
    if correlated: r = sorted(r)
    # assign radii
    for k in range(len(r)): throats[bw[k][0]].append(r[k])

    # assemble and return network
    network = Network(lb=[0.0 for k in range(d)],
        ub=targetsize, Lmax=basenet.Lmax, label='from_' + basenet.label)
    for pore in pores[:n]: network.add_pore(pore)
    for throat in throats: network.connect_pores(pore1=pores[throat[0]],
        pore2=pores[throat[1]], label=throat[2], r=throat[3])
    return network
sfritschi's avatar
sfritschi committed
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

def cell_list_scaling(basenet: Network, targetsize: List[int], \
    cutoff: float = float('inf'), sd: int = None, mute: bool = False):
    from random import seed, random, randint
    from itertools import product
    seed(sd)
    d = len(targetsize) # number of spatial dimensions
    # check target size multiplicator (must be >= 1)
    if any([i < 1 for i in targetsize]):
        raise NameError('targetsize must be >= 1!')
    # size of new network
    L = list(map(lambda lb,ub,i: (ub-lb)*i, basenet.lb, basenet.ub, targetsize))
    # check target size (must be > basenet.Lmax)
    if any([Lc < basenet.Lmax for Lc in L]):
        raise NameError('targetsize leads network < Lmax of basenet!')

    # pores, distributed based on dendrogram of basenet
    if (not mute): print("distributing pores...", end="", flush=True)
    # make indexable and discard in-/outflow pores
    basepores = [pore for pore in basenet.pores \
        if ((pore.label[:len(LABELS[1])] != LABELS[1]) \
        and (pore.label[:len(LABELS[2])] != LABELS[2]))]
    # dendrogram-based or uniform pore distribution
    pores = []
    if (cutoff != cutoff): # uniform
        print("\b"*21 + "uniform pore distribution")
        # loop over network sections & add uniformly distributed pores drawn from basenet
        for s in product(*[range(k) for k in targetsize]):
            for k, pore in enumerate(basepores):
                pos = [random()*l for l in L]
                pores.append(Pore(pos=pos, r=pore.r, label=LABELS[0], 
                    throats=pore.throats.copy()))
    else: # dendrogram-based
        # extract cluster hierarchy from basenet
        centroids = [pore.pos for pore in basepores]
        from scipy.cluster import hierarchy
        clustree = hierarchy.linkage(centroids, method = 'centroid')
        # determine cluster centroids and weights
        weights = len(basepores)*[1] # pores have weight = 1
        for cluster in clustree:
            p1 = int(cluster[0]); p2 = int(cluster[1])
            w1 = weights[p1]; w2 = weights[p2]
            centroids.append(list(map(lambda x1,x2: (w1*x1 + w2*x2)/(w1 + w2),
                centroids[p1], centroids[p2])))
            weights.append(w1 + w2)
        # loop over network sections (twisted basenet copies)
        for s in product(*[range(k) for k in targetsize]):
            # twist centers of sufficiently small cluster
            touched = [False]*len(centroids)
            # positions of pores based on rotations of linked cluster-pairs
            for k in range(len(centroids)-1,len(basepores)-1,-1):
                i = k-len(basepores) # index of cluster in clustree
                ctr = centroids[k] # center of rotation
                dist = clustree[i,2] # cluster distance
                # check if cluster/pore needs to be twisted
                if ((dist < cutoff) or touched[k]):
                    p1 = int(clustree[i,0]); p2 = int(clustree[i,1])
                    w1 = weights[p1]; w2 = weights[p2]
                    vec = random_direction(d)
                    centroids[p1] = \
                        [ctr[j] + w2*dist/(w1+w2)*vec[j] for j in range(d)]
                    centroids[p2] = \
                        [ctr[j] - w1*dist/(w1+w2)*vec[j] for j in range(d)]
                    touched[p1] = touched[p2] = True
            # add section pores in random order to pores of new network
            for k, pore in enumerate(basepores):
                pos = [c-lb + si*(ub-lb) \
                    for c,si,lb,ub in zip(centroids[k],s,basenet.lb,basenet.ub)]
                pores.insert(randint(0,len(pores)), Pore(pos=pos,
                    r=pore.r, label=LABELS[0], throats=pore.throats.copy()))
        print("\b"*21 + "left {0:d} of {1:d} clusters (incl. {2:d} pores) untouched".\
            format(sum([int(not j) for j in touched]), len(touched), len(basepores)))
        # flip pores outside back into domain
        for pore in pores:
            for k in range(d):
                if pore.pos[k] < 0:
                    pore.pos[k] = L[k] + pore.pos[k]
                elif pore.pos[k] >= L[k]:
                    pore.pos[k] = pore.pos[k] - L[k]

