numpy实战小练习集锦附代码

Abstract：Numpy是Python做数据分析所必须要掌握的基础库之一。这篇练习通过89道题目带你快速玩转Numpy。

介绍

Numpy是Python做数据分析所必须要掌握的基础库之一。这篇练习通过89道题目带你快速玩转Numpy。

练习

# coding:utf-8
import numpy as np 
import pandas as pd 

# 1.Print the numpy version and the configuration
print (np.__version__)
print np.show_config()

# 2. Create a null vector of size 10
Z = np.zeros(10)
print Z 

# 3.Create a null vector of size 10 but the fifth value which is 1
A = np.zeros(10)
A[4] = 1
print A 

# 4.Create a vector with values ranging from 10 to 49 
A = np.arange(50)
print A 

# 5.Reverse a vector (first element becomes last)
A = np.arange(50)
A = A[::-1]
print A  

# 6.Create a 3x3 matrix with values ranging from 0 to 8
Z = np.arange(9).reshape(3,3)
print Z 

# 7.Find indices of non-zero elements from [1,2,0,0,4,0]
nz = np.nonzero([1,2,0,0,4,0])
print (nz)

# 8.Create a 3x3 identity matrix
A = np.eye(3)
print A 

# 9.create a 3*3*3 array with random values
A = np.random.random((3,3,3))
print (Z)

# 10.Create a 10x10 array with random values and find the minimum and maximum values
Z = np.random.random((10,10))
Zmin,Zmax = Z.min(), Z.max()
print (Zmin,Zmax)

# 11.Create a random vector of size 30 and find the mean value
A = np.random.random(30)
m = A.mean()
print (m)

# 12.Create a 2d array with 1 on the border and 0 inside
Z = np.ones((10,10))
Z[1:-1,1:-1] = 0
print(Z)

# 13.How to add a border (filled with 0's) around an existing array?
A = np.ones((5,5))	# ones(): 返回给定形状和类型的新数组，用数字填充
A = np.pad(A,pad_width=1, mode='constant', constant_values=0)	# pad():filling the array
print A 

# 14.What is the result of the following expression?
print (0 * np.nan)
print (np.nan == np.nan)
print (np.nan - np.nan)
print (0.3 == 3 * 0.1)

# 15.Create a 5x5 matrix with values 1,2,3,4 just below the diagonal
A = np.diag(1+np.arange(4),k=-1)
print A 

# 16.Create a 8x8 matrix and fill it with a checkerboard pattern
A = np.zeros((8,8),dtype=int)
A[1::2,::2] = 1
A[::2,1::2] = 1
print A 

# 17.Consider a (6,7,8) shape array, what is the index (x,y,z) of the 100th element
print (np.unravel_index(100,(6,7,8))) 	# unravel_index(): 将平面索引的平面索引或数组转换为坐标数组的元组

# 18.Create a checkerboard 8x8 matrix using the tile function
Z = np.tile( np.array([[0,1],[1,0]]), (4,4))
print(Z)

# 19.Normalize a 5x5 random matrix
Z = np.random.random((5,5))
Zmax, Zmin = Z.max(), Z.min()
Z = (Z - Zmin)/(Zmax - Zmin)
print(Z)

# 20. Create a custom dtype that describes a color as four unsigned bytes (RGBA)
color = np.dtype([("r", np.ubyte, 1),
                  ("g", np.ubyte, 1),
                  ("b", np.ubyte, 1),
                  ("a", np.ubyte, 1)])

# 21.Multiply a 5x3 matrix by a 3x2 matrix (real matrix product)
A = np.dot(np.ones((5,3)),np.ones((3,2)))
print A 

B = np.dot(np.ones((1,2)),np.ones((2,2)))
print B 

# 22.Given a 1D array, negate all elements which are between 3 and 8, in place.
A = np.arange(11)
A[(3 < A) & (A <= 8)] *= -1
print A 

# 23.What is the output of the following script?
print (sum(range(5),-1))

# 24.What are the result of the following expressions?
print(np.array(0) / np.array(0))
print(np.array(0) // np.array(0))
print(np.array([np.nan]).astype(int).astype(float))

