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@bogovicj
Last active August 30, 2022 20:45
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What sigma makes a gaussian most similar to a cosine?
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{
"cells": [
{
"cell_type": "markdown",
"id": "f61e4621",
"metadata": {},
"source": [
"Empirically find an expression for the sigma of a gaussian that best fits the first half period of a cosine."
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "a7bf47eb",
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"\n",
"from sklearn import datasets, linear_model\n",
"from sklearn.metrics import mean_squared_error, r2_score"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "88284662",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"3.141592653589793"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.pi"
]
},
{
"cell_type": "code",
"execution_count": 19,
"id": "2aa69c58",
"metadata": {},
"outputs": [],
"source": [
"def cosFalloff( x, a ):\n",
" return 0.5 + 0.5 * np.cos( x * np.pi / a )\n",
"\n",
"\n",
"def gaussFalloff( x, s ):\n",
" return np.exp( -(x**2) / ( 2 * (s**2)))"
]
},
{
"cell_type": "code",
"execution_count": 20,
"id": "d66df3f2",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(256, 1028)"
]
},
"execution_count": 20,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# generate data\n",
"xvals = np.linspace(0, 3.14145, 128 )\n",
"avals = np.linspace(0.1, 500, 256)\n",
"svals = np.linspace(0.01, 2000, 1028 )\n",
"\n",
"x, a, s = np.meshgrid(xvals, avals, svals)\n",
"Z = (0.5 + 0.5 * np.cos( x ) - np.exp( -(x * a / np.pi )**2 / ( 2 * s**2 )))**2\n",
"Z.shape\n",
"Zint = np.sum( Z, axis=1 )\n",
"Zint.shape"
]
},
{
"cell_type": "code",
"execution_count": 21,
"id": "05b1cdbf",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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4qM7ShQEAAAAAwNjsywLG8aCjJ6YvKp/JlU6a8pavchjmmeXyBlUWRrTkFCyEeu7qIf1O95FxHxsAAAAAgH1rXxYwJOlPT55U48BA6aSUdnyVjbAK83RO3iBX2MsVLTtFi6brCx39wdKjulx0x31sAAAAAAD2pX1bwPj+5ms6fmCxGiOZMOVNXy70q18cXam6JPkLoZ5dOKzPdx8Y76EBAAAAANin9m0BoxojuaBiOlc2Yco7vlwcVmGeRSFLMgW9QvFyqWjR09WFCf2XpbfqKl0YAAAAAADcd/u2gCFJ7+m8rNaBXjVG0vZUtIIqzFOqwjx7mcKuU7Qk2bVIz1w7rP/QOz7mUwMAAAAAsP/s6wLGf9U8oxMzi0qnSmUdU94MVEZ1mGdeVFkYK7miFafouqcr1yb1xeW36nrRG/fRAQAAAADYV/Z1AeN40NETUxdUTlfbSLK2V20jqcM8Lc0V9AtFq6WiZam8FumZa0f0e/0j4z46AAAAAAD7yr4uYEjSuydeVmemp2zCKWt7KprBhjBPb5ApXC0VLlddGBcWpvSllUe1VPbHe3AAAAAAAPaRfV/A+DONczoxvb6NpGh6clFQhXmWpSwpFPRzRatO4bIpX4z0rWvH9Pv9+XEfHQAAAACAfWPfFzCGYySaTpVNSFnbVzEcI5FkWV6tVF0tFC07Rdd9nb82pT9ceVSr5WDMpwcAAAAAYH/Y9wUMSfq+ziuamu4pnXRKO6aiFVRdGGZVF0aaK+gVa10Y6fWGvn39mP5j/8C4jw4AAAAAwL5AAUPrYyT5ZL2NpHVjmKc3KBR2S0XLTuGirzPXp/WHq29Rr0zHfXwAAAAAAPY8Chiqxki+e/K8bDpV1pGylqeiEcj5dZhnUcrvZwq6haIVp3DJ1L/W1NOLR/XFwcR4Dw8AAAAAwD5AAaP2ve1Tmp7qKp10ytqmvOnLxf56mGdWKOgXCntO0YoULAY6fX1Gf7D6FiUuG/fxAQAAAADY025bwDCzXzezy2b2zMi1A2b2e2b2Uv15ZuTXfsHMTprZC2b2I9t18Hvt3Y3zemDquvKpYn2MJF4P8xyuVA26hcKVKguje72pby8d03/ut8Z7eAAAAAAA9rg76cD4N5Lev+naz0v6gnPuUUlfqL+XmT0u6QOSnqjf86tm5t+z026j40FHj09elD+VKp2ox0iagVzor4d5JkUV5tktFa5I/mKgU9dn9EfdR5W5Yty3AAAAAADAnnXbAoZz7ouSrm26/JSkj9dff1zST45c/4RzLnHOvSrppKR33Zujbr8n26/qwFRX2YRT1pbypl91YXheFeZZFPIHuYJeWWdheFq53tK3lo7pi4No3McHAAAAAGDPeqMZGIeccxckqf58sL5+TNKZkdedra/dwMw+ZGZfNbOvXlnYGd0L744v6sGpayomc2UT62MkLgyqF+TF2krVsFtlYXiLoU4tHtAfdR9V4crx3gAAAAAAAHvUvQ7xtC2uua1e6Jz7qHPuSefck/OzO2PK5EjQ0XdNXFQ4ldTbSExF06/GSIZdGFkhL6lWqoarTuGyp8XFtr69fEz/ZRCM+xYAAAAAANiT3mgB45KZHZGk+vPl+vpZSSdGXndc0vk3frz773tbr2p2qqtsolwP82xsDvPMq40kXadwRdJiqFcXZ/Xl3pvpwgAAAAAAYBu80QLGZyV9sP76g5I+M3L9A2YWm9lDkh6V9JW7O+L99X3xZT00eU3lRFF1YTQ9lQ1/Q5inl+byB4XC3noXxrXFtr61fFx/nIz7DgAAAAAA2HvuZI3qb0r6I0lvNbOzZvY3Jf2SpPeZ2UuS3ld/L+fcs5I+Kek5SZ+X9GHndtd6jiNBR49PXFA8NVDWccraprzhy0V1mKdUdWEkdZjnqlO4YnKLkV5ZmtWXeo+O9wYAAAAAANiDbhva4Jz7qZv80g/d5PUfkfSRuznUuL2teVpzk4/rQqetrO0pb3kqYl8WBrKiqFaqprn8fqGw5ytckYJlT1cXO/rW9An9cetFvaexM3I9AAAAAADYC+51iOee8H3xZT04eU3lZK68LeVNUxlvFeaZy++XdRaGqViK9OryAf1x/83jvgUAAAAAAPYUChhbOBJ09HjngpqTA2UT9RhJ05eL/fUwz6Ksxkj6wywMKVjydeX6hL61ckJfSbLx3gQAAAAAAHsIBYybeHvrNR2cXFXeKasCRsurujACby3M07JC/iCvChh1F0a2FOvlpTl9uffIuG8BAAAAAIA9gwLGTXxPdFUPTS5IE9UYSdbcIsyzKGVJsT5GsioFy74uLU7o26vH9bUkHe9NAAAAAACwR1DAuIkjQUePtS+qNTlQ1q7GSIqmpzIaGSO5SRdGuhTrpaV5sjAAAAAAALhHKGDcwtubp3VockX5ZFF3YXgqGsHGMM+ikJcW9UYSp6Ar+cu+Li1VXRjfTJJx3wYAAAAAALseBYxbeHu0oAc71+RNZGvbSIrGpi6MvKhWqg6GYZ5O4aqnwVKsk8vz+uP+w+O9CQAAAAAA9gAKGLdwJOjosc4FdSbWx0jypqcyDtbDPJ2T5WXdhVFWXRirkrcS6OLShJ7p0oUBAAAAAMDdooBxG29vnNbhiRUVE8V6F0bsrY+RSFJejZEEg0JB361lYfSWmnppeV5fGzww3psAAAAAAGCXo4BxG++IF/XgxIL8iUx5y1UFjKavMgqqMZJhF0ZWyEsKBf1SYVcKuiZbCXR+eVLf6p7Qt9PBuG8FAAAAAIBdiwLGbRz023pr65ImJ3rKOqNjJH7VhVEXMJQXsqRQ0K+LGKtSuGLqLjX14vJBfX3wpnHfCgAAAAAAuxYFjDvw9uZrOjyxorJTKG9JWdNUNOoChl//COuVqlUXhlPQcwq6Jq0EurA8qW9236Rn0/54bwQAAAAAgF2KAsYd+FPRsh7uLCicSJW3nfKmVDRMxaYujOFK1aBeqRquSsGKp5Xlpk6uzOtrgxPjvhUAAAAAAHYlChh3oBojuaipiX5VwGiZstExkmGYZ1HK0rzqwhiUCnpO4apJK2GdhfEmPZ/2xnszAAAAAADsQhQw7tDjjbM6MrGsspMrb9XbSBrexjDPspTlpfxhmGfPKehJ/oqnpeWWXlo9qK8ndGEAAAAAAPB6UcC4Q2+PlvVge0HRRKq8U20jyRueXOTJBV5VwJCqLoysqIoYg3ql6qqpXAl1bnlS3+6doAsDAAAAAIDXiQLGHZqrx0hmJnrK2+V6F0bsy0XBTcI8yzrQUwpWfC2ttPTSyry+lRwb780AAAAAALDLUMB4HZ6Iz+lwe0VuOEbSMBWxpzLy5fwbV6r69UaSsOsUrJqK5UhnV6b17d4JvZh1x307AAAAAADsGhQwXofvjlb0YGdBjU66FuaZNz2VkbcxzPOGLgxVWRirnhaXW3px9aC+Pjg+3psBAAAAAGAXoYDxOsz5bT3WvKADE13lnWKtCyNv+HKxvx7mObJS1R+UVaBn1ylc9ZStVF0Yz/SP04UBAAAAAMAdooDxOj3eOKcj7WVZO1fecsqbqraRhP7Nwzz7br0LY8XXtboL45vJ0fHeDAAAAAAAuwQFjNfp8bCrh9oLanaSqoDRsrUsDBf662GezlVjJGkhf1AXMbpS0DVlK7HOrU7p2f5xvZytjveGAAAAAADYBShgvE5zfluPNi9pttNT0SmVN6sxknKrMM+1LoxSwWC4kcTkrfpaWG7rhdVDdGEAAAAAAHAHKGC8AU/EZ3W0sySvnVVhns1hmKe/dZhnNszCWO/CSFbitSwMujAAAAAAALg1ChhvwOPhQA+