    # add pore buffer layers for spatial periodicity
    n = len(pores)
    copies = __add_buffer_layers(pores, L, basenet.Lmax)
    
    # Domain size including periodic buffer layers on all sides
    trueDomainSize = [L[i] + 2 * basenet.Lmax for i in range(d)]
    # Initialize cell-list; Place each pore in respective cell-set
    cellList = CellList(pores, trueDomainSize, basenet.Lmax, basenet.Lmax)
    # Print cell stats to console
    max_, min_, avg = cellList.cell_stats()
    return (max_, min_, avg)
    
565
    
566
567
568
569
570
571
572
573
574
575
576
577
578
579
def generate_dendrogram(basenet: Network, targetsize: List[int], \
    cutoff: float = float('inf'), sd: int = None, mute: bool = False) \
    -> Network:
    """Generate a new spatially periodic network.

    Based on an existing network basenet, generate a new network of size
    targetsize by using a dendrogram-based algorithm that accounts for the
    spatial distribution/clustering of pores.
    The pore-clustering dendrogram is taken from basenet. Pore radii and number
    of throats are sampled from basenet. Pores are connected based on the
    throat lengths from the basenet data. Throat radii are taken from basenet.
    Periodic throats are marked with a periodicity label, e.g., '1 0 -1' in 3d.
    If cutoff == float('nan'), pores are uniformly distributed.
    """
sfritschi's avatar
sfritschi committed
580
    from random import seed, random, randint, shuffle
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
    from itertools import product
    seed(sd)
    d = len(targetsize) # number of spatial dimensions
    # check target size multiplicator (must be >= 1)
    if any([i < 1 for i in targetsize]):
        raise NameError('targetsize must be >= 1!')
    # size of new network
    L = list(map(lambda lb,ub,i: (ub-lb)*i, basenet.lb, basenet.ub, targetsize))
    # check target size (must be > basenet.Lmax)
    if any([Lc < basenet.Lmax for Lc in L]):
        raise NameError('targetsize leads network < Lmax of basenet!')

