notebooks/python_intro.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "5a2e094b",
   "metadata": {},
   "source": [
    "![CC](https://i.creativecommons.org/l/by/4.0/88x31.png)\n",
    "\n",
    "This work is licensed under a [Creative Commons Attribution 4.0 International License](http://creativecommons.org/licenses/by/4.0/).\n",
    "\n",
    "Author(s): Janis Geise, Andre Weiner"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a91d6677-6c76-480a-b7ea-c8ff19940948",
   "metadata": {},
   "source": [
    "# A brief introduction to Python programming\n",
    "\n",
    "## Overview\n",
    "\n",
    "Note that this notebook does not provide a comprehensive introduction to Python programming. It aims to explain Python functionality frequently used throughout lecture and exercise notebooks that students typically struggle with at the beginning. If you are already an experienced Python programmer, feel free to quickly skim through the notebook or to skip it entirely. If you consider yourself as a beginner both in Python and programming in general, we provide a list of resources for self-study at the end of this notebook. The following topics will be covered in this notebook:\n",
    "\n",
    "- Built-in functions and data types\n",
    "- Functions and lambda functions\n",
    "- Object-oriented programming\n",
    "- Plotting with Matplotlib  \n",
    "  - Line plots  \n",
    "  - Scatter plots  \n",
    "  - Contour lines and filled contours\n",
    "  - sub-plots  \n",
    "- PyTorch tensors  \n",
    "  - Working with tensors  \n",
    "  - Common tensor operations\n",
    "- Handling column-like data with Pandas\n",
    "- Understanding error messages\n",
    "- References"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d9c2b894-f744-4894-9b1f-35575aa305d1",
   "metadata": {},
   "source": [
    "## Built-in functions and data types\n",
    "\n",
    "Python provides a number of [built-in functions](https://docs.python.org/3/library/functions.html) and data types to simplify and accelerate common tasks. While some of these functions and structures are intuitively clear for anyone with basic math and programming knowledge, e.g., `abs()` for computing the absolute value of a number, others may be harder to understand. This section discusses a few heavily-used built-in functions and data structures.\n",
    "\n",
    "### Lists, tuples, and dictionaries\n",
    "\n",
    "Lists in Python are iterable containers in which objects of different types can be stored. Common attributes of lists are that we can iterate through them, append or delete list items, or merge them. In contrast to lists, tuples have a fixed length, which is defined when creating the tuple. Dictionaries are containers for data that come as key-value-pairs. The key might be the name of a person and the value might be the person's email address."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "a4f95dd5",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['x', 'U']\n",
      "['x', 'U', 'p']\n",
      "The first label is x and the last label is p\n",
      "['U', 'p']\n",
      "['U', 'p', 'x', 'y']\n",
      "('U', 'p')\n",
      "{'x': 'm', 'U': 'm/s'}\n"
     ]
    }
   ],
   "source": [
    "# create a list of strings\n",
    "labels = [\"x\", \"U\"]\n",
    "print(labels)\n",
    "\n",
    "# append another label\n",
    "labels.append(\"p\")\n",
    "print(labels)\n",
    "\n",
    "# get the first and last elements of the list\n",
    "print(f\"The first label is {labels[0]} and the last label is {labels[-1]}\")\n",
    "\n",
    "# delete the first list element\n",
    "del labels[0]\n",
    "print(labels)\n",
    "\n",
    "# append one list to another\n",
    "print(labels + [\"x\", \"y\"])\n",
    "\n",
    "# convert a list to a tuple\n",
    "labels_tuple = tuple(labels)\n",
    "print(labels_tuple)\n",
    "\n",
    "# store the unit associated with the label in a dictionary\n",
    "labels_and_units = {}\n",
    "labels_and_units[\"x\"] = \"m\"\n",
    "labels_and_units[\"U\"] = \"m/s\"\n",
    "print(labels_and_units)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "bbe8fefd",
   "metadata": {},
   "outputs": [
    {
     "ename": "AttributeError",
     "evalue": "'tuple' object has no attribute 'append'",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mAttributeError\u001b[0m                            Traceback (most recent call last)",
      "Cell \u001b[0;32mIn [14], line 2\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[38;5;66;03m# the length of a tuple is fixed\u001b[39;00m\n\u001b[0;32m----> 2\u001b[0m \u001b[43mlabels_tuple\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mappend\u001b[49m(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124ma\u001b[39m\u001b[38;5;124m\"\u001b[39m)\n",
      "\u001b[0;31mAttributeError\u001b[0m: 'tuple' object has no attribute 'append'"
     ]
    }
   ],
   "source": [
    "# the length of a tuple is fixed\n",
    "labels_tuple.append(\"a\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2619325b",
   "metadata": {},
   "source": [
    "### Looping through iterables\n",
    "\n",
    "Both lists and tuples are iterables, meaning that we can iterate/loop through them. There are a number of strategies to iterate through one or multiple iterables, which are demonstrated in the next cell."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "b6a4ce39",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Label 0: U\n",
      "Label 1: p\n"
     ]
    }
   ],
   "source": [
    "# classical C-like looping:\n",
    "# 1. determine the length of the list  with len()\n",
    "# 2. create an iterator of indices starting from 0\n",
    "# 3. use the loop variable i to access list elements\n",
    "for i in range(len(labels)):\n",
    "    print(f\"Label {i}: {labels[i]}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "c8f17afd",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "U\n",
      "p\n"
     ]
    }
   ],
   "source": [
    "# a much more \"Pythonic\" way of looping over the list items\n",
    "for label in labels:\n",
    "    print(label)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "3a929fe2",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Label 0: U\n",
      "Label 1: p\n"
     ]
    }
   ],
   "source": [
    "# in case the list index is really needed, use enumerate()\n",
    "for i, label in enumerate(labels):\n",
    "    print(f\"Label {i}: {label}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "1c9d0db7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "U in m/s\n",
      "p in Pa\n"
     ]
    }
   ],
   "source": [
    "# Pythonic loop over multiple iterables\n",
    "units = (\"m/s\", \"Pa\")\n",
    "for label, unit in zip(labels, units):\n",
    "    print(f\"{label} in {unit}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "4b1567aa",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Label 0: U in m/s\n",
      "Label 1: p in Pa\n"
     ]
    }
   ],
   "source": [
    "# the same as above combined with enumerate\n",
    "for i, (label, unit) in enumerate(zip(labels, units)):\n",
    "    print(f\"Label {i}: {label} in {unit}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "520382c9",
   "metadata": {},
   "source": [
    "Both `zip()` and `enumerate()` return iterators. In contrast to lists or tuples, the content of iterators is only retrieved or created when it is really needed. For example, if we want to load and process large files stored on the hard drive, an iterator allows loading and processing one file after the other in order to reduce the memory consumption. However, in most cases considered here, we can simply convert the iterator into a list or tuple."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "a7707147",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[('U', 'm/s'), ('p', 'Pa')]\n",
      "<zip object at 0x7364e631c700>\n"
     ]
    },
    {
     "ename": "TypeError",
     "evalue": "'zip' object is not subscriptable",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "Cell \u001b[0;32mIn [20], line 11\u001b[0m\n\u001b[1;32m      8\u001b[0m \u001b[38;5;28mprint\u001b[39m(labels_and_units)\n\u001b[1;32m     10\u001b[0m \u001b[38;5;66;03m# moreover, we don't have an index-based access to the iterator\u001b[39;00m\n\u001b[0;32m---> 11\u001b[0m \u001b[38;5;28mprint\u001b[39m(\u001b[43mlabels_and_units\u001b[49m\u001b[43m[\u001b[49m\u001b[38;5;241;43m0\u001b[39;49m\u001b[43m]\u001b[49m)\n",
      "\u001b[0;31mTypeError\u001b[0m: 'zip' object is not subscriptable"
     ]
    }
   ],
   "source": [
    "# create an iterator for labels and units\n",
    "labels_and_units = zip(labels, units)\n",
    "\n",
    "# convert the iterator to a list of tuples and print the list\n",
    "print(list(labels_and_units))\n",
    "\n",
    "# printing the iterator directly does not have the desired effect\n",
    "print(labels_and_units)\n",
    "\n",
    "# moreover, we don't have an index-based access to the iterator\n",
    "print(labels_and_units[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6b15aef1",
   "metadata": {},
   "source": [
    "A common error source when working with `zip()` is the handling of iterables with varying lengths. The iteration stops when the length of the shorted iterable passed to `zip()` is reached."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "b0c2fac3-9db7-4e92-b5f4-b205b5b09976",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "('U', 'm/s') ('p', 'Pa')\n"
     ]
    }
   ],
   "source": [
    "labels.append(\"x\")\n",
    "# we unpack the iterator for printing using *\n",
    "print(*zip(labels, units))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ba7bdc0b",
   "metadata": {},
   "source": [
    "Looping over the keys and values of a dictionary works in a similar way as described for list and tuples. The methods `keys()`, `values()`, and `items()` provide us with iterators for the dictionary's keys, values, or key-value-pairs, respectively. Similar to the index-based access to the content of lists and tuples, we can access the value associated with a key using the `[]` operator."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "7c0c1b3a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The unit of x is m\n",
      "The unit of U is m/s\n",
      "The unit of x is m\n",
      "The unit of U is m/s\n",
      "The unit of x is m\n",
      "The unit of U is m/s\n"
     ]
    }
   ],
   "source": [
    "labels_and_units = {}\n",
    "labels_and_units[\"x\"] = \"m\"\n",
    "labels_and_units[\"U\"] = \"m/s\"\n",
    "\n",
    "# for each key/label, print its value/unit\n",
    "for key in labels_and_units.keys():\n",
    "    print(f\"The unit of {key} is {labels_and_units[key]}\")\n",
    "\n",
    "# loop over keys and values with zip\n",