# 25.How to round away from zero a float array ?
Z = np.random.uniform(-10,+10,10)
print (np.copysign(np.ceil(np.abs(Z)), Z))

# 26.How to find common values between two arrays?
A1 = np.random.randint(0,10,10)
A2 = np.random.randint(0,10,10)
print A1,A2
print (np.intersect1d(A1,A2))

# 27.How to ignore all numpy warnings (not recommended)?
defaults = np.seterr(all="ignore")
Z = np.ones(1) / 0
_ = np.seterr(**defaults)

with np.errstate(divide='ignore'):
	Z = np.ones(1) / 0

# 28. Is the following expressions true? 
# numpy.sqrt():按元素方式返回数组的正平方根
print np.sqrt(-1) == np.emath.sqrt(-1)


# 29. How to get the dates of yesterday, today and tomorrow?
yesterday = np.datetime64('today', 'D') - np.timedelta64(1, 'D')
today     = np.datetime64('today', 'D')
tomorrow  = np.datetime64('today', 'D') + np.timedelta64(1, 'D')
print yesterday,today,tomorrow

# 30.How to get all the dates corresponding to the month of July 2016? 
A = np.arange('2018-01','2018-02',dtype='datetime64[D]')
print A 
A = np.arange('2019-03','2019-05',dtype='datetime64[D]')
print A 

# 31.How to compute ((A+B)*(-A/2)) in place (without copy)?
A = np.ones(3)*1
B = np.ones(3)*2
C = np.ones(3)*3
print np.add(A,B,out=B)
print np.divide(A,2,out=A)
print np.negative(A,out=A)
print np.multiply(A,B,out=A)

# 32.Extract the integer part of a random array using 5 different methods
# uniform():从均匀分布绘制样本
# floor():逐元素地返回输入的底
# ceil():元素方式返回输入的上限
# astype():数组的复制，强制转换为指定的类型
# trunc():按元素方式返回输入的截断值
Z = np.random.uniform(0,10,10)
print Z 
print (Z - Z%1)
print (np.floor(Z))
print (np.ceil(Z) - 1)
print (Z.astype(int))
print (np.trunc(Z))

# 33.Create a 5x5 matrix with row values ranging from 0 to 4
A = np.zeros((5,5))
A += np.arange(5)
print A 

# 34.onsider a generator function that generates 10 integers and use it to build an array
# zeros():返回给定形状和类型的新数组，用零填充
# numpy.fromiter():从可迭代对象创建新的1维数组
def generate():
	for x in range(10):
		yield x
Z = np.fromiter(generate(),dtype=float,count=-1)
print Z 

# 35.Create a vector of size 10 with values ranging from 0 to 1, both excluded
# linsapce():在指定的间隔内返回均匀间隔的数字
Z = np.linspace(0,1,11,endpoint=False)[1:]
print(Z) 

# 36.Create a random vector of size 10 and sort it
Z = np.random.random(10)
Z.sort()
print Z 

# 37.How to sum a small array faster than np.sum? 
# add():按元素添加参数
Z = np.arange(10)
print np.add.reduce(Z)

# 38.Consider two random array A and B, check if they are equal
# allclose():如果两个数组在元素级别在容差内相等，则返回True
# array_equal():如果两个数组具有相同的形状和元素，则为True，否则为False
A = np.random.randint(0,2,5)
B = np.random.randint(0,2,5)
equal = np.allclose(A,B)
print (equal)
equal = np.array_equal(A,B)
print (equal)

C = np.random.randint(0,10,10)
D = np.random.randint(0,10,10)
print C,D 
print np.allclose(C,D)
print np.array_equal(C,D)

# 39.Make an array immutable (read-only)
# writeable:确保返回的数组可以写入
Z = np.zeros(10)
Z.flags.writeable = False

# 40.Consider a random 10x2 matrix representing cartesian coordinates, convert them to polar coordinates 
A = np.random.random((10,2))
X,Y = A[:,0],A[:,1]
R = np.sqrt(X**2+Y**2)
T = np.arctan2(Y,X)
print (R)
print (T)

