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@denis-bz denis-bz/lpgen34.py
Last active Oct 8, 2019

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from Denis-iMac ~bz/py/opt/lp/lpgen Tue 2019-10-08 Oct 10:50z
#!/usr/bin/env python
""" lpgen34.py LP testcase generator
d=3: 3n^2 x n^3, 3 1s in each column
n=55: A 9075 x 166375, 499125 nnz, glpsol simplex 100 minutes
d=4: 4n^3 x n^4, 4 1s in each column, n in each row
n=16: A 2^14 x 2^16, 2^18 nnz, glpsol simplex 10 hours
"""
# keywords: linear programming, test case, generator, Latin-square
# https://stackoverflow.com/questions/57936789/many-vertex-test-problems-for-the-simplex-method
# https://math.stackexchange.com/questions/3370934/3d-permutation-matrices -- 4d too
from __future__ import division, print_function
import numpy as np
from scipy import sparse as sp
__version__ = "2019.10.08" # 8 oct
__author_email__ = "denis-bz-py t-online.de"
#...............................................................................
def lpgen34( n, d=3, cint=9, seed=0, verbose=2 ):
""" -> A b c LP test: d=3: A 3n^2 x n^3, 3 1s in each column sparse csr
b = 1
c randint 0 .. cint / uniform
"""
# csr ? csc most efficient for sksparse.cholmod
Agen = { 2: A2, 3: A3, 4: A4 }[d]
A = Agen( n )
nr, nc = A.shape
b = np.ones( nr )
random = seed if isinstance(seed, np.random.RandomState) \
else np.random.RandomState( seed=seed )
if cint > 0:
c = random.randint( 0, cint+1, size=nc ).astype(float) # 0 .. cint inclusive
else:
c = random.uniform( size=nc )
if verbose:
print( "\nlpgen34: n %d d %d A %s %s %d non0 seed %d c %s ..." % (
n, d, A.shape, type(A).__name__, A.nnz, seed, c[:10] ))
if verbose >= 2:
for j in range( 0, nr, nr // d ):
print( A[j:j+5] .A ) # caller's printoptions
print( " ..." )
return A, b, c
def A2( n ):
""" -> A 2n x n^2, 2 1s in each column sparse csr """
# ~ lpgen_2d 2014
square = np.arange( n**2 ).reshape( n, n )
line = np.arange( n )
def row01( *ix ):
row = sp.lil_matrix( (1, n**2) )
row[0, square[ix]] = 1
return row.tocsr()
return sp.vstack( # csr* -> csr, else coo
# i j
[row01( i, line ) for i in line] +
[row01( line, j ) for j in line]
)
def A3( n ):
""" -> A 3n^2 x n^3, 3 1s in each column sparse csr """
cube = np.arange( n**3 ).reshape( n, n, n )
line = np.arange( n )
pairs = np.array([ [i, j] for i in line for j in line ])
def row01( *ix ):
row = sp.lil_matrix( (1, n**3) )
row[0, cube[ix]] = 1
return row.tocsr()
return sp.vstack(
# i j k
[row01( i, j, line ) for i, j in pairs] +
[row01( i, line, k ) for i, k in pairs] +
[row01( line, j, k ) for j, k in pairs]
)
def A4( n ):
""" -> A 4n^3 x n^4, 4 1s in each column sparse csr """
cube = np.arange( n**4 ).reshape( n, n, n, n )
line = np.arange( n )
triples = np.array([ [i, j, k] for i in line for j in line for k in line ])
def row01( *ix ):
row = sp.lil_matrix( (1, n**4) )
row[0, cube[ix]] = 1
return row.tocsr()
return sp.vstack(
# i j k, l
[row01( i, j, k, line ) for i, j, k in triples] +
[row01( i, j, line, l ) for i, j, l in triples] +
[row01( i, line, k, l ) for i, k, l in triples] +
[row01( line, j, k, l ) for j, k, l in triples]
)
#...............................................................................
