move things
This commit is contained in:
saji
parent
1486786c21
commit
f2a3f95fa8
30
py/.idea/jupyter-settings.xml
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30
py/.idea/jupyter-settings.xml
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<?xml version="1.0" encoding="UTF-8"?>
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<project version="4">
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<component name="JupyterPersistentConnectionParameters">
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<option name="knownRemoteServers">
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<list>
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<JupyterConnectionParameters>
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<option name="authType" value="notebook" />
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<option name="token" value="5a7fb936e2f1eafcdefbb7fa3ea339000213214ae7e35195" />
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<option name="urlString" value="http://127.0.0.1:8888" />
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<authParams2>
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<map>
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<entry key="token" value="5a7fb936e2f1eafcdefbb7fa3ea339000213214ae7e35195" />
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</map>
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</authParams2>
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</JupyterConnectionParameters>
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</list>
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</option>
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<option name="moduleParameters">
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<map>
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<entry key="$PROJECT_DIR$/.idea/py.iml">
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<value>
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<JupyterConnectionParameters>
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<option name="managed" value="true" />
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</JupyterConnectionParameters>
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</value>
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</entry>
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</map>
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</option>
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</component>
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</project>
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py/notebooks/test_solar.ipynb
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py/notebooks/test_solar.ipynb
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{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 2,
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"metadata": {
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"ExecuteTime": {
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"end_time": "2023-06-21T00:28:49.748311944Z",
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"start_time": "2023-06-21T00:28:49.744946948Z"
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},
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"collapsed": true,
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"jupyter": {
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"outputs_hidden": true
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}
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},
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"outputs": [
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{
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"name": "stderr",
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"output_type": "stream",
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"text": [
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"No GPU/TPU found, falling back to CPU. (Set TF_CPP_MIN_LOG_LEVEL=0 and rerun for more info.)\n"
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]
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}
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],
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"source": [
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"\n",
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"from pytelem.optimus import *\n",
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"from jax import jit"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"metadata": {
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"ExecuteTime": {
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"end_time": "2023-06-21T00:28:50.052452543Z",
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"start_time": "2023-06-21T00:28:50.050159245Z"
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},
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"collapsed": false,
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"jupyter": {
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"outputs_hidden": false
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}
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},
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"outputs": [
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{
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"ename": "NameError",
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"evalue": "name 'optim' is not defined",
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"output_type": "error",
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"traceback": [
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"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
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"\u001b[0;31mNameError\u001b[0m Traceback (most recent call last)",
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"Cell \u001b[0;32mIn[2], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m ffast \u001b[39m=\u001b[39m jit(optim\u001b[39m.\u001b[39msolar_position)\n",
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"\u001b[0;31mNameError\u001b[0m: name 'optim' is not defined"
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]
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}
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],
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"source": [
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"ffast = jit(optim.solar_position)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 6,
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"metadata": {
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"ExecuteTime": {
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"end_time": "2023-06-21T00:29:01.075229307Z",
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"start_time": "2023-06-21T00:29:01.042571064Z"
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},
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"collapsed": false,
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"jupyter": {
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"outputs_hidden": false
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}
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},
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"outputs": [],
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"source": [
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"timestamp = np.array(1687306901)\n",
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"timestamps = np.array([1687306901, 1687306902, 1687306903, 1687306906])"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"metadata": {
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"collapsed": false,
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"jupyter": {
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"outputs_hidden": false
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}
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},
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"outputs": [],
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"source": [
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"\n",
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"jd = timestamps / 86400.0 + 2440587.5\n",
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"jde = jd + DELTA_T / 86400.0\n",
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"jce = (jde - 2451545) / 36525\n",
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"\n",
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"jme = jce / 10\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 4,
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"metadata": {},
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"outputs": [],
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"source": [
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"\n",
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"# todo: make more elegant?\n",
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"# TODO: vectorize later? it's kinda complex\n",
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"\n",
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"# heliocentric longitude\n",
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"l_rad = np.zeros_like(timestamp)\n",
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"for idx, vec in enumerate(HELIO_L):\n",
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" l_rad = l_rad + helio_vector(vec, jme) * jme ** idx\n",
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"\n",
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"l_rad = l_rad / 10e8\n",
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"l_deg = np.rad2deg(l_rad) % 360\n",
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"\n",
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"# heliocentric latitude\n",
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"b_rad = np.zeros_like(timestamp)\n",
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"for idx, vec in enumerate(HELIO_B):\n",
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" b_rad = b_rad + helio_vector(vec, jme) * jme ** idx\n",
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"b_rad = b_rad / 10e8\n",
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"b_deg = b_rad % 360\n",
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"\n",
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"# heliocentric radius\n",
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"r_rad = np.zeros_like(timestamp)\n",
