00_Preliminaries.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 00 Preliminaries"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Jupyter notebook is an interactive computing environment for creating and sharing documents that contain live code, equations, and visualizations. In the notebook, dark cells can contain live code and you can evaluate cells by pressing `Shift + Return` key. Of course, you can edit the code in the cell and re-evalute the code. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the following, using cells, we introduce basic properties of Julia language"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Introduction to Julia"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# types"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# sum of integers\n",
    "1 + 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Int64"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# default type of integer is 64-bit Int\n",
    "typeof(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.0"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# sum of floating numbers\n",
    "1.0 + 3.0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Float64"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# default type of floating numbers is 64-bit Float\n",
    "typeof(1.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"hello world\""
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# strings\n",
    "\"hello world\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "String"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# type of string is called String\n",
    "typeof(\"hello world\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3-element Array{Int64,1}:\n",
       " 1\n",
       " 2\n",
       " 3"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 1-dimensional array = Vector\n",
    "[1, 2, 3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Array{Int64,1}"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# tells us this is a 1-dimensional integer array\n",
    "typeof([1, 2, 3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3×3 Array{Int64,2}:\n",
       " 1  4  7\n",
       " 2  5  8\n",
       " 3  6  9"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 2-dimensional array = Matrix\n",
    "[1 4 7; 2 5 8; 3 6 9]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Array{Int64,2}"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# tells us this is a 2-dimensional integer array\n",
    "typeof([1 4 7; 2 5 8; 3 6 9])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Float64"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# when different types are in a arithmetic operation, type conversion occurs\n",
    "typeof(1 + 1.0) #type promotion, conversion"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.0"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# divisions of integers always converted to float\n",
    "4/2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = 1.0\n",
    "b = 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Float64"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "typeof(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Int64"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "typeof(b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.0"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a + b"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# vectors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4-element Array{Int64,1}:\n",
       " 1\n",
       " 2\n",
       " 3\n",
       " 4"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 1-dimensional array = vector\n",
    "a = [1, 2, 3, 4]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# the number of elements can be accessed by size() or length()\n",
    "size(a, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Like FORTRAN and MATLAB, index always starts from 1, not 0\n",
    "a[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4-element Array{Int64,1}:\n",
       " 5\n",
       " 6\n",
       " 7\n",
       " 8"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b = [5, 6, 7, 8]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4-element Array{Int64,1}:\n",
       "  6\n",
       "  8\n",
       " 10\n",
       " 12"
      ]
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# sum of vectors\n",
    "a + b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4-element Array{Int64,1}:\n",
