{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Julia Basics\n",
    "\n",
    "This is a *basic* introduction to an IJulia notebook."
   ]
  },
  {
   "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": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "36.141120008059865"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "3*x + x^3 + sin(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3 + 4im"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "z = 3 + 4im"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-117 + 44im"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "z^3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-13.128783081462158 - 15.200784463067954im"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "exp(z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.0 + 1.0im"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sqrt(z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0 + 1.4142135623730951im"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sqrt(-2+0im)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "LoadError",
     "evalue": "KeyError: key 12 not found",
     "output_type": "error",
     "traceback": [
      "KeyError: key 12 not found",
      "",
      " in getindex(::Dict{Int64,Any}, ::Int64) at ./dict.jl:688"
     ]
    }
   ],
   "source": [
    "abs(Out[12])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.0"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "abs(3+4im)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3-element Array{Int64,1}:\n",
       " 1\n",
       " 2\n",
       " 3"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = [1,2,3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1×3 Array{Int64,2}:\n",
       " 1  2  3"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y = [1 2 3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1-element Array{Int64,1}:\n",
       " 14"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y * x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3×3 Array{Int64,2}:\n",
       " 1  2  3\n",
       " 2  4  6\n",
       " 3  6  9"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x * y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "LoadError",
     "evalue": "DimensionMismatch(\"dimensions must match\")",
     "output_type": "error",
     "traceback": [
      "DimensionMismatch(\"dimensions must match\")",
      "",
      " in promote_shape(::Tuple{Base.OneTo{Int64},Base.OneTo{Int64}}, ::Tuple{Base.OneTo{Int64}}) at ./operators.jl:406",
      " in promote_shape(::Tuple{Base.OneTo{Int64}}, ::Tuple{Base.OneTo{Int64},Base.OneTo{Int64}}) at ./operators.jl:402",
      " in promote_shape(::Array{Int64,1}, ::Array{Int64,2}) at ./operators.jl:397",
      " in _elementwise(::Base.#+, ::Type{Int64}, ::Array{Int64,1}, ::Array{Int64,2}) at ./arraymath.jl:57",
      " in +(::Array{Int64,1}, ::Array{Int64,2}) at ./arraymath.jl:49"
     ]
    }
   ],
   "source": [
    "x + y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3×3 Array{Int64,2}:\n",
       " 2  3  4\n",
       " 3  4  5\n",
       " 4  5  6"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = x .+ y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3-element Array{Int64,1}:\n",
       " 1\n",
       " 4\n",
       " 9"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x .* x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "20-element Array{Float64,1}:\n",
       " 0.865113 \n",
       " 0.933176 \n",
       " 0.618455 \n",
       " 0.617167 \n",
       " 0.401063 \n",
       " 0.73383  \n",
       " 0.435374 \n",
       " 0.0494422\n",
       " 0.937702 \n",
       " 0.26655  \n",
       " 0.369985 \n",
       " 0.361838 \n",
       " 0.498797 \n",
       " 0.173794 \n",
       " 0.948838 \n",
       " 0.108735 \n",
       " 0.262631 \n",
       " 0.0768341\n",
       " 0.825819 \n",
       " 0.620872 "
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = rand(20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9331756932130784"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x[2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4-element Array{Float64,1}:\n",
       " 0.933176\n",
