{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# 4.2 Universal Functions: Fast Element-Wise Array Functions（通用函数：快速点对点数组函数）\n", "\n", "universal function, 或 ufunc, 是用来在ndarray中实现element-wise操作的。\n", "\n", "可以认为这个ufunc可以把一些简单的函数做快速的向量化封装，输入是一个以上的标量，输出也是一个以上的标量。\n", "\n", "很多ufuncs都是点对点的变换，像sqrt或exp：" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import numpy as np\n", "arr = np.arange(10)\n", "arr" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([ 0. , 1. , 1.41421356, 1.73205081, 2. ,\n", " 2.23606798, 2.44948974, 2.64575131, 2.82842712, 3. ])" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.sqrt(arr)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([ 1.00000000e+00, 2.71828183e+00, 7.38905610e+00,\n", " 2.00855369e+01, 5.45981500e+01, 1.48413159e+02,\n", " 4.03428793e+02, 1.09663316e+03, 2.98095799e+03,\n", " 8.10308393e+03])" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.exp(arr)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "这些函数叫做一元通用函数（unary ufuncs）。其他一些函数，比如add或maximum，需要两个数组（binary ufuncs）,并返回一个数组作为结果：" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([ 0.18373557, -1.82728347, -0.11149882, -1.34286776, -1.09016986,\n", " 1.63308 , 1.05205535, -0.32746706])" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x = np.random.randn(8)\n", "y = np.random.randn(8)\n", "x" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([-0.42410809, 1.89603273, -1.13649816, -0.98559379, -0.16827718,\n", " 0.52828569, 1.57543351, 1.50045399])" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "y" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([ 0.18373557, 1.89603273, -0.11149882, -0.98559379, -0.16827718,\n", " 1.63308 , 1.57543351, 1.50045399])" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.maximum(x, y)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "这里mamimum点对点的比较x和y中的元素。\n", "\n", "尽管不常见，但ufunc也能返回多个数组。例如modf，这是一个向量版的divmod（python内建函数），modf会返回小数部分和整数部分：\n", "\n", ">本函数是实现a除以b，然后返回商与余数的元组。如果两个参数a,b都是整数，那么会采用整数除法，结果相当于（a//b, a % b)。如果a或b是浮点数，相当于（math.floor(a/b), a%b)。\n" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([ 1.51538382, -0.75054846, 0.02863286, 8.74026861, -3.44529124,\n", " -9.18401768, -0.68469611])" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "arr = np.random.randn(7) * 5\n", "arr" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([ 0.51538382, -0.75054846, 0.02863286, 0.74026861, -0.44529124,\n", " -0.18401768, -0.68469611])" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "remainder, whole_part = np.modf(arr)\n", "remainder" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([ 1., -0., 0., 8., -3., -9., -0.])" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "whole_part" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "ufunc能接受一个可选参数作为输出，这样可以直接更改原有的数组：" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([ 1.51538382, -0.75054846, 0.02863286, 8.74026861, -3.44529124,\n", " -9.18401768, -0.68469611])" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "arr" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/xu/anaconda/envs/py35/lib/python3.5/site-packages/ipykernel/__main__.py:1: RuntimeWarning: invalid value encountered in sqrt\n", " if __name__ == '__main__':\n" ] }, { "data": { "text/plain": [ "array([ 1.23100927, nan, 0.16921248, 2.95639453, nan,\n", " nan, nan])" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.sqrt(arr) # 没有改变原有的arr" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/xu/anaconda/envs/py35/lib/python3.5/site-packages/ipykernel/__main__.py:1: RuntimeWarning: invalid value encountered in sqrt\n", " if __name__ == '__main__':\n" ] }, { "data": { "text/plain": [ "array([ 1.23100927, nan, 0.16921248, 2.95639453, nan,\n", " nan, nan])" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.sqrt(arr, arr) # 改变了原有的arr" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([ 1.23100927, nan, 0.16921248, 2.95639453, nan,\n", " nan, nan])" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "arr" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "一些一元通用函数：\n", "\n", "![](../MarkdownPhotos/chp04/屏幕快照 2017-10-25 下午1.19.41.png)\n", "\n", "\n", "\n", "一些二元通用函数：\n", "![](../MarkdownPhotos/chp04/屏幕快照 2017-10-25 下午1.21.08.png)\n", "\n", "![](../MarkdownPhotos/chp04/屏幕快照 2017-10-25 下午1.21.42.png)\n", "\n" ] }, { "cell_type": "raw", "metadata": {}, "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python [py35]", "language": "python", "name": "Python [py35]" }, "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 }