       "  5\n",
       " 12\n",
       " 21\n",
       " 32"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Element-wise product\n",
    "a .* b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1×4 Array{Int64,2}:\n",
       " 1  2  3  4"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Row vector =  1-by-4 2-dimensional Array(Matrix)\n",
    "c = [1 2 3 4]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [
    {
     "ename": "LoadError",
     "evalue": "DimensionMismatch(\"dimensions must match: a has dims (Base.OneTo(1), Base.OneTo(4)), b has dims (Base.OneTo(4),), mismatch at 1\")",
     "output_type": "error",
     "traceback": [
      "DimensionMismatch(\"dimensions must match: a has dims (Base.OneTo(1), Base.OneTo(4)), b has dims (Base.OneTo(4),), mismatch at 1\")",
      "",
      "Stacktrace:",
      " [1] promote_shape at ./indices.jl:178 [inlined]",
      " [2] promote_shape at ./indices.jl:174 [inlined]",
      " [3] promote_shape at ./indices.jl:169 [inlined]",
      " [4] +(::Array{Int64,1}, ::Array{Int64,2}) at ./arraymath.jl:45",
      " [5] top-level scope at In[90]:2",
      " [6] include_string(::Function, ::Module, ::String, ::String) at ./loading.jl:1091"
     ]
    }
   ],
   "source": [
    "# sum of different-size vectors results in an error\n",
    "a + c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4×4 Array{Int64,2}:\n",
       " 1  2   3   4\n",
       " 2  4   6   8\n",
       " 3  6   9  12\n",
       " 4  8  12  16"
      ]
     },
     "execution_count": 91,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Matrix multiplication\n",
    "a * c"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# matrices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2×2 Array{Int64,2}:\n",
       " 1  2\n",
       " 3  4"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 2-dimensional array = Matrix\n",
    "A = [1 2; 3 4]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2, 2)"
      ]
     },
     "execution_count": 93,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# the size of Matrix can be accessed by size()\n",
    "size(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# first index specifies row, second index is column\n",
    "A[1, 1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2-element Array{Int64,1}:\n",
       " 2\n",
       " 4"
      ]
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# index slicing\n",
    "A[1:2, 2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2-element Array{Int64,1}:\n",
       " 2\n",
       " 4"
      ]
     },
     "execution_count": 96,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# : specifies all indices\n",
    "A[:, 2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2×2 Array{Int64,2}:\n",
       " 5  6\n",
       " 7  8"
      ]
     },
     "execution_count": 97,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "B = [5 6; 7 8]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2×2 Array{Int64,2}:\n",
       "  6   8\n",
       " 10  12"
      ]
     },
     "execution_count": 98,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Matrix sum\n",
    "A + B"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2×2 Array{Int64,2}:\n",
       " 19  22\n",
       " 43  50"
      ]
     },
     "execution_count": 99,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Matrix product\n",
    "A * B"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2×2 Array{Int64,2}:\n",
       "  5  12\n",
       " 21  32"
      ]
     },
     "execution_count": 100,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# element-wise product\n",
    "A .* B"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# initialization of vectors and matrices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10-element Array{Float64,1}:\n",
       " 0.0\n",
       " 0.0\n",
       " 0.0\n",
       " 0.0\n",
       " 0.0\n",
       " 0.0\n",
       " 0.0\n",
       " 0.0\n",
       " 0.0\n",
       " 0.0"
      ]
     },
     "execution_count": 101,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# initialization by zeros\n",
    "a = zeros(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10-element Array{Int64,1}:\n",
       " 0\n",
       " 0\n",
       " 0\n",
       " 0\n",
       " 0\n",
       " 0\n",
       " 0\n",
       " 0\n",
       " 0\n",
       " 0"
      ]
     },
