{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "<!--HEADER-->\n",
    "[*NBBinder test on a collection of notebooks about some thermodynamic properperties of water*](https://github.com/rmsrosa/nbbinder)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "<!--BADGES-->\n",
    "<a href=\"https://colab.research.google.com/github/rmsrosa/nbbinder/blob/master/tests/nb_builds/nb_water/04.00-High_Dim_Fittings.ipynb\"><img align=\"left\" src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open in Google Colab\" title=\"Open in Google Colab\"></a><a href=\"https://mybinder.org/v2/gh/rmsrosa/nbbinder/master?filepath=tests/nb_builds/nb_water/04.00-High_Dim_Fittings.ipynb\"><img align=\"left\" src=\"https://mybinder.org/badge.svg\" alt=\"Open in binder\" title=\"Open in binder\"></a><a href=\"https://nbviewer.jupyter.org/github/rmsrosa/nbbinder/blob/master/tests/nb_builds/nb_water/04.00-High_Dim_Fittings.ipynb\"><img align=\"left\" src=\"https://img.shields.io/badge/view%20in-nbviewer-orange\" alt=\"View in NBViewer\" title=\"View in NBViewer\"></a><a href=\"https://nbviewer.jupyter.org/github/rmsrosa/nbbinder/blob/master/tests/nb_builds/nb_water_slides/04.00-High_Dim_Fittings.slides.html\"><img align=\"left\" src=\"https://img.shields.io/badge/view-slides-darkgreen\" alt=\"View Slides\" title=\"View Slides\"></a>&nbsp;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "<!--NAVIGATOR-->\n",
    "[<- Low-Dimensional Fittings](03.00-Low_Dim_Fittings.ipynb) | [Water Contents](00.00-Water_Contents.ipynb) | [References](BA.00-References.ipynb) | [Choosing the Best Fit with AIC ->](05.00-Best_AIC_Fitting.ipynb)\n",
    "\n",
    "---\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# High-Dimensional Fittings\n",
    "\n",
    "Now we fit higher degree polynomials to the data and compare the results and errors."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "## Importing the libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "import csv\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Loading the data\n",
    "\n",
    "We load the data and define the header and the respective vectors with the temperature and with the density values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "water_csv = list(csv.reader(open('water.csv',\"r\"), delimiter=\",\"))\n",
    "header = dict([(water_csv[0][i],water_csv[1][i]) for i in range(3)])\n",
    "T, f = np.loadtxt(open('water.csv', \"r\"), delimiter=\",\", skiprows=2, usecols=(0,1), unpack=True)\n",
    "N = len(T)\n",
    "N_half = int(N/2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### The Vandermonde matrices\n",
    "\n",
    "We build a number of Vandermonde matrices, up to the number of data points available."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "A = list()\n",
    "for j in range(N_half):\n",
    "    A.append(np.vstack([T**i for i in range(j+1)]).T)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Solving the least-square problems"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "a = list()\n",
    "for j in range(N_half):\n",
    "    a.append(np.linalg.lstsq(A[j], f, rcond=None)[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Building the approximating polynomials"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "p = list()\n",
    "for j in range(N_half):\n",
    "    p.append(np.array(sum([a[j][i]*T**i for i in range(j+1)])))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Plotting the approximations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,5))\n",
    "plt.plot(T, f, 'o', label='Data', color='tab:blue')\n",
    "for j in range(N_half):\n",
    "    plt.plot(T, p[j], label=f'degree {j}')\n",
    "plt.title('Plot of the data and of the polynomial approximations', fontsize=14)\n",
    "plt.xlabel(header['temp'], fontsize=12)\n",
    "plt.ylabel(header['density'], fontsize=12) \n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Calculating the mean quadratic errors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "j=0: Error=1.75e-04\n",
      "j=1: Error=9.22e-06\n",
      "j=2: Error=1.33e-07\n",
      "j=3: Error=3.16e-09\n",
      "j=4: Error=3.27e-10\n",
      "j=5: Error=2.64e-10\n",
      "j=6: Error=2.64e-10\n"
     ]
    }
   ],
   "source": [
    "Err = list()\n",
    "for j in range(N_half):\n",
    "    Err.append(np.linalg.lstsq(A[j], f, rcond=None)[1][0]/N)\n",
    "    print(f'j={j}: Error={Err[j]:.2e}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Plotting the mean quadratic errors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,5))\n",
    "\n",
    "plt.plot(range(len(Err)), Err, 'o', color='tab:red', markersize=10)\n",
    "plt.grid(True)\n",
    "plt.yscale('log')\n",
    "plt.ylim(10**(-10), 10**(-3))\n",
    "plt.title('Mean quadratic error in terms of the degree of the approximating polynomial', fontsize=14)\n",
    "plt.xlabel('degree', fontsize=12)\n",
    "plt.ylabel('error', fontsize=12)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Notice how there is not much advantage going beyond degree four."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<!--NAVIGATOR-->\n",
    "\n",
    "---\n",
    "[<- Low-Dimensional Fittings](03.00-Low_Dim_Fittings.ipynb) | [Water Contents](00.00-Water_Contents.ipynb) | [References](BA.00-References.ipynb) | [Choosing the Best Fit with AIC ->](05.00-Best_AIC_Fitting.ipynb)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}