将两个约束圆形帽安装到数据上
问题描述 投票：0回答：1
我正在尝试对 python 中的一组数据点进行相当复杂的拟合，经过大量谷歌搜索和阅读后，我仍然不知道从哪里开始。 数据点是
datagrey = array([[-260.02020661, 1.98456848],
[-257.27847339, -1.71995935],
[-253.44004688, -4.89526893],
[-249.60162037, -8.59979676],
[-243.56980729, -12.3043246 ],
[-240.82807406, -15.47963417],
[-236.44130091, -17.59650722],
[-231.50618111, -20.7718168 ],
[-226.57106132, -24.47634463],
[-219.99090158, -28.18087247],
[-214.50743514, -30.82696378],
[-207.37892877, -34.00227335],
[-204.0888489 , -36.1191464 ],
[-197.50868917, -39.82367424],
[-193.67026266, -41.41132903],
[-187.09010293, -44.05742034],
[-178.86490327, -46.17429339],
[-171.18805025, -48.29116644],
[-165.15623716, -49.87882122],
[-160.22111737, -52.52491253],
[-153.64095764, -54.64178558],
[-148.70583784, -56.22944037],
[-142.12567811, -58.87553168],
[-138.83559824, -60.46318647],
[-132.80378516, -62.05084126],
[-128.96535865, -63.10927778],
[-124.57858549, -65.22615083],
[-120.19181234, -67.34302388],
[-115.80503919, -68.93067867],
[-108.67653281, -71.04755172],
[-103.19306637, -73.16442476],
[ -97.16125328, -74.75207955],
[ -88.38770698, -78.45660739],
[ -81.80754725, -79.51504391],
[ -74.13069423, -81.1026987 ],
[ -67.5505345 , -82.69035349],
[ -61.51872141, -83.74879001],
[ -53.29352175, -85.3364448 ],
[ -47.8100553 , -86.39488132],
[ -42.87493551, -86.92409958],
[ -36.84312242, -87.45331785],
[ -30.81130933, -87.45331785],
[ -22.03776303, -87.45331785],
[ -18.74768316, -87.45331785],
[ -13.26421672, -87.45331785],
[ -7.23240363, -86.92409958],
[ -0.6522439 , -86.92409958],
[ 4.28287589, -86.39488132],
[ 10.31468898, -86.39488132],
[ 18.53988864, -85.86566306],
[ 22.37831515, -85.86566306],
[ 28.95847488, -85.3364448 ],
[ 37.18367455, -84.80722654],
[ 42.11879434, -83.74879001],
[ 49.24730072, -82.69035349],
[ 54.73076716, -81.1026987 ],
[ 60.76258025, -78.98582565],
[ 66.79439333, -76.8689526 ],
[ 70.0844732 , -74.75207955],
[ 75.019593 , -72.10598824],
[ 81.59975273, -69.45989693],
[ 89.82495239, -65.22615083],
[ 95.85676548, -63.10927778],
[ 99.69519199, -61.52162299],
[ 102.98527185, -60.99240473],
[ 106.82369836, -59.93396821],
[ 112.3071648 , -58.34631342],
[ 115.04889802, -57.81709516],
[ 119.43567118, -56.22944037],
[ 123.27409769, -55.17100385],
[ 131.49929735, -51.99569427],
[ 136.43441715, -50.40803949],
[ 147.40135003, -46.70351165],
[ 142.46623023, -48.29116644],
[ 150.6914299 , -45.11585686],
[ 156.72324298, -40.88211076],
[ 165.49678929, -37.17758293],
[ 170.98025573, -34.53149162],
[ 175.91537553, -31.8854003 ],
[ 181.39884197, -30.29774552],
[ 184.14057519, -28.71009073],
[ 187.9790017 , -27.12243594],
[ 192.36577486, -25.00556289],
[ 197.30089465, -21.83025332],
[ 203.88105439, -19.18416201],
[ 210.46121412, -17.06728896],
[ 213.75129398, -15.47963417],
[ 220.33145371, -14.42119765],
[ 228.00830673, -11.24588807],
[ 232.94342653, -7.54136024],
[ 237.87854633, -5.95370545],
[ 246.10374599, -3.8368324 ],
[ 249.9421725 , -2.24917761],
[ 253.23225236, -1.19074109],
[ 255.97398558, 0.3969137 ]])
datagreen = array([[-263.31028648, -1.19074109],
[-264.95532641, -9.12901502],
[-264.95532641, -14.95041591],
[-266.0520197 , -20.7718168 ],
[-266.60036634, -26.59321768],