0rqlVj5EUTSmPh2Mk3oYwT5VlvVK1VDBwdRHDZKuBFlbaeql7UE+nh8d9SwAAAAAA7GgUMN6AGb+ltzQuaq7TVdmqt5E0rQrzjLYI8yyqlaprXRi9qgtjsBrp9MqMnukf16t0YQAAAAAAcFMUMN6gx+LzOtJalj+R1dtIqg6MMvY3hnmWpSwvqzGSrbowVlt6sXtQ36ILAwAAAACAm6KA8QY9Hg70cPuq2q2RMZJ6G0kZjoR5SlJerK9UHZQK+lLYk4Kup/5KQ2dWZ/Rc/xhdGAAAAAAA3AQFjDdoxm/pkcYlzXW6cu283kYiFQ1PLvI2hnk6V3VhpPUYyaCUX3dhqBvo6mpbL/UO6un04HhvCgAAAACAHYoCxl14LLqgY+1Fhe1MebPeRhKbiti/Mcyz7sLw0uEYiRT0JH/VU3elodOrM3p+cEync7owAAAAAADYjALGXfiuKNVDrQV12gMV7bIK82yYiroDY0OYZ1lKm7Iw/L4U9ExuNdCV1bZe7B7S0+nceG8KAAAAAIAdiALGXZjymnpzfEnz7a5cu1DRdCoaUtEwlZFXFTD8kTGSoqhXqg6zMKqNJH7XV3e1odPdGT1HFwYAAAAAADeggHGXHosv6Gh7SVE7rXIwRsZIyijYGOZZr1S1tJSfuLVRkrBrKldDXV7p6MXuYT2Xzo73pgAAAAAA2GEoYNylt4a5HmwuaLI9UNEuVDTqMZKGVR0YgXdjmOfaRhInv1+Nkvirnrrdhs50p/Xc4JjO0oUBAAAAAMAaChh3acpr6pHGJc23V2WtolqpWudgFHG9jcT31sM8i3ItzHOYhRH0qiyMYjXQ5dWOXugd0jN0YQAAAAAAsIYCxj3waHRRx1pLitupiqarV6qaythTGXo3hHluXKnq6k4Mk9f1tbLa1JnujL6THKELAwAAAACAGgWMe+CtYa4HmguaavdVtMt6jEQqYk9l5K93YUhVF0Y57MLYGOYZ9Ez5aqhLqx2d7B3Sc+nMeG8MAAAAAIAdggLGPTDlNfVIfElzra6sla+NkVRhnvVK1U1hnqq7MLxkJNCzZ/J6VRfGqe4BvZAc1QW6MAAAAAAAoIBxrzwaXdKx1qIarfUxkiKu1qmWW4V5FoUsK+Vn5do2kqAv+T1T1g11udvRS/2Dei6bGu+NAQAAAACwA1DAuEceCQs90LimqXZfZasYGSOxaowk8G4M86xXqnr1WlW/X3VhWM/X0mpTp7sH9NzgOF0YAAAAAIB9jwLGPVJtI7mo+VZXXjtX0dw4RrJWxBiOkWxYqVoqSEoFg6oLI+h5SruRLnYn9PJgXi9kk+O9OQAAAAAAxuy2BQwz+3Uzu2xmz4xc+wdmds7Mvll//OjIr/2CmZ00sxfM7Ee26+A70ZvDKzreWlSzlSofHSOJTS70qhyM0TDPYj3M00uG20ikoGuyrq/F1aZOd2f0bHJMl4vueG8OAAAAAIAxupMOjH8j6f1bXP8nzrl31B+fkyQze1zSByQ9Ub/nV83Mv1eH3eneGpZ6oLGg6VZfbm2MxFREnorQWy9iDLMwhitVs1J+UspP6yLGQPK7npJupAvdSb3Sn9dz6cR4bw4AAAAAgDG6bQHDOfdFSdfu8Pd7StInnHOJc+5VSSclvesuzrerdLyGHoov62BrRX47q8dIpDw2lfU2Em0aIxldqeoPRgM9TdYLtNRt6rXeAX0nOaKrdGEAAAAAAPapu8nA+Bkz+3Y9YjJTXzsm6czIa87W125gZh8ys6+a2VevLBR3cYyd5S3hZR1tLqvVSlQ0SxUNVR+xpzLyNoZ5ShtWqvr1SlV/pAtj0I10sTuplwcH9VzWHu/NAQAAAAAwJm+0gPFrkt4s6R2SLkj6x/V12+K1bqvfwDn3Uefck865J+dn986UySOh0wPNq5puDuRahfKmUxHXYZ6RpzLcIsyzLGXF+jaSYReG3ze5XqDra10YR+nCAAAAAADsS2+ogOGcu+ScK5xzpaR/qfUxkbOSToy89Lik83d3xN2l4zX0cHRFB1srCprVNpK8KRWRrXVg3CzM0/JSfnpjF0a/G691YbyQNcd7gwAAAAAAjMEbKmCY2ZGRb/+ypOGGks9K+oCZxWb2kKRHJX3l7o64+7w5vKKjzSW1WonKplMRD8dI6iJG6FVBnqNhnoWTlxVVF0bq1laqrnVh9Na7MK4XvfHeIAAAAAAA91lwuxeY2W9K+gFJc2Z2VtIvSvoBM3uHqvGQU5L+liQ55541s09Kek5SLunDzrm9E3Bxhx4JnR5sLOjp9lEtN9sqmp7yRjVGEkSe/HqMxPKRMM+8kGVenYXhV6MkfSnomfKep1431qXehF5uHdRz8Xm9d+9M3QAAAAAAcFu3LWA4535qi8sfu8XrPyLpI3dzqN2u4zX0QHRV881VnWtNqWgEKhpWdWDEpjL05AWezPeksqwKGM5JhatXqhYKElOe+HUnhintBlrotnS6fUAvNQ/r8fCUZvzWuG8VAAAAAID74m62kOAWhmMknVaiolVWYySxqiDPqFqpekOYZ1FIeSnLSnmJW8/C6Jm8nq9eL9aF3qRODg7phSwe7w0CAAAAAHAfUcDYJo+ETm+Kr2mm1Zc1CxVNp6IeIylDUzka5mm2HuZZFNUYSVoqSKogz2BQZWEUq6GudVs63Z/Ri+khLZX9cd8mAAAAAAD3BQWMbdLxGno4vqz55qrCZqai4ZQ36i6M2FMZ+VJQB3mOdmHkoytVR4oYfZP1fa12G7rQm9LLySG9kN12AggAAAAAgD2BAsY2eji8qmONRXVaA5XNUmVcbSIZrlQtQ++GMRIVZVXEyEt5mZOfrq9UDfqmvFdnYfQP