code for assignment

.gitignore

+__pycache__
+.hypothesis
+

README.md

+
+**Please note**: You cannot use any external packages or native libraries
+*except* where specifically mentioned. Be careful with when importing 
+packages!
+
+## Part 1 - Python (30 points)
+
+The first part of this assignment is intended to get you up and running with
+Python. We have provided a repository on [gitlab](). Please use the file 
+`l1p1.py` in this file to write your code.
+
+In the repository we have also provided some test cases which you can use
+to test your code. You'll need to install some packages first though. So set
+up a virtual environment for yourself and run `pip install -r requirements.txt`
+to install the pacakges you'll need. Then you can run one of the tests like
+so:
+
+```
+./test_assignment.sh
+```
+
+### Question 1 (10 points)
+
+Write a function to sort a list of integers. You can write any algorithm you
+want including, quicksort, merge sort, bubble sort, or random sort. However,
+you need to write the code yourself. Python and numpy both provide library
+methods for sorting lists but you cannot use them. 
+
+Here are some examples:
+```
+>>> sort_list([1,2,3])
+[1,2,3]
+>>> sort_list([5,4,3,2])
+[2,3,4,5]
+```
+
+### Question 2 (10 points)
+
+This question is inspired by one of the divisibility tricks in a recent
+[numberphile video](https://www.youtube.com/watch?v=yi-s-TTpLxY&t=178s).
+This time we're going to play around with number theory. The task here is to
+write a function that, given an integer and a single integer digit, returns
+an integer that inserts the digit in the integer such that the new integer is
+divisible by 7. The digits of the original integer must remain in the same
+order. If this is not possible then the function should throw an exception
+with message "not possible"
+
+Examples:
+
+```
+>>> div7(123, 4)
+4123
+>>> div7(39, 2)
+
+```
+
+Examples of incorrect output:
+
+```
+# not divisible by 7
+>>> div7(123,4)
+1234
+
+# cannot reorder digits in first argument
+>>> div7(124, 3)
+4123
+```
+
+### Question 3 (10 points)
+
+Note the import of numpy within the function. Don't alter this line, you can
+only use numpy in this particular function. Here the task is to extend the
+cubic function $y = a_1 x^3 + a_2 x^2 + a_3 x + a_4$ to handle multi-variate
+arguments. In other words, rather than having a scalar $x$ and a vector of
+coefficients, $a$. You will now have a vector of inputs for $x$ and a matrix
+of coefficients, $a$. Each column of $a$ is the coefficients for the $i$th
+element of the vector $x$. This function should still return a scalar value.
+
+Examples:
+
+```
+>>> cubic(np.array([1,2,3,4]), np.array([[1,2,3,4],[5,6,7,8],[9,10,11,12],[13,14,15,16]]))
+???
+```
+
+## Part 2 - Regression analysis (70 points)
+
+For this part we’re going to explore which factors contribute to the happiness
+score (the column called "happiness_score") for various countries (csv file).
+The idea is to predict the happiness score based on 13 factors. For these parts
+submit a single file of your python code called l1p2.ipynb. Please clearly
+comment the file so we can understand which parts of the code are associated
+with which project. For the writeup, also submit a pdf called l1p2.pdf. The
+Jupyter notebook file should produce this pdf. See below for directions on how
+to do this. It is your responsibility to ensure that this can be run on the
+grader's computer. We will use a python distribution set up with scikit-learn,
+numpy, pandas, and matplotlib.
+
+### Q2.1 (20 points)
+
+First we want to get an overview of the data. Write a report that contains the
+following parts:
+
+1. Use matplotlib to make a scatterplot of each variable against the 
+   happiness score.
+2. Explain the trends you see in each of the plots. Explain if you see any 
+   trend and what kind of trend you see (linear, quadratic, logrithmic, etc). 
+   (one sentence for each plot should be sufficient)
+3. before doing the later parts of the assignment, explain which factors you 
+   think are important for predicting the happiness index and why. (one paragraph)
+
+### Q2.2 (50 points)
+
+Now it’s time to build a model of the data. For this you should use the
+[KernelRidge](http://scikit-learn.org/stable/modules/generated/sklearn.kernel_ridge.KernelRidge.html#sklearn.kernel_ridge.KernelRidge)
+module from scipy.
+
+For the evaulation report both the $R^2$ value as well as the 5-fold cross
+validation results for each model.
+
+1. Check for any missing values in the dataset. Any missing values will cause
+   an error when you try to build a model.
+2. Come up with a way (and modify the dataset programmatically). **DO NOT
+   change the CSV file itself**. It's important to document your work use code
+   as much as possible so that your results are reproducable. We will diff the
+   csv file submitted against our copy and it cannot differ.
+3. Build a linear model and evaluate it (HINT: linear kernel)
+4. Build a polynomial model and evaluate it (HINT: polynomial kernel)
+5. Build a Gaussian model and evaluate it (HINT: Gaussian/RBF kernel)
+6. Compare the 3 different models:
+    * which degree of polynomial provided the best fit?
+    * which values of gamma and alpha for the fitting procedure gave the 
+      best fit?
+    * write which model is the best fit to the data and why 
+      (1 paragraph will be sufficient)
+
+### Converting a Jupyter notebook to pdf
+
+Jupyter comes with a function called [nbconvert]() that can convert Juyter
+notebooks to a variety of formats. To convert your notebook to pdf you'll also
+need LaTeX and [pandoc](https://pandoc.org/) installed. Once you've done this
+you can convert the notebook from the command line:
+
+```
+>>> jupyter nbconvert --to pdf l1p2.ipynb
+```
+
+### Procedure and Submission
+
+Please submit a ZIP-document with your answers to [Moodle](). Use the following
+naming scheme for your submission: “lastname_matrikelnumber_A1.zip”. The naming
+of the files is important. If you do not follow the submission instructions,
+then you will receive a grade of 0 for the lab.
+
+### Late submission
+
+Late Submissions are NOT possible. Any assignment submitted late will receive zero points.
+
+[Academic Honesty](http://vda.univie.ac.at/Teaching/FDA/19s/academicHonesty.html)
+