     "execution_count": 102,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# specifies the type of zeros\n",
    "a = zeros(Int64, 10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3×3 Array{Float64,2}:\n",
       " 0.0  0.0  0.0\n",
       " 0.0  0.0  0.0\n",
       " 0.0  0.0  0.0"
      ]
     },
     "execution_count": 103,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 2-dimensional zeros\n",
    "A = zeros(3, 3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3×3 Array{Int64,2}:\n",
       " 0  0  0\n",
       " 0  0  0\n",
       " 0  0  0"
      ]
     },
     "execution_count": 104,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# specifies the type of zeros\n",
    "A = zeros(Int64, 3, 3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10-element Array{Float64,1}:\n",
       " 0.3512698940715844\n",
       " 0.5208056889115671\n",
       " 0.8161519160999398\n",
       " 0.6893171507815663\n",
       " 0.16339370291168653\n",
       " 0.2074344055498667\n",
       " 0.7923413293873776\n",
       " 0.5381711539835212\n",
       " 0.13968943601098194\n",
       " 0.08779412598301461"
      ]
     },
     "execution_count": 105,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# draws from uniform distribution\n",
    "a = rand(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10-element Array{Float64,1}:\n",
       "  0.9803784033851787\n",
       " -1.108798169655759\n",
       "  0.7198272637584432\n",
       " -1.4337598738394353\n",
       "  1.7528267344477755\n",
       "  1.1432692851254522\n",
       " -0.2762710704844821\n",
       " -0.7568233494771059\n",
       "  0.14225011475497157\n",
       " -0.17518519975352004"
      ]
     },
     "execution_count": 106,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# draws from gaussian distribution\n",
    "a = randn(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1:10"
      ]
     },
     "execution_count": 107,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# specifies a range, 1 2 3 4 5 6 7 8 9 10\n",
    "a = 1:10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "UnitRange{Int64}"
      ]
     },
     "execution_count": 108,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# but range has some special type\n",
    "typeof(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10-element Array{Int64,1}:\n",
       "  1\n",
       "  2\n",
       "  3\n",
       "  4\n",
       "  5\n",
       "  6\n",
       "  7\n",
       "  8\n",
       "  9\n",
       " 10"
      ]
     },
     "execution_count": 109,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# type type can be converted to Array by collect()\n",
    "collect(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0:1.3207963267948966:6.283185307179586"
      ]
     },
     "execution_count": 110,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# more complex range\n",
    "t = range(1, stop=2*pi, length=5) #pi is a predefined constant"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5-element Array{Float64,1}:\n",
       " 1.0\n",
       " 2.3207963267948966\n",
       " 3.641592653589793\n",
       " 4.96238898038469\n",
       " 6.283185307179586"
      ]
     },
     "execution_count": 111,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# again, converted to Array\n",
    "collect(t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5×2 reshape(::UnitRange{Int64}, 5, 2) with eltype Int64:\n",
       " 1   6\n",
       " 2   7\n",
       " 3   8\n",
       " 4   9\n",
       " 5  10"
      ]
     },
     "execution_count": 112,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 1-dimensional Array(Range) can be reshaped to 2-dimensional Array(Range)\n",
    "A = reshape(1:10, 5, 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5×2 Array{Int64,2}:\n",
       " 1   6\n",
       " 2   7\n",
       " 3   8\n",
       " 4   9\n",
       " 5  10"
      ]
     },
     "execution_count": 113,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# again, converted to Array\n",
    "collect(A)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# plots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {},
   "outputs": [],
   "source": [
    "# In julia, there are several plotting packages. PyPlot is a wrapper package for Python's matplotlib.pyplot\n",
    "# this takes time... please be patient\n",
    "using PyPlot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "50-element Array{Float64,1}:\n",