    "for key, value in zip(labels_and_units.keys(), labels_and_units.values()):\n",
    "    print(f\"The unit of {key} is {value}\")\n",
    "\n",
    "# even short than above\n",
    "for key, value in labels_and_units.items():\n",
    "    print(f\"The unit of {key} is {value}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7bc08c49",
   "metadata": {},
   "source": [
    "### List and dictionary comprehensions\n",
    "\n",
    "Comprehensions are an efficient way of creating new lists or dictionaries without for-loops. Especially, if a task needs to be repeated multiple times, comprehensions are short, clear and efficient. The general syntax is:\n",
    "\n",
    "```\n",
    "# list comprehension\n",
    "result = [result_based_on_item for item in iterable]\n",
    "# dictionary comprehension\n",
    "result = {key_base_on_item : value_base_on_item for item in iterable}\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "92e5f8a6",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0, 1, 4, 9, 16, 25, 36, 49, 64, 81]\n",
      "{0: '(0)', 1: '(1)', 4: '(4)', 9: '(9)', 16: '(16)', 25: '(25)', 36: '(36)', 49: '(49)', 64: '(64)', 81: '(81)'}\n"
     ]
    }
   ],
   "source": [
    "# create a list of squared values\n",
    "list_of_numbers = [i**2 for i in range(10)]\n",
    "print(list_of_numbers)\n",
    "\n",
    "# create dictionary with string representations\n",
    "numbers_as_strings = {i : f\"({i})\" for i in list_of_numbers}\n",
    "print(numbers_as_strings)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "79ecb378",
   "metadata": {},
   "source": [
    "Another common pattern is the addition of a logical statement to the comprehension. The extended syntax is:\n",
    "\n",
    "```\n",
    "# simple if condition\n",
    "result = [result_based_on_item for item in iterable if condition_based_on_item]\n",
    "# if-else condition\n",
    "result = [result_true if condition else results_false for item in iterable]\n",
    "# if-else condition for dictionaries\n",
    "results = {(key_true if key_condition else key_false) : (value_true if value_condition else value_false ) for items in iterable}\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "59ca5fad",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0, 4, 16, 36, 64]\n",
      "{0: 'even', 1: 'odd', 4: 'even', 9: 'odd', 16: 'even', 25: 'odd', 36: 'even', 49: 'odd', 64: 'even', 81: 'odd'}\n"
     ]
    }
   ],
   "source": [
    "# print only even numbers\n",
    "even_numbers = [i for i in list_of_numbers if i % 2 == 0]\n",
    "print(even_numbers)\n",
    "\n",
    "# create a dictionary with even-odd-labeling\n",
    "even_odd = {i : (\"even\" if i % 2 == 0 else \"odd\") for i in list_of_numbers}\n",
    "print(even_odd)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "78eaa8c7",
   "metadata": {},
   "source": [
    "It is also possible to nest multiple comprehensions and conditionals. However, the resulting statements are often hard to read and error-prone. As a rule of thumb, there should be never more than two `for` statements inside the square or curly brackets."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1007fa65-d91a-4922-8cab-25b44f94f3ad",
   "metadata": {},
   "source": [
    "## Functions and Lambda functions\n",
    "\n",
    "Functions are the simplest and most common way to avoid code duplication and to improve the program's modularity and readability. In the function header, zero or more function parameters may be defined. Optionally, we can provide default arguments (values) for some of the parameters. The optional parameters always follow at the end of the parameter list. Moreover, functions may or may not return a result."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "b3390d0c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Hello Horace Lamb!\n"
     ]
    }
   ],
   "source": [
    "# function without return argument\n",
    "def print_greeting(first_name, family_name):\n",
    "    print(f\"Hello {first_name} {family_name}!\")\n",
    "\n",
    "print_greeting(\"Horace\", \"Lamb\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "0d3990aa",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a=1, b=2\n",
      "a=1; b=2\n"
     ]
    }
   ],
   "source": [
    "# function with optional and return argument\n",
    "def format_arguments(parameters, arguments, separator=\", \"):\n",
    "    formatted_arguments = separator.join(\n",
    "        [f\"{param}={arg}\" for param, arg in zip(parameters, arguments)]\n",
    "    )\n",
    "    return formatted_arguments\n",
    "\n",
    "# print with default separator\n",
    "print(format_arguments((\"a\", \"b\"), (1, 2)))\n",
    "\n",
    "# print with different separator\n",
    "print(format_arguments((\"a\", \"b\"), (1, 2), \"; \"))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1348af8b",
   "metadata": {},
   "source": [
    "Even though Python is an interpreted language without strict typing, it is good practice to use so-called type hints in the function definition. However, note that the type hints are not checked or enforced by the interpreter. Their main purpose is improved code readability and improved documentation, e.g., when using automatic documentation generators like [Sphinx](https://www.sphinx-doc.org/en/master/)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "c5f2aa9b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a=1; b=2\n"
     ]
    }
   ],
   "source": [
    "# same as the last function above but with type hints\n",
    "def format_arguments(parameters: list, arguments: list, separator: str = \", \") -> str:\n",
    "    formatted_arguments = separator.join(\n",
    "        [f\"{param}={arg}\" for param, arg in zip(parameters, arguments)]\n",
    "    )\n",
    "    return formatted_arguments\n",
    "\n",
    "print(format_arguments((\"a\", \"b\"), (1, 2), \"; \"))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6e8849d2",
   "metadata": {},
   "source": [
    "Python supports multiple assignments in a single statement (line). Moreover, functions can return multiple arguments packed in a tuple. We can assign this tuple to a variable, or we can unpack the tuple into the individual return arguments."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "7c66cbd0",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "('x in m', 'y in m/s')\n",
      "The figure shows x in m plotted against y in m/s\n",
      "The figure shows x in m plotted against y in m/s\n"
     ]
    }
   ],
   "source": [
    "# more specific type hinting\n",
    "from typing import Tuple\n",
    "\n",
    "def format_labels(x_label: str, y_label: str, x_unit: str, y_unit: str) -> Tuple[str, str]:\n",
    "    label_with_unit_x = f\"{x_label} in {x_unit}\"\n",
    "    label_with_unit_y = f\"{y_label} in {y_unit}\"\n",
    "    return label_with_unit_x, label_with_unit_y\n",
    "\n",
    "# print the packed return arguments\n",
    "print(format_labels(\"x\", \"y\", \"m\", \"m/s\"))\n",
    "\n",
    "# unpack into individual parameters, then print\n",
    "label_x, label_y = format_labels(\"x\", \"y\", \"m\", \"m/s\")\n",
    "print(f\"The figure shows {label_x} plotted against {label_y}\")\n",
    "\n",
    "# we can combine the unpacking and printing in a single statement using *\n",
    "print(\"The figure shows {:s} plotted against {:s}\".format(*format_labels(\"x\", \"y\", \"m\", \"m/s\")))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "abdfbfad",
   "metadata": {},
   "source": [
    "Lambda functions are small functions with limited complexity. In contrast to normal functions, lambda-functions consist of a single expression and are typically defined in a single line of code. Due to their limited complexity, they are often defined in place as arguments for other functions. The general syntax is:\n",
    "\n",
    "```\n",
    "lambda argument_1, argument_2, ..., argument_N: what_to_do\n",
    "```\n",
    "If the same lambda-functions ais employed repeatedly, we can also assign it to a variable."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "2dd265d2-a58f-4148-be3d-9cae56f659de",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Folder case_0 has suffix 0\n",
      "Folder case_5 has suffix 5\n",
      "Folder case_10 has suffix 10\n",
      "Folder case_15 has suffix 15\n",
      "Folder case_20 has suffix 20\n",
      "Wrong sorting:  ['case_0', 'case_10', 'case_15', 'case_20', 'case_5']\n",
      "Correct sorting:  ['case_0', 'case_5', 'case_10', 'case_15', 'case_20']\n"
     ]
    }
   ],
   "source": [
    "# use lambda function to extract name suffix\n",
    "get_suffix = lambda name, separator: name.split(separator)[-1]\n",
    "folders = [f\"case_{i}\" for i in range(0, 21, 5)]\n",
    "suffixes = [get_suffix(folder, \"_\") for folder in folders]\n",
    "for folder, suffix in zip(folders, suffixes):\n",
    "    print(f\"Folder {folder} has suffix {suffix}\")\n",
    "\n",
    "# imagine you want to sort the folders according to their suffix;\n",
    "# naively, we could pass the list of folders to the sorted function\n",
    "print(\"Wrong sorting: \", sorted(folders))\n",
    "# as you can see in the output, the items are sorted character by character;\n",
    "# therefore, case_10 is listed before case_5; in some situations we may easily\n",
    "# miss such a mistake, e.g., when testing only suffixes between 0 and 9\n",
    "\n",
    "# solution: we need to be more precise about the sorting criterion;\n",
    "# we want to sort based on the suffix and we want the suffix to be interpreted as integer and not as string\n",
    "# the criterion can be passed to the sort function using the 'key' parameter\n",
    "print(\"Correct sorting: \", sorted(folders, key=lambda case: int(case.split(\"_\")[-1])))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "21b53a6e",
   "metadata": {},
   "source": [
    "## Object-orientated programming in python\n",
    "\n",
    "As many other programming languages, Python supports object-orientated programming. The following section provides a brief overview of object-orientated programming in python.\n",
    "\n",
    "### General structure and initialization\n",
    "\n",
    "In Python, user-defined data types are defined with the keyword `class`. The class itself needs to have an `.__init__()` method in order to initialize attributes and methods."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "792f60d1",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "new class attribute: 42\n"
     ]
    }
   ],
   "source": [
    "# let's define a simple class\n",
    "class SimpleClass():\n",
    "    # currently the __init__() method is empty, so the class won't do anything\n",
    "    def __init__(self):\n",
    "        pass\n",
    "    \n",
    "# the class can now be instantiated\n",
