1 really simple fit.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# I need to do some interpolation\n",
    "\n",
    "This notebook shows how you can use [Sherpa](https://sherpa.readthedocs.io/) to do some\n",
    "simple interpolation after \"fitting\" your data. It is a fairly basic task but hopefully illustrates\n",
    "some of the basic components of Sherpa.\n",
    "\n",
    "As winter has finally arrived in New England$^*$, I've taken to making the kids porridge for breakfast.\n",
    "However, as shown below, the tabulated values for the amount of oatmeal and water (as we add milk\n",
    "to taste, rather than when cooking) don't cover every serving size. So far I have been \n",
    "winging it$^\\dagger$, but\n",
    "that seems rather un-scientific, so let's see what the power of science$^\\ddagger$ can do for me.\n",
    "\n",
    "$^*$ well, it had when I originally wrote the notebook\n",
    "\n",
    "$^\\dagger$ also known as piecewise linear interpolation\n",
    "\n",
    "$^\\ddagger$ well, really it's simple maths, but this doesn't sound so exciting"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Last run\n",
    "\n",
    "When was this notebook last run?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'2024-09-30 11:15'"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import datetime\n",
    "datetime.datetime.now().strftime(\"%Y-%m-%d %H:%M\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'4.17.0'"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# This will only work once Sherpa has been installed, which we haven't mentioned yet!\n",
    "import sherpa\n",
    "sherpa.__version__"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I want to include some inline plots, so need matplotlib enabled for the notebook. NumPy is also useful\n",
    "with Sherpa."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Setting up Sherpa\n",
    "\n",
    "For this notebook I am going to use CIAO 4.16 installed with conda (to match the\n",
    "myBinder environment). You can use the standalone version of Sherpa with the\n",
    "following:\n",
    "\n",
    "```\n",
    "% conda create -n sherpa-standalone-notebooks \\\n",
    "  -c https://cxc.cfa.harvard.edu/conda/ciao -c conda-forge \\\n",
    "  ciao pyciao sherpa ds9 ciao-contrib jupyterlab python=3.11\n",
    "...\n",
    "... a lot of text\n",
    "...\n",
    "#\n",
    "# To activate this environment, use\n",
    "#\n",
    "#     $ conda activate sherpa-notebooks\n",
    "#\n",
    "# To deactivate an active environment, use\n",
    "#\n",
    "#     $ conda deactivate\n",
    "\n",
    "% conda activate sherpa-standalone-notebooks\n",
    "```\n",
    "\n",
    "Note that this was all done before starting up the notebook, which can be done by cloning the repository:\n",
    "\n",
    "    % git clone https://github.com/DougBurke/sherpa-standalone-notebooks\n",
    "    % cd sherpa-standalone-notebooks\n",
    "    % jupyter lab\n",
    "\n",
    "and then selecting the \"really simple fit\" option on the web page this creates.\n",
    "\n",
    "## What is the data?\n",
    "\n",
    "Here's the tabulated values from the Oatmeal packaging:\n",
    "\n",
    "<table>\n",
    " <thead>\n",
    " <tr><th>Servings</th><th>Oatmeal (cups)</th><th>Water (cups)</th></tr>\n",
    " </thead>\n",
    " <tbody>\n",
    " <tr><td>1</td><td>0.5</td><td>1</td></tr>\n",
    " <tr><td>1.5</td><td>0.75</td><td>1.5</td></tr>\n",
    " <tr><td>2</td><td>1</td><td>1.75</td></tr>\n",
    " <tr><td>4</td><td>2</td><td>3.25</td></tr>\n",
    " <tr><td>8</td><td>4</td><td>6</td></tr>\n",
    " <tr><td>17</td><td>8</td><td>16</td></tr>\n",
    " </tbody>\n",
    "</table>\n",
    "\n",
    "Leaving aside the insanity of the use of cups as a sensible unit for\n",
    "cooking, which is a topic for another day, I want to calculate the amount\n",
    "of Oatmeal ($y_1$) and water ($y_2$) for a given serving size of porridge ($x$).\n",
    "\n",
    "This can be represented as three Python lists:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = [1, 1.5, 2, 4, 8, 17]\n",
    "y1 = [0.5, 0.75, 1, 2, 4, 8]\n",
    "y2 = [1, 1.5, 1.75, 3.25, 6, 16]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I expect these to be close to linear, but what do they really look like? Let's\n",
    "\"load\" them into Sherpa to find out. First I load up the main \"UI\" module for\n",
    "Sherpa (I have no need for the more complex routines in `sherpa.astro.ui` so\n",
    "can just use the `sherpa.ui` module):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sherpa import ui"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is okay if you see some warning messages here, as Sherpa supports a number of optional\n",
    "packages.\n",
    "\n",
    "Now the data can be loaded into Sherpa. As there's two datasets - $(x, y_1)$ and $(x, y_2)$ - I am\n",