if __name__ == "__main__":
import sys
np.set_printoptions( threshold=20, edgeitems=32, linewidth=150,
formatter = dict( float = lambda x: "%.2g" % x )) # float arrays %.2g
d = 4
n = 16
cint = 9 # c randint 0 .. cint+1 / uniform
bmul = 1
save = "" # > save.lp
seed = 0
# to change these params, run this.py a=1 b=None c='expr' ...
# in sh or ipython --
for arg in sys.argv[1:]:
exec( arg )
A, b, c = lpgen34( n, d=d, cint=cint, seed=seed )
if save:
import glp # numpy/scipy arrays <-> glpk
b *= bmul
lp = glp.LP( A=A, b=b, blo=b, c=c, problemname=save ) # Ax = b, 0 <= x
glp.save_lp( save + ".lp.gz", lp ) # .glp / .lp cplex / .mod gmpl / .mps
GLPSOL: GLPK LP/MIP Solver, v4.65
Parameter(s) specified in the command line:
--simplex --glp out/d4/n16/n16-d4.glp.gz --log n16-d4-simplex.glpsollog -w
n16-d4-simplex.sol.gz
Reading problem data from 'out/d4/n16/n16-d4.glp.gz'...
Problem: tmp
16384 rows, 65536 columns, 262144 non-zeros
337570 lines were read
GLPK Simplex Optimizer, v4.65
16384 rows, 65536 columns, 262144 non-zeros
Preprocessing...
16384 rows, 65536 columns, 262144 non-zeros
Scaling...
A: min|aij| = 1.000e+00 max|aij| = 1.000e+00 ratio = 1.000e+00
Problem data seem to be well scaled
Constructing initial basis...
Size of triangular part is 14911
0: obj = 2.545500000e+04 inf = 2.206e+04 (1351)
Perturbing LP to avoid stalling [1095]...
4052: obj = 2.421639806e+04 inf = 1.803e+04 (1269) 30
6826: obj = 2.370167224e+04 inf = 1.680e+04 (1253) 25
9185: obj = 2.347877243e+04 inf = 1.606e+04 (1234) 22
...
115427: obj = 1.844185458e+04 inf = 1.023e-01 (2) 1
115528: obj = 1.844263480e+04 inf = 2.827e-02 (1) 1
115568: obj = 1.844248525e+04 inf = 3.512e-10 (0)
*115631: obj = 1.843436001e+04 inf = 4.034e-10 (25387) 1
*115732: obj = 1.841254258e+04 inf = 3.672e-10 (25397) 1
*115834: obj = 1.839785970e+04 inf = 4.376e-10 (25162) 1
...
*424999: obj = 4.681508048e+03 inf = 2.874e-10 (1095) 1
*425101: obj = 4.681503844e+03 inf = 4.419e-10 (424) 1
*425204: obj = 4.681501026e+03 inf = 3.373e-10 (682) 1
Removing LP perturbation [425306]...
*425306: obj = 4.681500010e+03 inf = 3.516e-10 (0)
OPTIMAL LP SOLUTION FOUND
Time used: 37264.3 secs
Memory used: 185.0 Mb -- `top` phase 2: 320 Mb
Writing basic solution to 'n16-d4-simplex.sol.gz'...
81929 lines were written
37264.73 real 37233.17 user 24.64 sys
This file has been truncated, but you can view the full file.