[-267.69705963, -31.8854003 ],
[-268.24540627, -37.70680119],
[-268.79375292, -44.05742034],
[-268.79375292, -49.87882122],
[-269.89044621, -54.11256732],
[-269.89044621, -60.99240473],
[-269.89044621, -66.81380562],
[-270.43879285, -73.16442476],
[-270.9871395 , -80.04426217],
[-270.9871395 , -83.74879001],
[-271.53548614, -89.5701909 ],
[-271.53548614, -95.39159178],
[-271.53548614, -100.6837744 ],
[-270.9871395 , -107.03439355],
[-270.43879285, -113.3850127 ],
[-268.79375292, -120.26485011],
[-268.24540627, -124.49859621],
[-267.69705963, -130.31999709],
[-266.60036634, -138.25827103],
[-264.95532641, -144.07967191],
[-263.85863312, -149.9010728 ],
[-262.76193983, -154.66403716],
[-261.66524654, -160.48543805],
[-260.02020661, -165.77762067],
[-260.56855326, -172.65745808],
[-257.82682003, -178.47885896],
[-255.08508681, -185.88791464],
[-252.34335359, -191.18009726],
[-248.50492708, -197.00149815],
[-245.76319386, -201.76446251],
[-243.02146064, -205.9982086 ],
[-239.73138078, -211.29039123],
[-236.44130091, -214.99491906],
[-232.6028744 , -220.28710169],
[-228.76444789, -223.46241126],
[-225.47436803, -227.1669391 ],
[-222.18428816, -230.34224867],
[-219.99090158, -232.98833998],
[-215.05578179, -237.75130434],
[-212.31404857, -241.98505044],
[-208.47562206, -247.27723306],
[-206.28223548, -251.51097916],
[-202.44380897, -255.215507 ],
[-198.05703582, -259.4492531 ],
[-191.47687609, -264.21221746],
[-187.09010293, -266.85830877],
[-182.70332978, -269.50440008],
[-177.76820998, -273.20892792],
[-173.92978347, -277.44267402],
[-169.54301032, -281.67642011],
[-164.60789052, -284.85172969],
[-159.12442408, -290.14391231],
[-154.73765092, -292.26078536],
[-150.89922442, -294.37765841],
[-145.96410462, -297.02374972],
[-142.67402475, -299.14062277],
[-137.19055831, -302.84515061],
[-132.25543851, -305.49124192],
[-126.77197207, -307.60811497],
[-122.38519892, -311.3126428 ],
[-116.90173247, -313.95873412],
[-111.41826603, -316.07560716],
[-104.28975966, -319.780135 ],
[ -99.9029865 , -322.42622631],
[ -94.41952006, -324.54309936],
[ -88.93605362, -327.18919067],
[ -80.71085396, -329.30606372],
[ -75.22738751, -330.36450025],
[ -70.29226772, -331.95215503],
[ -63.16376134, -334.06902808],
[ -57.13194826, -336.7151194 ],
[ -52.19682846, -338.83199244],
[ -47.26170866, -340.94886549],
[ -38.48816235, -342.00730202],
[ -31.90800262, -342.00730202],
[ -23.13445632, -343.06573854],
[ -16.00594994, -343.59495681],
[ -8.87744357, -344.12417507],
[ -1.74893719, -345.18261159],
[ 3.18618261, -345.18261159],
[ 8.66964905, -346.24104812],
[ 14.15311549, -347.29948464],
[ 20.73327522, -347.29948464],
[ 22.9266618 , -347.8287029 ],
[ 27.8617816 , -348.35792117],
[ 33.89359468, -348.35792117],
[ 37.73202119, -347.29948464],
[ 45.95722085, -346.77026638],
[ 53.63407387, -346.77026638],
[ 60.2142336 , -346.77026638],
[ 64.05266011, -347.29948464],
[ 71.72951313, -347.29948464],
[ 75.56793964, -347.8287029 ],
[ 84.88983259, -348.88713943],
[ 92.01833897, -348.35792117],
[ 99.14684534, -345.18261159],
[ 106.27535172, -343.06573854],
[ 112.3071648 , -342.00730202],
[ 121.08071111, -339.36121071],
[ 130.40260406, -337.24433766],
