這是CS190.1x第一次作業(yè)，主要教你如何使用numpy。numpy可以說是python科學(xué)計(jì)算的基礎(chǔ)包了，用途非常廣泛。相關(guān)ipynb文件見我github。

這次作業(yè)主要分成5個(gè)部分，分別是：數(shù)學(xué)復(fù)習(xí)，numpy介紹，numpy和線性代數(shù)，lambda表達(dá)式和CTR預(yù)覽（lab4的內(nèi)容，不明白有什么意義，略過）

Part 1 Math review

第一部分主要介紹了線性代數(shù)的知識(shí)，包括向量的加減乘除和矩陣的加減乘除，代碼也不用貼了。

Part 2 NumPy

numpy是python用于向量計(jì)算的包，它對(duì)向量和矩陣計(jì)算提供了非常好的接口，而且對(duì)速度和內(nèi)存的優(yōu)化也做的非常好。本部分會(huì)詳細(xì)的介紹numpy。

Scalar multiplication

向量與常數(shù)相乘

# It is convention to import NumPy with the alias np import numpy as np # TODO: Replace <FILL IN> with appropriate code # Create a numpy array with the values 1, 2, 3 simpleArray = np.array([1,2,3]) # Perform the scalar product of 5 and the numpy array timesFive = 5 * simpleArray print simpleArray print timesFive

Element-wise multiplication and dot product

numpy提供了元素相乘和點(diǎn)乘

# TODO: Replace <FILL IN> with appropriate code # Create a ndarray based on a range and step size. u = np.arange(0, 5, .5) v = np.arange(5, 10, .5)elementWise = u * v dotProduct = np.dot(u,v) print 'u: {0}'.format(u) print 'v: {0}'.format(v) print '\nelementWise\n{0}'.format(elementWise) print '\ndotProduct\n{0}'.format(dotProduct)

Matrix math

numpy提供了矩陣的轉(zhuǎn)置，點(diǎn)乘，求逆運(yùn)算

# TODO: Replace <FILL IN> with appropriate code from numpy.linalg import invA = np.matrix([[1,2,3,4],[5,6,7,8]]) print 'A:\n{0}'.format(A) # Print A transpose print '\nA transpose:\n{0}'.format(A.T)# Multiply A by A transpose AAt = A.dot(np.matrix.transpose(A)) print '\nAAt:\n{0}'.format(AAt)# Invert AAt with np.linalg.inv() AAtInv = inv(AAt) print '\nAAtInv:\n{0}'.format(AAtInv)# Show inverse times matrix equals identity # We round due to numerical precision print '\nAAtInv * AAt:\n{0}'.format((AAtInv * AAt).round(4))

Part 3 Additional NumPy and Spark linear algebra

Slices

熟悉python的list的人對(duì)這個(gè)應(yīng)該不陌生。

# TODO: Replace <FILL IN> with appropriate code features = np.array([1, 2, 3, 4]) print 'features:\n{0}'.format(features)# The last three elements of features lastThree = features[-3:]print '\nlastThree:\n{0}'.format(lastThree)

Combining ndarray objects

這里介紹np.hstack()：按照列來合并； np.vstack()：按照行來合并。

# TODO: Replace <FILL IN> with appropriate code zeros = np.zeros(8) ones = np.ones(8) print 'zeros:\n{0}'.format(zeros) print '\nones:\n{0}'.format(ones)zerosThenOnes = np.hstack((zeros,ones)) # A 1 by 16 array zerosAboveOnes = np.vstack((zeros,ones)) # A 2 by 8 arrayprint '\nzerosThenOnes:\n{0}'.format(zerosThenOnes) print '\nzerosAboveOnes:\n{0}'.format(zerosAboveOnes)

PySpark's DenseVector

PySpark提供了DenseVector（在pyspark.mllib.lianlg）來存儲(chǔ)數(shù)組，這和numpy有點(diǎn)類似。

from pyspark.mllib.linalg import DenseVector # TODO: Replace <FILL IN> with appropriate code numpyVector = np.array([-3, -4, 5]) print '\nnumpyVector:\n{0}'.format(numpyVector)# Create a DenseVector consisting of the values [3.0, 4.0, 5.0] myDenseVector = DenseVector([3.0, 4.0, 5.0]) # Calculate the dot product between the two vectors. denseDotProduct = myDenseVector.dot(numpyVector)print 'myDenseVector:\n{0}'.format(myDenseVector) print '\ndenseDotProduct:\n{0}'.format(denseDotProduct)

Part 4 Python lambda expressions

lambda之前出現(xiàn)了這么多次，不明白為啥才講。。。囧。講lambda的博客也是特別多，大家有興趣可以搜搜看。

# Example function def addS(x):return x + 's' print type(addS) print addS print addS('cat')# As a lambda addSLambda = lambda x: x + 's' print type(addSLambda) print addSLambda print addSLambda('cat')# TODO: Replace <FILL IN> with appropriate code # Recall that: "lambda x, y: x + y" creates a function that adds together two numbers multiplyByTen = lambda x: x * 10 print multiplyByTen(5)# Note that the function still shows its name as <lambda> print '\n', multiplyByTen

lambda fewer steps than def

這里給出了lamda比def要靈活的例子

# Code using def that we will recreate with lambdas def plus(x, y):return x + ydef minus(x, y):return x - yfunctions = [plus, minus] print functions[0](4, 5) print functions[1](4, 5)# TODO: Replace <FILL IN> with appropriate code # The first function should add two values, while the second function should subtract the second # value from the first value. lambdaFunctions = [lambda x,y : x+y , lambda x,y : x-y] print lambdaFunctions[0](4, 5) print lambdaFunctions[1](4, 5)