       " 0.618455\n",
       " 0.617167\n",
       " 0.401063"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x[2:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7-element Array{Float64,1}:\n",
       " 0.435374\n",
       " 0.937702\n",
       " 0.369985\n",
       " 0.498797\n",
       " 0.948838\n",
       " 0.262631\n",
       " 0.825819"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x[7:2:end] # x[7], x[9], x[11], ... end of array"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9-element Array{Float64,1}:\n",
       " 0.865113\n",
       " 0.933176\n",
       " 0.618455\n",
       " 0.617167\n",
       " 0.73383 \n",
       " 0.937702\n",
       " 0.948838\n",
       " 0.825819\n",
       " 0.620872"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x[x .> 0.5]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Any function `f` can be applied elementwise to an array `x` by the syntax `f.(x)`.\n",
    "\n",
    "You may be thinking that Matlab and Numpy do this without dots, but it turns out that the `.` in `f.(x)` enables extensive possibilities that aren't possible in other language.  See also [this blog post on the real power of this syntax](http://julialang.org/blog/2017/01/moredots).\n",
    "\n",
    "e.g. compute $e^{\\sin x_i}$ for each element $x_i$=`x[i]` of the array `x`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "20-element Array{Float64,1}:\n",
       " 2.14078\n",
       " 2.23338\n",
       " 1.78564\n",
       " 1.78377\n",
       " 1.47757\n",
       " 1.95369\n",
       " 1.52463\n",
       " 1.05066\n",
       " 2.23938\n",
       " 1.30135\n",
       " 1.43563\n",
       " 1.42475\n",
       " 1.61344\n",
       " 1.18877\n",
       " 2.25407\n",
       " 1.11463\n",
       " 1.29644\n",
       " 1.07978\n",
       " 2.0857 \n",
       " 1.78916"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "exp.(sin.(x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plotting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "using PyPlot # thin wrapper around Python Matplotlib"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x3232ada50>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "1-element Array{Any,1}:\n",
       " PyObject <matplotlib.lines.Line2D object at 0x322f17250>"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = linspace(0,1,20)\n",
    "plot(x, x.*x, \"bo-\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's plot a more complicated function, $\\sqrt{e^{x^2}} = e^{x^2/2}$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x30853c190>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "PyObject <matplotlib.text.Text object at 0x322f615d0>"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = linspace(0, 3, 100)\n",
    "plot(x, sqrt(exp(x.*x)), \"r-\")\n",
    "title(\"a simple quadratic curve\")\n",
    "xlabel(L\"x\")\n",
    "ylabel(L\"\\sqrt{e^{x^2}}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x322f17350>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "PyObject <matplotlib.legend.Legend object at 0x323328610>"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = linspace(0.1, 3, 100)\n",
    "loglog(x, x.^(-2), \"r-\")\n",
    "loglog(x, x.^(-3), \"b-\")\n",
    "title(\"a couple of power laws\")\n",
    "xlabel(L\"x\")\n",
    "legend([L\"1/x^2\", L\"1/x^3\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Linear algebra"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3×4 Array{Int64,2}:\n",
       " 1   2   3   4\n",
       " 5   6   7   8\n",
       " 9  10  11  12"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = [1 2 3 4; 5 6 7 8; 9 10 11 12]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3×4 Array{Int64,2}:\n",
       " 1   2   3   4\n",
       " 5   6   7   8\n",
       " 9  10  11  12"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = [1 2 3 4\n",
    "     5 6 7 8\n",
    "     9 10 11 12]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4×4 Array{Float64,2}:\n",
       " 0.354297  0.796286  0.817323  0.0345978\n",
       " 0.690757  0.545312  0.10516   0.960872 \n",
       " 0.534802  0.541574  0.910064  0.547655 \n",
