From 1cf7be0a9caf4bd8e56636154a8de3a02f78d550 Mon Sep 17 00:00:00 2001 From: Nicolas Rougier Date: Sun, 16 Aug 2015 19:56:47 +0200 Subject: [PATCH] Remove ipython notebook (incompatible format) --- README.ipynb | 1386 -------------------------------------------------- 1 file changed, 1386 deletions(-) delete mode 100644 README.ipynb diff --git a/README.ipynb b/README.ipynb deleted file mode 100644 index 2106c12..0000000 --- a/README.ipynb +++ /dev/null @@ -1,1386 +0,0 @@ -{ - "metadata": {}, - "nbformat": 3, - "nbformat_minor": 0, - "worksheets": [ - { - "cells": [ - { - "cell_type": "heading", - "level": 1, - "metadata": {}, - "source": [ - "100 numpy exercises" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The goal is both to offer a quick reference for new and old users and to\n", - "provide also a set of exercices for those who teach. If you remember\n", - "having asked or answered a (short) problem, you can send a pull request.\n", - "The format is:\n" - ] - }, - { - "cell_type": "raw", - "metadata": {}, - "source": [ - "#. Find indices of non-zero elements from [1,2,0,0,4,0]\n", - "\n", - " .. code:: python\n", - "\n", - " # Author: Somebody\n", - "\n", - " print np.nonzero([1,2,0,0,4,0])" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Here is what the page looks like so far:\n", - "\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Repository is at: \n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The corresponding [IPython\n", - "notebook](https://github.com/rougier/numpy-100/blob/master/README.ipynb)\n", - "is available from the github repo, thanks to the\n", - "[rst2ipynb](https://github.com/esc/rst2ipynb) conversion tool by\n", - "[Valentin Haenel](http://haenel.co)\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Thanks to Michiaki Ariga, there is now a [Julia\n", - "version](https://github.com/chezou/julia-100-exercises).\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Import the numpy package under the name `np`\n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import numpy as np" - ], - "language": "python", - "metadata": {}, - "outputs": [] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Print the numpy version and the configuration.\n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "print np.__version__\n", - "np.__config__.show()" - ], - "language": "python", - "metadata": {}, - "outputs": [] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Create a null vector of size 10\n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "Z = np.zeros(10)\n", - "print Z" - ], - "language": "python", - "metadata": {}, - "outputs": [] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Create a null vector of size 10 but the fifth value which is 1\n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "Z = np.zeros(10)\n", - "Z[4] = 1\n", - "print Z" - ], - "language": "python", - "metadata": {}, - "outputs": [] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Create a vector with values ranging from 10 to 49\n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "Z = np.arange(10,50)\n", - "print Z" - ], - "language": "python", - "metadata": {}, - "outputs": [] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Create a 3x3 matrix with values ranging from 0 to 8\n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "Z = np.arange(9).reshape(3,3)\n", - "print Z" - ], - "language": "python", - "metadata": {}, - "outputs": [] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Find indices of non-zero elements from \\[1,2,0,0,4,0\\]\n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "nz = np.nonzero([1,2,0,0,4,0])\n", - "print nz" - ], - "language": "python", - "metadata": {}, - "outputs": [] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Create a 3x3 identity matrix\n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "Z = np.eye(3)\n", - "print Z" - ], - "language": "python", - "metadata": {}, - "outputs": [] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Create a 5x5 matrix with values 1,2,3,4 just below the diagonal\n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "Z = np.diag(1+np.arange(4),k=-1)\n", - "print Z" - ], - "language": "python", - "metadata": {}, - "outputs": [] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Create a 3x3x3 array with random values\n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "Z = np.random.random((3,3,3))\n", - "print Z" - ], - "language": "python", - "metadata": {}, - "outputs": [] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Create