|
1
|
|
|
#!/usr/bin/env python |
|
2
|
|
|
# -*- coding: utf-8 -*- |
|
3
|
|
|
|
|
4
|
|
|
""" |
|
5
|
|
|
A polynomial vectorizer for The Cannon. |
|
6
|
|
|
""" |
|
7
|
|
|
|
|
8
|
|
|
from __future__ import (division, print_function, absolute_import, |
|
9
|
|
|
unicode_literals) |
|
10
|
|
|
|
|
11
|
|
|
__all__ = ["PolynomialVectorizer"] |
|
12
|
|
|
|
|
13
|
|
|
import numpy as np |
|
14
|
|
|
from collections import (Counter, OrderedDict) |
|
15
|
|
|
from itertools import combinations_with_replacement |
|
16
|
|
|
from six import string_types |
|
17
|
|
|
|
|
18
|
|
|
from .base import BaseVectorizer |
|
19
|
|
|
|
|
20
|
|
|
|
|
21
|
|
|
class PolynomialVectorizer(BaseVectorizer): |
|
22
|
|
|
""" |
|
23
|
|
|
A vectorizer that models spectral fluxes as combination of polynomial terms. |
|
24
|
|
|
Note that either `label_names` *and* `order` must be provided, or the `terms` |
|
25
|
|
|
keyword argument needs to be explicitly specified. |
|
26
|
|
|
|
|
27
|
|
|
|
|
28
|
|
|
:param label_names: [optional] |
|
29
|
|
|
A list of label names that are terms in the label vector. |
|
30
|
|
|
|
|
31
|
|
|
:param order: [optional] |
|
32
|
|
|
The maximal order for the vectorizer. |
|
33
|
|
|
|
|
34
|
|
|
:param terms: [optional] |
|
35
|
|
|
A structured list of tuples that defines the full extent of the label |
|
36
|
|
|
vector. Note that `terms` *must* be `None` if `label_names` or `order` |
|
37
|
|
|
are provided. |
|
38
|
|
|
""" |
|
39
|
|
|
|
|
40
|
|
|
def __init__(self, label_names=None, order=None, terms=None, **kwargs): |
|
41
|
|
|
|
|
42
|
|
|
# Check to see if we have a terms/(label_names and order) dichotamy/ |
|
43
|
|
|
if (terms is None and None in (label_names, order)) \ |
|
44
|
|
|
or (terms is not None and order is not None): |
|
45
|
|
|
raise ValueError("order must be None if terms are provided, " |
|
46
|
|
|
"and terms must be None if label_names and order are provided") |
|
47
|
|
|
|
|
48
|
|
|
if terms is None: |
|
49
|
|
|
# Parse human-readable terms. |
|
50
|
|
|
terms = terminator(label_names, order, **kwargs) |
|
51
|
|
|
|
|
52
|
|
|
elif label_names is None: |
|
53
|
|
|
# Parse label names from the terms. |
|
54
|
|
|
label_names = get_label_names(parse_label_vector_description(terms)) |
|
55
|
|
|
|
|
56
|
|
|
# Convert terms to use indices. |
|
57
|
|
|
terms = parse_label_vector_description(terms, label_names=label_names) |
|
58
|
|
|
|
|
59
|
|
|
super(PolynomialVectorizer, self).__init__( |
|
60
|
|
|
label_names=label_names, terms=terms, **kwargs) |
|
61
|
|
|
return None |
|
62
|
|
|
|
|
63
|
|
|
|
|
64
|
|
|
def get_label_vector(self, labels): |
|
65
|
|
|
""" |
|
66
|
|
|
Return the values of the label vector, given the scaled labels. |
|
67
|
|
|
|
|
68
|
|
|
:param labels: |
|
69
|
|
|
The scaled and offset labels to use to calculate the label vector(s). |
|
70
|
|
|
This can be a ond-dimensional vector of `K` labels, or a |
|
71
|
|
|
two-dimensional array of `N` by `K` labels. |
|
72
|
|
|
""" |
|
73
|
|
|
|
|
74
|
|
|
labels = np.atleast_2d(labels) |
|
75
|
|
|
if labels.ndim > 2: |
|
76
|
|
|
raise ValueError("labels must be a 1-d or 2-d array") |
|
77
|
|
|
|
|
78
|
|
|
columns = [np.ones(labels.shape[0], dtype=float)] |
|
79
|
|
|
for term in self.terms: |
|
80
|
|
|
column = 1. # This works; don't use np.multiply/np.product. |
|
81
|
|
|
for index, order in term: |
|
82
|
|
|
column *= labels[:, index]**order |
|
83
|
|