[ 138.62780372, -334.59824635],
[ 146.85300339, -331.42293677],
[ 153.43316312, -329.30606372],
[ 160.01332285, -325.60153589],
[ 166.04513593, -321.89700805],
[ 171.52860238, -318.19248021],
[ 175.91537553, -315.5463889 ],
[ 181.39884197, -311.3126428 ],
[ 185.23726848, -306.02046018],
[ 189.07569499, -303.37436887],
[ 192.9141215 , -299.66984103],
[ 195.65585472, -295.9653132 ],
[ 198.94593459, -293.84844015],
[ 202.7843611 , -290.67313057],
[ 205.52609432, -287.497821 ],
[ 208.26782754, -283.79329316],
[ 213.75129398, -279.0303288 ],
[ 218.13806713, -275.85501923],
[ 221.428147 , -270.56283661],
[ 225.81492015, -265.79987225],
[ 228.55665337, -262.09534441],
[ 230.75003995, -259.97847136],
[ 232.39507988, -257.86159831],
[ 235.1368131 , -254.68628874],
[ 237.33019968, -249.92332438],
[ 238.42689297, -247.27723306],
[ 239.52358626, -244.63114175],
[ 241.16862619, -240.92661392],
[ 243.36201277, -238.28052261],
[ 246.10374599, -234.04677651],
[ 248.29713257, -230.34224867],
[ 250.49051914, -226.63772083],
[ 252.13555908, -223.46241126],
[ 252.68390572, -221.34553821],
[ 254.32894565, -218.17022864],
[ 255.42563894, -214.4657008 ],
[ 258.71571881, -210.2319547 ],
[ 260.36075874, -205.9982086 ],
[ 262.00579867, -202.29368077],
[ 264.19918525, -199.64758946],
[ 265.29587854, -197.00149815],
[ 265.84422518, -193.82618857],
[ 266.39257182, -191.18009726],
[ 268.5859584 , -186.94635116],
[ 269.68265169, -183.77104159],
[ 270.23099833, -180.06651375],
[ 271.32769162, -177.9496407 ],
[ 271.87603827, -175.30354939],
[ 272.97273155, -172.12823982],
[ 274.06942484, -167.36527546],
[ 275.16611813, -162.60231109],
[ 275.71446478, -158.89778326],
[ 276.26281142, -151.48872759],
[ 276.26281142, -147.25498149],
[ 276.26281142, -145.13810844],
[ 276.26281142, -141.4335806 ],
[ 276.81115806, -137.72905277],
[ 277.90785135, -133.49530667],
[ 277.35950471, -129.26156057],
[ 277.90785135, -126.086251 ],
[ 278.456198 , -122.38172316],
[ 278.456198 , -118.67719532],
[ 279.00454464, -114.97266749],
[ 279.00454464, -110.73892139],
[ 279.00454464, -108.09283008],
[ 277.90785135, -101.74221093],
[ 277.35950471, -98.56690136],
[ 276.81115806, -95.39159178],
[ 275.71446478, -92.21628221],
[ 274.06942484, -86.92409958],
[ 274.61777149, -83.21957175],
[ 274.61777149, -79.51504391],
[ 274.06942484, -75.28129781],
[ 273.5210782 , -73.69364303],
[ 273.5210782 , -69.98911519],
[ 274.61777149, -66.81380562],
[ 275.16611813, -63.63849604],
[ 274.06942484, -59.40474994],
[ 272.97273155, -56.22944037],
[ 271.87603827, -52.52491253],
[ 271.87603827, -48.8203847 ],
[ 271.32769162, -45.11585686],
[ 270.77934498, -41.41132903],
[ 269.13430505, -37.70680119],
[ 269.13430505, -34.00227335],
[ 268.03761176, -29.76852725],
[ 267.48926511, -27.65165421],
[ 266.94091847, -25.00556289],
[ 266.39257182, -21.83025332],
[ 265.29587854, -19.18416201],
[ 262.55414531, -13.89197939],
[ 260.36075874, -8.59979676],
[ 258.71571881, -4.36605066],
[ 258.16737216, -1.19074109]])
它们看起来像这样：
我想用两个圆形帽形成的形状来近似它们（见下文），定义为
x^2 + (y-c_alpha)^2 = R_alpha^2 for y < 0x^2 + (y-c_beta)^2 = R_beta^2 for y < 0有约束
R_alpha^2 = R_beta^2 + (c_alpha-c_beta)^2 - 2*(c_alpha-c_beta)*R_beta*cos(sigma)其中