       "  0.8414709848078965\n",
       "  0.9444931469173716\n",
       "  0.9951331505698849\n",
       "  0.9905824706805856\n",
       "  0.9310934906953738\n",
       "  0.8199655052530715\n",
       "  0.663361739318773\n",
       "  0.4699675320173844\n",
       "  0.2505086424976974\n",
       "  0.017156392873725015\n",
       " -0.21714736062615594\n",
       " -0.439407990795863\n",
       " -0.6372987892984507\n",
       "  ⋮\n",
       " -0.5184698032563613\n",
       " -0.7040672865242514\n",
       " -0.8506167742747077\n",
       " -0.9499905437029796\n",
       " -0.9966772657394525\n",
       " -0.9880876666773427\n",
       " -0.9246981308510646\n",
       " -0.810024280074289\n",
       " -0.650425995137961\n",
       " -0.45475469299336263\n",
       " -0.233862421839966\n",
       " -4.898587196589413e-16"
      ]
     },
     "execution_count": 115,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = range(1, stop=4*pi, length=50)\n",
    "y = sin.(x) # dot is needed for element-wise sin"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "p = plot(x, y, label=[\"sin\"], linewidth=3)\n",
    "xlabel(\"time [sec]\", fontsize=15)\n",
    "ylabel(\"sin(x) [cm]\", fontsize=15)\n",
    "\n",
    "savefig(\"01_sin.png\", dpi=200) # let's check the output file in Jupyter"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Introduction to MDToolbox.jl"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Basics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {},
   "outputs": [],
   "source": [
    "# MDToolbox is a our-inhouse package for stastical analysis of MD trajectories\n",
    "# this takes time... please be patient\n",
    "using MDToolbox\n",
    "ENV[\"COLUMNS\"] = 130; # set display width for MDToolbox"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1x214 TrjArray{Float64,Int64}\n",
       "| A                          | A                          |  …   A                          | A                          |\n",
       "| 1MET                       | 2ARG                       |  …   213LEU                     | 214GLY                     |\n",
       "| 2CA                        | 10CA                       |  …   1650CA                     | 1658CA                     |\n",
       "|     9.97    -9.03     9.82 |    10.38    -6.71     6.85 |  …       4.71   -15.48     6.74 |     5.09   -17.11     9.36 |"
      ]
     },
     "execution_count": 118,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# first, read a pdb of coarse-grained (Ca-atom) Adenylate Kinase structure\n",
    "# mdload() automatically detects files types from its extension and read the data. Currently, PDB, PSF, DCD, and NetCDF are available. \n",
    "t = mdload(\"data/AdK_closed.pdb\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "TrjArray{Float64,Int64}"
      ]
     },
     "execution_count": 119,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# variable t has a original type TrjArray which is defined in MDToolbox for representing MD trajectory data\n",
    "typeof(t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1x1 TrjArray{Float64,Int64}\n",
       "| A                          |\n",
       "| 1MET                       |\n",
       "| 1CA                        |\n",
       "|     9.97    -9.03     9.82 |"
      ]
     },
     "execution_count": 120,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# In TrjArray, columns corresponds to atoms and rows corresponds to frames (snapshots) of MD trajectory. \n",
    "t[:, 1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1x13 TrjArray{Float64,Int64}\n",
       "| A                          | A                          |  …   A                          | A                          |\n",
       "| 2ARG                       | 36ARG                      |  …   167ARG                     | 206ARG                     |\n",
       "| 1CA                        | 2CA                        |  …   12CA                       | 13CA                       |\n",
       "|    10.38    -6.71     6.85 |    -2.02    11.35    -0.08 |  …      -5.02     5.32   -12.12 |    -5.77   -13.47     6.38 |"
      ]
     },
     "execution_count": 121,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Also, we can flexibly select atom by giving some strings\n",
    "# for example, we can select only ARG residues\n",
    "t[:, \"resname ARG\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1x13 TrjArray{Float64,Int64}\n",
