File size: 36,399 Bytes
cfca8a4
ec0919d
69c3f28
cfca8a4
9b9db9e
a3a2513
 
5908dc9
 
bf37f2a
bdd2ad4
0a0cfdc
bdd2ad4
03e8b8d
0683428
898f500
5290229
6b04774
bf37f2a
 
 
b5b74c3
 
5908dc9
 
 
 
5f486e9
c835184
 
5908dc9
399aef5
5908dc9
f1c202a
5908dc9
 
 
 
 
 
 
 
 
 
e968e20
09f006f
5908dc9
09f006f
 
bf37f2a
5908dc9
 
 
5f486e9
 
 
 
e968e20
5908dc9
 
e968e20
5908dc9
cfca8a4
d7444a2
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
cfca8a4
333f394
 
e0cdb7c
333f394
 
85d18bf
 
 
3538029
 
 
 
 
 
90f5e4c
f068a46
90f5e4c
f068a46
ecc6ae8
90f5e4c
 
 
 
 
6143e3c
 
 
 
 
 
 
f068a46
012bfcc
333f394
 
012bfcc
333f394
012bfcc
 
 
333f394
012bfcc
333f394
012bfcc
 
 
 
 
333f394
012bfcc
34fadcf
 
 
012bfcc
2e104cc
012bfcc
 
 
333f394
012bfcc
333f394
012bfcc
333f394
012bfcc
333f394
012bfcc
 
81d46f1
 
012bfcc
683071f
 
 
 
 
7f5b38a
 
2ca2654
 
 
 
964082a
 
 
 
67558da
fe36e3a
67558da
 
e68c63f
 
 
 
 
15fbc5f
 
 
8cfda07
0a0cfdc
 
df4b0b3
e0cdb7c
 
 
 
 
609b9fc
 
 
 
898f500
 
3538029
 
 
 
c27a9c8
a3a2513
436d629
f068a46
436d629
f068a46
436d629
 
 
 
 
 
 
6decb44
 
85d18bf
 
 
 
964082a
 
306955e
 
 
43d7ca3
5cee3b5
102209f
aadb328
0683428
 
 
 
f068a46
 
 
8b29fef
5cee3b5
 
 
181a454
762987c
 
181a454
 
 
 
5cee3b5
5617815
b5b74c3
 
5617815
 
 
 
b5b74c3
 
 
5cee3b5
6decb44
5cee3b5
609b9fc
5cee3b5
 
81d46f1
 
21ae49d
5cee3b5
b935024
6decb44
7f2ee62
 
 
 
5cee3b5
 
 
 
 
67558da
5cee3b5
 
 
 
 
 
 
 
9640492
76d478e
898f500
b5b74c3
 
5cee3b5
 
 
9a46c88
 
 
 
 
609b9fc
 
 
 
c0da614
3c4ee8e
 
 
 
 
 
e0cdb7c
3c4ee8e
 
e0cdb7c
 
 
a8bf212
c0da614
9c1e6af
5cee3b5
 
 
 
 
 
 
 
 
 
a58c3d5
8d92d8e
 
a58c3d5
5cee3b5
a58c3d5
8d92d8e
 
a58c3d5
0aafc34
b5b74c3
d3b73f7
0aafc34
 
 
 
b5b74c3
 
0aafc34
 
 
 
b5b74c3
 
0aafc34
a58c3d5
76d478e
a58c3d5
 
 
 
 
 
1bd5604
c0da614
d974a2c
59765a8
 
c1807a5
0aafc34
 
 
 
ec0919d
 
 
 
 
61d9c14
b971eee
cce046c
b5fd9da
b971eee
0aafc34
 
 
 
 
 
0e9470e
 
df4b0b3
a8bf212
0aafc34
 
 
 
 
1ba0d77
 
 
df4b0b3
1ba0d77
 
c0da614
 
a8bf212
c0da614
a8bf212
 
df4b0b3
 
 
76d478e
 
 
1e13cd6
76d478e
 
df4b0b3
76d478e
df4b0b3
e68c63f
 
b5b74c3
 
0aafc34
1e13cd6
b5b74c3
 
 
 
0aafc34
b5b74c3
 
 
 
0aafc34
b5b74c3
 
 
 
 
 
 
9c1e6af
b5b74c3
0aafc34
b5b74c3
 
 
 
 
9c1e6af
0aafc34
 
76e7a47
0aafc34
6decb44
 
 
0aafc34
9c1e6af
67558da
81d46f1
0aafc34
5cee3b5
e3e2116
 
 
 
df4b0b3
 
 
 
 
 
 
 
 
 
 
 
76d478e
 
df4b0b3
 
5f486e9
 
 
 
09f006f
 
5f486e9
76d478e
 
 
 
 
fa43750
76d478e
df4b0b3
 
9c1e6af
 
fa43750
9c1e6af
 
 
 
 
 
 
 
e0a69cb
9c1e6af
7f2ee62
6decb44
 
 
9c1e6af
 
 
 
 
226786e
 
 
2e104cc
226786e
 
 
 
0e9470e
67558da
9c1e6af
0e9470e
 
 
 
81d46f1
7dd54ff
e3e2116
e2ae8ef
0e9470e
 
0aafc34
0a0cfdc
 
5cee3b5
9c1e6af
0aafc34
 
 
 
 
 