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"for idx, vec in enumerate(HELIO_R):\n",
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" r_rad = r_rad + helio_vector(vec, jme) * jme ** idx\n",
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"r_rad = r_rad / 10e8\n",
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"r_deg = r_rad % 360\n",
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"\n",
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"theta = (l_deg + 180) % 360\n",
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"beta = -1 * b_deg\n",
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"\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 11,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"(4, 5)\n"
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]
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}
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],
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"source": [
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"\n",
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"def cubic_poly(a,b,c,d):\n",
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" return a + b * jce + c * jce ** 2 + (jce ** 3) / d\n",
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"X0 = cubic_poly(297.85036, 445267.111480, -0.0019142, 189474)\n",
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"X1 = cubic_poly(357.52772, 35999.050340, -0.0001603, -300000)\n",
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"X2 = cubic_poly(134.96298, 477198.867398, 0.0086972, 56250)\n",
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"X3 = cubic_poly(93.27191, 483202.017538, -0.0036825, 327270)\n",
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"X4 = cubic_poly(125.04452, 1934.136261, 0.0020708, 450000)\n",
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"\n",
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"X = np.vstack([X0, X1, X2, X3, X4]).T\n",
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"print(X.shape)\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 13,
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"metadata": {},
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"outputs": [],
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"source": [
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"\n",
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"nut = NUTATION_ABCD_ARRAY\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 14,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"(4, 63)"
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]
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},
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"execution_count": 14,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"(nut[:,0] + jce[..., np.newaxis] * nut[:,1])"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 25,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"(4, 5)\n",
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"(63, 5)\n",
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"d psi shape (4, 63)\n",
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"[-0.00333032 -0.00333032 -0.00333032 -0.00333032]\n"
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]
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}
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],
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"source": [
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"\n",
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"print(X.shape)\n",
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"print(NUTATION_YTERM_ARRAY.shape)\n",
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"d_psi = (nut[:,0] + jce[..., np.newaxis] * nut[:,1]) * np.sin(np.sum(X[:, np.newaxis, :] * NUTATION_YTERM_ARRAY[np.newaxis, ...], axis=-1))\n",
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"\n",
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"print(f\"d psi shape {d_psi.shape}\")\n",
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"\n",
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"nut_long = np.sum(d_psi, axis=-1) / 36,000,000\n",
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"\n",
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"print(nut_long)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 12,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"(4, 11)\n"
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]
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}
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],
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"source": [
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"u = timestamps[:, np.newaxis] ** np.arange(0,11)\n",
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"print(u.shape)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 14,
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"metadata": {},
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"outputs": [],
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"source": [
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"\n",
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"epsilon_0 = np.array(\n",
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" [[\n",
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" 84381.448,\n",
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" -4680.93,\n",
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" 1.55,\n",
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" 1999.25,\n",
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" -51.38,\n",
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" -249.67,\n",
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" -39.05,\n",
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" 7.12,\n",
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" 27.87,\n",
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" 5.79,\n",
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" 2.45,\n",
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" ]]\n",
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" )\n",
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"res = u * epsilon_0\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 16,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"Array([-8.6115017e+12, -5.7323689e+12, -6.4693841e+12, -1.1346544e+13], dtype=float32)"
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]
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},
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"execution_count": 16,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"res.sum(axis=-1)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": []
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3 (ipykernel)",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.11.3"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 4
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}
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# hyperspeed analytics and planning
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import numpy as np
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from scipy.integrate import solve_bvp, solve_ivp
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from numba import njit, vectorize, guvectorize
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def fsolve_discrete(): ...
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py/poetry.lock
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py/poetry.lock
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@ -19,12 +19,15 @@ jinja2 = "^3.1.2"
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pyqtgraph = "^0.13.3"
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pyqtgraph = "^0.13.3"
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scipy = "^1.10.1"
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scipy = "^1.10.1"
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numba = "^0.57.0"
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numba = "^0.57.0"
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jax = {extras = ["cpu"], version = "^0.4.12"}
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[tool.poetry.group.dev.dependencies]
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[tool.poetry.group.dev.dependencies]
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mypy = "^1.3.0"
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mypy = "^1.3.0"
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pytest = "^7.3.2"
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pytest = "^7.3.2"
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types-pyyaml = "^6.0.12.10"
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types-pyyaml = "^6.0.12.10"
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ipykernel = "^6.23.2"
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jupyter = "^1.0.0"
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[build-system]
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[build-system]
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requires = ["poetry-core"]
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requires = ["poetry-core"]
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578
py/pytelem/optimus.py
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578
py/pytelem/optimus.py
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@ -0,0 +1,578 @@
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# hyperspeed forward and backwards analytics engine
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||||||
|
import numpy.typing as npt
|
||||||
|
from scipy.integrate import solve_bvp, solve_ivp
|
||||||
|
|
||||||
|
from jax import jit, grad, vmap
|
||||||
|
|
||||||
|
import jax.numpy as np
|
||||||
|
|
||||||
|
|
||||||
|
# TODO: define 3d vector space - x,y,z oriented around car/world?
|
||||||
|
# solvers should not care about position but we should be able to convert
|
||||||
|
# transforms between car/world spaces.
|
||||||
|
|
||||||
|
# let's define x as the forward-backward axis (with forward being positive)
|
||||||
|
# y as the lateral axis, with right being positive
|
||||||
|
# and z being the vertical, with up being positive.
|
||||||
|
|
||||||
|
# for simplicities’ sake, the car only rotates on the y-axis (up and down hills).
|
||||||
|
# z rotation can be determined from distance along the route.
|
||||||
|
|
||||||
|
# some data (wind) is only a 2d vector at a given time point.
|
||||||
|
|
||||||
|
|
||||||
|
def fsolve_discrete():
|
||||||
|
...
