File size: 10,823 Bytes
2571f24 | 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 | import sys
import collections
from ShapeID.DiffEqs.solvers import FixedGridODESolver
from ShapeID.DiffEqs.misc import _scaled_dot_product, _has_converged
import ShapeID.DiffEqs.rk_common
_BASHFORTH_COEFFICIENTS = [
[], # order 0
[11],
[3, -1],
[23, -16, 5],
[55, -59, 37, -9],
[1901, -2774, 2616, -1274, 251],
[4277, -7923, 9982, -7298, 2877, -475],
[198721, -447288, 705549, -688256, 407139, -134472, 19087],
[434241, -1152169, 2183877, -2664477, 2102243, -1041723, 295767, -36799],
[14097247, -43125206, 95476786, -139855262, 137968480, -91172642, 38833486, -9664106, 1070017],
[30277247, -104995189, 265932680, -454661776, 538363838, -444772162, 252618224, -94307320, 20884811, -2082753],
[
2132509567, -8271795124, 23591063805, -46113029016, 63716378958, -63176201472, 44857168434, -22329634920,
7417904451, -1479574348, 134211265
],
[
4527766399, -19433810163, 61633227185, -135579356757, 214139355366, -247741639374, 211103573298, -131365867290,
58189107627, -17410248271, 3158642445, -262747265
],
[
13064406523627, -61497552797274, 214696591002612, -524924579905150, 932884546055895, -1233589244941764,
1226443086129408, -915883387152444, 507140369728425, -202322913738370, 55060974662412, -9160551085734,
703604254357
],
[
27511554976875, -140970750679621, 537247052515662, -1445313351681906, 2854429571790805, -4246767353305755,
4825671323488452, -4204551925534524, 2793869602879077, -1393306307155755, 505586141196430, -126174972681906,
19382853593787, -1382741929621
],
[
173233498598849, -960122866404112, 3966421670215481, -11643637530577472, 25298910337081429, -41825269932507728,
53471026659940509, -53246738660646912, 41280216336284259, -24704503655607728, 11205849753515179,
-3728807256577472, 859236476684231, -122594813904112, 8164168737599
],
[
362555126427073, -2161567671248849, 9622096909515337, -30607373860520569, 72558117072259733,
-131963191940828581, 187463140112902893, -210020588912321949, 186087544263596643, -129930094104237331,
70724351582843483, -29417910911251819, 9038571752734087, -1934443196892599, 257650275915823, -16088129229375
],
[
192996103681340479, -1231887339593444974, 5878428128276811750, -20141834622844109630, 51733880057282977010,
-102651404730855807942, 160414858999474733422, -199694296833704562550, 199061418623907202560,
-158848144481581407370, 100878076849144434322, -50353311405771659322, 19338911944324897550,
-5518639984393844930, 1102560345141059610, -137692773163513234, 8092989203533249
],
[
401972381695456831, -2735437642844079789, 13930159965811142228, -51150187791975812900, 141500575026572531760,
-304188128232928718008, 518600355541383671092, -710171024091234303204, 786600875277595877750,
-706174326992944287370, 512538584122114046748, -298477260353977522892, 137563142659866897224,
-49070094880794267600, 13071639236569712860, -2448689255584545196, 287848942064256339, -15980174332775873
],
[
333374427829017307697, -2409687649238345289684, 13044139139831833251471, -51099831122607588046344,
151474888613495715415020, -350702929608291455167896, 647758157491921902292692, -967713746544629658690408,
1179078743786280451953222, -1176161829956768365219840, 960377035444205950813626, -639182123082298748001432,
343690461612471516746028, -147118738993288163742312, 48988597853073465932820, -12236035290567356418552,
2157574942881818312049, -239560589366324764716, 12600467236042756559
],
[
691668239157222107697, -5292843584961252933125, 30349492858024727686755, -126346544855927856134295,
399537307669842150996468, -991168450545135070835076, 1971629028083798845750380, -3191065388846318679544380,
4241614331208149947151790, -4654326468801478894406214, 4222756879776354065593786, -3161821089800186539248210,
1943018818982002395655620, -970350191086531368649620, 387739787034699092364924, -121059601023985433003532,
28462032496476316665705, -4740335757093710713245, 498669220956647866875, -24919383499187492303
],
]
_MOULTON_COEFFICIENTS = [
[], # order 0
[1],
[1, 1],
[5, 8, -1],
[9, 19, -5, 1],
[251, 646, -264, 106, -19],
[475, 1427, -798, 482, -173, 27],
[19087, 65112, -46461, 37504, -20211, 6312, -863],
[36799, 139849, -121797, 123133, -88547, 41499, -11351, 1375],
[1070017, 4467094, -4604594, 5595358, -5033120, 3146338, -1291214, 312874, -33953],
[2082753, 9449717, -11271304, 16002320, -17283646, 13510082, -7394032, 2687864, -583435, 57281],
[
134211265, 656185652, -890175549, 1446205080, -1823311566, 1710774528, -1170597042, 567450984, -184776195,
36284876, -3250433
],
[
262747265, 1374799219, -2092490673, 3828828885, -5519460582, 6043521486, -4963166514, 3007739418, -1305971115,
384709327, -68928781, 5675265
],
[
703604254357, 3917551216986, -6616420957428, 13465774256510, -21847538039895, 27345870698436, -26204344465152,