|
columns.append(column) |
|
84
|
|
|
return np.vstack(columns) |
|
85
|
|
|
|
|
86
|
|
|
|
|
87
|
|
|
def get_label_vector_derivative(self, labels): |
|
88
|
|
|
""" |
|
89
|
|
|
Return the derivatives of the label vector with respect to fluxes. |
|
90
|
|
|
|
|
91
|
|
|
:param labels: |
|
92
|
|
|
The scaled labels to calculate the label vector derivatives. This can |
|
93
|
|
|
be a one-dimensional vector of `K` labels (using the same order and |
|
94
|
|
|
length provided by self.label_names), or a two-dimensional array of |
|
95
|
|
|
`N` by `K` values. The returning array will be of shape `(N, D)`, |
|
96
|
|
|
where `D` is the number of terms in the label vector description. |
|
97
|
|
|
""" |
|
98
|
|
|
|
|
99
|
|
|
L, T = (len(labels), len(self.terms)) |
|
100
|
|
|
|
|
101
|
|
|
slicer = np.arange(L) |
|
102
|
|
|
indices_used = np.zeros(L, dtype=bool) |
|
103
|
|
|
|
|
104
|
|
|
columns = np.ones((T + 1, L), dtype=float) |
|
105
|
|
|
columns[0] = 0.0 # First theta derivative always zero. |
|
106
|
|
|
|
|
107
|
|
|
for t, term in enumerate(self.terms, start=1): |
|
108
|
|
|
|
|
109
|
|
|
indices_used[:] = False |
|
110
|
|
|
|
|
111
|
|
|
for index, order in term: |
|
112
|
|
|
|
|
113
|
|
|
dy = order * (labels[index]**(order - 1)) |
|
114
|
|
|
y = labels[index]**order |
|
115
|
|
|
|
|
116
|
|
|
# If it's the index w.r.t. it, take derivative. |
|
117
|
|
|
columns[t, index] *= dy |
|
118
|
|
|
|
|
119
|
|
|
# Otherwise, calculate as normal. |
|
120
|
|
|
columns[t, slicer != index] *= y |
|
121
|
|
|
indices_used[index] = True |
|
122
|
|
|
|
|
123
|
|
|
columns[t, ~indices_used] = 0 |
|
124
|
|
|
|
|
125
|
|
|
return columns |
|
126
|
|
|
|
|
127
|
|
|
|
|
128
|
|
|
def get_human_readable_label_vector(self, mul="*", pow="^", bracket=False): |
|
129
|
|
|
""" |
|
130
|
|
|
Return a human-readable form of the label vector. |
|
131
|
|
|
|
|
132
|
|
|
:param mul: [optional] |
|
133
|
|
|
String to use to represent a multiplication operator. For example, |
|
134
|
|
|
if giving LaTeX label definitions one may want to use '\cdot' for |
|
135
|
|
|
the `mul` term. |
|
136
|
|
|
|
|
137
|
|
|
:param pow: [optional] |
|
138
|
|
|
String to use to represent a power operator. |
|
139
|
|
|
|
|
140
|
|
|
:param bracket: [optional] |
|
141
|
|
|
Show brackets around each term. |
|
142
|
|
|
|
|
143
|
|
|
:returns: |
|
144
|
|
|
A human-readable string representing the label vector. |
|
145
|
|
|
""" |
|
146
|
|
|
return human_readable_label_vector( |
|
147
|
|
|
self.terms, self.label_names, mul=mul, pow=pow, bracket=bracket) |
|
148
|
|
|
|
|
149
|
|
|
|
|
150
|
|
|
@property |
|
151
|
|
|
def human_readable_label_vector(self): |
|
152
|
|
|
""" |
|
153
|
|
|
Return a human-readable form of the label vector. |
|
154
|
|
|
""" |
|
155
|
|
|
return self.get_human_readable_label_vector() |
|
156
|
|
|
|
|
157
|
|
|
|
|
158
|
|
|
def get_human_readable_label_term(self, term_index, label_names=None, |
|
159
|
|
|
**kwargs): |
|
160
|
|
|
""" |
|
161
|
|
|
Return a human-readable form of a single term in the label vector. |
|
162
|
|
|
|
|
163
|
|
|
:param term_index: |
|
164
|
|
|
The term in the label vector to return. |
|
165
|
|
|
|
|
166
|
|
|
:param label_names: [optional] |
|
167
|
|
|
The label names to use. For example, these could be LaTeX |
|
168
|
|
|
representations of the label names. |
|
169
|
|
|
|
|
170
|
|
|
:returns: |
|
171
|
|
|