    "new_class = SimpleClass()\n",
    "\n",
    "# and we can add some attributes\n",
    "new_class.new_attribute = 42\n",
    "\n",
    "print(\"new class attribute:\", new_class.new_attribute)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "db9824b9",
   "metadata": {},
   "source": [
    "The keyword `self` represents the instance of the class and is required for accessing any attributes or methods of the class."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "c0371438",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x, y = 1, 2\n",
      "1 + 2 = 3\n",
      "5 + 37 = 42\n"
     ]
    }
   ],
   "source": [
    "# we can initialize a class directly with attributes and methods as well:\n",
    "class AddNumbers():\n",
    "    # in this case, the value for y is given by default\n",
    "    def __init__(self, x, y = 2):\n",
    "        self.x = x\n",
    "        self.y = y\n",
    "    \n",
    "    # method for adding two numbers\n",
    "    def add_two_numbers(self):\n",
    "        return self.x + self.y\n",
    "    \n",
    "# since the value for y is given by default we can instanciate the class only ba passing in x as argument\n",
    "add = AddNumbers(x=1)\n",
    "print(f\"x, y = {add.x}, {add.y}\")\n",
    "print(f\"{add.x} + {add.y} = {add.add_two_numbers()}\")\n",
    "\n",
    "# alternatively, we can assign values for x and y when creating the instance\n",
    "add_2 = AddNumbers(x=5, y=37)\n",
    "print(f\"{add_2.x} + {add_2.y} = {add_2.add_two_numbers()}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cbd86067",
   "metadata": {},
   "source": [
    "### Inheritance\n",
    "\n",
    "Python supports inheritance, which allows to inherit methods and properties from other classes. This is quite convenient, because methods which are already implemented can be used and extended without the necessity to write everything from scratch. Considering the previous example, imagine we now want to add two numbers and then compute the mean of it:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "df953bf5",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mean of 5 and 3 =  4.0\n"
     ]
    }
   ],
   "source": [
    "# we could implement a completly new class from scratch...\n",
    "class ComputeMean():\n",
    "    def __init__(self, x, y):\n",
    "        self.x = x\n",
    "        self.y = y\n",
    "    \n",
    "    # method for adding two numbers\n",
    "    def mean_of_two_numbers(self):\n",
    "        return (self.x + self.y) / 2\n",
    "    \n",
    "# now compute the mean of two numbers\n",
    "comp_mean = ComputeMean(5, 3)\n",
    "print(\"mean of 5 and 3 = \", comp_mean.mean_of_two_numbers())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "f39cec05",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mean of 8 and 4 =  6.0\n",
      "8 + 4 =  12\n"
     ]
    }
   ],
   "source": [
    "# ... but a more efficient way is inheriting the properties of our previously implemented class 'AddNumbers':\n",
    "class ComputeMean(AddNumbers):\n",
    "    def __init__(self, x, y):\n",
    "        # we need to initialize the parent class with the method 'super()' and also the attributes we want to access\n",
    "        super().__init__(x, y)\n",
    "        \n",
    "    def mean_of_two_numbers(self):\n",
    "        # now we can use the method 'add_two_numbers()' we already implemented in the parent class\n",
    "        return AddNumbers.add_two_numbers(self) / 2\n",
    "    \n",
    "# compute the mean of 8 and 4\n",
    "comp_mean = ComputeMean(8, 4)\n",
    "print(\"mean of 8 and 4 = \", comp_mean.mean_of_two_numbers())\n",
    "\n",
    "# but we can also directly access the 'add_two_numbers' method from the parent class without calling it\n",
    "print(\"8 + 4 = \", comp_mean.add_two_numbers())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d2d72e32",
   "metadata": {},
   "source": [
    "The parent class from which we want to inherit the properties needs to be passed into our child class as argument, as can be seen in the above examples. Further, we need to initilize the parent class by calling the built-in `super()` method. This allows us to access methods and other properties of the parent class without the need to implement them again in the child class. When calling the `super()` method, the attributes we want to initialize need to be passed into the `__init()__` method as well, e.g. the following would not work, since we didn't initialize the attribute `y`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "9a5b7b03",
   "metadata": {},
   "outputs": [
    {
     "ename": "TypeError",
     "evalue": "AddNumbers.__init__() missing 1 required positional argument: 'x'",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "Cell \u001b[0;32mIn [35], line 10\u001b[0m\n\u001b[1;32m      7\u001b[0m         \u001b[38;5;28;01mreturn\u001b[39;00m AddNumbers\u001b[38;5;241m.\u001b[39madd_two_numbers(\u001b[38;5;28mself\u001b[39m) \u001b[38;5;241m/\u001b[39m \u001b[38;5;241m2\u001b[39m\n\u001b[1;32m      9\u001b[0m \u001b[38;5;66;03m# compute the mean of 8 and 4\u001b[39;00m\n\u001b[0;32m---> 10\u001b[0m comp_mean \u001b[38;5;241m=\u001b[39m \u001b[43mComputeMean\u001b[49m\u001b[43m(\u001b[49m\u001b[43mx\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[38;5;241;43m4\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43my\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[38;5;241;43m8\u001b[39;49m\u001b[43m)\u001b[49m\n\u001b[1;32m     11\u001b[0m \u001b[38;5;28mprint\u001b[39m(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mmean of 8 and 4 = \u001b[39m\u001b[38;5;124m\"\u001b[39m, comp_mean\u001b[38;5;241m.\u001b[39mmean_of_two_numbers())\n",
      "Cell \u001b[0;32mIn [35], line 4\u001b[0m, in \u001b[0;36mComputeMean.__init__\u001b[0;34m(self, x, y)\u001b[0m\n\u001b[1;32m      2\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21m__init__\u001b[39m(\u001b[38;5;28mself\u001b[39m, x, y):\n\u001b[1;32m      3\u001b[0m     \u001b[38;5;66;03m# if we forget to initialize the attributes, then we won't have access to it\u001b[39;00m\n\u001b[0;32m----> 4\u001b[0m     \u001b[38;5;28;43msuper\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[38;5;21;43m__init__\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\n",
      "\u001b[0;31mTypeError\u001b[0m: AddNumbers.__init__() missing 1 required positional argument: 'x'"
     ]
    }
   ],
   "source": [
    "class ComputeMean(AddNumbers):\n",
    "    def __init__(self, x, y):\n",
    "        # if we forget to initialize the attributes, then we won't have access to it\n",
    "        super().__init__()\n",
    "        \n",
    "    def mean_of_two_numbers(self):\n",
    "        return AddNumbers.add_two_numbers(self) / 2\n",
    "    \n",
    "# compute the mean of 8 and 4\n",
    "comp_mean = ComputeMean(x=4, y=8)\n",
    "print(\"mean of 8 and 4 = \", comp_mean.mean_of_two_numbers())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "0b209f6b-e0d0-4778-afff-f2877592979a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mean of 8 and 4 =  5.0\n"
     ]
    }
   ],
   "source": [
    "class ComputeMean(AddNumbers):\n",
    "    def __init__(self, x, y):\n",
    "        # let's just initialize y and see what happens\n",
    "        super().__init__(y)\n",
    "        \n",
    "    def mean_of_two_numbers(self):\n",
    "        return AddNumbers.add_two_numbers(self) / 2\n",
    "    \n",
    "# compute the mean of 8 and 4\n",
    "comp_mean = ComputeMean(x=4, y=8)\n",
    "print(\"mean of 8 and 4 = \", comp_mean.mean_of_two_numbers())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8b72d140-6ef9-4f0e-834e-d5266ee880c5",
   "metadata": {},
   "source": [
    "In this case, the parameter `y` which is passed into our `super().__init__()` method is interpreted as `x`, since the `y` parameter is already set by default and therefore not required. The Python interpreter assumes that, if only one argument is given, it has to be the parameter `x`. If we want Python to interpret this one parameter as `y`, we have to use a keyword argument:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "f7a2c99b-8775-4d46-89e4-9dac3396ccdb",
   "metadata": {},
   "outputs": [
    {
     "ename": "TypeError",
     "evalue": "AddNumbers.__init__() missing 1 required positional argument: 'x'",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "Cell \u001b[0;32mIn [37], line 10\u001b[0m\n\u001b[1;32m      7\u001b[0m         \u001b[38;5;28;01mreturn\u001b[39;00m AddNumbers\u001b[38;5;241m.\u001b[39madd_two_numbers(\u001b[38;5;28mself\u001b[39m) \u001b[38;5;241m/\u001b[39m \u001b[38;5;241m2\u001b[39m\n\u001b[1;32m      9\u001b[0m \u001b[38;5;66;03m# compute the mean of 8 and 4\u001b[39;00m\n\u001b[0;32m---> 10\u001b[0m comp_mean \u001b[38;5;241m=\u001b[39m \u001b[43mComputeMean\u001b[49m\u001b[43m(\u001b[49m\u001b[43mx\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[38;5;241;43m4\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43my\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[38;5;241;43m8\u001b[39;49m\u001b[43m)\u001b[49m\n\u001b[1;32m     11\u001b[0m \u001b[38;5;28mprint\u001b[39m(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mmean of 8 and 4 = \u001b[39m\u001b[38;5;124m\"\u001b[39m, comp_mean\u001b[38;5;241m.\u001b[39mmean_of_two_numbers())\n",
      "Cell \u001b[0;32mIn [37], line 4\u001b[0m, in \u001b[0;36mComputeMean.__init__\u001b[0;34m(self, x, y)\u001b[0m\n\u001b[1;32m      2\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21m__init__\u001b[39m(\u001b[38;5;28mself\u001b[39m, x, y):\n\u001b[1;32m      3\u001b[0m     \u001b[38;5;66;03m# this time we specificly initialize the parameter y as y\u001b[39;00m\n\u001b[0;32m----> 4\u001b[0m     \u001b[38;5;28;43msuper\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[38;5;21;43m__init__\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43my\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43my\u001b[49m\u001b[43m)\u001b[49m\n",
      "\u001b[0;31mTypeError\u001b[0m: AddNumbers.__init__() missing 1 required positional argument: 'x'"
     ]
    }
   ],
   "source": [
    "class ComputeMean(AddNumbers):\n",
    "    def __init__(self, x, y):\n",
    "        # this time we specificly initialize the parameter y as y\n",
    "        super().__init__(y=y)\n",
    "        \n",
    "    def mean_of_two_numbers(self):\n",
    "        return AddNumbers.add_two_numbers(self) / 2\n",
    "    \n",
    "# compute the mean of 8 and 4\n",
    "comp_mean = ComputeMean(x=4, y=8)\n",
    "print(\"mean of 8 and 4 = \", comp_mean.mean_of_two_numbers())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a361f061-edc9-4978-a71b-4592596ea6de",
   "metadata": {},
   "source": [
    "Now we get the error message again, showing us that we forgot to initialize the `x` parameter.\n",
