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Anjum48/sigmoid_video.py

Created May 31, 2023 09:39
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sigmoid_video.py
import numpy as np
import matplotlib.pyplot as plt
import random
import matplotlib.animation as animation
from matplotlib import cm
# s curve function
def _f(a,b,c,t):
return c*1/(1+a*np.exp(-b*t))
# function for s curve with added noise
def _y(a,b,c,d,t):
return abs(c/(1+a*np.exp(-b*t))+np.random.normal(0,d))
# the time series at which points are observed
_t = np.arange(1,120,1)
# observed and true values of the s-curve for integer values of t
f = [43.723616034283943, 48.266580975107217, 53.275212159450973, 58.795856792825646,
64.879174084617475, 71.580470799769714, 78.960048190561636, 87.083556938055253,
96.022355600521379, 105.85386671473393, 116.66192310116948, 128.53709506424013,
141.5769870372946, 155.88648979144884, 171.57797161265069, 188.77138887675781,
207.59429326740255, 228.1817095693043, 250.67585465655233, 275.22566515990553,
301.98609858030431, 331.11717062914062, 362.78269070698775, 397.14865814499052,
434.38128465822456, 474.64461397696414, 518.09771842115811, 564.89146481498233,
615.16485903497653, 669.04099986779647, 726.62269861844629, 787.98785050875972,
853.18467623290428, 922.22698534347012, 995.08964500886123, 1071.7044650754437,
1151.9567298029981, 1235.6826144811646, 1322.6677180006561, 1412.6469177396746,
1505.3057095390855, 1600.2831335834537, 1697.1763093065156, 1795.5465138138186,
1894.9266454960866, 1994.8298255288225, 2094.7588132380479, 2194.215854583143,
2292.7125522167221, 2389.7793440369678, 2484.9742050168547, 2577.8902413784981,
2668.1619211658631, 2755.4697733666812, 2839.5434805437112, 2920.1633793353594,
2997.160462273443, 3070.4150381097552, 3139.8542533870909, 3205.4487046224694,
3267.2083793191546, 3325.1781575854652, 3379.4330877343814, 3430.0736225011201,
3477.2209709613221, 3521.0126879510767, 3561.5985902692487, 3599.137058999871,
3633.7917610969921, 3665.7288015273439, 3695.1142999112944, 3722.1123725472939,
3746.8834915335397, 3769.5831868717055, 3790.3610543615559, 3809.3600311899618,
3826.715901845901, 3842.5569988833886, 3857.0040657113091, 3870.1702516936716,
3882.1612131477909, 3893.0752971468264, 3903.0037882357337, 3912.0312011688984,
3920.2356055207242, 3927.6889704810196, 3934.4575203181407, 3940.6020928812341,
3946.1784951342242, 3951.2378510897142, 3955.8269386647025, 3959.9885129371073,
3963.7616140671225, 3967.1818587838879, 3970.2817148473991, 3973.0907582977011,
3975.6359136154538, 3977.941677155382, 3980.0303243899798, 3981.9221016266465,
3983.6354029467188, 3985.1869331678331, 3986.5918576584759, 3987.8639398410955,
3989.0156672124454, 3990.0583666906268, 3991.0023100707972, 3991.8568103380594,
3992.6303095487706, 3993.3304589518016, 3993.9641919805886, 3994.5377907058119,
3995.0569462981925, 3995.5268140115572, 3995.9520631584564, 3996.3369225144625,
3996.6852215529962, 3997.0004278802385, 3997.2856812093846]
y = [107.64996241684651, 75.644293785293215, 238.03834193128432, 212.84885430223056,
129.20759397417027, 56.393322676763646, 170.12889442681342, 33.366488761391047,
225.47781802730543, 10.952977852756348, 34.181242119954476, 11.503160420741779,
140.66878464822102, 167.22673954320516, 187.4695305651741, 124.86097874381383,
205.41008895562359, 201.8017249612241, 288.25758938303255, 381.68713597628516,
454.89582917386525, 457.39038542311926, 197.2879868717402, 304.2219466604754,
451.92884422920019, 403.73303635917949, 534.11348429490295, 677.94499039009679,
617.26532641811457, 728.88982652908317, 768.02740562418035, 819.42701562256366,
