{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# uncertainties\n",
    "\n",
    "see: https://uncertainties-python-package.readthedocs.io/en/latest/"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from uncertainties import ufloat\n",
    "import uncertainties.umath as umath\n",
    "import uncertainties.unumpy as unp\n",
    "import numpy as np\n",
    "from smpl import io"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Single number"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = ufloat(1,0.1)\n",
    "print(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "print(x*x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is error propagation of the function $f(x)=x^2$ yielding $\\Delta f = \\frac{\\partial f(x)}{\\partial x} \\Delta x=2\\Delta x$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "y = ufloat(1,0.2)\n",
    "print(x*y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here $f(x,y)=x*y$ gives $\\Delta f = \\sqrt{(\\frac{\\partial f(x)}{\\partial x} \\Delta x)^2 +(\\frac{\\partial f(y)}{\\partial y} \\Delta y)^2}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "umath.sin(2*y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Arrays"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = np.loadtxt(io.find_file('test_linear_data.txt',3))\n",
    "xdata = data[:,0]\n",
    "xerr = data[:,2]\n",
    "ydata = data[:,1]\n",
    "yerr = data[:,3]\n",
    "x = unp.uarray(xdata,xerr)\n",
    "y = unp.uarray(ydata,yerr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "print(x)\n",
    "print(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "print(x*y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Error propagation for each number in the array."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "print(unp.sin(x)*y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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