\* Problem: n16-d4 *\
Minimize
obj: + 5 x_1 + 3 x_3 + 3 x_4 + 7 x_5 + 9 x_6 + 3 x_7 + 5 x_8 + 2 x_9
+ 4 x_10 + 7 x_11 + 6 x_12 + 8 x_13 + 8 x_14 + x_15 + 6 x_16 + 7 x_17
+ 7 x_18 + 8 x_19 + x_20 + 5 x_21 + 9 x_22 + 8 x_23 + 9 x_24 + 4 x_25
+ 3 x_26 + 3 x_28 + 5 x_29 + 2 x_31 + 3 x_32 + 8 x_33 + x_34 + 3 x_35
+ 3 x_36 + 3 x_37 + 7 x_38 + x_40 + 9 x_41 + 9 x_42 + 4 x_44 + 7 x_45
+ 3 x_46 + 2 x_47 + 7 x_48 + 2 x_49 + 4 x_52 + 5 x_53 + 5 x_54 + 6 x_55
+ 8 x_56 + 4 x_57 + x_58 + 4 x_59 + 9 x_60 + 8 x_61 + x_62 + x_63
+ 7 x_64 + 9 x_65 + 9 x_66 + 3 x_67 + 6 x_68 + 7 x_69 + 2 x_70 + 3 x_72
+ 5 x_73 + 9 x_74 + 4 x_75 + 4 x_76 + 6 x_77 + 4 x_78 + 4 x_79 + 3 x_80
+ 4 x_81 + 4 x_82 + 8 x_83 + 4 x_84 + 3 x_85 + 7 x_86 + 5 x_87 + 5 x_88
+ x_90 + 5 x_91 + 9 x_92 + 3 x_93 + 5 x_95 + x_97 + 2 x_98 + 4 x_99
+ 2 x_100 + 3 x_102 + 2 x_103 + 7 x_105 + 5 x_106 + 9 x_107 + 2 x_109
+ 7 x_110 + 2 x_111 + 9 x_112 + 2 x_113 + 3 x_114 + 3 x_115 + 2 x_116
+ 3 x_117 + 4 x_118 + x_119 + 2 x_120 + 9 x_121 + x_122 + 4 x_123
+ 6 x_124 + 8 x_125 + 2 x_126 + 3 x_127 + 6 x_130 + 6 x_132 + 3 x_133
+ 3 x_134 + 8 x_135 + 8 x_136 + 8 x_137 + 2 x_138 + 3 x_139 + 2 x_140
+ 8 x_142 + 8 x_143 + 3 x_144 + 8 x_145 + 2 x_146 + 8 x_147 + 4 x_148
+ 3 x_149 + 4 x_151 + 3 x_152 + 6 x_153 + 9 x_154 + 8 x_155 + 8 x_157
+ 5 x_158 + 9 x_159 + 9 x_161 + 6 x_162 + 5 x_163 + 3 x_164 + x_165
+ 8 x_166 + 4 x_168 + 9 x_169 + 6 x_170 + 5 x_171 + 7 x_172 + 8 x_173
+ 8 x_174 + 9 x_175 + 2 x_176 + 8 x_177 + 6 x_178 + 6 x_179 + 9 x_180
+ x_181 + 6 x_182 + 8 x_183 + 8 x_184 + 3 x_185 + 2 x_186 + 3 x_187
+ 6 x_188 + 3 x_189 + 6 x_190 + 5 x_191 + 7 x_192 + 8 x_194 + 4 x_195
+ 6 x_196 + 5 x_197 + 8 x_198 + 2 x_199 + 3 x_200 + 9 x_201 + 7 x_202
+ 5 x_203 + 3 x_204 + 4 x_205 + 5 x_206 + 3 x_207 + 3 x_208 + 7 x_209
+ 9 x_210 + 9 x_211 + 9 x_212 + 7 x_213 + 3 x_214 + 2 x_215 + 3 x_216
+ 9 x_217 + 7 x_218 + 7 x_219 + 5 x_220 + x_221 + 2 x_222 + 2 x_223
+ 8 x_224 + x_225 + 5 x_226 + 8 x_227 + 4 x_228 + 2 x_230 + 5 x_231
+ 5 x_232 + 8 x_234 + x_235 + x_236 + 3 x_238 + 8 x_239 + 8 x_240
