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@jeffhussmann
Created February 1, 2013 17:33
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tools for Friday, Feb 1 class
{
"metadata": {
"name": "jhussmann_020113_tools"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": "Suppose we want to evaluate a function of two variables on a regularly spaced grid and visualize the results.\n\nThere are tools that make this easy to do in the `numpy` and `matplotlib` modules."
},
{
"cell_type": "code",
"collapsed": false,
"input": "import numpy as np\nimport matplotlib.pyplot as plt",
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 1
},
{
"cell_type": "markdown",
"metadata": {},
"source": "Let's define some arbitary function of two (scalar) variables."
},
{
"cell_type": "code",
"collapsed": false,
"input": "def arbitrary_function(x, y):\n if x < 0:\n return -1.0\n else:\n return np.sin(x) * np.exp(y)",
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 2
},
{
"cell_type": "markdown",
"metadata": {},
"source": "If given arrays of input values rather than scalars, this function doesn't automatically operate element-wise like MATLAB. (If it did, the first element of the output array would be -1.)"
},
{
"cell_type": "code",
"collapsed": false,
"input": "xs = [-1, 1, 2, 3, 4.]\nys = [1, 1, 2, 3, 4.]\narbitrary_function(xs, ys)",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "pyout",
"prompt_number": 3,
"text": "array([ -2.28735529, 2.28735529, 6.7188497 , 2.83447113, -41.32001618])"
}
],
"prompt_number": 3
},
{
"cell_type": "markdown",
"metadata": {},
"source": "`np.vectorize` takes as input a function and returns a new function that does have this automatic element-wise behavior."
},
{
"cell_type": "code",
"collapsed": false,
"input": "vectorized_function = np.vectorize(arbitrary_function)\nvectorized_function(xs, ys)",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "pyout",
"prompt_number": 4,
"text": "array([ -1. , 2.28735529, 6.7188497 , 2.83447113, -41.32001618])"
}
],
"prompt_number": 4
},
{
"cell_type": "markdown",
"metadata": {},
"source": "`np.linspace` produces a regulary spaced 1-D \"grid\"."
},
{
"cell_type": "code",
"collapsed": false,
"input": "xs = np.linspace(-1, 1, num=5)\nys = np.linspace(-1, 1, num=5)\n\nprint xs\nprint ys",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "[-1. -0.5 0. 0.5 1. ]\n[-1. -0.5 0. 0.5 1. ]\n"
}
],
"prompt_number": 5
},
{
"cell_type": "markdown",
"metadata": {},
"source": "`np.meshgrid` makes a convenient representation of an n-D grid out of n 1-D inputs. "
},
{
"cell_type": "code",
"collapsed": false,
"input": "xx, yy = np.meshgrid(xs, ys)\n\nprint xx\nprint yy",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "[[-1. -0.5 0. 0.5 1. ]\n [-1. -0.5 0. 0.5 1. ]\n [-1. -0.5 0. 0.5 1. ]\n [-1. -0.5 0. 0.5 1. ]\n [-1. -0.5 0. 0.5 1. ]]\n[[-1. -1. -1. -1. -1. ]\n [-0.5 -0.5 -0.5 -0.5 -0.5]\n [ 0. 0. 0. 0. 0. ]\n [ 0.5 0.5 0.5 0.5 0.5]\n [ 1. 1. 1. 1. 1. ]]\n"
}
],
"prompt_number": 6
},
{
"cell_type": "markdown",
"metadata": {},
"source": "`plt.imshow` can be used to visualize functions of two variables, using color as the third \"dimension\". "
},
{
"cell_type": "code",
"collapsed": false,
"input": "plt.imshow(vectorized_function(xx, yy),\n interpolation='nearest',\n extent=[-1, 1, -1, 1],\n origin='lower',\n )",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "pyout",
"prompt_number": 7,
"text": "<matplotlib.image.AxesImage at 0x9ffadcc>"
},
{
"output_type": "display_data",
"png": 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IBNyf/vQn55xzQ0NDrq6ubnxdZ2enW7FihVu+fLnbv3+/H6OajIyMuA0bNkz4qPb+5/fD\nDz+4SCTiIpGIW7Vq1Zx4fpOdjwMHDrgDBw6Mr3n11Vfd8uXL3Zo1a6b8GD7bPOy5tbW1uVWrVrlI\nJOKeeeYZ9/XXX/s57rQ0Nja6goICl5ub60KhkHv//fdn5Lx5zs3RS8gAfOX72xYAcxPxAGBCPACY\nEA8AJsQDgAnxAGDyf0FRHgCT5MN+AAAAAElFTkSuQmCC\n"
}
],
"prompt_number": 7
},
{
"cell_type": "markdown",
"metadata": {},
"source": "Lets make the grid finer for a better looking picture."
},
{
"cell_type": "code",
"collapsed": false,
"input": "fine_xs = np.linspace(-1, 1, num=200)\nfine_ys = np.linspace(-1, 1, num=200)\nfine_xx, fine_yy = np.meshgrid(fine_xs, fine_ys)\n\nplt.imshow(vectorized_function(fine_xx, fine_yy),\n interpolation='nearest',\n extent=[-1, 1, -1, 1],\n origin='lower',\n )",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "pyout",
"prompt_number": 8,
"text": "<matplotlib.image.AxesImage at 0xa3642cc>"
},
{
"output_type": "display_data",
"png": 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WFFWPbZWh1BicC+NbOUrNqWxsw8V9K4MoD2FZ4Rr36Mpwj20oytvG4JSQi5yL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\nxYoVyV/+8hdW7uWXX06+9KU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}
],
"prompt_number": 8
},
{
"cell_type": "markdown",
"metadata": {},
"source": "We can mix scalar and array arguments to a vectorized function."
},
{
"cell_type": "code",
"collapsed": false,
"input": "def arbitrary_function_2(x, y, a):\n if x < 0:\n return -1.0\n else:\n return np.sin(a*x) * np.exp(y)\n\nvectorized_function_2 = np.vectorize(arbitrary_function_2)",
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 9
},
{
"cell_type": "code",
"collapsed": false,
"input": "plt.imshow(vectorized_function_2(fine_xx, fine_yy, 3.0),\n extent=[-1, 1, -1, 1],\n origin='lower',\n )",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "pyout",
"prompt_number": 10,
"text": "<matplotlib.image.AxesImage at 0xa54248c>"
},
{
"output_type": "display_data",
"png": 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6OB/gXB5GMWLoYhrzNP9FisBoxbh5JDJVDCi/yjhH6CGIoxTC6c++SgzyflBb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\ndoRGHg0NDTtCI4+GhoYd4f8HZ+M23tBvgq8AAAAASUVORK5CYII=\n"
}
],
"prompt_number": 10
},
{
"cell_type": "code",
"collapsed": false,
"input": "plt.imshow(vectorized_function_2(fine_xx, fine_yy, 6.0),\n extent=[-1, 1, -1, 1],\n origin='lower',\n )",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "pyout",
"prompt_number": 11,
"text": "<matplotlib.image.AxesImage at 0xa762c8c>"
},
{
"output_type": "display_data",
"png": 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uNs0A4h25Zce0X6z0XKSRalMX3kaF6Rf1TWvFK3Jx78NOWhjTeZUpN3o+nZDx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\n46/zdS35bm5A3DBbU4VqS/tLoywdl+n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}
],
"prompt_number": 11
}
],
"metadata": {}
}
]
}
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