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{
"metadata": {
"name": "The Basics"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": "Econ 873: Tutorial 2 - The basics\n====================================\n\nIn this tutorial we will get our feet wet with some basic computational tasks in **Python**. Once again, a good resource is Tom Sargent and John Stachurski's Quant Econ tutorials http://quant-econ.net/. For this lecture you should consult **Part 1: Programming in Python**, especially *An Introductory Example* and *Python Essentials*. From **Part 2: The Scientific Libraries**, the sections on *NumPy,SciPy* and *Matplotlib* will be covered. \n\nAnother useful resource is http://learnpythonthehardway.org.\n\nNumPy\n--------\n\nWe start our discussion with *NumPy*. This package introduces the array data type, which is like a matrix. However, an array can have many dimensions. For instance, a vector is an array, but so is a 3 dimensional matrix. The word matrix applies to the two dimensional case with rows and columns. \n\nAs you may recall, we first need to import *NumPy*. We will do so and make sure that it is working by creating an array."
},
{
"cell_type": "code",
"collapsed": false,
"input": "import numpy as np\n\na = np.linspace(start = 1, stop = 10, num = 5)\nprint a",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "[ 1. 3.25 5.5 7.75 10. ]\n"
}
],
"prompt_number": 41
},
{
"cell_type": "markdown",
"metadata": {},
"source": "It looks like *NumPy* is working. If you are interested in reading the documentation for *NumPy* you can visit http://docs.scipy.org/doc/numpy/contents.html. However, everything you need should be included in my lectures or the Sargent/Stachurski lectures. \n\nNow lets go through the motions of creating some simple arrays."
},
{
"cell_type": "code",
"collapsed": false,
"input": "'''\nCreate an array from a list object\n'''\n\na = ([1.0, 2.0], [3.0, 4.0])\nprint 'The Type of a is:'\nprint type(a)\nprint ''\n\na = np.array(a)\nprint 'The type of a is now:'\nprint type(a)\nprint ''\n\nprint 'The shape of a is:'\nprint a.shape\nprint ''\n\nprint 'This is a:'\nprint a\nprint ''\n\nprint 'The transpose of a:'\nprint np.transpose(a)\nprint ''\n\nprint 'The inverse of a:'\nprint np.linalg.inv(a)\nprint ''\n",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "The Type of a is:\n<type 'tuple'>\n\nThe type of a is now:\n<type 'numpy.ndarray'>\n\nThe shape of a is:\n(2, 2)\n\nThis is a:\n[[ 1. 2.]\n [ 3. 4.]]\n\nThe transpose of a:\n[[ 1. 3.]\n [ 2. 4.]]\n\nThe inverse of a:\n[[-2. 1. ]\n [ 1.5 -0.5]]\n\n"
}
],
"prompt_number": 42
},
{
"cell_type": "markdown",
"metadata": {},
"source": "In order to find out what *NumPy* is capable of, you can type **np. + TAB**. This tab completion feature is quite handy. Some other ways to create arrays:"
},
{
"cell_type": "code",
"collapsed": false,
"input": "b = np.zeros([2,2])\n\nprint 'The array b:'\nprint b\nprint ''\n\nc = np.ones([2,1])\n\nprint 'The array c:'\nprint c\nprint ''\n\nd = np.identity(2)\n\nprint 'The array d:'\nprint d\nprint ''\n \n ",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "The array b:\n[[ 0. 0.]\n [ 0. 0.]]\n\nThe array c:\n[[ 1.]\n [ 1.]]\n\nThe array d:\n[[ 1. 0.]\n [ 0. 1.]]\n\n"
}
],
"prompt_number": 43
},
{
"cell_type": "markdown",
"metadata": {},
"source": "Suppose you want to extract an element of an array. This can be done as follows:"
},
{
"cell_type": "code",
"collapsed": false,
