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@sbarratt
Created August 28, 2016 18:11
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Scientific Computing in Python"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"import numpy as np\n",
"from random import random\n",
"from IPython.display import Image\n",
"import matplotlib.pyplot as plt\n",
"\n",
"%matplotlib inline"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Numpy\n",
"---\n",
"The array type."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Create arrays by hand"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"x: [1 2 3]\n",
"type: int64\n",
"ndim: 1\n",
"shape: (3,)\n"
]
}
],
"source": [
"x = np.array([1, 2, 3])\n",
"print (\"x:\", x)\n",
"print (\"type:\", x.dtype)\n",
"print (\"ndim:\", x.ndim)\n",
"print (\"shape:\", x.shape)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Create 2-d arrays by hand"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"X: [[ 0. 1.]\n",
" [ 1. 0.]]\n",
"type: float64\n",
"ndim: 2\n",
"shape: (2, 2)\n"
]
}
],
"source": [
"X = np.array([\n",
" [0, 1.],\n",
" [1., 0]\n",
" ])\n",
"print (\"X:\", X)\n",
"print (\"type:\", X.dtype)\n",
"print (\"ndim:\", X.ndim)\n",
"print (\"shape:\", X.shape)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Facilities for creating arrays"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"a: [ 0. 0.11111111 0.22222222 0.33333333 0.44444444 0.55555556\n",
" 0.66666667 0.77777778 0.88888889 1. ]\n",
"b: [0 1 2 3 4 5 6 7 8 9]\n",
"c: [ 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]\n",
"A: [[ 0. 0.]\n",
" [ 0. 0.]]\n",
"B: [[ 0.66788612 0.60029783]\n",
" [ 0.61820622 0.24980989]]\n"
]
}
],
"source": [
"a = np.linspace(0, 1, 10)\n",
"b = np.arange(10)\n",
"c = np.ones(10)\n",
"A = np.zeros((2,2))\n",
"B = np.random.random((2, 2))\n",
"print (\"a:\", a)\n",
"print (\"b:\", b)\n",
"print (\"c:\", c)\n",
"print (\"A:\", A)\n",
"print (\"B:\", B)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Apply functions to arrays"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"b+c: [ 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.]\n",
"b*c: [ 0. 1. 2. 3. 4. 5. 6. 7. 8. 9.]\n",
"e^a: [ 1. 1.11751907 1.24884887 1.39561243 1.5596235 1.742909\n",
" 1.94773404 2.17662993 2.43242545 2.71828183]\n",
"max(B): 0.667886116228\n",
"mean(b): 4.5\n"
]
}
],
"source": [
"print (\"b+c:\", b+c)\n",
"print (\"b*c:\", b*c)\n",
"print (\"e^a:\", np.exp(a))\n",
"print (\"max(B):\", np.max(B))\n",
"print (\"mean(b):\", np.mean(b))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Make your own functions"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"f(b): [ 4 1 0 1 4 9 16 25 36 49]\n"
]
}
],
"source": [
"f = lambda x: (x-2)**2\n",
"f = np.vectorize(f)\n",
"print (\"f(b):\", f(b))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Multiply arrays"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"b.c: 45.0\n",
"B.[0.5, 0.5]: [ 0.63409197 0.43400806]\n"
]
}
],
"source": [
"print (\"b.c:\", b.dot(c))\n",
"print (\"B.[0.5, 0.5]:\", B.dot(np.array([0.5, 0.5])))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Can Python be fast?\n",
"Adding vectors using a [vectorized](https://en.wikipedia.org/wiki/Array_programming) operation significantly speeds up the operation. When using numpy, always try to vectorize your operations by avoiding for loops and using built-in functions."
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"x = np.random.random(1000)\n",
"y = np.random.random(1000)"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"1000 loops, best of 3: 234 µs per loop\n"
]
}
],
"source": [
"%timeit [a+b for a,b in zip(x,y)]"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The slowest run took 73.28 times longer than the fastest. This could mean that an intermediate result is being cached.\n",
"1000000 loops, best of 3: 1.25 µs per loop\n"
]
}
],
"source": [
"%timeit x + y"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Markov Chains using Numpy and Matplotlib\n",
"---"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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gNTUVn4hNpMrNzSW21Pnz5wHAxsZGmeLp6QkAp0+fxmf76aefAOCtt94y1heTQXpQYjE9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\n/QAAAABJRU5ErkJggg==\n",
"text/plain": [
"<IPython.core.display.Image object>"
]
},
"execution_count": 23,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"Image(filename='hamilton_graph.png')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"[Hamilton](https://ideas.repec.org/a/fip/fedlrv/y2005ijulp435-452nv.87no.4.html) estimated the above stochanstic Markov Chain as a model of the U.S. economy on a monthly basis (ng is normal growth, mr is mild recession and sr is severe recession)."
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"P = np.array([\n",
" [0.971, 0.029, 0],\n",
" [0.145, 0.778, 0.077],\n",
" [0, 0.508, 0.492]\n",
" ])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's make sure that the rows sum to 1, in other words they represent a valid probability distribution."
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([ 1., 1., 1.])"
]
},
"execution_count": 25,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.sum(P, axis=1)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's simulate the economy for 30 years, putting the monthly result in a variable called `paths`."