cos(sigma) = -c_beta/R_betac_beta < 0R_betac_betaR_alpha
想法似乎不太复杂，但是实现起来有几个难点我不知道如何解决：
- 要拟合的函数必须隐式定义，因为为绿色上限写入
将排除部分数据。y(x) = sqrt(...) - 它必须以某种方式分段定义，因此它知道将灰色数据与灰色上限相匹配，将绿色数据与绿色上限相匹配。或者我是否必须单独安装每个上限，然后以某种方式强制执行约束？那会怎样？
任何提示都会有很大帮助，当然，非常感谢代码片段。预先感谢！
1个回答
0
投票
投票
由于某些原因，拟合效果不可能很好 - 首先，您的数据只有一个“实例”（无论它是什么）（钟摆摆动等），添加多个实验实例会有所帮助。另外，您假设圆弧以 y 轴为中心并且没有椭圆形变形，但事实并非如此。
from typing import Sequence
import matplotlib.pyplot as plt
import numpy as np
from scipy.optimize import minimize, Bounds
def infer_params(params: Sequence[float]) -> tuple[
float, float, float, float,
]:
c_alpha, c_beta, r_alpha = params
x_intercept2 = r_alpha**2 - c_alpha**2
r_beta = np.sqrt(x_intercept2 + c_beta**2)
return c_alpha, c_beta, r_alpha, r_beta
def fit_error(
params: np.ndarray,
xy_alpha: np.ndarray,
xy_beta: np.ndarray,
) -> float:
c_alpha, c_beta, r_alpha, r_beta = infer_params(params)
# Assuming that our decision centres are true, these are the experimental radii
radii_alpha = np.linalg.norm(xy_alpha - (0, c_alpha), axis=1)
radii_beta = np.linalg.norm(xy_beta - (0, c_beta), axis=1)
error_alpha = radii_alpha - r_alpha
error_beta = radii_beta - r_beta
# Least-squares error
return error_alpha.dot(error_alpha) + error_beta.dot(error_beta)
def estimate(
y_alpha: np.ndarray,
x_beta: np.ndarray,
y_beta: np.ndarray,
) -> tuple[
Bounds,
tuple[float, float, float],
]:
yalpha_min = y_alpha.min()
ybeta_min = y_beta.min()
c0_beta = y_beta[x_beta.argmax()]
r0_beta = c0_beta - ybeta_min
# x**2 + (y - c)**2 = r**2
# x = sqrt(r**2 - c**2)
x0_intercept = np.sqrt(r0_beta**2 - c0_beta**2)
# c**2 + x**2 = r**2 (1), x known
# r - c = y (2), y known
c0_alpha = 0.5/yalpha_min * (yalpha_min**2 - x0_intercept**2)
r0_alpha = c0_alpha - yalpha_min
x0 = c0_alpha, c0_beta, r0_alpha
bounds = Bounds(
# c_alpha c_beta r_alpha
lb=(yalpha_min, ybeta_min, x0_intercept),
ub=(10*c0_alpha, -c0_beta, 10*c0_alpha),
)
return bounds, x0
def load_data() -> tuple[np.ndarray, np.ndarray]:
# "grey"
xy_alpha = np.array((
(-260.02020661, 1.98456848),
(-257.27847339, -1.71995935),
(-253.44004688, -4.89526893),
(-249.60162037, -8.59979676),
(-243.56980729, -12.3043246 ),
(-240.82807406, -15.47963417),
(-236.44130091, -17.59650722),
(-231.50618111, -20.7718168 ),
(-226.57106132, -24.47634463),
(-219.99090158, -28.18087247),
(-214.50743514, -30.82696378),
(-207.37892877, -34.00227335),
(-204.0888489 , -36.1191464 ),
(-197.50868917, -39.82367424),
(-193.67026266, -41.41132903),
(-187.09010293, -44.05742034),
(-178.86490327, -46.17429339),
(-171.18805025, -48.29116644),
(-165.15623716, -49.87882122),
(-160.22111737, -52.52491253),
(-153.64095764, -54.64178558),
(-148.70583784, -56.22944037),
(-142.12567811, -58.87553168),
(-138.83559824, -60.46318647),
(-132.80378516, -62.05084126),
(-128.96535865, -63.10927778),
(-124.57858549, -65.22615083),
(-120.19181234, -67.34302388),
(-115.80503919, -68.93067867),
(-108.67653281, -71.04755172),
(-103.19306637, -73.16442476),
( -97.16125328, -74.75207955),
( -88.38770698, -78.45660739),
( -81.80754725, -79.51504391),
( -74.13069423, -81.1026987 ),
( -67.5505345 , -82.69035349),
( -61.51872141, -83.74879001),
( -53.29352175, -85.3364448 ),
( -47.8100553 , -86.39488132),