6KX0MF0YAAAAAIB9gQLGNno4kE40rulAqy9r5cobTkVDa2MkbljA8G/swlhbqZq4tS4Mv2+yXtWFcb47VWdh0IUBAAAAANj7KGBso47X0MPRZc03VhU3syoHYxjmGZuKsA7zHB0jKUuprDsw0pEiRt2F4fc8Zb1QV3vrXRir5WC8NwoAAAAAwDajgLHNHgyv6VhzUZ1mItcsVDTcxjGSwKuyMEa7MIpSystqpWpaVmMkiRT0pWBQZ2H0GrrQn9SrybxeyPjLCAAAAADY2/gv3232cCC9Kb6mA82evGauoqH1MZJoZIxkc5hnWRcx0lJeWq9UTda7MNJeqKu9tl7rz+ql9BBdGAAAAACAPY0CxjbreA09EF3RfHNVjVaqolmuj5FEnorIUxn6W4d5FoUsK+QndRfGQGsf6vta7lZdGK8kB3Uys7HeJwAAAAAA24kCxn0wHCOZaCZyjXJkjERrm0huCPOsczCsqEdJ1ooYTn7f6i6MqOrCGBzQi9lB9cp0vDcKAAAAAMA2oYBxHzwcSMej6zrQ7Mlv5VUBY2SMpIw8Od/bGOa5eaVqWlbbSBJVHwOT6/ta7jV0oT+lV5ODOpmX471RAAAAAAC2CQWM+2A4RjLXWFWjmapc20ZSh3nW20huCPMcWanqZ1UWxuhKVb/nadCLdKXX1muDWb2U0oUBAAAAANibKGDcJw+G13S8saiJ5kCuUW0jKWOpiExFbGujJJvDPNdGSTZsJHEKBnUXRi/Qcq+h870pvZLO04UBAAAAANiTKGDcJw8H0rH4umabPfnNXGXslDeqMM8yNJWBVVkYvt0wRjJcqVplYbj1UZK+yetXXRhX+2291p/TK9mcEpeN92YBAAAAALjHKGDcJx2voQejK5pvrKrZrLaRlNHIGEnkqQw8Od+/cYxkdKVq5uSnqsI86yyMshdosdfU+bWNJPl4bxYAAAAAgHuMAsZ99GBwXUfiJU02B1KjVDHMwoiGYZ5VDsaWYZ5FUW0kSYejJFrLwvD6vgb9SFf7HZ0azOrlbJYuDAAAAADAnkIB4z56IDC9KV7QbLOnsJmpiJ2KSHURw6tGSUJv6zDPwsmyoholSaocDD9Z78IoeoEW+w2d70/plfSgXskoYAAAAAAA9g4KGPdRx2voRLSg+Xi4jaRU0RiOkajeRlLnYNwszLPOw6jCPOsujIHJ+p56vbjuwpjTS9mcMleM94YBAAAAALhHKGDcZw8G13WksaTJRiJrFFUXxugYSVCtVN0yzLNwaytVRzeSVKMknopeoOu9pi4OJvVaOq+TWTLemwUAAAAA4B6hgHGfPRCYjkfXNNfsKmhkVQ7G2hiJqYg8Of8mYZ5FsbZStQrzrLsw6jESG/jq9yNd6k3o1GBWr+QH6MIAAAAAAOwJFDDus7Uxksaq2s1ULi5VNFxdvKi7MOocjBvCPEu3vlI1HVmpOqi7MHqesn6oxV5TFwZTOpXO69V8MN4bBgAAAADgHqCAMQYPBtd1tLGoqeZA1sxVxlIZq87BWF+pKt82dmGU5fpK1WxTFkYieYlkfV/dfqRL/QmdGszpleyACleO94YBAAAAALhLFDDG4IHAdCy6rgONrsJGrqJRjoyQmMrA5AJPLvA2hnlKG1eqZm7jKMnA5PWt6sLoN3RhMKWX04N6Oe+P72YBAAAAALgHKGCMQcdr6E3hcIwkkWtUYyRlLBXh+hhJlYWxKcxz80rV1MlPtWGlqvq+VnsNXel3dDqZ1alsmi4MAAAAAMCuRgFjTE4EizocL2uqOZDXzNe3kcRSEXkqQ5ML/aoDw7/5StVqG0lZFzGqAobfr7IwrvVbujCY1CvpQZ3Ke+O9YQAAAAAA7gIFjDEZjpHMNrqKGrnKRlXAKCNTEarqwBiOkmwO8xxZqerlwy4Mt9aF4SUmN/C12o91uT+h08msXs5mxnvDAAAAAADcBQoYYzIcIznYWFWrkVTbSIZdGPU2kiL0VIb+jWGezsmGXRhZKS+/caWq1/eUDLswkimdyub1arY63psGAAAAAOANooAxRieCRR2KljVdj5GUsas2kUR1FkZYZWC4oC5ebO7CqIsYXnpjF4Y/MLleoNV+rEt1F8Yr+dR4bxgAAAAAgDeIAsYYPRCYjkfXNBP3FDcylcMgz9jWujDcMMwz2LSNZC3Mc+NKVW8kC8MbjHRhDKZ0KqULAwAAAACwO1HAGKOO19Cx8LoONlbVbqRyjUJFYzhGIpXDLozhOlXPbgzzLEtZMQzy3JSFMTCV/UAr/ViXBhM6nc7qtXxyvDcNAAAAAMAbQAFjzE4EizoaL2q62ZffKKocjA1jJHUXxrCIsWmMpMrBKOpOjE1ZGInJBp4G/UjXB02dH0zrVDan0zldGAAAAACA3YUCxpg9EJiOhIv1GEmqslFWWRjDMZLQVNYjJC64yUrVohon8bJSfl3E8BLJH0h+31PZD7TUa+rSYEKvJXN6JaMLAwAAAACwu1DAGLOO19CJcEEH42qMRHG51oFRRlIReSqjOgfD2yLMs3RSXlbrVNdWqqoeJ6k6MWzgaTCosjDOJ1M6nR2gCwMAAAAAsKtQwNgBTgRLOhwvaabRV9DIVTaqMZIiMhWhVAZVFoaCkSLGUL1SVcOVqulwlGRjmGfRD7Q8iHWpP6nT6ZxO5Z3x3TAAAAAAAK8TBYwd4ETgVWMkjeE2klJF7KoujLDaRlIGpjKoihg3hHkWpawoqpWquVsP9EzWt5LYwFe/F+vaoKXzybROpXM6SxcGAAAAAGCXoICxA6yPkayo00ikuKjXqVbbSIqRbSTOtxvDPIcrVYvhSlV340rVvikfBFrqN3SxP6Gz6axey1vjvXEAAAAAAO4QBYwd4kSwpMPRsqYbfYWNXEVjmIVhKsPqswusysLwbYssjHojybCIMVypupaFYdLAU78f6dqgXXVhZPO6QBcGAAAAAGAXoICxQxwNTEej6zoQV2MkLnL1NhKtbyMJPbnQl/P9ahvJ0DDMs3D1WtV6lCSrVqp6I1kY2bALYzChs+kBvZY3x3fTAAAAAADcIQoYO8SU19TR4LoONqoxEmvmdZDn6BhJ1YWxFubpjfzlK0vZWheGWwvz9LLRLAyTBr56g0gLg7bOJdM6lc3RhQEAAAAA2PEoYOwgJ4IlHQxXNBUPFMS5ykZZr1MddmBUQZ5l4Em+bQzzlKSilMp6nWoxOkaycSNJ1g/rLoxJncnowgAAAAAA7HwUMHaQ4RjJXKOrRiOTi6ttJBu7MKoMDBd4W4d55iMrVbOyGiOpAz2HXRhuQxfGjE7nB3S56I735gEAAAAAuIXbFjDM7ISZ/b6ZPW9mz5rZz9bXD5jZ75nZS/XnmZH3/IKZnTSzF8zsR7bzBvaSKa+pE+GC5uJVTTQSWaNQWa9TXcvBCEwu9G4e5unchpWqXurkZZKfuA1dGOkg1PKg6sI4m87qVB6N9+YBAAAAALiFO+nAyCX9Xefcd0l6j6QPm9njkn5e0hecc49K+kL9vepf+4CkJyS9X9Kvmpm/HYffi476KzoSLWkqHiiM87Ugz7UiRmQqRzswNod5FuXGlarDMM9Ma4Ge3sDk+r5W+/GGLAy6MAAAAAAAO9VtCxjOuQvOua/XX69Iel7SMUlPSfp4/bKPS/rJ+uunJH3COZc4516VdFLSu+7xufeso4HpSFhtI2k1Urm4XOvCKMN6jCSqOzC2CvO8k5WqqWSJp3QQaGnQ0IXBlM6mszqTh+O7cQAAAAAAbuF1ZWCY2YOS3inpy5IOOecuSFWRQ9LB+mXHJJ0ZedvZ+trm3+tDZvZVM/vqlYXiDRx9b5rymjoWXteheFntOJXXyFVEwxwMUxlqfaXqVmGeW61UzeqNJMMcjIHJH3gq+8FaF8aFdEqnsjldpQsDAAAAALAD3XEBw8w6kj4l6eecc8u3eukW19wNF5z7qHPuSefck/OzTJiMOuqv6GC0oulGvxojaZQqozoLI1zfSDLswtgQ5ilVORijK1WzkQ6MeqWql1RdGMkg1FJSdWFUG0nowgAAAAAA7Dx3VMAws1BV8eI3nHOfri9fMrMj9a8fkXS5vn5W0omRtx+XdP7eHHd/WB8j6arVSKWorDow6iyMMjC5oOrCkHeTMM/RlapZKRtmYdQjJH5ShXmWA18r/VhXB21dSKd1Jj9AFwYAAAAAYMe5ky0kJuljkp53zv3KyC99VtIH668/KOkzI9c/YGaxmT0k6VFJX7l3R977hmMk89GqOnEqr1GobLgqAyOytY0kzjeVNwvzdE5WuGqlalHKT+sxkszVmRh1FsbAVzKI6i6MSZ1JZ3U2D8Z38wAAAAAAbOFOOjDeK+mvS/pBM/tm/fGjkn5J0vvM7CVJ76u/l3PuWUmflPScpM9L+rBzjpCL1+mov6LD8ZKmG31Fca4yLlUMV6oOwzzDqvvilmGem0dJsqpw4a2tVDUVA1+rg1hXBx1dSKd0Op/R9aI3vpsHAAAAAGCT2/6vdufcH2jrXAtJ+qGbvOcjkj5yF+fa944GpkPBkmbjrs41JjWIY5WRryKqx0hCq0ZJQk8uNZlvUmFSaWsdGCrrIM9guFLVq/MwqiJGkZq81FQkngb9SEvNhi4kUzoTz+q14LpmiCYBAAAAAOwQr2sLCe6f4RjJXLSqiTiVHxdrHRhlaPU61fVtJGsdGKNhnmVZjZKMrFStRknqbSQjWRj5INDKINZC0ta5ZIYuDAAAAADAjkIBYwertpEsazruK4ozubjaRlJEqvIwRrowFGwR5ilVYZ4jK1XXwjyzaozEq4sYqrswrvVbupRM6kw2qzMFf3sAAAAAAHYG/gt1BzsamI6Gi5qNu2o3Uiku1kZIishUBvUoie/dOsxzUw6GN1ypmjn5yXoXRlZ3YVxJOvVGkmktlf3x/QAAAAAAAKhRwNjBprymjgXXNRevqhMnCuJCZVxWYyRrRYz1jSRrHRibwzzrQM/hSlUvHxYyRgI9E5MSX/1BqMVBs+rCSGf1Wn6z+BMAAAAAAO4fChg73CF/VYfCZc3EPcWNaoxkPQuj6sBwQb2JxK/yMOSNjJE4JxXlhpWqwyKGP7JS1RtmYSR1F8agowvZtM7nU3RhAAAAAADGjgLGDnc0MB0KlzQT9dWKU9kwByOUyqgO8xxmYQzDPDfnYGxaqerlpbzUrW0kqXIwqiKG6wfqDSItJk1dTCZ1OpvV2Xx89w8AAAAAgEQBY8cbHSOZiBMFca5yQwdGHeYZVh0Y8m3rIkbpqjDPogry9LKy6sDIqjyM4WYSS01ZEmh52IVBFgYAAAAAYAeggLELDMdIpqJ+NUYSlSrjahtJEY2OkVRdGPLt5mGedRHDy+vxkWy9A8NPTP7Akxv46g0iXU9aupRO6lw2QxcGAAAAAGCsKGDsAtU2kuuajXtqx6ksLlREwy6MkTGScCQHY6sxkqKscjDy4ShJ3YExmoWRSpZ4a10YlwcdnU0P6Fw+qdVyML4fAgAAAABgX6OAsQtMeU0dDpY0H62sjZG42I0UMVRtI6m7MOR51UYS39sY5umczLm1lao23EaSaW2EZLhStRwE6g1iXU9aupJO6Ew2qzN5Od4fBAAAAABg36KAsUscDVZ0MKrGSBrDMZJwOEKiKtQzNJWBpzLwqlWqNwnz3LxS1R8J8xyuVrXEU5oEWh40dDmpNpKcyafowgAAAAAAjAUFjF