|
||||||
|
|
||||||
|
|
||||||
|
def dist_to_pos(dist: float):
|
||||||
|
"convert a distance along the race path to a position in 3d space"
|
||||||
|
|
||||||
|
|
||||||
|
### All units are BASE SI (no prefix except for kilogram)
|
||||||
|
ATM_MOLAR_MASS = 0.0289644 # kg/mol
|
||||||
|
STANDARD_TEMP = 288.15 # K
|
||||||
|
STANDARD_PRES = 101325.0 # Pa
|
||||||
|
|
||||||
|
AIR_GAS_CONSTANT = 8.31432 # N*m/s^2
|
||||||
|
|
||||||
|
EARTH_TEMP_LAPSE = -0.0065
|
||||||
|
EARTH_GRAVITY = 9.80665 # m/s^2
|
||||||
|
EARTH_RADIUS = 6378140.0 # m
|
||||||
|
EARTH_AXIS_INCLINATION = 23.45 # degrees
|
||||||
|
|
||||||
|
|
||||||
|
# FIXME: use named constants here
|
||||||
|
|
||||||
|
|
||||||
|
@jit
|
||||||
|
def get_pressure_el(
|
||||||
|
el: float,
|
||||||
|
Ps=STANDARD_PRES,
|
||||||
|
Ts: float = STANDARD_TEMP,
|
||||||
|
T_lapse: float = EARTH_TEMP_LAPSE,
|
||||||
|
):
|
||||||
|
"""Gets the pressure at a point given eleveation - assumes
|
||||||
|
standard pressure,temperature, gas constants, etc"""
|
||||||
|
|
||||||
|
return Ps * (Ts / (Ts + T_lapse * el)) ** (
|
||||||
|
(ATM_MOLAR_MASS * EARTH_GRAVITY) / (AIR_GAS_CONSTANT / T_lapse)
|
||||||
|
)
|
||||||
|
|
||||||
|
|
||||||
|
@jit
|
||||||
|
def estimate_temp(el: float, Ts: float = STANDARD_TEMP, T_lapse=EARTH_TEMP_LAPSE):
|
||||||
|
return Ts + el * T_lapse
|
||||||
|
|
||||||
|
|
||||||
|
def make_cubic(a, b, c, d):
|
||||||
|
"""returns a simple cubic function"""
|
||||||
|
|
||||||
|
def poly(x):
|
||||||
|
return a + b * x + c * (x**2) + (x**3) / d
|
||||||
|
|
||||||
|
return jit(poly)
|
||||||
|
|
||||||
|
|
||||||
|
@jit
|
||||||
|
@vmap
|
||||||
|
def get_radiation_direct(yday, altitude_deg):
|
||||||
|
"""Calculate the direct radiation at a given day of the year given the angle of the sun
|
||||||
|
from the horizon."""
|
||||||
|
|
||||||
|
flux = 1160 + (75 * np.sin(2 * np.pi / 365 * (yday - 275)))
|
||||||
|
|
||||||
|
optical_depth = 0.174 + (0.035 * np.sin(2 * np.pi / 365 * (yday - 100)))
|
||||||
|
|
||||||
|
air_mass_ratio = 1 / np.sin(np.radians(altitude_deg))
|
||||||
|
# from Masters, p. 412
|
||||||
|
|
||||||
|
return flux * np.exp(-1 * optical_depth * air_mass_ratio) * (altitude_deg > 0)
|
||||||
|
|
||||||
|
|
||||||
|
# We start by defining MANY constants.
|
||||||
|
# to skip this, Ctrl-F to END COEFF
|
||||||
|
# START COEFF
|
||||||
|
|
||||||
|
|
||||||
|
# heliocentric longitude, latitude, radius (section 3.2) coefficients
|
||||||
|
|
||||||
|
# heliocentric longitude coefficients
|
||||||
|
L0_TABLE = np.array(
|
||||||
|
[
|
||||||
|
[175347046.0, 0.0, 0.0],
|
||||||
|
[3341656.0, 4.6692568, 6283.07585],
|
||||||
|
[34894.0, 4.6261, 12566.1517],
|
||||||
|
[3497.0, 2.7441, 5753.3849],
|
||||||
|
[3418.0, 2.8289, 3.5231],
|
||||||
|
[3136.0, 3.6277, 77713.7715],
|
||||||
|
[2676.0, 4.4181, 7860.4194],
|
||||||
|
[2343.0, 6.1352, 3930.2097],
|
||||||
|
[1324.0, 0.7425, 11506.7698],
|
||||||