A human-readable string representing a single term in the label vector. |
|
172
|
|
|
""" |
|
173
|
|
|
|
|
174
|
|
|
if term_index == 0: return "1" |
|
175
|
|
|
else: |
|
176
|
|
|
return human_readable_label_term(self.terms[term_index - 1], |
|
177
|
|
|
label_names=label_names or self.label_names, **kwargs) |
|
178
|
|
|
|
|
179
|
|
|
|
|
180
|
|
|
def _is_structured_label_vector(label_vector): |
|
181
|
|
|
""" |
|
182
|
|
|
Return whether the provided label vector is structured as a polynomial |
|
183
|
|
|
vector description appropriately or not. |
|
184
|
|
|
|
|
185
|
|
|
:param label_vector: |
|
186
|
|
|
A structured or unstructured description of a polynomial label vector. |
|
187
|
|
|
""" |
|
188
|
|
|
if not isinstance(label_vector, (list, tuple)): |
|
189
|
|
|
return False |
|
190
|
|
|
|
|
191
|
|
|
for descriptor in label_vector: |
|
192
|
|
|
if not isinstance(descriptor, (list, tuple)): |
|
193
|
|
|
return False |
|
194
|
|
|
|
|
195
|
|
|
for term in descriptor: |
|
196
|
|
|
if not isinstance(term, (list, tuple)) \ |
|
197
|
|
|
or len(term) != 2 \ |
|
198
|
|
|
or not isinstance(term[-1], (int, float)): |
|
199
|
|
|
return False |
|
200
|
|
|
|
|
201
|
|
|
if len(label_vector) == 0 or sum(map(len, label_vector)) == 0: |
|
202
|
|
|
return False |
|
203
|
|
|
return True |
|
204
|
|
|
|
|
205
|
|
|
|
|
206
|
|
|
def parse_label_vector_description(description, label_names=None, **kwargs): |
|
207
|
|
|
""" |
|
208
|
|
|
Return a structured form of a label vector from unstructured, |
|
209
|
|
|
human-readable input. |
|
210
|
|
|
|
|
211
|
|
|
:param description: |
|
212
|
|
|
A human-readable or structured form of a label vector. |
|
213
|
|
|
|
|
214
|
|
|
:type description: |
|
215
|
|
|
str or list |
|
216
|
|
|
|
|
217
|
|
|
:param label_names: [optional] |
|
218
|
|
|
If `label_names` are provided, instead of label names being provided as |
|
219
|
|
|
the output parameter, the corresponding index location will be given. |
|
220
|
|
|
|
|
221
|
|
|
:returns: |
|
222
|
|
|
A structured form of the label vector as a multi-level list. |
|
223
|
|
|
|
|
224
|
|
|
|
|
225
|
|
|
:Example: |
|
226
|
|
|
|
|
227
|
|
|
>>> parse_label_vector("Teff^4 + logg*Teff^3 + feh + feh^0*Teff") |
|
228
|
|
|
[ |
|
229
|
|
|
[ |
|
230
|
|
|
("Teff", 4), |
|
231
|
|
|
], |
|
232
|
|
|
[ |
|
233
|
|
|
("logg", 1), |
|
234
|
|
|
("Teff", 3) |
|
235
|
|
|
], |
|
236
|
|
|
[ |
|
237
|
|
|
("feh", 1), |
|
238
|
|
|
], |
|
239
|
|
|
[ |
|
240
|
|
|
("feh", 0), |
|
241
|
|
|
("Teff", 1) |
|
242
|
|
|
] |
|
243
|
|
|
] |
|
244
|
|
|
""" |
|
245
|
|
|
|
|
246
|
|
|
if _is_structured_label_vector(description): |
|
247
|
|
|
return description |
|
248
|
|
|
|
|
249
|
|
|
# Allow for custom characters, but don't advertise it. |
|
250
|
|
|
# (Astronomers have bad enough habits already.) |
|
251
|
|
|
kwds = dict(zip(("sep", "mul", "pow"), "+*^")) |
|
252
|
|
|
kwds.update(kwargs) |
|
253
|
|
|
sep, mul, pow = (kwds[k] for k in ("sep", "mul", "pow")) |
|
254
|
|
|
|
|
255
|
|
|
if isinstance(description, string_types): |
|
256
|
|
|
description = description.split(sep) |
|
257
|
|
|
description = [_.strip() for _ in description] |
|
258
|
|
|
|
|
259
|
|
|
# Functions to parse the parameter (or index) and order for each term. |
|
260
|
|
|
get_power = lambda t: float(t.split(pow)[1].strip()) if pow in t else 1 |
|
261
|
|
|
if label_names is None: |
|
262
|
|
|
get_label = lambda d: d.split(pow)[0].strip() |
|
263
|
|