"input": "print 'The top left element of d'\nprint d[0,0]\nprint ''\n\nprint 'The left column of d'\nprint d[:,0]\nprint ''\n\nprint 'The bottom Right element of d:'\nprint d[1,1]\nprint 'Or alternatively'\nprint d[-1,-1]",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "The top left element of d\n1.0\n\nThe left column of d\n[ 1. 0.]\n\nThe bottom Right element of d:\n1.0\nOr alternatively\n1.0\n"
}
],
"prompt_number": 44
},
{
"cell_type": "markdown",
"metadata": {},
"source": "First, note that indexing starts at 0. Therefore, the first element is always 0 and so on. This takes some getting used to. As well, to pick out the last element of a sequence you can either use its index or the shortcut $-1$. To see this more clearly, I use the following example:"
},
{
"cell_type": "code",
"collapsed": false,
"input": "a = np.linspace(0,5,6)\nprint 'The array a:'\nprint a\nprint ''\n\nprint 'Extracting elements of a:'\nprint a[-1]\nprint a[-2]\nprint a[-3]\nprint a[2]\nprint a[1]\nprint a[0]\n\n",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "The array a:\n[ 0. 1. 2. 3. 4. 5.]\n\nExtracting elements of a:\n5.0\n4.0\n3.0\n2.0\n1.0\n0.0\n"
}
],
"prompt_number": 45
},
{
"cell_type": "markdown",
"metadata": {},
"source": "There are some useful array methods discuessed in the Stachurski/Sargent notes. A few examples.\n\n"
},
{
"cell_type": "code",
"collapsed": false,
"input": "a = np.array([4, 2, 3, 1])\n\nprint 'The original array'\nprint a\nprint ''\n\nprint 'We can sum it up'\nprint a.sum()\nprint ''\n\nprint 'Find the mean'\nprint a.mean()\nprint ''\n\nprint 'Find the max'\nprint a.max()\nprint ''\n\nprint 'Find the standard deviation'\nprint a.std()\n",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "The original array\n[4 2 3 1]\n\nWe can sum it up\n10\n\nFind the mean\n2.5\n\nFind the max\n4\n\nFind the standard deviation\n1.11803398875\n"
}
],
"prompt_number": 46
},
{
"cell_type": "markdown",
"metadata": {},
"source": "Next we may want to do standard operations on matrices. Adding, subtracting and scalar multiplication are pretty simple. Matrix multiplication presents a small hiccup. "
},
{
"cell_type": "code",
"collapsed": false,
"input": "A = np.ones([2,2])\nB = np.ones([2,2])\n\nprint 'Scalar multiplication'\nprint A * 2\nprint ''\n\nprint 'Addition of two matrices'\nprint A + B\nprint ''\n\nprint 'Scalar addition'\nprint A + 2\nprint ''\n\nprint 'Bad matrix multiplication'\nprint A * B\nprint ''\n\nprint 'Good matrix multiplication'\nprint np.dot(A, B)\nprint ''",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "Scalar multiplication\n[[ 2. 2.]\n [ 2. 2.]]\n\nAddition of two matrices\n[[ 2. 2.]\n [ 2. 2.]]\n\nScalar addition\n[[ 3. 3.]\n [ 3. 3.]]\n\nBad matrix multiplication\n[[ 1. 1.]\n [ 1. 1.]]\n\nGood matrix multiplication\n[[ 2. 2.]\n [ 2. 2.]]\n\n"
}
],
"prompt_number": 47
},
{
"cell_type": "markdown",
"metadata": {},
"source": "The dot product method is the appropriate way to multiply matrices. Not surprisingly, it works for 1d arrays, or vectors as well. Furthermore, we can solve a system of equations, find the determinant and inverse as follows:"
},
{
"cell_type": "code",
"collapsed": false,
"input": "x = np.array([1,2,3])\ny = np.array([3,2,1])\n\nprint 'The dot product of x and y'\nprint np.dot(x,y)\nprint ''\n\nA = np.array([[2,1],[3,2]])\nb = np.array([1,1])\n\nprint 'The matrix A is'\nprint A\nprint ''\n\nprint 'The vector b is:'\nprint b\nprint ''\n\nprint 'Find the determinant of A'\nprint np.linalg.det(A)\nprint ''\n\nprint 'Find the inverse of A'\nprint np.linalg.inv(A)\nprint ''\n\nprint 'Solve Ax = b'\nprint np.linalg.solve(A,b)\nprint''",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "The dot product of x and y\n10\n\nThe matrix A is\n[[2 1]\n [3 2]]\n\nThe vector b is:\n[1 1]\n\nFind the determinant of A\n1.0\n\nFind the inverse of A\n[[ 2. -1.]\n [-3. 2.]]\n\nSolve Ax = b\n[ 1. -1.]\n\n"