       "| A                          | A                          |  …   A                          | A                          |\n",
       "| 2ARG                       | 36ARG                      |  …   167ARG                     | 206ARG                     |\n",
       "| 1CA                        | 2CA                        |  …   12CA                       | 13CA                       |\n",
       "|    10.38    -6.71     6.85 |    -2.02    11.35    -0.08 |  …      -5.02     5.32   -12.12 |    -5.77   -13.47     6.38 |"
      ]
     },
     "execution_count": 122,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# when giving strings, we can skip row index\n",
    "t[\"resname ARG\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1x5 TrjArray{Float64,Int64}\n",
       "| A                          | A                          |  …   A                          | A                          |\n",
       "| 1MET                       | 5LEU                       |  …   9PRO                       | 10GLY                      |\n",
       "| 1CA                        | 2CA                        |  …   4CA                        | 5CA                        |\n",
       "|     9.97    -9.03     9.82 |     3.15    -4.58     0.47 |  …      -5.58     1.27    -6.07 |    -8.75    -0.37    -5.26 |"
      ]
     },
     "execution_count": 123,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# also, residue indices can be specified\n",
    "t[\"resid 1 5:6 9:10\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Warning: boxsize information discarded in some trajectories\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "20001x214 TrjArray{Float64,Int64}\n",
       "| A                          | A                          |  …   A                          | A                          |\n",
       "| 1MET                       | 2ARG                       |  …   213LEU                     | 214GLY                     |\n",
       "| 2CA                        | 10CA                       |  …   1650CA                     | 1658CA                     |\n",
       "|     9.97    -9.03     9.82 |    10.38    -6.71     6.85 |  …       4.71   -15.48     6.74 |     5.09   -17.11     9.36 |\n",
       "|     0.01    17.58     8.30 |     1.70    14.27     9.20 |         -8.40    13.66     9.10 |   -10.49    16.81     8.96 |\n",
       "|    -0.06    17.26     8.54 |     2.00    14.04     8.56 |         -8.59    13.96     8.62 |   -10.21    17.38     8.81 |\n",
       "|    -0.31    17.06     7.99 |     2.05    14.15     8.76 |         -8.46    13.68     8.40 |    -9.88    17.18     8.51 |\n",
       "|    -0.95    17.10     9.79 |     1.55    14.26     9.27 |         -8.52    13.69    11.42 |   -10.67    16.72    12.16 |\n",
       "|     0.17    17.04     8.59 |     2.41    13.95     8.49 |  …      -8.57    13.72     8.49 |   -10.59    16.89     8.00 |\n",
       "|    -0.45    16.92     7.98 |     2.15    14.17     8.52 |         -8.59    13.53     8.48 |   -10.43    16.83     8.60 |\n",
       "|    -0.17    17.49     8.17 |     2.04    14.49     8.98 |         -8.44    13.74     8.39 |   -10.41    16.97     8.61 |\n",
       "|    -0.43    17.14     8.01 |     1.99    14.20     8.20 |         -8.59    13.13     9.19 |   -10.42    16.41     8.74 |\n",
       "|    -0.51    16.90     8.33 |     2.15    14.16     8.45 |         -8.50    13.42     9.36 |   -10.32    16.74     9.22 |\n",
       "|    -0.35    17.09     8.27 |     2.02    14.10     8.26 |  …      -8.77    13.15     9.10 |   -10.30    16.62     9.03 |\n",
       "|             ⋮              |             ⋮              |  ⋱               ⋮              |             ⋮              |\n",
       "|     5.05    19.23    -5.01 |     5.72    16.97    -2.00 |  …      -3.34    17.21    -7.57 |    -4.00    19.70   -10.33 |\n",
       "|     5.48    20.07    -4.71 |     6.04    18.01    -1.54 |         -3.08    18.28    -6.33 |    -2.82    21.01    -8.95 |\n",
       "|     5.32    19.30    -5.48 |     5.78    17.74    -2.02 |         -3.30    17.52    -7.66 |    -4.19    20.58    -9.70 |\n",
       "|     4.22    19.91    -4.99 |     5.25    17.55    -2.16 |         -4.20    17.76    -6.27 |    -4.65    20.42    -8.92 |\n",
       "|     4.95    19.92    -5.91 |     5.76    17.95    -2.74 |         -3.29    18.10    -7.60 |    -3.55    21.32    -9.57 |\n",