# 41.Create random vector of size 10 and replace the maximum value by 0
# argmax():返回沿轴的最大值的索引
Z = np.random.random(10)
Z[Z.argmax()] = 0
print (Z)

# 42.Create a structured array with x and y coordinates covering the [0,1]x[0,1] area
# meshgrid():从坐标向量返回坐标矩阵
Z = np.zeros((5,5), [('x',float),('y',float)])
Z['x'], Z['y'] = np.meshgrid(np.linspace(0,1,5),
                             np.linspace(0,1,5))
print(Z)

# 43.Given two arrays, X and Y, construct the Cauchy matrix C (Cij =1/(xi - yj))
# outer():计算两个向量的外积
# numpy.linalg.det():计算数组的行列式
X = np.arange(8)
Y = X + 0.5
C = 1.0 / np.subtract.outer(X,Y)
print (np.linalg.det(C))

# 44.Print the minimum and maximum representable value for each numpy scalar type
for dtype in [np.int8, np.int32, np.int64]:
	print (np.iinfo(dtype).min)
	print (np.iinfo(dtype).max)
for dtype in [np.float32, np.float64]:
	print (np.finfo(dtype).min)
	print (np.finfo(dtype).max)
	print (np.finfo(dtype).eps)

# 45.Print the minimum and maximum representable value for each numpy scalar type
np.set_printoptions(threshold=np.nan)
Z = np.zeros((8,8))
print Z 

# 46.How to find the closest value (to a given scalar) in a vector? 
A = np.arange(100)
v = np.random.uniform(0,100)
index = (np.abs(A - v)).argmin()
print (A[index])

# 47.创建一个表示位置(x,y)和颜色(r,g,b)的结构化数组
Z = np.zeros(10, [ ('position', [ ('x', float, 1),
                                  ('y', float, 1)]),
                    ('color',    [ ('r', float, 1),
                                 ('g', float, 1),
                                  ('b', float, 1)])])
print (Z)

# 48.对一个表示坐标形状为(100,2)的随机向量，找到点与点的距离
Z = np.random.random((10,2))
X,Y = np.atleast_2d(Z[:,0], Z[:,1])
D = np.sqrt((X-X.T)**2 + (Y-Y.T)**2)
print (D)

# 49.如何将32位的浮点数(float)转换为对应的整数(integer)?
A = np.arange(10,dtype=np.int32)
A = A.astype(np.float32, copy=False)
print A

# 50.对于numpy数组，enumerate的等价操作是什么？
# enumerate:多维索引迭代器;返回迭代器产生数组坐标和值的对
Z = np.arange(9).reshape(3,3)
print Z
for index,value in np.ndenumerate(Z):
	print (index, value)
for index in np.ndindex(Z.shape):
	print (index, Z[index])

# 51.生成一个通用的二维Gaussian-like数组
X, Y = np.meshgrid(np.linspace(-1,1,10), np.linspace(-1,1,10))
D = np.sqrt(X*X+Y*Y)
sigma, mu = 1.0, 0.0
G = np.exp(-( (D-mu)**2 / ( 2.0 * sigma**2 ) ) )
print (G)

# 52.对一个二维数组，如何在其内部随机放置p个元素?
# numpy.random.choice():从给定的1-D数组生成随机样本
# numpy.put():用给定值替换数组的指定元素
n = 10
p = 4
A = np.zeros((n,n))
np.put(A, np.random.choice(range(n*n), p, replace=False), 1)
print A 

# 53.减去一个矩阵中的每一行的平均值
X = np.random.rand(5,10)
Y = X - X.mean(axis=1,keepdims=True)
print Y 

Y = X - X.mean(axis=1).reshape(-1,1)
print Y

# 54.如何通过第n列对一个数组进行排序?
Z = np.random.randint(0,10,(3,3))
print Z 
print (Z[Z[:,1].argsort()])

# 55.如何检查一个二维数组是否有空列？
Z = np.random.randint(0,3,(3,10))
print ((~Z.any(axis=0).any()))

# 56.如何用迭代器(iterator)计算两个分别具有形状(1,3)和(3,1)的数组?
A = np.arange(3).reshape(3,1)
B = np.arange(3).reshape(1,3)
it = np.nditer([A,B,None])
for x,y,z in it:
	z[...] = x + y
print (it.operands[2])