}
],
"prompt_number": 48
},
{
"cell_type": "markdown",
"metadata": {},
"source": "The above example solved the following system of equations:\n$$2x_1 + x_2 = 1 $$\n$$3x_1 + 2x_2 = 1 $$\n\nOr more compactly:\n\n$$ A x = b $$\n\nFor:\n\n$$A = \\begin{bmatrix} 2 & 1 \\\\ 3 &2\n\\end{bmatrix} \\qquad b = \\begin{bmatrix} 1 \\\\ 1\\end{bmatrix}$$\n\nYou may check that the solution is:\n$$ x_1 = 1 \\qquad x_2 = -1 $$"
},
{
"cell_type": "markdown",
"metadata": {},
"source": "Writing Loops and If Statements\n---------------\n\nA handy thing to do in any programming language is writing loops. This is useful in situations where we have to do something over and over again. Here is an example of a Python for loop."
},
{
"cell_type": "code",
"collapsed": false,
"input": "for i in range(4):\n print i",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "0\n1\n2\n3\n"
}
],
"prompt_number": 49
},
{
"cell_type": "markdown",
"metadata": {},
"source": "We may also want to write while loops. However, be careful as these loops will go on forever if the while condition is not met."
},
{
"cell_type": "code",
"collapsed": false,
"input": "iterate = 0\nmax_it = 4\n\nwhile iterate < max_it:\n print iterate\n iterate += 1",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "0\n1\n2\n3\n"
}
],
"prompt_number": 50
},
{
"cell_type": "markdown",
"metadata": {},
"source": "Notice that we often make use of logical statements like $x < y$. Some examples of doing so:"
},
{
"cell_type": "code",
"collapsed": false,
"input": "x = 2\ny = 3\n\nprint x < y\n\nprint y < x\n\nif x < y:\n print 'x is less than y'\nelse:\n print 'x is greater than y'",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "True\nFalse\nx is less than y\n"
}
],
"prompt_number": 2
},
{
"cell_type": "markdown",
"metadata": {},
"source": "Matplotlib\n----------------\n\nIn this section we will introduce the plotting package *Matplotlib*. It is very similar to the plotting capabilities of Matlab. It is very flexible. We will just scratch the surface of its capabilities. \n\nFirst we need to import pyplot, which is the part of the module we will use for now. This is a good chance to create a function and then to plot a vectorized version of it. The function will be a simple polynomial:\n\n$$y = 1 + 2 x + 3 x^2 + 4 x^3 $$"
},
{
"cell_type": "code",
"collapsed": false,
"input": "import numpy as np\nfrom matplotlib import pyplot as plt\n\ndef poly(x):\n return 1.0 + 2.0 * x + 3.0 * x ** 2.0 + 4.0 * x ** 3.0\n\nxgrid = np.linspace(start = -5, stop = 5, num = 50)\n\nplt.plot(xgrid, poly(xgrid))\nplt.show()",
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
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ihg8fzujRo5k+fTput5uysjJSU1OJiIjg/PPPp6SkhNTUVJ5//nnuvffeU372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\n",
"text": "<matplotlib.figure.Figure at 0x5d02588>"
}
],
"prompt_number": 6
},
{
"cell_type": "markdown",
"metadata": {},
"source": "Notice that we put a **plt.** in front of any pyplot method. As well, we have to use the **show** method for the plot to be displayed. Otherwise the plot is created but we can't see it. We can modify the display as follows."