l1p1.py

+
+##############
+# Question 1 #
+##############
+# Define sort function
+def sort_list(l):
+  pass
+
+##############
+# Question 2 #
+##############
+# Given a random number and a random digit, design an algorithm to place the 
+# digit so that the number is divisible by 3
+def div7(n, i):
+  pass 
+
+##############
+# Question 3 #
+##############
+# Extend the cubic function y = a_1 x^3 + a_2 x^2 + a_3 x + a_4 to handle a 
+# multi-variate input
+def cubic(x, A):
+  import numpy as np
+  pass
+
+

l1p2.ipynb

+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Q2.1"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "1. Use `matplotlib` to show scatterplots of each variable"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from matplotlib import pyplot as plt\n",
+    "import numpy as np\n",
+    "#import pandas as pd\n",
+    "\n",
+    "# you can also use pandas to load the data\n",
+    "data = np.loadtxt('happiness.csv', skiprows=1, delimiter=',', converters = {3: lambda s: float(s[1])})\n",
+    "\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "{replace this text with your explanation text about trends in each plot}"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "{replace this text with which factors you think are important and why}"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Q2.2"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Load data and set up packages"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from sklearn.kernel_ridge import KernelRidge\n",
+    "from sklearn.model_selection import train_test_split\n",
+    "from sklearn.model_selection import RepeatedKFold"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Check the dataset for missing values and, if any are found, address them programmatically"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Linear model"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "{text results here}"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Quadratic model"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "{text results here}"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Gaussian model"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "{text results here}"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Comparison"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "{replace with your comparison paragraph/images}"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.6.8"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}

test_assignment.sh

+#!/usr/bin/env sh
+
+python -m pytest
+

tests/test_cubic.py

+
+import numpy as np
+
+import l1p1
+
+def test_case_1():
+  x = np.array([1, 2, 3, 4])
+  A = np.array([[1, 2, 3, 4], 
+                [5, 6, 7, 8], 
+                [9, 10, 11, 12], 
+                [13, 14, 15, 16]])
+  assert l1p1.cubic(x, A) == 45
+

tests/test_div7.py

+
+from hypothesis import given, settings, unlimited
+import hypothesis.strategies as st
+
+import l1p1
+
+def test_case_1():
+  v = l1p1.div7(123, 4)
+  assert (v%7) == 0
+  assert v == 4123
+
+def test_case_2():
+  v = l1p1.div7(39, 2)
+  assert (v%7) == 0
+  assert v == 329
+
+@given(st.integers(min_value=10), st.integers(min_value=0, max_value=9))
+def test_digit_order(n, i):
+  assert i < n
+
+@given(st.integers(min_value=10), st.integers(min_value=0, max_value=9))
+def test_div_by_7(n, i):
+  # don't worry about errors
+  try:
+    assert l1p1.div(n, i) % 7 == 0
+  except Exception as e:
+    assert str(e) == "not possible"
+
+

tests/test_sort.py

+
+from hypothesis import given, settings, unlimited
+import hypothesis.strategies as st
+
+import l1p1
+
+def is_sorted(l):
+  if(len(l) < 2):
+      return True
+  else:
+    return all([x<=y for x,y in zip(l[:-1],l[1:])])
+
+def test_simple_sort():
+  l = [3, 6, 1, 4]
+  l_sorted = [1, 3, 4, 6]
+  assert l1p1.sort_list(l) == l_sorted
+
+def test_already_sorted():
+  l = [1, 2, 3, 4, 5]
+  assert l1p1.sort_list(l) == l
+
+def test_reverse_sorted():
+  l = [5, 4, 3, 2, 1]
+  assert l1p1.sort_list(l) == reversed(l)
+
+@given(st.lists(st.integers()))
+def test_random_lists(l):
+  assert is_sorted(l1p1.sort_list(l))
+