    # pores, distributed based on dendrogram of basenet
    if (not mute): print("distributing pores...", end="", flush=True)
    # make indexable and discard in-/outflow pores
    basepores = [pore for pore in basenet.pores \
        if ((pore.label[:len(LABELS[1])] != LABELS[1]) \
        and (pore.label[:len(LABELS[2])] != LABELS[2]))]
    # dendrogram-based or uniform pore distribution
    pores = []
    if (cutoff != cutoff): # uniform
        print("\b"*21 + "uniform pore distribution")
        # loop over network sections & add uniformly distributed pores drawn from basenet
sfritschi's avatar
sfritschi committed
604
        runningIndex = 0
605
606
607
608
        for s in product(*[range(k) for k in targetsize]):
            for k, pore in enumerate(basepores):
                pos = [random()*l for l in L]
                pores.append(Pore(pos=pos, r=pore.r, label=LABELS[0], 
sfritschi's avatar
sfritschi committed
609
610
                    throats=pore.throats.copy(), index=runningIndex))
                runningIndex += 1
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
    else: # dendrogram-based
        # extract cluster hierarchy from basenet
        centroids = [pore.pos for pore in basepores]
        from scipy.cluster import hierarchy
        clustree = hierarchy.linkage(centroids, method = 'centroid')
        # determine cluster centroids and weights
        weights = len(basepores)*[1] # pores have weight = 1
        for cluster in clustree:
            p1 = int(cluster[0]); p2 = int(cluster[1])
            w1 = weights[p1]; w2 = weights[p2]
            centroids.append(list(map(lambda x1,x2: (w1*x1 + w2*x2)/(w1 + w2),
                centroids[p1], centroids[p2])))
            weights.append(w1 + w2)
        # loop over network sections (twisted basenet copies)
        for s in product(*[range(k) for k in targetsize]):
            # twist centers of sufficiently small cluster
            touched = [False]*len(centroids)
            # positions of pores based on rotations of linked cluster-pairs
            for k in range(len(centroids)-1,len(basepores)-1,-1):
                i = k-len(basepores) # index of cluster in clustree
                ctr = centroids[k] # center of rotation
                dist = clustree[i,2] # cluster distance
                # check if cluster/pore needs to be twisted
                if ((dist < cutoff) or touched[k]):
                    p1 = int(clustree[i,0]); p2 = int(clustree[i,1])
                    w1 = weights[p1]; w2 = weights[p2]
                    vec = random_direction(d)
                    centroids[p1] = \
                        [ctr[j] + w2*dist/(w1+w2)*vec[j] for j in range(d)]
                    centroids[p2] = \
                        [ctr[j] - w1*dist/(w1+w2)*vec[j] for j in range(d)]
                    touched[p1] = touched[p2] = True
            # add section pores in random order to pores of new network
            for k, pore in enumerate(basepores):
                pos = [c-lb + si*(ub-lb) \
                    for c,si,lb,ub in zip(centroids[k],s,basenet.lb,basenet.ub)]
sfritschi's avatar
sfritschi committed
647
648
649
650
651
                pores.append(Pore(pos=pos, r=pore.r, label=LABELS[0],
                    throats=pore.throats.copy()))
        # Finally, shuffle pores (random order)
        shuffle(pores)
                
652
653
        print("\b"*21 + "left {0:d} of {1:d} clusters (incl. {2:d} pores) untouched".\
            format(sum([int(not j) for j in touched]), len(touched), len(basepores)))
sfritschi's avatar
sfritschi committed
654
655
656
        # flip pores outside back into domain and set respective index of all pores
        for i, pore in enumerate(pores):
            pore.index = i
657
658
659
660
661
662
663
664
665
            for k in range(d):
                if pore.pos[k] < 0:
                    pore.pos[k] = L[k] + pore.pos[k]
                elif pore.pos[k] >= L[k]:
                    pore.pos[k] = pore.pos[k] - L[k]

    # add pore buffer layers for spatial periodicity
    n = len(pores)
    copies = __add_buffer_layers(pores, L, basenet.Lmax)
666
667
668
    
    # Domain size including periodic buffer layers on all sides
    trueDomainSize = [L[i] + 2 * basenet.Lmax for i in range(d)]
sfritschi's avatar
sfritschi committed
669
670
671
    # Initialize cell-list; Place each pore in respective cell-set
    cellList = CellList(pores, trueDomainSize, basenet.Lmax, basenet.Lmax)
        
