{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# NumPy - Numeric Python\n",
    "NumPy is the core library for scientifc computing Python. The module provides high-performance implementations for dealing with n-dimensional arrays and tools for working with these arrays."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## How to work with NumPy\n",
    "The fundamental data structure in NumPy is called _array_. An array is a n-dimensional container. It can be used for \n",
    "\n",
    "* vectors\n",
    "* matrices\n",
    "* n-dimensional data\n",
    "\n",
    "Internally a NumPy array is stored row major (C order) by default. Note that this is different to Matlab where arrays are stored column major."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Import NumPy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib notebook\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Creating NumPy arrays"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# integer vector, 1D array\n",
    "v = np.array([1, 2, 3])\n",
    "v"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# matrix, 2D array\n",
    "M = np.array([[1, 2], \n",
    "              [3, 4]], dtype=float)\n",
    "M"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# volume, 3D array\n",
    "V = np.array([[[1, 2, 3], [4, 5, 6]], [[7, 8 , 9], [10, 11, 12]]])\n",
    "V"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Initial placeholders"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# create array of zeros with 3 rows and 4 columns\n",
    "np.zeros((3, 4))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# create array of ones \n",
    "np.ones((2, 3, 4), dtype=np.int16)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# create array of evenly spaced values\n",
    "# args: start, stop, step: inclusive start, exclusive stop\n",
    "np.arange(3, 11, 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# create array with evenly spaced values using number of samples\n",
    "# start, stop, num_samples\n",
    "x = np.linspace(-1, 4, 20)\n",
    "\n",
    "_, ax = plt.subplots(figsize=(5, 3.5))\n",
    "ax.plot(x, np.sin(x))\n",
    "\n",
    "_, ax = plt.subplots(figsize=(5, 3.5))\n",
    "ax.plot(np.sin(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# create a constant array \n",
    "np.full((2, 3), 7)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# create a n x n identity matrix\n",
    "np.eye(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# create an array with random values\n",
    "np.random.random((2, 3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# create an empty array (attention: memory is uninitialized!)\n",
    "np.empty((3, 2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "base = np.array([1, 2, 3])\n",
    "\n",
    "a = []\n",
    "for i in range(10):\n",
    "    a.append(base.copy())\n",
    "a = np.array(a)\n",
    "    \n",
    "b = np.stack([base.copy()] * 10)\n",
    "c = np.repeat(base[None], 10, axis=0)\n",
    "d = np.tile(base, (10, 1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "print(a)\n",
    "assert np.allclose(a, b) and np.allclose(b, c) and np.allclose(c, d)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Inspecting array"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# array dimensions\n",
    "V.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# number of dimensions\n",
    "V.ndim"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# number of elements\n",
    "V.size"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# data type of array elements\n",
    "V.dtype"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Array operations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# sum\n",
    "V.sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# min\n",
    "V.min()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# max\n",
    "V.max()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# mean\n",
    "V.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# standard deviation\n",
    "V.std()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Arithmetic Operations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "a = np.arange(3)\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# addition\n",
    "a + a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "a + 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# exp\n",
    "np.exp(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# * is elementwise multiplication\n",
    "# @ is __matmul__\n",
    "# a is one-dimensional\n",
    "for inner in [(a * a).sum(), a @ a, a.dot(a), a.T.dot(a)]:\n",
    "    print(inner)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "for outer in [np.outer(a, a), a[None] * a[:, None]]:\n",
    "    print(outer)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Slicing, Indexing\n",
    "In python indexing starts at 0!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# get first element\n",
    "a\n",
    "a[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "M"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# get 1st row\n",
    "M[0] # = M[0,:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# get last column\n",
    "M[:,-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "v = np.arange(10)\n",
    "v"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# get every second element\n",
    "# [start:stop:step]\n",
    "v[1::2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# boolean indexing\n",
    "v[v > 3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "v > 3"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}