|
[1273.0, 2.0371, 529.691],
|
||||||
|
[1199.0, 1.1096, 1577.3435],
|
||||||
|
[990.0, 5.233, 5884.927],
|
||||||
|
[902.0, 2.045, 26.298],
|
||||||
|
[857.0, 3.508, 398.149],
|
||||||
|
[780.0, 1.179, 5223.694],
|
||||||
|
[753.0, 2.533, 5507.553],
|
||||||
|
[505.0, 4.583, 18849.228],
|
||||||
|
[492.0, 4.205, 775.523],
|
||||||
|
[357.0, 2.92, 0.067],
|
||||||
|
[317.0, 5.849, 11790.629],
|
||||||
|
[284.0, 1.899, 796.298],
|
||||||
|
[271.0, 0.315, 10977.079],
|
||||||
|
[243.0, 0.345, 5486.778],
|
||||||
|
[206.0, 4.806, 2544.314],
|
||||||
|
[205.0, 1.869, 5573.143],
|
||||||
|
[202.0, 2.458, 6069.777],
|
||||||
|
[156.0, 0.833, 213.299],
|
||||||
|
[132.0, 3.411, 2942.463],
|
||||||
|
[126.0, 1.083, 20.775],
|
||||||
|
[115.0, 0.645, 0.98],
|
||||||
|
[103.0, 0.636, 4694.003],
|
||||||
|
[102.0, 0.976, 15720.839],
|
||||||
|
[102.0, 4.267, 7.114],
|
||||||
|
[99.0, 6.21, 2146.17],
|
||||||
|
[98.0, 0.68, 155.42],
|
||||||
|
[86.0, 5.98, 161000.69],
|
||||||
|
[85.0, 1.3, 6275.96],
|
||||||
|
[85.0, 3.67, 71430.7],
|
||||||
|
[80.0, 1.81, 17260.15],
|
||||||
|
[79.0, 3.04, 12036.46],
|
||||||
|
[75.0, 1.76, 5088.63],
|
||||||
|
[74.0, 3.5, 3154.69],
|
||||||
|
[74.0, 4.68, 801.82],
|
||||||
|
[70.0, 0.83, 9437.76],
|
||||||
|
[62.0, 3.98, 8827.39],
|
||||||
|
[61.0, 1.82, 7084.9],
|
||||||
|
[57.0, 2.78, 6286.6],
|
||||||
|
[56.0, 4.39, 14143.5],
|
||||||
|
[56.0, 3.47, 6279.55],
|
||||||
|
[52.0, 0.19, 12139.55],
|
||||||
|
[52.0, 1.33, 1748.02],
|
||||||
|
[51.0, 0.28, 5856.48],
|
||||||
|
[49.0, 0.49, 1194.45],
|
||||||
|
[41.0, 5.37, 8429.24],
|
||||||
|
[41.0, 2.4, 19651.05],
|
||||||
|
[39.0, 6.17, 10447.39],
|
||||||
|
[37.0, 6.04, 10213.29],
|
||||||
|
[37.0, 2.57, 1059.38],
|
||||||
|
[36.0, 1.71, 2352.87],
|
||||||
|
[36.0, 1.78, 6812.77],
|
||||||
|
[33.0, 0.59, 17789.85],
|
||||||
|
[30.0, 0.44, 83996.85],
|
||||||
|
[30.0, 2.74, 1349.87],
|
||||||
|
[25.0, 3.16, 4690.48],
|
||||||
|
]
|
||||||
|
)
|
||||||
|
L1_TABLE = np.array(
|
||||||
|
[
|
||||||
|
[628331966747.0, 0.0, 0.0],
|
||||||
|
[206059.0, 2.678235, 6283.07585],
|
||||||
|
[4303.0, 2.6351, 12566.1517],
|
||||||
|
[425.0, 1.59, 3.523],
|
||||||
|
[119.0, 5.796, 26.298],
|
||||||
|
[109.0, 2.966, 1577.344],
|
||||||
|
[93.0, 2.59, 18849.23],
|
||||||
|
[72.0, 1.14, 529.69],
|
||||||
|
[68.0, 1.87, 398.15],
|
||||||
|
[67.0, 4.41, 5507.55],
|
||||||
|
[59.0, 2.89, 5223.69],
|
||||||
|
[56.0, 2.17, 155.42],
|
||||||
|
[45.0, 0.4, 796.3],
|
||||||
|
[36.0, 0.47, 775.52],
|
||||||
|
[29.0, 2.65, 7.11],
|
||||||
|
[21.0, 5.34, 0.98],
|
||||||
|
[19.0, 1.85, 5486.78],
|
||||||
|
[19.0, 4.97, 213.3],
|
||||||
|
[17.0, 2.99, 6275.96],
|
||||||
|
[16.0, 0.03, 2544.31],
|
||||||
|
[16.0, 1.43, 2146.17],
|
||||||
|
[15.0, 1.21, 10977.08],
|
||||||
|
[12.0, 2.83, 1748.02],
|
||||||
|
[12.0, 3.26, 5088.63],
|
||||||
|
[12.0, 5.27, 1194.45],
|
||||||
|
[12.0, 2.08, 4694.0],
|
||||||
|
[11.0, 0.77, 553.57],
|
||||||
