{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Using Geodesics (Back-ends & Plotting)\n", "### Importing required modules\n", "\n", "**Note that, for the Julia backend to work, you should have `einsteinpy_geodesics` installed, along with its dependencies (e.g. `julia`). Read more [here](https://github.com/einsteinpy/einsteinpy-geodesics/#requirements).**" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "\n", "from einsteinpy.geodesic import Geodesic, Timelike, Nulllike\n", "from einsteinpy.plotting import GeodesicPlotter, StaticGeodesicPlotter, InteractiveGeodesicPlotter" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 1: Exploring Schwarzschild Time-like Spiral Capture, using Python Backend and GeodesicPlotter\n", "\n", "### Defining initial conditions" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "# Initial Conditions\n", "position = [2.15, np.pi / 2, 0.]\n", "momentum = [0., 0., -1.5]\n", "a = 0. # Schwarzschild Black Hole\n", "end_lambda = 10.\n", "step_size = 0.005\n", "return_cartesian = True\n", "time_like = True\n", "julia = False # Using Python" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Calculating Geodesic" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "e:\\coding\\gsoc\\github repos\\myfork\\einsteinpy\\src\\einsteinpy\\geodesic\\geodesic.py:136: RuntimeWarning:\n", "\n", "\n", " Using Python backend to solve the system. This backend is currently in beta and the\n", " solver may not be stable for certain sets of conditions, e.g. long simulations\n", " (`end_lambda > 50.`) or high initial radial distances (`position[0] > ~5.`).\n", " In these cases or if the output does not seem accurate, it is highly recommended to\n", " switch to the Julia backend, by setting `julia=True`, in the constructor call.\n", " \n", "\n" ] }, { "data": { "text/plain": [ "Geodesic Object:\n", " Type = (Time-like),\n", " Position = ([2.15, 1.5707963267948966, 0.0]),\n", " Momentum = ([0.0, 0.0, -1.5]),\n", " Spin Parameter = (0.0)\n", " Solver details = (\n", " Backend = (Python)\n", " Step-size = (0.005),\n", " End-Lambda = (10.0)\n", " Trajectory = (\n", " (array([0.000e+00, 5.000e-03, 1.000e-02, ..., 9.990e+00, 9.995e+00,\n", " 1.000e+01]), array([[ 2.15000000e+00, 0.00000000e+00, 1.31649531e-16,\n", " 0.00000000e+00, 0.00000000e+00, -1.50000000e+00],\n", " [ 2.14999615e+00, -1.61252735e-02, 1.31652998e-16,\n", " 2.26452642e-02, 1.49020159e-19, -1.50000000e+00],\n", " [ 2.14998455e+00, -3.22521873e-02, 1.31663397e-16,\n", " 4.52748906e-02, 2.98024624e-19, -1.50000000e+00],\n", " ...,\n", " [-1.08571331e+01, -9.57951275e+00, 8.86589316e-16,\n", " 1.14573395e+00, 4.59929900e-17, -1.50000000e+00],\n", " [-1.09329973e+01, -9.50157334e+00, 8.86940089e-16,\n", " 1.14568933e+00, 4.59962746e-17, -1.50000000e+00],\n", " [-1.10083027e+01, -9.42303446e+00, 8.87290849e-16,\n", " 1.14564476e+00, 4.59995565e-17, -1.50000000e+00]]))\n", " ),\n", " Output Position Coordinate System = (Cartesian)\n", " )" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "geod = Geodesic(\n", " position=position,\n", " momentum=momentum,\n", " a=a,\n", " end_lambda=end_lambda,\n", " step_size=step_size,\n", " time_like=time_like, # Necessary to switch between Time-like and Null-like Geodesics, while using `Geodesic`\n", " return_cartesian=return_cartesian,\n", " julia=julia\n", ")\n", "\n", "geod" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Plotting using `GeodesicPlotter`\n", "\n", "Note that, `GeodesicPlotter` automatically switches between \"Static\" and \"Interactive\" plots. Since, we are in a Jupyter Notebook or Interactive Environment, it uses the \"Interactive\" backend." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "gpl = GeodesicPlotter()" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/html": [ " \n", " " ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "colorscale": [ [ 0, "#000" ], [ 1, "#000" ] ], "name": "BH Event Horizon (Outer)", "opacity": 0.75, "showlegend": true, "showscale": false, "type": "surface", "x": [ [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0.12814043996142582, 0.12708840872065935, 0.12394958932224837, 0.11877552109393741, 0.11165116209299053, 0.10269349409723973, 0.09204960176752713, 0.07989425752164034, 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