{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Peroxide Guide"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This notebook used [evcxr-jupyter](https://github.com/google/evcxr/blob/master/evcxr_jupyter/README.md)\n",
    "\n",
    "These examples correspond to `peroxide = 0.6.4`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Import"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "extern crate peroxide;\n",
    "use peroxide::*;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Module Structure"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```bash\n",
    "├── macros\n",
    "│   ├── matlab_macro.rs\n",
    "│   ├── mod.rs\n",
    "│   └── r_macro.rs\n",
    "├── ml\n",
    "│   ├── mod.rs\n",
    "│   └── reg.rs\n",
    "├── numerical\n",
    "│   ├── interp.rs\n",
    "│   ├── mod.rs\n",
    "│   └── spline.rs\n",
    "├── operation\n",
    "│   ├── extra_ops.rs\n",
    "│   └── mod.rs\n",
    "├── statistics\n",
    "│   ├── mod.rs\n",
    "│   ├── rand.rs\n",
    "│   └── stat.rs\n",
    "├── structure\n",
    "│   ├── dual.rs\n",
    "│   ├── matrix.rs\n",
    "│   ├── mod.rs\n",
    "│   ├── polynomial.rs\n",
    "│   └── vector.rs\n",
    "└── util\n",
    "    ├── mod.rs\n",
    "    ├── non_macro.rs\n",
    "    └── print.rs\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Vector (`Vec<f64>`)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1) Declare Vector"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can declare vector rust-way"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1, 2, 3, 4]\n"
     ]
    }
   ],
   "source": [
    "let a: Vec<f64> = vec![1.,2.,3.,4.];\n",
    "a.print(); // Convenient to print"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And also R-way"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1, 2, 3, 4]\n"
     ]
    }
   ],
   "source": [
    "let b = c!(1,2,3,4); // R-like macro to declare Vec<f64>\n",
    "b.print();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And you can use R's `seq` function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1, 3, 5, 7, 9]\n"
     ]
    }
   ],
   "source": [
    "let c = seq!(1,10,2); // start, end, step\n",
    "c.print();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2) Functional Programming Tool"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is original rust way to FP"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2, 3, 4, 5]\n"
     ]
    }
   ],
   "source": [
    "a.clone().into_iter().map(|x| x + 1.).collect::<Vector>().print();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is `Peroxide` way"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2, 3, 4, 5]\n"
     ]
    }
   ],
   "source": [
    "a.fmap(|x| x + 1.).print();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can use `fmap, reduce, zip_with` as follows"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10\n",
      "[2, 4, 6, 8]\n"
     ]
    }
   ],
   "source": [
    "// reduce\n",
    "a.reduce(0, |x, y| x + y).print();\n",
    "// zip_with\n",
    "a.zip_with(|x, y| x + y, &b).print();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3) Simple Vector operation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There is VectorOps Trait\n",
    "\n",
    "```rust\n",
    "pub trait VecOps {\n",
    "    type Scalar;\n",
    "    fn add(&self, other: &Self) -> Self;\n",
    "    fn sub(&self, other: &Self) -> Self;\n",
    "    fn mul(&self, other: &Self) -> Self;\n",
    "    fn div(&self, other: &Self) -> Self;\n",
    "    fn dot(&self, other: &Self) -> Self::Scalar;\n",
    "}\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2, 4, 6, 8]\n",
      "[0, 0, 0, 0]\n",
      "[1, 4, 9, 16]\n",
      "[1, 1, 1, 1]\n",
      "30\n"
     ]
    }
   ],
   "source": [
    "// Addition\n",
    "a.add(&b).print();\n",
    "a.sub(&b).print();\n",
    "a.mul(&b).print();\n",
    "a.div(&b).print();\n",
    "a.dot(&b).print();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Matrix"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1) Declare Matrix"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are various ways to declare matrix.\n",
    "Belows are all same"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "// Function way\n",
    "let m1 = matrix(vec![1,2,3,4], 2, 2, Row);\n",
    "let m2 = matrix(c!(1,2,3,4), 2, 2, Row);\n",
    "let m2_2 = matrix(c!(1,3,2,4), 2, 2, Col);\n",
    "let m3 = matrix(seq!(1, 4, 1), 2, 2, Row);\n",
    "\n",
    "// Macro way\n",
    "let m4 = matrix!(1;4;1, 2, 2, Row);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "      c[0] c[1]\n",
      " r[0]    1    2\n",
      " r[1]    3    4\n"
     ]
    }
   ],
   "source": [
    "m4.print();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Peroxide allows smart print (But it's not applied to Jupyter)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "        c[0]   c[1]\n",