|
else: |
|
264
|
|
|
get_label = lambda d: list(label_names).index(d.split(pow)[0].strip()) |
|
265
|
|
|
|
|
266
|
|
|
label_vector = [] |
|
267
|
|
|
for descriptor in (item.split(mul) for item in description): |
|
268
|
|
|
|
|
269
|
|
|
labels = map(get_label, descriptor) |
|
270
|
|
|
orders = map(get_power, descriptor) |
|
271
|
|
|
|
|
272
|
|
|
term = OrderedDict() |
|
273
|
|
|
for label, order in zip(labels, orders): |
|
274
|
|
|
term[label] = term.get(label, 0) + order # Sum repeat term powers. |
|
275
|
|
|
|
|
276
|
|
|
# Prevent uses of x^0 etc clogging up the label vector. |
|
277
|
|
|
valid_terms = [(l, o) for l, o in term.items() if o != 0] |
|
278
|
|
|
if not np.all(np.isfinite([o for l, o in valid_terms])): |
|
279
|
|
|
raise ValueError("non-finite power provided") |
|
280
|
|
|
|
|
281
|
|
|
if len(valid_terms) > 0: |
|
282
|
|
|
label_vector.append(valid_terms) |
|
283
|
|
|
|
|
284
|
|
|
if sum(map(len, label_vector)) == 0: |
|
285
|
|
|
raise ValueError("no valid terms provided") |
|
286
|
|
|
|
|
287
|
|
|
return label_vector |
|
288
|
|
|
|
|
289
|
|
|
|
|
290
|
|
|
def human_readable_label_term(term, label_names=None, mul="*", pow="^", |
|
291
|
|
|
bracket=False): |
|
292
|
|
|
""" |
|
293
|
|
|
Return a human-readable form of a single term in the label vector. |
|
294
|
|
|
|
|
295
|
|
|
:param term: |
|
296
|
|
|
A structured term. |
|
297
|
|
|
|
|
298
|
|
|
:param label_names: [optional] |
|
299
|
|
|
The names for each label in the label vector. |
|
300
|
|
|
|
|
301
|
|
|
:param mul: [optional] |
|
302
|
|
|
String to use to represent a multiplication operator. For example, |
|
303
|
|
|
if giving LaTeX label definitions one may want to use '\cdot' for |
|
304
|
|
|
the `mul` term. |
|
305
|
|
|
|
|
306
|
|
|
:param pow: [optional] |
|
307
|
|
|
String to use to represent a power operator. |
|
308
|
|
|
|
|
309
|
|
|
:param bracket: [optional] |
|
310
|
|
|
Show brackets around each term. |
|
311
|
|
|
|
|
312
|
|
|
:returns: |
|
313
|
|
|
A human-readable string representing the label vector. |
|
314
|
|
|
""" |
|
315
|
|
|
ct = [] |
|
316
|
|
|
for i, o in term: |
|
317
|
|
|
if isinstance(i, int) and label_names is not None: |
|
318
|
|
|
label_name = label_names[i] |
|
319
|
|
|
else: |
|
320
|
|
|
label_name = i |
|
321
|
|
|
if o > 1: |
|
322
|
|
|
d = (0, 1)[o - int(o) > 0] |
|
323
|
|
|
ct.append("{0}{1}{2:.{3}f}".format(label_name, pow, o, d)) |
|
324
|
|
|
else: |
|
325
|
|
|
ct.append(label_name) |
|
326
|
|
|
|
|
327
|
|
|
if bracket and len(ct) > 1: |
|
328
|
|
|
return "({})".format(mul.join(ct)) |
|
329
|
|
|
else: |
|
330
|
|
|
return mul.join(ct) |
|
331
|
|
|
|
|
332
|
|
|
|
|
333
|
|
|
def human_readable_label_vector(terms, label_names=None, mul="*", pow="^", |
|
334
|
|
|
bracket=False): |
|
335
|
|
|
""" |
|
336
|
|
|
Return a human-readable form of the label vector. |
|
337
|
|
|
|
|
338
|
|
|
:param terms: |
|
339
|
|
|
The structured terms of the label vector. |
|
340
|
|
|
|
|
341
|
|
|
:param label_names: [optional] |
|
342
|
|
|
The names for each label in the label vector. |
|
343
|
|
|
|
|
344
|
|
|
:param mul: [optional] |
|
345
|
|
|
String to use to represent a multiplication operator. For example, |
|
346
|
|
|
if giving LaTeX label definitions one may want to use '\cdot' for |
|
347
|
|
|
the `mul` term. |
|
348
|
|
|
|
|
349
|
|
|
:param pow: [optional] |
|
350
|
|
|
String to use to represent a power operator. |