 
9c1e6af
 
0aafc34
 
 
 
 
 
 
9c1e6af
0aafc34
bf37f2a
 
5cee3b5
181a454
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
9c1e6af
76e7a47
181a454
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
8b29fef
181a454
 
 
 
 
 
 
 
 
 
5cee3b5
0dfd8e3
1ba0d77
 
0dfd8e3
 
 
 
 
 
 
1ba0d77
 
 
5cee3b5
 
 
 
0dfd8e3
 
8b29fef
0dfd8e3
 
 
b5b74c3
0dfd8e3
 
b5b74c3
0dfd8e3
 
 
 
102209f
 
 
 
 
 
 
 
 
 
2309acf
102209f
 
0dfd8e3
bf37f2a
 
 
 
 
 
 
 
 
 
 
 
 
 
898f500
b5b74c3
7f2c133
bf37f2a
 
 
 
 
 
 
b5b74c3
 
bf37f2a
 
 
 
 
b5b74c3
 
bf37f2a
964b669
 
 
 
b5b74c3
 
964b669
4854265
b5b74c3
 
 
 
4854265
102209f
5908dc9
b5b74c3
d3b73f7
b5b74c3
d3b73f7
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
b5b74c3
 
 
 
 
 
4d915b2
 
b5b74c3
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
898f500
b5b74c3
 
5908dc9
b5b74c3
a3a2513
b5b74c3
 
 
 
964082a
bf37f2a
a8ee367
 
 
7847c48
 
 
b5b74c3
7847c48
bf37f2a
 
a8ee367
 
 
bf37f2a
7847c48
 
 
 
bf37f2a
 
cc6661a
a8ee367
 
bf37f2a
d3b73f7
7847c48
 
 
bf37f2a
59cf3d0
cc6661a
a8ee367
 
bf37f2a
d3b73f7
7847c48
 
 
964082a
6b04774
 
 
 
 
c0da614
 
 
 
 
 
 
 
 
 
 
 
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
import os
import sys
from argparse import ArgumentParser, ArgumentDefaultsHelpFormatter
from collections import namedtuple
import pathlib
import numpy as np
import pandas as pd
import sympy
from sympy import sympify, Symbol, lambdify
import subprocess
import tempfile
import shutil
from pathlib import Path
from datetime import datetime
import warnings
from .export import sympy2jax

global_equation_file = 'hall_of_fame.csv'
global_n_features = None
global_variable_names = []
global_extra_sympy_mappings = {}
global_multioutput = False
global_nout = 1

sympy_mappings = {
    'div':  lambda x, y : x/y,
    'mult': lambda x, y : x*y,
    'sqrt_abs':lambda x    : sympy.sqrt(abs(x)),
    'square':lambda x   : x**2,
    'cube': lambda x    : x**3,
    'plus': lambda x, y : x + y,
    'sub':  lambda x, y : x - y,
    'neg':  lambda x    : -x,
    'pow':  lambda x, y : abs(x)**y,
    'cos':  lambda x    : sympy.cos(x),
    'sin':  lambda x    : sympy.sin(x),
    'tan':  lambda x    : sympy.tan(x),
    'cosh': lambda x    : sympy.cosh(x),
    'sinh': lambda x    : sympy.sinh(x),
    'tanh': lambda x    : sympy.tanh(x),
    'exp':  lambda x    : sympy.exp(x),
    'acos': lambda x    : sympy.acos(x),
    'asin': lambda x    : sympy.asin(x),
    'atan': lambda x    : sympy.atan(x),
    'acosh':lambda x    : sympy.acosh(abs(x) + 1),
    'acosh_abs':lambda x : sympy.acosh(abs(x) + 1),
    'asinh':lambda x    : sympy.asinh(x),
    'atanh':lambda x    : sympy.atanh(sympy.Mod(x+1, 2)-1),
    'atanh_clip':lambda x : sympy.atanh(sympy.Mod(x+1, 2)-1),
    'abs':  lambda x    : abs(x),
    'mod':  lambda x, y : sympy.Mod(x, y),
    'erf':  lambda x    : sympy.erf(x),
    'erfc': lambda x    : sympy.erfc(x),
    'log_abs': lambda x : sympy.log(abs(x)),
    'log10_abs':lambda x : sympy.log(abs(x), 10),
    'log2_abs': lambda x : sympy.log(abs(x), 2),
    'log1p_abs': lambda x : sympy.log(abs(x) + 1),
    'floor': lambda x   : sympy.floor(x),
    'ceil': lambda x    : sympy.ceil(x),
    'sign': lambda x    : sympy.sign(x),
    'gamma': lambda x   : sympy.gamma(x),
}

