compose_mix.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import scipy\n",
    "from scipy.optimize import curve_fit\n",
    "import plotly\n",
    "from plotly import graph_objects as go\n",
    "import math\n",
    "from spring_math import *"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### In this notebook, we demonstrate how two animations are composed as is done in SwiftUI interpolatingSpring API."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {},
   "outputs": [],
   "source": [
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(6.116720400008489, 652.428350268076), (6.13338706700597, 653.2213545268136), (6.15005373400345, 654.0201636575206), (6.16672040100093, 654.8243791426647), (6.18338706799841, 655.6336042517919), (6.20005373499589, 656.4474442891585), (6.2167204020079225, 657.2655068324672), (6.233387069005403, 658.0874019732312), (6.250053736002883, 658.9127425444221), (6.266720403000363, 659.7411443459251), (6.283387069997843, 660.572226364154), (6.3000537370098755, 661.4056109820662), (6.316720404007356, 662.240924190368), (6.333387071004836, 663.0777957852991), (6.350053738002316, 663.9158595637901), (6.366720404999796, 664.7547535115659), (6.3833870719972765, 665.5941199855783), (6.400053739009309, 666.4336058863091), (6.416720406006789, 667.2728628308794), (6.433387073004269, 668.111547312258), (6.450053740001749, 668.9493208555232), (6.4667204069992295, 669.7858501667425), (6.48338707399671, 670.6208072759096), (6.500053741008742, 671.4538696695424), (6.516720408006222, 672.2847204238669), (6.533387075003702, 673.1130483239949), (6.550053742001182, 673.9385479800407), (6.566720408998663, 674.7609199358036), (6.583387075996143, 675.5798707714772), (6.600053743008175, 676.3951131961202), (6.616720410005655, 677.2063661406346), (6.633387077003135, 678.0133548369847), (6.6500537440006156, 678.815810894428), (6.666720410998096, 679.6134723692034), (6.683387078010128, 680.4060838242726), (6.700053745007608, 681.1933963896104), (6.716720412005088, 681.9751678091726), (6.7333870790025685, 682.7511624850724), (6.750053746000049, 683.5211515148455), (6.766720412997529, 684.2849127232487), (6.783387080009561, 685.0422306846808), (6.800053747007041, 685.792896746306), (6.8167204140045214, 686.5367090386311), (6.833387081002002, 687.2734724836506), (6.850053747999482, 688.002998796648), (6.866720414996962, 688.7251064830535), (6.883387082008994, 689.4396208266971), (6.900053749006474, 690.1463738790086), (6.916720416003955, 690.8452044366695), (6.933387083001435, 691.5359580173111), (6.950053749998915, 692.2184868295795), (6.966720416996395, 692.8926497389148), (6.983387084008427, 693.5583122256512), (7.0000537510059075, 694.2153463443804), (7.016720418003388, 694.863630672935), (7.033387085000868, 695.5030502599755), (7.050053751998348, 696.1334965677695), (7.066720418995828, 696.754867411431), (7.0833870860078605, 697.3670668915191), (7.100053753005341, 697.9700053282584), (7.116720420002821, 698.5635991866657), (7.133387087000301, 699.1477710008905), (7.150053753997781, 699.7224492951356), (7.166720421009813, 700.2875684988552), (7.183387088007294, 700.8430688638837), (7.200053755004774, 701.3888963736028), (7.216720422002254, 701.9250026518415), (7.233387088999734, 702.4513448686267), (7.2500537559972145, 702.9678856438843), (7.266720423009247, 703.4745929465462), (7.283387090006727, 703.9714399959521), (7.300053757004207, 704.458405156673), (7.316720424001687, 704.9354718336832), (7.333387090999167, 705.4026283653038), (7.350053757996648, 705.85986791491), (7.36672042500868, 706.307188359164), (7.38338709200616, 706.744592178881), (7.40005375900364, 707.1720863446834), (7.41672042600112, 707.589682203589), (7.433387092998601, 707.9973953642562), (7.450053759996081, 708.3952455817697), (7.466720427008113, 708.7832566400266), (7.483387094005593, 709.1614562370471), (7.500053761003073, 709.529875866388), (7.5167204280005535, 709.8885507000177), (7.533387094998034, 710.2375194709753), (7.550053762010066, 710.5768243544759), (7.566720429007546, 710.9065108521318), (7.583387096005026, 711.2266276733092), (7.6000537630025065, 711.5372266183291), (7.616720429999987, 711.838362461777), (7.633387096997467, 712.1300928365902), (7.650053764009499, 712.4124781175165), (7.666720431006979, 712.6855813078472), (7.683387098004459, 712.9494679244314), (7.70005376500194, 713.2042058849078), (7.71672043199942, 713.4498653957062), (7.7333870989969, 713.6865188413689), (7.750053766008932, 713.9142406740567), (7.766720433006412, 714.1331073064051), (7.7833871000038926, 714.3431970036775), (7.800053767001373, 714.5445897784151), (7.816720433998853, 714.7373672864029), (7.833387100996333, 714.9216127243891), (7.850053768008365, 715.0974107286793), (7.8667204350058455, 715.2648472770638), (7.883387102003326, 715.4240095909221), (7.900053769000806, 715.5749860399966), (7.916720435998286, 715.7178660489097), (7.933387102995766, 715.8527400057553), (7.9500537700077984, 715.9796991721215), (7.966720437005279, 716.0988355963386), (7.983387104002759, 716.2102420276399), (8.000053771000239, 716.3140118330575), (8.01672043799772, 716.4102389164502), (8.033387105009751, 716.4990176393244), (8.050053772007232, 716.5804427447232), (8.066720439004712, 716.6546092825287), (8.083387106002192, 716.721612537477), (8.100053772999672, 716.7815479593886), (8.116720439997152, 716.8345110957624), (8.133387107009185, 716.8805975264808), (8.150053774006665, 716.919902801315), (8.166720441004145, 