|
351
|
|
|
|
|
352
|
|
|
:param bracket: [optional] |
|
353
|
|
|
Show brackets around each term. |
|
354
|
|
|
|
|
355
|
|
|
:returns: |
|
356
|
|
|
A human-readable string representing the label vector. |
|
357
|
|
|
""" |
|
358
|
|
|
if not isinstance(terms, (list, tuple)): |
|
359
|
|
|
raise TypeError("label vector is not a structured set of terms") |
|
360
|
|
|
|
|
361
|
|
|
human_terms = ["1"] |
|
362
|
|
|
for term in terms: |
|
363
|
|
|
human_terms.append(human_readable_label_term( |
|
364
|
|
|
term, label_names=label_names, mul=mul, pow=pow)) |
|
365
|
|
|
return " + ".join(human_terms) |
|
366
|
|
|
|
|
367
|
|
|
|
|
368
|
|
|
def terminator(label_names, order, cross_term_order=-1, **kwargs): |
|
369
|
|
|
""" |
|
370
|
|
|
Create the terms required for a label vector description based on the label |
|
371
|
|
|
names provided and the order given. |
|
372
|
|
|
|
|
373
|
|
|
:param label_names: |
|
374
|
|
|
The names of the labels to use in describing the label vector. |
|
375
|
|
|
|
|
376
|
|
|
:param order: |
|
377
|
|
|
The maximum order of the terms (e.g., order 3 implies A^3 is a term). |
|
378
|
|
|
|
|
379
|
|
|
:param cross_term_order: [optional] |
|
380
|
|
|
The maximum order of the cross-terms (e.g., cross_term_order 2 implies |
|
381
|
|
|
A^2*B is a term). If the provided `cross_term_order` value is negative, |
|
382
|
|
|
then `cross_term_order = order - 1` will be assumed. |
|
383
|
|
|
|
|
384
|
|
|
:param mul: [optional] |
|
385
|
|
|
The operator to use to represent multiplication in the description of |
|
386
|
|
|
the label vector. |
|
387
|
|
|
|
|
388
|
|
|
:param pow: [optional] |
|
389
|
|
|
The operator to use to represent exponents in the description of the |
|
390
|
|
|
label vector. |
|
391
|
|
|
|
|
392
|
|
|
:returns: |
|
393
|
|
|
A human-readable form of the label vector. |
|
394
|
|
|
""" |
|
395
|
|
|
sep, mul, pow = kwargs.pop(["sep", "mul", "pow"], "+*^") |
|
396
|
|
|
|
|
397
|
|
|
#I make no apologies: it's fun to code like this for short complex functions |
|
398
|
|
|
items = [] |
|
399
|
|
|
if 0 > cross_term_order: |
|
400
|
|
|
cross_term_order = order - 1 |
|
401
|
|
|
|
|
402
|
|
|
for o in range(1, 1 + max(order, 1 + cross_term_order)): |
|
403
|
|
|
for t in map(Counter, combinations_with_replacement(label_names, o)): |
|
404
|
|
|
# Python 2 and 3 behave differently here, so generate an ordered |
|
405
|
|
|
# dictionary based on sorting the keys. |
|
406
|
|
|
t = OrderedDict([(k, t[k]) for k in sorted(t.keys())]) |
|
407
|
|
|
if len(t) == 1 and order >= max(t.values()) \ |
|
408
|
|
|
or len(t) > 1 and cross_term_order >= max(t.values()): |
|
409
|
|
|
c = [pow.join([[l], [l, str(p)]][p > 1]) for l, p in t.items()] |
|
410
|
|
|
if c: items.append(mul.join(map(str, c))) |
|
411
|
|
|
return " {} ".format(sep).join(items) |
|
412
|
|
|
|
|
413
|
|
|
|
|
414
|
|
|
def get_label_names(label_vector): |
|
415
|
|
|
""" |
|
416
|
|
|
Return the label names that contribute to the structured label vector |
|
417
|
|
|
description provided. |
|
418
|
|
|
|
|
419
|
|
|
:param label_vector: |
|
420
|
|
|
A structured description of the label vector. |
|
421
|
|
|
|
|
422
|
|
|
:returns: |
|
423
|
|
|
A list of the label names that make up the label vector. |
|
424
|
|
|
""" |
|
425
|
|
|
return list(OrderedDict.fromkeys([label for term in label_vector \ |
|
426
|
|
|
for label, power in term if power != 0])) |
|
427
|
|
|
|