672
673
674
    # throats, connect pores
    if (not mute): print("\b"*21 + "connecting")
    throats = []
675
    k = 0 # count of unrealised throats
sfritschi's avatar
sfritschi committed
676
    
sfritschi's avatar
sfritschi committed
677
    # DEBUG
sfritschi's avatar
sfritschi committed
678
    #max_throat_diff = 0.
679
680
681
682
683
    for i, pore in enumerate(pores[:n]):
        # (re)run triangulation if maximal number of neighbors exceeds
        # threshold given by 2x init. maximum (large nnbrs -> expensive search)
        # check throats and neighborhood
        if (not mute):
sfritschi's avatar
sfritschi committed
684
            print(f"progress {((i+1) / n)*100.:.1f}%", end="\r", flush=True)
685
        if (len(pore.throats) == 0): continue # no further connection needed
sfritschi's avatar
sfritschi committed
686
687
        
        # find candidates in neighborhood and respective throat lengths
sfritschi's avatar
sfritschi committed
688
689
        # TODO: Search neighboring cells in parallel
        candidates = cellList.find_candidates(pore)
sfritschi's avatar
sfritschi committed
690
        
691
692
        # establish throat connections between pore and best candidate
        while (len(pore.throats) > 0):
sfritschi's avatar
sfritschi committed
693
            """
694
695
696
            if (not mute):
                print("\b"*12 + ", throat {0:3d}".format(len(pore.throats)),
                    end="", flush=True)
sfritschi's avatar
sfritschi committed
697
            """
698
            throat = pore.throats.pop()
699
700
701
            lt = distance(*throat_ends(throat,
                [ub-lb for lb,ub in zip(basenet.lb,basenet.ub)])) # target len.
            # find best candidate
sfritschi's avatar
sfritschi committed
702
            if (len(candidates) == 0):
703
                k = k+1; continue # no candidates left, give up
sfritschi's avatar
sfritschi committed
704
            nbor, lt = min(candidates.items(), key=lambda pl: abs(pl[1] - lt))
sfritschi's avatar
sfritschi committed
705
706
707
708
709
            """
            diff = abs(lt - ltc)
            if (max_throat_diff < diff):
                max_throat_diff = diff
            """
sfritschi's avatar
sfritschi committed
710
711
            # Remove nbor from candidates
            del candidates[nbor]
712
713
714
715
716
717
718
            nborc = nbor # memorize potential periodic copy
            # find original of buffer layer pore
            if (nbor.label != LABELS[0]):
                j, lbl = nbor.label.split(' ',1)
                nbor = pores[int(j)]
            else:
                lbl = LABELS[0]
719
            # connect pore to nbor
720
721
722
723
724
            throats.append([pore, nbor, lbl, throat.r])
            # remove most similar throat of nbor
            ranking = [(distance(*throat_ends(nthroat,
                [ub-lb for lb,ub in zip(basenet.lb,basenet.ub)])),
                nthroat) for nthroat in nbor.throats]
sfritschi's avatar
sfritschi committed
725
726
            _, nthroat = min(ranking, key=lambda lth: abs(lth[0] - lt))
            nbor.throats.remove(nthroat)
727
728
            # remove fully connected nbor from search neighborhood
            if (len(nbor.throats) == 0):
sfritschi's avatar
sfritschi committed
729
                cellList.expel(nbor)
sfritschi's avatar
sfritschi committed
730
                                
731
                for cpore in copies[nbor]:
sfritschi's avatar
sfritschi committed
732
                    cellList.expel(cpore)
733
        # remove fully connected pore from search neighborhood
sfritschi's avatar
sfritschi committed
734
        cellList.expel(pore)
735
        
736
        for cpore in copies[pore]:
sfritschi's avatar
sfritschi committed
737
            cellList.expel(cpore)
738
        
739
    print("\b"*24 + "{0:d} throats in total, {1:d} unrealised".\
740
        format(len(throats), k))
sfritschi's avatar
sfritschi committed
741
742
    #print("Max. throat length difference: %e" % max_throat_diff)
    
743
744
745
746
    # assemble and return network
    network = Network(lb=[0.0 for k in range(d)],
        ub=L, Lmax=basenet.Lmax, label='from_' + basenet.label)
    for pore in pores[:n]: network.add_pore(pore)
747
748
    for throat in throats: network.connect_pores(pore1=throat[0],
        pore2=throat[1], label=throat[2], r=throat[3])
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
    return network


def __add_buffer_layers(pores: List[Pore], targetsize: List[float],
    Lbuffer: float) -> Dict[Pore,Set[Pore]]:
    """Add pore buffer layers for spatial periodicity.
    