# 57.创建一个具有name属性的数组类
class NamedArray(np.ndarray):
	def __new__(cls, array, name="no name"):
		obj = np.asarray(array).view(cls)
		obj.name = name
		return obj
	def __array__finalize__(self, obj):
		if obj is None: return
		self.info = getattr(obj, 'name', "no name")
Z = NamedArray(np.arange(10), "range_10")
print (Z.name)

# 58.考虑一个给定的向量，如何对由第二个向量索引的每个元素加1(小心重复的索引)?
Z = np.ones(10)
I = np.random.randint(0,len(Z),20)
Z += np.bincount(I, minlength=len(Z))
print(Z)

# 59.根据索引列表(I)，如何将向量(X)的元素累加到数组(F)?
# numpy.bincount():计算非负整数数组中每个值的出现次数
X = [1,2,3,4,5,6]
I = [1,3,5,7,9,4]
F = np.bincount(I,X)
print F 

# 60.考虑一个(dtype=ubyte) 的 (w,h,3)图像，计算其唯一颜色的数量
w,h = 16,16
I = np.random.randint(0,2,(h,w,3)).astype(np.ubyte)
F = I[...,0]*(256*256) + I[...,1]*256 +I[...,2]
n = len(np.unique(F))
print n

# 61.考虑一个四维数组，如何一次性计算出最后两个轴(axis)的和？
# randint():将随机整数从低（包括）返回到高（不包含）.
A = np.random.randint(0,10,(3,4,3,4))
print A 
sum = A.sum(axis=(-2,-1))
print sum

# 62.考虑一个一维向量D，如何使用相同大小的向量S来计算D子集的均值？
D = np.random.uniform(0,1,100)
S = np.random.randint(0,10,100)
D_sums = np.bincount(S)
D_counts = np.bincount(S)
D_means = D_sums / D_counts
print (D_means)

print (pd.Series(D).groupby(S).mean())

# 63.如何获得点积 dot prodcut的对角线?
# np.sum
A = np.random.uniform(0,1,(5,5))
B = np.random.uniform(0,1,(5,5))
print np.sum(A*B.T, axis=1)
# np.diag
print np.diag(np.dot(A,B))
# np.einsum()
print np.einsum("ij,ji->i", A, B)

# 64.考虑一个向量[1,2,3,4,5],如何建立一个新的向量，在这个新向量中每个值之间有3个连续的零？
Z = np.array([1,2,3,4,5])
nz = 3
Z0 = np.zeros(len(Z) + (len(Z)-1)*(nz))
Z0[::nz+1] = Z 
print Z0

# 65.考虑一个维度(5,5,3)的数组，如何将其与一个(5,5)的数组相乘？
A = np.arange(25).reshape(5,5)
A[0,1] = A[1,0]
print A 

# 66.考虑一个可以描述10个三角形的triplets，找到可以分割全部三角形的line segment
faces = np.random.randint(0,100,(10,3))
F = np.roll(faces.repeat(2,axis=1),-1,axis=1)
F = np.sort(F,axis=1)
G = F.view( dtype=[('p0',F.dtype),('p1',F.dtype)] )
G = np.unique(G)
print G 

# 67.给定一个二进制的数组C，如何产生一个数组A满足np.bincount(A)==C
# np.repeat
C = np.bincount([1,1,2,3,4,4,6])
A = np.repeat(np.arange(len(C)), C)
print A 

# 68.如何通过滑动窗口计算一个数组的平均数?
# np.cumsum
def moving_average(a,n=3):
	ret = np.cumsum(a, dtype=float)
	ret[n:] = ret[n:] - ret[:-n]
	return ret[n - 1:] / n
Z = np.arange(20)
print (moving_average(Z, n=3))