( -42.87493551, -86.92409958),
( -36.84312242, -87.45331785),
( -30.81130933, -87.45331785),
( -22.03776303, -87.45331785),
( -18.74768316, -87.45331785),
( -13.26421672, -87.45331785),
( -7.23240363, -86.92409958),
( -0.6522439 , -86.92409958),
( 4.28287589, -86.39488132),
( 10.31468898, -86.39488132),
( 18.53988864, -85.86566306),
( 22.37831515, -85.86566306),
( 28.95847488, -85.3364448 ),
( 37.18367455, -84.80722654),
( 42.11879434, -83.74879001),
( 49.24730072, -82.69035349),
( 54.73076716, -81.1026987 ),
( 60.76258025, -78.98582565),
( 66.79439333, -76.8689526 ),
( 70.0844732 , -74.75207955),
( 75.019593 , -72.10598824),
( 81.59975273, -69.45989693),
( 89.82495239, -65.22615083),
( 95.85676548, -63.10927778),
( 99.69519199, -61.52162299),
( 102.98527185, -60.99240473),
( 106.82369836, -59.93396821),
( 112.3071648 , -58.34631342),
( 115.04889802, -57.81709516),
( 119.43567118, -56.22944037),
( 123.27409769, -55.17100385),
( 131.49929735, -51.99569427),
( 136.43441715, -50.40803949),
( 147.40135003, -46.70351165),
( 142.46623023, -48.29116644),
( 150.6914299 , -45.11585686),
( 156.72324298, -40.88211076),
( 165.49678929, -37.17758293),
( 170.98025573, -34.53149162),
( 175.91537553, -31.8854003 ),
( 181.39884197, -30.29774552),
( 184.14057519, -28.71009073),
( 187.9790017 , -27.12243594),
( 192.36577486, -25.00556289),
( 197.30089465, -21.83025332),
( 203.88105439, -19.18416201),
( 210.46121412, -17.06728896),
( 213.75129398, -15.47963417),
( 220.33145371, -14.42119765),
( 228.00830673, -11.24588807),
( 232.94342653, -7.54136024),
( 237.87854633, -5.95370545),
( 246.10374599, -3.8368324 ),
( 249.9421725 , -2.24917761),
( 253.23225236, -1.19074109),
( 255.97398558, 0.3969137 ),
))
# "green"
xy_beta = np.array((
(-263.31028648, -1.19074109),
(-264.95532641, -9.12901502),
(-264.95532641, -14.95041591),
(-266.0520197 , -20.7718168 ),
(-266.60036634, -26.59321768),
(-267.69705963, -31.8854003 ),
(-268.24540627, -37.70680119),
(-268.79375292, -44.05742034),
(-268.79375292, -49.87882122),
(-269.89044621, -54.11256732),
(-269.89044621, -60.99240473),
(-269.89044621, -66.81380562),
(-270.43879285, -73.16442476),
(-270.9871395 , -80.04426217),
(-270.9871395 , -83.74879001),
(-271.53548614, -89.5701909 ),
(-271.53548614, -95.39159178),
(-271.53548614, -100.6837744 ),
(-270.9871395 , -107.03439355),
(-270.43879285, -113.3850127 ),
(-268.79375292, -120.26485011),
(-268.24540627, -124.49859621),
(-267.69705963, -130.31999709),
(-266.60036634, -138.25827103),
(-264.95532641, -144.07967191),
(-263.85863312, -149.9010728 ),
(-262.76193983, -154.66403716),
(-261.66524654, -160.48543805),
(-260.02020661, -165.77762067),
(-260.56855326, -172.65745808),
(-257.82682003, -178.47885896),
(-255.08508681, -185.88791464),
(-252.34335359, -191.18009726),
(-248.50492708, -197.00149815),
(-245.76319386, -201.76446251),
(-243.02146064, -205.9982086 ),
(-239.73138078, -211.29039123),
(-236.44130091, -214.99491906),
(-232.6028744 , -220.28710169),
(-228.76444789, -223.46241126),
(-225.47436803, -227.1669391 ),
(-222.18428816, -230.34224867),
(-219.99090158, -232.98833998),
(-215.05578179, -237.75130434),
(-212.31404857, -241.98505044),