    Returns a dict where each key is a pore and the corresponding value
    is a set containing the copies of that pore.
    """
    n = len(pores) # number of pores inside domain
    d = len(targetsize) # number of spatial dimensions
    # label = pore index + periodicity label (-1,0,1) in each dim.
    for k, pore in enumerate(pores): pore.label = str(k) + d * ' 0'
    # add pore buffer layers
    copies = {pore:set() for pore in pores} # {pore:{set of periodic copies}}
sfritschi's avatar
sfritschi committed
765
    runningIndex = n
766
767
768
769
770
    for k in range(d):
        # left bound
        pores_layer = [pore for pore in pores \
            if targetsize[k]-Lbuffer <= pore.pos[k] < targetsize[k]]
        for pore in pores_layer:
sfritschi's avatar
sfritschi committed
771
            pcopy = Pore(pore.pos, pore.r, throats=pore.throats, index=runningIndex, id=pore.id)
772
773
774
775
776
            pcopy.pos[k] = pcopy.pos[k]-targetsize[k]
            lbl = pore.label.split(); lbl[k + 1] = '-1'
            pcopy.label = ' '.join(lbl) # periodicity label
            pores.append(pcopy)
            copies[pores[int(lbl[0])]].add(pcopy)
sfritschi's avatar
sfritschi committed
777
            runningIndex += 1
778
779
780
781
        # right bound
        pores_layer = [pore for pore in pores \
            if 0 <= pore.pos[k] < Lbuffer]
        for pore in pores_layer:
sfritschi's avatar
sfritschi committed
782
            pcopy = Pore(pore.pos, pore.r, throats=pore.throats, index=runningIndex, id=pore.id)
783
784
785
786
787
            pcopy.pos[k] = pcopy.pos[k]+targetsize[k]
            lbl = pore.label.split(); lbl[k + 1] = '1'
            pcopy.label = ' '.join(lbl) # periodicity label
            pores.append(pcopy)
            copies[pores[int(lbl[0])]].add(pcopy)
sfritschi's avatar
sfritschi committed
788
            runningIndex += 1
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
    # reset labels of pores inside domain (without buffer layers)
    for pore in pores[:n]: pore.label = LABELS[0]
    return copies


def open_periodic_network(network: Network, c: int, inouts: Dict = {}):
    """Open periodic throats in the spatial direction c>0 of a network.
    
    To avoid identical in/out pores resulting from different periodic throats
    connecting to the same original pore, one can keep track of newly generated
    in/out pores through the inouts pore dict {orig1:{"0 0 1":copy1, ...}, ...}.
    """
    # loop over (periodic) throats
    for throat in network.throats.copy(): # shallow copy (iteration changes set)
        # is throat a periodic connection in direction c?
        if len(throat.label) == 0: continue
        direct = [int(c) for c in throat.label.split()]
        if direct[c-1] == 0: continue
        # open periodic throat connection
        __open_periodic_throat(network, throat, direct, c, inouts)


def __open_periodic_throat(network: Network,
    throat: Throat, direct: List[int], c: int, inouts: Set[Pore]) \
    -> Set[Throat]:
    """Open a periodic throat connection.
    
    direct is the encoded periodicity label of the throat and c>0 is the
    spatial direction used for the in-/outflow labeling. The inouts dict
    is used to avoid the formation of pores with identical positions.
    """
    d = len(network.lb) # number of spatial dimensions
    p1 = throat.pore1; p2 = throat.pore2; r = throat.r
    # identify existing in/out pore or construct new one
    # needed in case of many periodic throats connecting to the same pore
    def get_inout_pore(pore_o, direct, pos, label, inouts) -> Pore:
        dirkey = str([abs(d) for d in direct]) # periodicity direction key
        # find existing inout pore copy (or periodic original)
        if pore_o in inouts: # is there an inout copy of the original pore?
            if dirkey in inouts[pore_o]: # is there copy in right direct?
                return inouts[pore_o][dirkey] # yes, return inout copy
        # if no inout copy exists, create a new one
        pore = Pore(pos, pore_o.r, label)
        if pore_o in inouts: # add new direct
            inout = inouts[pore_o] # dict dirkey:inout-pore
            inout[dirkey] = pore
        else: inouts[pore_o] = {dirkey:pore} # add original to inout dict
        return pore
    # pore2
    pos = [0.0 for j in range(d)] # init new position object
    # copy and shift pore2
    for j in range(d):
        pos[j] = p2.pos[j] + direct[j] * (network.ub[j]-network.lb[j])
    p2c = get_inout_pore(p2, direct, pos,
        LABELS[1+round((direct[c-1]+1)/2)] + str(c), inouts)
    network.add_pore(p2c)
    t1 = network.connect_pores(p1, p2c, throat.r)
    # pore1
    pos = [0.0 for j in range(d)] # init new position object
    # copy and shift pore1
    for j in range(d):
        pos[j] = p1.pos[j] - direct[j] * (network.ub[j]-network.lb[j])
    p1c = get_inout_pore(p1, direct, pos,
        LABELS[1+round((-direct[c-1]+1)/2)] + str(c), inouts)
    network.add_pore(p1c)
    t2 = network.connect_pores(p2, p1c, throat.r)
    # remove periodic throat
    network.throats.remove(throat)
    p1.throats.remove(throat); p2.throats.remove(throat)
    return {t1, t2}


def cut_network(network: Network, x: float, c: int, label: str = '',
    inouts: Dict = {}):
    """Cut a (periodic) network at position x_c with c>0.

    New pores are labelled and introduced at throat intersection points
    with the cutting plane. Before cutting, periodic throat connections
    in the c-direction are opened by calling open_periodic_network,
    which makes use of the inouts pore dictionary.
    """
    d = len(network.lb) # number of spatial dimensions
    # open periodic pores in direction c
    open_periodic_network(network, c, inouts)
    # cut throats incl. cut periodic ones being periodic normal to direction c
    throats = network.throats.copy() # shallow copy (iteration changes set)
    while len(throats) > 0:
        throats_next = set() # cut possible periodic pores in a 2nd round
        # cut throats ...
        for throat in throats:
            p1 = throat.pore1; p2 = throat.pore2
            # ... intersecting with cutting plane at x_c
            if (p1.pos[c-1] - x) * (x - p2.pos[c-1]) > 0:
                # treat periodic pores
                if len(throat.label) != 0:
                    direct = \
                        [int(k) for k in throat.label.split()] # periodicity
                    for k, cn in enumerate(direct):
                        if cn != 0: break # find first +/-1 periodic component
                    throats_periodic = __open_periodic_throat( \
                        network, throat, direct, k+1, inouts)
                    throats_next = throats_next | throats_periodic
                    continue
                # cut position
                f = (x - p1.pos[c-1]) / (p2.pos[c-1] - p1.pos[c-1])
                pos = [(p2.pos[j]-p1.pos[j])*f + p1.pos[j] for j in range(d)]
                pos[c-1] = x # to avoid tiny rounding errors
                # introduce and connect pore
                pore = Pore(pos, r=0.0, label=LABELS[3] + str(c) + label)
                network.add_pore(pore)
                # throat p1 - pore (reconnect throat from p2 to p1)
                throat.pore2 = pore; pore.throats.add(throat)
                # throat pore - p2 (new throat object)
                p2.throats.remove(throat)
                network.connect_pores(pore, p2, throat.r)
        # cut newly opened periodic throats
        throats = throats_next


def erase_network(network: Network, x: float, c: int, direct: bool, label: str):
    """Remove pores and connected throats from a network.
    
