{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Exercise: Python lists and iterations" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this notebook we explore the use of lists and iterations. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Speed comparisons" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We start, however, with a word of caution. The use of lists and for-loops can be painfully slow. Here we show some examples. We use the *magic command* `%timeit` to perform the timing measurement. It runs the command(s) multiple times and presents the mean execution time and its standard deviation. This provides a more reliable metric than the output from a single time measurement. \n", "\n", "While `%timeit` measures the command(s) on the same line, the double `%%` implies that the whole cell will be measured." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Creating a list, range, numpy array" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "n = 1_000 # Note that we can use the '_' in integer representations" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Creating a list via iteration is notoriously slow." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "61.8 µs ± 1.24 µs per loop (mean ± std. dev. of 7 runs, 10000 loops each)\n" ] } ], "source": [ "%%timeit\n", "x_list = []\n", "for i in range(n):\n", " x_list.append(i)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We must be careful that the variable `x_list` is only used inside the `timeit` call and is not retained." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "ename": "NameError", "evalue": "name 'x_list' is not defined", "output_type": "error", "traceback": [ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[0;31mNameError\u001b[0m Traceback (most recent call last)", "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mx_list\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m", "\u001b[0;31mNameError\u001b[0m: name 'x_list' is not defined" ] } ], "source": [ "x_list" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We create a new copy without timing." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "x_list = []\n", "for i in range(n):\n", " x_list.append(i)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The creation of a numpy array is much faster." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "import numpy as np" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "965 ns ± 44.5 ns per loop (mean ± std. dev. of 7 runs, 1000000 loops each)\n" ] } ], "source": [ "%timeit np.arange(n) # Timing only of this line\n", "x_arange = np.arange(n) # Repeating the command for later use of the variable" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that the built-in function `range` is rather fast. This is because it is an `iterator` rather than a list or array." ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "147 ns ± 4.34 ns per loop (mean ± std. dev. of 7 runs, 10000000 loops each)\n" ] } ], "source": [ "%timeit range(n)\n", "x_range = range(n)" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "list" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "type(x_list)" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "range" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "type(x_range)" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "numpy.ndarray" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "type(x_arange)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Iteration versus array operation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's iterate over the list and sum the squares of the elements." ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "272 µs ± 9.7 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)\n" ] } ], "source": [ "%%timeit\n", "sum_of_squares = 0\n", "for x in x_list:\n", " sum_of_squares += x**2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Using a `range` rather than a `list` does not improve the speed." ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "294 µs ± 12.6 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)\n" ] } ], "source": [ "%%timeit\n", "sum_of_squares = 0\n", "for x in x_range:\n", " sum_of_squares += x**2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Whereas the vectorized evaluation of an `np.array` operation is superior." ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "5.62 µs ± 383 ns per loop (mean ± std. dev. of 7 runs, 100000 loops each)\n" ] } ], "source": [ "%%timeit\n", "sum_of_squares = np.sum(x_arange**2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As will be shown in the following, lists are still very useful objects in python, and iteration can be used for many tasks. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Iterating through a list of parameters to draw multiple lines on a plot\n", "\n", "Suppose we have a function of $x$ that also depends on a parameter (call it $r$). We want to plot the function vs. $x$ for multiple values of $r$, either on the same plot or on separate plots. We can do this with a lot of cutting-and-pasting, but how can we do it based on a list of $r$ values, which we can easily modify?" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import seaborn; seaborn.set() # for plot formatting" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [], "source": [ "def sine_map(r, x):\n", " \"\"\"Sine map function: f_r(x) = r sin(pi x)\n", " \"\"\"\n", " return r * np.sin(np.pi * x) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Suppose the $r$ values initially of interest are 0.3, 0.5, 0.8, and 0.9. First the multiple copy approach:" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x_pts = np.linspace(0,1, num=101, endpoint=True)\n", "\n", "fig = plt.figure()\n", "ax = fig.add_subplot(1,1,1)\n", "ax.set_aspect(1)\n", "\n", "ax.plot(x_pts, x_pts, color='black') # black y=x line\n", "\n", "ax.plot(x_pts, sine_map(0.3, x_pts), label='$r = 0.3$')\n", "ax.plot(x_pts, sine_map(0.5, x_pts), label='$r = 0.5$')\n", "ax.plot(x_pts, sine_map(0.8, x_pts), label='$r = 0.8$')\n", "ax.plot(x_pts, sine_map(0.9, x_pts), label='$r = 0.9$')\n", "\n", "ax.legend()\n", "ax.set_xlabel(r'$x$')\n", "ax.set_ylabel(r'$f(x)$')\n", "ax.set_title('sine map')\n", "\n", "fig.tight_layout()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This certainly works, but making changes is awkward and prone to error because we have to find where to change (or add another) $r$ but we might not remember to change it correctly everywhere.\n", "\n", "With minor changes we have a much better implementation (try modifying the list of $r$ values):" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "r_list = [0.3, 0.5, 0.8, 0.9] # this could also be a numpy array\n", "\n", "x_pts = np.linspace(0,1, num=101, endpoint=True)\n", "\n", "fig = plt.figure()\n", "ax = fig.add_subplot(1,1,1)\n", "ax.set_aspect(1)\n", "\n", "ax.plot(x_pts, x_pts, color='black') # black y=x line\n", "\n", "# Step through the list. r is a dummy variable.\n", "# Note the use of an f-string and LaTeX by putting rf in front of the label.\n", "for r in r_list:\n", " ax.plot(x_pts, sine_map(r, x_pts), label=rf'$r = {r:.1f}$')\n", "\n", "ax.legend()\n", "ax.set_xlabel(r'$x$')\n", "ax.set_ylabel(r'$f(x)$')\n", "ax.set_title('sine map')\n", "\n", "fig.tight_layout()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now suppose we want each the different $r$ values to be plotted on separate graphs? We could make multiple copies of the single plot. Instead, lets make a function to do any single plot and call it for each $r$ in the list." ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "r_list = [0.3, 0.5, 0.8, 0.9] # this could also be a numpy array\n", "\n", "def plot_sine_map(r):\n", " x_pts = np.linspace(0,1, num=101, endpoint=True)\n", "\n", " fig = plt.figure()\n", " ax = fig.add_subplot(1,1,1)\n", " ax.set_aspect(1)\n", "\n", " ax.plot(x_pts, x_pts, color='black') # black y=x line\n", "\n", "# Note the use of an f-string and LaTeX by putting rf in front of the label.\n", " ax.plot(x_pts, sine_map(r, x_pts), label=rf'$r = {r:.1f}$')\n", "\n", " ax.legend()\n", " ax.set_xlabel(r'$x$')\n", " ax.set_ylabel(r'$f(x)$')\n", " ax.set_title(rf'sine map for $r = {r:.1f}$')\n", " \n", " fig.tight_layout()\n", "\n", " \n", "# Step through the list. r is a dummy variable.\n", "for r in r_list:\n", " plot_sine_map(r)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "What if instead of distinct plots we wanted subplots of the same figure? Then create the figure and subplot axes outside of the function and have the function return the modified axis object." ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "r_list = [0.3, 0.5, 0.8, 0.9] # this could also be a numpy array\n", "\n", "def plot_sine_map(r, ax_passed):\n", " x_pts = np.linspace(0,1, num=101, endpoint=True)\n", "\n", " ax_passed.set_aspect(1)\n", "\n", " ax_passed.plot(x_pts, x_pts, color='black') # black y=x line\n", "\n", "# Note the use of an f-string and LaTeX by putting rf in front of the label.\n", " ax_passed.plot(x_pts, sine_map(r, x_pts), label=rf'$r = {r:.1f}$')\n", "\n", " ax_passed.legend()\n", " ax_passed.set_xlabel(r'$x$')\n", " ax_passed.set_ylabel(r'$f(x)$')\n", " ax_passed.set_title(rf'sine map for $r = {r:.1f}$')\n", " \n", " return ax_passed\n", "\n", "fig = plt.figure(figsize=(8, 8))\n", " \n", "# Step through the list. r is a dummy variable.\n", "rows = 2\n", "cols = 2\n", "for index, r in enumerate(r_list):\n", " ax = fig.add_subplot(rows, cols, index+1)\n", " ax = plot_sine_map(r, ax)\n", "\n", "fig.tight_layout()\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Aside: List comprehensions \n", "\n", "In the plotting examples we used for loops to iterate through parameters or plots because it is familiar to anyone who has done programming. In Python, however, it is often preferred to use a different construction called a list comprehension. Here is a quick comparison of using for loop and using a list comprehension, followed by some representative further examples of list comprehensions. You can find much more information and other examples in the online Python documentation and other sources. (The examples here are from [https://hackernoon.com/list-comprehension-in-python-8895a785550b].)" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[1, 4, 9, 16]\n" ] } ], "source": [ "numbers = [1, 2, 3, 4]\n", "squares = []\n", "\n", "for n in numbers:\n", " squares.append(n**2)\n", "\n", "print(squares) # Output: [1, 4, 9, 16]" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[1, 4, 9, 16]\n" ] } ], "source": [ "numbers = [1, 2, 3, 4]\n", "squares = [n**2 for n in numbers]\n", "\n", "print(squares) # Output: [1, 4, 9, 16]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Connecting back to the speed measurements that we made arlier, the construction of lists using list comprehension can be quite fast." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "392 ns ± 21.9 ns per loop (mean ± std. dev. of 7 runs, 1000000 loops each)\n" ] } ], "source": [ "%timeit [n_i for n_i in range(n)]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "List comprehension is often used in *pythonic* one-liners! (not always easy to read)" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[2, 3, 4]\n" ] } ], "source": [ "# Find common numbers from two lists using list comprehension\n", "list_a = [1, 2, 3, 4]\n", "list_b = [2, 3, 4, 5]\n", "\n", "common_num = [a for a in list_a for b in list_b if a == b]\n", "\n", "print(common_num) # Output: [2, 3, 4]" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[(1, 2), (1, 7), (2, 7), (3, 2), (3, 7)]\n" ] } ], "source": [ "# Return numbers from the list which are not equal as a tuple:\n", "list_a = [1, 2, 3]\n", "list_b = [2, 7]\n", "\n", "different_num = [(a, b) for a in list_a for b in list_b if a != b]\n", "\n", "print(different_num) # Output: [(1, 2), (1, 7), (2, 7), (3, 2), (3, 7)]" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "['hello', 'world', 'in', 'python']\n" ] } ], "source": [ "# Iterate over strings\n", "list_a = [\"Hello\", \"World\", \"In\", \"Python\"]\n", "\n", "small_list_a = [str.lower() for str in list_a]\n", "\n", "print(small_list_a) # Output: ['hello', 'world', 'in', 'python']" ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[1, 1], [4, 8], [9, 27]]\n" ] } ], "source": [ "# Making a list of lists\n", "list_a = [1, 2, 3]\n", "\n", "square_cube_list = [ [a**2, a**3] for a in list_a]\n", "\n", "print(square_cube_list) # Output: [[1, 1], [4, 8], [9, 27]]" ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[(1, 3), (1, 4), (2, 3), (2, 1), (2, 4), (3, 1), (3, 4)]" ] }, "execution_count": 34, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Using an if statement to make a list of unequal pairs of numbers\n", "[(x, y) for x in [1,2,3] for y in [3,1,4] if x != y]\n", "# Output: [(1, 3), (1, 4), (2, 3), (2, 1), (2, 4), (3, 1), (3, 4)]" ] } ], "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": "3.7.12" } }, "nbformat": 4, "nbformat_minor": 2 }