    "going to use identifiers of `1` and `2` (and will be explicit in using these identifiers, even though\n",
    "many of the Sherpa functions will default to an identifier of `1` when not given):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "ui.load_arrays(1, x, y1)\n",
    "ui.load_arrays(2, x, y2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For this analysis I am going to ignore errors, which means use a least-square statistic when I fit, and\n",
    "turn off the error bars in the data and residual plots$\\dagger$:\n",
    "\n",
    "----\n",
    "\n",
    "$\\dagger$ the `get_plot_prefs` call is new in CIAO 4.16. In previous versions of this notebook I used `get_data_plot_prefs` and was\n",
    "not able to change the preferences for the residual plot."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "ui.set_stat('leastsq')\n",
    "ui.get_plot_prefs('data')['yerrorbars'] = False\n",
    "ui.get_plot_prefs('resid')['yerrorbars'] = False"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With these changes, I can display the data (the warning message can be ignored here, since we\n",
    "do not care about errors):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ui.plot_data(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ui.plot_data(2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So, they both look reasonably linear, although the second one less so. How do they compare?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ui.plot_data(1)\n",
    "ui.plot_data(2, overplot=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "My guess, from looking at this plot, is that the first dataset (the blue points) can be modelled by a\n",
    "staight line, whereas the second dataset (the green points) needs a quadratic.\n",
    "\n",
    "Sherpa has a `polynom1d` model to handle low-order polynomials. I am going to\n",
    "create an instance of this model and set it as the \"source\" model of the\n",
    "first dataset - i.e. use it to describe the data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "ui.set_source(1, ui.polynom1d.m1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This line did two things:\n",
    "\n",
    "1. the statement `ui.polynom1d.m1` created an instance of the `polynom1d` model called `m1`\n",
    "2. the `ui.set_source` call set this as the model to be fit to the first dataset (much more\n",
    "   complicated expressions can be used, but for this notebook a single component is all that\n",
    "   is needed).\n",
    "\n",
    "The `m1` component has a number of parameters, which can be displayed with a call to `print`\n",
    "or, as of the 4.12.2 release of Shera,you can display them directly in the Jupyter notebook:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "polynom1d.m1\n",
      "   Param        Type          Value          Min          Max      Units\n",
      "   -----        ----          -----          ---          ---      -----\n",
      "   m1.c0        thawed            1 -3.40282e+38  3.40282e+38           \n",
      "   m1.c1        frozen            0 -3.40282e+38  3.40282e+38           \n",
      "   m1.c2        frozen            0 -3.40282e+38  3.40282e+38           \n",
      "   m1.c3        frozen            0 -3.40282e+38  3.40282e+38           \n",
      "   m1.c4        frozen            0 -3.40282e+38  3.40282e+38           \n",
      "   m1.c5        frozen            0 -3.40282e+38  3.40282e+38           \n",
      "   m1.c6        frozen            0 -3.40282e+38  3.40282e+38           \n",
      "   m1.c7        frozen            0 -3.40282e+38  3.40282e+38           \n",
      "   m1.c8        frozen            0 -3.40282e+38  3.40282e+38           \n",
      "   m1.offset    frozen            0 -3.40282e+38  3.40282e+38           \n"
     ]
    }
   ],
   "source": [
    "print(m1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>/*\n",
       "Copyright (C) 2020  Smithsonian Astrophysical Observatory\n",
       "\n",
       "\n",
       " This program is free software; you can redistribute it and/or modify\n",
       " it under the terms of the GNU General Public License as published by\n",
       " the Free Software Foundation; either version 3 of the License, or\n",
       " (at your option) any later version.\n",
       "\n",
       " This program is distributed in the hope that it will be useful,\n",
       " but WITHOUT ANY WARRANTY; without even the implied warranty of\n",
       " MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n",
       " GNU General Public License for more details.\n",
       "\n",
       " You should have received a copy of the GNU General Public License along\n",
       " with this program; if not, write to the Free Software Foundation, Inc.,\n",
       " 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.\n",
