{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# CS109A Introduction to Data Science \n", "\n", "\n", "## Pre - Lab 3: `numpy`, plotting\n", "## PRE-LAB : DO THIS PART BEFORE COMING TO LAB\n", "\n", "**Harvard University**
\n", "**Fall 2019**
\n", "**Instructors:** Pavlos Protopapas, Kevin Rader, and Chris Tanner
\n", "\n", "**Material prepared by**: David Sondak, Will Claybaugh, Pavlos Protopapas, and Eleni Kaxiras\n", "\n", "---" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "#RUN THIS CELL \n", "import requests\n", "from IPython.core.display import HTML\n", "styles = requests.get(\"https://raw.githubusercontent.com/Harvard-IACS/2018-CS109A/master/content/styles/cs109.css\").text\n", "HTML(styles)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Numerical Python: `numpy`\n", "Review the concepts on numpy: Scientific `Python` code uses a fast array structure, called the `numpy` array. Those who have worked in `Matlab` will find this very natural. For reference, the `numpy` documention can be found here: [`numpy`](http://www.numpy.org/). \n", "\n", "\n", "Let's make a numpy array." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "import numpy as np" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([ 1, 4, 9, 16])" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "my_array = np.array([1,4,9,16])\n", "my_array" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Numpy arrays support the same operations as lists! Below we compute length, slice, and iterate. " ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "len(array): 4\n", "array[2:4]: [ 9 16]\n", "element: 1\n", "element: 4\n", "element: 9\n", "element: 16\n" ] } ], "source": [ "print(\"len(array):\", len(my_array)) # Length of array\n", "\n", "print(\"array[2:4]:\", my_array[2:4]) # A slice of the array\n", "\n", "# Iterate over the array\n", "for ele in my_array:\n", " print(\"element:\", ele)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**In general you should manipulate numpy arrays by using numpy module functions** (e.g. `np.mean`). This is for efficiency purposes, and a discussion follows below this section.\n", "\n", "You can calculate the mean of the array elements either by calling the method `.mean` on a numpy array or by applying the function `np.mean` with the `numpy` array as an argument." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "7.5\n", "7.5\n" ] } ], "source": [ "# Two ways of calculating the mean\n", "\n", "print(my_array.mean())\n", "\n", "print(np.mean(my_array))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The way we constructed the `numpy` array above seems redundant. After all we already had a regular `python` list. Indeed, it is the other ways we have to construct `numpy` arrays that make them super useful. \n", "\n", "There are many such `numpy` array *constructors*. Here are some commonly used constructors. Look them up in the documentation." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([0., 0., 0., 0., 0., 0., 0., 0., 0., 0.])" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "zeros = np.zeros(10) # generates 10 floating point zeros\n", "zeros" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "`Numpy` gains a lot of its efficiency from being strongly typed. That is, all elements in the array have the same type, such as integer or floating point. The default type, as can be seen above, is a float of size appropriate for the machine (64 bit on a 64 bit machine)." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "dtype('float64')" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "zeros.dtype" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([1, 1, 1, 1, 1, 1, 1, 1, 1, 1])" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.ones(10, dtype='int') # generates 10 integer ones" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If the elements of an array are of a different type, `numpy` will force them into the same type (the longest in terms of bytes)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " \n" ] }, { "data": { "text/plain": [ "array(['1', '2.3', 'eleni', 'True'], dtype='\n", " \n", "Notice that the list slicing syntax still works! \n", "`array[2:,3]` says \"in the array, get rows 2 through the end, column 3]\" \n", "`array[3,:]` says \"in the array, get row 3, all columns\"." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Numpy functions will by default work on the entire array:" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "12.0" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.sum(ones_2d)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The axis `0` is the one going downwards (i.e. the rows), whereas axis `1` is the one going across (the columns). You will often use functions such as `mean` or `sum` along a particular axis. If you `sum` along axis 0 you are summing across the rows and will end up with one value per column. As a rule, any axis you list in the axis argument will dissapear." ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([3., 3., 3., 3.])" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.sum(ones_2d, axis=0)" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([4., 4., 4.])" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.sum(ones_2d, axis=1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