+ 4 x_241 + 4 x_242 + 9 x_244 + 3 x_245 + 7 x_246 + 3 x_247 + 2 x_248
+ x_249 + x_250 + 2 x_251 + x_252 + 4 x_253 + 2 x_254 + 5 x_255
+ 5 x_256 + 5 x_257 + 2 x_258 + 5 x_259 + 7 x_260 + 7 x_261 + 6 x_262
+ x_263 + 6 x_264 + 7 x_265 + 2 x_266 + 3 x_267 + x_268 + 9 x_269
+ 5 x_270 + 9 x_271 + 9 x_272 + 2 x_273 + 9 x_275 + x_276 + 9 x_277
+ 6 x_279 + 4 x_281 + 8 x_282 + 4 x_283 + 3 x_284 + 3 x_285 + 8 x_286
+ 8 x_287 + 7 x_288 + 3 x_290 + 8 x_291 + 7 x_292 + 7 x_293 + x_294
+ 8 x_295 + 4 x_296 + 7 x_297 + 4 x_299 + 9 x_300 + 6 x_302 + 4 x_303
+ 2 x_304 + 4 x_305 + 6 x_306 + 3 x_307 + 3 x_308 + 7 x_309 + 8 x_310
+ 5 x_311 + 8 x_313 + 5 x_314 + 4 x_315 + 7 x_316 + 4 x_317 + x_318
+ 3 x_319 + 3 x_320 + 9 x_321 + 2 x_322 + 5 x_323 + 2 x_324 + 3 x_325
+ 5 x_326 + 7 x_327 + 2 x_328 + 7 x_329 + x_330 + 6 x_331 + 5 x_332
+ 3 x_335 + x_336 + 9 x_337 + 9 x_338 + 6 x_339 + 6 x_340 + 7 x_341
+ 8 x_342 + 8 x_343 + 7 x_344 + 8 x_346 + 6 x_347 + 8 x_348 + 9 x_349
+ 8 x_350 + 3 x_351 + 6 x_352 + x_353 + 7 x_354 + 4 x_355 + 9 x_356
+ 2 x_357 + 8 x_359 + 2 x_360 + 7 x_361 + 8 x_362 + 4 x_363 + 4 x_364
+ x_365 + 7 x_366 + 6 x_367 + 9 x_368 + 4 x_369 + x_370 + 5 x_371
+ 9 x_372 + 7 x_373 + x_374 + 3 x_375 + 5 x_376 + 7 x_377 + 3 x_378
+ 6 x_379 + 6 x_380 + 7 x_381 + 9 x_382 + x_383 + 9 x_384 + 6 x_385
+ 3 x_387 + 8 x_388 + 4 x_389 + x_390 + 4 x_391 + 5 x_392 + 3 x_394
+ x_395 + 4 x_396 + 4 x_397 + 4 x_398 + 8 x_401 + 4 x_402 + 6 x_403
+ 9 x_404 + 3 x_405 + 3 x_406 + 2 x_407 + x_408 + 2 x_409 + x_410
+ 3 x_411 + 4 x_412 + x_413 + x_414 + 7 x_416 + 8 x_417 + 4 x_418
+ 3 x_419 + 5 x_420 + 6 x_421 + 3 x_422 + 2 x_423 + 9 x_424 + 8 x_425
+ x_426 + 4 x_427 + 8 x_429 + 3 x_430 + 9 x_431 + 5 x_432 + 5 x_433
+ x_434 + 7 x_435 + 8 x_436 + 6 x_437 + 4 x_438 + 7 x_439 + 3 x_440
+ 5 x_441 + 3 x_442 + 6 x_443 + 4 x_444 + 7 x_445 + 3 x_446 + 5 x_448
+ 9 x_449 + 3 x_450 + 7 x_451 + 5 x_452 + 5 x_453 + 8 x_454 + 8 x_456
+ 3 x_457 + 6 x_458 + 9 x_459 + 3 x_460 + 2 x_461 + 7 x_462 + 3 x_464
+ 3 x_466 + 6 x_467 + x_468 + 9 x_469 + 2 x_470 + 9 x_471 + 4 x_472
+ 9 x_473 + x_474 + 3 x_475 + 2 x_476 + 4 x_477 + 9 x_478 + 7 x_479
