{
 "cells": [
  {
   "cell_type": "markdown",
   "source": [
    "Building a declination table\n",
    "============================"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "source": [
    "from kanon.units import Sexagesimal\n",
    "from kanon.units.precision import set_precision, get_context, TruncatureMode\n",
    "from kanon.tables import HTable\n",
    "from kanon.tables.htable import join_multiple\n",
    "import math\n",
    "\n",
    "# For these calculations we will round after every operations.\n",
    "\n",
    "get_context().mutate(tmode=TruncatureMode.ROUND)"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "source": [
    "OBLIQUITY = \"23;51,20\""
   ],
   "outputs": [],
   "metadata": {
    "tags": [
     "parameters"
    ]
   }
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "source": [
    "# We construct a table of sine from 0 to 90.\n",
    "x = list(Sexagesimal.range(91))\n",
    "y = [round(Sexagesimal.from_float(math.sin(math.radians(n)), 3)) for n in x]\n",
    "sin_table = HTable([x, y], names=(\"Arg\", \"Val\"), index=\"Arg\")\n",
    "\n",
    "sin_table"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "source": [
    "# We apply a multiplication on all the sine values to get obl_table = Sin(x) * obl\n",
    "\n",
    "obl = sin_table.get(Sexagesimal(OBLIQUITY))\n",
    "\n",
    "obl_table = sin_table.apply(\"Val\", lambda x: x * obl)\n",
    "obl_table\n"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "source": [
    "# Arcsin is sin_table taken from Val to Arg instead of Arg to Val.\n",
    "\n",
    "arcsin_table = sin_table.copy(set_index=\"Val\")\n",
    "\n",
    "# For example, if we want arcsin(0.3) :\n",
    "\n",
    "arcsin_table.get(0.3)\n"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "source": [
    "# Finally, we apply arcsin_table.get on every obl_table values to find decl_table = arcsin(obl_table)\n",
    "\n",
    "decl_table = obl_table.apply(\"Val\", arcsin_table.get)\n",
    "decl_table"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "source": [
    "# Let's make the same calculation with an interpolated sine table.\n",
    "\n",
    "# First, extract every 12th row until the 60th then every 6th.\n",
    "\n",
    "sin_table_grid = sin_table[\n",
    "    [i for i in range(91) if i <= 60 and i % 12 == 0 or i > 60 and i % 6 == 0]\n",
    "]\n",
    "\n",
    "sin_table_grid"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "source": [
    "# We can populate it with its interpolation method (linear by default).\n",
    "\n",
    "sin_table_pop_linear = sin_table_grid.populate(list(Sexagesimal.range(91)), method=\"interpolate\")\n",
    "\n",
    "sin_table_pop_linear"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "source": [
    "# You can use other types of interpolation, for example a quadratic interpolation.\n",
    "\n",
    "from kanon.tables.interpolations import quadratic_interpolation\n",
    "\n",
    "sin_table_grid.interpolate = quadratic_interpolation\n",
    "\n",
    "# This interpolation method needs a higher precision to avoid weird results.\n",
    "with set_precision(pmode=5):\n",
    "    sin_table_pop_quadratic = sin_table_grid.populate(list(Sexagesimal.range(91)), method=\"interpolate\")\n",
    "\n",
    "sin_table_pop_quadratic"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "source": [
    "# Another type of interpolation can come from filling a interpolation grid made from populate\n",
    "# With this you can use methods interpolating the whole table at once, like euclidean distribution interpolations\n",
    "\n",
    "sin_table_pop_euclidean = sin_table_grid.populate(list(Sexagesimal.range(91)))\n",
    "sin_table_pop_euclidean = sin_table_pop_euclidean.fill(\"distributed_convex\")\n",
    "\n",
    "sin_table_pop_euclidean"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "source": [
    "# Comparing the 2nd difference between the true sine table and the interpolated ones.\n",
    "\n",
    "true_2diff = sin_table.diff(n=2, new_name=\"True Sine 2-diff\")\n",
    "interpolated_linear_2diff = sin_table_pop_linear.diff(n=2, new_name=\"Linear Sine 2-diff\")\n",
    "interpolated_quadratic_2diff = sin_table_pop_quadratic.diff(n=2, new_name=\"Quadratic Sine 2-diff\")\n",
    "interpolated_euclidean_2diff = sin_table_pop_euclidean.diff(n=2, new_name=\"Distributed Sine 2-diff\")\n",
    "\n",
    "# Now we have 4 tables with the same arguments. We can compare them side to side by joining them.\n",
    "\n",
    "join_multiple(true_2diff, interpolated_linear_2diff, interpolated_quadratic_2diff, interpolated_euclidean_2diff)"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "source": [
    "# With this newly built table we are able to construct a new declination table.\n",
    "\n",
    "obl_linear = sin_table_pop_linear.get(Sexagesimal(OBLIQUITY))\n",
    "\n",
    "obl_table_linear = sin_table_pop_linear.apply(\"Val\", lambda x: x * obl)\n",
    "arcsin_table_linear = sin_table_pop_linear.copy(set_index=\"Val\")\n",
    "\n",
    "obl_table_linear.apply(\"Val\", arcsin_table_linear.get)"
   ],
   "outputs": [],
   "metadata": {}
  }
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