      " r[0] 2.0000      1\n",
      " r[1]      2      3\n"
     ]
    }
   ],
   "source": [
    "let m0 = matrix(c!(1.99999, 1, 2, 3), 2, 2, Row);\n",
    "m0.print();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2) Concatenate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "      c[0] c[1] c[2]\n",
      " r[0]    1    3    5\n",
      " r[1]    2    4    6\n"
     ]
    }
   ],
   "source": [
    "let a = matrix!(1;4;1, 2, 2, Col);\n",
    "let b = matrix(c!(5, 6), 2, 1, Col);\n",
    "let c = cbind!(a, b);\n",
    "c.print();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "      c[0] c[1]\n",
      " r[0]    1    2\n",
      " r[1]    3    4\n",
      " r[2]    5    6\n"
     ]
    }
   ],
   "source": [
    "let d = matrix!(1;4;1, 2, 2, Row);\n",
    "let e = matrix(c!(5, 6), 1, 2, Row);\n",
    "let f = rbind!(d, e);\n",
    "f.print();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3) Matrix Operation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Caution: `std::ops` consume value. If you want to re-use the value, use `clone`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Addition\n",
      "      c[0] c[1]\n",
      " r[0]    2    5\n",
      " r[1]    5    8\n",
      "\n",
      "Subtraction\n",
      "      c[0] c[1]\n",
      " r[0]    0   -1\n",
      " r[1]    1    0\n",
      "\n",
      "Component-wise multiplication\n",
      "      c[0] c[1]\n",
      " r[0]    1    6\n",
      " r[1]    6   16\n",
      "\n",
      "Matrix multiplication\n",
      "      c[0] c[1]\n",
      " r[0]    5   11\n",
      " r[1]   11   25\n"
     ]
    }
   ],
   "source": [
    "let a = matrix!(1;4;1, 2, 2, Row);\n",
    "let b = matrix!(1;4;1, 2, 2, Col);\n",
    "\n",
    "println!(\"Addition\");\n",
    "(a.clone() + b.clone()).print();\n",
    "println!(\"\");\n",
    "\n",
    "println!(\"Subtraction\");\n",
    "(a.clone() - b.clone()).print();\n",
    "println!(\"\");\n",
    "\n",
    "println!(\"Component-wise multiplication\");\n",
    "(a.clone() * b.clone()).print(); // Component-wise multiplication\n",
    "println!(\"\");\n",
    "\n",
    "println!(\"Matrix multiplication\");\n",
    "(a.clone() % b.clone()).print(); // Matrix multiplication"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4) LU Decomposition"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Column Permutation: [(0, 1)]\n",
      "Row Permutation: [(0, 1)]\n",
      "Lower Triangular Matrix:\n",
      "       c[0] c[1]\n",
      " r[0]    1    0\n",
      " r[1]  0.5    1\n",
      "Upper Triangular Matrix:\n",
      "       c[0] c[1]\n",
      " r[0]    4    3\n",
      " r[1]    0 -0.5\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "()"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "let a = matrix!(1;4;1, 2, 2, Row);\n",
    "let pqlu = a.lu(); // Option<PQLU>\n",
    "\n",
    "// Unwrap process\n",
    "match pqlu {\n",
    "    None => println!(\"No LU Decomposition\"),\n",
    "    Some(abcd) => {\n",
    "        let (p, q, l, u) = (abcd.p, abcd.q, abcd.l, abcd.u);\n",
    "        println!(\"Column Permutation: {:?}\", p);\n",
    "        println!(\"Row Permutation: {:?}\", q);\n",
    "        println!(\"Lower Triangular Matrix:\\n {}\", l);\n",
    "        println!(\"Upper Triangular Matrix:\\n {}\", u);\n",
    "    }\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 5) Determinant"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-2\n"
     ]
    }
   ],
   "source": [
    "let a = matrix!(1;4;1, 2, 2, Row);\n",
    "a.det().print();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 6) Inverse"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "      c[0] c[1]\n",
      " r[0]   -2    1\n",
      " r[1]  1.5 -0.5\n",
      "\n",
      "      c[0] c[1]\n",
      " r[0]   -2    1\n",
      " r[1]  1.5 -0.5\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "()"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a.inv().unwrap().print();\n",
    "\n",
    "// or\n",
    "println!(\"\");\n",
    "match a.inv() {\n",
    "    None => println!(\"No inverse!\"),\n",
    "    Some(m) => m.print(),\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 7) Extract Column or Row"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1, 3]\n",
      "[2, 4]\n",
      "[1, 2]\n",
      "[3, 4]\n"
     ]
    }
   ],
   "source": [
    "let a = matrix!(1;4;1, 2, 2, Row);\n",
    "a.col(0).print();\n",
    "a.col(1).print();\n",
    "a.row(0).print();\n",
    "a.row(1).print();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 8) Functional Programming"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "      c[0] c[1]\n",
      " r[0]    2    3\n",
      " r[1]    4    5\n"
     ]
    }
   ],
   "source": [
    "a.fmap(|x| x + 1f64).print();"
   ]
  }
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