3ikO/pcLCk2bi7NkZSxq4uYqxvIikDk/NvspHEOal0N65UzYZFjNGVqqZy4KtbZ2FcTKZ0Pp+hCwMAAAAAMBYUMHaJ9TGSVU1GicI4V1mvVB1uI1kL8wy9rcM8pY2BnvVKVctdnYdRd2FkkpeaLPGVJqGWBg1dTds6n87ofDGhXpmO54cAAAAAANi3KGDsIkeDFc2FK5qK+2rEmRSVaxkYRVSFeRaRp9I3Oe8m61SHYZ6bVqpu6MKoN5JYYiqGXRiDli4ON5IU2fh+CAAAAACAfYkCxi4yHCOZi7vqNBJ5jUJFPBLkGUploGobSehJwS3CPDevVM3WAz39tSwMkxJPSRJqKWnoatLRhWxGZ/JJujAAAAAAAPcVBYxdZMpr6mh4XQfCriaiRGGUy8XlxiJGvYmk9G8T5lkHeo6uVPWzjYUMLzF5iadiEGh1EOta0tKFdIouDAAAAADAfUcBY5c57Hd1KFzWdNxXczhGMrqFpP5wtwvzLKoOjGqUZHSMZH0TiZ9URQwlnpLBxi6M8zlZGAAAAACA+4cCxi5zyPd0KFzUgaindpzKj4s6zLNaqVrUXRhVJ4Yn51kV5unZxt9o2IFRFGtBnlaPkviZk5eOjJMknvLEX+vCuJxO6Fw+owsFBQwAAAAAwP1BAWOXWd9GsqLJeFCNkURuwzaSYTfGhg4Mz9s4RiJtsVL1xhyMaozEpMRf68K4lEzqfDatM/mkEscoCQAAAABg+1HA2IUO+13NBauajvpqxqkUF+sFjKgeIwmsCvP0bx3muWGl6jDQMx8WMdZHSizxlCeBVuoujIvJlM7lMzqbJ+P9YQAAAAAA9gUKGLvQ6BhJZzhGsqkLY1jEGGZh3DTMc4uVqlXhog7yTKuVqn5icomnwSDUctLQlbSjS9mUzhUdujAAAAAAANuOAsYuNBwjmY1WNRkPFEW5XDSag2H1OtX1Lgzn29ZhnptWqlpRZ2Hkbn2MZMsujLYupFM6n83oPF0YAAAAAIBtRgFjlzrsd3UwXF4bI7G4VLEhB6MuYvjDLgzv5mGem1eq1htJhqtVq0JGtVLVJb4GSdWFcTXt6Hw2ozN0YQAAAAAAthkFjF3qqO/rcLCkA1FXE3EqPyrk4nqMJKrHSOoRktKvuzC2CvN0bj3Mc7hStXAbAj3X1qrWXRhZ3YWxkLR1KZukCwMAAAAAsO0oYOxSHa+h+WBZs2FXnShRFGdyYVkXLobjI+sfVYin3RjmKa13YJTl+krVwsnLtV7IWOvCMLnEV3/YhZF0dDGf0vmipcwV4/uBAAAAAAD2NAoYu9hhv6tD4ZKmo75acSZbC/McWac6DPIMPLnAu3mYZ1l1YKhcX6nqp2W1hSRbz8HwMlvrwliuuzAup5P1RpL++H4YAAAAAIA9jQLGLnbU9zUfrOhA1FU7ShVEhcq4XCtiuGC9iFHWORi3DfPM11eqWqGRHIx6tWpSdWGUia9+EmkxaepSUo+R0IUBAAAAANgmFDB2sY7X0OFgUQejlWobSZxLUbnWfVFEtl68CDy5oF6neqswz00rVddyMDKNbCUxWeIrTQKtJJGup01dTid1MZ/WhYIuDAAAAADAvUcBY5c77Pc0F6xoOuqpFaeyqFQRO7l6G0n1URcyfE9lcIswz6KUObflStVqhKT+nJhspAvjetLSlXSiDvNs0oUBAAAAALjnKGDscof8QIfDJR2IevUYSS4XbVypOgz1rNap3j7M84aVqvUYyVoORh3oqdRTmoRaTWItJC1dyqosDLowAAAAAAD3GgWMXa7jNTTvL2suXNVUNFCjkVVjJGsFDFMRWlXEGI6SeLaegWGbRklutlI1d2uBnv5wnCTxVCS+ekmopbSpK2m9kYQuDAAAAADAPUYBYw847Pd0MFzWTNxTK8rkrW0jqYoYbli8qDsvhhtJbhbmOQz09PJSVndgVGMkdZjnyEpVpZ6SJNRKUm8kySZ1sZiiCwMAAAAAcE9RwNgDDvmBDgbLOhBW20jCKJerN5EUkaoOjOFHvY1Enlf91d8qzLMo11eqlnUORjaShTGyVtXWujCiugtjQueyGV0sYhWuHMvPAwAAAACw91DA2AM6XkOH/SXNhl1NRX3F0XAbiau6LyKNjJCMZGHcLMxz80rVrN5KktdrVVMnP5X81OQnJiW+kkHVhXG17sI4n8/oQtEb3w8FAAAAALCnUMDYI+b9vubCFc1EfbXiVH49RjIa5lkMN5L4VReGCzw5u0mY5+hK1aJcHyEZ7cAYdmGkpiL11U0iLSVVF8bFbErn6cIAAAAAANwjFDD2iLUxkqirztoYSblhC0kZ1B+hV3VheNVGkpuGeQ5XqpZOXj6ShTEcKVnLwvDkEk/JINRS0tC1tKVL2RRdGAAAAACAe4YCxh4xHCOptpH01YhGtpFEGlmpWo2PlP56kOdNwzw3rFR19TjJphyMeiOJpZ7y1FcvDXV90KILAwAAAABwT1HA2EMO+X3NBRvHSFy8vo2kysHQWqCn80wKbhHmuWGlatWBYflomGeVhTHcSOIGvgaDUMtprKtpW5eyKV3Mp+jCAAAAAADcNQoYe8i8H2g+WNZ02FMnTBVFuVxYbsy/CExloPV1qrcJ81wL9CzqDoyiKmD4o50YdRHDMk95GqibRFocZmHk07pURHRhAAAAAADuCgWMPaTjNXTQX6nGSOJqjMTqMRIXbhwjKcNqlMT5VRHjpmGeoytVCycvK9dWqvp1F0Y1RrLehZEkoVbSWNfSli5nkzqXT+syXRgAAAAAgLtAAWOPGY6RTIUDtaJMflSojMpqG0kkFXUXhvNHwjx9b+swz80rVYtyfYRkGOS5ZReGr9VBrMW0qct1F8b5IhrfDwUAAAAAsOvdtoBhZifM7PfN7Hkze9bMfra+/g/M7JyZfbP++NGR9/yCmZ00sxfM7Ee28waw0SE/0vzaNpJEUZxJ4UgGxoYwT1Vhnv6mIM+bjZIUI0WMbDQLQ/LyuoCRmMpBoCQNtJw0dC1t63I2qYvFpC7kq+P7wQAAAAAAdrXgDl6TS/q7zrmvm9mEpK+Z2e/Vv/ZPnHO/PPpiM3tc0gckPSHpqKT/YGZvcc4V9/Lg2FrLi3Q4WNJcuKLpuK8rUVv9uFAZ+fU2EtsQ5ullVTeG/OqzlSZtjqsYhnl69UrVolSZm7xc8jOnMpPK1OSF1ShJmZmypMrCuJa0dDXu6GI2rfP+so7cyd9xAAAAAABsctsODOfcBefc1+uvVyQ9L+nYLd7ylKRPOOcS59yrkk5Kete9OCzuzLyXaD5Y0VTYVzvKFISFXFSud1+EtjZKUg7DPAPv1mGem1aqro2Q5NrUhSF5iacy8dVPQq2msa4mnWojCV0YAAAAAIA36HVlYJjZg5LeKenL9aWfMbNvm9mvm9lMfe2YpDMjbzurLQoeZvYhM/uqmX31ygLNGffScIxkNhyOkeRSWKoMndxwjCSox0jqPAzn2a3DPDetVLVicxbGxpWqSj1laaDVJKqyMLIJXcymdakIx/eDAQAAAADsWndcwDCzjqRPSfo559yypF+T9GZJ75B0QdI/Hr50i7e7Gy4491Hn3JPOuSfnZ/3Xe27cQsuLNF9vI5mO+mpGmby4UBm5Kswz3FjEKIdBnt6twzw3r1S1vNy6CyOTvHTYhRHVWRgtujAAAAAAAG/YHRUwzCxUVbz4DefcpyXJOXfJOVc450pJ/1LrYyJnJZ0YeftxSefv3ZFxJ+a9RAeCqoDRjlL5YSEXjYZ51iMkgarOi8BUBncQ5jm6UrVwa+Mkft2F4aXrK1WHXRjdNNRi2tJC1tbFfIouDAAAAADA63YnW0hM0sckPe+c+5WR60dGXvaXJT1Tf/1ZSR8ws9jMHpL0qKSv3Lsj406sbSOpx0jiOJeiUi50dZjn+jaSMqyyMOSth3nK21TAkKSiXO/AGG4jWRslWe/CsPprSz0VI10YV9L1LIzLRXc8PxgAAAAAwK50Jzsh3ivpr0t62sy+WV/7e5J+yszeoWo85JSkvyVJzrlnzeyTkp5TtcHkw2wguf9aXqTD/rIOBF1NhgM1o0y9qN5GErqRbST1CEngyQWlXGYyz5M8JxVlVcQYdl8Mvy5LWWF1EcOrOi9CJy+zOgujKor4iZTHntI00EoSaTFu6XI6oYvhlM77yzrI5BAAAAAA4A7dtoDhnPsDbZ1r8blbvOcjkj5yF+fCPTDvp5oLlnUg6qkdpVoKC6VRqTL01sdIQrdWxCh9TxZ4ckUp5SbzPSkfqT2Nhnl6VQ6GV5QqCxsJ9LT1PIxMstRUJL4GcaiVNNa1rF11YQRLulxc00G/Pb4fEAAAAABg1zDnbsjXvP+HMLsiqSvp6rjPAuxgc+IZAW6FZwS4OZ4P4NZ4RoBbu9/PyAPOufnNF3dEAUOSzOyrzrknx30OYKfiGQFujWcEuDmeD+DWeEaAW9spz8gdr1EFAAAAAAAYFwoYAAAAAABgx9tJBYyPjvsAwA7HMwLcGs8IcHM8H8Ct8YwAt7YjnpEdk4EBAAAAAABwMzupAwMAAAAAAGBLFDAAAAAAAMCON/YChpm938xeMLOTZvbz4z4PMA5mdsLMft/MnjezZ83sZ+vrB8zs98zspfrzzMh7fqF+bl4wsx8Z3+mB+8PMfDP7hpn9Vv09zwcwwsymzezfmdl36n+e/GmeE6BiZv9T/e9Yz5jZb5pZg+cD+5mZ/bqZXTazZ0auve5nwsy+18yern/tn5mZbee5x1rAMDNf0r+Q9BclPS7pp8zs8XGeCRiTXNLfdc59l6T3SPpw/Sz8vKQvOOcelfSF+nvVv/YBSU9Ier+kX62fJ2Av+1lJz498z/MBbPRPJX3eOfeYpLerel54TrDvmdkxSf+jpCedc98tyVf19z/PB/azf6Pq7+9Rb+SZ+DVJH5L0aP2x+fe8p8bdgfEuSSedc68451JJn5D01JjPBNx3zrkLzrmv11+vqPqXzmOqnoeP1y/7uKSfrL9+StInnHOJc+5VSSdVPU/AnmRmxyX9mKR/NXKZ5wOomdmkpD8n6WOS5JxLnXOL4jkBhgJJTTMLJLUknRfPB/Yx59wXJV3bdPl1PRNmdkTSpHPuj1y1HeTfjrxnW4y7gHFM0pmR78/W14B9y8welPROSV+WdMg5d0GqihySDtYv49nBfvO/SfpfJJUj13g+gHUPS7oi6V/Xo1b/ysza4jkB5Jw7J+mXJZ2WdEHSknPud8XzAWz2ep+JY/XXm69vm3EXMLaaj2GvK/YtM+tI+pSkn3POLd/qpVtc49nBnmRmf0nSZefc1+70LVtc4/nAXhdI+h5Jv+ace6ekrurW35vgOcG+Uc/xPyXpIUlHJbXN7Kdv9ZYtrvF8YD+72TNx35+VcRcwzko6MfL9cVXtXMC+Y2ahquLFbzjnPl1fvlS3Zqn+fLm+zrOD/eS9kn7CzE6pGjX8QTP7P8XzAYw6K+msc+7L9ff/TlVBg+cEkH5Y0qvOuSvOuUzSpyX9GfF8AJu93mfibP315uvbZtwFjD+R9KiZPWRmkapgkM+O+UzAfVen9X5M0vPOuV8Z+aXPSvpg/fUHJX1m5PoHzCw2s4dUBeZ85X6dF7ifnHO/4Jw77px7UNU/J/6jc+6nxfMBrHHOXZR0xszeWl/6IUnPiecEkKrRkfeYWav+d64fUpU3xvMBbPS6nol6zGTFzN5TP1t/Y+Q92yLYzt/8dpxzuZn9jKTfUZUG/OvOuWfHeSZgTN4r6a9LetrMvllf+3uSfknSJ83sb6r6h+9flSTn3LNm9klV/3KaS/qwc66476cGxovnA9jof5D0G/X/FHpF0n+r6n9W8ZxgX3POfdnM/p2kr6v6+/0bkj4qqSOeD+xTZvabkn5A0pyZnZX0i3pj/271t1VtNGlK+v/qj+07dxUWCgAAAAAAsHONe4QEAAAAAADgtihgAAAAAACAHY8CBgAAAAAA2PEoYAAAAAAAgB2PAgYAAAAAANjxKGAAAAAAAIAdjwIGAAAAAADY8f5/caKR+mOZa1cAAAAASUVORK5CYII=\n",