},
{
"cell_type": "code",
"collapsed": false,
"input": "'''\nChanging the line width and colour. Also this is how your write a multi line comment!\nSee!!!\n'''\nplt.plot(xgrid, poly(xgrid), 'r-', linewidth = 4)\nplt.show()",
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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"text": "<matplotlib.figure.Figure at 0x5e35748>"
}
],
"prompt_number": 7
},
{
"cell_type": "code",
"collapsed": false,
"input": "#This is a single line comment. \n\n#And this is how we change the line type\n\nplt.plot(xgrid, poly(xgrid), 'g--', linewidth = 4)\nplt.show()",
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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"text": "<matplotlib.figure.Figure at 0x87572e8>"
}
],
"prompt_number": 8
},
{
"cell_type": "code",
"collapsed": false,
"input": "'''\nWhat about adding labels and a title?\n'''\nfrom matplotlib import pyplot as plt\n%matplotlib inline\nplt.plot(xgrid, poly(xgrid), 'g--', linewidth = 4, label ='f(x)')\nplt.plot(xgrid, xgrid**2, 'r-', linewidth = 4, label ='g(x)')\nplt.xlabel('x')\nplt.ylabel('y')\nplt.title('A Cubic Polynomial Function')\nplt.legend(loc = 'upper left') #there are many options for where the legend can go.\nplt.show()",
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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UghQAwLaz2xDYI1DkyMgQPMMgIqM4f+s85v8yHzE3YnTKHSwdcPm1y7BuYi1O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\nTkSuQmCC\n",
"text": "<matplotlib.figure.Figure at 0x5f54710>"
}
],
"prompt_number": 9
},
{
"cell_type": "markdown",
"metadata": {},
"source": "SciPy\n------\n\nSciPy is a very useful and large module that can help in lots of computational tasks. We will make use of the **Stats** package. First we will import it, though often it is helpful to just import the functions we want. Below I draw a single random normal variable from the $\\mathcal{N}(\\mu, \\sigma^2)$ distribution with $\\mu = 1$ and $\\sigma^2 = 4$. Notice the scale parameter is the standard deviation."
},
{
"cell_type": "code",
"collapsed": false,
"input": "import scipy.stats as ss\n\nx = ss.norm.rvs(size = 1, loc = 1.0, scale = 2.0)\n\nprint 'A random normal draw'\nprint x\nprint ''",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "A random normal draw\n[ 2.72658018]\n\n"
}
],
"prompt_number": 10
},
{
"cell_type": "markdown",
"metadata": {},
"source": "Want to check that this is working? Lets draw a lot of them and see if the histogram approaches the .pdf of the known distribution."