Lambda expression arguments

這一部分應(yīng)該是說lambda的入?yún)⒉灰粯?#xff0c;但是效果一樣

# Examples. Note that the spacing has been modified to distinguish parameters from tuples.# One-parameter function a1 = lambda x: x[0] + x[1] a2 = lambda (x0, x1): x0 + x1 print 'a1( (3,4) ) = {0}'.format( a1( (3,4) ) ) print 'a2( (3,4) ) = {0}'.format( a2( (3,4) ) )# Two-parameter function b1 = lambda x, y: (x[0] + y[0], x[1] + y[1]) b2 = lambda (x0, x1), (y0, y1): (x0 + y0, x1 + y1) print '\nb1( (1,2), (3,4) ) = {0}'.format( b1( (1,2), (3,4) ) ) print 'b2( (1,2), (3,4) ) = {0}'.format( b2( (1,2), (3,4) ) )# TODO: Replace <FILL IN> with appropriate code # Use both syntaxes to create a function that takes in a tuple of two values and swaps their order # E.g. (1, 2) => (2, 1) swap1 = lambda x: (x[1],x[0]) swap2 = lambda (x0, x1): (x1,x0) print 'swap1((1, 2)) = {0}'.format(swap1((1, 2))) print 'swap2((1, 2)) = {0}'.format(swap2((1, 2)))# Using either syntax, create a function that takes in a tuple with three values and returns a tuple # of (2nd value, 3rd value, 1st value). E.g. (1, 2, 3) => (2, 3, 1) swapOrder = lambda x:(x[1],x[2],x[0]) print 'swapOrder((1, 2, 3)) = {0}'.format(swapOrder((1, 2, 3)))# Using either syntax, create a function that takes in three tuples each with two values. The # function should return a tuple with the values in the first position summed and the values in the # second position summed. E.g. (1, 2), (3, 4), (5, 6) => (1 + 3 + 5, 2 + 4 + 6) => (9, 12) sumThree = lambda x,y,z :(x[0]+y[0]+z[0],x[1]+y[1]+z[1]) print 'sumThree((1, 2), (3, 4), (5, 6)) = {0}'.format(sumThree((1, 2), (3, 4), (5, 6)))

Functional programming

# Create a class to give our examples the same syntax as PySpark class FunctionalWrapper(object):def __init__(self, data):self.data = datadef map(self, function):"""Call `map` on the items in `data` using the provided `function`"""return FunctionalWrapper(map(function, self.data))def reduce(self, function):"""Call `reduce` on the items in `data` using the provided `function`"""return reduce(function, self.data)def filter(self, function):"""Call `filter` on the items in `data` using the provided `function`"""return FunctionalWrapper(filter(function, self.data))def __eq__(self, other):return (isinstance(other, self.__class__)and self.__dict__ == other.__dict__)def __getattr__(self, name): return getattr(self.data, name)def __getitem__(self, k): return self.data.__getitem__(k)def __repr__(self): return 'FunctionalWrapper({0})'.format(repr(self.data))def __str__(self): return 'FunctionalWrapper({0})'.format(str(self.data))# Map example# Create some data mapData = FunctionalWrapper(range(5))# Define a function to be applied to each element f = lambda x: x + 3# Imperative programming: loop through and create a new object by applying f mapResult = FunctionalWrapper([]) # Initialize the result for element in mapData:mapResult.append(f(element)) # Apply f and save the new value print 'Result from for loop: {0}'.format(mapResult)# Functional programming: use map rather than a for loop print 'Result from map call: {0}'.format(mapData.map(f))# Note that the results are the same but that the map function abstracts away the implementation # and requires less code# TODO: Replace <FILL IN> with appropriate code dataset = FunctionalWrapper(range(10))# Multiply each element by 5 mapResult = dataset.map(lambda x :x*5) # Keep the even elements # Note that "x % 2" evaluates to the remainder of x divided by 2 filterResult = dataset.filter(lambda x : x%2==0) # Sum the elements reduceResult = dataset.reduce(lambda x,y: x+y)print 'mapResult: {0}'.format(mapResult) print '\nfilterResult: {0}'.format(filterResult) print '\nreduceResult: {0}'.format(reduceResult)

Composability

# Example of a mult-line expression statement # Note that placing parentheses around the expression allow it to exist on multiple lines without # causing a syntax error. (dataset.map(lambda x: x + 2).reduce(lambda x, y: x * y))# TODO: Replace <FILL IN> with appropriate code # Multiply the elements in dataset by five, keep just the even values, and sum those values finalSum = dataset.map(lambda x :x*5).filter(lambda x : x%2==0).reduce(lambda x,y: x+y) print finalSum

轉(zhuǎn)載于:https://www.cnblogs.com/-Sai-/p/6737661.html

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