/
eigen.py
476 lines (415 loc) · 18.1 KB
/
eigen.py
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
###############################################################################
##
## Copyright (C) 2011-2014, NYU-Poly.
## Copyright (C) 2006-2011, University of Utah.
## All rights reserved.
## Contact: contact@vistrails.org
##
## This file is part of VisTrails.
##
## "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.
## - Neither the name of the University of Utah nor the names of its
## contributors may be used to endorse or promote products derived from
## this software without specific prior written permission.
##
## 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 HOLDER 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."
##
###############################################################################
import copy
from itertools import imap, chain
import math
import operator
import scipy
import tempfile
from vistrails.core.data_structures.bijectivedict import Bidict
from vistrails.core.utils import append_to_dict_of_lists
from .pipeline_utils import pipeline_bbox, pipeline_centroid
##############################################################################
# This is the analogy implementation
##############################################################################
# EigenBase
def mzeros(*args, **kwargs):
az = scipy.zeros(*args, dtype=float, **kwargs)
return scipy.matrix(az)
def mones(*args, **kwargs):
az = scipy.ones(*args, dtype=float, **kwargs)
return scipy.matrix(az)
#mzeros = lambda *args, **kwargs: scipy.matrix(scipy.zeros(*args, **kwargs))
# mones = lambda *args, **kwargs: scipy.matrix(scipy.ones(*args, **kwargs))
class EigenBase(object):
##########################################################################
# Constructor and initialization
def __init__(self,
pipeline1,
pipeline2):
self._p1 = pipeline1
self._p2 = pipeline2
self._debug = False
self.init_vertex_similarity()
self.init_edge_similarity()
def init_vertex_similarity(self):
num_verts_p1 = len(self._p1.graph.vertices)
num_verts_p2 = len(self._p2.graph.vertices)
m_i = mzeros((num_verts_p1, num_verts_p2))
m_o = mzeros((num_verts_p1, num_verts_p2))
def get_vertex_map(g):
return Bidict([(v, k) for (k, v)
in enumerate(g.iter_vertices())])
# vertex_maps: vertex_id to matrix index
self._g1_vertex_map = get_vertex_map(self._p1.graph)
self._g2_vertex_map = get_vertex_map(self._p2.graph)
for i in xrange(num_verts_p1):
for j in xrange(num_verts_p2):
v1_id = self._g1_vertex_map.inverse[i]
v2_id = self._g2_vertex_map.inverse[j]
(in_s8y, out_s8y) = self.compare_modules(v1_id, v2_id)
m_i[i,j] = in_s8y
m_o[i,j] = out_s8y
# print m_i
# print m_o
self._input_vertex_s8y = m_i
self._output_vertex_s8y = m_o
self._vertex_s8y = (m_i + m_o) / 2.0
def init_edge_similarity(self):
def get_edge_map(g):
itor = enumerate(imap(lambda x: x[2],
g.iter_all_edges()))
return Bidict([(v, k) for (k, v)
in itor])
# edge_maps: edge_id to matrix index
self._g1_edge_map = get_edge_map(self._p1.graph)
self._g2_edge_map = get_edge_map(self._p2.graph)
m_e = mzeros((len(self._g1_edge_map),
len(self._g2_edge_map)))
for i in xrange(len(self._g1_edge_map)):
for j in xrange(len(self._g2_edge_map)):
c1_id = self._g1_edge_map.inverse[i]
c2_id = self._g2_edge_map.inverse[j]
s8y = self.compare_connections(c1_id, c2_id)
m_e[i, j] = s8y
self._edge_s8y = m_e
##########################################################################
# Atomic comparisons for modules and connections
def create_type_portmap(self, ports):
result = {}
for port_name, port_descs in ports.iteritems():
for port_desc in port_descs:
sp = tuple(port_desc)
append_to_dict_of_lists(result, sp, port_name)
return result
def compare_modules(self, p1_id, p2_id):
"""Returns two values \in [0, 1] that is how similar the
modules are intrinsically, ie. without looking at
neighborhoods. The first value gives similarity wrt input
ports, the second to output ports."""