+ 4 x_480 + 9 x_481 + 4 x_482 + x_483 + 2 x_484 + 7 x_485 + 2 x_486
+ 3 x_487 + 9 x_488 + 7 x_489 + 6 x_490 + 6 x_491 + 2 x_492 + 3 x_493
+ 6 x_494 + 8 x_496 + 7 x_498 + 6 x_499 + 5 x_500 + 9 x_501 + 6 x_502
+ 5 x_503 + 2 x_504 + 7 x_505 + x_506 + 9 x_507 + 2 x_508 + 2 x_509
+ 5 x_510 + 6 x_511 + 4 x_512 + 2 x_513 + 2 x_514 + x_515 + 9 x_517
+ 2 x_519 + 8 x_520 + 3 x_521 + 8 x_523 + 8 x_524 + x_525 + 5 x_527
+ 8 x_528 + 2 x_529 + 3 x_530 + 5 x_531 + 3 x_532 + 8 x_533 + 6 x_534
+ 4 x_535 + 6 x_536 + 3 x_537 + 6 x_538 + 2 x_539 + 6 x_540 + 5 x_541
+ 5 x_542 + 9 x_543 + 4 x_544 + 6 x_545 + 5 x_546 + x_547 + 3 x_548
+ 3 x_549 + 8 x_550 + 9 x_551 + 5 x_552 + 5 x_553 + 6 x_554 + 9 x_556
+ 7 x_557 + 5 x_558 + x_559 + 5 x_560 + 6 x_561 + 6 x_562 + 8 x_563
+ 7 x_564 + 5 x_565 + 3 x_566 + 2 x_567 + 9 x_568 + 9 x_569 + 3 x_570
+ 2 x_571 + 5 x_572 + 4 x_573 + x_574 + 5 x_575 + 8 x_576 + 3 x_577
+ 5 x_578 + 8 x_579 + 4 x_580 + x_581 + 7 x_582 + 8 x_583 + x_584
+ 2 x_585 + x_586 + x_587 + 7 x_588 + 5 x_589 + 4 x_591 + x_592 + x_593
+ 6 x_594 + 6 x_595 + 2 x_597 + 3 x_598 + 7 x_599 + 9 x_600 + 2 x_601
+ 4 x_602 + 9 x_603 + 6 x_605 + 9 x_606 + 2 x_607 + 4 x_608 + 7 x_609
+ 3 x_610 + 5 x_612 + 4 x_613 + 2 x_615 + 3 x_616 + x_617 + 7 x_618
+ x_619 + 3 x_620 + 4 x_621 + x_622 + 7 x_623 + 4 x_624 + 2 x_626
+ 7 x_627 + 4 x_628 + 2 x_630 + 6 x_631 + 9 x_632 + 2 x_633 + 4 x_634
+ 9 x_635 + 9 x_636 + 5 x_637 + 4 x_638 + 4 x_639 + 9 x_640 + 8 x_641
+ x_642 + 5 x_643 + 7 x_644 + x_646 + 3 x_647 + 9 x_648 + 2 x_649
+ 8 x_650 + 2 x_651 + 4 x_652 + 8 x_653 + 2 x_654 + 9 x_655 + 8 x_656
+ 7 x_657 + 8 x_658 + 2 x_659 + 3 x_660 + 3 x_661 + 6 x_662 + 3 x_664
+ 6 x_665 + 3 x_666 + 9 x_667 + 6 x_668 + 3 x_669 + 2 x_670 + 2 x_671
+ 2 x_672 + 6 x_673 + 4 x_674 + 6 x_675 + 4 x_677 + 9 x_678 + 2 x_679
+ x_680 + 6 x_681 + x_682 + 7 x_683 + 5 x_684 + 6 x_685 + x_686
+ 6 x_687 + 6 x_688 + 6 x_689 + 6 x_690 + 2 x_691 + 5 x_692 + 2 x_693
+ 2 x_694 + 3 x_695 + 2 x_696 + 9 x_697 + 3 x_698 + 8 x_699 + 5 x_700
+ 4 x_701 + 5 x_702 + x_703 + 5 x_704 + 8 x_705 + 2 x_706 + 9 x_707