def pysr(X, y, weights=None,
         binary_operators=None,
         unary_operators=None,
         procs=4,
         loss='L2DistLoss()',
         populations=20,
         niterations=100,
         ncyclesperiteration=300,
         alpha=0.1,
         annealing=False,
         fractionReplaced=0.10,
         fractionReplacedHof=0.10,
         npop=1000,
         parsimony=1e-4,
         migration=True,
         hofMigration=True,
         shouldOptimizeConstants=True,
         topn=10,
         weightAddNode=1,
         weightInsertNode=3,
         weightDeleteNode=3,
         weightDoNothing=1,
         weightMutateConstant=10,
         weightMutateOperator=1,
         weightRandomize=1,
         weightSimplify=0.01,
         perturbationFactor=1.0,
         timeout=None,
         extra_sympy_mappings=None,
         equation_file=None,
         verbosity=1e9,
         progress=True,
         maxsize=20,
         fast_cycle=False,
         maxdepth=None,
         variable_names=None,
         batching=False,
         batchSize=50,
         select_k_features=None,
         warmupMaxsizeBy=0.0,
         constraints=None,
         useFrequency=True,
         tempdir=None,
         delete_tempfiles=True,
         julia_optimization=3,
         julia_project=None,
         user_input=True,
         update=True,
         temp_equation_file=False,
         output_jax_format=False,
         optimizer_algorithm="BFGS",
         optimizer_nrestarts=3,
         optimize_probability=1.0,
         optimizer_iterations=10,
        ):
    """Run symbolic regression to fit f(X[i, :]) ~ y[i] for all i.
    Note: most default parameters have been tuned over several example
    equations, but you should adjust `niterations`,
    `binary_operators`, `unary_operators` to your requirements.

    :param X: np.ndarray or pandas.DataFrame, 2D array. Rows are examples,
        columns are features. If pandas DataFrame, the columns are used
        for variable names (so make sure they don't contain spaces).
    :param y: np.ndarray, 1D array (rows are examples) or 2D array (rows
        are examples, columns are outputs). Putting in a 2D array will
        trigger a search for equations for each feature of y.
    :param weights: np.ndarray, same shape as y. Each element is how to
        weight the mean-square-error loss for that particular element
        of y.
    :param binary_operators: list, List of strings giving the binary operators
        in Julia's Base. Default is ["+", "-", "*", "/",].
    :param unary_operators: list, Same but for operators taking a single scalar.
        Default is [].
    :param procs: int, Number of processes (=number of populations running).
    :param loss: str, String of Julia code specifying the loss function.
        Can either be a loss from LossFunctions.jl, or your own
        loss written as a function. Examples of custom written losses
        include: `myloss(x, y) = abs(x-y)` for non-weighted, or 
        `myloss(x, y, w) = w*abs(x-y)` for weighted.
        Among the included losses, these are as follows. Regression:
        `LPDistLoss{P}()`, `L1DistLoss()`, `L2DistLoss()` (mean square),
        `LogitDistLoss()`, `HuberLoss(d)`, `L1EpsilonInsLoss(ϵ)`,
        `L2EpsilonInsLoss(ϵ)`, `PeriodicLoss(c)`, `QuantileLoss(τ)`.
        Classification: `ZeroOneLoss()`, `PerceptronLoss()`, `L1HingeLoss()`,
        `SmoothedL1HingeLoss(γ)`, `ModifiedHuberLoss()`, `L2MarginLoss()`,
        `ExpLoss()`, `SigmoidLoss()`, `DWDMarginLoss(q)`.
    :param populations: int, Number of populations running.
    :param niterations: int, Number of iterations of the algorithm to run. The best
        equations are printed, and migrate between populations, at the
        end of each.
    :param ncyclesperiteration: int, Number of total mutations to run, per 10
        samples of the population, per iteration.
    :param alpha: float, Initial temperature.
    :param annealing: bool, Whether to use annealing. You should (and it is default).
    :param fractionReplaced: float, How much of population to replace with migrating
        equations from other populations.
    :param fractionReplacedHof: float, How much of population to replace with migrating
        equations from hall of fame.
    :param npop: int, Number of individuals in each population
    :param parsimony: float, Multiplicative factor for how much to punish complexity.
    :param migration: bool, Whether to migrate.
    :param hofMigration: bool, Whether to have the hall of fame migrate.
    :param shouldOptimizeConstants: bool, Whether to numerically optimize
        constants (Nelder-Mead/Newton) at the end of each iteration.
    :param topn: int, How many top individuals migrate from each population.
    :param perturbationFactor: float, Constants are perturbed by a max
        factor of (perturbationFactor*T + 1). Either multiplied by this
        or divided by this.
    :param weightAddNode: float, Relative likelihood for mutation to add a node
    :param weightInsertNode: float, Relative likelihood for mutation to insert a node
    :param weightDeleteNode: float, Relative likelihood for mutation to delete a node
    :param weightDoNothing: float, Relative likelihood for mutation to leave the individual
    :param weightMutateConstant: float, Relative likelihood for mutation to change
        the constant slightly in a random direction.
    :param weightMutateOperator: float, Relative likelihood for mutation to swap
        an operator.
    :param weightRandomize: float, Relative likelihood for mutation to completely
        delete and then randomly generate the equation
    :param weightSimplify: float, Relative likelihood for mutation to simplify
        constant parts by evaluation
    :param timeout: float, Time in seconds to timeout search
    :param equation_file: str, Where to save the files (.csv separated by |)
    :param verbosity: int, What verbosity level to use. 0 means minimal print statements.
    :param progress: bool, Whether to use a progress bar instead of printing to stdout.
    :param maxsize: int, Max size of an equation.
    :param maxdepth: int, Max depth of an equation. You can use both maxsize and maxdepth.
        maxdepth is by default set to = maxsize, which means that it is redundant.
    :param fast_cycle: bool, (experimental) - batch over population subsamples. This
        is a slightly different algorithm than regularized evolution, but does cycles
        15% faster. May be algorithmically less efficient.
    :param variable_names: list, a list of names for the variables, other
        than "x0", "x1", etc.
    :param batching: bool, whether to compare population members on small batches
        during evolution. Still uses full dataset for comparing against
        hall of fame.
    :param batchSize: int, the amount of data to use if doing batching.
    :param select_k_features: (None, int), whether to run feature selection in
        Python using random forests, before passing to the symbolic regression
        code. None means no feature selection; an int means select that many
        features.
    :param warmupMaxsizeBy: float, whether to slowly increase max size from
        a small number up to the maxsize (if greater than 0).
        If greater than 0, says the fraction of training time at which
        the current maxsize will reach the user-passed maxsize.
    :param constraints: dict of int (unary) or 2-tuples (binary),
        this enforces maxsize constraints on the individual
        arguments of operators. E.g., `'pow': (-1, 1)`
        says that power laws can have any complexity left argument, but only
        1 complexity exponent. Use this to force more interpretable solutions.
    :param useFrequency: bool, whether to measure the frequency of complexities,
        and use that instead of parsimony to explore equation space. Will
        naturally find equations of all complexities.
    :param julia_optimization: int, Optimization level (0, 1, 2, 3)
    :param tempdir: str or None, directory for the temporary files
    :param delete_tempfiles: bool, whether to delete the temporary files after finishing
    :param julia_project: str or None, a Julia environment location containing
        a Project.toml (and potentially the source code for SymbolicRegression.jl).
        Default gives the Python package directory, where a Project.toml file
        should be present from the install.
    :param user_input: Whether to ask for user input or not for installing (to
        be used for automated scripts). Will choose to install when asked.
    :param update: Whether to automatically update Julia packages.
    :param temp_equation_file: Whether to put the hall of fame file in
        the temp directory. Deletion is then controlled with the
        delete_tempfiles argument.
    :param output_jax_format: Whether to create a 'jax_format' column in the output,
        containing jax-callable functions and the default parameters in a jax array.
    :returns: pd.DataFrame or list, Results dataframe,
        giving complexity, MSE, and equations (as strings), as well as functional
        forms. If list, each element corresponds to a dataframe of equations
        for each output.