    Pores with positions < or > x_c for direct = True or False, respectively,
    are removed (c>0). At the same time, pores at x_c are labelled and network
    bounds updated.
    """
    for pore in network.pores.copy():
        # remove pores (and connected throats)
        if ((pore.pos[c-1] < x) and direct) or \
            ((x < pore.pos[c-1]) and not direct): network.remove_pore(pore)
        # relabel pores on cutting plane x_c
        elif pore.pos[c-1] == x: pore.label = label
    # update network bounds
    if direct: network.lb[c-1] = x
    else: network.ub[c-1] = x


def save_network_to(filename: str, network: Network):
    """Save pore network to hdf5 file."""
    import h5py
    f = h5py.File(filename, 'x')
    # write network label
    label = network.label.encode('ascii','ignore')
    f.create_dataset('network_label', (1,), dtype='S'+str(len(label)),
        data=[label])
    # bounds, Lmax
    f.create_dataset('lb', data=network.lb)
    f.create_dataset('ub', data=network.ub)
    f.create_dataset('Lmax', data=[network.Lmax])

    # write pore data
    p_grp = f.create_group('pores')
    # id
    wrk = [pore.id for pore in network.pores]
    p_grp.create_dataset('id', data=wrk)
    # radius
    wrk = [pore.r for pore in network.pores]
    p_grp.create_dataset('r', data=wrk)
    # position
    for k in range(len(network.lb)):
        wrk = [pore.pos[k] for pore in network.pores]
        p_grp.create_dataset('pos/x' + str(k), data=wrk)
    # label
    wrk = [pore.id for pore in network.pores if len(pore.label) != 0]
    if len(wrk) > 0:
        p_grp.create_dataset('label/id', data=wrk)
        wrk = [pore.label.encode('ascii','ignore') \
            for pore in network.pores if len(pore.label) != 0]
        from functools import reduce
        length = reduce(lambda a,b: max(a,b), [len(lbl) for lbl in wrk])
        p_grp.create_dataset('label/strg', (len(wrk),), dtype='S'+str(length),
            data=wrk)
        
    # write throat data
    t_grp = f.create_group('throats')
    # id
    wrk = [throat.id for throat in network.throats]
    t_grp.create_dataset('id', data=wrk)
    # radius
    wrk = [throat.r for throat in network.throats]
    t_grp.create_dataset('r', data=wrk)
    # pores
    wrk = [throat.pore1.id for throat in network.throats]
    t_grp.create_dataset('pore1', data=wrk)
    wrk = [throat.pore2.id for throat in network.throats]
    t_grp.create_dataset('pore2', data=wrk)
    # label
    wrk = [throat.id for throat in network.throats \
        if len(throat.label) != 0]
    if len(wrk) > 0:
        t_grp.create_dataset('label/id', data=wrk)
        wrk = [throat.label.encode('ascii','ignore') \
            for throat in network.throats if len(throat.label) != 0]
        from functools import reduce
        length = reduce(lambda a,b: max(a,b), [len(lbl) for lbl in wrk])
        t_grp.create_dataset('label/strg', (len(wrk),), dtype='S'+str(length),
            data=wrk)


def load_network_from(filename: str) -> Network:
    """Load pore network from hdf5 file."""
    import h5py
    import numpy as np
    f = h5py.File(filename, 'r')
    # global network properties
    network = Network(label=f['network_label'][0].decode('utf-8'),
        lb=list(f['lb']), ub=list(f['ub']), Lmax=f['Lmax'][0])

    # pores
    pid = np.array(f['pores/id'])
    pores = {} # id:pore dictionary
    for id in pid:
For faster browsing, not all history is shown. View entire blame