a 8x8 matrix and fill it with a checkerboard pattern\n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "Z = np.zeros((8,8),dtype=int)\n", - "Z[1::2,::2] = 1\n", - "Z[::2,1::2] = 1\n", - "print Z" - ], - "language": "python", - "metadata": {}, - "outputs": [] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Create a 10x10 array with random values and find the minimum and maximum\n", - "values\n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "Z = np.random.random((10,10))\n", - "Zmin, Zmax = Z.min(), Z.max()\n", - "print Zmin, Zmax" - ], - "language": "python", - "metadata": {}, - "outputs": [] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Create a checkerboard 8x8 matrix using the tile function\n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "Z = np.tile( np.array([[0,1],[1,0]]), (4,4))\n", - "print Z" - ], - "language": "python", - "metadata": {}, - "outputs": [] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Normalize a 5x5 random matrix (between 0 and 1)\n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "Z = np.random.random((5,5))\n", - "Zmax,Zmin = Z.max(), Z.min()\n", - "Z = (Z - Zmin)/(Zmax - Zmin)\n", - "print Z" - ], - "language": "python", - "metadata": {}, - "outputs": [] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Multiply a 5x3 matrix by a 3x2 matrix (real matrix product)\n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "Z = np.dot(np.ones((5,3)), np.ones((3,2)))\n", - "print Z" - ], - "language": "python", - "metadata": {}, - "outputs": [] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Create a 5x5 matrix with row values ranging from 0 to 4\n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "Z = np.zeros((5,5))\n", - "Z += np.arange(5)\n", - "print Z" - ], - "language": "python", - "metadata": {}, - "outputs": [] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Create a vector of size 10 with values ranging from 0 to 1, both\n", - "excluded\n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "Z = np.linspace(0,1,12,endpoint=True)[1:-1]\n", - "print Z" - ], - "language": "python", - "metadata": {}, - "outputs": [] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Create a random vector of size 10 and sort it\n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "Z = np.random.random(10)\n", - "Z.sort()\n", - "print Z" - ], - "language": "python", - "metadata": {}, - "outputs": [] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Consider two random array A anb B, check if they are equal.\n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "A = np.random.randint(0,2,5)\n", - "B = np.random.randint(0,2,5)\n", - "equal = np.allclose(A,B)\n", - "print equal" - ], - "language": "python", - "metadata": {}, - "outputs": [] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Create a random vector of size 30 and find the mean value\n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "Z = np.random.random(30)\n", - "m = Z.mean()\n", - "print m" - ], - "language": "python", - "metadata": {}, - "outputs": [] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Make an array immutable (read-only)\n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "Z = np.zeros(10)\n", - "Z.flags.writeable = False\n", - "Z[0] = 1" - ], - "language": "python", - "metadata": {}, - "outputs": [] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Consider a random 10x2 matrix representing cartesian coordinates,\n", - "convert them to polar coordinates\n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "Z = np.random.random((10,2))\n", - "X,Y = Z[:,0], Z[:,1]\n", - "R = np.sqrt(X**2+Y**2)\n", - "T = np.arctan2(Y,X)\n", - "print R\n", - "print T" - ], - "language": "python", - "metadata": {}, - "outputs": [] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Create random vector of size 10 and replace the maximum value by 0\n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "Z = np.random.random(10)\n", - "Z[Z.argmax()] = 0\n", - "print Z" - ], - "language": "python", - "metadata": {}, - "outputs": [] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Create a structured array with `x` and `y` coordinates covering the\n", - "\\[0,1\\]x\\[0,1\\] area.