    """
    if binary_operators is None:
        binary_operators = '+ * - /'.split(' ')
    if unary_operators is None:
        unary_operators = []
    if extra_sympy_mappings is None:
        extra_sympy_mappings = {}
    if variable_names is None:
        variable_names = []
    if constraints is None:
        constraints = {}

    assert optimizer_algorithm in ['NelderMead', 'BFGS']

    if isinstance(X, pd.DataFrame):
        variable_names = list(X.columns)
        X = np.array(X)

    use_custom_variable_names = (len(variable_names) != 0)

    if len(X.shape) == 1:
        X = X[:, None]

    _check_assertions(X, binary_operators, unary_operators,
                     use_custom_variable_names, variable_names, weights, y)
    _check_for_julia_installation()


    if len(X) > 10000 and not batching:
        warnings.warn("Note: you are running with more than 10,000 datapoints. You should consider turning on batching (https://pysr.readthedocs.io/en/latest/docs/options/#batching). You should also reconsider if you need that many datapoints. Unless you have a large amount of noise (in which case you should smooth your dataset first), generally < 10,000 datapoints is enough to find a functional form with symbolic regression. More datapoints will lower the search speed.")

    if maxsize > 40:
        warnings.warn("Note: Using a large maxsize for the equation search will be slow and use significant memory. You should consider turning `useFrequency` to False, and perhaps use `warmupMaxsizeBy`.")

    X, variable_names = _handle_feature_selection(
            X, select_k_features,
            use_custom_variable_names, variable_names, y
        )

    if maxdepth is None:
        maxdepth = maxsize
    if isinstance(binary_operators, str):
        binary_operators = [binary_operators]
    if isinstance(unary_operators, str):
        unary_operators = [unary_operators]

    if len(y.shape) == 1 or (len(y.shape) == 2 and y.shape[1] == 1):
        multioutput = False
        nout = 1
        y = y.reshape(-1)
    elif len(y.shape) == 2:
        multioutput = True
        nout = y.shape[1]
    else:
        raise NotImplementedError("y shape not supported!")

    kwargs = dict(X=X, y=y, weights=weights,
                 alpha=alpha, annealing=annealing, batchSize=batchSize,
                 batching=batching, binary_operators=binary_operators,
                 fast_cycle=fast_cycle,
                 fractionReplaced=fractionReplaced,
                 ncyclesperiteration=ncyclesperiteration,
                 niterations=niterations, npop=npop, topn=topn,
                 verbosity=verbosity, progress=progress, update=update,
                 julia_optimization=julia_optimization, timeout=timeout,
                 fractionReplacedHof=fractionReplacedHof,
                 hofMigration=hofMigration, maxdepth=maxdepth,
                 maxsize=maxsize, migration=migration,
                 optimizer_algorithm=optimizer_algorithm,
                 optimizer_nrestarts=optimizer_nrestarts,
                 optimize_probability=optimize_probability,
                 optimizer_iterations=optimizer_iterations,
                 parsimony=parsimony, perturbationFactor=perturbationFactor,
                 populations=populations, procs=procs,
                 shouldOptimizeConstants=shouldOptimizeConstants,
                 unary_operators=unary_operators, useFrequency=useFrequency,
                 use_custom_variable_names=use_custom_variable_names,
                 variable_names=variable_names, warmupMaxsizeBy=warmupMaxsizeBy,
                 weightAddNode=weightAddNode,
                 weightDeleteNode=weightDeleteNode,
                 weightDoNothing=weightDoNothing,
                 weightInsertNode=weightInsertNode,
                 weightMutateConstant=weightMutateConstant,
                 weightMutateOperator=weightMutateOperator,
                 weightRandomize=weightRandomize,
                 weightSimplify=weightSimplify,
                 constraints=constraints,
                 extra_sympy_mappings=extra_sympy_mappings,
                 julia_project=julia_project, loss=loss,
                 output_jax_format=output_jax_format,
                 multioutput=multioutput, nout=nout)