|
[10.0, 1.3, 6286.6],
|
||||||
|
[10.0, 4.24, 1349.87],
|
||||||
|
[9.0, 2.7, 242.73],
|
||||||
|
[9.0, 5.64, 951.72],
|
||||||
|
[8.0, 5.3, 2352.87],
|
||||||
|
[6.0, 2.65, 9437.76],
|
||||||
|
[6.0, 4.67, 4690.48],
|
||||||
|
]
|
||||||
|
)
|
||||||
|
L2_TABLE = np.array(
|
||||||
|
[
|
||||||
|
[52919.0, 0.0, 0.0],
|
||||||
|
[8720.0, 1.0721, 6283.0758],
|
||||||
|
[309.0, 0.867, 12566.152],
|
||||||
|
[27.0, 0.05, 3.52],
|
||||||
|
[16.0, 5.19, 26.3],
|
||||||
|
[16.0, 3.68, 155.42],
|
||||||
|
[10.0, 0.76, 18849.23],
|
||||||
|
[9.0, 2.06, 77713.77],
|
||||||
|
[7.0, 0.83, 775.52],
|
||||||
|
[5.0, 4.66, 1577.34],
|
||||||
|
[4.0, 1.03, 7.11],
|
||||||
|
[4.0, 3.44, 5573.14],
|
||||||
|
[3.0, 5.14, 796.3],
|
||||||
|
[3.0, 6.05, 5507.55],
|
||||||
|
[3.0, 1.19, 242.73],
|
||||||
|
[3.0, 6.12, 529.69],
|
||||||
|
[3.0, 0.31, 398.15],
|
||||||
|
[3.0, 2.28, 553.57],
|
||||||
|
[2.0, 4.38, 5223.69],
|
||||||
|
[2.0, 3.75, 0.98],
|
||||||
|
]
|
||||||
|
)
|
||||||
|
L3_TABLE = np.array(
|
||||||
|
[
|
||||||
|
[289.0, 5.844, 6283.076],
|
||||||
|
[35.0, 0.0, 0.0],
|
||||||
|
[17.0, 5.49, 12566.15],
|
||||||
|
[3.0, 5.2, 155.42],
|
||||||
|
[1.0, 4.72, 3.52],
|
||||||
|
[1.0, 5.3, 18849.23],
|
||||||
|
[1.0, 5.97, 242.73],
|
||||||
|
]
|
||||||
|
)
|
||||||
|
L4_TABLE = np.array([[114.0, 3.142, 0.0], [8.0, 4.13, 6283.08], [1.0, 3.84, 12566.15]])
|
||||||
|
L5_TABLE = np.array([[1.0, 3.14, 0.0]])
|
||||||
|
|
||||||
|
HELIO_L = [L0_TABLE, L1_TABLE, L2_TABLE, L3_TABLE, L4_TABLE, L5_TABLE]
|
||||||
|
|
||||||
|
# heliocentric latitude coefficients
|
||||||
|
B0_TABLE = np.array(
|
||||||
|
[
|
||||||
|
[280.0, 3.199, 84334.662],
|
||||||
|
[102.0, 5.422, 5507.553],
|
||||||
|
[80.0, 3.88, 5223.69],
|
||||||
|
[44.0, 3.7, 2352.87],
|
||||||
|
[32.0, 4.0, 1577.34],
|
||||||
|
]
|
||||||
|
)
|
||||||
|
B1_TABLE = np.array([[9.0, 3.9, 5507.55], [6.0, 1.73, 5223.69]])
|
||||||
|
|
||||||
|
HELIO_B = [B0_TABLE, B1_TABLE]
|
||||||
|
|
||||||
|
# heliocentric radius coefficients
|
||||||
|
R0_TABLE = np.array(
|
||||||
|
[
|
||||||
|
[100013989.0, 0.0, 0.0],
|
||||||
|
[1670700.0, 3.0984635, 6283.07585],
|
||||||
|
[13956.0, 3.05525, 12566.1517],
|
||||||
|
[3084.0, 5.1985, 77713.7715],
|
||||||
|
[1628.0, 1.1739, 5753.3849],
|
||||||
|
[1576.0, 2.8469, 7860.4194],
|
||||||
|
[925.0, 5.453, 11506.77],
|
||||||
|
[542.0, 4.564, 3930.21],
|
||||||
|
[472.0, 3.661, 5884.927],
|
||||||
|
[346.0, 0.964, 5507.553],
|
||||||
|
[329.0, 5.9, 5223.694],
|
||||||
|
[307.0, 0.299, 5573.143],
|
||||||
|
[243.0, 4.273, 11790.629],
|
||||||
|
[212.0, 5.847, 1577.344],
|
||||||
|
[186.0, 5.022, 10977.079],
|
||||||
|
[175.0, 3.012, 18849.228],
|
||||||
|
[110.0, 5.055, 5486.778],
|
||||||
|
[98.0, 0.89, 6069.78],
|
||||||
|
[86.0, 5.69, 15720.84],
|
||||||
|
[86.0, 1.27, 161000.69],
|
||||||
|
[65.0, 0.27, 17260.15],
|
||||||
|
[63.0, 0.92, 529.69],
|
||||||
|
[57.0, 2.01, 83996.85],
|
||||||
|
[56.0, 5.24, 71430.7],