(-208.47562206, -247.27723306),
(-206.28223548, -251.51097916),
(-202.44380897, -255.215507 ),
(-198.05703582, -259.4492531 ),
(-191.47687609, -264.21221746),
(-187.09010293, -266.85830877),
(-182.70332978, -269.50440008),
(-177.76820998, -273.20892792),
(-173.92978347, -277.44267402),
(-169.54301032, -281.67642011),
(-164.60789052, -284.85172969),
(-159.12442408, -290.14391231),
(-154.73765092, -292.26078536),
(-150.89922442, -294.37765841),
(-145.96410462, -297.02374972),
(-142.67402475, -299.14062277),
(-137.19055831, -302.84515061),
(-132.25543851, -305.49124192),
(-126.77197207, -307.60811497),
(-122.38519892, -311.3126428 ),
(-116.90173247, -313.95873412),
(-111.41826603, -316.07560716),
(-104.28975966, -319.780135 ),
( -99.9029865 , -322.42622631),
( -94.41952006, -324.54309936),
( -88.93605362, -327.18919067),
( -80.71085396, -329.30606372),
( -75.22738751, -330.36450025),
( -70.29226772, -331.95215503),
( -63.16376134, -334.06902808),
( -57.13194826, -336.7151194 ),
( -52.19682846, -338.83199244),
( -47.26170866, -340.94886549),
( -38.48816235, -342.00730202),
( -31.90800262, -342.00730202),
( -23.13445632, -343.06573854),
( -16.00594994, -343.59495681),
( -8.87744357, -344.12417507),
( -1.74893719, -345.18261159),
( 3.18618261, -345.18261159),
( 8.66964905, -346.24104812),
( 14.15311549, -347.29948464),
( 20.73327522, -347.29948464),
( 22.9266618 , -347.8287029 ),
( 27.8617816 , -348.35792117),
( 33.89359468, -348.35792117),
( 37.73202119, -347.29948464),
( 45.95722085, -346.77026638),
( 53.63407387, -346.77026638),
( 60.2142336 , -346.77026638),
( 64.05266011, -347.29948464),
( 71.72951313, -347.29948464),
( 75.56793964, -347.8287029 ),
( 84.88983259, -348.88713943),
( 92.01833897, -348.35792117),
( 99.14684534, -345.18261159),
( 106.27535172, -343.06573854),
( 112.3071648 , -342.00730202),
( 121.08071111, -339.36121071),
( 130.40260406, -337.24433766),
( 138.62780372, -334.59824635),
( 146.85300339, -331.42293677),
( 153.43316312, -329.30606372),
( 160.01332285, -325.60153589),
( 166.04513593, -321.89700805),
( 171.52860238, -318.19248021),
( 175.91537553, -315.5463889 ),
( 181.39884197, -311.3126428 ),
( 185.23726848, -306.02046018),
( 189.07569499, -303.37436887),
( 192.9141215 , -299.66984103),
( 195.65585472, -295.9653132 ),
( 198.94593459, -293.84844015),
( 202.7843611 , -290.67313057),
( 205.52609432, -287.497821 ),
( 208.26782754, -283.79329316),
( 213.75129398, -279.0303288 ),
( 218.13806713, -275.85501923),
( 221.428147 , -270.56283661),
( 225.81492015, -265.79987225),
( 228.55665337, -262.09534441),
( 230.75003995, -259.97847136),
( 232.39507988, -257.86159831),
( 235.1368131 , -254.68628874),
( 237.33019968, -249.92332438),
( 238.42689297, -247.27723306),
( 239.52358626, -244.63114175),
( 241.16862619, -240.92661392),
( 243.36201277, -238.28052261),
( 246.10374599, -234.04677651),
( 248.29713257, -230.34224867),
( 250.49051914, -226.63772083),
( 252.13555908, -223.46241126),
( 252.68390572, -221.34553821),
( 254.32894565, -218.17022864),
( 255.42563894, -214.4657008 ),
( 258.71571881, -210.2319547 ),
( 260.36075874, -205.9982086 ),
( 262.00579867, -202.29368077),
( 264.19918525, -199.64758946),
( 265.29587854, -197.00149815),