    kwargs = {**_set_paths(tempdir), **kwargs}

    if temp_equation_file:
        equation_file = kwargs['tmpdir'] / f'hall_of_fame.csv'
    elif equation_file is None:
        date_time = datetime.now().strftime("%Y-%m-%d_%H%M%S.%f")[:-3]
        equation_file = 'hall_of_fame_' + date_time + '.csv'

    kwargs = {**dict(equation_file=equation_file), **kwargs}


    pkg_directory = kwargs['pkg_directory']
    manifest_file = None
    if kwargs['julia_project'] is not None:
        manifest_filepath = Path(kwargs['julia_project']) / 'Manifest.toml'
    else:
        manifest_filepath = pkg_directory / 'Manifest.toml'

    kwargs['need_install'] = False

    if not (manifest_filepath).is_file():
        kwargs['need_install'] = (not user_input) or _yesno("I will install Julia packages using PySR's Project.toml file. OK?")
        if kwargs['need_install']:
            print("OK. I will install at launch.")
            assert update

    kwargs['def_hyperparams'] = _create_inline_operators(**kwargs)

    _handle_constraints(**kwargs)

    kwargs['constraints_str'] = _make_constraints_str(**kwargs)
    kwargs['def_hyperparams'] = _make_hyperparams_julia_str(**kwargs)
    kwargs['def_datasets'] = _make_datasets_julia_str(**kwargs)

    _create_julia_files(**kwargs)
    _final_pysr_process(**kwargs)
    _set_globals(**kwargs)

    equations = get_hof(**kwargs)

    if delete_tempfiles:
        shutil.rmtree(kwargs['tmpdir'])

    return equations



def _set_globals(X, equation_file, extra_sympy_mappings, variable_names,
                multioutput, nout, **kwargs):
    global global_n_features
    global global_equation_file
    global global_variable_names
    global global_extra_sympy_mappings
    global global_multioutput
    global global_nout
    global_n_features = X.shape[1]
    global_equation_file = equation_file
    global_variable_names = variable_names
    global_extra_sympy_mappings = extra_sympy_mappings
    global_multioutput = multioutput
    global_nout = nout


def _final_pysr_process(julia_optimization, runfile_filename, timeout, **kwargs):
    command = [
        f'julia', f'-O{julia_optimization:d}',
        str(runfile_filename),
    ]
    if timeout is not None:
        command = [f'timeout', f'{timeout}'] + command
    _cmd_runner(command, **kwargs)

def _cmd_runner(command, **kwargs):
    if kwargs['verbosity'] > 0:
        print("Running on", ' '.join(command))
    process = subprocess.Popen(command, stdout=subprocess.PIPE, bufsize=-1)
    try:
        while True:
            line = process.stdout.readline()
            if not line: break
            decoded_line = (line.decode('utf-8')
                                .replace('\\033[K',  '\033[K')
                                .replace('\\033[1A', '\033[1A')
                                .replace('\\033[1B', '\033[1B')
                                .replace('\\r',      '\r')
                                .encode(sys.stdout.encoding, errors='replace'))

            sys.stdout.buffer.write(decoded_line)
            sys.stdout.flush()

        process.stdout.close()
        process.wait()
    except KeyboardInterrupt:
        print("Killing process... will return when done.")
        process.kill()

def _create_julia_files(dataset_filename, def_datasets,  hyperparam_filename, def_hyperparams,
                        fractionReplaced, ncyclesperiteration, niterations, npop,
                        runfile_filename, topn, verbosity, julia_project, procs, weights,
                        X, variable_names, pkg_directory, need_install, update, **kwargs):
    with open(hyperparam_filename, 'w') as f:
        print(def_hyperparams, file=f)
    with open(dataset_filename, 'w') as f:
        print(def_datasets, file=f)
    with open(runfile_filename, 'w') as f:
        if julia_project is None:
            julia_project = pkg_directory
        else:
            julia_project = Path(julia_project)
        print(f'import Pkg', file=f)
        print(f'Pkg.activate("{_escape_filename(julia_project)}")', file=f)
        if need_install:
            print(f'Pkg.instantiate()', file=f)
            print(f'Pkg.update()', file=f)
            print(f'Pkg.precompile()', file=f)
        elif update:
            print(f'Pkg.update()', file=f)
        print(f'using SymbolicRegression', file=f)
        print(f'include("{_escape_filename(hyperparam_filename)}")', file=f)
        print(f'include("{_escape_filename(dataset_filename)}")', file=f)
        if len(variable_names) == 0:
            varMap = "[" + ",".join([f'"x{i}"' for i in range(X.shape[1])]) + "]"
        else:
            varMap = "[" + ",".join(['"' + vname + '"' for vname in variable_names]) + "]"

