{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Using Geodesics (Back-ends & Plotting)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "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": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Initial Conditions\n",
    "position = [4., np.pi / 3, 0.]\n",
    "momentum = [0., 0., -1.5]\n",
    "a = 0. # Schwarzschild Black Hole"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Calculating Geodesic"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Geodesic Object:(\n",
       "            Type : (Time-like),\n",
       "            Metric : (Schwarzschild),\n",
       "            Metric Parameters : ((0.0,)),\n",
       "            Initial 4-Position : ([0.         4.         1.04719755 0.        ]),\n",
       "            Initial 4-Momentum : ([-0.77055175  0.          0.         -1.5       ]),\n",
       "            Trajectory = (\n",
       "                (array([    0,     1,     2, ..., 15540, 15541, 15542]), array([[ 7.70551750e-04,  3.46410160e+00, -2.16506351e-04, ...,\n",
       "        -5.07812502e-05,  5.41265877e-05, -1.50000000e+00],\n",
       "       [ 1.54110350e-03,  3.46410157e+00, -4.33012700e-04, ...,\n",
       "        -1.01562501e-04,  1.08253176e-04, -1.50000000e+00],\n",
       "       [ 2.31165526e-03,  3.46410152e+00, -6.49519046e-04, ...,\n",
       "        -1.52343754e-04,  1.62379763e-04, -1.50000000e+00],\n",
       "       ...,\n",
       "       [ 2.10892615e+01,  5.06915642e-01, -1.93331152e+00, ...,\n",
       "        -7.67875285e+01,  8.37708122e-01, -1.50000000e+00],\n",
       "       [ 2.11285953e+01,  5.06465005e-01, -1.93307239e+00, ...,\n",
       "        -7.82825155e+01,  8.37749353e-01, -1.50000000e+00],\n",
       "       [ 2.11686915e+01,  5.06014321e-01, -1.93283308e+00, ...,\n",
       "        -7.98370238e+01,  8.37790569e-01, -1.50000000e+00]]))\n",
       "            ),\n",
       "            Output Position Coordinate System = (Cartesian)\n",
       "        ))"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "geod = Timelike(\n",
    "    metric = \"Schwarzschild\",\n",
    "    metric_params = (a,),\n",
    "    position=position,\n",
    "    momentum=momentum,\n",
    "    steps=15543, # As close as we can get before the integration becomes highly unstable\n",
    "    delta=0.0005,\n",
    "    return_cartesian=True,\n",
    "    omega=0.01, # Small omega values lead to more stable integration\n",
    "    suppress_warnings=True, # Uncomment to view the tolerance warning\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": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "gpl = GeodesicPlotter()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.plotly.v1+json": {
       "config": {
        "plotlyServerURL": "https://plot.ly"
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       "data": [
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         "name": "BH Event Horizon (Outer)",
         "opacity": 0.75,
         "showlegend": true,
         "showscale": false,
         "type": "surface",
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   "source": [
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   "source": [
    "gpl.clear()\n",
    "gpl.plot2D(geod, coordinates=(1, 3), color=\"green\", title=\"Face-On View\") # \"face-on\" view\n",
    "gpl.show()"
   ]
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Each interactive plot instance (`gpl`) has a `fig` attribute that is a `plotly.graph_objs._figure.Figure` object. So, one can easily make modifications to the plots as they would to any plotly figure. For instance, we can update the title to clarify that the plot above is showing a face-on view."
   ]
  },
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   "metadata": {},
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           "sequential": [
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             0,
             "#0d0887"
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             0.1111111111111111,
             "#46039f"
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            [
             0.2222222222222222,
             "#7201a8"
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             0.3333333333333333,
             "#9c179e"
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             "#bd3786"
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             0.8888888888888888,
             "#fdca26"
            ],
            [
             1,
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            ]
           ],
           "sequentialminus": [
            [
             0,
             "#0d0887"
            ],
            [
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             "#46039f"
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            [
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            [
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             "#fdca26"
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           ]
          },
          "colorway": [
           "#636efa",
           "#EF553B",
           "#00cc96",
           "#ab63fa",
           "#FFA15A",
           "#19d3f3",
           "#FF6692",
           "#B6E880",
           "#FF97FF",
           "#FECB52"
          ],
          "font": {
           "color": "#2a3f5f"
          },
          "geo": {
           "bgcolor": "white",
           "lakecolor": "white",
           "landcolor": "#E5ECF6",
           "showlakes": true,
           "showland": true,
           "subunitcolor": "white"
          },
          "hoverlabel": {
           "align": "left"
          },
          "hovermode": "closest",
          "mapbox": {
           "style": "light"
          },
          "paper_bgcolor": "white",
          "plot_bgcolor": "#E5ECF6",
          "polar": {
           "angularaxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           },
           "bgcolor": "#E5ECF6",
           "radialaxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           }
          },
          "scene": {
           "xaxis": {
            "backgroundcolor": "#E5ECF6",
            "gridcolor": "white",
            "gridwidth": 2,
            "linecolor": "white",
            "showbackground": true,
            "ticks": "",
            "zerolinecolor": "white"
           },
           "yaxis": {
            "backgroundcolor": "#E5ECF6",
            "gridcolor": "white",
            "gridwidth": 2,
            "linecolor": "white",
            "showbackground": true,
            "ticks": "",
            "zerolinecolor": "white"
           },
           "zaxis": {
            "backgroundcolor": "#E5ECF6",
            "gridcolor": "white",
            "gridwidth": 2,
            "linecolor": "white",
            "showbackground": true,
            "ticks": "",
            "zerolinecolor": "white"
           }
          },
          "shapedefaults": {
           "line": {
            "color": "#2a3f5f"
           }
          },
          "ternary": {
           "aaxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           },
           "baxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           },
           "bgcolor": "#E5ECF6",
           "caxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           }
          },
          "title": {
           "x": 0.05
          },
          "xaxis": {
           "automargin": true,
           "gridcolor": "white",
           "linecolor": "white",
           "ticks": "",
           "title": {
            "standoff": 15
           },
           "zerolinecolor": "white",
           "zerolinewidth": 2
          },
          "yaxis": {
           "automargin": true,
           "gridcolor": "white",
           "linecolor": "white",
           "ticks": "",
           "title": {
            "standoff": 15
           },
           "zerolinecolor": "white",
           "zerolinewidth": 2
          }
         }
        },
        "title": {
         "text": "Parametric Plot",
         "x": 0.46,
         "xanchor": "center",
         "y": 0.9,
         "yanchor": "top"
        },
        "xaxis": {
         "title": {
          "text": "Lambda (Affine Parameter)"
         }
        },
        "yaxis": {
         "title": {
          "text": "Coordinates"
         }
        }
       }
      }
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "gpl.clear()\n",
    "gpl.parametric_plot(geod, colors=(\"red\", \"green\", \"blue\"))\n",
    "gpl.show()"
   ]
  }
 ],
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