|
||||||
|
[49.0, 3.25, 2544.31],
|
||||||
|
[47.0, 2.58, 775.52],
|
||||||
|
[45.0, 5.54, 9437.76],
|
||||||
|
[43.0, 6.01, 6275.96],
|
||||||
|
[39.0, 5.36, 4694.0],
|
||||||
|
[38.0, 2.39, 8827.39],
|
||||||
|
[37.0, 0.83, 19651.05],
|
||||||
|
[37.0, 4.9, 12139.55],
|
||||||
|
[36.0, 1.67, 12036.46],
|
||||||
|
[35.0, 1.84, 2942.46],
|
||||||
|
[33.0, 0.24, 7084.9],
|
||||||
|
[32.0, 0.18, 5088.63],
|
||||||
|
[32.0, 1.78, 398.15],
|
||||||
|
[28.0, 1.21, 6286.6],
|
||||||
|
[28.0, 1.9, 6279.55],
|
||||||
|
[26.0, 4.59, 10447.39],
|
||||||
|
]
|
||||||
|
)
|
||||||
|
R1_TABLE = np.array(
|
||||||
|
[
|
||||||
|
[103019.0, 1.10749, 6283.07585],
|
||||||
|
[1721.0, 1.0644, 12566.1517],
|
||||||
|
[702.0, 3.142, 0.0],
|
||||||
|
[32.0, 1.02, 18849.23],
|
||||||
|
[31.0, 2.84, 5507.55],
|
||||||
|
[25.0, 1.32, 5223.69],
|
||||||
|
[18.0, 1.42, 1577.34],
|
||||||
|
[10.0, 5.91, 10977.08],
|
||||||
|
[9.0, 1.42, 6275.96],
|
||||||
|
[9.0, 0.27, 5486.78],
|
||||||
|
]
|
||||||
|
)
|
||||||
|
R2_TABLE = np.array(
|
||||||
|
[
|
||||||
|
[4359.0, 5.7846, 6283.0758],
|
||||||
|
[124.0, 5.579, 12566.152],
|
||||||
|
[12.0, 3.14, 0.0],
|
||||||
|
[9.0, 3.63, 77713.77],
|
||||||
|
[6.0, 1.87, 5573.14],
|
||||||
|
[3.0, 5.47, 18849.23],
|
||||||
|
]
|
||||||
|
)
|
||||||
|
R3_TABLE = np.array([[145.0, 4.273, 6283.076], [7.0, 3.92, 12566.15]])
|
||||||
|
R4_TABLE = np.array([[4.0, 2.56, 6283.08]])
|
||||||
|
|
||||||
|
HELIO_R = [R0_TABLE, R1_TABLE, R2_TABLE, R3_TABLE, R4_TABLE]
|
||||||
|
|
||||||
|
# longitude and obliquity nutation coefficients
|
||||||
|
NUTATION_ABCD_ARRAY = np.array(
|
||||||
|
[
|
||||||
|
[-171996, -174.2, 92025, 8.9],
|
||||||
|
[-13187, -1.6, 5736, -3.1],
|
||||||
|
[-2274, -0.2, 977, -0.5],
|
||||||
|
[2062, 0.2, -895, 0.5],
|
||||||
|
[1426, -3.4, 54, -0.1],
|
||||||
|
[712, 0.1, -7, 0],
|
||||||
|
[-517, 1.2, 224, -0.6],
|
||||||
|
[-386, -0.4, 200, 0],
|
||||||
|
[-301, 0, 129, -0.1],
|
||||||
|
[217, -0.5, -95, 0.3],
|
||||||
|
[-158, 0, 0, 0],
|
||||||
|
[129, 0.1, -70, 0],
|
||||||
|
[123, 0, -53, 0],
|
||||||
|
[63, 0, 0, 0],
|
||||||
|
[63, 0.1, -33, 0],
|
||||||
|
[-59, 0, 26, 0],
|
||||||
|
[-58, -0.1, 32, 0],
|
||||||
|
[-51, 0, 27, 0],
|
||||||
|
[48, 0, 0, 0],
|
||||||
|
[46, 0, -24, 0],
|
||||||
|
[-38, 0, 16, 0],
|
||||||
|
[-31, 0, 13, 0],
|
||||||
|
[29, 0, 0, 0],
|
||||||
|
[29, 0, -12, 0],
|
||||||
|
[26, 0, 0, 0],
|
||||||
|
[-22, 0, 0, 0],
|
||||||
|
[21, 0, -10, 0],
|
||||||
|
[17, -0.1, 0, 0],
|
||||||
|
[16, 0, -8, 0],
|
||||||
|
[-16, 0.1, 7, 0],
|
||||||
|
[-15, 0, 9, 0],
|
||||||
|
[-13, 0, 7, 0],
|
||||||
|
[-12, 0, 6, 0],
|
||||||
|
[11, 0, 0, 0],
|
||||||
|
[-10, 0, 5, 0],
|
||||||
|
[-8, 0, 3, 0],
|
||||||
|
[7, 0, -3, 0],
|
||||||
|
[-7, 0, 0, 0],
|
||||||
|
[-7, 0, 3, 0],
|
||||||
|
[-7, 0, 3, 0],
|
||||||
|
[6, 0, 0, 0],
|
||||||
|
[6, 0, -3, 0],
|
||||||
|
[6, 0, -3, 0],
|
||||||
|
[-6, 0, 3, 0],
|
||||||
|
[-6, 0, 3, 0],
|