Exercise
\n", "\n", "Create a two-dimensional array of size $3\\times 5$ and do the following:\n", " * Print out the array\n", " * Print out the shape of the array\n", " * Create two slices of the array:\n", " 1. The first slice should be the last row and the third through last column\n", " 2. The second slice should be rows $1-3$ and columns $3-5$\n", " * Square each element in the array and print the result\n", " \n", "(*solutions follow but try not to look at them!*)" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [], "source": [ "# your code here\n" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[5. 4. 3. 2. 1. ]\n", " [1. 2. 3. 4. 5. ]\n", " [1.1 2.2 3.3 4.4 5.5]] \n", "\n", "(3, 5) \n", "\n", "[3.3 4.4 5.5] \n", "\n", "[[4. 5. ]\n", " [4.4 5.5]] \n", "\n", "[[25. 16. 9. 4. 1. ]\n", " [ 1. 4. 9. 16. 25. ]\n", " [ 1.21 4.84 10.89 19.36 30.25]]\n" ] } ], "source": [ "# Solution\n", "A = np.array([ [5, 4, 3, 2, 1], [1, 2, 3, 4, 5], [1.1, 2.2, 3.3, 4.4, 5.5] ])\n", "print(A, \"\\n\")\n", "\n", "# set length(shape)\n", "dims = A.shape\n", "print(dims, \"\\n\")\n", "\n", "# slicing\n", "print(A[-1, 2:], \"\\n\")\n", "print(A[1:3, 3:5], \"\\n\")\n", "\n", "# squaring\n", "A2 = A * A\n", "print(A2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### `numpy` supports matrix operations\n", "2d arrays are numpy's way of representing matrices. As such there are lots of built-in methods for manipulating them" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Earlier when we generated the one-dimensional arrays of ones and random numbers, we gave `ones` and `random` the number of elements we wanted in the arrays. In two dimensions, we need to provide the shape of the array, i.e., the number of rows and columns of the array." ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "scrolled": true }, "outputs": [ { "data": { "text/plain": [ "array([[1., 1., 1., 1.],\n", " [1., 1., 1., 1.],\n", " [1., 1., 1., 1.]])" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "three_by_four = np.ones([3,4])\n", "three_by_four" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You can transpose the array:" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(3, 4)" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ "three_by_four.shape" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [], "source": [ "four_by_three = three_by_four.T" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(4, 3)" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ "four_by_three.shape" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Matrix multiplication is accomplished by `np.dot`. The `*` operator will do element-wise multiplication." ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "scrolled": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[4. 4. 4.]\n", " [4. 4. 4.]\n", " [4. 4. 4.]]\n" ] }, { "data": { "text/plain": [ "array([[3., 3., 3., 3.],\n", " [3., 3., 3., 3.],\n", " [3., 3., 3., 3.],\n", " [3., 3., 3., 3.]])" ] }, "execution_count": 30, "metadata": {}, "output_type": "execute_result" } ], "source": [ "print(np.dot(three_by_four, four_by_three)) # 3 x 3 matrix\n", "np.dot(four_by_three, three_by_four) # 4 x 4 matrix" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### `Numpy `Arrays vs. `Python` Lists?\n", "\n", "1. Why the need for `numpy` arrays? Can't we just use `Python` lists?\n", "2. Iterating over `numpy` arrays is slow. Slicing is faster.\n", "\n", "`Python` lists may contain items of different types. This flexibility comes at a price: `Python` lists store *pointers* to memory locations. On the other hand, `numpy` arrays are typed, where the default type is floating point. Because of this, the system knows how much memory to allocate, and if you ask for an array of size $100$, it will allocate one hundred contiguous spots in memory, where the size of each spot is based on the type. This makes access extremely fast.\n", "\n", "\"Drawing\"\n", "\n", "(image from Jake Vanderplas's Data Science Handbook)\n", "\n", "Unfortunately, looping over an array slows things down. In general you should not access `numpy` array elements by iteration. This is because of type conversion. `Numpy` stores integers and floating points in `C`-language format. When you operate on array elements through iteration, `Python` needs to convert that element to a `Python` `int` or `float`, which is a more complex beast (a `struct` in `C` jargon). This has a cost.\n", "\n", "\"Drawing\"\n", "\n", "(image from Jake Vanderplas's Data Science Handbook)\n", "\n", "If you want to know more, we will suggest that you read \n", "- [Jake Vanderplas's Data Science Handbook](https://jakevdp.github.io/PythonDataScienceHandbook/). \n", "- [Wes McKinney's Python for Data Analysis](https://hollis.harvard.edu/primo-explore/fulldisplay?docid=01HVD_ALMA512247401160003941&context=L&vid=HVD2&lang=en_US&search_scope=everything&adaptor=Local%20Search%20Engine&tab=everything&query=any,contains,Wes%20McKinney%27s%20Python%20for%20Data%20Analysis&sortby=rank&offset=0) (HOLLIS)