        if weights is not None:
            print(f'EquationSearch(X, y, weights=weights, niterations={niterations:d}, varMap={varMap}, options=options, numprocs={procs})', file=f)
        else:
            print(f'EquationSearch(X, y, niterations={niterations:d}, varMap={varMap}, options=options, numprocs={procs})', file=f)


def _make_datasets_julia_str(X, X_filename, weights, weights_filename, y, y_filename,
                            multioutput, **kwargs):
    def_datasets = """using DelimitedFiles"""
    np.savetxt(X_filename, X.astype(np.float32), delimiter=',')
    if multioutput:
        np.savetxt(y_filename, y.astype(np.float32), delimiter=',')
    else:
        np.savetxt(y_filename, y.reshape(-1, 1).astype(np.float32), delimiter=',')
    if weights is not None:
        if multioutput:
            np.savetxt(weights_filename, weights.astype(np.float32), delimiter=',')
        else:
            np.savetxt(weights_filename, weights.reshape(-1, 1).astype(np.float32), delimiter=',')
    def_datasets += f"""
X = copy(transpose(readdlm("{_escape_filename(X_filename)}", ',', Float32, '\\n')))"""

    if multioutput:
        def_datasets+= f"""
y = copy(transpose(readdlm("{_escape_filename(y_filename)}", ',', Float32, '\\n')))"""
    else:
        def_datasets+= f"""
y = readdlm("{_escape_filename(y_filename)}", ',', Float32, '\\n')[:, 1]"""

    if weights is not None:
        if multioutput:
            def_datasets += f"""
weights = copy(transpose(readdlm("{_escape_filename(weights_filename)}", ',', Float32, '\\n')))"""
        else:
            def_datasets += f"""
weights = readdlm("{_escape_filename(weights_filename)}", ',', Float32, '\\n')[:, 1]"""
    return def_datasets

def _make_hyperparams_julia_str(X, alpha, annealing, batchSize, batching, binary_operators, constraints_str,
                               def_hyperparams, equation_file, fast_cycle, fractionReplacedHof, hofMigration,
                               maxdepth, maxsize, migration,
                               optimizer_algorithm, optimizer_nrestarts,
                               optimize_probability, optimizer_iterations, npop,
                               parsimony, perturbationFactor, populations, procs, shouldOptimizeConstants,
                               unary_operators, useFrequency, use_custom_variable_names,
                               variable_names, warmupMaxsizeBy, weightAddNode,
                               ncyclesperiteration, fractionReplaced, topn, verbosity, progress, loss,
                               weightDeleteNode, weightDoNothing, weightInsertNode, weightMutateConstant,
                               weightMutateOperator, weightRandomize, weightSimplify, weights, **kwargs):
    try:
        term_width = shutil.get_terminal_size().columns
    except:
        _, term_width = subprocess.check_output(['stty', 'size']).split()
    def tuple_fix(ops):
        if len(ops) > 1:
            return ', '.join(ops)
        elif len(ops) == 0:
            return ''
        else:
            return ops[0] + ','

    def_hyperparams += f"""\n
plus=(+)
sub=(-)
mult=(*)
square=SymbolicRegression.square
cube=SymbolicRegression.cube
pow=(^)
div=(/)
log_abs=SymbolicRegression.log_abs
log2_abs=SymbolicRegression.log2_abs
log10_abs=SymbolicRegression.log10_abs
log1p_abs=SymbolicRegression.log1p_abs
acosh_abs=SymbolicRegression.acosh_abs
atanh_clip=SymbolicRegression.atanh_clip
sqrt_abs=SymbolicRegression.sqrt_abs
neg=SymbolicRegression.neg
greater=SymbolicRegression.greater
relu=SymbolicRegression.relu
logical_or=SymbolicRegression.logical_or
logical_and=SymbolicRegression.logical_and
_custom_loss = {loss}

options = SymbolicRegression.Options(binary_operators={'(' + tuple_fix(binary_operators) + ')'},
unary_operators={'(' + tuple_fix(unary_operators) + ')'},
{constraints_str}
parsimony={parsimony:f}f0,
loss=_custom_loss,
alpha={alpha:f}f0,
maxsize={maxsize:d},
maxdepth={maxdepth:d},
fast_cycle={'true' if fast_cycle else 'false'},
migration={'true' if migration else 'false'},
hofMigration={'true' if hofMigration else 'false'},
fractionReplacedHof={fractionReplacedHof}f0,
shouldOptimizeConstants={'true' if shouldOptimizeConstants else 'false'},
hofFile="{_escape_filename(equation_file)}",
npopulations={populations:d},
optimizer_algorithm="{optimizer_algorithm}",
optimizer_nrestarts={optimizer_nrestarts:d},
optimize_probability={optimize_probability:f}f0,
optimizer_iterations={optimizer_iterations:d},
perturbationFactor={perturbationFactor:f}f0,
annealing={"true" if annealing else "false"},
batching={"true" if batching else "false"},
batchSize={min([batchSize, len(X)]) if batching else len(X):d},
mutationWeights=[
    {weightMutateConstant:f},
    {weightMutateOperator:f},
    {weightAddNode:f},
    {weightInsertNode:f},
    {weightDeleteNode:f},
    {weightSimplify:f},
    {weightRandomize:f},
    {weightDoNothing:f}
],
warmupMaxsizeBy={warmupMaxsizeBy:f}f0,
useFrequency={"true" if useFrequency else "false"},
npop={npop:d},
ncyclesperiteration={ncyclesperiteration:d},
fractionReplaced={fractionReplaced:f}f0,
topn={topn:d},
verbosity=round(Int32, {verbosity:f}),
progress={'true' if progress else 'false'},
terminal_width={term_width:d}
"""