\n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "Z = np.zeros((10,10), [('x',float),('y',float)])\n", - "Z['x'], Z['y'] = np.meshgrid(np.linspace(0,1,10),\n", - " np.linspace(0,1,10))\n", - "print Z" - ], - "language": "python", - "metadata": {}, - "outputs": [] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Print the minimum and maximum representable value for each numpy scalar\n", - "type\n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "for dtype in [np.int8, np.int32, np.int64]:\n", - " print np.iinfo(dtype).min\n", - " print np.iinfo(dtype).max\n", - "for dtype in [np.float32, np.float64]:\n", - " print np.finfo(dtype).min\n", - " print np.finfo(dtype).max\n", - " print np.finfo(dtype).eps" - ], - "language": "python", - "metadata": {}, - "outputs": [] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Create a structured array representing a position (x,y) and a color\n", - "(r,g,b)\n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - " Z = np.zeros(10, [ ('position', [ ('x', float, 1),\n", - " ('y', float, 1)]),\n", - " ('color', [ ('r', float, 1),\n", - " ('g', float, 1),\n", - " ('b', float, 1)])])\n", - "print Z" - ], - "language": "python", - "metadata": {}, - "outputs": [] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Consider a random vector with shape (100,2) representing coordinates,\n", - "find point by point distances\n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "Z = np.random.random((10,2))\n", - "X,Y = np.atleast_2d(Z[:,0]), np.atleast_2d(Z[:,1])\n", - "D = np.sqrt( (X-X.T)**2 + (Y-Y.T)**2)\n", - "print D\n", - "\n", - "# Much faster with scipy\n", - "import scipy\n", - "Z = np.random.random((10,2))\n", - "D = scipy.spatial.distance.cdist(Z,Z)\n", - "print D" - ], - "language": "python", - "metadata": {}, - "outputs": [] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Generate a generic 2D Gaussian-like array\n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "X, Y = np.meshgrid(np.linspace(-1,1,10), np.linspace(-1,1,10))\n", - "D = np.sqrt(X*X+Y*Y)\n", - "sigma, mu = 1.0, 0.0\n", - "G = np.exp(-( (D-mu)**2 / ( 2.0 * sigma**2 ) ) )\n", - "print G" - ], - "language": "python", - "metadata": {}, - "outputs": [] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "How to tell if a given 2D array has null columns ?\n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "# Author: Warren Weckesser\n", - "\n", - "Z = np.random.randint(0,3,(3,10))\n", - "print (~Z.any(axis=0)).any()" - ], - "language": "python", - "metadata": {}, - "outputs": [] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Find the nearest value from a given value in an array\n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "Z = np.random.uniform(0,1,10)\n", - "z = 0.5\n", - "m = Z.flat[np.abs(Z - z).argmin()]\n", - "print m" - ], - "language": "python", - "metadata": {}, - "outputs": [] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Consider the following file:\n" - ] - }, - { - "cell_type": "raw", - "metadata": {}, - "source": [ - "1,2,3,4,5\n", - "6,,,7,8\n", - ",,9,10,11" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "How to read it ?\n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "Z = np.genfromtxt(\"missing.dat\", delimiter=\",\")" - ], - "language": "python", - "metadata": {}, - "outputs": [] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Consider a generator function that generates 10 integers and use it to\n", - "build an array\n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "def generate():\n", - " for x in xrange(10):\n", - " yield x\n", - "Z = np.fromiter(generate(),dtype=float,count=-1)\n", - "print Z" - ], - "language": "python", - "metadata": {}, - "outputs": [] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Consider a given vector, how to add 1 to each element indexed by a\n", - "second vector (be careful with repeated indices) ?\n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "# Author: Brett Olsen\n", - "\n", - "Z = np.ones(10)\n", - "I = np.random.randint(0,len(Z),20)\n", - "Z += np.bincount(I, minlength=len(Z))\n", - "print Z" - ], - "language": "python", - "metadata": {}, - "outputs": [] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "How to accumulate elements of a vector (X) to an array (F) based on an\n", - "index list (I) ?