       "|     5.51    19.83    -6.13 |     6.17    17.83    -2.95 |  …      -3.14    20.28    -6.96 |    -3.09    22.29   -10.16 |\n",
       "|     5.44    18.36    -6.74 |     6.03    16.77    -3.32 |         -3.27    19.64    -6.97 |    -2.93    21.45   -10.27 |\n",
       "|     5.74    20.09    -6.28 |     6.23    18.23    -2.98 |         -3.01    20.33    -6.18 |    -3.12    22.74    -9.10 |\n",
       "|     6.04    18.34    -6.62 |     6.46    16.60    -3.25 |         -3.30    19.20    -7.51 |    -0.94    17.60    -5.02 |\n",
       "|     5.21    19.82    -6.52 |     5.87    18.11    -3.17 |         -3.51    19.23    -7.09 |    -1.03    18.26    -4.41 |\n",
       "|     5.64    20.34    -5.55 |     5.91    18.01    -2.53 |  …      -3.65    20.90    -6.31 |    -0.95    20.03    -3.81 |"
      ]
     },
     "execution_count": 124,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# adding trajectory data to t\n",
    "t = mdload(\"data/AdK.nc\", top=t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1x214 TrjArray{Float64,Int64}\n",
       "| A                          | A                          |  …   A                          | A                          |\n",
       "| 1MET                       | 2ARG                       |  …   213LEU                     | 214GLY                     |\n",
       "| 2CA                        | 10CA                       |  …   1650CA                     | 1658CA                     |\n",
       "|    -0.06    17.26     8.54 |     2.00    14.04     8.56 |  …      -8.59    13.96     8.62 |   -10.21    17.38     8.81 |"
      ]
     },
     "execution_count": 125,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# frames can be specified by row indices\n",
    "t[3, :]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3x3 TrjArray{Float64,Int64}\n",
       "| A                          | A                          | A                          |\n",
       "| 1MET                       | 2ARG                       | 3ILE                       |\n",
       "| 1CA                        | 2CA                        | 3CA                        |\n",
       "|     9.97    -9.03     9.82 |    10.38    -6.71     6.85 |     7.60    -6.67     4.34 |\n",
       "|     0.01    17.58     8.30 |     1.70    14.27     9.20 |     0.65    11.01     7.67 |\n",
       "|    -0.06    17.26     8.54 |     2.00    14.04     8.56 |     0.44    10.84     7.39 |"
      ]
     },
     "execution_count": 126,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# combinatios of frames and atom selection is available\n",
    "t[1:3 , \"resid 1:3\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " PyMOL(TM) Molecular Graphics System, Version 2.4.0.\n",
      " Copyright (c) Schrodinger, LLC.\n",
      " All Rights Reserved.\n",
      " \n",
      "    Created by Warren L. DeLano, Ph.D. \n",
      " \n",
      "    PyMOL is user-supported open-source software.  Although some versions\n",
      "    are freely available, PyMOL is not in the public domain.\n",
      " \n",
      "    If PyMOL is helpful in your work or study, then please volunteer \n",
      "    support for our ongoing efforts to create open and affordable scientific\n",
      "    software by purchasing a PyMOL Maintenance and/or Support subscription.\n",
      "\n",
      "    More information can be found at \"http://www.pymol.org\".\n",
      " \n",
      "    Enter \"help\" for a list of commands.\n",
      "    Enter \"help <command-name>\" for information on a specific command.\n",
      "\n",
      " Hit ESC anytime to toggle between text and graphics.\n",
      "\n",
      " Detected OpenGL version 2.1. Shaders available.\n",
      " Detected GLSL version 1.20.\n",
      " OpenGL graphics engine:\n",
      "  GL_VENDOR:   ATI Technologies Inc.\n",
      "  GL_RENDERER: AMD Radeon Pro Vega 64 OpenGL Engine\n",
      "  GL_VERSION:  2.1 ATI-3.10.18\n",
      " Detected 20 CPU cores.  Enabled multithreaded rendering.\n",
      "PyMOL>set ray_trace_fog, 0\n",
      " Setting: ray_trace_fog set to 0.00000.\n",
      "PyMOL>set ray_shadows, 0\n",
      " Setting: ray_shadow set to off.\n",
      "PyMOL>set antialias, 1\n",
      " Setting: antialias set to 1.\n",
      "PyMOL>set volume_mode, 1\n",
      " Setting: volume_mode set to 1.\n",
      " Setting-Warning: volume_mode is not supported in Open-Source version of PyMOL\n",