},
{
"cell_type": "code",
"collapsed": false,
"input": "import numpy as np \nimport scipy.stats as ss # import scipy.stats module under namespace ss.\nimport matplotlib.pyplot as plt #import the pyplot module under namespace plt\n\n#So that the plots show up in the web browser\n%matplotlib inline \n\n\nx = ss.norm.rvs(size = 1000, loc = 1.0, scale = 2.0)\ngrid = np.linspace(-6, 8, 30)\n\nplt.hist(x, bins = 40, normed = True)\nplt.plot(grid, ss.norm.pdf(grid, loc = 1.0, scale = 2.0),'r-', lw=4)\nplt.show()\n",
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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"text": "<matplotlib.figure.Figure at 0xd4d3e50>"
}
],
"prompt_number": 55
},
{
"cell_type": "markdown",
"metadata": {},
"source": "I will talk about all the .plt functions later, but for now lets analyze how we used scipy.stats to draw a lot of random numbers and evaluate the pdf. First, whenever we use SciPy.stats methods for the normal distribution we start the command with **ss.norm**. Within the normal distribution we have a whole bunch of methods which can be found here: http://docs.scipy.org/doc/scipy-0.13.0/reference/generated/scipy.stats.norm.html. We used the pdf and rvs methods.\n\nAnother thing you may want to do is to run a simple linear regression. To do so we will:\n\n- Create some data\n- Run a regression\n- Plot the least squares line\n\nThe model will be:\n\n$$ y_i = \\beta_0 + \\beta_1 x_i + \\varepsilon_i$$\n\nWhere $\\varepsilon_i$ is distributed normally with mean 0 and variance $\\sigma^2$. We will set the true $\\beta = (1,2)$ and $\\sigma^2 = 9$. The sample size $I = 1000$."
},
{
"cell_type": "code",
"collapsed": false,
"input": "I = 1000\nbeta0 = 1.0\nbeta1 = 2.0\nsigma = 3.0\n\nepsilon = ss.norm.rvs(size = I, loc = 0.0, scale = sigma)\n\nx = ss.norm.rvs(size = I, loc = 0.0, scale = 1.0)\n\ny = beta0 + beta1 * x + epsilon\n\nbeta1hat, beta0hat, r2, p_value, std_err = ss.linregress(x,y)\n\nfitted = beta0hat + beta1hat * x \n\nplt.scatter(x,y, label = 'Data')\nplt.plot(x, fitted, 'r-', linewidth = 4, label = 'Fitted Values')\nplt.xlabel('x')\nplt.ylabel('y')\nplt.title('Linear Regression')\nplt.legend(loc = 'lower right')\nplt.show()\n\nprint 'Intercept Slope'\nprint beta0hat, beta1hat",
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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ICMDq1cugKMpVrzl27BgcjjooLLTXABcupCIvL8+5edBVqVkT2L37+oKlpABR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"text": "<matplotlib.figure.Figure at 0xe7d38d0>"
},
{
"output_type": "stream",
"stream": "stdout",
"text": "Intercept Slope\n1.0569051497 2.03798609196\n"
}
],
"prompt_number": 11
},
{
"cell_type": "markdown",
"metadata": {},
"source": "Homework\n-----------\n\nQuestion 1 is due by the next tutorial. Question 2 will be due as part of the computational assignment in the last week of class. However, the goal is that you have enough knowledge to do it now, so you may wish to get a jump on it!\n\n\n1. Download and install Python using the directions from the first tutorial. Create a notebook that adds 1 + 1 and features the statement 'Hello My Name is: '. Insert your name and follow the directions I gave for publishing the notebook. Send me the link.\n2. Solve the following system of equations using *NumPy*.\n\n $$2x_1 + 2x_2 - x_3 = -3 $$\n $$4x_1 + 2x_3 = 8$$\n $$6x_2 - 3x_3 = -12$$\n \n You should first check that the matrix $A$ is not singular.\n \n3. Consider a simple AR(1) model.\n\n $$y_t = \\rho y_{t-1} + \\varepsilon_t $$ \n \n Where $\\rho = 0.9$ and $\\varepsilon$ is distributed normally with mean $0$ and $\\sigma^2 = 2$. I want you to generate a realization of the AR(1) of length $T=250$ and plot it and then estimate $\\rho$ using OLS. Assume that the time 0 realization of $y_t$ is $0$. You will need to write a loop to recursively generate the new value of $y_t$ at each time. Note that the unconditional mean is $0$ so that there is no intercept. If you estimate the process with an intercept then you should find that it is close to $0$. However, try and read the documentation for SciPy to find out how to estimate it without the intercept. "
}
],
"metadata": {}
}
]
}
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