    "\n",
    "### Decorators\n",
    "\n",
    "Functions are represented as objects in python and can therefore be passed into other functions as arguments or returned by functions. Decorators use this property, by taking function objects as arguments and then modifying its behavior. The following examples where adopted from [Python Decorators in 15 Minutes](https://www.youtube.com/watch?v=r7Dtus7N4pI)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "2e472d80-291b-4d01-8991-b771707949b3",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "function 1\n",
      "function 1\n"
     ]
    }
   ],
   "source": [
    "# let's define a function which only prints its name\n",
    "def function1():\n",
    "    print(\"function 1\")\n",
    "    \n",
    "# now we define a function taking another function as argument and then calling this function    \n",
    "def function2(f):\n",
    "    f()\n",
    "    \n",
    "# now we can execute function1...\n",
    "function1()\n",
    "\n",
    "# ... or we can pass function1 into function2 and execute it within function2:\n",
    "function2(function1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "84ad9276-5531-4764-af75-dbac5d54b751",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "calling function3 with function1 as argument:\n",
      " <function function3.<locals>.some_wrapper_function at 0x7364e5984670>\n"
     ]
    }
   ],
   "source": [
    "# we can extend this example by adding another function into our function2\n",
    "def function3(f):\n",
    "    # let's use this function to execute whatever function is passed into function3\n",
    "    def some_wrapper_function():\n",
    "        print(\"starting function\")\n",
    "        f()\n",
    "        print(\"function ended\")\n",
    "\n",
    "    return some_wrapper_function\n",
    "\n",
    "# calling the wrapper function\n",
    "print(\"calling function3 with function1 as argument:\\n\", function3(function1))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "640d61c0-9e9d-4961-a0dd-a9b0c3247632",
   "metadata": {},
   "source": [
    "As shown in this example, $function1$ is not executed within the $some\\_wrapper\\_function$. This is because $function3$ returns $some\\_wrapper\\_function$ as an object. In order to execute this object, we need to add parenthesis:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "286a9953-e6e0-47f6-bbf9-51d9d8159594",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "starting function\n",
      "function 1\n",
      "function ended\n"
     ]
    }
   ],
   "source": [
    "# function3 returns an object, still need to execute the function\n",
    "function3(function1)()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2387f41e-ba73-46ee-b746-caa2e03bee40",
   "metadata": {},
   "source": [
    "Now we get the expected output. Using this notation, however, can get quite confusing, especially if more complex functions are involved. To avoid this we can assign the returned function object to another variable:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "d5552a33-3859-40bc-b927-082aa64e51a8",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "starting function\n",
      "function 1\n",
      "function ended\n"
     ]
    }
   ],
   "source": [
    "# we can assign the function call to another object, e.g. x and then call x()\n",
    "x = function3(function1)\n",
    "\n",
    "# now the variable x represents the function3 object called with function1 as argument and we can just execute it\n",
    "x()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fdd629b9-5dfe-48f6-ac63-161db61e2b8e",
   "metadata": {},
   "source": [
    "Instead of assigning the function object to a variable and then execute this object, Python provides a short hand notation called decorators:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "097296a7-3f2d-4883-8597-ece6519a2c33",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "starting function\n",
      "executing function x using a decorator\n",
      "function ended\n"
     ]
    }
   ],
   "source": [
    "# a decorator is a short notation of executing the function object\n",
    "@function3       # this is equivalent to: x = function3(x)\n",
    "def x():\n",
    "    print(\"executing function x using a decorator\")\n",
    "    \n",
    "# since x is an object, we need to add parenthesis to execute it\n",
    "x()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "76ef67d1-dafd-459e-a17e-ec008dfdd8e1",
   "metadata": {},
   "source": [
    "## Plotting with Matplotlib\n",
    "\n",
    "[Matplotlib](https://matplotlib.org/stable/index.html) is a library for creating plots and visualizing data. This section deals with the basic usage of Matplotlib in order to create simple plots. A more thorough introduction can be found in the references.\n",
    "\n",
    "### Line plots\n",
    "\n",
    "Simple line plots can be created with the method `plot()` located in `matplotlib.pyplot`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "4deebb77-59b6-4d32-9608-b6b12448aa58",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import torch as pt\n",
    "\n",
    "# create some data\n",
    "x = pt.linspace(0, 6, 100)\n",
    "y = pt.sin(x)\n",
    "y2 = pt.cos(x)\n",
    "\n",
    "# now let's plot the data\n",
    "plt.plot(x, y, color=\"black\", label=\"$sin(x)$\")\n",
    "\n",
    "# we can customize the lines as well\n",
    "plt.plot(x, y2, color=\"red\", label=\"$cos(x)$\", marker=\"o\", fillstyle=\"none\", linestyle=\"None\")\n",
    "\n",
    "# add axis labels, a legend and a title\n",
    "plt.legend()\n",
    "plt.xlabel(\"x\")\n",
    "plt.ylabel(\"y\")\n",
    "plt.title(\"$sin(x)$ vs. $cos(x)$\")\n",
    "\n",
    "# in order to diplay the plot, we need to call the show() method\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2553d210-8e55-4c73-b689-7e3a55dc3570",
   "metadata": {},
   "source": [
    "### Scatter plots\n",
    "\n",
    "In the same way, we can create scatter plots using the `scatter` method:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "526e0f9e-ad04-4b15-94d8-f53747739d41",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# this time, let's plot the data as scatter plot, s = size of markers\n",
    "plt.scatter(x, y, color=\"black\", label=\"$sin(x)$\", s=5, marker=\"s\")\n",
    "plt.scatter(x, y2, color=\"red\", label=\"$cos(x)$\", s=20, marker=\"o\", facecolors=\"none\")\n",
    "\n",
    "# zoom in a little bit by setting new x- and y-limits\n",
    "plt.xlim(1.75, 5.75)\n",
    "plt.ylim(-1.05, 0.5)\n",
    "\n",
    "# the rest is the same...\n",
    "plt.legend()\n",
    "plt.xlabel(\"x\")\n",
    "plt.ylabel(\"y\")\n",
    "plt.title(\"$sin(x)$ vs. $cos(x)$\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a4e5c5a4-2284-4b6a-ba6c-a2fe9fc38f67",
   "metadata": {},
   "source": [
    "### Contour and filled contour plots\n",
    "\n",
    "Further, contour plots can be created in order to visualize $3D-$data with the `contour()` method:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "ec2575ed-7ffa-43ac-843e-89273fe3040d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from numpy import meshgrid\n",
    "# create 3D-data\n",
    "x = pt.linspace(0, 1, 100)\n",
    "y = pt.linspace(10, 20, 100)\n",
    "\n",
    "# in order to get one datapoint for each (x, y) tuple, we create a grid of (x, y) tuples with meshgrid\n",
    "x_new, y_new = meshgrid(x, y)\n",
    "\n",
    "# now we can use the grid to generate a matrix of data in z-direction, so for each (x, y) tuple there exist one z data point\n",
    "z = x_new**2 * y_new**2\n",
    "\n",
    "# now create contour plot, levels = number of isolines in the plot\n",
    "plt.contour(x, y, z, levels=30)\n",
    "\n",
    "# again we can add some labels and a colorbar\n",
    "plt.xlabel(\"x\")\n",
    "plt.ylabel(\"y\")\n",
    "plt.colorbar()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "13527d12-5b07-4edf-927e-3cab16901900",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# alternatively, we can use the contourf() method for making 3D-plots:\n",
    "plt.contourf(x, y, z)\n",
    "plt.xlabel(\"x\")\n",
    "plt.ylabel(\"y\")\n",
    "\n",
    "# in general, the colorbar can be further customized\n",
    "cbar = plt.colorbar()\n",
    "cbar.set_label(label=\"$z$\", fontsize=12)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a836e94c-bdb1-4cfb-92e7-2c9022f78c0c",
   "metadata": {},
   "source": [
    "### Sub-plots\n",
    "\n",
    "Instead of only creating one plot at a time, Matplotlib provides a `subplots()` method for creating multiple plots within one figure, which also allows us to customize our plots further. There exists a variety of options, which can be found in the [subfigures](https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.subplots.html) documentation. A possible implementation could be:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "83e841f3-8bd2-4b1a-8ee1-c2007117f4c8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 2000x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# use the data we already created when plotting the sin(x) and cos(x), but this time we want them to be in seperate plots\n",
    "x = pt.linspace(0, 6, 100)\n",
    "y = pt.sin(x)\n",
    "y_2 = pt.cos(x)\n",
    "\n",
    "# now we create a subfigure with 2 columns and one row, but both plots should have the same y-axis, further\n",
    "# we want the figure to have a size of 20x4 (width x heigth)\n",
    "fig, ax = plt.subplots(nrows=1, ncols=2, figsize=(20, 4), sharey=True)\n",
    "\n",
    "# let's plot the data ax referes to the axis on which we want to plot the data (counting from left -> right)\n",
    "ax[0].plot(x, y, color=\"black\", label=\"$sin(x)$\")\n",
    "ax[1].plot(x, y, color=\"red\", label=\"$cos(x)$\")\n",
    "\n",
    "# when adding labels, the method is now called with a 'set_...' in front of the methods\n",
    "ax[0].set_ylabel(\"$y$\", usetex=True, fontsize=16)\n",
    "\n",
    "# we can increase the space between the x-ticks and the axis label using the keyword 'labelpad' as well\n",
    "ax[0].set_xlabel(\"$x$\", usetex=True, fontsize=16, labelpad=25)\n",
    "ax[1].set_xlabel(\"$x$\", usetex=True, fontsize=16, labelpad=10)\n",
    "\n",
    "# we can set different subtitles as well\n",
    "ax[0].set_title(\"$sin(x)$\")\n",
    "ax[1].set_title(\"$cos(x)$\")\n",
    "\n",
    "# and also customize the legend\n",
    "ax[0].legend(loc=\"upper right\", fontsize=14)\n",
    "ax[1].legend(loc=\"lower left\", fontsize=10)\n",
    "\n",
    "# and adjust the white space between the subplots, so it looks a little bit nicer\n",
    "fig.tight_layout()\n",
    "fig.subplots_adjust(wspace=0.05, top=0.9)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "849473c7-5798-43a1-bd9d-8ab57caedee1",
