Julia_Workshop02.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "cfd19ca1",
   "metadata": {},
   "source": [
    "# Julia Workshop, Control Flow"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bdd1fbea",
   "metadata": {},
   "source": [
    "## Loops "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "f3203619",
   "metadata": {},
   "outputs": [],
   "source": [
    "#=\n",
    "1. While Loops\n",
    "2. For Loops \n",
    "=#"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "8bc18221",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "9\n",
      "10\n"
     ]
    }
   ],
   "source": [
    "#while loops\n",
    "n = 0\n",
    "while n < 10\n",
    "    n+= 1\n",
    "    println(n)\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "f4f74bea",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Hi, my name is Ted\n",
      "Hi, my name is Rob\n",
      "Hi, my name is Barney\n",
      "Hi, my name is Lily\n"
     ]
    }
   ],
   "source": [
    "names = [\"Ted\", \"Rob\", \"Barney\", \"Lily\"]\n",
    "i = 1 \n",
    "while i<= length(names)\n",
    "    name = names[i]\n",
    "    println(\"Hi, my name is $name\")\n",
    "    i += 1\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "24fc44c7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "9\n",
      "10\n"
     ]
    }
   ],
   "source": [
    "for n in 1:10 \n",
    "    println(n)\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "058fe22b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Hi, my name is Ted\n",
      "Hi, my name is Rob\n",
      "Hi, my name is Barney\n",
      "Hi, my name is Lily\n"
     ]
    }
   ],
   "source": [
    "names = [\"Ted\", \"Rob\", \"Barney\", \"Lily\"]\n",
    "for name in names\n",
    "    println(\"Hi, my name is $name\")\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "a10f68aa",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "9\n",
      "10\n"
     ]
    }
   ],
   "source": [
    "for n = 1:10 \n",
    "    println(n)\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "0df1c052",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5×5 Matrix{Float64}:\n",
       " 0.0  0.0  0.0  0.0  0.0\n",
       " 0.0  0.0  0.0  0.0  0.0\n",
       " 0.0  0.0  0.0  0.0  0.0\n",
       " 0.0  0.0  0.0  0.0  0.0\n",
       " 0.0  0.0  0.0  0.0  0.0"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m, n = 5, 5\n",
    "a= zeros(m,n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "29bfdc8b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5×5 Matrix{Float64}:\n",
       " 2.0  3.0  4.0  5.0   6.0\n",
       " 3.0  4.0  5.0  6.0   7.0\n",
       " 4.0  5.0  6.0  7.0   8.0\n",
       " 5.0  6.0  7.0  8.0   9.0\n",
       " 6.0  7.0  8.0  9.0  10.0"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "for i in 1:m\n",
    "    for j in 1:n \n",
    "        a[i,j] = i + j\n",
    "    end \n",
    "end \n",
    "a\n",
    "        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "3cdeb9e8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5×5 Matrix{Float64}:\n",
       " 0.0  0.0  0.0  0.0  0.0\n",
       " 0.0  0.0  0.0  0.0  0.0\n",
       " 0.0  0.0  0.0  0.0  0.0\n",
       " 0.0  0.0  0.0  0.0  0.0\n",
       " 0.0  0.0  0.0  0.0  0.0"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b = zeros((m,n))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "3e457f4f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5×5 Matrix{Float64}:\n",
       " 2.0  3.0  4.0  5.0   6.0\n",
       " 3.0  4.0  5.0  6.0   7.0\n",
       " 4.0  5.0  6.0  7.0   8.0\n",
       " 5.0  6.0  7.0  8.0   9.0\n",
       " 6.0  7.0  8.0  9.0  10.0"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "for i in 1:m, j in 1:n\n",
    "    b[i,j]= i +j \n",
    "end \n",
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "0d7d727d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5×5 Matrix{Int64}:\n",
       " 2  3  4  5   6\n",
       " 3  4  5  6   7\n",
       " 4  5  6  7   8\n",
       " 5  6  7  8   9\n",
       " 6  7  8  9  10"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# more \"julia\" way to create addition table, didnt need to pre initial the matrix \n",
    "c = [i + j for i in 1:m, j in 1:n]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "80de964f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1×1 Matrix{Int64}:\n",
       " 2"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "2×2 Matrix{Int64}:\n",
       " 2  3\n",
       " 3  4"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "3×3 Matrix{Int64}:\n",
       " 2  3  4\n",
       " 3  4  5\n",
       " 4  5  6"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "4×4 Matrix{Int64}:\n",
       " 2  3  4  5\n",
       " 3  4  5  6\n",
       " 4  5  6  7\n",
       " 5  6  7  8"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "5×5 Matrix{Int64}:\n",
       " 2  3  4  5   6\n",
       " 3  4  5  6   7\n",
       " 4  5  6  7   8\n",
       " 5  6  7  8   9\n",
       " 6  7  8  9  10"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "6×6 Matrix{Int64}:\n",
       " 2  3  4   5   6   7\n",
       " 3  4  5   6   7   8\n",
       " 4  5  6   7   8   9\n",
       " 5  6  7   8   9  10\n",
       " 6  7  8   9  10  11\n",
       " 7  8  9  10  11  12"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "7×7 Matrix{Int64}:\n",
       " 2  3   4   5   6   7   8\n",
       " 3  4   5   6   7   8   9\n",
       " 4  5   6   7   8   9  10\n",