+ 9 x_708 + 5 x_709 + 6 x_710 + 4 x_711 + 8 x_713 + 5 x_714 + 5 x_715
+ 5 x_716 + x_717 + 7 x_723 + 6 x_724 + 3 x_725 + 5 x_726 + 4 x_727
+ 3 x_728 + 4 x_729 + 5 x_730 + x_731 + 3 x_732 + 6 x_733 + 7 x_734
+ 4 x_735 + 7 x_738 + 3 x_739 + 3 x_740 + 9 x_743 + 4 x_744 + 4 x_745
+ 5 x_746 + 8 x_747 + 8 x_748 + x_750 + 5 x_751 + 9 x_752 + 9 x_753
+ 6 x_754 + x_755 + 4 x_756 + 4 x_758 + 7 x_759 + 7 x_760 + 7 x_761
+ 6 x_762 + 2 x_763 + 6 x_764 + 2 x_766 + 7 x_767 + 7 x_768 + 2 x_769
+ 6 x_770 + x_771 + 3 x_772 + 7 x_773 + 5 x_775 + 4 x_776 + 5 x_777
+ 5 x_778 + 3 x_779 + 8 x_780 + x_782 + 5 x_783 + 4 x_784 + x_785
+ 5 x_786 + 6 x_788 + 8 x_789 + 8 x_790 + 6 x_791 + 3 x_792 + 4 x_793
+ 4 x_794 + 3 x_795 + 6 x_796 + 5 x_797 + 9 x_798 + 8 x_799 + x_800
+ 3 x_801 + 8 x_802 + x_803 + 5 x_804 + 8 x_805 + 3 x_807 + 7 x_808
+ x_809 + 7 x_810 + 8 x_811 + 7 x_813 + 5 x_814 + 9 x_815 + 9 x_816
+ 6 x_817 + 8 x_818 + 7 x_819 + 5 x_820 + 9 x_821 + x_822 + 5 x_825
+ 6 x_826 + 3 x_827 + 6 x_828 + x_829 + 7 x_830 + 7 x_831 + 7 x_833
+ 6 x_834 + 4 x_836 + 2 x_837 + 7 x_838 + 5 x_839 + 2 x_840 + 8 x_841
+ 5 x_842 + 6 x_843 + 6 x_844 + 4 x_845 + x_846 + 5 x_847 + 4 x_848
+ 5 x_849 + 5 x_850 + 6 x_851 + 3 x_852 + 8 x_853 + x_854 + 4 x_855
+ 2 x_856 + 9 x_857 + 7 x_858 + 4 x_859 + x_860 + 8 x_861 + 2 x_862
+ 3 x_863 + 3 x_864 + 4 x_865 + x_866 + 6 x_867 + 2 x_868 + 5 x_869
+ 4 x_870 + 9 x_871 + x_872 + 5 x_873 + 9 x_874 + 4 x_875 + 5 x_876
+ 7 x_877 + 4 x_878 + 4 x_879 + 2 x_880 + 2 x_881 + x_882 + 3 x_883
+ x_885 + 9 x_886 + x_887 + 6 x_888 + 9 x_889 + 8 x_890 + 6 x_891
+ 3 x_892 + 7 x_894 + 3 x_895 + 2 x_896 + 5 x_897 + 9 x_898 + 7 x_899
+ 3 x_900 + 4 x_901 + 7 x_902 + 6 x_903 + 7 x_904 + 3 x_905 + 6 x_906
+ 9 x_907 + 3 x_908 + 7 x_909 + x_910 + 3 x_911 + 7 x_912 + 8 x_913
+ 8 x_914 + 4 x_915 + 5 x_916 + 3 x_917 + 6 x_918 + 9 x_919 + 6 x_920
+ 2 x_921 + 9 x_922 + 3 x_923 + 5 x_924 + 7 x_925 + 9 x_926 + 7 x_928
+ x_929 + 2 x_930 + 5 x_931 + 5 x_933 + 8 x_934 + 9 x_935 + 8 x_936
+ 2 x_937 + 5 x_938 + 3 x_939 + x_940 + 7 x_941 + 3 x_942 + 8 x_943