(m1_inputs, m1_outputs) = self.get_ports(self._p1.modules[p1_id])
(m2_inputs, m2_outputs) = self.get_ports(self._p2.modules[p2_id])
m2_input_hist = self.create_type_portmap(m2_inputs)
m2_output_hist = self.create_type_portmap(m2_outputs)
output_similarity = 0.0
total = 0
# Outputs can be covariant, inputs can be contravariant
# FIXME: subtypes, etc etc
for (port_name, port_descs) in m1_outputs.iteritems():
# we use max() .. because we want to count
# nullary ports as well
total_descs = max(len(port_descs), 1)
total += total_descs
# assert len(port_descs) == 1
if (m2_outputs.has_key(port_name) and
m2_outputs[port_name] == port_descs):
output_similarity += float(total_descs)
else:
for port_desc in port_descs:
port_desc = tuple(port_desc)
if m2_output_hist.has_key(port_desc):
output_similarity += 1
if len(m1_outputs):
output_similarity /= total
else:
output_similarity = 0.2
if (self._p1.modules[p1_id].name !=
self._p2.modules[p2_id].name):
output_similarity *= 0.99
input_similarity = 0.0
total = 0
# FIXME: consider supertypes, etc etc
for (port_name, port_descs) in m1_inputs.iteritems():
# we use max() .. because we want to count
# nullary ports as well
total_descs = max(len(port_descs), 1)
total += total_descs
if (m2_inputs.has_key(port_name) and
m2_inputs[port_name] == port_descs):
input_similarity += 1.0
else:
for port_desc in port_descs:
port_desc = tuple(port_desc)
if m2_input_hist.has_key(port_desc):
input_similarity += 1
if len(m1_inputs):
input_similarity /= total
else:
input_similarity = 0.2
if (self._p1.modules[p1_id].name !=
self._p2.modules[p2_id].name):
input_similarity *= 0.99
return (input_similarity, output_similarity)
def compare_connections(self, p1_id, p2_id):
"""Returns a value \in [0, 1] that says how similar
the two connections are."""
c1 = self._p1.connections[p1_id]
c2 = self._p2.connections[p2_id]
# FIXME: Make this softer in the future
if self._debug:
print "COMPARING %s:%s -> %s:%s with %s:%s -> %s:%s" % \
(self._p1.modules[c1.sourceId].name, c1.source.name,
self._p1.modules[c1.destinationId].name, c1.destination.name,
self._p2.modules[c2.sourceId].name, c2.source.name,
self._p2.modules[c2.destinationId].name, c2.destination.name),
if c1.source.name != c2.source.name:
if self._debug:
print 0.0
return 0.0
if c1.destination.name != c2.destination.name:
if self._debug:
print 0.0
return 0.0
m_c1_sid = self._g1_vertex_map[c1.sourceId]
m_c1_did = self._g1_vertex_map[c1.destinationId]
m_c2_sid = self._g2_vertex_map[c2.sourceId]
m_c2_did = self._g2_vertex_map[c2.destinationId]
if self._debug:
print (self._output_vertex_s8y[m_c1_sid, m_c2_sid] +
self._input_vertex_s8y[m_c1_did, m_c2_did]) / 2.0
return (self._output_vertex_s8y[m_c1_sid, m_c2_sid] +
self._input_vertex_s8y[m_c1_did, m_c2_did]) / 2.0
##########################################################################
# Utility
@staticmethod
def pm(m, digits=5):
def get_digits(x):
if x == 0: return 0
return int(math.log(abs(x) * 10.0, 10.0))
vd = scipy.vectorize(get_digits)
dm = vd(m)
widths = dm.max(0)
(l, c) = m.shape
for i in xrange(l):
EigenBase.pv(m[i,:],
digits=digits,
left_digits=widths)
@staticmethod
def pv(v, digits=5, left_digits=None):
