timing.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Timing of Passing Variance and Standard Deviation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "using LsqFit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "500-element Array{Float64,1}:\n",
       " -0.0118268  \n",
       " -0.00898858 \n",
       "  0.0350296  \n",
       "  0.024487   \n",
       " -0.0115987  \n",
       " -0.0550782  \n",
       " -0.00132984 \n",
       "  0.11274    \n",
       " -0.0046853  \n",
       " -0.000245233\n",
       "  0.123724   \n",
       " -0.203811   \n",
       "  0.0135445  \n",
       "  ⋮          \n",
       " -0.245624   \n",
       " -0.649134   \n",
       " -2.10216    \n",
       "  1.60312    \n",
       " -1.78739    \n",
       "  2.14365    \n",
       " -4.17214    \n",
       "  4.63409    \n",
       "  0.268578   \n",
       "  7.51552    \n",
       "  2.61642    \n",
       " -3.60903    "
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model(t, p) = p[1] * exp.(-p[2] * t)\n",
    "tdata = linspace(0,50,500)\n",
    "ydata = model(tdata, [1.0, 2.0]) + 0.1.*tdata.*randn(length(tdata))\n",
    "p0 = [0.5, 0.5]\n",
    "fit = curve_fit(model, tdata, ydata, p0)\n",
    "r = fit.resid"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  0.597241 seconds (386.06 k allocations: 20.982 MiB, 1.25% gc time)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "2×2 Array{Float64,2}:\n",
       " 8.75331e-8  9.97119e-8\n",
       " 9.97119e-8  1.19886e-7"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function pass_std(r, p0, tdata, ydata)\n",
    "    std_error = abs.(r)\n",
    "    sqrt_wt = 1./std_error\n",
    "    f(p) = sqrt_wt .* ( model(tdata, p) - ydata )\n",
    "    wt = sqrt_wt.^2\n",
    "    fit = LsqFit.lmfit(f, p0, wt)\n",
    "    estimate_covar(fit)\n",
    "end\n",
    "@time pass_std(r, p0, tdata, ydata)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  1.169573 seconds (1.45 M allocations: 77.075 MiB, 1.72% gc time)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "2×2 Array{Float64,2}:\n",
       " 3.08189e-10  3.42388e-10\n",
       " 3.42388e-10  3.80553e-10"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# make sure you've restarted the kernel\n",
    "function pass_var(r, p0)\n",
    "    var_error =r.^2\n",
    "    wt = 1./var_error\n",
    "    sqrt_wt = sqrt.(wt)\n",
    "    f(p) = sqrt_wt .* ( model(tdata, p) - ydata ) \n",
    "    fit = LsqFit.lmfit(f, p0, wt)\n",
    "    estimate_covar(fit)\n",
    "end\n",
    "@time pass_var(r, p0)"
   ]
  }
 ],
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