       " 0.246295  0.804683  0.217789  0.227035 "
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = rand(4,4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1000×1000 Array{Float64,2}:\n",
       " -1.65081   -0.240849    0.303505   …  -1.7985      1.58347     2.17258   \n",
       "  1.1676    -1.14529    -0.79521        0.757942    0.136036   -0.202522  \n",
       " -0.42534   -0.636201   -0.271092       0.636029    0.432697    0.982919  \n",
       "  0.548365   0.813392    0.180881       0.892248   -2.66757     0.623155  \n",
       "  0.358272  -1.32407    -1.62438       -0.583573    1.39367     1.84467   \n",
       " -0.522505   0.635723   -1.83343    …   0.373494    0.880843    0.197541  \n",
       " -1.36032    0.328761    0.966728       0.214797   -0.519872    0.786407  \n",
       " -1.96225   -1.18058     0.0220994      1.03323     1.73717    -1.02543   \n",
       " -2.3271     2.59105    -0.105579      -0.740164   -0.588027   -1.22532   \n",
       "  0.455888  -1.17448    -1.23745        1.26299    -0.996511   -0.0343119 \n",
       " -1.37476   -0.695493   -0.349228   …   0.623711   -0.118538   -2.10232   \n",
       "  0.385374   0.500938    0.328916       1.69133     0.0510919  -1.33315   \n",
       "  0.367484  -0.88171    -0.0158286     -0.0158428   0.0727947   0.330221  \n",
       "  ⋮                                 ⋱                                     \n",
       "  2.07491    0.301412   -2.88188       -2.13433    -1.46011    -1.33492   \n",
       "  0.445576   0.200213    0.867564       2.16332    -0.607085   -0.719657  \n",
       "  1.15989    1.38095     0.0995334  …   0.656682   -0.286683    1.1383    \n",
       "  1.49364    1.61671     1.74414        2.3082     -0.608303   -0.857497  \n",
       "  1.00611   -0.49429    -0.999569      -1.72488     0.0250074   1.70796   \n",
       " -0.653577  -0.867363   -1.2563        -1.27231     0.629835    0.731937  \n",
       "  0.381445   0.974918   -0.0255441     -0.824598   -1.34282     0.00359473\n",
       "  0.695848   0.0786676   1.72538    …  -0.0131363  -0.859186   -0.483053  \n",
       " -0.775784  -1.15708    -0.238277       0.658991   -0.40027     1.3225    \n",
       "  0.733769   0.673854   -1.31093        0.176824   -1.0881     -1.46115   \n",
       " -0.240597   0.142289    0.265261       0.365702   -1.2539      0.0856285 \n",
       " -1.05008   -0.707914    0.447666       0.743693    0.61162     1.02591   "
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = randn(1000,1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1000-element Array{Float64,1}:\n",
       "  0.704118 \n",
       " -0.096427 \n",
       " -0.733399 \n",
       " -0.343855 \n",
       "  1.94833  \n",
       " -0.712985 \n",
       "  0.37097  \n",
       "  0.438342 \n",
       " -0.486407 \n",
       "  0.772552 \n",
       "  0.370966 \n",
       " -1.60214  \n",
       "  0.0380739\n",
       "  ⋮        \n",
       " -1.5625   \n",
       "  0.67892  \n",
       " -0.305153 \n",
       "  0.872263 \n",
       "  1.37475  \n",
       " -0.0145622\n",
       "  1.55491  \n",
       " -2.12784  \n",
       " -1.57598  \n",
       "  0.625179 \n",
       "  1.07015  \n",
       " -0.840333 "
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b = randn(1000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's solve $Ax = b$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1000-element Array{Float64,1}:\n",
       "  0.582043\n",
       "  1.18294 \n",
       " -0.045209\n",
       " -0.671191\n",
       "  1.51479 \n",
       " -2.11266 \n",
       " -0.849299\n",
       "  1.68512 \n",
       "  0.101655\n",
       "  0.228883\n",
       " -0.619881\n",
       " -0.755786\n",
       " -4.20192 \n",
       "  ⋮       \n",
       " -1.57702 \n",
       "  3.67938 \n",
       " -1.59842 \n",
       "  2.11529 \n",
       " -2.26215 \n",
       " -0.348302\n",
       " -2.48251 \n",
       "  2.41252 \n",
       "  2.1558  \n",
       " -2.08519 \n",
       " -1.97143 \n",
       " -1.54951 "
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = inv(A) * b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1000-element Array{Float64,1}:\n",