\n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "# Author: Alan G Isaac\n", - "\n", - "X = [1,2,3,4,5,6]\n", - "I = [1,3,9,3,4,1]\n", - "F = np.bincount(I,X)\n", - "print F" - ], - "language": "python", - "metadata": {}, - "outputs": [] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Considering a (w,h,3) image of (dtype=ubyte), compute the number of\n", - "unique colors\n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "# Author: Nadav Horesh\n", - "\n", - "w,h = 16,16\n", - "I = np.random.randint(0,2,(h,w,3)).astype(np.ubyte)\n", - "F = I[...,0]*256*256 + I[...,1]*256 +I[...,2]\n", - "n = len(np.unique(F))\n", - "print np.unique(I)" - ], - "language": "python", - "metadata": {}, - "outputs": [] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Considering a four dimensions array, how to get sum over the last two\n", - "axis at once ?\n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "A = np.random.randint(0,10,(3,4,3,4))\n", - "sum = A.reshape(A.shape[:-2] + (-1,)).sum(axis=-1)\n", - "print" - ], - "language": "python", - "metadata": {}, - "outputs": [] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Considering a one-dimensional vector D, how to compute means of subsets\n", - "of D using a vector S of same size describing subset indices ?\n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "# Author: Jaime Fern\u00e1ndez del R\u00edo\n", - "\n", - "D = np.random.uniform(0,1,100)\n", - "S = np.random.randint(0,10,100)\n", - "D_sums = np.bincount(S, weights=D)\n", - "D_counts = np.bincount(S)\n", - "D_means = D_sums / D_counts\n", - "print D_means" - ], - "language": "python", - "metadata": {}, - "outputs": [] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Consider the vector \\[1, 2, 3, 4, 5\\], how to build a new vector with 3\n", - "consecutive zeros interleaved between each value ?\n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "# Author: Warren Weckesser\n", - "\n", - "Z = np.array([1,2,3,4,5])\n", - "nz = 3\n", - "Z0 = np.zeros(len(Z) + (len(Z)-1)*(nz))\n", - "Z0[::nz+1] = Z\n", - "print Z0" - ], - "language": "python", - "metadata": {}, - "outputs": [] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Consider an array of dimension (5,5,3), how to mulitply it by an array\n", - "with dimensions (5,5) ?\n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "A = np.ones((5,5,3))\n", - "B = 2*np.ones((5,5))\n", - "print A * B[:,:,None]" - ], - "language": "python", - "metadata": {}, - "outputs": [] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "How to swap two rows of an array ?\n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "# Author: Eelco Hoogendoorn\n", - "\n", - "A = np.arange(25).reshape(5,5)\n", - "A[[0,1]] = A[[1,0]]\n", - "print A" - ], - "language": "python", - "metadata": {}, - "outputs": [] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Consider a one-dimensional array Z, build a two-dimensional array whose\n", - "first row is (Z\\[0\\],Z\\[1\\],Z\\[2\\]) and each subsequent row is shifted\n", - "by 1 (last row should be (Z\\[-3\\],Z\\[-2\\],Z\\[-1\\])\n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "# Author: Joe Kington / Erik Rigtorp\n", - "from numpy.lib import stride_tricks\n", - "\n", - "def rolling(a, window):\n", - " shape = (a.size - window + 1, window)\n", - " strides = (a.itemsize, a.itemsize)\n", - " return stride_tricks.as_strided(a, shape=shape, strides=strides)\n", - "Z = rolling(np.arange(10), 3)\n", - "print Z" - ], - "language": "python", - "metadata": {}, - "outputs": [] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Consider a set of 10 triplets describing 10 triangles (with shared\n", - "vertices), find the set of unique line segments composing all the\n", - "triangles.\n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "# Author: Nicolas P. Rougier\n", - "\n", - "faces = np.random.randint(0,100,(10,3))\n", - "F = np.roll(faces.repeat(2,axis=1),-1,axis=1)\n", - "F = F.reshape(len(F)*3,2)\n", - "F = np.sort(F,axis=1)\n", - "G = F.view( dtype=[('p0',F.dtype),('p1',F.dtype)] )\n", - "G = np.unique(G)\n", - "print G" - ], - "language": "python", - "metadata": {}, - "outputs": [] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Given an array C that is a bincount, how to produce an array A such that\n", - "np.bincount(A) == C ?\n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "# Author: Jaime Fern\u00e1ndez del R\u00edo\n", - "\n", - "C = np.bincount([1,1,2,3,4,4,6])\n", - "A = np.repeat(np.arange(len(C)), C)\n", - "print A" - ], - "language": "python", - "metadata": {}, - "outputs": [] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "How to compute averages using a sliding window over an array ?