\n", "You will find them both incredible resources for this class.\n", "\n", "Why is slicing faster? The reason is technical: slicing provides a *view* onto the memory occupied by a `numpy` array, instead of creating a new array. That is the reason the code above this cell works nicely as well. However, if you iterate over a slice, then you have gone back to the slow access.\n", "\n", "By contrast, functions such as `np.dot` are implemented at `C`-level, do not do this type conversion, and access contiguous memory. If you want this kind of access in `Python`, use the `struct` module or `Cython`. Indeed many fast algorithms in `numpy`, `pandas`, and `C` are either implemented at the `C`-level, or employ `Cython`." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2 - Plotting with matplot lib (and beyond)\n", " \n", "\n", "Conveying your findings convincingly is an absolutely crucial part of any analysis. Therefore, you must be able to write well and make compelling visuals. Creating informative visuals is an involved process and we won't cover that in this lab. However, part of creating informative data visualizations means generating *readable* figures. If people can't read your figures or have a difficult time interpreting them, they won't understand the results of your work. Here are some non-negotiable commandments for any plot:\n", "* Label $x$ and $y$ axes\n", "* Axes labels should be informative\n", "* Axes labels should be large enough to read\n", "* Make tick labels large enough\n", "* Include a legend if necessary\n", "* Include a title if necessary\n", "* Use appropriate line widths\n", "* Use different line styles for different lines on the plot\n", "* Use different markers for different lines\n", "\n", "There are other important elements, but that list should get you started on your way.\n", "\n", "Here is the anatomy of a figure:\n", " \"Drawing\"\n", " \n", "taken from [showcase example code: anatomy.py](https://tacaswell.github.io/matplotlib/examples/showcase/anatomy.html)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Before diving in, one more note should be made. We will not focus on the internal aspects of `matplotlib`. Today's lab will really only focus on the basics and developing good plotting practices. There are many excellent tutorials out there for `matplotlib`. For example,\n", "* [`matplotlib` homepage](https://matplotlib.org/)\n", "* [`matplotlib` tutorial](https://github.com/matplotlib/AnatomyOfMatplotlib)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### `matplotlib`" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First, let's generate some data." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
Exercise
\n", "Use the following three functions to make some plots:\n", "\n", "* Logistic function:\n", " \\begin{align*}\n", " f\\left(z\\right) = \\dfrac{1}{1 + be^{-az}}\n", " \\end{align*}\n", " where $a$ and $b$ are parameters.\n", "* Hyperbolic tangent:\n", " \\begin{align*}\n", " g\\left(z\\right) = b\\tanh\\left(az\\right) + c\n", " \\end{align*}\n", " where $a$, $b$, and $c$ are parameters.\n", "* Rectified Linear Unit:\n", " \\begin{align*}\n", " h\\left(z\\right) = \n", " \\left\\{\n", " \\begin{array}{lr}\n", " z, \\quad z > 0 \\\\\n", " \\epsilon z, \\quad z\\leq 0\n", " \\end{array}\n", " \\right.\n", " \\end{align*}\n", " where $\\epsilon < 0$ is a small, positive parameter.\n", "\n", "You are given the code for the first two functions. Notice that $z$ is passed in as a `numpy` array and that the functions are returned as `numpy` arrays. Parameters are passed in as floats.\n", "\n", "You should write a function to compute the rectified linear unit. The input should be a `numpy` array for $z$ and a positive float for $\\epsilon$." ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [], "source": [ "# Your code here" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [], "source": [ "# solution\n", "import numpy as np\n", "\n", "def logistic(z: np.ndarray, a: float, b: float) -> np.ndarray:\n", " \"\"\" Compute logistic function\n", " Inputs:\n", " a: exponential parameter\n", " b: exponential prefactor\n", " z: numpy array; domain\n", " Outputs:\n", " f: numpy array of floats, logistic function\n", " \"\"\"\n", " \n", " den = 1.0 + b * np.exp(-a * z)\n", " return 1.0 / den\n", "\n", "def stretch_tanh(z: np.ndarray, a: float, b: float, c: float) -> np.ndarray:\n", " \"\"\" Compute stretched hyperbolic tangent\n", " Inputs:\n", " a: horizontal stretch parameter (a>1 implies a horizontal squish)\n", " b: vertical stretch parameter\n", " c: vertical shift parameter\n", " z: numpy array; domain\n", " Outputs:\n", " g: numpy array of floats, stretched tanh\n", " \"\"\"\n", " return b * np.tanh(a * z) + c\n", "\n", "def relu(z: np.ndarray, eps: float = 0.01) -> np.ndarray:\n", " \"\"\" Compute rectificed linear unit\n", " Inputs:\n", " eps: small positive parameter\n", " z: numpy array; domain\n", " Outputs:\n", " h: numpy array; relu\n", " \"\"\"\n", " return np.fmax(z, eps * z)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now let's make some plots. First, let's just warm up and plot the logistic function." ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [], "source": [ "x = np.linspace(-5.0, 5.0, 100) # Equally spaced grid of 100 pts between -5 and 5\n", "\n", "f = logistic(x, 1.0, 1.0) # Generate data" ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "\n", "# This is only needed in Jupyter notebooks! Displays the plots for us.