       "  0.582043\n",
       "  1.18294 \n",
       " -0.045209\n",
       " -0.671191\n",
       "  1.51479 \n",
       " -2.11266 \n",
       " -0.849299\n",
       "  1.68512 \n",
       "  0.101655\n",
       "  0.228883\n",
       " -0.619881\n",
       " -0.755786\n",
       " -4.20192 \n",
       "  ⋮       \n",
       " -1.57702 \n",
       "  3.67938 \n",
       " -1.59842 \n",
       "  2.11529 \n",
       " -2.26215 \n",
       " -0.348302\n",
       " -2.48251 \n",
       "  2.41252 \n",
       "  2.1558  \n",
       " -2.08519 \n",
       " -1.97143 \n",
       " -1.54951 "
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = A \\ b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1000-element Array{Complex{Float64},1}:\n",
       "   23.8373+20.5315im\n",
       "   23.8373-20.5315im\n",
       "   16.9749+26.496im \n",
       "   16.9749-26.496im \n",
       "   16.5081+26.5372im\n",
       "   16.5081-26.5372im\n",
       "   31.0478+5.66555im\n",
       "   31.0478-5.66555im\n",
       "   29.4471+11.4433im\n",
       "   29.4471-11.4433im\n",
       "   28.0514+14.2995im\n",
       "   28.0514-14.2995im\n",
       "    30.288+6.98167im\n",
       "          ⋮         \n",
       " -0.353185-3.43256im\n",
       "    3.2686+1.52675im\n",
       "    3.2686-1.52675im\n",
       "   3.89872+0.0im    \n",
       "   1.85608+2.95923im\n",
       "   1.85608-2.95923im\n",
       " -0.532069+2.10994im\n",
       " -0.532069-2.10994im\n",
       "    1.4669+1.1996im \n",
       "    1.4669-1.1996im \n",
       "   -1.4334+0.0im    \n",
       "  0.659698+0.0im    "
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "λ = eigvals(A)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You may be wondering how to type `λ`.  It turns out you can just type `\\lambda` (the LaTeX code for λ) and then hit *tab*.  You can type much more complicated variable names this way.  (This is all thanks to Julia's support for something called [Unicode](https://en.wikipedia.org/wiki/Unicode).)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x̂₂′ = 7 # x\\hat<tab>\\_2<tab>\\prime<tab>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x323328050>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "A = randn(1000,1000)\n",
    "λ = eigvals(A)\n",
    "plot(real(λ), imag(λ), \"b.\")\n",
    "axis(\"equal\")\n",
    "xlabel(L\"\\Re \\lambda\")\n",
    "ylabel(L\"\\Im \\lambda\")\n",
    "savefig(\"foo.pdf\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5×5 Array{Float64,2}:\n",
       " 0.654851   0.870059  0.0121391  0.28378    0.281063\n",
       " 0.185478   0.835295  0.921174   0.211865   0.792001\n",
       " 0.402456   0.174917  0.385094   0.104552   0.449979\n",
       " 0.0853418  0.462815  0.404998   0.0762736  0.566363\n",
       " 0.501122   0.769946  0.985798   0.533097   0.331967"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = rand(5,5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(Complex{Float64}[2.33956+0.0im,0.202439+0.471556im,0.202439-0.471556im,-0.504527+0.0im,0.0435738+0.0im],\n",
       "Complex{Float64}[0.439548+0.0im 0.731467+0.0im … -0.0449559+0.0im -0.283944+0.0im; 0.564317+0.0im -0.317749+0.340296im … 0.184355+0.0im -0.177871+0.0im; … ; 0.32097+0.0im -0.134243+0.232145im … 0.41431+0.0im 0.840298+0.0im; 0.551383+0.0im -0.0572381-0.042745im … -0.818658+0.0im 0.331318+0.0im])"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "λ, X = eig(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5-element Array{Complex{Float64},1}:\n",
       "   2.33956+0.0im     \n",
       "  0.202439+0.471556im\n",
       "  0.202439-0.471556im\n",
       " -0.504527+0.0im     \n",
       " 0.0435738+0.0im     "
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "λ"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5×5 Array{Complex{Float64},2}:\n",
       " 0.439548+0.0im    0.731467+0.0im       …  -0.0449559+0.0im  -0.283944+0.0im\n",
       " 0.564317+0.0im   -0.317749+0.340296im       0.184355+0.0im  -0.177871+0.0im\n",
       "  0.28513+0.0im  -0.0230972-0.413087im       0.349483+0.0im  -0.268076+0.0im\n",