      "PyMOL>set antialias_shader, 2\n",
      " Setting: antialias_shader set to 2.\n",
      " Setting-Warning: antialias_shader is not supported in Open-Source version of PyMOL\n",
      "PyMOL>set line_smooth, on\n",
      " Setting: line_smooth set to on.\n",
      "PyMOL>set valence, 1\n",
      " Setting: valence set to on.\n",
      "PyMOL>set session_compression, 1\n",
      " Setting: session_compression set to on.\n",
      "PyMOL>set movie_panel, 1\n",
      " Setting: movie_panel set to 1.\n",
      "PyMOL>set scene_buttons, 1\n",
      " Setting: scene_buttons set to on.\n",
      "PyMOL>set ray_trace_frames, 0\n",
      " Setting: ray_trace_frames set to off.\n",
      "PyMOL>set show_frame_rate\n",
      " Setting: show_frame_rate set to on.\n",
      " ObjectMoleculeReadPDBStr: read MODEL 1\n",
      " ObjectMoleculeReadPDBStr: read MODEL 2\n",
      " ObjectMoleculeReadPDBStr: read MODEL 3\n",
      " ObjectMoleculeReadPDBStr: read MODEL 4\n",
      " ObjectMoleculeReadPDBStr: read MODEL 5\n",
      " ObjectMoleculeReadPDBStr: read MODEL 6\n",
      " ObjectMoleculeReadPDBStr: read MODEL 7\n",
      " ObjectMoleculeReadPDBStr: read MODEL 8\n",
      " ObjectMoleculeReadPDBStr: read MODEL 9\n",
      " ObjectMoleculeReadPDBStr: read MODEL 10\n",
      " ObjectMoleculeReadPDBStr: read MODEL 11\n",
      " CmdLoad: \"\" loaded as \"run_10-20\".\n",
      " ShaderPrg-Error: fragment shader compilation failed.; name='volume'\n",
      " ShaderPrg-Error-InfoLog:\n",
      "ERROR: 0:65: Use of undeclared identifier 'color'\n",
      "ERROR: 0:67: Use of undeclared identifier 'color'\n",
      "ERROR: 0:67: Use of undeclared identifier 'color'\n",
      "ERROR: 0:68: Use of undeclared identifier 'color'\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Process(`\u001b[4mpymol\u001b[24m \u001b[4mrun_10-20.pdb\u001b[24m`, ProcessExited(0))"
      ]
     },
     "execution_count": 127,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# if you want to visualize selected data, then\n",
    "mdsave(\"run_10-20.pdb\", t[10:20, :]);\n",
    "run(`pymol run_10-20.pdb`)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(:x, :y, :z, :boxsize, :chainname, :chainid, :resname, :resid, :atomname, :atomid, :mass, :radius, :charge, :sasa, :list_bond, :list_angle, :list_dihedral, :list_improper, :list_cmap, :natom, :nframe)"
      ]
     },
     "execution_count": 128,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# TrjArray has many variables in it for describing properties of a molecule\n",
    "fieldnames(TrjArray)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "214-element Array{String,1}:\n",
       " \"CA\"\n",
       " \"CA\"\n",
       " \"CA\"\n",
       " \"CA\"\n",
       " \"CA\"\n",
       " \"CA\"\n",
       " \"CA\"\n",
       " \"CA\"\n",
       " \"CA\"\n",
       " \"CA\"\n",
       " \"CA\"\n",
       " \"CA\"\n",
       " \"CA\"\n",
       " ⋮\n",
       " \"CA\"\n",
       " \"CA\"\n",
       " \"CA\"\n",
       " \"CA\"\n",
       " \"CA\"\n",
       " \"CA\"\n",
       " \"CA\"\n",
       " \"CA\"\n",
       " \"CA\"\n",
       " \"CA\"\n",
       " \"CA\"\n",
       " \"CA\""
      ]
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Atom names as Strings\n",
    "t.atomname"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "214-element Array{Int64,1}:\n",
       "   1\n",
       "   2\n",
       "   3\n",
       "   4\n",
       "   5\n",
       "   6\n",
       "   7\n",
       "   8\n",
       "   9\n",
       "  10\n",
       "  11\n",
       "  12\n",
       "  13\n",
       "   ⋮\n",
       " 203\n",
       " 204\n",
       " 205\n",
       " 206\n",
       " 207\n",
       " 208\n",
       " 209\n",
       " 210\n",
       " 211\n",
       " 212\n",
       " 213\n",
       " 214"
      ]
     },
     "execution_count": 130,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Residue IDs as 1-D Array\n",
    "t.resid"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {},
   "outputs": [],
   "source": [
    "# For sebsequent tutorials, let's clear the memory or shut down the kernel\n",
    "t = nothing # free t"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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  "kernelspec": {
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  "language_info": {
   "file_extension": ".jl",
   "mimetype": "application/julia",
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