716.9525223793155), (8.183387108001625, 716.9785515707991), (8.200053774999105, 716.9980854816474), (8.216720441996586, 717.0112189599712), (8.233387109008618, 717.0180465450833), (8.250053776006098, 717.0186624189286), (8.266720443003578, 717.0131603597359), (8.283387110001058, 717.0016336980647), (8.300053776998539, 716.984175275153), (8.316720443996019, 716.9608774035438), (8.33338711100805, 716.9318318301004), (8.350053778005531, 716.8971297010748), (8.366720445003011, 716.856861529612), (8.383387112000491, 716.8111171653721), (8.400053778997972, 716.7599857663079), (8.416720446010004, 716.7035557728294), (8.433387113007484, 716.6419148836407), (8.450053780004964, 716.57515003411), (8.466720447002444, 716.5033473764803), (8.483387113999925, 716.4265922621412), (8.500053780997405, 716.3449692258098), (8.516720448009437, 716.258561972014), (8.533387115006917, 716.167453362761), (8.550053782004397, 716.0717254077697), (8.566720449001878, 715.9714592561675), (8.583387115999358, 715.8667351900233), (8.600053782996838, 715.7576326195046), (8.61672045000887, 715.644230080191), (8.63338711700635, 715.5266052310538), (8.65005378400383, 715.404834854962), (8.66672045100131, 715.2789948602407), (8.683387117998791, 715.1491602837962), (8.700053784996271, 715.0154052955445), (8.716720452008303, 714.8778032047964), (8.733387119005783, 714.7364264667865), (8.750053786003264, 714.5913466916286), (8.766720453000744, 714.4426346538987), (8.783387119998224, 714.2903603033515), (8.800053787010256, 714.1345927774039)]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {},
   "outputs": [],
   "source": [
    "data0 = np.array(data0)\n",
    "data = np.array(data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {},
   "outputs": [],
   "source": [
    "datac = concat(data0, data, start_offset)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {},
   "outputs": [],
   "source": [
    "t, y = t_y_from_data(datac, 0, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "ccc315b373674157b363fcb8109ea41a",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "FigureWidget({\n",
       "    'data': [{'type': 'scatter',\n",
       "              'uid': '079bd469-ea73-4b95-9920-777a2827e5cc',\n",
       " …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "go.FigureWidget([go.Scatter(x=t, y=y)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {},
   "outputs": [],
   "source": [
    "# start 694, end 594 for iPhone 12\n",
    "# start 620, end 520 for iPhone 8 plus\n",
    "t, y = t_y_from_data(data0, 694, 594)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {},
   "outputs": [],
   "source": [
    "mean, cov = curve_fit(spring, t, y, (0, 1, 0.25, 1), bounds=([-np.inf, 0, 0, -np.inf], [np.inf, np.inf, np.inf, np.inf]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.01632131, 1.        , 0.25      , 2.00000048])"
      ]
     },
     "execution_count": 132,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.30418610e-12, 3.22939776e-12, 3.66264860e-12, 1.00797455e-11])"
      ]
     },
     "execution_count": 133,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sqrt(np.diag(cov))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {},
   "outputs": [],
   "source": [
    "t, y = t_y_from_data(data[1:], 0, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {},
   "outputs": [],
   "source": [
    "destination = 694"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_continuing = destination + (-100) * spring(t + start_offset, 0, 1, 0.25, 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "metadata": {},
   "outputs": [],
   "source": [
    "component = (y - y_continuing) / (destination - y_continuing)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 138,
   "metadata": {},
   "outputs": [],
   "source": [
    "mean, cov = curve_fit(spring, t, component, (0, 1, 0.1, 2), bounds=([-np.inf, 0, 0, -np.inf], [np.inf, np.inf, np.inf, np.inf]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.01259383,  1.00049083,  0.2520721 ,  2.024185  ])"
      ]
     },
     "execution_count": 139,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2.19761510e-04, 7.71742312e-05, 9.67202085e-05, 6.95966921e-04])"
      ]
     },
     "execution_count": 140,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sqrt(np.diag(cov))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 141,
   "metadata": {},
   "outputs": [],
   "source": [
    "mixed = y_continuing + (destination - y_continuing) * spring(t, 0, 1, 0.25, 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "b8abe33afe13468bb418b071290fd049",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "FigureWidget({\n",
       "    'data': [{'type': 'scatter',\n",
       "              'uid': '81785ae5-43c9-4de3-b31d-799bf840c68d',\n",
       " …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "go.FigureWidget([go.Scatter(x=t, y=y), go.Scatter(x=t, y=mixed)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.8625059022325177"
      ]
     },
     "execution_count": 143,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_smse(y, mixed)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
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   "name": "python3"
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  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
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   "file_extension": ".py",
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