   "metadata": {},
   "source": [
    "## PyTorch\n",
    "\n",
    "### Working with tensors\n",
    "\n",
    "The [PyTorch](https://pytorch.org/docs/stable/index.html) library provides efficient data structures for operating with large amounts of data, e.g. tensors as well as tools for deep learning and neural networks. The following section gives a brief overview on what tensors are and how to how to operate with them. [Tensors](https://pytorch.org/docs/stable/tensors.html) store elements of a certain type, e.g., floating point numbers in a multi-dimensional matrix. In general, tensors need to be initialized for example with zeros before operating with them, similar to [numpy arrays](https://numpy.org/doc/stable/reference/generated/numpy.array.html). The size of a tensor is defined when initializing the tensor using the keyword argument `size`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "5a811278-30ea-4f6a-8857-ae069e1466d1",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1x1 tensor:\n",
      " tensor([[0.]])\n",
      "\n",
      "3x1 column vector:\n",
      " tensor([[0.],\n",
      "        [0.],\n",
      "        [0.]])\n",
      "\n",
      "3x3 matrix:\n",
      " tensor([[1., 1., 1.],\n",
      "        [1., 1., 1.],\n",
      "        [1., 1., 1.]])\n"
     ]
    }
   ],
   "source": [
    "import torch as pt\n",
    "\n",
    "# creating a 1x1 tensor filled with zeros, the size argument takes a tuple with (number of rows, number of columns)\n",
    "t = pt.zeros(size=(1, 1))\n",
    "print(\"1x1 tensor:\\n\", t)\n",
    "\n",
    "# similarily, we can create an column vector [x, y, z]^T filled with zeros\n",
    "t = pt.zeros(size=(3, 1))\n",
    "print(\"\\n3x1 column vector:\\n\", t)\n",
    "\n",
    "# in the same way, we can also create a 3x3 matrix filled with ones\n",
    "t = pt.ones(size=(3, 3))\n",
    "print(\"\\n3x3 matrix:\\n\", t)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c84e8605-3374-40bc-ab3f-178fb1f2436e",
   "metadata": {},
   "source": [
    "Alternatively, other data types such as lists can be converted to tensors. It is important that the list elements have to be of the same data type."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "df86f6d0-ef87-4414-839f-d96dbcc0a54f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "original list:\n",
      " [1, 2, 3]\n",
      "\n",
      "converted to tensor:\n",
      " tensor([1, 2, 3])\n",
      "\n",
      "original list:\n",
      " [[1, 2], [3, 4]]\n",
      "\n",
      "converted to tensor:\n",
      " tensor([[1, 2],\n",
      "        [3, 4]])\n"
     ]
    }
   ],
   "source": [
    "# creating a list and converting it to a tensor\n",
    "a = [1, 2, 3]\n",
    "a_tensor = pt.tensor(a)\n",
    "print(\"original list:\\n\", a)\n",
    "print(\"\\nconverted to tensor:\\n\", a_tensor)\n",
    "\n",
    "# this also works for nested lists\n",
    "b = [[1, 2], [3, 4]]\n",
    "b_tensor = pt.tensor(b)\n",
    "print(\"\\noriginal list:\\n\", b)\n",
    "print(\"\\nconverted to tensor:\\n\", b_tensor)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2c469cc7-a278-4ee5-b90b-7d3900d9d6e7",
   "metadata": {},
   "source": [
    "When converting lists to tensors, some problems may occur as shown in the following examples:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "52bd4d3d-39ff-4387-8ff8-869c5e4116ee",
   "metadata": {},
   "outputs": [
    {
     "ename": "TypeError",
     "evalue": "new(): invalid data type 'str'",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "Cell \u001b[0;32mIn [50], line 3\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[38;5;66;03m# all list elements have to be of the same data type, otherwise an error occurs:\u001b[39;00m\n\u001b[1;32m      2\u001b[0m a \u001b[38;5;241m=\u001b[39m [\u001b[38;5;241m1\u001b[39m, \u001b[38;5;241m2\u001b[39m, \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124ma\u001b[39m\u001b[38;5;124m\"\u001b[39m]\n\u001b[0;32m----> 3\u001b[0m b \u001b[38;5;241m=\u001b[39m \u001b[43mpt\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mtensor\u001b[49m\u001b[43m(\u001b[49m\u001b[43ma\u001b[49m\u001b[43m)\u001b[49m\n",
      "\u001b[0;31mTypeError\u001b[0m: new(): invalid data type 'str'"
     ]
    }
   ],
   "source": [
    "# all list elements have to be of the same data type, otherwise an error occurs:\n",
    "a = [1, 2, \"a\"]\n",
    "b = pt.tensor(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "e8ccd821-35ee-4f54-b710-cf71cf912963",
   "metadata": {},
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "expected sequence of length 2 at dim 1 (got 3)",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "Cell \u001b[0;32mIn [51], line 5\u001b[0m\n\u001b[1;32m      2\u001b[0m a \u001b[38;5;241m=\u001b[39m [[\u001b[38;5;241m1\u001b[39m, \u001b[38;5;241m2\u001b[39m], [\u001b[38;5;241m3\u001b[39m, \u001b[38;5;241m4\u001b[39m, \u001b[38;5;241m5\u001b[39m]]\n\u001b[1;32m      4\u001b[0m \u001b[38;5;66;03m# this is not working, because 1st element is 2 long and 2nd element has a length of 3\u001b[39;00m\n\u001b[0;32m----> 5\u001b[0m b \u001b[38;5;241m=\u001b[39m \u001b[43mpt\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mtensor\u001b[49m\u001b[43m(\u001b[49m\u001b[43ma\u001b[49m\u001b[43m)\u001b[49m\n",
      "\u001b[0;31mValueError\u001b[0m: expected sequence of length 2 at dim 1 (got 3)"
     ]
    }
   ],
   "source": [
    "# also if nested lists are to be converted, the dimensions have to be consistent throughout the list\n",
    "a = [[1, 2], [3, 4, 5]]\n",
    "\n",
    "# this is not working, because 1st element is 2 long and 2nd element has a length of 3\n",
    "b = pt.tensor(a)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7c5a1eaf-6c93-4baf-8a21-f7a09730c66e",
   "metadata": {},
   "source": [
    "When initializing a tensor, the size of the tensor needs to be defined. The general syntax for the `size` argument is `size=(dim=0, dim=1, dim=2, ...)`, the first dimension `dim=0` refers to the number of rows and `dim=1` to the number of columns. The $3^{rd}$ dimension denotes the number of elements within each element of the (dim=0 * dim=1) sized matrix and so on. When operating with tensors, single elements can be accessed as well as complete columns, rows or matrices within the tensor, which will be illustrated by the following examples. A more comprehensive introduction can be found in the [PyTorch docs](https://pytorch.org/tutorials/beginner/introyt/tensors_deeper_tutorial.html) for tensors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "2ec6823c-fdd1-4323-9b4d-7980d3bed429",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3x3 tensor with random numbers:\n",
      " tensor([[ 0.8542, -0.5405,  0.0738],\n",
      "        [-1.2996, -0.7715,  0.0630],\n",
      "        [-0.1926,  1.5318,  0.7864]])\n"
     ]
    }
   ],
   "source": [
    "# create a 2x3 tensor filled with random numbers\n",
    "random_tensor = pt.randn(size=(3, 3))\n",
    "\n",
    "# this tensor has 3 rows and 3 columns\n",
    "print(\"3x3 tensor with random numbers:\\n\", random_tensor)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "52f3ed8e-529b-44c0-8e9a-2e75679faad7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2nd element of 1st row:  tensor(-0.5405)\n",
      "last element of 1st row: tensor(0.0738)\n",
      "\n",
      "all columns of 1st row: tensor([ 0.8542, -0.5405,  0.0738])\n",
      "all rows of 2nd colunm: tensor([-0.5405, -0.7715,  1.5318])\n",
      "\n",
      "2x2 matrix of tensor:\n",
      " tensor([[ 0.8542, -0.5405],\n",
      "        [-1.2996, -0.7715]])\n",
      "\n",
      "2x2 matrix of tensor:\n",
      " tensor([[-0.7715,  0.0630],\n",
      "        [ 1.5318,  0.7864]])\n"
     ]
    }
   ],
   "source": [
    "# now let's access the 2nd element of the first row (indices start at zero)\n",
    "print(\"2nd element of 1st row: \", random_tensor[0, 1])\n",
    "\n",
    "# we can also access the last element of the 1st row by using [-1] as index:\n",
    "print(\"last element of 1st row:\", random_tensor[0, -1])\n",
    "\n",
    "# complete rows or columns can be accessed by using [:]\n",
    "print(\"\\nall columns of 1st row:\", random_tensor[0, :])\n",
    "print(\"all rows of 2nd colunm:\", random_tensor[:, 1])\n",
    "\n",
    "# now lets get the a 2x2 submatrix of the tensoor containing the rows 1, 2 and columns 1, 2:\n",
    "print(\"\\n2x2 matrix of tensor:\\n\", random_tensor[:2, :2])\n",
    "\n",
    "# similarily, we can get the elements of the last two rows and columns:\n",
    "print(\"\\n2x2 matrix of tensor:\\n\", random_tensor[1:, 1:])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "0a54991b-9139-477b-a17c-b3e8d085fbac",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "original tensor:\n",
      " tensor([[0.1845, 0.8458, 0.7495, 0.2527],\n",
      "        [0.6816, 0.2572, 0.0531, 0.6476],\n",
      "        [0.0690, 0.2585, 0.7352, 0.8128],\n",
      "        [0.1855, 0.8100, 0.8889, 0.6107]])\n",
      "\n",
      "rows 1-3 & columns 2-4:\n",
      " tensor([[0.0531, 0.6476],\n",
      "        [0.7352, 0.8128]])\n"
     ]
    }
   ],
   "source": [
    "# further, we can specify ranges which we want to access\n",
    "random_tensor = pt.rand(size=(4, 4))\n",
    "print(\"original tensor:\\n\", random_tensor)\n",
    "      \n",
    "# get columns 1-3 and rows 2-4\n",
    "print(\"\\nrows 1-3 & columns 2-4:\\n\", random_tensor[1:3, 2:4])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "100f2d3d-7bed-446a-8fc8-cb4f00c73872",
   "metadata": {},
   "source": [
    "As can be seen in this example, when using the range `[1:3, 2:4]`, the stop indices `3, 4` are excluded resulting in a 2x2 tensor as output. In general, the size of a tensor can be determined by using the `size()` method:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "57fa6f4b-9a2c-4b1f-a09e-ae29ef034315",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "size of the original tensor:  torch.Size([4, 4])\n",
      "\n",
      "size of the sub-matrix within the tensor:  torch.Size([2, 2])\n"
     ]
    }
   ],
   "source": [
    "# get the size of this tensor\n",
    "print(\"size of the original tensor: \", random_tensor.size())\n",
    "print(\"\\nsize of the sub-matrix within the tensor: \", random_tensor[1:3, 2:4].size())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c7b2a831-d32e-4357-931d-59d3df32d699",
   "metadata": {},
   "source": [
    "### Common tensor operations\n",
    "\n",
    "#### Algebraic operations\n",
    "\n",
    "A great advantage of using tensors is the fact that algebraic operations, such as elements-wise addition, can easily be done using `+, -, *, /`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "4ca167cf-8c8f-4e73-8f78-10dc3fd4f9cb",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([2, 3, 4])\n",