    def_hyperparams += '\n)'
    return def_hyperparams


def _make_constraints_str(binary_operators, constraints, unary_operators, **kwargs):
    constraints_str = "una_constraints = ["
    first = True
    for op in unary_operators:
        val = constraints[op]
        if not first:
            constraints_str += ", "
        constraints_str += f"{val:d}"
        first = False
    constraints_str += """],
bin_constraints = ["""
    first = True
    for op in binary_operators:
        tup = constraints[op]
        if not first:
            constraints_str += ", "
        constraints_str += f"({tup[0]:d}, {tup[1]:d})"
        first = False
    constraints_str += "],"
    return constraints_str


def _handle_constraints(binary_operators, constraints, unary_operators, **kwargs):
    for op in unary_operators:
        if op not in constraints:
            constraints[op] = -1
    for op in binary_operators:
        if op not in constraints:
            constraints[op] = (-1, -1)
        if op in ['plus', 'sub']:
            if constraints[op][0] != constraints[op][1]:
                raise NotImplementedError(
                    "You need equal constraints on both sides for - and *, due to simplification strategies.")
        elif op == 'mult':
            # Make sure the complex expression is in the left side.
            if constraints[op][0] == -1:
                continue
            elif constraints[op][1] == -1 or constraints[op][0] < constraints[op][1]:
                constraints[op][0], constraints[op][1] = constraints[op][1], constraints[op][0]


def _create_inline_operators(binary_operators, unary_operators, **kwargs):
    def_hyperparams = ""
    for op_list in [binary_operators, unary_operators]:
        for i in range(len(op_list)):
            op = op_list[i]
            is_user_defined_operator = '(' in op

            if is_user_defined_operator:
                def_hyperparams += op + "\n"
                # Cut off from the first non-alphanumeric char:
                first_non_char = [
                    j for j in range(len(op))
                    if not (op[j].isalpha() or op[j].isdigit())][0]
                function_name = op[:first_non_char]
                op_list[i] = function_name
    return def_hyperparams


def _handle_feature_selection(X, select_k_features, use_custom_variable_names, variable_names, y):
    if select_k_features is not None:
        selection = run_feature_selection(X, y, select_k_features)
        print(f"Using features {selection}")
        X = X[:, selection]

        if use_custom_variable_names:
            variable_names = [variable_names[selection[i]] for i in range(len(selection))]
    return X, variable_names


def _set_paths(tempdir):
    # System-independent paths
    pkg_directory = Path(__file__).parents[1]
    default_project_file = pkg_directory / "Project.toml"
    tmpdir = Path(tempfile.mkdtemp(dir=tempdir))
    hyperparam_filename = tmpdir / f'hyperparams.jl'
    dataset_filename = tmpdir / f'dataset.jl'
    runfile_filename = tmpdir / f'runfile.jl'
    X_filename = tmpdir / "X.csv"
    y_filename = tmpdir / "y.csv"
    weights_filename = tmpdir / "weights.csv"
    return dict(pkg_directory=pkg_directory,
	    default_project_file=default_project_file,
	    X_filename=X_filename,
            dataset_filename=dataset_filename,
            hyperparam_filename=hyperparam_filename,
            runfile_filename=runfile_filename, tmpdir=tmpdir,
            weights_filename=weights_filename, y_filename=y_filename)


def _check_assertions(X, binary_operators, unary_operators, use_custom_variable_names, variable_names, weights, y):
    # Check for potential errors before they happen
    assert len(unary_operators) + len(binary_operators) > 0
    assert len(X.shape) == 2
    assert len(y.shape) in [1, 2]
    assert X.shape[0] == y.shape[0]
    if weights is not None:
        assert weights.shape == y.shape
        assert X.shape[0] == weights.shape[0]
    if use_custom_variable_names:
        assert len(variable_names) == X.shape[1]

def _check_for_julia_installation():
    try:
        process = subprocess.Popen(["julia", "-v"], stdout=subprocess.PIPE, bufsize=-1)
        while True:
            line = process.stdout.readline()
            if not line: break
        process.stdout.close()
        process.wait()
    except FileNotFoundError:
        import os
        raise RuntimeError(f"Your current $PATH is: {os.environ['PATH']}\nPySR could not start julia. Make sure julia is installed and on your $PATH.")
    process.kill()


def run_feature_selection(X, y, select_k_features):
    """Use a gradient boosting tree regressor as a proxy for finding
        the k most important features in X, returning indices for those
        features as output."""