( 265.84422518, -193.82618857),
( 266.39257182, -191.18009726),
( 268.5859584 , -186.94635116),
( 269.68265169, -183.77104159),
( 270.23099833, -180.06651375),
( 271.32769162, -177.9496407 ),
( 271.87603827, -175.30354939),
( 272.97273155, -172.12823982),
( 274.06942484, -167.36527546),
( 275.16611813, -162.60231109),
( 275.71446478, -158.89778326),
( 276.26281142, -151.48872759),
( 276.26281142, -147.25498149),
( 276.26281142, -145.13810844),
( 276.26281142, -141.4335806 ),
( 276.81115806, -137.72905277),
( 277.90785135, -133.49530667),
( 277.35950471, -129.26156057),
( 277.90785135, -126.086251 ),
( 278.456198 , -122.38172316),
( 278.456198 , -118.67719532),
( 279.00454464, -114.97266749),
( 279.00454464, -110.73892139),
( 279.00454464, -108.09283008),
( 277.90785135, -101.74221093),
( 277.35950471, -98.56690136),
( 276.81115806, -95.39159178),
( 275.71446478, -92.21628221),
( 274.06942484, -86.92409958),
( 274.61777149, -83.21957175),
( 274.61777149, -79.51504391),
( 274.06942484, -75.28129781),
( 273.5210782 , -73.69364303),
( 273.5210782 , -69.98911519),
( 274.61777149, -66.81380562),
( 275.16611813, -63.63849604),
( 274.06942484, -59.40474994),
( 272.97273155, -56.22944037),
( 271.87603827, -52.52491253),
( 271.87603827, -48.8203847 ),
( 271.32769162, -45.11585686),
( 270.77934498, -41.41132903),
( 269.13430505, -37.70680119),
( 269.13430505, -34.00227335),
( 268.03761176, -29.76852725),
( 267.48926511, -27.65165421),
( 266.94091847, -25.00556289),
( 266.39257182, -21.83025332),
( 265.29587854, -19.18416201),
( 262.55414531, -13.89197939),
( 260.36075874, -8.59979676),
( 258.71571881, -4.36605066),
( 258.16737216, -1.19074109),
))
return xy_alpha, xy_beta
def plot_circle(ax: plt.Axes, c: float, r: float, label: str) -> None:
arc_angle = np.arccos(c/r)
angle = np.linspace(
start=1.5*np.pi - arc_angle,
stop=1.5*np.pi + arc_angle,
num=101,
)
x = r*np.cos(angle)
y = r*np.sin(angle) + c
ax.plot(x, y, label=label)
def plot_circles(ax: plt.Axes, param: Sequence[float], label: str) -> None:
c_alpha, c_beta, r_alpha, r_beta = infer_params(param)
plot_circle(ax, c_alpha, r_alpha, f'{label} alpha')
plot_circle(ax, c_beta, r_beta, f'{label} beta')
def plot(
x_alpha: np.ndarray,
y_alpha: np.ndarray,
x_beta: np.ndarray,
y_beta: np.ndarray,
p0: Sequence[float],
p: Sequence[float]
) -> plt.Figure:
fig, ax = plt.subplots()
ax.scatter(x_alpha, y_alpha, s=4, color='grey', label='alpha')
ax.scatter(x_beta, y_beta, s=4, color='green', label='beta')
plot_circles(ax, p0, 'estimate')
plot_circles(ax, p, 'fit')
ax.legend()
return fig
def main() -> None:
xy_alpha, xy_beta = load_data()
x_alpha, y_alpha = xy_alpha.T
x_beta, y_beta = xy_beta.T
bounds, x0 = estimate(y_alpha, x_beta, y_beta)
result = minimize(
fun=fit_error, x0=x0, bounds=bounds,
args=(xy_alpha, xy_beta),
)
assert result.success
print(bounds.lb, '<=')
print(result.x, '<=')
print(bounds.ub)
plot(x_alpha, y_alpha, x_beta, y_beta, x0, result.x)
plt.show()
if __name__ == '__main__':
main()
[ -87.45331785 -348.88713943 203.70877721] <=
[393.18432891 -80.54487763 473.49530205] <=
[1935.27152213 114.97266749 1935.27152213]
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