       "  0.32097+0.0im   -0.134243+0.232145im        0.41431+0.0im   0.840298+0.0im\n",
       " 0.551383+0.0im  -0.0572381-0.042745im      -0.818658+0.0im   0.331318+0.0im"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(Complex{Float64}[2.33956+0.0im,0.202439+0.471556im,0.202439-0.471556im,-0.504527+0.0im,0.0435738+0.0im],\n",
       "Complex{Float64}[0.439548+0.0im 0.731467+0.0im … -0.0449559+0.0im -0.283944+0.0im; 0.564317+0.0im -0.317749+0.340296im … 0.184355+0.0im -0.177871+0.0im; … ; 0.32097+0.0im -0.134243+0.232145im … 0.41431+0.0im 0.840298+0.0im; 0.551383+0.0im -0.0572381-0.042745im … -0.818658+0.0im 0.331318+0.0im])"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "λ, X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[1m\u001b[34mINFO: Precompiling module DataStructures.\n",
      "\u001b[0m"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div id=\"interact-js-shim\">\n",
       "    <script charset=\"utf-8\">\n",
       "(function (IPython, $, _, MathJax) {\n",
       "    $.event.special.destroyed = {\n",
       "\tremove: function(o) {\n",
       "\t    if (o.handler) {\n",
       "\t\to.handler.apply(this, arguments)\n",
       "\t    }\n",
       "\t}\n",
       "    }\n",
       "\n",
       "    var OutputArea = IPython.version >= \"4.0.0\" ? require(\"notebook/js/outputarea\").OutputArea : IPython.OutputArea;\n",
       "\n",
       "    var redrawValue = function (container, type, val) {\n",
       "\tvar selector = $(\"<div/>\");\n",
       "\tvar oa = new OutputArea(_.extend(selector, {\n",
       "\t    selector: selector,\n",
       "\t    prompt_area: true,\n",
       "\t    events: IPython.events,\n",
       "\t    keyboard_manager: IPython.keyboard_manager\n",
       "\t})); // Hack to work with IPython 2.1.0\n",
       "\n",
       "\tswitch (type) {\n",
       "\tcase \"image/png\":\n",
       "            var _src = 'data:' + type + ';base64,' + val;\n",
       "\t    $(container).find(\"img\").attr('src', _src);\n",
       "\t    break;\n",
       "\tcase \"text/latex\":\n",
       "\t\tif (MathJax){\n",
       "\t\t\tvar math = MathJax.Hub.getAllJax(container)[0];\n",
       "\t\t\tMathJax.Hub.Queue([\"Text\", math, val.replace(/^\\${1,2}|\\${1,2}$/g, '')]);\n",
       "\t\t\tbreak;\n",
       "\t\t}\n",
       "\tdefault:\n",
       "\t    var toinsert = OutputArea.append_map[type].apply(\n",
       "\t\toa, [val, {}, selector]\n",
       "\t    );\n",
       "\t    $(container).empty().append(toinsert.contents());\n",
       "\t    selector.remove();\n",
       "\t}\n",
       "    }\n",
       "\n",
       "\n",
       "    $(document).ready(function() {\n",
       "\tfunction initComm(evt, data) {\n",
       "\t    var comm_manager = data.kernel.comm_manager;\n",
       "        //_.extend(comm_manager.targets, require(\"widgets/js/widget\"))\n",
       "\t    comm_manager.register_target(\"Signal\", function (comm) {\n",
       "            comm.on_msg(function (msg) {\n",
       "                var val = msg.content.data.value;\n",
       "                $(\".signal-\" + comm.comm_id).each(function() {\n",
       "                var type = $(this).data(\"type\");\n",
       "                if (typeof(val[type]) !== \"undefined\" && val[type] !== null) {\n",
       "                    redrawValue(this, type, val[type], type);\n",
       "                }\n",
       "                });\n",
       "                delete val;\n",
       "                delete msg.content.data.value;\n",
       "            });\n",
       "\t    });\n",
       "\n",
       "\t    // coordingate with Comm and redraw Signals\n",
       "\t    // XXX: Test using Reactive here to improve performance\n",
       "\t    $([IPython.events]).on(\n",
       "\t\t'output_appended.OutputArea', function (event, type, value, md, toinsert) {\n",
       "\t\t    if (md && md.reactive) {\n",
       "                // console.log(md.comm_id);\n",
       "                toinsert.addClass(\"signal-\" + md.comm_id);\n",
       "                toinsert.data(\"type\", type);\n",
       "                // Signal back indicating the mimetype required\n",