      "\n",
      "x =  tensor([[3, 0, 1],\n",
      "        [1, 0, 1]])\n",
      "\n",
      "y =  tensor([[3, 2, 3],\n",
      "        [0, 1, 2]])\n",
      "\n",
      "x + y =  tensor([[6, 2, 4],\n",
      "        [1, 1, 3]])\n"
     ]
    }
   ],
   "source": [
    "# create two tensors\n",
    "a = pt.tensor([1, 2, 3])\n",
    "b = pt.tensor([1, 1, 1])\n",
    "\n",
    "# now add them element-wise:\n",
    "c = a + b\n",
    "print(c)\n",
    "\n",
    "# of course, this can be extended to higher dimensions:\n",
    "x = pt.randint(low=0, high=5, size=(2, 3))\n",
    "y = pt.randint(low=0, high=5, size=(2, 3))\n",
    "print(\"\\nx = \", x)\n",
    "print(\"\\ny = \", y)\n",
    "print(\"\\nx + y = \", x + y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "79fd6216-4898-477c-843e-4a1333eb83c5",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x = \n",
      " tensor([[0, 2, 2],\n",
      "        [1, 1, 0]])\n",
      "\n",
      "y = \n",
      " tensor([[1],\n",
      "        [2],\n",
      "        [1]])\n",
      "\n",
      "x * y = \n",
      " tensor([[6],\n",
      "        [3]])\n"
     ]
    }
   ],
   "source": [
    "# a matrix-vector product can be computed using @\n",
    "x = pt.randint(low=0, high=3, size=(2, 3))\n",
    "y = pt.randint(low=0, high=3, size=(3, 1))\n",
    "print(\"x = \\n\", x)\n",
    "print(\"\\ny = \\n\", y)\n",
    "\n",
    "# compute the matrix-vector product of x and y\n",
    "print(\"\\nx * y = \\n\", x @ y)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "76a4b533-2c0f-461a-a9a3-05efc68d5782",
   "metadata": {},
   "source": [
    "#### flatten()\n",
    " \n",
    "The `flatten()` method reshapes an arbitrary $n$-dimensional tensor to a one-dimensional tensor:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "5c7f9b2b-cdcc-4d81-866d-70114a88d79b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "original tensor:\n",
      " tensor([[0.0477, 0.1436, 0.2791],\n",
      "        [0.2164, 0.3674, 0.8587]])\n",
      "\n",
      "flattened tensor:\n",
      " tensor([0.0477, 0.1436, 0.2791, 0.2164, 0.3674, 0.8587])\n",
      "\n",
      "size of original tensor: torch.Size([2, 3])\n",
      "size of flattened tensor: torch.Size([6])\n"
     ]
    }
   ],
   "source": [
    "# create tensor\n",
    "x = pt.rand(size=(2, 3))\n",
    "\n",
    "# then flatten the tensor\n",
    "y = x.flatten()\n",
    "\n",
    "print(\"original tensor:\\n\", x)\n",
    "print(\"\\nflattened tensor:\\n\", y)\n",
    "print(\"\\nsize of original tensor:\", x.size())\n",
    "print(\"size of flattened tensor:\", y.size())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2dccd061-c671-4b84-8a1e-acfe072d64f3",
   "metadata": {},
   "source": [
    "#### reshape()\n",
    "\n",
    "In contrast to `flatten()`, `reshape()` can be used to reshape a tensor to specific dimensions instead of reshaping it to a one-dimensional tensor. An important requirement for using the `reshape()` method is that the output tensor has the same number of elements as the input tensor."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "913011ae-2fa1-4b0f-9074-b20df5200f0c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "original tensor:\n",
      " tensor([[1.6751e-01, 5.2408e-01],\n",
      "        [1.2265e-01, 9.9639e-01],\n",
      "        [4.5478e-05, 9.4439e-02],\n",
      "        [9.5436e-01, 2.5640e-01],\n",
      "        [3.2345e-01, 3.0902e-01],\n",
      "        [2.2105e-01, 8.5098e-01]])\n",
      "\n",
      "reshaped tensor:\n",
      " tensor([[1.6751e-01, 5.2408e-01, 1.2265e-01, 9.9639e-01, 4.5478e-05, 9.4439e-02,\n",
      "         9.5436e-01, 2.5640e-01, 3.2345e-01, 3.0902e-01, 2.2105e-01, 8.5098e-01]])\n",
      "\n",
      "reshaped tensor:\n",
      " tensor([[1.6751e-01, 5.2408e-01, 1.2265e-01, 9.9639e-01],\n",
      "        [4.5478e-05, 9.4439e-02, 9.5436e-01, 2.5640e-01],\n",
      "        [3.2345e-01, 3.0902e-01, 2.2105e-01, 8.5098e-01]])\n"
     ]
    }
   ],
   "source": [
    "# create tensor with 6 rows and 2 columns\n",
    "x = pt.rand(size=(6, 2))\n",
    "print(\"original tensor:\\n\", x)\n",
    "\n",
    "# reshape it to a row-vector\n",
    "y = pt.reshape(x, shape=(1, 12))\n",
    "print(\"\\nreshaped tensor:\\n\", y)\n",
    "\n",
    "# alternatively, reshape it to a matrix with 3 rows and 4 columns\n",
    "z = pt.reshape(x, shape=(3, 4))\n",
    "print(\"\\nreshaped tensor:\\n\", z)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c9514101-af69-4ee9-810e-102936589328",
   "metadata": {},
   "source": [
    "When using `reshape()` the dimensions have to match, meaning the number of elements need to be the same. The following will not work:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "dc3769e0-5464-41e9-af95-4486b2151868",
   "metadata": {},
   "outputs": [
    {
     "ename": "RuntimeError",
     "evalue": "shape '[3, 3]' is invalid for input of size 12",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mRuntimeError\u001b[0m                              Traceback (most recent call last)",
      "Cell \u001b[0;32mIn [60], line 5\u001b[0m\n\u001b[1;32m      2\u001b[0m x \u001b[38;5;241m=\u001b[39m pt\u001b[38;5;241m.\u001b[39mrand(size\u001b[38;5;241m=\u001b[39m(\u001b[38;5;241m6\u001b[39m, \u001b[38;5;241m2\u001b[39m))\n\u001b[1;32m      4\u001b[0m \u001b[38;5;66;03m# this will not work since x has 6*2=12 elements and y would only have 3*3=9 elements\u001b[39;00m\n\u001b[0;32m----> 5\u001b[0m y \u001b[38;5;241m=\u001b[39m \u001b[43mpt\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mreshape\u001b[49m\u001b[43m(\u001b[49m\u001b[43mx\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mshape\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m3\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m3\u001b[39;49m\u001b[43m)\u001b[49m\u001b[43m)\u001b[49m\n",
      "\u001b[0;31mRuntimeError\u001b[0m: shape '[3, 3]' is invalid for input of size 12"
     ]
    }
   ],
   "source": [
    "# create tensor\n",
    "x = pt.rand(size=(6, 2))\n",
    "\n",
    "# this will not work since x has 6*2=12 elements and y would only have 3*3=9 elements\n",
    "y = pt.reshape(x, shape=(3, 3))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a0f40806-acca-4496-9cc6-434c6b6ef56c",
   "metadata": {},
   "source": [
    "#### squeeze() and unsqueeze()\n",
    "\n",
    "The `squeeze()` method removes dimensions with the size of $1$ from a tensor. If we have for example a $3x2x1$-dimensional tensor, using the `squeeze()` method would lead to a tensor with the dimensions of $3x2$ by removing the $3^{rd}$ dimension (since the $3^{rd}$ dimension is $1$). If there exist multiple dimensions with the size of $1$, using `squeeze()` removes all of them. A specific dimension which shall be removed can be specified by the keyword argument `dim`, in case this is unwanted. The `squeeze()` method is frequently used, e.g. when passing features into a neural network, as shown in [lecture 3](https://github.com/AndreWeiner/ml-cfd-lecture/blob/main/notebooks/ml_intro.ipynb). Consequently, the `unsqueeze()` method inserts a dimension of the size $1$ at a specified dimension of the input tensor."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "id": "5e141f4d-390a-48dd-9e9b-f9c410f01fca",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "original tensor:\n",
      " tensor([[0.0253],\n",
      "        [0.2249],\n",
      "        [0.8712]])\n",
      "\n",
      "squeezed tensor:\n",
      " tensor([0.0253, 0.2249, 0.8712])\n",
      "\n",
      "unsqueezed tensor (dim=0):\n",
      " tensor([[0.0253, 0.2249, 0.8712]])\n",
      "\n",
      "unsqueezed tensor (dim=1):\n",
      " tensor([[0.0253],\n",
      "        [0.2249],\n",
      "        [0.8712]])\n",
      "\n",
      "size of original tensor: torch.Size([3, 1])\n",
      "size of squeezed tensor: torch.Size([3])\n",
      "size of unsqueezed tensor (dim=0): torch.Size([1, 3])\n",
      "size of unsqueezed tensor (dim=0): torch.Size([3, 1])\n"
     ]
    }
   ],
   "source": [
    "# create tensor\n",
    "x = pt.rand(size=(3, 1))\n",
    "\n",
    "# then squeeze the tensor\n",
    "y = x.squeeze()\n",
    "\n",
    "# unsqueeze the tensor in \"row\"-dimension\n",
    "z = y.unsqueeze(dim=0)\n",
    "\n",
    "# unsqueeze the tensor in \"column\"-dimension\n",
    "z_2 = y.unsqueeze(dim=1)\n",
    "\n",
    "print(\"original tensor:\\n\", x)\n",
    "print(\"\\nsqueezed tensor:\\n\", y)\n",
    "print(\"\\nunsqueezed tensor (dim=0):\\n\", z)\n",
    "print(\"\\nunsqueezed tensor (dim=1):\\n\", z_2)\n",
    "\n",
    "print(\"\\nsize of original tensor:\", x.size())\n",
    "print(\"size of squeezed tensor:\", y.size())\n",
    "print(\"size of unsqueezed tensor (dim=0):\", z.size())\n",
    "print(\"size of unsqueezed tensor (dim=0):\", z_2.size())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "b41c97aa-ba86-4531-809b-61ed011f7629",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "original tensor:\n",
      " tensor([[[[0.2098, 0.6956]],\n",
      "\n",
      "         [[0.0179, 0.2699]],\n",
      "\n",
      "         [[0.9126, 0.5275]]]])\n",
      "\n",
      "squeezed tensor:\n",
      " tensor([[0.2098, 0.6956],\n",
      "        [0.0179, 0.2699],\n",
      "        [0.9126, 0.5275]])\n",
      "\n",
      "squeezed tensor for 3rd dim:\n",
      " tensor([[[0.2098, 0.6956],\n",
      "         [0.0179, 0.2699],\n",
      "         [0.9126, 0.5275]]])\n",
      "\n",
      "size of original tensor: torch.Size([1, 3, 1, 2])\n",
      "size of squeezed tensor: torch.Size([3, 2])\n",
      "size of squeezed tensor for 3rd dim: torch.Size([1, 3, 2])\n"
     ]
    }
   ],
   "source": [
    "# by using the keyword argument 'dim', the dimension to be removed can be specified in case there exist multiple dimensions with the size of 1\n",
    "x = pt.rand(size=(1, 3, 1, 2))\n",
    "\n",
    "# remove all dimesions with the size of 1\n",
    "y = x.squeeze()\n",
    "\n",
    "# only remove the last dimension\n",
    "z = x.squeeze(dim=2)\n",
    "\n",
    "print(\"original tensor:\\n\", x)\n",
    "print(\"\\nsqueezed tensor:\\n\", y)\n",
    "print(\"\\nsqueezed tensor for 3rd dim:\\n\", z)\n",
    "\n",
    "print(\"\\nsize of original tensor:\", x.size())\n",
    "print(\"size of squeezed tensor:\", y.size())\n",
    "print(\"size of squeezed tensor for 3rd dim:\", z.size())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "520f7f6f-c7bf-46b5-8bb4-20f6d7d88bcf",
   "metadata": {},
   "source": [
    "#### zeros() vs. zeros_like()\n",
    "\n",