"text/plain": [
"<Figure size 1332x756 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# What shape is\n",
"\n",
"fig, ax = plt.subplots()\n",
"fig = plt.gcf()\n",
"fig.set_size_inches(18.5, 10.5)\n",
"ax.imshow(Zint, vmin = 0, vmax = 1.5)\n",
"plt.show()\n",
"\n",
"# looks clearly linear"
]
},
{
"cell_type": "code",
"execution_count": 22,
"id": "ef09130e",
"metadata": {
"scrolled": false
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 1152x720 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# find the line \n",
"minSs = np.argmin( Zint, axis = 1 )\n",
"\n",
"a = avals[:, np.newaxis]\n",
"s = svals[minSs, np.newaxis]\n",
"reg = linear_model.LinearRegression()\n",
"reg.fit(a, s)\n",
"s_pred = reg.predict(a)\n",
"\n",
"plt.scatter(a, s, color=\"black\", alpha = 0.2, s=75)\n",
"plt.plot(a, s_pred, color=\"blue\", linewidth=3)\n",
"fig = plt.gcf()\n",
"fig.set_size_inches(16, 10)"
]
},
{
"cell_type": "code",
"execution_count": 23,
"id": "d2c38f1f",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[0.03706937]\n",
"0.40535876907923957\n"
]
}
],
"source": [
"dir(reg)\n",
"print( reg.intercept_)\n",
"print(reg.coef_[0][0])\n",
"\n",
"def sigmaFromPeriod( a ):\n",
" return reg.intercept_ + reg.coef_[0][0] * a\n",
"\n",
"def plotCompare( a ):\n",
" x = np.linspace( 0, a, 128 )\n",
" \n",
" plt.plot( x, cosFalloff(x,a), color=\"black\", label='cos')\n",
" print( sigmaFromPeriod(a) )\n",
" plt.plot( x, gaussFalloff(x,sigmaFromPeriod(a)), color=\"blue\", label='gauss')\n",
" plt.legend()\n",
" fig = plt.gcf()\n",
" fig.set_size_inches(16, 10)"
]
},
{
"cell_type": "code",
"execution_count": 24,
"id": "705a47b9",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[0.44242814]\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 1152x720 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# does this function reallyu produce a reasonable gaussian approximation?\n",
"plotCompare(1)\n",
"# yes"
]
},
{
"cell_type": "code",
"execution_count": 25,
"id": "295590d2",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[20.30500782]\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 1152x720 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plotCompare(50)"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "82aea61e",
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3 (ipykernel)",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.10.5"
}
},
"nbformat": 4,
"nbformat_minor": 5
}
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