       "\n",
       "*/\n",
       "\n",
       ":root {\n",
       "  --sherpa-border-color: var(--jp-border-color2, #e0e0e0);\n",
       "  --sherpa-background-color: var(--jp-layout-color0, white);\n",
       "  --sherpa-background-color-row-even: var(--jp-layout-color1, white);\n",
       "  --sherpa-background-color-row-odd: var(--jp-layout-color2, #eeeeee);\n",
       "\n",
       "  /* https://medium.com/ge-design/iot-cool-gray-is-a-great-background-color-for-data-visualization-ebf18c318418 */\n",
       "  --sherpa-background-color-dark1: #EBEFF2;\n",
       "  --sherpa-background-color-dark2: #D8E0E5;\n",
       "}\n",
       "\n",
       "div.sherpa-text-fallback {\n",
       "    display: none;\n",
       "}\n",
       "\n",
       "div.sherpa {\n",
       "    display: block;\n",
       "}\n",
       "\n",
       "div.sherpa details summary {\n",
       "    display: list-item;  /* needed for notebook, not lab */\n",
       "    font-size: larger;\n",
       "}\n",
       "\n",
       "div.sherpa details div.datavals {\n",
       "    display: grid;\n",
       "    grid-template-columns: 1fr 3fr;\n",
       "    column-gap: 0.5em;\n",
       "}\n",
       "\n",
       "div.sherpa div.dataname {\n",
       "    font-weight: bold;\n",
       "    border-right: 1px solid var(--sherpa-border-color);\n",
       "}\n",
       "\n",
       "div.sherpa div.dataval { }\n",
       "\n",
       "div.sherpa div.datavals div:nth-child(4n + 1) ,\n",
       "div.sherpa div.datavals div:nth-child(4n + 2) {\n",
       "    background: var(--sherpa-background-color-row-odd);\n",
       "}\n",
       "\n",
       "div.sherpa table.model tbody {\n",
       "    border-bottom: 1px solid var(--sherpa-border-color);\n",
       "}\n",
       "\n",
       "div.sherpa table.model tr.block {\n",
       "    border-top: 1px solid var(--sherpa-border-color);\n",
       "}\n",
       "\n",
       "div.sherpa table.model th.model-odd ,\n",
       "div.sherpa table.model th.model-even {\n",
       "    border-right: 1px solid var(--sherpa-border-color);\n",
       "}\n",
       "\n",
       "div.sherpa table.model th.model-odd {\n",
       "    background: var(--sherpa-background-color-dark1);\n",
       "}\n",
       "\n",
       "div.sherpa table.model th.model-even {\n",
       "    background: var(--sherpa-background-color-dark2);\n",
       "}\n",
       "\n",
       "div.sherpa .failed {\n",
       "    background: orange;\n",
       "    font-size: large;\n",
       "    padding: 1em;\n",
       "}\n",
       "</style><div class=\"sherpa-text-fallback\">&lt;Polynom1D model instance &#x27;polynom1d.m1&#x27;&gt;</div><div hidden class=\"sherpa\"><details open><summary>Model</summary><table class=\"model\"><caption>Expression: polynom1d.m1</caption><thead><tr><th>Component</th><th>Parameter</th><th>Thawed</th><th>Value</th><th>Min</th><th>Max</th><th>Units</th></tr></thead><tbody><tr><th class=\"model-odd\" scope=\"rowgroup\" rowspan=10>polynom1d.m1</th><td>c0</td><td><input disabled type=\"checkbox\" checked></input></td><td>1.0</td><td>-MAX</td><td>MAX</td><td></td></tr><tr><td>c1</td><td><input disabled type=\"checkbox\"></input></td><td>0.0</td><td>-MAX</td><td>MAX</td><td></td></tr><tr><td>c2</td><td><input disabled type=\"checkbox\"></input></td><td>0.0</td><td>-MAX</td><td>MAX</td><td></td></tr><tr><td>c3</td><td><input disabled type=\"checkbox\"></input></td><td>0.0</td><td>-MAX</td><td>MAX</td><td></td></tr><tr><td>c4</td><td><input disabled type=\"checkbox\"></input></td><td>0.0</td><td>-MAX</td><td>MAX</td><td></td></tr><tr><td>c5</td><td><input disabled type=\"checkbox\"></input></td><td>0.0</td><td>-MAX</td><td>MAX</td><td></td></tr><tr><td>c6</td><td><input disabled type=\"checkbox\"></input></td><td>0.0</td><td>-MAX</td><td>MAX</td><td></td></tr><tr><td>c7</td><td><input disabled type=\"checkbox\"></input></td><td>0.0</td><td>-MAX</td><td>MAX</td><td></td></tr><tr><td>c8</td><td><input disabled type=\"checkbox\"></input></td><td>0.0</td><td>-MAX</td><td>MAX</td><td></td></tr><tr><td>offset</td><td><input disabled type=\"checkbox\"></input></td><td>0.0</td><td>-MAX</td><td>MAX</td><td></td></tr></tbody></table></details></div>"
      ],
      "text/plain": [
       "<Polynom1D model instance 'polynom1d.m1'>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Parameters - e.g. `m1.c0` and `m1.c1` - control the model values, and their meaning depends\n",
    "on the model (in this case `polynom1d`). The model documentation - e.g. `help(m1)` - provides\n",
    "information on the model and its parameters, but this **must** be done on a model \"instance\",\n",
    "since using the model class (i.e. `ui.polynom1d`) does not provide anything useful.\n",
    "\n",
    "\n",