    "In the previous examples, tensors were always initialized with zeros using the `zeros()` method. The `zeros_like()` method, however, is an efficient way to generate a tensor filled with zeros by using another tensor. For example, consider having a tensor $x$ filled with some values and we want to create a tensor $y$, which has the same size of $x$ but is filled with zeros. Instead of using `y = pt.zeros(size=x.size())` we can create $y$ as `y = pt.zeros_like(x)`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "a80f8421-72cc-4ae8-a7c2-041acaecac6e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor initialized with zeros:\n",
      " tensor([[0., 0.],\n",
      "        [0., 0.]])\n",
      "\n",
      "tensor initialized with random numbers:\n",
      " tensor([[0.9372, 0.7361],\n",
      "        [0.4246, 0.0939]])\n",
      "\n",
      "using zeros_like() method:\n",
      " tensor([[0., 0.],\n",
      "        [0., 0.]])\n"
     ]
    }
   ],
   "source": [
    "# creating a tensor filled with zeros\n",
    "x = pt.zeros(size=(2, 2))\n",
    "\n",
    "# create tensor filled with some random numbers\n",
    "y = pt.rand(size=(2, 2))\n",
    "\n",
    "# use zeros_like() to create tensor of the same shape as y, but filled with zeros\n",
    "z = pt.zeros_like(y)\n",
    "\n",
    "print(\"tensor initialized with zeros:\\n\", x)\n",
    "print(\"\\ntensor initialized with random numbers:\\n\", y)\n",
    "print(\"\\nusing zeros_like() method:\\n\", z)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a0066c69-dbcf-48c2-bbad-b85ac877c9f5",
   "metadata": {},
   "source": [
    "#### min() vs. argmin() \n",
    "The `min()` method in torch returns the minimum of a $n-$dimensional tensor. In a lot of cases, additionally the position of the minimum element is required. To get the index of the minimum element, we can use the `argmin()` method of torch. The maximum element and it's position can analogously be determined by using `max()` and `argmax()` respectively."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "id": "9067a27b-004e-41f8-8c15-68080579ebe4",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x =  tensor([[0.3612, 0.5508, 0.3000, 0.8544, 0.4987]])\n",
      "min(x) = 0.3000 at position 2\n"
     ]
    }
   ],
   "source": [
    "# creating tensor filled with random numbers\n",
    "x = pt.rand(size=(1, 5))\n",
    "\n",
    "print(\"x = \", x)\n",
    "print(f\"min(x) = {'{:.4f}'.format(pt.min(x).item())} at position {pt.argmin(x).item()}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "34aa1d6f-c022-435e-8421-6403f015cfb7",
   "metadata": {},
   "source": [
    "#### Combining tensor operations\n",
    "\n",
    "We only looked at single tensor operations so far. When programming in Python, however, we can combine these methods in order shorten the code while at the same time making it more efficient. The following example illustrates a possible implementation for calculating the $L_2-$norm of a vector:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "id": "b863c52e-a42d-419d-ba0f-82b21a06f3d2",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "L2(x, y) =  0.0909828171133995\n",
      "L2(x, y) =  0.0909828171133995\n"
     ]
    }
   ],
   "source": [
    "# let's define two vectors\n",
    "x = pt.rand(size=(3, 1))\n",
    "y = pt.rand(size=(3, 1))\n",
    "\n",
    "# now we want to calculate the L2-norm between the vector elements without combining methods\n",
    "l2 = x-y\n",
    "l2 = l2.square()\n",
    "l2 = l2.mean()\n",
    "print(\"L2(x, y) = \", l2.item())\n",
    "\n",
    "# a more clear and efficient way:\n",
    "print(\"L2(x, y) = \", (x-y).square().mean().item())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "122fa1a7-9ad2-448a-8bea-9598f25d12b7",
   "metadata": {},
   "source": [
    "## 5. Handling column-like data with Pandas\n",
    "\n",
    "[Pandas](https://pandas.pydata.org/) is a library providing many tools for data analysis. In Pandas so called `DataFrame`s are largely used, which is a similar way of structuring data as in the built-in `dict()`. Since Pandas provides a vast amount of tools, within this section only the `read_csv()` method, which is frequently used throughout the lecture and exercise, shall be presented.\n",
    "\n",
    "The `read_csv()` method can be used to read in $.csv$ files column-like data. Although the method is named `read_csv()`, other file types can be read in as well, while the data within the files can be separated by any arbitrary separator. This separator has to be specified as keyword argument when calling the function. The following example illustrates a possible use of the `read_csv()` method. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "id": "96815d1e-1d14-4a86-99ce-d69687dd4b8e",
   "metadata": {},
   "outputs": [],
   "source": [
    "dummy_str = \"\"\"\n",
    "       XFOIL         Version 6.93\n",
    "  \n",
    " Calculated polar for: NACA 67-414                                     \n",
    "  \n",
    " 1 1 Reynolds number fixed          Mach number fixed         \n",
    "  \n",
    " xtrf =   1.000 (top)        1.000 (bottom)  \n",
    " Mach =   0.500     Re =     5.000 e 6     Ncrit =  13.000 13.000\n",
    "  \n",
    "  alpha     CL        CD       CDp       CM    Top_Xtr Bot_Xtr    CQ       CDq  \n",
    " ------- -------- --------- --------- -------- ------- ------- -------- --------\n",
    "   0.000   0.4239 0.0032031 0.0010239  -0.1011  0.7862  0.7914  0.00000  0.00000\n",
    "   0.250   0.4581 0.0032021 0.0010260  -0.1015  0.7833  0.7957  0.00000  0.00000\n",
    "   0.500   0.4914 0.0032155 0.0010364  -0.1017  0.7799  0.7989  0.00000  0.00000\n",
    "   0.750   0.5251 0.0032287 0.0010587  -0.1020  0.7757  0.8017  0.00000  0.00000\n",
    "   1.000   0.5594 0.0032471 0.0010826  -0.1024  0.7717  0.8043  0.00000  0.00000\n",
    "   1.250   0.5917 0.0032885 0.0011012  -0.1023  0.7661  0.8058  0.00000  0.00000\n",
    "   1.500   0.6259 0.0032757 0.0011005  -0.1027  0.7603  0.8069  0.00000  0.00000\n",
    "   1.750   0.6575 0.0032830 0.0011012  -0.1025  0.7521  0.8084  0.00000  0.00000\n",
    "   2.000   0.6872 0.0033220 0.0011216  -0.1018  0.7399  0.8093  0.00000  0.00000\n",
    "\"\"\"\n",
    "\n",
    "# we wrap the string above in a file-like object\n",
    "from io import StringIO\n",
    "\n",
    "dummy_csv = StringIO(dummy_str)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "22a13c35-ca3e-437c-ac27-2fead62d8a32",
   "metadata": {},
   "source": [
    "Now, we want to read in this data using the `read_csv()` method. Firstly, we need to get rid of the header since it contains no relevant data. This can be achieved by using the keyword `skiprow=9`, meaning we want to ignore whatever data is in rows $0-9$. Secondly, we have to define the separator as white space `sep=r\"\\s+\"`, because our data is not separated by commas, which is the default value for the `read_csv()` method. Lastly, we want the names of the columns in the file to be the names in the dataframe in order to access them later by name. This can be done using the keyword `header=0`, meaning we want the strings in the $1^{st}$ row to be set as column names (we neglect the rows $0...9$, therefore pandas starts to read in at row $10$ of the original data file)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "id": "8a51672e-71a9-448e-b7a6-c2ef2162445f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     alpha        CL         CD        CDp        CM  Top_Xtr  Bot_Xtr  \\\n",
      "0  -------  --------  ---------  ---------  --------  -------  -------   \n",
      "1    0.000    0.4239  0.0032031  0.0010239   -0.1011   0.7862   0.7914   \n",
      "2    0.250    0.4581  0.0032021  0.0010260   -0.1015   0.7833   0.7957   \n",
      "3    0.500    0.4914  0.0032155  0.0010364   -0.1017   0.7799   0.7989   \n",
      "4    0.750    0.5251  0.0032287  0.0010587   -0.1020   0.7757   0.8017   \n",
      "\n",
      "         CQ       CDq  \n",
      "0  --------  --------  \n",
      "1   0.00000   0.00000  \n",
      "2   0.00000   0.00000  \n",
      "3   0.00000   0.00000  \n",
      "4   0.00000   0.00000  \n"
     ]
    }
   ],
   "source": [
    "from pandas import read_csv\n",
    "\n",
    "# let's import this file\n",
    "# for a real .csv file, replace dummy_csv with the file path\n",
    "data = read_csv(dummy_csv, sep=r\"\\s+\", skiprows=9, header=0)\n",
    "\n",
    "# we can print out the first few lines to see if we did everything correcly using data.head():\n",
    "print(data.head())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f0f12955-02f1-478e-a547-d14fa43cb51a",
   "metadata": {},
   "source": [
    "Alternatively, we can specify which columns we want to read in using the keyword `usecols` and change the names of these columns as well with the keyword `names`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "id": "a3790862-03f1-4b79-bd83-0b4e5f9503e8",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "       aoa        cl\n",
      "0  -------  --------\n",
      "1    0.000    0.4239\n",
      "2    0.250    0.4581\n",
      "3    0.500    0.4914\n",
      "4    0.750    0.5251\n"
     ]
    }
   ],
   "source": [
    "# only read in the 1st two columns and give them a different name\n",
    "data = read_csv(StringIO(dummy_str), sep=r\"\\s+\", skiprows=9, header=0, usecols=[0, 1], names=[\"aoa\", \"cl\"])\n",
    "print(data.head())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9d6b0af1-b617-4bcd-8440-b00d400cca7e",
   "metadata": {},
   "source": [
    "The data in the dataframe can now be accessed by the names of the columns, similarly to dicts, e.g., by typing `aoa = data[\"aoa\"]`, we would assign all the data of the `aoa` column to the variable `aoa`."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ab299f15-c5e1-4fd6-b54e-afdecc50a02d",
   "metadata": {},
   "source": [
    "## Dealing with error messages and debugging code\n",
    "\n",
    "When writing code, making mistakes is envidable. The following section deals with common mistakes when writing code and how to interpret and solve error messages. However, the here presented suggestions and examples should be understand just as guidance, since everybody follows a slighty different approach when it comes to dealing with bugs.\n",
    "\n",
    "In general, the usage of an integrated development environment (IDE) such as [Visual Studio Code](https://code.visualstudio.com/) or [PyCharm](https://www.jetbrains.com/pycharm/) is highly recommended. IDE's provide useful tools for software development, e.g. a debugger, in which the written code can be debugged. The code can here be executed line-by-line while all relevant information is displayed and directly accessible. Further, IDE's provide useful functionality such as autocomplete and automatically enclosing any open brackets, which makes writing code faster and less prone to errors.\n",
    "\n",