\n", "%matplotlib inline \n", "\n", "plt.plot(x, f); # Use the semicolon to suppress some iPython output (not needed in real Python scripts)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Wonderful! We have a plot. Let's clean it up a bit by putting some labels on it." ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [ { "data": { "image/png": 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njQ87jsQ5FYFInGlsaeW6J9+nh8FPLz2OtBT9GMvh0TkCkTjz/Zc/YMX2Kn4+ZwqD+/QMO44kAP0qIRJH3lizi0fe2cLnTxjOmbpoTLqIikAkTpRUN3Dzc8sZPyCXb5yt8wLSdTQ0JBIH3J2bfr2cmsYWnrpmJhmpmlFUuo6OCETiwKN/3cKf1pVy62cmMLa/JpOTrqUiEIlx63ZVc+fLH3Dq+COYM3NY2HEkAakIRGJYU0sb//nMUnIzUjWPkARG5whEYthP31zPqh17mDtnCv1ytMiMBENHBCIxasm23dz31gYumjJY6wtIoFQEIjGovqmVG55dRmGvLG47d2LYcSTBaWhIJAbd9coHbC6r5cmrZ5CXmRZ2HElwOiIQiTHvbq7g0b9u4XPHD+OEUf3CjiNJQEUgEkPqm1q5+bllDO6TpVlFpdtoaEgkhvzvq2vZUl7Hk1fP0Gpj0m10RCASIxZtqeDhdzYzZ6aGhKR7qQhEYkBDcytff345A3tl8fWzNCQk3UvHniIx4GdvbmBjaS2PXTWdHA0JSTfTEYFIyFbv2MMDf9rIv04ezEljC8KOI0lIRSASopbWNr7+/HJ690zj2+dMCDuOJKlAi8DMZpnZWjPbYGa37Gefi81stZmtMrMng8wjEmsefmczK7ZXcfv5R9G7Z3rYcSRJBTYYaWYpwH3A6UAx8J6ZzXP31e32GQN8AzjR3Xeb2RFB5RGJNUUVdfz4tXWcNqE/Zx2luYQkPEEeEUwHNrj7JndvAp4Gzt9nn6uB+9x9N4C7lwSYRyRmuDu3vriSFDO+d8GRml5aQhVkEQwCitrdLo7e195YYKyZvWNmC8xsVkcPZGbXmNkiM1tUWloaUFyR7jNv2Q7eXlfKzbPGU9grK+w4kuSCLIKOfsXxfW6nAmOAk4FLgV+YWe+PfZH7XHef6u5TCwr0rgqJb7trm7j9pdUcO6Q3V2jFMYkBQRZBMTCk3e3BwI4O9vmtuze7+2ZgLZFiEElYd768hqr6Zu68cBIpPTQkJOELsgjeA8aY2QgzSwdmA/P22edF4BQAM+tHZKhoU4CZREK1cFM5zy4q5ov/PJIJhXlhxxEBAiwCd28BrgNeAdYAz7r7KjO73czOi+72ClBuZquBt4Cb3L08qEwiYWpqaePWF1cyuE8W139aB74SOwK9lt3d5wPz97nvtnafO/C16IdIQpv79kY2lNTwyJXTyEpPCTuOyEd0ZbFIN9hSVstP39zAZyYVcso4XS4jsUVFIBIwd+fbv11JWkoPrT8sMUlFIBKw36/YyZ/Xl3HjGWPpn5cZdhyRj1ERiASouqGZ219azVGD8phz/PCw44h0SBOfiwToR6+uo7SmkQc/O1XXDEjM0hGBSEBWbq/isb9t4fIZQzlmyMcumBeJGSoCkQC0tkUmleubnc5NZ2rpSYltKgKRADz93jaWFVVy62cm0CsrLew4IgekIhDpYmU1jdz1h7XMGNGXC47dd8JdkdijIhDpYt9/+QNqG1u444KjtM6AxAUVgUgXendzBc8tLubqk0Yypn9u2HFEOkVFINJFmlvb+PaLKxnUO4uvnDo67DginaYiEOkiv/zrFtbuqua2cyfSM12X6Ej8UBGIdIEPqxq4+7V1nDr+CM6Y2D/sOCIHZb9FYGa/iv55fffFEYlP3/v9alranO+eq4XoJf4c6IhgipkNA64ysz5m1rf9R3cFFIl1b68r5ffLd/LlU0YzNL9n2HFEDtqBBjIfAP4AjAQW84+L0Xv0fpGk1tjSynfmrWJ4fk+uOUk/EhKf9lsE7n4vcK+Z3e/u13ZjJpG4MfdPm9hcVstjV00nM02rjkl8+sSTxSoBkY5tK6/jZ29FVh07aWxB2HFEDpneNSRyCNyd78xbSWoP49vnaNUxiW8qApFD8MqqXby1tpT/PH0sA3pp1TGJbyoCkYNU29jC7S+tYvyAXD53wvCw44gcNhWByEG694317Khq4I4LjiItRT9CEv/0v1jkIKz9sJqH/rKZS6YOYepwXU4jiUFFINJJbW3Ot15cQW5mKrecpVXHJHGoCEQ66bklxby3ZTffOHsCfbLTw44j0mVUBCKdUFHbxJ3z1zBteB8umjw47DgiXUpFINIJd85fQ3VDC3dcMIkePTSpnCQWFYHIJ1iwqZxfR1cdGzdAq45J4lERiBxAY0srt/5mBUP6ZvEfp44JO45IILSMksgBzP3TJjaW1vLIldPIStekcpKYAj0iMLNZZrbWzDaY2S0H2O8iM3MzmxpkHpGDsbmslp9GJ5U7ZdwRYccRCUxgRWBmKcB9wFnAROBSM/vY7Fxmlgv8B7AwqCwiB8vd+eYLK8hI7cFt52pSOUlsQR4RTAc2uPsmd28CngbO72C/7wF3AQ0BZhE5KM8tLuZvm8q55azx9M/TpHKS2IIsgkFAUbvbxdH7PmJmxwFD3P13B3ogM7vGzBaZ2aLS0tKuTyrSTllNI/89fw1Th/Xh0mlDw44jErggi6CjN1v7RxvNegB3Azd80gO5+1x3n+ruUwsKtACIBOuO362mtrGFOy/UNQOSHIIsgmJgSLvbg4Ed7W7nAkcBfzSzLcBMYJ5OGEuY3lpbwotLd3Dtp0Yxpr+uGZDkEGQRvAeMMbMRZpYOzAbm7d3o7lXu3s/dh7v7cGABcJ67Lwowk8h+1TS2cOsLKxh9RA5fPnV02HFEuk1gReDuLcB1wCvAGuBZd19lZreb2XlBfV+RQ/XDP3zAzj0N/OBfJ5GRqmsGJHkEekGZu88H5u9z32372ffkILOIHMh7Wyp4bMFWPnf8cKYM0zoDklw0xYQkvYbmVr7+/HIG9sripjPHhR1HpNtpiglJej95fT2bSmt57KrpZGfoR0KSj44IJKktLapk7tsbuWTqEE4aq7cmS3JSEUjSamhu5aZfL6N/Xia3njMh7DgiodFxsCSte99Yz/qSGh69chp5mWlhxxEJjY4IJCktLark529v4uKpgzlZM4tKklMRSNKpb2rla88upX9uBrd+RjOLimhoSJLOD/7wAZtKa3niizPolaUhIREdEUhSeWdDGY/+dQufP2E4J47uF3YckZigIpCkUVXfzE2/XsbIgmy+Pmt82HFEYoaGhiRp3PbbleyqbuT5a0/Q+sMi7eiIQJLCi+9v57dLd3D9p8dw7JDeYccRiSkqAkl4RRV1fOvFlUwb3ocvn6LppUX2pSKQhNbS2sZXn1mKAT+++FhStOKYyMfoHIEktHvf3MDirbu5Z/axDOnbM+w4IjFJRwSSsP66oYyfvrmeCycP4vxjB4UdRyRmqQgkIZXVNHL9M0sZ2S+b751/VNhxRGKahoYk4bS1Of/5zFKq6pu1xoBIJ+iIQBLO/X/ayJ/Xl/GdcycyoTAv7DgiMU9FIAnlL+vL+NGrazn3mIFcNn1o2HFE4oKKQBLGjsp6/uPp9xlVkMP3L5yEmd4qKtIZKgJJCI0trVz7xBKaWtp4YM4UnRcQOQj6aZGE8F8vrWZZUSX3Xz6ZUQU5YccRiSs6IpC496sFW3ly4Ta+9KmRnDWpMOw4InFHRSBxbcGmcv5r3ipOGVfAzWdqammRQ6EikLhVVFHHvz+xhKH5Pbnn0uM0j5DIIVIRSFyqbmjmi79cRHNrGw9+dip5mVpyUuRQqQgk7jS3tvHvTyxhY2kN918+RSeHRQ6T3jUkccXd+c68Vfx5fRnfv3AS/zRG6w6LHC4dEUhcmfv2Jp5cuI1rTx7FbF05LNIlVAQSN55fXMydL3/AOUcXctMZ48KOI5IwAi0CM5tlZmvNbIOZ3dLB9q+Z2WozW25mb5jZsCDzSPx664MSbn5+OSeOzudHFx9DD71DSKTLBFYEZpYC3AecBUwELjWzifvs9j4w1d2PBp4D7goqj8SvxVt3c+0Ti5lQmMsDV0whIzUl7EgiCSXII4LpwAZ33+TuTcDTwPntd3D3t9y9LnpzATA4wDwSh1Zur+LKR96lf14mj3x+Orl6m6hIlwuyCAYBRe1uF0fv258vAC93tMHMrjGzRWa2qLS0tAsjSixbt6uaOQ8tJCcjlce/MIOC3IywI4kkpCCLoKNBXO9wR7MrgKnADzva7u5z3X2qu08tKCjowogSqzaV1nDZgwtJS+nBE1fP1MLzIgEK8jqCYmBIu9uDgR377mRmpwG3Ap9y98YA80ic2Fhaw2UPLsDdefKamYzolx12JJGEFuQRwXvAGDMbYWbpwGxgXvsdzOw44OfAee5eEmAWiRPrdlVzyc8X0NLqPHH1DEYfkRt2JJGEF1gRuHsLcB3wCrAGeNbdV5nZ7WZ2XnS3HwI5wK/NbKmZzdvPw0kSWL1jD7PnLqCHwTNfmsn4AVpvWKQ7BDrFhLvPB+bvc99t7T4/LcjvL/Fj8dYKrnp0ET3TU3jyag0HiXQnXVksoXvzg11c/ouF9OmZxrNfOl4lINLNNOmchOq5xcV8/fnlTCzM45Erp9EvR28RFeluKgIJhbvzk9fXc88b6zlxdD4/nzOVHC04LxIK/eRJt2tobuXm55Yzb9kOLpoymP/5l0mkp2qUUiQsKgLpViXVDVz7+BIWb93NzbPGce2nRmGmCeREwqQikG6zeOturn18MdUNLfzf5ZM5e1Jh2JFEBBWBdAN35/GF27j9pVUM7J3FL6+azoRCXSMgEitUBBKoPQ3NfPOFFfxu+U5OGVfATy45jl49NYOoSCxREUhglhZV8pWnlrCjsoGbzoycD9CCMiKxR0UgXa6ltY37/7iRe95YT/+8TJ790kymDOsbdiwR2Q8VgXSpDSU13PDsUpYVV3HuMQO54/yjNBQkEuNUBNIlmlvbePDPm7jn9fX0TE/hvssm85mj9a4gkXigIpDDtmTbbr75wgo++LCaWUcO4PYLjuSI3MywY4lIJ6kI5JCV1TTyo1fX8vR7RQzIy+TBz07l9In9w44lIgdJRSAHramljcf+toV73lhPfVMrXzhxBF89fazmChKJU/rJlU5ra3NeWr6DH726jm0VdXxqbAHfPmcio4/ICTuaiBwGFYF8InfnrbUl/O8r61i9cw/jB+TyyOencfK4As0TJJIAVASyX+7Oa6t3ce+b61m5fQ9D+mZx9yXHcP4xg3RhmEgCURHIxzS2tPLbpTt46M+bWburmmH5PbnroqP5l+MGkZai6aJFEo2KQD5SUt3AM+8W8diCrZRWNzJ+QC4/vvgYzjtmIKkqAJGEpSJIcm1tzoLN5Ty5cBt/WPkhLW3OSWMLuPvikZw4Ol/nAESSgIogSRVV1PHCku08t6SIoop68jJT+fwJw7l85jAtHi+SZFQESaSkuoH5y3cyb9kOlmyrBODE0fnccPo4zjxyAFnpKSEnFJEwqAgS3NbyWl5dtYtXVn3I4m27cYfxA3K56cxxnHfMQIb07Rl2RBEJmYogwTQ0t7Joy27+uLaEN9eWsKm0FoAJhXlc/+kxnD2pkLH9c0NOKSKxREUQ5xpbWllRXMXCzRW8s6GMRVt309TSRnpqD2aOzOeKGcM4bUJ/hubrN38R6ZiKIM6UVDewdFsl7xdVsmTrbpYWVdLY0gZEhnzmzBzGiaPzmTkyn57p+ucVkU+mV4oY5e5sr6zng53VrN65hxXbq1i5vYqdVQ0ApPYwJg7M44qZw5g2vC/ThvchPycj5NQiEo9UBCFraW1je2U9m8pq2VhSw4aSGtaX1LBuVzXVDS0f7TeyIJvpI/oyaVAvjhvamyMH9iIzTe/yEZHDpyIImLtTUdvEjsoGtlfWUby7nqKKOrZW1LGtvI6i3XU0t/pH++dnpzP6iBzOP3Yg4wfkMaEwj3EDcjXFs4gERq8uh6iltY3ddc1U1DZRVtNIaXUjZTWNlFQ3smtPAx9WNfDhngZ2VjXQFB3D3ysnI5WhfXsybkAuZxw5gJEF2Yzsl82Iftka3hGRbhdoEZjZLOAeIAX4hbt/f5/tGcBjwBSgHLjE3bcEmWkvd6expY2axhZqG1uoboh81DS2sKe+mT0Nzeypb6Gyvomq+maq6prZXddE5d4/65tx//jjZqT2oH9eJv3zMpg0qBdnHjmAAXmZDOydxeA+kY9eWWmaukFEYkZgRWBmKcB9wOlAMfCemc1z99XtdvsCsNvdR/zDA/cAAATgSURBVJvZbOAHwCVB5HnmvW38/O1N1DW2UtvUQl1TK61tHbyS7yMnI5VeWWn0ykqjT3YaA3tn0adnOn2z08nPifzZLyeDgtwM+uVkkJeZqhd5EYkrQR4RTAc2uPsmADN7GjgfaF8E5wPfjX7+HPAzMzP3jn7XPjx9szOYWJhHdnoqPTNS6JmeQnZGKjkZqWSnp5KbmUpOZiq5GWnkZaWSl5lGbmaqZt0UkYQXZBEMAora3S4GZuxvH3dvMbMqIB8oa7+TmV0DXAMwdOjQQwpz+sT+WlhdRKQDQf6629H4yL6/6XdmH9x9rrtPdfepBQUFXRJOREQigiyCYmBIu9uDgR3728fMUoFeQEWAmUREZB9BFsF7wBgzG2Fm6cBsYN4++8wDPhf9/CLgzSDOD4iIyP4Fdo4gOuZ/HfAKkbePPuzuq8zsdmCRu88DHgJ+ZWYbiBwJzA4qj4iIdCzQ6wjcfT4wf5/7bmv3eQPwb0FmEBGRA9N7I0VEkpyKQEQkyakIRESSnMXbm3TMrBTYGnaOQ9CPfS6USwLJ9pyT7fmCnnM8GebuHV6IFXdFEK/MbJG7Tw07R3dKtuecbM8X9JwThYaGRESSnIpARCTJqQi6z9ywA4Qg2Z5zsj1f0HNOCDpHICKS5HREICKS5FQEIiJJTkUQAjO70czczPqFnSVIZvZDM/vAzJab2W/MrHfYmYJiZrPMbK2ZbTCzW8LOEzQzG2Jmb5nZGjNbZWbXh52pu5hZipm9b2a/CztLV1ERdDMzG0JkHedtYWfpBq8BR7n70cA64Bsh5wlEu/W5zwImApea2cRwUwWuBbjB3ScAM4EvJ8Fz3ut6YE3YIbqSiqD73Q3cTAcrsSUad3/V3VuiNxcQWZwoEX20Pre7NwF71+dOWO6+092XRD+vJvLCOCjcVMEzs8HAZ4BfhJ2lK6kIupGZnQdsd/dlYWcJwVXAy2GHCEhH63Mn/IviXmY2HDgOWBhukm7xEyK/yLWFHaQrBboeQTIys9eBAR1suhX4JnBG9yYK1oGer7v/NrrPrUSGEp7ozmzdqFNrbyciM8sBnge+6u57ws4TJDM7Byhx98VmdnLYebqSiqCLuftpHd1vZpOAEcAyM4PIMMkSM5vu7h92Y8Qutb/nu5eZfQ44B/h0Ai9D2pn1uROOmaURKYEn3P2FsPN0gxOB88zsbCATyDOzx939ipBzHTZdUBYSM9sCTHX3eJzFsFPMbBbwY+BT7l4adp6gmFkqkZPhnwa2E1mv+zJ3XxVqsABZ5LeZXwIV7v7VsPN0t+gRwY3ufk7YWbqCzhFIkH4G5AKvmdlSM3sg7EBBiJ4Q37s+9xrg2UQugagTgTnAqdF/26XR35QlDumIQEQkyemIQEQkyakIRESSnIpARCTJqQhERJKcikBEJMmpCEREkpyKQEQkyakIRA6TmU2LrrmQaWbZ0fn5jwo7l0hn6YIykS5gZncQmX8mCyh29ztDjiTSaSoCkS5gZulE5hhqAE5w99aQI4l0moaGRLpGXyCHyNxKmSFnETkoOiIQ6QJmNo/IymQjgEJ3vy7kSCKdpvUIRA6TmX0WaHH3J6PrF//VzE519zfDzibSGToiEBFJcjpHICKS5FQEIiJJTkUgIpLkVAQiIklORSAikuRUBCIiSU5FICKS5P4/3QSwQYKgUwMAAAAASUVORK5CYII=\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(x, f)\n", "plt.xlabel('x')\n", "plt.ylabel('f')\n", "plt.title('Logistic Function');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Okay, it's getting better. Still super ugly. I see these kinds of plots at conferences all the time. Unreadable. We can do better. Much, much better. First, let's throw on a grid." ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(x, f)\n", "plt.xlabel('x')\n", "plt.ylabel('f')\n", "plt.title('Logistic Function')\n", "plt.grid(True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "At this point, our plot is starting to get a little better but also a little crowded.\n", "\n", "#### A note on gridlines\n", "Gridlines can be very helpful in many scientific disciplines. They help the reader quickly pick out important points and limiting values. On the other hand, they can really clutter the plot. Some people recommend never using gridlines, while others insist on them being present. The correct approach is probably somewhere in between. Use gridlines when necessary, but dispense with them when they take away more than they provide. Ask yourself if they help bring out some important conclusion from the plot. If not, then best just keep them away.\n", "\n", "Before proceeding any further, I'm going to change notation. The plotting interface we've been working with so far is okay, but not as flexible as it can be. In fact, I don't usually generate my plots with this interface. I work with slightly lower-level methods, which I will introduce to you now. The reason I need to make a big deal about this is because the lower-level methods have a slightly different API. This will become apparent in my next example." ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [ { "data": { "image/png": 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OzOkTGN1XewxL22hEIJIgZr69lhcWbuH6U0ZpTwE5ICoEIgng3dUl/OSlFXxpfD+uPWlE2HEkzqgQiMS5LWU1fOOpjzi0Tw53n3+E9hmWA6ZCIBLH6iNN/OcTC6hraOQ3l00gO0On/eTA6f8akTh2598+ZuGmMn596TGMOCT+VsSU2KARgUic+uviLTwWXT7ijPH9wo4jcUyFQCQObdhZxc3PLeHowd25adphYceROKdCIBJn6iKNXPvkR3Qx+OXFR5OWoj9jaR+dIxCJMz9+cQVLNpfz4PQJDOzRNew4kgD0VkIkjry+fBuPvLuey48bymm6aEw6iAqBSJzYXlHLTc8u5rC+udxyhs4LSMfR1JBIHHB3bvzjYirrIjw1YwoZqVpRVDqORgQiceDRf6znrZU7uPVLYxiVr8XkpGOpEIjEuJXbKrjrxRWcdNghTJ8yJOw4koBUCERiWH2kiW89vZDcjFStIySB0TkCkRj2yzdWsWzLbmZOn0DvHG0yI8HQiEAkRi3YuIv731zN+RMGan8BCZQKgUgMqqlv5PpnFtGvWxa3nzU27DiS4DQ1JBKD7n55BetKqnjy6snkZaaFHUcSnEYEIjHmg3WlPPqP9Xzl2CEcd2jvsONIElAhEIkhNfWN3PTsIgb2yNKqotJpNDUkEkP+55Ui1u+s5smrJ2u3Mek0GhGIxIh560t5+N11TJ+iKSHpXCoEIjGgtqGR7zy3mP7dsvjO6ZoSks6lsadIDPjVG6tZs6OKx66cRI6mhKSTaUQgErKPt+zmgbfW8O/HDOSEUX3CjiNJSIVAJESRxia+89xiundN47Yzx4QdR5JUoIXAzKaZWZGZrTazm/fR5gIz+9jMlpnZk0HmEYk1D7+7jiWby7njnHF075oedhxJUoFNRppZCnA/cApQDHxoZrPd/eMWbUYCtwDHu/suMzskqDwisWZTaTU/e3UlJ4/J5/RxWktIwhPkiGASsNrd17p7PTALOGevNlcD97v7LgB33x5gHpGY4e7c+sJSUsz40bmHa3lpCVWQH08YAGxqcbsYmLxXm1EAZvYukAL8wN1f2vuBzGwGMAMgPz+fwsLCIPIGqrKyMi5zt0ey9flA+vvelghvr6zjsjHpFH30PkXBRgtMsv2OITH7HGQhaO0tjrfy/COBqcBA4B0zG+fuZf/0Q+4zgZkABQUFPnXq1A4PG7TCwkLiMXd7JFuf29rfXVX1XP+ztzhqUHd+OP04UrrE72gg2X7HkJh9DnJqqBgY1OL2QGBLK23+7O4N7r4OKKK5MIgkrLteXE55TQN3nTc+rouAJI4gC8GHwEgzG2Zm6cBFwOy92rwAnAhgZr1pnipaG2AmkVC9v3Ynz8wr5qrPD2dMv7yw44gAARYCd48A1wIvA8uBZ9x9mZndYWZnR5u9DOw0s4+BN4Eb3X1nUJlEwlQfaeLWF5YysEcW131RA1+JHYFey+7uc4A5e913e4vvHfh29Eskoc18ew2rt1fyyBUTyUpPCTuOyKd0ZbFIJ1hfUsUv31jNl8b348TRulxGYosKgUjA3J3b/ryUtJQu2n9YYpIKgUjA/rZkK++sKuGGU0eRn5cZdhyRf6FCIBKgitoG7vjLx4wbkMf0Y4eGHUekVVr4XCRA97yykh2VdTz05QJdMyAxSyMCkYAs3VzOY++t59LJgzlyUPew44jskwqBSAAam5oXleuZnc6Np2nrSYltKgQiAZj14UYWbSrj1i+NoVtWWthxRPZLhUCkg5VU1nH3S0VMHtaTc48aEHYckc+kQiDSwX784gqq6iLcee447TMgcUGFQKQDfbCulGfnF3P1CcMZmZ8bdhyRNlEhEOkgkSbntheWMqB7Ft84aUTYcUTaTNcRiHSQ1zZEKNpWzYPTJ9A1XX9aEj80IhDpAJ+U1/LC6npOOuwQTh2bH3YckQOyz0JgZn+I/ve6zosjEp9+9LePaXT4wVnaiF7iz/5GBBPMbAhwpZn1MLOeLb86K6BIrHt75Q7+tngrZw5PY3CvrmHHETlg+5vIfAB4CRgOzOefN6P36P0iSa0u0sj3Zy9jaK+unD4s7DQiB2efIwJ3v8/dxwAPu/twdx/W4ktFQASY+dZa1pVUccc540hP0ZSQxKfPPFns7td0RhCReLNxZzW/erN517ETRvUJO47IQdOnhkQOgrvz/dlLSe1i3Hamdh2T+KZCIHIQXl62jTeLdvCtU0bRt5t2HZP4pkIgcoCq6iLc8ZdlHNY3l68cNzTsOCLtpkIgcoDue30VW8prufPccaSl6E9I4p/+LxY5AEWfVPC7v6/jwoJBFAzV5TSSGFQIRNqoqcn53gtLyM1M5ebTteuYJA4VApE2enZBMR+u38UtZ4yhR3Z62HFEOowKgUgblFbVc9ec5Uwc2oPzjxkYdhyRDqVCINIGd81ZTkVthDvPHU+XLrqCWBKLCoHIZ5i7did/jO46Nrqvdh2TxKNCILIfdZFGbv3TEgb1zOK/ThoZdhyRQGgbJZH9mPnWWtbsqOKRKyaSlZ4SdhyRQAQ6IjCzaWZWZGarzezm/bQ738zczAqCzCNyINaVVPHL6KJyJ44+JOw4IoEJrBCYWQpwP3A6MBa42Mz+ZXUuM8sF/gt4P6gsIgfK3fnu80vISO3C7WdpUTlJbEGOCCYBq919rbvXA7OAc1pp9yPgbqA2wCwiB+TZ+cW8t3YnN59+GPl5WlROEluQ5wgGAJta3C4GJrdsYGZHA4Pc/a9mdsO+HsjMZgAzAPLz8yksLOz4tAGrrKyMy9ztEa993l3n/ODv1Yzs3oV+1WspLFzXpp+L1/62h/qcGIIsBK192No/PWjWBbgXuPyzHsjdZwIzAQoKCnzq1Kkdk7ATFRYWEo+52yNe+/zNWR9R31TDr6/4HCPz2/5x0Xjtb3uoz4khyKmhYmBQi9sDgS0tbucC44BCM1sPTAFm64SxhOnNou28sHAL13zh0AMqAiLxLMhC8CEw0syGmVk6cBEwe89Bdy93997uPtTdhwJzgbPdfV6AmUT2qbIuwq3PL2HEITl8/aQRYccR6TSBFQJ3jwDXAi8Dy4Fn3H2Zmd1hZmcH9bwiB+unL61g6+5afvLv48lI1TUDkjwCvaDM3ecAc/a67/Z9tJ0aZBaR/flwfSmPzd3AV44dyoQh2mdAkouWmJCkV9vQyHeeW0z/blnceNrosOOIdDotMSFJ7+evrWLtjioeu3IS2Rn6k5DkoxGBJLWFm8qY+fYaLiwYxAmj+oQdRyQUKgSStGobGrnxj4vIz8vk1jPHhB1HJDQaB0vSuu/1VazaXsmjV0wkLzMt7DgiodGIQJLSwk1lPPj2Wi4oGMhUrSwqSU6FQJJOTX0j335mIfm5Gdz6Ja0sKqKpIUk6P3lpBWt3VPHEVZPplqUpIRGNCCSpvLu6hEf/sZ7LjxvK8SN6hx1HJCaoEEjSKK9p4MY/LmJ4n2y+M+2wsOOIxAxNDUnSuP3PS9lWUcdz1xyn/YdFWtCIQJLCCx9t5s8Lt3DdF0dy1KDuYccRiSkqBJLwNpVW870XljJxaA++fqKWlxbZmwqBJLRIYxPffHohBvzsgqNI6dLaxnkiyU3nCCSh3ffGauZv2MUvLjqKQT27hh1HJCZpRCAJ6x+rS/jlG6s475gBnHPUgLDjiMQsFQJJSCWVdVz39EKG987mR+eMCzuOSEzT1JAknKYm51tPL6S8pkF7DIi0gUYEknB+89Ya3llVwvfPGsuYfnlhxxGJeSoEklD+vqqEe14p4qwj+3PJpMFhxxGJCyoEkjC2lNXwX7M+4tA+Ofz4vPGY6aOiIm2hQiAJoS7SyDVPLKA+0sQD0yfovIDIAdBfiySEH/7lYxZtKuM3lx7DoX1ywo4jElc0IpC494e5G3jy/Y187QvDOX18v7DjiMQdFQKJa3PX7uSHs5dx4ug+3HSalpYWORgqBBK3NpVW859PLGBwr6784uKjtY6QyEFSIZC4VFHbwFW/n0dDYxMPfbmAvExtOSlysFQIJO40NDbxn08sYM2OSn5z6QSdHBZpJ31qSOKKu/P92ct4Z1UJPz5vPJ8bqX2HRdpLIwKJKzPfXsuT72/kmqmHcpGuHBbpECoEEjeem1/MXS+u4Mwj+nHjqaPDjiOSMAItBGY2zcyKzGy1md3cyvFvm9nHZrbYzF43syFB5pH49eaK7dz03GKOH9GLey44ki76hJBIhwmsEJhZCnA/cDowFrjYzMbu1ewjoMDdjwCeBe4OKo/Er/kbdnHNE/MZ0y+XBy6bQEZqStiRRBJKkCOCScBqd1/r7vXALOCclg3c/U13r47enAsMDDCPxKGlm8u54pEPyM/L5JHLJ5Grj4mKdLggPzU0ANjU4nYxMHk/7b8KvNjaATObAcwAyM/Pp7CwsIMidp7Kysq4zN0e7e3z5oom7vqghvQU49rDnWXz3+u4cAHQ7zg5JGKfgywErU3ieqsNzS4DCoAvtHbc3WcCMwEKCgp86tSpHRSx8xQWFhKPudujPX1eu6OSGx6cS9fMDJ7+2rEM653dseECoN9xckjEPgdZCIqBQS1uDwS27N3IzE4GbgW+4O51AeaROLFmRyWXPDQXd+fJGVPiogiIxLMgzxF8CIw0s2Fmlg5cBMxu2cDMjgYeBM529+0BZpE4sXJbBRc+OJdIo/PE1ZMZcUhu2JFEEl5ghcDdI8C1wMvAcuAZd19mZneY2dnRZj8FcoA/mtlCM5u9j4eTJPDxlt1cNHMuXQye/toUDuur/YZFOkOgS0y4+xxgzl733d7i+5ODfH6JH/M3lHLlo/Pomp7Ck1drOkikM+nKYgndGyu2celv36dH1zSeiZMTwyKJRIvOSaienV/Md55bzNh+eTxyxUR652SEHUkk6agQSCjcnZ+/topfvL6K40f04sHpBeRow3mRUOgvTzpdbUMjNz27mNmLtnD+hIH897+NJz1Vs5QiYVEhkE61vaKWax5fwPwNu7hp2miu+cKhmGkBOZEwqRBIp5m/YRfXPD6fitoIv770GM4Y3y/sSCKCCoF0Anfn8fc3csdfltG/exa/v3ISY/rpGgGRWKFCIIHaXdvAd59fwl8Xb+XE0X34+YVH062rVhAViSUqBBKYtWWN3HbfO2wpq+XG05rPB2hDGZHYo0IgHS7S2MRvCtfw8/dr6dsti2e+NoUJQ3qGHUtE9kGFQDrU6u2VXP/MQhYVlzO5bwozZ3xeU0EiMU6FQDpEQ2MTD72zll+8toqu6Sncf8kxZJcWqQiIxAEVAmm3BRt38d3nl7DikwqmHd6XO849nENyMyksLAo7moi0gQqBHLSSyjrueaWIWR9uom9eJg99uYBTxuaHHUtEDpAKgRyw+kgTj723nl+8voqa+ka+evwwvnnKKK0VJBKn9JcrbdbU5Pxl8RbueWUlG0ur+cKoPtx25lhGHJITdjQRaQcVAvlM7s6bRdv5n5dX8vHW3RzWN5dHLp/I1NF9tE6QSAJQIZB9cnde/Xgb972xiqWbdzOoZxb3Xngk5xw5QBeGiSQQFQL5F3WRRv68cAu/e2cdRdsqGNKrK3effwT/dvQA0lK0XLRIolEhkE9tr6jl6Q828djcDeyoqOOwvrn87IIjOfvI/qSqAIgkLBWCJNfU5Mxdt5Mn39/IS0s/IdLknDCqD/deMJzjR/TSOQCRJKBCkKQ2lVbz/ILNPLtgE5tKa8jLTOXy44Zy6ZQh2jxeJMmoECSR7RW1zFm8ldmLtrBgYxkAx4/oxfWnjOa0w/uSlZ4SckIRCYMKQYLbsLOKV5Zt4+VlnzB/4y7c4bC+udx42mjOPrI/g3p2DTuiiIRMhSDB1DY0Mm/9LgqLtvNG0XbW7qgCYEy/PK774kjOGN+PUfm5IacUkViiQhDn6iKNLCku5/11pby7uoR5G3ZRH2kiPbULU4b34rLJQzh5TD6De+mdv4i0ToUgzmyvqGXhxjI+2lTGgg27WLipjLpIE9A85TN9yhCOH9GLKcN70TVdv14R+Wx6pYhR7s7mshpWbK3g4627WbK5nKWby9laXgtAahdjbP88LpsyhIlDezJxaA965WSEnFpE4pEKQcgijU1sLqthbUkVa7ZXsnp7Jau2V7JyWwUVtZFP2/wA4AkAAAZgSURBVA3vk82kYT0ZP6AbRw/uzuH9u5GZpk/5iEj7qRAEzN0prapnfXkjLy3dSvGuGjaVVrOhtJqNO6vZtKuahkb/tH2v7HRGHJLDOUf157C+eYzpl8fovrla4llEAqNXl4MUaWxiV3UDpVX1lFTWsaOijpLKOrZX1LFtdy2flNfyye5atpbXUh+dw+e9BQDkZKQyuGdXRvfN5dTD+zK8TzbDe2czrHe2pndEpNMFWgjMbBrwCyAF+K27/3iv4xnAY8AEYCdwobuvDzLTHu5OXaSJyroIVXURKmqbvyrrIuyuaWB3bQO7ayKU1dRTXtNAeXUDu6rrKdvz35oG3P/1cTNSu5Cfl0l+XgbjB3TjtMP70jcvk12b13Da5yYysEcW3bLStHSDiMSMwAqBmaUA9wOnAMXAh2Y2290/btHsq8Audx9hZhcBPwEuDCLP0x9u5MG311Jd10hVfYTq+kYam1p5Jd9LTkYq3bLS6JaVRo/sNPp3z6JH13R6ZqfTK6f5v71zMuiTm0HvnAzyMlNbfZEvLNzAuAHdguiaiEi7BDkimASsdve1AGY2CzgHaFkIzgF+EP3+WeBXZmburb3Xbp+e2RmM7ZdHdnoqXTNS6JqeQnZGKjkZqWSnp5KbmUpOZiq5GWnkZaWSl5lGbmaqVt0UkYRnAbzmNj+w2fnANHe/Knp7OjDZ3a9t0WZptE1x9PaaaJuSvR5rBjADID8/f8KsWbMCyRykyspKcnKSa0vHZOtzsvUX1Od4cuKJJ85394LWjgU5ImhtEnzvqtOWNrj7TGAmQEFBgU+dOrXd4TpbYWEh8Zi7PZKtz8nWX1CfE0WQ8x7FwKAWtwcCW/bVxsxSgW5AaYCZRERkL0EWgg+BkWY2zMzSgYuA2Xu1mQ18Jfr9+cAbQZwfEBGRfQtsasjdI2Z2LfAyzR8ffdjdl5nZHcA8d58N/A74g5mtpnkkcFFQeUREpHWBXkfg7nOAOXvdd3uL72uB/wgyg4iI7J8+GykikuRUCEREkpwKgYhIkgvsgrKgmNkOYEPYOQ5Cb6DkM1sllmTrc7L1F9TneDLE3fu0diDuCkG8MrN5+7qqL1ElW5+Trb+gPicKTQ2JiCQ5FQIRkSSnQtB5ZoYdIATJ1udk6y+ozwlB5whERJKcRgQiIklOhUBEJMmpEITAzG4wMzez3mFnCZKZ/dTMVpjZYjP7k5l1DztTUMxsmpkVmdlqM7s57DxBM7NBZvammS03s2Vmdl3YmTqLmaWY2Udm9tews3QUFYJOZmaDaN7HeWPYWTrBq8A4dz8CWAncEnKeQLTYn/t0YCxwsZmNDTdV4CLA9e4+BpgCfD0J+rzHdcDysEN0JBWCzncvcBOt7MSWaNz9FXePRG/OpXlzokT06f7c7l4P7NmfO2G5+1Z3XxD9voLmF8YB4aYKnpkNBL4E/DbsLB1JhaATmdnZwGZ3XxR2lhBcCbwYdoiADAA2tbhdTBK8KO5hZkOBo4H3w03SKX5O8xu5prCDdKRA9yNIRmb2GtC3lUO3At8FTu3cRMHaX3/d/c/RNrfSPJXwRGdm60Rt2ns7EZlZDvAc8E133x12niCZ2ZnAdnefb2ZTw87TkVQIOpi7n9za/WY2HhgGLDIzaJ4mWWBmk9z9k06M2KH21d89zOwrwJnAFxN4G9K27M+dcMwsjeYi8IS7Px92nk5wPHC2mZ0BZAJ5Zva4u18Wcq520wVlITGz9UCBu8fjKoZtYmbTgJ8BX3D3HWHnCYqZpdJ8MvyLwGaa9+u+xN2XhRosQNb8bub3QKm7fzPsPJ0tOiK4wd3PDDtLR9A5AgnSr4Bc4FUzW2hmD4QdKAjRE+J79udeDjyTyEUg6nhgOnBS9He7MPpOWeKQRgQiIklOIwIRkSSnQiAikuRUCEREkpwKgYhIklMhEBFJcioEIiJJToVARCTJqRCItJOZTYzuuZBpZtnR9fnHhZ1LpK10QZlIBzCzO2lefyYLKHb3u0KOJNJmKgQiHcDM0mleY6gWOM7dG0OOJNJmmhoS6Rg9gRya11bKDDmLyAHRiECkA5jZbJp3JhsG9HP3a0OOJNJm2o9ApJ3M7MtAxN2fjO5f/A8zO8nd3wg7m0hbaEQgIpLkdI5ARCTJqRCIiCQ5FQIRkSSnQiAikuRUCEREkpwKgYhIklMhEBFJcv8LQZHsUiDIbVUAAAAASUVORK5CYII=\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1,1) # Get figure and axes objects\n", "\n", "ax.plot(x, f) # Make a plot\n", "\n", "# Create some labels\n", "ax.set_xlabel('x')\n", "ax.set_ylabel('f')\n", "ax.set_title('Logistic Function')\n", "\n", "# Grid\n", "ax.grid(True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Wow, it's *exactly* the same plot! Notice, however, the use of `ax.set_xlabel()` instead of `plt.xlabel()`. The difference is tiny, but you should be aware of it. I will use this plotting syntax from now on.\n", "\n", "What else do we need to do to make this figure better? Here are some options:\n", "* Make labels bigger!\n", "* Make line fatter\n", "* Make tick mark labels bigger\n", "* Make the grid less pronounced\n", "* Make figure bigger\n", "\n", "Let's get to it." ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1,1, figsize=(10,6)) # Make figure bigger\n", "\n", "ax.plot(x, f, lw=4) # Linewidth bigger\n", "ax.set_xlabel('x', fontsize=24) # Fontsize bigger\n", "ax.set_ylabel('f', fontsize=24) # Fontsize bigger\n", "ax.set_title('Logistic Function', fontsize=24) # Fontsize bigger\n", "ax.grid(True, lw=1.5, ls='--', alpha=0.75) # Update grid" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Notice:\n", "* `lw` stands for `linewidth`. We could also write `ax.plot(x, f, linewidth=4)`\n", "* `ls` stands for `linestyle`.\n", "* `alpha` stands for transparency." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Things are looking good now! Unfortunately, people still can't read the tick mark labels. Let's remedy that presently." ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1,1, figsize=(10,6)) # Make figure bigger\n", "\n", "# Make line plot\n", "ax.plot(x, f, lw=4)\n", "\n", "# Update ticklabel size\n", "ax.tick_params(labelsize=24)\n", "\n", "# Make labels\n", "ax.set_xlabel(r'$x$', fontsize=24) # Use TeX for mathematical rendering\n", "ax.set_ylabel(r'$f(x)$', fontsize=24) # Use TeX for mathematical rendering\n", "ax.set_title('Logistic Function', fontsize=24)\n", "\n", "ax.grid(True, lw=1.5, ls='--', alpha=0.75)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The only thing remaining to do is to change the $x$ limits. Clearly these should go from $-5$ to $5$." ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1,1, figsize=(10,6)) # Make figure bigger\n", "\n", "# Make line plot\n", "ax.plot(x, f, lw=4)\n", "\n", "# Set axes limits\n", "ax.set_xlim(x.min(), x.max())\n", "\n", "# Update ticklabel size\n", "ax.tick_params(labelsize=24)\n", "\n", "# Make labels\n", "ax.set_xlabel(r'$x$', fontsize=24) # Use TeX for mathematical rendering\n", "ax.set_ylabel(r'$f(x)$', fontsize=24) # Use TeX for mathematical rendering\n", "ax.set_title('Logistic Function', fontsize=24)\n", "\n", "ax.grid(True, lw=1.5, ls='--', alpha=0.75)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You can play around with figures forever making them perfect. At this point, everyone can read and interpret this figure just fine. Don't spend your life making the perfect figure. Make it good enough so that you can convey your point to your audience. Then save if it for later." ] }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [], "source": [ "fig.savefig('logistic.png')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Done! Let's take a look.