julia/julia-first-steps.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "# Julia – a modern approach to scientific computing\n",
    "\n",
    "![](julia-logo-325-by-225.png)\n",
    "\n",
    "https://www.julialang.org\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "Evaluate the following cell by selecting it and then hit Shift+Return. Watch the top right status indicator of the Jupyter Notebook kernel to have started up Julia. The result will appear below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 1,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "1 + 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "Check the version of Julia you're currently running:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "v\"1.5.0\""
      ]
     },
     "execution_count": 3,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "VERSION"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "Vectors and matrices have a simple syntax. Notice, that the `'` means to transpose this vector."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3×1 LinearAlgebra.Adjoint{Float64,Array{Float64,2}}:\n",
       "  1.0\n",
       "  4.4\n",
       " -9.0"
      ]
     },
     "execution_count": 4,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b = [1 4.4 -9]'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3×3 Array{Float64,2}:\n",
       "  1.0  9.0   1.0\n",
       "  0.0  1.0   0.0\n",
       " -1.1  0.0  -1.0"
      ]
     },
     "execution_count": 5,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = [  1   9   1\n",
    "       0   1   0\n",
    "    -1.1   0  -1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "… and here we solve this as a linear system of equations: $A \\cdot x = b$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3×1 Array{Float64,2}:\n",
       "  475.9999999999999\n",
       "    4.400000000000001\n",
       " -514.5999999999999"
      ]
     },
     "execution_count": 6,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = A \\ b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3×1 Array{Float64,2}:\n",
       "  1.0\n",
       "  4.400000000000001\n",
       " -9.0"
      ]
     },
     "execution_count": 7,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A * x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "## Batman Curve\n",
    "\n",
    "Transcribed from _Julia: A Fast Language for Numerical Computing_,\n",
    "by Alan Edelman,  \n",
    "[SIAM News, Volume 49 | Number 02 | March 2016](https://sinews.siam.org/Details-Page/julia-a-fast-language-for-numerical-computing-1)\n",
    "\n",
    "![](batman-demo-300.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "┌ Info: Precompiling PyPlot [d330b81b-6aea-500a-939a-2ce795aea3ee]\n",
      "└ @ Base loading.jl:1278\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "execution_count": 8,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Matplotlib is building the font cache; this may take a moment.\n"
     ]
    }
   ],
   "source": [
    "# Note: the first time in a project, it can take over a minute to precompile PyPlot\n",
    "using PyPlot\n",
    "function batman()\n",
    "\n",
    "    # bat functions: semicircle, ellipse, shoulders, bottom, cowl\n",
    "    σ(x) = sqrt.(1 .- x.^2)\n",
    "    e(x) = 3σ(x/7)\n",
    "    s(x) = 4.2 .- .5x - 2.8σ(.5x .- .5)\n",
    "    b(x) = σ(abs.(2 .- x) .- 1) - x.^2/11 .+ .5x .- 3\n",
    "    c(x) = [1.7, 1.7, 2.6, .9]\n",
    "\n",
    "    # plot symmetrically across y-axis\n",
    "    p(x,f) = plot(-x,f(x), color=\"black\") , plot(x,f(x), color=\"black\")\n",
    "    p((3:.1:7),e);p(4:.1:7,t->-e(t))   # ellipse\n",
    "    p(1:.1:3,s);p(0:.1:4,b)            # shoulders and bottom\n",
    "    p([0,.5,.8,1],c)\n",
    "end\n",
    "batman();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
   ],
   "source": [
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Julia 1.5",
   "env": {
    "JULIA_DEPOT_PATH": "/home/user/.julia/:/ext/julia/depot/",
    "JULIA_PROJECT": "/home/user/.julia/environment/v1.5"
   },
   "language": "julia",
   "metadata": {
    "cocalc": {
     "description": "The Julia Programming Language",
     "priority": 10,
     "url": "https://julialang.org/"
    }
   },
   "name": "julia-1.5"
  },
  "language_info": {
   "file_extension": ".jl",
   "mimetype": "application/julia",
   "name": "julia",
   "version": "1.5.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}