\n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "# Author: Jaime Fern\u00e1ndez del R\u00edo\n", - "\n", - "def moving_average(a, n=3) :\n", - " ret = np.cumsum(a, dtype=float)\n", - " ret[n:] = ret[n:] - ret[:-n]\n", - " return ret[n - 1:] / n\n", - "Z = np.arange(20)\n", - "print moving_average(Z, n=3)" - ], - "language": "python", - "metadata": {}, - "outputs": [] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "How to get the documentation of the numpy add function from the command\n", - "line ?\n" - ] - }, - { - "cell_type": "raw", - "metadata": {}, - "source": [ - "python -c \"import numpy; numpy.info(numpy.add)\"" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "How to negate a boolean, or to change the sign of a float inplace ?\n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "# Author: Nathaniel J. Smith\n", - "\n", - "Z = np.random.randint(0,2,100)\n", - "np.logical_not(arr, out=arr)\n", - "\n", - "Z = np.random.uniform(-1.0,1.0,100)\n", - "np.negative(arr, out=arr)" - ], - "language": "python", - "metadata": {}, - "outputs": [] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Considering a 10x3 matrix, extract rows with unequal values (e.g.\n", - "\\[2,2,3\\])\n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "# Author: Robert Kern\n", - "\n", - "Z = np.random.randint(0,5,(10,3))\n", - "E = np.logical_and.reduce(Z[:,1:] == Z[:,:-1], axis=1)\n", - "U = Z[~E]\n", - "print Z\n", - "print U" - ], - "language": "python", - "metadata": {}, - "outputs": [] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Convert a vector of ints into a matrix binary representation.\n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "# Author: Warren Weckesser\n", - "\n", - "I = np.array([0, 1, 2, 3, 15, 16, 32, 64, 128])\n", - "B = ((I.reshape(-1,1) & (2**np.arange(8))) != 0).astype(int)\n", - "print B[:,::-1]\n", - "\n", - "# Author: Daniel T. McDonald\n", - "\n", - "I = np.array([0, 1, 2, 3, 15, 16, 32, 64, 128], dtype=np.uint8)\n", - "print np.unpackbits(I[:, np.newaxis], axis=1)" - ], - "language": "python", - "metadata": {}, - "outputs": [] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Consider 2 sets of points P0,P1 describing lines (2d) and a point p, how\n", - "to compute distance from p to each line i (P0\\[i\\],P1\\[i\\]) ?\n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "def distance(P0, P1, p):\n", - " T = P1 - P0\n", - " L = (T**2).sum(axis=1)\n", - " U = -((P0[:,0]-p[...,0])*T[:,0] + (P0[:,1]-p[...,1])*T[:,1]) / L\n", - " U = U.reshape(len(U),1)\n", - " D = P0 + U*T - p\n", - " return np.sqrt((D**2).sum(axis=1))\n", - "\n", - "P0 = np.random.uniform(-10,10,(10,2))\n", - "P1 = np.random.uniform(-10,10,(10,2))\n", - "p = np.random.uniform(-10,10,( 1,2))\n", - "print distance(P0, P1, p)" - ], - "language": "python", - "metadata": {}, - "outputs": [] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Consider 2 sets of points P0,P1 describing lines (2d) and a set of\n", - "points P, how to compute distance from each point j (P\\[j\\]) to each\n", - "line i (P0\\[i\\],P1\\[i\\]) ?\n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "Answer needed actually" - ], - "language": "python", - "metadata": {}, - "outputs": [] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Consider an arbitrary array, write a function that extract a subpart\n", - "with a fixed shape and centered on a given element (pad with a `fill`\n", - "value when necessary)\n" - ] - }, - { - "cell_type": "raw", - "metadata": {}, - "source": [ - "# Author: Nicolas Rougier\n", - "\n", - "Z = np.random.randint(0,10,(10,10))\n", - "shape = (5,5)\n", - "fill = 0\n", - "position = (1,1)\n", - "\n", - "R = np.ones(shape, dtype=Z.dtype)*fill\n", - "P = np.array(list(position)).astype(int)\n", - "Rs = np.array(list(R.shape)).astype(int)\n", - "Zs = np.array(list(Z.shape)).astype(int)\n", - "\n", - "R_start = np.zeros((len(shape),)).astype(int)\n", - "R_stop = np.array(list(shape)).astype(int)\n", - "Z_start = (P-Rs//2)\n", - "Z_stop = (P+Rs//2)+Rs%2\n", - "\n", - "R_start = (R_start - np.minimum(Z_start,0)).tolist()\n", - "Z_start = (np.maximum(Z_start,0)).tolist()\n", - "R_stop = np.maximum(R_start, (R_stop - np.maximum(Z_stop-Zs,0))).tolist()\n", - "Z_stop = (np.minimum(Z_stop,Zs)).tolist()\n", - "\n", - "r = [slice(start,stop) for start,stop in zip(R_start,R_stop)]\n", - "z = [slice(start,stop) for start,stop in zip(Z_start,Z_stop)]\n", - "R[r] = Z[z]\n", - "print Z\n", - "print R" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Consider an array Z = \\[1,2,3,4,5,6,7,8,9,10,11,12,13,14\\], how to\n", - "generate an array R = \\[\\[1,2,3,4\\], \\[2,3,4,5\\], \\[3,4,5,6\\], ...,\n", - "\\[11,12,13,14\\]\\] ?