       " 5  6   7   8   9  10  11\n",
       " 6  7   8   9  10  11  12\n",
       " 7  8   9  10  11  12  13\n",
       " 8  9  10  11  12  13  14"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "8×8 Matrix{Int64}:\n",
       " 2   3   4   5   6   7   8   9\n",
       " 3   4   5   6   7   8   9  10\n",
       " 4   5   6   7   8   9  10  11\n",
       " 5   6   7   8   9  10  11  12\n",
       " 6   7   8   9  10  11  12  13\n",
       " 7   8   9  10  11  12  13  14\n",
       " 8   9  10  11  12  13  14  15\n",
       " 9  10  11  12  13  14  15  16"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "9×9 Matrix{Int64}:\n",
       "  2   3   4   5   6   7   8   9  10\n",
       "  3   4   5   6   7   8   9  10  11\n",
       "  4   5   6   7   8   9  10  11  12\n",
       "  5   6   7   8   9  10  11  12  13\n",
       "  6   7   8   9  10  11  12  13  14\n",
       "  7   8   9  10  11  12  13  14  15\n",
       "  8   9  10  11  12  13  14  15  16\n",
       "  9  10  11  12  13  14  15  16  17\n",
       " 10  11  12  13  14  15  16  17  18"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "10×10 Matrix{Int64}:\n",
       "  2   3   4   5   6   7   8   9  10  11\n",
       "  3   4   5   6   7   8   9  10  11  12\n",
       "  4   5   6   7   8   9  10  11  12  13\n",
       "  5   6   7   8   9  10  11  12  13  14\n",
       "  6   7   8   9  10  11  12  13  14  15\n",
       "  7   8   9  10  11  12  13  14  15  16\n",
       "  8   9  10  11  12  13  14  15  16  17\n",
       "  9  10  11  12  13  14  15  16  17  18\n",
       " 10  11  12  13  14  15  16  17  18  19\n",
       " 11  12  13  14  15  16  17  18  19  20"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for n in 1:10 \n",
    "    a = [i + j for i in 1:n , j in 1:n ]\n",
    "    display(a)\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bb5fca04",
   "metadata": {},
   "source": [
    "## Conditionals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "aada2f26",
   "metadata": {},
   "outputs": [],
   "source": [
    "#= \n",
    "if cond1\n",
    "    option1 \n",
    "elseif \n",
    "    cond2\n",
    "else \n",
    "    cond3\n",
    "end\n",
    "=#"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "ef9f351f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = 10\n",
    "y = 5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "dee23a87",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10 is larger than 5\n"
     ]
    }
   ],
   "source": [
    "if x > y\n",
    "    println(\"$x is larger than $y\")\n",
    "elseif y > x\n",
    "    println(\"$y is larger than $x\")\n",
    "else \n",
    "    println(\"$x and $y are equal\")\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "c6121c7a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "if x > y \n",
    "    x \n",
    "else \n",
    "    y \n",
    "end "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "ecc372b7",
   "metadata": {},
   "outputs": [],
   "source": [
    "#= \n",
    "a ? b : c \n",
    "if a \n",
    "    b\n",
    "else \n",
    "    c\n",
    "end \n",
    "=#"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "7705a9fe",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(x > y) ? x : y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "c8a2b539",
   "metadata": {},
   "outputs": [
    {
     "ename": "LoadError",
     "evalue": "TypeError: non-boolean (Matrix{Int64}) used in boolean context",
     "output_type": "error",
     "traceback": [
      "TypeError: non-boolean (Matrix{Int64}) used in boolean context",
      "",
      "Stacktrace:",
      " [1] top-level scope",
      "   @ In[32]:1"
     ]
    }
   ],
   "source": [
    "#a && b "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "656050d6",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10 is larger than 5\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "false"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(x>y) && println(\"$x is larger than $y\")\n",
    "(x< y) && println(\"$y is larger than $x\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e9b14f71",
   "metadata": {},
   "source": [
    "## Functions "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "773a4cd3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "sayhi (generic function with 1 method)"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function sayhi(name)\n",
    "    println(\"Hi $name, how are you?\")\n",
    "end "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "2224f2b8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "f (generic function with 1 method)"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function f(x)\n",
    "    x^2\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "a193a425",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Hi Carolian, how are you?\n"
     ]
    }
   ],
   "source": [
    "sayhi(\"Carolina\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "dc6dd264",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "16"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f(4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "3664c54c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "sayhi (generic function with 1 method)"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sayhi(name) = print(\"Hi $name, how are you?\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "9ce88464",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Hi Mary, how are you?"