# FIXME - some scipy indexing seems to be currently
# inconsistent across different deployed versions. Fix this.
if isinstance(v, scipy.matrix):
v = scipy.array(v)[0]
(c,) = v.shape
print "[ ",
for j in xrange(c):
if left_digits != None:
d = left_digits[0,j]
else:
d = 0
fmt = ("%" +
str(d + digits + 1) +
"." + str(digits) + "f ")
print (fmt % v[j]),
print "]"
def print_s8ys(self):
print "Input s8y"
self.pm(self._input_vertex_s8y)
print "\nOutput s8y"
self.pm(self._output_vertex_s8y)
print "\nConnection s8y"
self.pm(self._edge_s8y)
print "\nCombined s8y"
self.pm(self._vertex_s8y)
# FIXME: move this somewhere decent.
def get_ports(self, module, include_optional=False):
"""get_ports(module) -> (input_ports, output_ports)
Returns all ports for a given module name, all the way
up the class hierarchy."""
def remove_descriptions(d):
def update_elements(spec):
return [v.name for v
in spec.descriptors()]
for k in d.keys():
v = update_elements(d[k])
if len(v):
d[k] = v
else:
del d[k]
inputs = dict([(port.name, port) for
port in module.destinationPorts()
if (not port.optional or include_optional)])
outputs = dict([(port.name, port) for
port in module.sourcePorts()
if (not port.optional or include_optional)])
remove_descriptions(inputs)
remove_descriptions(outputs)
return (inputs, outputs)
##############################################################################
# EigenPipelineSimilarity2
class EigenPipelineSimilarity2(EigenBase):
def __init__(self, *args, **kwargs):
alpha = kwargs.pop('alpha')
EigenBase.__init__(self, *args, **kwargs)
self.init_operator(alpha=alpha)
def init_operator(self, alpha):
def edges(pip, v_id):
def from_fn(x): return (x[1], x[2])
def to_fn(x): return (x[0], x[2])
return chain(imap(from_fn, pip.graph.iter_edges_from(v_id)),
imap(to_fn, pip.graph.iter_edges_to(v_id)))
num_verts_p1 = len(self._p1.graph.vertices)
num_verts_p2 = len(self._p2.graph.vertices)
n = num_verts_p1 * num_verts_p2
def ix(a,b): return num_verts_p2 * a + b
# h is the raw substochastic matrix
from scipy import sparse
h = sparse.lil_matrix((n, n))
# a is the dangling node vector
a = mzeros(n)
for i in xrange(num_verts_p1):
v1_id = self._g1_vertex_map.inverse[i]
for j in xrange(num_verts_p2):
ix_ij = ix(i,j)
v2_id = self._g2_vertex_map.inverse[j]
running_sum = 0.0
for (_, p1_edge) in edges(self._p1, v1_id):
for (_, p2_edge) in edges(self._p2, v2_id):
e1_id = self._g1_edge_map[p1_edge]
e2_id = self._g2_edge_map[p2_edge]
running_sum += self._edge_s8y[e1_id, e2_id]
if running_sum == 0.0:
a[0, ix_ij] = 1.0
continue
for (p1_v, p1_edge_id) in edges(self._p1, v1_id):
for (p2_v, p2_edge_id) in edges(self._p2, v2_id):
e1_id = self._g1_edge_map[p1_edge_id]
e2_id = self._g2_edge_map[p2_edge_id]
p1_v_id = self._g1_vertex_map[p1_v]
p2_v_id = self._g2_vertex_map[p2_v]
value = self._edge_s8y[e1_id, e2_id] / running_sum
h[ix_ij, ix(p1_v_id, p2_v_id)] = value
self._alpha = alpha
self._n = n
self._h = h
self._a = a
self._e = mones(n) / n
