HIP101905-check.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.optimize import least_squares, curve_fit\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "tc = np.array([953,\n",
    "1327,\n",
    "1641,\n",
    "1302,\n",
    "1505,\n",
    "1647,\n",
    "1573,\n",
    "1427,\n",
    "1291,\n",
    "1150,\n",
    "1347,\n",
    "1348,\n",
    "1033,\n",
    "1328,\n",
    "1455,\n",
    "1647,\n",
    "1736,\n",
    "1447,\n",
    "1570,\n",
    "1477,\n",
    "1574,\n",
    "1594,\n",
    "1580,\n",
    "1347,\n",
    "1647,\n",
    "1647], dtype=np.float64)\n",
    "\n",
    "ab = np.array([-0.005,\n",
    "0.062,\n",
    "0.054,\n",
    "0.063,\n",
    "0.112,\n",
    "0.08,\n",
    "0.097,\n",
    "0.093,\n",
    "0.084,\n",
    "0.042,\n",
    "0.05,\n",
    "0.05,\n",
    "0.003,\n",
    "0.09,\n",
    "0.19,\n",
    "0.17,\n",
    "0.17,\n",
    "0.23,\n",
    "0.19,\n",
    "0.21,\n",
    "0.18,\n",
    "0.22,\n",
    "0.14,\n",
    "0.16,\n",
    "0.14,\n",
    "0.15])\n",
    "\n",
    "err = np.array([0.012, 0.008, 0.002, 0.004, 0.005, 0.017, \n",
    "       0.013, 0.009, 0.016, 0.006, 0.005, 0.005, \n",
    "       0.031, 0.004, 0.006, 0.011, 0.01, 0.01,\n",
    "       0.031, 0.012, 0.014, 0.01, 0.021, 0.014, \n",
    "       0.006, 0.066])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### least-squares fit without uncertainties:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def resid(par, x, y):\n",
    "    \"\"\"residuals of linear fit\"\"\"  \n",
    "    m, b = par\n",
    "    return y - (m*x + b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "soln = least_squares(resid, [0.,0.], args=(tc, ab))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "best-fit slope is: 2.20e-04\n"
     ]
    }
   ],
   "source": [
    "print('best-fit slope is: {0:.2e}'.format(soln['x'][0]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(tc, ab)\n",
    "xx = np.linspace(min(tc), max(tc), 100)\n",
    "plt.plot(xx, soln['x'][0]*xx + soln['x'][1], c='orange')\n",
    "plt.xlabel(r'T$_c$')\n",
    "plt.ylabel(r'[X/H]');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### least-squares fit with uncertainties:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def chi(par, x, y, yerr):\n",
    "    \"\"\"error-weighted residuals of linear fit\"\"\"  \n",
    "    r = resid(par, x, y)\n",
    "    return r/yerr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "soln = least_squares(chi, [0., 0.], args=(tc, ab, err))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "best-fit slope is: 4.23e-05\n"
     ]
    }
   ],
   "source": [
    "print('best-fit slope is: {0:.2e}'.format(soln['x'][0]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.errorbar(tc, ab, err, fmt='o', ls='')\n",
    "xx = np.linspace(min(tc), max(tc), 100)\n",
    "plt.plot(xx, soln['x'][0]*xx + soln['x'][1], c='orange')\n",
    "plt.xlabel(r'T$_c$')\n",
    "plt.ylabel(r'[X/H]');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### checking with linear algebra:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "Y = np.copy(ab)\n",
    "A = np.ones((len(ab),2))\n",
    "A[:,0] = tc\n",
    "Cinv = np.diag(1./err**2) # sorry Hogg"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "ACA = np.dot(A.T, np.dot(Cinv, A))\n",
    "ACY = np.dot(A.T, np.dot(Cinv, Y))\n",
    "soln = np.linalg.solve(ACA, ACY)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "best-fit slope is: 4.23e-05\n"
     ]
    }
   ],
   "source": [
    "print('best-fit slope is: {0:.2e}'.format(soln[0]))"
   ]
  }
 ],
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