788.04269661376838, 1016.4573174924733, 1137.7235689874294, 947.83405244780897,
996.48743686367652, 1467.6315386660849, 1250.9504924124185, 1536.4436760895942,
1461.8396409582242, 1640.9866287797483, 1534.468731605717, 1906.7615586382337,
1763.7863548454397, 2017.9110034235543, 2056.2614086348867, 2048.1548195727805,
2390.1413523091219, 2211.4613065477506, 2491.4135842189789, 2628.9074086839596,
2739.4225587555588, 2505.7456511682417, 2615.1113563315175, 3106.1805804247019,
3011.2364283040265, 3109.0005441173803, 3075.5685776905339, 3163.8849100225507,
3378.8253871787128, 3269.4296466560263, 3345.6872745083624, 3523.2744933424242,
3445.2254022292273, 3523.8527872843574, 3419.066957109414, 3643.4758745491936,
3639.8258099536629, 3663.491424107187, 3670.0470771043165, 3843.4877746757547,
3698.6798155844672, 3783.8738219272536, 3809.5095544095061, 3853.0073182972542,
3708.6473522752531, 4065.2531114095095, 3965.6247858108045, 3936.569950277787,
3832.4227471130566, 3856.313366930161, 3697.578731615949, 3861.2882573059915,
3803.9775412821677, 3974.4093591269816, 3820.9622954701817, 3808.941102006147,
4049.7394097249962, 3859.7000474242068, 4020.5594156009602, 3977.3167191564257,
3917.1219937629903, 3764.8918669464924, 3937.9162636736573, 3940.8749799135685,
4005.1404397169922, 4032.7789472279251, 3989.4915477996387, 4057.3531010554461,
4013.6726137807759, 3985.4071469252058, 3943.3014318463042, 4016.6254087962311,
4062.560331786301, 4038.0817403385199, 4043.1318296967193, 4113.549877647798,
4019.4294152727889, 3999.0073588161522, 4094.6441108375552, 3933.0748050644411,
4104.3562663660023, 4051.9917629860529, 3885.8223745044797, 3918.0688583897108,
3995.4162178647953, 4004.6417834949148, 3944.2031935737714]
# these are the s-curve parameters at each time-step using historic data
opt_param = {1:[80, 0.099999999999999992, 7900], 2:[20, 0.01, 1900],
3:[80, 0.19, 7900], 4:[70, 0.19, 7100],
5:[20, 0.099999999999999992, 2400], 6:[30, 0.01, 4100],
7:[30, 0.01, 4200], 8:[30, 0.01, 3800], 9:[30, 0.01, 4100],
10:[20, 0.01, 2500], 11:[20, 0.01, 2300], 12:[20, 0.01, 2100],
13:[20, 0.01, 2200], 14:[20, 0.01, 2200], 15:[20, 0.01, 2300],
16:[20, 0.01, 2300], 17:[20, 0.01, 2400], 18:[60, 0.02, 6500],
19:[80, 0.040000000000000001, 7300],
20:[120, 0.069999999999999993, 7900],
21:[170, 0.099999999999999992, 7600],
22:[200, 0.11, 7800], 23:[130, 0.080000000000000002, 7800],
24:[110, 0.069999999999999993, 7700],
25:[130, 0.080000000000000002, 7700],
26:[50, 0.080000000000000002, 3100],
27:[130, 0.080000000000000002, 7700],
28:[160, 0.089999999999999997, 7900],
29:[160, 0.089999999999999997, 7900],
30:[150, 0.089999999999999997, 7600],
31:[150, 0.089999999999999997, 7600],
32:[150, 0.089999999999999997, 7600],
33:[150, 0.089999999999999997, 7500],
34:[150, 0.089999999999999997, 7600],
35:[140, 0.099999999999999992, 5600],
36:[140, 0.089999999999999997, 7100],
37:[60, 0.099999999999999992, 2700],
38:[150, 0.089999999999999997, 7600],
39:[130, 0.089999999999999997, 6600],
40:[150, 0.089999999999999997, 7500],
41:[120, 0.089999999999999997, 6200],
42:[120, 0.089999999999999997, 6200],
43:[80, 0.099999999999999992, 3500],
44:[100, 0.089999999999999997, 5300],
45:[80, 0.099999999999999992, 3500],
46:[80, 0.099999999999999992, 3500],
47:[80, 0.099999999999999992, 3500],
48:[80, 0.099999999999999992, 3500],
49:[90, 0.099999999999999992, 3800],
50:[80, 0.099999999999999992, 3500],
51:[90, 0.099999999999999992, 3800],
52:[90, 0.099999999999999992, 3800],
53:[90, 0.089999999999999997, 4800],
54:[90, 0.099999999999999992, 3800],