    from sklearn.ensemble import RandomForestRegressor, GradientBoostingRegressor
    from sklearn.feature_selection import SelectFromModel, SelectKBest

    clf = GradientBoostingRegressor(n_estimators=100, learning_rate=0.1, max_depth=1, random_state=0, loss='ls') #RandomForestRegressor()
    clf.fit(X, y)
    selector = SelectFromModel(clf, threshold=-np.inf,
            max_features=select_k_features, prefit=True)
    return selector.get_support(indices=True)

def get_hof(equation_file=None, n_features=None, variable_names=None,
            extra_sympy_mappings=None, output_jax_format=False,
            multioutput=None, nout=None, **kwargs):
    """Get the equations from a hall of fame file. If no arguments
    entered, the ones used previously from a call to PySR will be used."""

    global global_n_features
    global global_equation_file
    global global_variable_names
    global global_extra_sympy_mappings
    global global_multioutput
    global global_nout

    if equation_file is None: equation_file = global_equation_file
    if n_features is None: n_features = global_n_features
    if variable_names is None: variable_names = global_variable_names
    if extra_sympy_mappings is None: extra_sympy_mappings = global_extra_sympy_mappings
    if multioutput is None: multioutput = global_multioutput
    if nout is None: nout = global_nout

    global_equation_file = equation_file
    global_n_features = n_features
    global_variable_names = variable_names
    global_extra_sympy_mappings = extra_sympy_mappings
    global_multioutput = multioutput
    global_nout = nout

    try:
        if multioutput:
            all_outputs = [pd.read_csv(f'out{i}_' + str(equation_file) + '.bkup', sep="|") for i in range(1, nout+1)]
        else:
            all_outputs = [pd.read_csv(str(equation_file) + '.bkup', sep="|")]
    except FileNotFoundError:
        raise RuntimeError("Couldn't find equation file! The equation search likely exited before a single iteration completed.")

    ret_outputs = []

    for output in all_outputs:

        scores = []
        lastMSE = None
        lastComplexity = 0
        sympy_format = []
        lambda_format = []
        if output_jax_format:
            jax_format = []
        use_custom_variable_names = (len(variable_names) != 0)
        local_sympy_mappings = {
                **extra_sympy_mappings,
                **sympy_mappings
        }

        if use_custom_variable_names:
            sympy_symbols = [sympy.Symbol(variable_names[i]) for i in range(n_features)]
        else:
            sympy_symbols = [sympy.Symbol('x%d'%i) for i in range(n_features)]

        for i in range(len(output)):
            eqn = sympify(output.loc[i, 'Equation'], locals=local_sympy_mappings)
            sympy_format.append(eqn)
            if output_jax_format:
                func, params = sympy2jax(eqn, sympy_symbols)
                jax_format.append({'callable': func, 'parameters': params})
            tmp_lambda = lambdify(sympy_symbols, eqn)
            lambda_format.append(lambda X: tmp_lambda(*X.T))
            curMSE = output.loc[i, 'MSE']
            curComplexity = output.loc[i, 'Complexity']

            if lastMSE is None:
                cur_score = 0.0
            else:
                cur_score = - np.log(curMSE/lastMSE)/(curComplexity - lastComplexity)

            scores.append(cur_score)
            lastMSE = curMSE
            lastComplexity = curComplexity

        output['score'] = np.array(scores)
        output['sympy_format'] = sympy_format
        output['lambda_format'] = lambda_format
        output_cols = ['Complexity', 'MSE', 'score', 'Equation', 'sympy_format', 'lambda_format']
        if output_jax_format:
            output_cols += ['jax_format']
            output['jax_format'] = jax_format

        ret_outputs.append(output[output_cols])

    if multioutput:
        return ret_outputs
    else:
        return ret_outputs[0]

def best_row(equations=None):
    """Return the best row of a hall of fame file using the score column.
    By default this uses the last equation file.
    """
    if equations is None: equations = get_hof()
    if isinstance(equations, list):
        return [eq.iloc[np.argmax(eq['score'])] for eq in equations]
    else:
        return equations.iloc[np.argmax(equations['score'])]

def best_tex(equations=None):
    """Return the equation with the best score, in latex format
    By default this uses the last equation file.
    """
    if equations is None: equations = get_hof()
    if isinstance(equations, list):
        return [sympy.latex(best_row(eq)['sympy_format'].simplify()) for eq in equations]
    else:
        return sympy.latex(best_row(equations)['sympy_format'].simplify())

def best(equations=None):
    """Return the equation with the best score, in sympy format.
    By default this uses the last equation file.
    """
    if equations is None: equations = get_hof()
    if isinstance(equations, list):
        return [best_row(eq)['sympy_format'].simplify() for eq in equations]
    else:
        return best_row(equations)['sympy_format'].simplify()

def best_callable(equations=None):
    """Return the equation with the best score, in callable format.
    By default this uses the last equation file.
    """
    if equations is None: equations = get_hof()
    if isinstance(equations, list):
        return [best_row(eq)['lambda_format'] for eq in equations]
    else:
        return best_row(equations)['lambda_format']

def _escape_filename(filename):
    """Turns a file into a string representation with correctly escaped backslashes"""
    repr = str(filename)
    repr = repr.replace('\\', '\\\\')
    return repr

# https://gist.github.com/garrettdreyfus/8153571
def _yesno(question):
    """Simple Yes/No Function."""
    prompt = f'{question} (y/n): '
    ans = input(prompt).strip().lower()
    if ans not in ['y', 'n']:
        print(f'{ans} is invalid, please try again...')
        return _yesno(question)
    if ans == 'y':
        return True
    return False