||||||
|
[5, 0, 0, 0],
|
||||||
|
[-5, 0, 3, 0],
|
||||||
|
[-5, 0, 3, 0],
|
||||||
|
[-5, 0, 3, 0],
|
||||||
|
[4, 0, 0, 0],
|
||||||
|
[4, 0, 0, 0],
|
||||||
|
[4, 0, 0, 0],
|
||||||
|
[-4, 0, 0, 0],
|
||||||
|
[-4, 0, 0, 0],
|
||||||
|
[-4, 0, 0, 0],
|
||||||
|
[3, 0, 0, 0],
|
||||||
|
[-3, 0, 0, 0],
|
||||||
|
[-3, 0, 0, 0],
|
||||||
|
[-3, 0, 0, 0],
|
||||||
|
[-3, 0, 0, 0],
|
||||||
|
[-3, 0, 0, 0],
|
||||||
|
[-3, 0, 0, 0],
|
||||||
|
[-3, 0, 0, 0],
|
||||||
|
]
|
||||||
|
)
|
||||||
|
|
||||||
|
NUTATION_YTERM_ARRAY = np.array(
|
||||||
|
[
|
||||||
|
[0, 0, 0, 0, 1],
|
||||||
|
[-2, 0, 0, 2, 2],
|
||||||
|
[0, 0, 0, 2, 2],
|
||||||
|
[0, 0, 0, 0, 2],
|
||||||
|
[0, 1, 0, 0, 0],
|
||||||
|
[0, 0, 1, 0, 0],
|
||||||
|
[-2, 1, 0, 2, 2],
|
||||||
|
[0, 0, 0, 2, 1],
|
||||||
|
[0, 0, 1, 2, 2],
|
||||||
|
[-2, -1, 0, 2, 2],
|
||||||
|
[-2, 0, 1, 0, 0],
|
||||||
|
[-2, 0, 0, 2, 1],
|
||||||
|
[0, 0, -1, 2, 2],
|
||||||
|
[2, 0, 0, 0, 0],
|
||||||
|
[0, 0, 1, 0, 1],
|
||||||
|
[2, 0, -1, 2, 2],
|
||||||
|
[0, 0, -1, 0, 1],
|
||||||
|
[0, 0, 1, 2, 1],
|
||||||
|
[-2, 0, 2, 0, 0],
|
||||||
|
[0, 0, -2, 2, 1],
|
||||||
|
[2, 0, 0, 2, 2],
|
||||||
|
[0, 0, 2, 2, 2],
|
||||||
|
[0, 0, 2, 0, 0],
|
||||||
|
[-2, 0, 1, 2, 2],
|
||||||
|
[0, 0, 0, 2, 0],
|
||||||
|
[-2, 0, 0, 2, 0],
|
||||||
|
[0, 0, -1, 2, 1],
|
||||||
|
[0, 2, 0, 0, 0],
|
||||||
|
[2, 0, -1, 0, 1],
|
||||||
|
[-2, 2, 0, 2, 2],
|
||||||
|
[0, 1, 0, 0, 1],
|
||||||
|
[-2, 0, 1, 0, 1],
|
||||||
|
[0, -1, 0, 0, 1],
|
||||||
|
[0, 0, 2, -2, 0],
|
||||||
|
[2, 0, -1, 2, 1],
|
||||||
|
[2, 0, 1, 2, 2],
|
||||||
|
[0, 1, 0, 2, 2],
|
||||||
|
[-2, 1, 1, 0, 0],
|
||||||
|
[0, -1, 0, 2, 2],
|
||||||
|
[2, 0, 0, 2, 1],
|
||||||
|
[2, 0, 1, 0, 0],
|
||||||
|
[-2, 0, 2, 2, 2],
|
||||||
|
[-2, 0, 1, 2, 1],
|
||||||
|
[2, 0, -2, 0, 1],
|
||||||
|
[2, 0, 0, 0, 1],
|
||||||
|
[0, -1, 1, 0, 0],
|
||||||
|
[-2, -1, 0, 2, 1],
|
||||||
|
[-2, 0, 0, 0, 1],
|
||||||
|
[0, 0, 2, 2, 1],
|
||||||
|
[-2, 0, 2, 0, 1],
|
||||||
|
[-2, 1, 0, 2, 1],
|
||||||
|
[0, 0, 1, -2, 0],
|
||||||
|
[-1, 0, 1, 0, 0],
|
||||||
|
[-2, 1, 0, 0, 0],
|
||||||
|
[1, 0, 0, 0, 0],
|
||||||
|
[0, 0, 1, 2, 0],
|
||||||
|
[0, 0, -2, 2, 2],
|
||||||
|
[-1, -1, 1, 0, 0],
|
||||||
|
[0, 1, 1, 0, 0],
|
||||||
|
[0, -1, 1, 2, 2],
|
||||||
|
[2, -1, -1, 2, 2],
|
||||||
|
[0, 0, 3, 2, 2],
|
||||||
|
[2, -1, 0, 2, 2],
|
||||||
|
]
|
||||||
|
)
|
||||||
|
# END COEFF
|
||||||
|
|
||||||
|
# now, we write to the actual code
|
||||||
|
|
||||||
|
DELTA_T = 67
|
||||||
|
|
||||||
|
|
||||||
|
@jit
|
||||||
|
def helio_vector(vec, jme):
|
||||||
|
"""This function calculates equation 9 across the vector"""
|
||||||
|
return np.sum(
|
||||||
|
vec[:, 0] * np.cos(vec[:, 1] + vec[:, 2] * jme[..., np.newaxis]), axis=-1
|
||||||
|
)
|
||||||
|
|
||||||
|
|
||||||
|
def solar_position(timestamp, latitude, longitude):
|
||||||
|
"""Calculate the position of the sun at a given location and time.