def step(self, pi_k):
r = pi_k * self._h * self._alpha
t = pi_k * self._alpha * self._a.transpose()
r += self._v * (t[0,0] + 1.0 - self._alpha)
return r
def solve_v(self, s8y):
fl = s8y.flatten()
self._v = fl / fl.sum()
v = copy.copy(self._e)
step = 0
def write_current_matrix():
f = open('%s/%s_%03d.v' % (tempfile.gettempdir(),
self._debug_matrix_file, step), 'w')
x = v.reshape(len(self._p1.modules),
len(self._p2.modules))
for i in xrange(len(self._p1.modules)):
for j in xrange(len(self._p2.modules)):
f.write('%f ' % x[i,j])
f.write('\n')
f.close()
while 1:
if self._debug:
write_current_matrix()
new = self.step(v)
r = (v-new)
r = scipy.multiply(r,r)
s = r.sum()
if s < 0.0000001 and step >= 10:
return v
step += 1
v = new
def solve(self):
def write_debug_pipeline_positions(pipeline, mmap, f):
f.write('%d %d\n' % (len(pipeline.modules),
len(pipeline.connections)))
for k, v in mmap.iteritems():
f.write('%d %d\n' % (k, v))
c = pipeline_centroid(pipeline)
mn, mx = pipeline_bbox(pipeline)
f.write('%f %f %f %f\n' % (mn.x, mn.y, mx.x, mx.y))
for i, m in pipeline.modules.iteritems():
nc = m.center - c
f.write('%d %s %f %f\n' % (i, m.name, nc.x, nc.y))
for i, c in pipeline.connections.iteritems():
f.write('%d %d %d\n' % (i, c.sourceId, c.destinationId))
if self._debug:
out = open('%s/pipelines.txt' % tempfile.gettempdir(), 'w')
write_debug_pipeline_positions(self._p1, self._g1_vertex_map, out)
write_debug_pipeline_positions(self._p2, self._g2_vertex_map, out)
self.print_s8ys()
out.close()
self._debug_matrix_file = 'input_matrix'
r_in = self.solve_v(self._input_vertex_s8y)
self._debug_matrix_file = 'output_matrix'
r_out = self.solve_v(self._output_vertex_s8y)
r_in = r_in.reshape(len(self._p1.modules),
len(self._p2.modules))
r_out = r_out.reshape(len(self._p1.modules),
len(self._p2.modules))
s = r_in.sum(1)
s[s==0.0] = 1
r_in /= s
s = r_out.sum(1)
s[s==0.0] = 1
r_out /= s
r_combined = scipy.multiply(r_in, r_out)
# Breaks ties on combined similarity
r_in = r_in * 0.9 + r_combined * 0.1
r_out = r_out * 0.9 + r_combined * 0.1
if self._debug:
print "== G1 =="
for (k,v) in sorted(self._g1_vertex_map.iteritems(), key=operator.itemgetter(1)):
print v, k, self._p1.modules[k].name
print "== G2 =="
for (k,v) in sorted(self._g2_vertex_map.iteritems(), key=operator.itemgetter(1)):
print v, k, self._p2.modules[k].name
print "input similarity"
self.pm(r_in, digits=3)
print "output similarity"
self.pm(r_out, digits=3)
print "combined similarity"
self.pm(r_combined, digits=3)
inputmap = dict([(self._g1_vertex_map.inverse[ix],
self._g2_vertex_map.inverse[v[0,0]])
for (ix, v) in
enumerate(r_in.argmax(1))])
outputmap = dict([(self._g1_vertex_map.inverse[ix],
self._g2_vertex_map.inverse[v[0,0]])
for (ix, v) in
enumerate(r_out.argmax(1))])
combinedmap = dict([(self._g1_vertex_map.inverse[ix],
self._g2_vertex_map.inverse[v[0,0]])
for (ix, v) in
enumerate(r_combined.argmax(1))])
# print inputmap
# print outputmap
return inputmap, outputmap, combinedmap