    "I am not going to include the help here, as it is quite long (since it also includes some standard Python documentation for classes), but it does tell me that the `polynom1d` model is defined as (assuming that $\\rm{offset} \\equiv 0$):\n",
    "\n",
    "$$y = \\sum_{i=0}^8 c_i x^i$$\n",
    "\n",
    "so `c0` is the intercept term and `c1` the slope for a straight line.\n",
    "\n",
    "The `type` column - which is either `frozen` or `thawed` (which seems quite apt as earlier today\n",
    "I was out shovelling snow) - indicates whether the parameter can be varied during a fit. In this\n",
    "case the model starts out with only the intercept term being free to be fit.\n",
    "\n",
    "With these parameter settings, the model evaluates to `1` for each point. The model can be\n",
    "displayed with a call to `ui.plot_model`, but that's not going to be particularly illuminating.\n",
    "It's a bit more interesting to compare the model to the data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ui.plot_fit(1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The parameters can be modified manually, such as adding a linear component to the model:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "m1.c1 = 1\n",
    "ui.plot_fit(1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "However, the whole point of using Sherpa is to get it to do the fit!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Dataset               = 1\n",
      "Method                = levmar\n",
      "Statistic             = leastsq\n",
      "Initial fit statistic = 143.312\n",
      "Final fit statistic   = 53.2188 at function evaluation 4\n",
      "Data points           = 6\n",
      "Degrees of freedom    = 5\n",
      "Change in statistic   = 90.0937\n",
      "   m1.c0          -2.875       +/- 0.408248    \n"
     ]
    }
   ],
   "source": [
    "ui.fit(1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The optimiser - in this case, one based on the Levenberg-Marquardt algorithm from \n",
    "[MINPACK](https://people.sc.fsu.edu/~jburkardt/f_src/minpack/minpack.html), although in this\n",
    "case most optimisers should work - has found the best-fit solution by minimising the\n",
    "least-squares distance between the data and model:\n",
    "\n",
    "$$\\sum_i (y_i - \\rm{model}_i)^2$$\n",
    "\n",
    "Hopefully it's a better fit; let's check:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ui.plot_fit(1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Oops, the only parameter fit was the intercept (`m1.c0`) because I had forgotten to \"thaw\" the slope parameter. This can actually be seen in the output of the `fit` command earlier, since:\n",
    "\n",
    "* only the `m1.c0` parameter value was displayed\n",
    "* the \"`Degrees of Freedom`\" was given as 5, and as there are only 6 data points this means that only one\n",
    "  parameter was fit.\n",
    "   \n",
    "Rectifying this mistake gives a better fit (both visually, and numerically since the fit statistic has\n",
    "changed from $\\sim 53$ to $\\sim 0.04$):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Dataset               = 1\n",
      "Method                = levmar\n",
      "Statistic             = leastsq\n",
      "Initial fit statistic = 53.2188\n",
      "Final fit statistic   = 0.0361154 at function evaluation 6\n",
      "Data points           = 6\n",
      "Degrees of freedom    = 4\n",
      "Change in statistic   = 53.1826\n",
      "   m1.c0          0.0851134    +/- 0.575695    \n",
      "   m1.c1          0.46983      +/- 0.0726992   \n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ui.thaw(m1.c1)\n",
    "ui.fit(1)\n",
    "ui.plot_fit(1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The residuals - defined as `data - model` - can be displayed using `ui.plot_resid`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ui.plot_resid(1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So, over this range, a linear model is only out by at most $\\sim 0.2$.\n",
    "\n",
    "Let's see how well a linear model does with the second dataset (the `ui.plot_fit_resid` call creates two plots; the top one the `fit` plot and the bottom one the `resid` one):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Dataset               = 2\n",
      "Method                = levmar\n",
      "Statistic             = leastsq\n",
      "Initial fit statistic = 255.875\n",
      "Final fit statistic   = 1.89763 at function evaluation 6\n",
      "Data points           = 6\n",
      "Degrees of freedom    = 4\n",
      "Change in statistic   = 253.977\n",
      "   m2.c0          -0.248624    +/- 0.575695    \n",
      "   m2.c1          0.925127     +/- 0.0726992   \n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ui.set_source(2, ui.polynom1d.m2)\n",
    "# I could have said ui.thaw(m2.c1), but the parameter attributes can also be changed directly\n",
    "m2.c1.frozen = False\n",