+ 5 x_944 + 5 x_945 + x_946 + 9 x_947 + 7 x_948 + 2 x_949 + x_950
+ x_952 + x_954 + x_955 + 6 x_956 + 8 x_957 + 8 x_958 + 3 x_959
+ 2 x_960 + 7 x_962 + 4 x_963 + 6 x_964 + 5 x_966 + 3 x_967 + 3 x_968
+ 9 x_969 + 4 x_970 + 9 x_971 + 6 x_973 + 5 x_974 + 3 x_975 + x_978
+ 2 x_979 + 2 x_981 + 2 x_982 + 9 x_983 + 6 x_984 + 7 x_985 + 8 x_986
+ 9 x_987 + 8 x_988 + 2 x_989 + 4 x_990 + 7 x_991 + 7 x_992 + 5 x_993
+ 7 x_994 + 2 x_995 + 4 x_996 + x_997 + x_998 + x_999 + 7 x_1000
+ 9 x_1001 + 9 x_1003 + 2 x_1005 + x_1006 + 4 x_1007 + 6 x_1008
+ 6 x_1010 + 6 x_1011 + 2 x_1012 + 8 x_1013 + 6 x_1014 + 6 x_1015
+ 5 x_1016 + 2 x_1017 + 5 x_1018 + 3 x_1020 + 9 x_1021 + 9 x_1022
+ 7 x_1023 + 4 x_1025 + x_1026 + 3 x_1027 + 5 x_1028 + 7 x_1029
+ 6 x_1030 + 2 x_1031 + 7 x_1032 + 3 x_1033 + 4 x_1034 + 9 x_1035
+ 7 x_1036 + x_1039 + 8 x_1040 + 3 x_1041 + 5 x_1042 + x_1044 + x_1045
+ 3 x_1046 + 7 x_1047 + 9 x_1048 + 3 x_1049 + 7 x_1050 + 2 x_1052
+ 4 x_1053 + 4 x_1054 + 6 x_1055 + x_1057 + 7 x_1058 + 6 x_1059
+ 5 x_1060 + 5 x_1061 + 7 x_1062 + 3 x_1063 + 6 x_1064 + 8 x_1065
+ 8 x_1066 + 2 x_1067 + x_1068 + 8 x_1070 + 7 x_1071 + 7 x_1072
+ 4 x_1074 + 8 x_1075 + 4 x_1077 + 5 x_1078 + 7 x_1079 + 2 x_1080
+ 4 x_1081 + 9 x_1082 + 7 x_1083 + 5 x_1084 + 4 x_1086 + 9 x_1087
+ 4 x_1088 + 2 x_1090 + 5 x_1091 + 5 x_1092 + 3 x_1093 + x_1096
+ 9 x_1097 + 9 x_1098 + 2 x_1099 + x_1100 + x_1102 + 6 x_1103
+ 3 x_1104 + 4 x_1105 + 3 x_1106 + 6 x_1107 + 4 x_1108 + 2 x_1109
+ 3 x_1110 + 6 x_1111 + 3 x_1112 + 3 x_1113 + 8 x_1114 + x_1115
+ 3 x_1116 + 3 x_1117 + x_1118 + 5 x_1119 + 3 x_1120 + 6 x_1121
+ 4 x_1122 + 8 x_1123 + 5 x_1124 + 7 x_1125 + x_1126 + 8 x_1127
+ 2 x_1128 + 4 x_1131 + 2 x_1132 + x_1133 + 2 x_1134 + 2 x_1135
+ 3 x_1136 + 4 x_1137 + 7 x_1138 + 5 x_1139 + x_1140 + 3 x_1141
+ x_1142 + x_1144 + 4 x_1145 + 2 x_1147 + x_1148 + 3 x_1149 + x_1150
+ 4 x_1151 + 7 x_1152 + 5 x_1153 + 6 x_1154 + 9 x_1155 + 2 x_1156
+ 5 x_1157 + 2 x_1158 + 2 x_1159 + x_1160 + 3 x_1161 + 8 x_1162
+ 3 x_1163 + 7 x_1165 + 3 x_1166 + 8 x_1167 + 2 x_1168 + 4 x_1169
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