19058185652796, -10344711794985, 4063327863170, -1092096992268, 179842822566, -13695779093
],
[
1382741929621, 8153167962181, -15141235084110, 33928990133618, -61188680131285, 86180228689563, -94393338653892,
80101021029180, -52177910882661, 25620259777835, -9181635605134, 2268078814386, -345457086395, 24466579093
],
[
8164168737599, 50770967534864, -102885148956217, 251724894607936, -499547203754837, 781911618071632,
-963605400824733, 934600833490944, -710312834197347, 418551804601264, -187504936597931, 61759426692544,
-14110480969927, 1998759236336, -132282840127
],
[
16088129229375, 105145058757073, -230992163723849, 612744541065337, -1326978663058069, 2285168598349733,
-3129453071993581, 3414941728852893, -2966365730265699, 2039345879546643, -1096355235402331, 451403108933483,
-137515713789319, 29219384284087, -3867689367599, 240208245823
],
[
8092989203533249, 55415287221275246, -131240807912923110, 375195469874202430, -880520318434977010,
1654462865819232198, -2492570347928318318, 3022404969160106870, -2953729295811279360, 2320851086013919370,
-1455690451266780818, 719242466216944698, -273894214307914510, 77597639915764930, -15407325991235610,
1913813460537746, -111956703448001
],
[
15980174332775873, 114329243705491117, -290470969929371220, 890337710266029860, -2250854333681641520,
4582441343348851896, -7532171919277411636, 10047287575124288740, -10910555637627652470, 9644799218032932490,
-6913858539337636636, 3985516155854664396, -1821304040326216520, 645008976643217360, -170761422500096220,
31816981024600492, -3722582669836627, 205804074290625
],
[
12600467236042756559, 93965550344204933076, -255007751875033918095, 834286388106402145800,
-2260420115705863623660, 4956655592790542146968, -8827052559979384209108, 12845814402199484797800,
-15345231910046032448070, 15072781455122686545920, -12155867625610599812538, 8008520809622324571288,
-4269779992576330506540, 1814584564159445787240, -600505972582990474260, 149186846171741510136,
-26182538841925312881, 2895045518506940460, -151711881512390095
],
[
24919383499187492303, 193280569173472261637, -558160720115629395555, 1941395668950986461335,
-5612131802364455926260, 13187185898439270330756, -25293146116627869170796, 39878419226784442421820,
-51970649453670274135470, 56154678684618739939910, -50320851025594566473146, 37297227252822858381906,
-22726350407538133839300, 11268210124987992327060, -4474886658024166985340, 1389665263296211699212,
-325187970422032795497, 53935307402575440285, -5652892248087175675, 281550972898020815
],
]
_DIVISOR = [
None, 11, 2, 12, 24, 720, 1440, 60480, 120960, 3628800, 7257600, 479001600, 958003200, 2615348736000, 5230697472000,
31384184832000, 62768369664000, 32011868528640000, 64023737057280000, 51090942171709440000, 102181884343418880000
]
_MIN_ORDER = 4
_MAX_ORDER = 12
_MAX_ITERS = 4
class AdamsBashforthMoulton(FixedGridODESolver):
def __init__(
self, func, y0, rtol=1e-3, atol=1e-4, implicit=True, max_iters=_MAX_ITERS, max_order=_MAX_ORDER, **kwargs
):
super(AdamsBashforthMoulton, self).__init__(func, y0, **kwargs)
self.rtol = rtol
self.atol = atol
self.implicit = implicit
self.max_iters = max_iters
self.max_order = int(min(max_order, _MAX_ORDER))
self.prev_f = collections.deque(maxlen=self.max_order - 1)
self.prev_t = None
def _update_history(self, t, f):
if self.prev_t is None or self.prev_t != t:
self.prev_f.appendleft(f)
self.prev_t = t
def step_func(self, func, t, dt, y):
self._update_history(t, func(t, y))
order = min(len(self.prev_f), self.max_order - 1)
if order < _MIN_ORDER - 1:
# Compute using RK4.
dy = rk_common.rk4_alt_step_func(func, t, dt, y, k1=self.prev_f[0])
return dy
else:
# Adams-Bashforth predictor.
bashforth_coeffs = _BASHFORTH_COEFFICIENTS[order]
ab_div = _DIVISOR[order]
dy = tuple(dt * _scaled_dot_product(1 / ab_div, bashforth_coeffs, f_) for f_ in zip(*self.prev_f))
# Adams-Moulton corrector.
if self.implicit:
moulton_coeffs = _MOULTON_COEFFICIENTS[order + 1]
am_div = _DIVISOR[order + 1]
delta = tuple(dt * _scaled_dot_product(1 / am_div, moulton_coeffs[1:], f_) for f_ in zip(*self.prev_f))
converged = False
for _ in range(self.max_iters):
dy_old = dy
f = func(t + dt, tuple(y_ + dy_ for y_, dy_ in zip(y, dy)))
dy = tuple(dt * (moulton_coeffs[0] / am_div) * f_ + delta_ for f_, delta_ in zip(f, delta))
converged = _has_converged(dy_old, dy, self.rtol, self.atol)
if converged:
break
if not converged:
print('Warning: Functional iteration did not converge. Solution may be incorrect.', file=sys.stderr)
self.prev_f.pop()
self._update_history(t, f)
return dy
@property
def order(self):
return 4
class AdamsBashforth(AdamsBashforthMoulton):
def __init__(self, func, y0, **kwargs):
super(AdamsBashforth, self).__init__(func, y0, implicit=False, **kwargs)
|