       "                var comm_manager = IPython.notebook.kernel.comm_manager;\n",
       "                var comm = comm_manager.comms[md.comm_id];\n",
       "                comm.then(function (c) {\n",
       "                    c.send({action: \"subscribe_mime\",\n",
       "                       mime: type});\n",
       "                    toinsert.bind(\"destroyed\", function() {\n",
       "                        c.send({action: \"unsubscribe_mime\",\n",
       "                               mime: type});\n",
       "                    });\n",
       "                })\n",
       "\t\t    }\n",
       "\t    });\n",
       "\t}\n",
       "\n",
       "\ttry {\n",
       "\t    // try to initialize right away. otherwise, wait on the status_started event.\n",
       "\t    initComm(undefined, IPython.notebook);\n",
       "\t} catch (e) {\n",
       "\t    $([IPython.events]).on('kernel_created.Kernel kernel_created.Session', initComm);\n",
       "\t}\n",
       "    });\n",
       "})(IPython, jQuery, _, MathJax);\n",
       "</script>\n",
       "    <script>\n",
       "        window.interactLoadedFlag = true\n",
       "       $(\"#interact-js-shim\").bind(\"destroyed\", function () {\n",
       "           if (window.interactLoadedFlag) {\n",
       "               console.warn(\"JavaScript required by Interact will be removed if you remove this cell or run using Interact more than once.\")\n",
       "           }\n",
       "       })\n",
       "       $([IPython.events]).on(\"kernel_starting.Kernel kernel_restarting.Kernel\", function () { window.interactLoadedFlag = false })\n",
       "   </script>\n",
       "</div>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "using Interact"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [],
      "text/plain": [
       "Interact.Options{:SelectionSlider,Int64}(Signal{Int64}(505, nactions=1),\"n\",505,\"505\",Interact.OptionDict(DataStructures.OrderedDict(\"10\"=>10,\"11\"=>11,\"12\"=>12,\"13\"=>13,\"14\"=>14,\"15\"=>15,\"16\"=>16,\"17\"=>17,\"18\"=>18,\"19\"=>19…),Dict(306=>\"306\",29=>\"29\",74=>\"74\",905=>\"905\",176=>\"176\",892=>\"892\",285=>\"285\",318=>\"318\",873=>\"873\",975=>\"975\"…)),Any[],Any[],true,\"horizontal\")"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x31e614350>)"
      ]
     },
     "execution_count": 47,
     "metadata": {
      "comm_id": "aaf65e16-ba9f-47b4-9a45-93adba93d698",
      "reactive": true
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f = figure()\n",
    "@manipulate for n in 10:1000\n",
    "    withfig(f) do\n",
    "        A = randn(n,n)\n",
    "        λ = eigvals(A)\n",
    "        plot(real(λ), imag(λ), \"b.\")\n",
    "        axis(\"equal\")\n",
    "        xlabel(L\"\\Re \\lambda\")\n",
    "        ylabel(L\"\\Im \\lambda\")\n",
    "    end\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Calling Python\n",
    "\n",
    "Being a young language, Julia doesn't have as many mature libraries and packages as a language like Python.  Fortunately, Julia code can *call Python libraries* directly, with the help of the [PyCall package](https://github.com/JuliaPy/PyCall.jl):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "using PyCall"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "@pyimport scipy.special as special"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.006591139357460717,-0.011912976705951313,14.037328963730229,22.92221496638217)"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "special.airy(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "@pyimport scipy.optimize as opt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0"
      ]
     },
     "execution_count": 52,
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    "opt.newton(cos, 1.4) - pi/2"
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  },
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   "cell_type": "code",
   "execution_count": 53,
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    {
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       "0.7390851332151607"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
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