\n", "![](../images/logistic.png)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Resources\n", "If you want to see all the styles available, please take a look at the documentation.\n", "* [Line styles](https://matplotlib.org/2.0.1/api/lines_api.html#matplotlib.lines.Line2D.set_linestyle)\n", "* [Marker styles](https://matplotlib.org/2.0.1/api/markers_api.html#module-matplotlib.markers)\n", "* [Everything you could ever want](https://matplotlib.org/2.0.1/api/lines_api.html#matplotlib.lines.Line2D.set_marker)\n", "\n", "We haven't discussed it yet, but you can also put a legend on a figure. You'll do that in the next exercise. Here are some additional resources:\n", "* [Legend](https://matplotlib.org/api/_as_gen/matplotlib.pyplot.legend.html)\n", "* [Grid](https://matplotlib.org/api/_as_gen/matplotlib.pyplot.grid.html)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
Exercise
\n", "\n", "Do the following:\n", "* Make a figure with the logistic function, hyperbolic tangent, and rectified linear unit.\n", "* Use different line styles for each plot\n", "* Put a legend on your figure\n", "\n", "Here's an example of a figure:\n", "![](../images/nice_plots.png)\n", "\n", "You don't need to make the exact same figure, but it should be just as nice and readable." ] }, { "cell_type": "code", "execution_count": 42, "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# your code here\n", "\n", "# First get the data\n", "f = logistic(x, 2.0, 1.0)\n", "g = stretch_tanh(x, 2.0, 0.5, 0.5)\n", "h = relu(x)\n", "\n", "fig, ax = plt.subplots(1,1, figsize=(10,6)) # Create figure object\n", "\n", "# Make actual plots\n", "# (Notice the label argument!)\n", "ax.plot(x, f, lw=4, ls='-', label=r'$L(x;1)$')\n", "ax.plot(x, g, lw=4, ls='--', label=r'$\\tanh(2x)$')\n", "ax.plot(x, h, lw=4, ls='-.', label=r'$relu(x; 0.01)$')\n", "\n", "# Make the tick labels readable\n", "ax.tick_params(labelsize=24)\n", "\n", "# Set axes limits to make the scale nice\n", "ax.set_xlim(x.min(), x.max())\n", "ax.set_ylim(h.min(), 1.1)\n", "\n", "# Make readable labels\n", "ax.set_xlabel(r'$x$', fontsize=24)\n", "ax.set_ylabel(r'$h(x)$', fontsize=24)\n", "ax.set_title('Activation Functions', fontsize=24)\n", "\n", "# Set up grid\n", "ax.grid(True, lw=1.75, ls='--', alpha=0.75)\n", "\n", "# Put legend on figure\n", "ax.legend(loc='best', fontsize=24);\n", "\n", "fig.savefig('nice_plots.png')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There a many more things you can do to the figure to spice it up. Remember, there must be a tradeoff between making a figure look good and the time you put into it. \n", "\n", "**The guiding principle should be that your audience needs to easily read and understand your figure.**\n", "\n", "There are of course other types of figures including, but not limited to, \n", "* Scatter plots (you will use these all the time)\n", "* Bar charts\n", "* Histograms\n", "* Contour plots\n", "* Surface plots\n", "* Heatmaps\n", "\n", "We will learn more about these different types of plotting in Lab5." ] }, { "cell_type": "code", "execution_count": 45, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 45, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "#import config # User-defined config file\n", "#plt.rcParams.update(config.pars) # Update rcParams to make nice plots\n", "\n", "# First get the data\n", "f1 = logistic(x, 1.0, 1.0)\n", "f2 = logistic(x, 2.0, 1.0)\n", "f3 = logistic(x, 3.0, 1.0)\n", "\n", "fig, ax = plt.subplots(1,1, figsize=(10,6)) # Create figure object\n", "\n", "# Make actual plots\n", "# (Notice the label argument!)\n", "ax.plot(x, f1, ls='-', label=r'$L(x;-1)$')\n", "ax.plot(x, f2, ls='--', label=r'$L(x;-2)$')\n", "ax.plot(x, f3, ls='-.', label=r'$L(x;-3)$')\n", "\n", "# Set axes limits to make the scale nice\n", "ax.set_xlim(x.min(), x.max())\n", "ax.set_ylim(h.min(), 1.1)\n", "\n", "# Make readable labels\n", "ax.set_xlabel(r'$x$')\n", "ax.set_ylabel(r'$h(x)$')\n", "ax.set_title('Logistic Functions')\n", "\n", "# Set up grid\n", "ax.grid(True, lw=1.75, ls='--', alpha=0.75)\n", "\n", "# Put legend on figure\n", "ax.legend(loc='best')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "That's a good-looking plot! Notice that we didn't need to have all those annoying `fontsize` specifications floating around. If you want to reset the defaults, just use `plt.rcdefaults()`.\n", "\n", "Now, how in the world did this work? Obviously, there is something special about the `config` file. I didn't give you a config file, but the next exercise requires you to create one." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### No Excuses\n", "With all of these resourses, there is no reason to have a bad figure. " ] } ], "metadata": { "anaconda-cloud": {}, "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": "3.7.3" } }, "nbformat": 4, "nbformat_minor": 1 }