    "ui.fit(2)\n",
    "ui.plot_fit_resid(2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So, the residuals look a little bigger here, about $\\sim 1$. Let's check, this time calculating the residuals rather than using `ui.get_resid_plot`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "resid2 = np.asarray(y2) - m2(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The model - in this case `m2` - when given an array will return an array of values of the model evaluated at\n",
    "these points. I used this to create the `resid2` array, which has a minimum and maximum of:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-1.1523893415533468"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "resid2.min()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5214710416238386"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "resid2.max()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "An obvious question is does a quadratic model give a better approximation than the linear model for this data set? To make it easy to compare, I add a third dataset, and fit a quadratic model to it:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Dataset               = 3\n",
      "Method                = levmar\n",
      "Statistic             = leastsq\n",
      "Initial fit statistic = 255.875\n",
      "Final fit statistic   = 0.108069 at function evaluation 8\n",
      "Data points           = 6\n",
      "Degrees of freedom    = 3\n",
      "Change in statistic   = 255.767\n",
      "   m3.c0          0.64415      +/- 0.881369    \n",
      "   m3.c1          0.498841     +/- 0.326848    \n",
      "   m3.c2          0.0237181    +/- 0.0177299   \n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ui.load_arrays(3, x, y2)\n",
    "ui.set_source(3, ui.polynom1d.m3)\n",
    "ui.thaw(m3.c0, m3.c1, m3.c2)  # thaw can be applied to multiple parameters\n",
    "ui.fit(3)\n",
    "ui.plot_fit_resid(3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As expected, the residuals are smaller, but how do the models compare visually?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ui.plot_data(2)\n",
    "ui.plot_source(2, overplot=True)\n",
    "ui.plot_source(3, overplot=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I could add extra terms to the polynomial, or a different model, but I think that we have what we need.\n",
    "I can wrap the models up in a simple function to display the interpolated (i.e. model) values for a given\n",
    "number of servings by calling the models with a single-element array. The only slightly-tricky thing to\n",
    "remember is to make sure the input array has a floating-point type, otherwise the output will be in\n",
    "integer format."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "def ingredients(nservings):\n",
    "    \"\"\"How much oatmeal and water do I need?\n",
    "    \n",
    "    Parameters\n",
    "    ----------\n",
    "    nservings: int\n",
    "        The number of servings\n",
    "        \n",
    "    Returns\n",
    "    -------\n",
    "    (oatmeal, water_lin, water_quad)\n",
    "        The number of cups of oatmeal and water. The water values are\n",
    "        calculated using a linear and quadratic approximation respectively.\n",
    "    \"\"\"\n",
    "    \n",
    "    x = [nservings * 1.0]\n",
    "    oats = m1(x)[0]\n",
    "    water_l = m2(x)[0]\n",
    "    water_q = m3(x)[0]\n",
    "    return {'oats': oats, 'water (linear)': water_l, 'water (quadratic)': water_q}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With this, I can now happily cook breakfast for the kids! The only decision - other than how many dried cranberries\n",
    "to add to the mix - is whether to use the linear or quadratic version!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'oats': 0.5549438449680721,\n",
       " 'water (linear)': 0.6765029729133807,\n",
       " 'water (quadratic)': 1.1667091967194232}"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ingredients(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'oats': 1.4946047126187016,\n",
       " 'water (linear)': 2.526756221096228,\n",
       " 'water (quadratic)': 2.354135374844933}"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ingredients(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'oats': 1.9644351464440164,\n",
       " 'water (linear)': 3.4518828451876518,\n",
       " 'water (quadratic)': 3.0190027563625113}"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ingredients(4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# NO WARRANTY IS PROVIDED OR IMPLIED\n",
    "\n",
    "Please note that no warrant is provided with this work. I take no responsibilty if using these\n",
    "values leads to an inedible breakfast situation. Or a porridge explosion."
   ]
  }
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