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"N_months = 12*30\n",
"state = 0\n",
"path = [state]\n",
"\n",
"for _ in range(N_months-1):\n",
" state = np.random.choice([0, 1, 2], p=P[state, :])\n",
" path.append(state)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"To make sure our simulation worked, print out the results of the first 12 months."
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n"
]
}
],
"source": [
"print (path[:12])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"It's hard to see what's happening just by looking at numbers, let's visualize them using matplotlib."
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.text.Text at 0x1062d1a90>"
]
},
"execution_count": 28,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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0eHnyOvIwtKOklI9bbx5G3jEve85diN55UVK+aAO+2GmK6pLUYQC+k9h2O4Dy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\nRoFOE9d9kwAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1062ad240>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(path)\n",
"plt.xlabel(\"Month\")\n",
"plt.ylabel(\"Economy State\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's plot what happened during the first year."
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.text.Text at 0x1063e9c50>"
]
},
"execution_count": 29,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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XOTskf9Xqnr8bKTwREdFX6fGU0uOJiOhcejwRETHwUnhK6fFUq87565wdkr9q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\n9f8Bl/fbdL7kkkYAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1062e2668>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.title(\"Year 1\")\n",
"plt.scatter(range(12), path[:12])\n",
"plt.xlabel(\"Month\")\n",
"plt.ylabel(\"Economy State\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The \"steady-state\" of a markov chain is the probability of ending up in each state given a random starting position. We can calculate it by finding the left-eigenvector of the Probability Transition Matrix with an eigenvalue of 1."
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"E, V = np.linalg.eig(P.T)"
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"According to Hamilton...\n",
"* We spend 81.28 % of months in Normal Growth\n",
"* We spend 16.26 % of months in Mild Recession\n",
"* We spend 2.46 % of months in Severe Recession\n"
]
}
],
"source": [
"x_s = V[:, 0] / np.sum(V[:, 0])\n",
"\n",
"print (\"According to Hamilton...\")\n",
"print (\"* We spend %.2f %% of months in Normal Growth\" % (x_s[0] * 100))\n",
"print (\"* We spend %.2f %% of months in Mild Recession\" % (x_s[1] * 100))\n",
"print (\"* We spend %.2f %% of months in Severe Recession\" % (x_s[2] * 100))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Scipy Image\n",
"---"
]
},
{
"cell_type": "code",
"execution_count": 32,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"from scipy.ndimage.filters import gaussian_filter, sobel, prewitt\n",
"from scipy import misc"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Scipy has a lot of image and signal processing functionality. Let's try it out on a built in image, called `ascent`."
]
},
{
"cell_type": "code",
"execution_count": 33,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"face = misc.ascent()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"As expected, a grayscale image is just a 2-D numpy array of numbers between 0 and 255."
]
},
{
"cell_type": "code",
"execution_count": 34,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([[ 83, 83, 83, ..., 117, 117, 117],\n",
" [ 82, 82, 83, ..., 117, 117, 117],\n",
" [ 80, 81, 83, ..., 117, 117, 117],\n",
" ..., \n",
" [178, 178, 178, ..., 57, 59, 57],\n",
" [178, 178, 178, ..., 56, 57, 57],\n",
" [178, 178, 178, ..., 57, 57, 58]])"
]
},
"execution_count": 34,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"face"
]
},
{
"cell_type": "code",
"execution_count": 35,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.image.AxesImage at 0x107c684e0>"
]
},
"execution_count": 35,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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dRdXIAicJIwec0G63WyYKTXW2m7UeeS7bw7AflYnqgtDvpTuSyWSQSCQEwOT5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\nFMSczMmczChzCmJO5mROZpT/C5driFn7n7BBAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x107895588>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.imshow(face, cmap='Greys_r')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Blurring\n",
"Let's apply a [gaussian filter](https://en.wikipedia.org/wiki/Gaussian_filter) to blur the image."
]
},
{
"cell_type": "code",
"execution_count": 36,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.image.AxesImage at 0x107e9ae10>"
]
},
"execution_count": 36,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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PiV/8X0FBB6J3eA9FXEDUDsu/Xjb+TmPrmEagfwkgTtkVDPM0CA+1dAm6vpixqeX3wa9/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\nAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x107c84d30>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"face_gf = gaussian_filter(face, sigma = 5)\n",
"plt.imshow(face_gf, cmap='Greys_r')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Edge Detection\n",
"Let's apply a [sobel filter](https://en.wikipedia.org/wiki/Sobel_operator) to detect edges in the image."
]
},
{
"cell_type": "code",
"execution_count": 37,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.image.AxesImage at 0x1098337f0>"
]
},
"execution_count": 37,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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XaUw7J+pJXgy1BQJRwMEk6+7udhwLTyaVq7E9uQHg+vXrjvq56ki3oMQMCoWC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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x107eb2c88>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"face_sobel = sobel(face, mode='constant')\n",
"plt.imshow(face_sobel, cmap='Greys_r')"
]
}
],
"metadata": {
"anaconda-cloud": {},
"kernelspec": {
"display_name": "Python [quant]",
"language": "python",
"name": "Python [quant]"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.5.2"
}
},
"nbformat": 4,
"nbformat_minor": 0
}
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