     ]
    }
   ],
   "source": [
    "sayhi(\"Mary\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "9d1151e0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "#9 (generic function with 1 method)"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hello = name -> println(\"Hi $name, its great to see you!\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "23b9ce33",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "#11 (generic function with 1 method)"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f3 = x -> x^2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "60cbec17",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Hi Caro, its great to see you!\n"
     ]
    }
   ],
   "source": [
    "hello(\"Caro\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "a9f5c109",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "36"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f3(6)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5a5b3b05",
   "metadata": {},
   "source": [
    "## Duck Typing in Julia "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "6486c6f1",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Hi 3243224, how are you?"
     ]
    }
   ],
   "source": [
    "sayhi(3243224)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "47bc728c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3×3 Matrix{Float64}:\n",
       " 0.708259  0.428387  0.207797\n",
       " 0.865846  0.183984  0.0749384\n",
       " 0.850326  0.997695  0.0501011"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = rand(3,3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "fe3aaf4c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3×3 Matrix{Float64}:\n",
       " 1.04924   0.589543  0.189688\n",
       " 0.836267  0.479533  0.197462\n",
       " 1.5087    0.597814  0.253971"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "4cd48f33",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3-element Vector{Float64}:\n",
       " 0.32166174091608335\n",
       " 0.16482304932204017\n",
       " 0.132806418238418"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v = rand(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "452dcc2d",
   "metadata": {},
   "outputs": [
    {
     "ename": "LoadError",
     "evalue": "MethodError: no method matching ^(::Vector{Float64}, ::Int64)\n\u001b[0mClosest candidates are:\n\u001b[0m  ^(\u001b[91m::Union{AbstractChar, AbstractString}\u001b[39m, ::Integer) at strings/basic.jl:730\n\u001b[0m  ^(\u001b[91m::Complex{<:AbstractFloat}\u001b[39m, ::Integer) at complex.jl:860\n\u001b[0m  ^(\u001b[91m::Complex{<:Integer}\u001b[39m, ::Integer) at complex.jl:862\n\u001b[0m  ...",
     "output_type": "error",
     "traceback": [
      "MethodError: no method matching ^(::Vector{Float64}, ::Int64)\n\u001b[0mClosest candidates are:\n\u001b[0m  ^(\u001b[91m::Union{AbstractChar, AbstractString}\u001b[39m, ::Integer) at strings/basic.jl:730\n\u001b[0m  ^(\u001b[91m::Complex{<:AbstractFloat}\u001b[39m, ::Integer) at complex.jl:860\n\u001b[0m  ^(\u001b[91m::Complex{<:Integer}\u001b[39m, ::Integer) at complex.jl:862\n\u001b[0m  ...",
      "",
      "Stacktrace:",
      " [1] literal_pow",
      "   @ ./intfuncs.jl:340 [inlined]",
      " [2] f(x::Vector{Float64})",
      "   @ Main ./In[35]:2",
      " [3] top-level scope",
      "   @ In[55]:1"
     ]
    }
   ],
   "source": [
    "f(v)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6f2c1900",
   "metadata": {},
   "source": [
    "## Mutating v Non Mutating Functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "b1b2bc60",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3-element Vector{Int64}:\n",
       " 3\n",
       " 5\n",
       " 2"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v = [3,5,2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "0a52ad58",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3-element Vector{Int64}:\n",
       " 2\n",
       " 3\n",
       " 5"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sort(v)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "3fec55d1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3-element Vector{Int64}:\n",
       " 3\n",
       " 5\n",
       " 2"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "9e50db3c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3-element Vector{Int64}:\n",
       " 2\n",
       " 3\n",
       " 5"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sort!(v)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "15cc5f23",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3-element Vector{Int64}:\n",
       " 2\n",
       " 3\n",
       " 5"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5d93fab0",
   "metadata": {},
   "source": [
    "## Broadcasting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "id": "26ae5ffb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3×3 Matrix{Int64}:\n",
       " 1  2  3\n",
       " 4  5  6\n",
       " 7  8  9"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = [i + 3*j for j in 0:2, i in 1:3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "ff4b238f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3×3 Matrix{Int64}:\n",
       "  30   36   42\n",
       "  66   81   96\n",
       " 102  126  150"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "c009493b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3×3 Matrix{Int64}:\n",
       "  1   4   9\n",
       " 16  25  36\n",
       " 49  64  81"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f.(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "id": "a43bd3f8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A[2,2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "id": "586a99ad",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "25"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A[2,2]^2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "id": "e6b3fcbe",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.0"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b[2,2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "id": "09e5d88a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3-element Vector{Int64}:\n",
       " 1\n",
       " 2\n",
       " 3"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v = [1, 2, 3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "id": "9069f411",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3-element Vector{Int64}:\n",
       " 1\n",
       " 4\n",
       " 9"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f.(v)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d6cace4d",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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