\n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "# Author: St\u00e9fan van der Walt\n", - "\n", - "Z = np.arange(1,15,dtype=uint32)\n", - "R = stride_tricks.as_strided(Z,(11,4),(4,4))\n", - "print R" - ], - "language": "python", - "metadata": {}, - "outputs": [] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Consider two arrays A and B of shape (8,3) and (2,2). How to find rows\n", - "of A that contain elements of each row of B regardless of the order of\n", - "the elements in B ?\n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "# Author: Gabe Schwartz\n", - "\n", - "A = np.random.randint(0,5,(8,3))\n", - "B = np.random.randint(0,5,(2,2))\n", - "\n", - "C = (A[..., np.newaxis, np.newaxis] == B)\n", - "rows = (C.sum(axis=(1,2,3)) >= B.shape[1]).nonzero()[0]\n", - "print rows" - ], - "language": "python", - "metadata": {}, - "outputs": [] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Extract all the contiguous 3x3 blocks from a random 10x10 matrix.\n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "# Author: Chris Barker\n", - "\n", - "Z = np.random.randint(0,5,(10,10))\n", - "n = 3\n", - "i = 1 + (Z.shape[0]-3)\n", - "j = 1 + (Z.shape[1]-3)\n", - "C = stride_tricks.as_strided(Z, shape=(i, j, n, n), strides=Z.strides + Z.strides)\n", - "print C" - ], - "language": "python", - "metadata": {}, - "outputs": [] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Create a 2D array subclass such that Z\\[i,j\\] == Z\\[j,i\\]\n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "# Author: Eric O. Lebigot\n", - "# Note: only works for 2d array and value setting using indices\n", - "\n", - "class Symetric(np.ndarray):\n", - " def __setitem__(self, (i,j), value):\n", - " super(Symetric, self).__setitem__((i,j), value)\n", - " super(Symetric, self).__setitem__((j,i), value)\n", - "\n", - "def symetric(Z):\n", - " return np.asarray(Z + Z.T - np.diag(Z.diagonal())).view(Symetric)\n", - "\n", - "S = symetric(np.random.randint(0,10,(5,5)))\n", - "S[2,3] = 42\n", - "print S" - ], - "language": "python", - "metadata": {}, - "outputs": [] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Consider a set of p matrices wich shape (n,n) and a set of p vectors\n", - "with shape (n,1). How to compute the sum of of the p matrix products at\n", - "once ? (result has shape (n,1))\n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "# Author: St\u00e9fan van der Walt\n", - "\n", - "p, n = 10, 20\n", - "M = np.ones((p,n,n))\n", - "V = np.ones((p,n,1))\n", - "S = np.tensordot(M, V, axes=[[0, 2], [0, 1]])\n", - "print S\n", - "\n", - "# It works, because:\n", - "# M is (p,n,n)\n", - "# V is (p,n,1)\n", - "# Thus, summing over the paired axes 0 and 0 (of M and V independently),\n", - "# and 2 and 1, to remain with a (n,1) vector." - ], - "language": "python", - "metadata": {}, - "outputs": [] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Given a two dimensional array, how to extract unique rows ?\n" - ] - }, - { - "cell_type": "heading", - "level": 1, - "metadata": {}, - "source": [ - "Note" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "See\n", - "[stackoverflow](http://stackoverflow.com/questions/16970982/find-unique-rows-in-numpy-array/)\n", - "for explanations.\n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "# Author: Jaime Fern\u00e1ndez del R\u00edo\n", - "\n", - "Z = np.random.randint(0,2,(6,3))\n", - "T = np.ascontiguousarray(Z).view(np.dtype((np.void, Z.dtype.itemsize * Z.shape[1])))\n", - "_, idx = np.unique(T, return_index=True)\n", - "uZ = Z[idx]\n", - "print uZ" - ], - "language": "python", - "metadata": {}, - "outputs": [] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "How to implement the Game of Life using numpy arrays ?\n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "# Author: Nicolas Rougier\n", - "\n", - "def iterate(Z):\n", - " # Count neighbours\n", - " N = (Z[0:-2,0:-2] + Z[0:-2,1:-1] + Z[0:-2,2:] +\n", - " Z[1:-1,0:-2] + Z[1:-1,2:] +\n", - " Z[2: ,0:-2] + Z[2: ,1:-1] + Z[2: ,2:])\n", - "\n", - " # Apply rules\n", - " birth = (N==3) & (Z[1:-1,1:-1]==0)\n", - " survive = ((N==2) | (N==3)) & (Z[1:-1,1:-1]==1)\n", - " Z[...] = 0\n", - " Z[1:-1,1:-1][birth | survive] = 1\n", - " return Z\n", - "\n", - "Z = np.random.randint(0,2,(50,50))\n", - "for i in range(100): Z = iterate(Z)" - ], - "language": "python", - "metadata": {}, - "outputs": [] - } - ], - "metadata": {} - } - ] -} \ No newline at end of file