    "When encountering an error, the python interpreter displays an error message, as already shown in some of the previous examples. The error message itself consists of the position of the error (line where the error was encountered) and what the error actually is (error message). In more complex code, Python additionally provides a so called $traceback$ of the error, which represents the complete \"path\" from the main script (or function) to the line of code where the error was encountered.\n",
    "\n",
    "Let's have a look at some common errors and possible way how to fix them."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "id": "81f8a1f2-7acc-4000-9aac-999663b95cb1",
   "metadata": {},
   "outputs": [
    {
     "ename": "IndentationError",
     "evalue": "unindent does not match any outer indentation level (<tokenize>, line 5)",
     "output_type": "error",
     "traceback": [
      "\u001b[0;36m  File \u001b[0;32m<tokenize>:5\u001b[0;36m\u001b[0m\n\u001b[0;31m    else:\u001b[0m\n\u001b[0m    ^\u001b[0m\n\u001b[0;31mIndentationError\u001b[0m\u001b[0;31m:\u001b[0m unindent does not match any outer indentation level\n"
     ]
    }
   ],
   "source": [
    "# 1st example: indentation error\n",
    "for i in range(3):\n",
    "    if i == 1:\n",
    "        print(i)\n",
    "   else:\n",
    "        print(i+1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dae5d6ee-8ef3-49a7-9d9e-1e2c2dc25717",
   "metadata": {},
   "source": [
    "In this example, the code itself seems to be fine. A look at the end of the error message, however, tells us that there is something wrong with the `else` statement. The `IndentationError` occurs, if the blocks of code are not aligned correctly. We can fix this by adding one space in front of the `else` statement, so that it is aligned with the `if` statement."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "id": "02a85e75-a79d-4bc9-bdf9-763a3fdcc256",
   "metadata": {},
   "outputs": [
    {
     "ename": "TypeError",
     "evalue": "subplot() takes 1 or 3 positional arguments but 2 were given",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "Cell \u001b[0;32mIn [71], line 17\u001b[0m\n\u001b[1;32m     15\u001b[0m x \u001b[38;5;241m=\u001b[39m [\u001b[38;5;241m1\u001b[39m, \u001b[38;5;241m2\u001b[39m, \u001b[38;5;241m3\u001b[39m]\n\u001b[1;32m     16\u001b[0m y \u001b[38;5;241m=\u001b[39m [\u001b[38;5;241m0.5\u001b[39m, \u001b[38;5;241m0.8\u001b[39m, \u001b[38;5;241m1.5\u001b[39m]\n\u001b[0;32m---> 17\u001b[0m \u001b[43mplot_data\u001b[49m\u001b[43m(\u001b[49m\u001b[43mx\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43my\u001b[49m\u001b[43m)\u001b[49m\n",
      "Cell \u001b[0;32mIn [71], line 6\u001b[0m, in \u001b[0;36mplot_data\u001b[0;34m(x, y)\u001b[0m\n\u001b[1;32m      5\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mplot_data\u001b[39m(x, y):\n\u001b[0;32m----> 6\u001b[0m     fig, ax \u001b[38;5;241m=\u001b[39m \u001b[43mplt\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43msubplot\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m1\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m1\u001b[39;49m\u001b[43m)\u001b[49m\n\u001b[1;32m      7\u001b[0m     ax\u001b[38;5;241m.\u001b[39mplot(x, y, color\u001b[38;5;241m=\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mblack\u001b[39m\u001b[38;5;124m\"\u001b[39m)\n\u001b[1;32m      8\u001b[0m     ax\u001b[38;5;241m.\u001b[39mset_xlabel(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mx\u001b[39m\u001b[38;5;124m\"\u001b[39m)\n",
      "File \u001b[0;32m~/.local/lib/python3.10/site-packages/matplotlib/pyplot.py:1534\u001b[0m, in \u001b[0;36msubplot\u001b[0;34m(*args, **kwargs)\u001b[0m\n\u001b[1;32m   1531\u001b[0m fig \u001b[38;5;241m=\u001b[39m gcf()\n\u001b[1;32m   1533\u001b[0m \u001b[38;5;66;03m# First, search for an existing subplot with a matching spec.\u001b[39;00m\n\u001b[0;32m-> 1534\u001b[0m key \u001b[38;5;241m=\u001b[39m \u001b[43mSubplotSpec\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43m_from_subplot_args\u001b[49m\u001b[43m(\u001b[49m\u001b[43mfig\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43margs\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m   1536\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m ax \u001b[38;5;129;01min\u001b[39;00m fig\u001b[38;5;241m.\u001b[39maxes:\n\u001b[1;32m   1537\u001b[0m     \u001b[38;5;66;03m# If we found an Axes at the position, we can reuse it if the user passed no\u001b[39;00m\n\u001b[1;32m   1538\u001b[0m     \u001b[38;5;66;03m# kwargs or if the Axes class and kwargs are identical.\u001b[39;00m\n\u001b[1;32m   1539\u001b[0m     \u001b[38;5;28;01mif\u001b[39;00m (ax\u001b[38;5;241m.\u001b[39mget_subplotspec() \u001b[38;5;241m==\u001b[39m key\n\u001b[1;32m   1540\u001b[0m         \u001b[38;5;129;01mand\u001b[39;00m (kwargs \u001b[38;5;241m==\u001b[39m {}\n\u001b[1;32m   1541\u001b[0m              \u001b[38;5;129;01mor\u001b[39;00m (ax\u001b[38;5;241m.\u001b[39m_projection_init\n\u001b[1;32m   1542\u001b[0m                  \u001b[38;5;241m==\u001b[39m fig\u001b[38;5;241m.\u001b[39m_process_projection_requirements(\u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mkwargs)))):\n",
      "File \u001b[0;32m~/.local/lib/python3.10/site-packages/matplotlib/gridspec.py:576\u001b[0m, in \u001b[0;36mSubplotSpec._from_subplot_args\u001b[0;34m(figure, args)\u001b[0m\n\u001b[1;32m    574\u001b[0m     rows, cols, num \u001b[38;5;241m=\u001b[39m args\n\u001b[1;32m    575\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[0;32m--> 576\u001b[0m     \u001b[38;5;28;01mraise\u001b[39;00m _api\u001b[38;5;241m.\u001b[39mnargs_error(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124msubplot\u001b[39m\u001b[38;5;124m\"\u001b[39m, takes\u001b[38;5;241m=\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124m1 or 3\u001b[39m\u001b[38;5;124m\"\u001b[39m, given\u001b[38;5;241m=\u001b[39m\u001b[38;5;28mlen\u001b[39m(args))\n\u001b[1;32m    578\u001b[0m gs \u001b[38;5;241m=\u001b[39m GridSpec\u001b[38;5;241m.\u001b[39m_check_gridspec_exists(figure, rows, cols)\n\u001b[1;32m    579\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m gs \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m:\n",
      "\u001b[0;31mTypeError\u001b[0m: subplot() takes 1 or 3 positional arguments but 2 were given"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 2nd example: how to deal with tracebacks\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# create some function for plotting data\n",
    "def plot_data(x, y):\n",
    "    fig, ax = plt.subplot(1, 1)\n",
    "    ax.plot(x, y, color=\"black\")\n",
    "    ax.set_xlabel(\"x\")\n",
    "    ax.set_ylabel(\"y\")\n",
    "    plt.show()\n",
    "    \n",
    "# 'if __name__==\"__main__\":' means that the following code is only executed when this script is executed as 'main',\n",
    "# but if we call the 'plot_data' function from another script, this won't be executed\n",
    "if __name__==\"__main__\":\n",
    "    x = [1, 2, 3]\n",
    "    y = [0.5, 0.8, 1.5]\n",
    "    plot_data(x, y)\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "18fc3c49-0f62-44cc-98bd-332864f65214",
   "metadata": {},
   "source": [
    "In this example, the error message looks quite complicated. Note that the exact message depends on the installed version of matplotlib. The last line of the error message tells us that we encountered a `TypeError` due to invalid arguments for the method `plt.subplot()`. Whenever getting an error caused by libraries, it is likely that we made a mistake in our code rather than that the library has a bug, since in general libraries are tested and regularly updated. So in this case it makes sense to start at the top of the error message. The first entry tells us that the error has something to do with calling out `plot_data()` function in the main script. Within this function, the statement `fig, ax = plt.subplot(1, 1)` is listed as next in the error message. Something in this line caused matplotlib to raise a `TypeError` as shown by the $3^{rd}$ entry of the error message. By looking again into our `plot_data()` function, we can see that we typed `plt.subplot()` instead of `plt.subplots()` which then lead to this error because we our arguemnts where meant for the latter function.\n",
    "\n",
    "In a lot of cases the cause of an error is rather simple as shown in the previous examples. Some commonly made mistakes may be:\n",
    "\n",
    "- forgotten or wrong brackets, e.g. using `()` instead of `[]` when trying to access elements of a list (in contrast to other languages such as Matlab, where `()` is used to access elements)\n",
    "- too many brackets, e.g. because some expression was deleted but the closing bracket is still present: `call_some_method(parameter))`\n",
    "- confusing similar methods, such as `plt.xlabel(\"...\")` vs. `ax.set_xlabel(\"...\")` methods within the matplotlib.pyplot library\n",
    "- using a wrong separator when reading in files, e.g., with the pandas library\n",
    "- Python is quite sensitive to indents (in contrast to other languages such as C++), meaning each block of code needs to be aligned"
   ]
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    "## References\n",
    "\n",
    "### Python documentation:\n",
    "\n",
    "- [python docs](https://docs.python.org/3.3/library/functions.html) for built-in functions\n",
    "- [python docs](https://docs.python.org/3/tutorial/controlflow.html) for flow control statements\n",
    "- [python docs](https://docs.python.org/3/tutorial/datastructures.html#looping-techniques) for lists\n",
    "- [python docs](https://docs.python.org/3/tutorial/classes.html) for classes (especially section 9.3, 9.5)\n",
    "- [python docs](https://docs.python.org/3/glossary.html#term-decorator) for decorators\n",
    "- [python docs](https://docs.python.org/3.3/library/functions.html#property) for the @property decorator\n",
    "- [flowTorch](https://flowmodelingcontrol.github.io/flowtorch-docs/1.1/index.html) library\n",
    "- [Matplotlib](https://matplotlib.org/stable/index.html) library\n",
    "- [read_csv](https://pandas.pydata.org/docs/reference/api/pandas.read_csv.html) method in pandas\n",
    "- [Pandas](https://pandas.pydata.org/docs/user_guide/index.html#user-guide) user guide\n",
    "- [PyTorch docs](https://pytorch.org/docs/stable/index.html) general\n",
    "- [PyTorch docs](https://pytorch.org/tutorials/beginner/introyt/tensors_deeper_tutorial.html) for tensors\n",
    "\n",
    "### Other references:\n",
    "\n",
    "- [lambda expressions](https://realpython.com/python-lambda/)\n",
    "- [decorators](https://realpython.com/primer-on-python-decorators/)\n",
    "- [Python Decorators in 15 Minutes](https://www.youtube.com/watch?v=r7Dtus7N4pI)"
   ]
  }
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