{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from chempy.units import default_units as u\n",
    "from chempy.util.regression import least_squares, plot_fit, irls, plot_least_squares_fit, least_squares_units\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "help(least_squares)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = [0, 1, 2, 3, 4+1e-9]\n",
    "y = [3, 3.8, 5.2, 5.2, 10.8]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Simple OLS with plotting:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "res = least_squares(x, y)\n",
    "plot_least_squares_fit(x, y, res)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Iterative least squares:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "res_irls = irls(x, y, irls.gaussian, itermax=20)\n",
    "plot_least_squares_fit(x, y, res_irls)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "y*u.m"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "res_units = least_squares_units(x*u.s, y*u.m)\n",
    "#plot_least_squares(x*u.s, y*u.m, res_units, x_unit=u.s, y_unit=u.m)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "res_units"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "err = [.1, .2, .2, .8, 3]*u.m\n",
    "res_weighted = least_squares_units(x*u.s, y*u.m, err**-2)\n",
    "plot_least_squares_fit(x*u.s, y*u.m, res_weighted, err, x_unit=u.s, y_unit=u.m)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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