|
||||||
|
|
||||||
|
Args:
|
||||||
|
timestamp (array-like): The timestamp(s) to calculate.
|
||||||
|
|
||||||
|
Returns:
|
||||||
|
ndarray: An array containing the altitude and azimuth for each timestamp.
|
||||||
|
"""
|
||||||
|
timestamp = np.array(timestamp)
|
||||||
|
jd = timestamp / 86400.0 + 2440587.5
|
||||||
|
jc = (jd - 2451545) / 36525
|
||||||
|
|
||||||
|
jde = jd + DELTA_T / 86400.0
|
||||||
|
jce = (jde - 2451545) / 36525
|
||||||
|
|
||||||
|
jm = jc / 10
|
||||||
|
jme = jce / 10
|
||||||
|
|
||||||
|
# todo: make more elegant?
|
||||||
|
# TODO: vectorize later? it's kinda complex
|
||||||
|
|
||||||
|
# heliocentric longitude
|
||||||
|
l_rad = np.zeros_like(timestamp)
|
||||||
|
for idx, vec in enumerate(HELIO_L):
|
||||||
|
l_rad = l_rad + helio_vector(vec, jme) * jme**idx
|
||||||
|
|
||||||
|
l_rad = l_rad / 10e8
|
||||||
|
l_deg = np.rad2deg(l_rad) % 360
|
||||||
|
|
||||||
|
# heliocentric latitude
|
||||||
|
b_rad = np.zeros_like(timestamp)
|
||||||
|
for idx, vec in enumerate(HELIO_B):
|
||||||
|
b_rad = b_rad + helio_vector(vec, jme) * jme**idx
|
||||||
|
b_rad = b_rad / 10e8
|
||||||
|
b_deg = np.rad2deg(b_rad) % 360
|
||||||
|
|
||||||
|
# heliocentric radius
|
||||||
|
r_rad = np.zeros_like(timestamp)
|
||||||
|
for idx, vec in enumerate(HELIO_R):
|
||||||
|
r_rad = r_rad + helio_vector(vec, jme) * jme**idx
|
||||||
|
r_rad = r_rad / 10e8
|
||||||
|
r_deg = np.rad2deg(r_rad) % 360
|
||||||
|
|
||||||
|
theta = (l_deg + 180) % 360
|
||||||
|
beta = -1 * b_deg
|
||||||
|
|
||||||
|
def cubic_poly(a, b, c, d):
|
||||||
|
return a + b * jce + c * jce**2 + (jce**3) / d
|
||||||
|
|
||||||
|
X0 = cubic_poly(297.85036, 445267.111480, -0.0019142, 189474)
|
||||||
|
X1 = cubic_poly(357.52772, 35999.050340, -0.0001603, -300000)
|
||||||
|
X2 = cubic_poly(134.96298, 477198.867398, 0.0086972, 56250)
|
||||||
|
X3 = cubic_poly(93.27191, 483202.017538, -0.0036825, 327270)
|
||||||
|
X4 = cubic_poly(125.04452, 1934.136261, 0.0020708, 450000)
|
||||||
|
|
||||||
|
X = np.vstack([X0, X1, X2, X3, X4]).T
|
||||||
|
|
||||||
|
nut = NUTATION_ABCD_ARRAY
|
||||||
|
|
||||||
|
## TODO: these are gross - use loops instead of broadcasting?
|
||||||
|
d_psi = (nut[:, 0] + jce[..., np.newaxis] * nut[:, 1]) * np.sin(
|
||||||
|
np.sum(X[:, np.newaxis, :] * NUTATION_YTERM_ARRAY[np.newaxis, ...], axis=2)
|
||||||
|
)
|
||||||
|
d_psi = np.sum(d_psi, axis=-1) / 36, 000, 000
|
||||||
|
|
||||||
|
|
||||||
|
d_epsilon = (nut[:, 2] + jce[..., np.newaxis] * nut[:, 3]) * np.cos(
|
||||||
|
np.sum(X[:, np.newaxis, :] * NUTATION_YTERM_ARRAY[np.newaxis, ...], axis=2)
|
||||||
|
)
|
||||||
|
d_epsilon = np.sum(d_epsilon, axis=-1) / 36, 000, 000
|
||||||
|
|
||||||
|
u = jme[:, np.newaxis] / 10 * np.arange(0,10).reshape((1,-1))
|
||||||
|
epsilon_0 = np.array(
|
||||||
|
[
|
||||||
|
84381.448,
|
||||||
|
-4680.93,
|
||||||
|
1.55,
|
||||||
|
1999.25,
|
||||||
|
-51.38,
|
||||||
|
-249.67,
|
||||||
|
-39.05,
|
||||||
|
7.12,
|
||||||
|
27.87,
|
||||||
|
5.79,
|
||||||
|
2.45,
|
||||||
|
]
|
||||||
|
)
|
||||||
|
epsilon = np.sum(u * epsilon_0, axis=-1) / 3600 + d_epsilon
|
||||||
|
d_tau = -20.4898 / (3600 * r_deg)
|
||||||
|
sun_longitude = theta + d_psi + d_tau
|
||||||
|
|
||||||
Loading…
Reference in a new issue