55:[90, 0.099999999999999992, 3700],
56:[90, 0.099999999999999992, 3800],
57:[80, 0.089999999999999997, 4400],
58:[80, 0.089999999999999997, 4400],
59:[80, 0.089999999999999997, 4400],
60:[80, 0.089999999999999997, 4400],
61:[80, 0.089999999999999997, 4400],
62:[80, 0.089999999999999997, 4400],
63:[100, 0.099999999999999992, 4000],
64:[80, 0.089999999999999997, 4400],
65:[100, 0.099999999999999992, 4000],
66:[100, 0.099999999999999992, 4000],
67:[100, 0.099999999999999992, 4000],
68:[100, 0.099999999999999992, 4000],
69:[100, 0.099999999999999992, 4000],
70:[100, 0.099999999999999992, 4000],
71:[100, 0.099999999999999992, 4000],
72:[100, 0.099999999999999992, 4000],
73:[100, 0.099999999999999992, 4000],
74:[100, 0.099999999999999992, 4000],
75:[100, 0.099999999999999992, 4000],
76:[100, 0.099999999999999992, 4000],
77:[100, 0.099999999999999992, 4000],
78:[100, 0.099999999999999992, 4000],
79:[100, 0.099999999999999992, 4000],
80:[100, 0.099999999999999992, 4000],
81:[100, 0.099999999999999992, 4000],
82:[100, 0.099999999999999992, 4000],
83:[100, 0.099999999999999992, 4000],
84:[100, 0.099999999999999992, 4000],
85:[100, 0.099999999999999992, 4000],
86:[100, 0.099999999999999992, 4000],
87:[100, 0.099999999999999992, 4000],
88:[100, 0.099999999999999992, 4000],
89:[100, 0.099999999999999992, 4000],
90:[100, 0.099999999999999992, 4000],
91:[100, 0.099999999999999992, 4000],
92:[100, 0.099999999999999992, 4000],
93:[100, 0.099999999999999992, 4000],
94:[100, 0.099999999999999992, 4000],
95:[100, 0.099999999999999992, 4000],
96:[100, 0.099999999999999992, 4000],
97:[100, 0.099999999999999992, 4000],
98:[100, 0.099999999999999992, 4000],
99:[100, 0.099999999999999992, 4000],
100:[100, 0.099999999999999992, 4000],
101:[100, 0.099999999999999992, 4000],
102:[100, 0.099999999999999992, 4000],
103:[100, 0.099999999999999992, 4000],
104:[100, 0.099999999999999992, 4000],
105:[100, 0.099999999999999992, 4000],
106:[100, 0.099999999999999992, 4000],
107:[100, 0.099999999999999992, 4000],
108:[100, 0.099999999999999992, 4000],
109:[100, 0.099999999999999992, 4000],
110:[100, 0.099999999999999992, 4000],
111:[100, 0.099999999999999992, 4000],
112:[100, 0.099999999999999992, 4000],
113:[100, 0.099999999999999992, 4000],
114:[100, 0.099999999999999992, 4000],
115:[100, 0.099999999999999992, 4000],
116:[100, 0.099999999999999992, 4000],
117:[100, 0.099999999999999992, 4000],
118:[100, 0.099999999999999992, 4000],
119:[100, 0.099999999999999992, 4000],
120:[100, 0.099999999999999992, 4000]}
# plot the true curve and the observed points
plt.rcParams["font.family"] = 'serif'
plt.rcParams['font.size'] = 10
fig, ax = plt.subplots(figsize=(6,4))
scat = ax.scatter(_t,y,marker='x',c='b')
plt.plot(_t,f,c='k',lw='2',zorder=1,label='True')
plt.ylim(0,6500)
plt.xlim(0,120)
plt.grid(ls=':')
plt.tight_layout()
line, = ax.plot([], [], c='r',lw=2,zorder=2,label='Predicted')
line2, = ax.plot([], [], c='b',ls='--')
plt.legend(loc=2)
def data_gen(t=1):
while t < 119.9:
t += 0.1
opt1 = opt_param[int(t)]
opt2 = opt_param[int(t)+1]
y1 = _f(opt1[0],opt1[1],opt1[2],_t)
y2 = _f(opt2[0],opt2[1],opt2[2],_t)
frac = float(t%1)
yield t, frac*y2+(1-frac)*y1
def run(data):
t, x = data
line2.set_data([t,t],[0,9000])
line.set_data(_t,x)
scat.set_color(['b']*int(t)+['silver']*(len(y)-int(t)))
return line, line2, scat
ani = animation.FuncAnimation(fig, run, data_gen, blit=False, interval=2,
repeat=False,save_count=1200)
FFwriter=animation.FFMpegWriter(fps=75, extra_args=['-vcodec', 'libx264'])
ani.save('mymovie.mp4', writer=FFwriter,dpi=150)
plt.show()
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