# 69.Consider a one-dimensional array Z, build a two-dimensional array whose first row is (Z[0],Z[1],Z[2]) and each subsequent row is shifted by 1 (last row should be (Z[-3],Z[-2],Z[-1]) 
# from.numpy.lib
from numpy.lib import stride_tricks
def rolling(a, window):
	shape = (a.size - window + 1, window)
	strides = (a.itemsize, a.itemsize)
	return stride_tricks.as_strided(a, shape=shape, strides=strides)
Z = rolling(np.arange(10),3)
print Z 

# 70.如何对布尔值取反，或者原位(in-place)改变浮点数的符号(sign)？
# np.logical_not, np.negative
Z = np.random.randint(0,2,100)
print np.logical_not(Z,out=Z)
Z = np.random.uniform(-1.0,1.0,100)
print np.negative(Z, out=Z)


# 71.考虑两组点集P0和P1去描述一组线(二维)和一个点p,如何计算点p到每一条线 i (P0[i],P1[i])的距离？
def distance(P0,P1,p):
	T = P1 - P0
	L = (T**2).sum(axis=1)
	U = -((P0[:,0]-p[...,0])*T[:,0] + (P0[:,1]-p[...,1])*T[:,1]) / L
	U = U.reshape(len(U),1)
	D = P0 + U*T - p
	return np.sqrt((D**2).sum(axis=1))
P0 = np.random.uniform(-10,10,(10,2))
P1 = np.random.uniform(-10,10,(10,2))
p = np.random.uniform(-10,10,(1,2))
print (distance(P0,P1,p))

# 72.考虑两组点集P0和P1去描述一组线(二维)和一组点集P，如何计算每一个点 j(P[j]) 到每一条线 i (P0[i],P1[i])的距离？
P0 = np.random.uniform(-10,10,(10,2))
P1 = np.random.uniform(-10,10,(10,2))
p = np.random.uniform(-10, 10, (10,2))
print (np.array([distance(P0,P1,p_i) for p_i in p]))

# 73.虑一个数组Z = [1,2,3,4,5,6,7,8,9,10,11,12,13,14],如何生成一个数组R = [[1,2,3,4], [2,3,4,5], [3,4,5,6], ...,[11,12,13,14]]?
# stride_tricks.as_strided
Z = np.arange(1,15,dtype=np.uint32)
R = stride_tricks.as_strided(Z,(11,4),(4,4))
print R

# 74.计算一个矩阵的秩
# np.linalg.svd
Z = np.random.uniform(0,1,(10,10))
U, S, V = np.linalg.svd(Z)
rank = np.sum(S > 1e-10)
print rank 

# 75.如何找到一个数组中出现频率最高的值？
# np.bincount, argmax
Z = np.random.randint(0,10,50)
print (np.bincount(Z).argmax())

# 76.从一个10x10的矩阵中提取出连续的3x3区块
# stride_tricks.as_strided
Z = np.random.randint(0,5,(10,10))
n = 3
i = 1 + (Z.shape[0]-3)
j = 1 + (Z.shape[1]-3)
C = stride_tricks.as_strided(Z,shape=(i,j,n,n),strides=Z.strides + Z.strides)
print C 

# 77.创建一个满足 Z[i,j] == Z[j,i]的子类
# class 
class Symetric(np.ndarray):
    def __setitem__(self, index, value):
        i,j = index
        super(Symetric, self).__setitem__((i,j), value)
        super(Symetric, self).__setitem__((j,i), value)

def symetric(Z):
    return np.asarray(Z + Z.T - np.diag(Z.diagonal())).view(Symetric)

S = symetric(np.random.randint(0,10,(5,5)))
S[2,3] = 42
print (S)

# 78.考虑p个 nxn 矩阵和一组形状为(n,1)的向量，如何直接计算p个矩阵的乘积(n,1)？
# np.tensordot
p,n = 10,20
M = np.ones((p,n,n))
V = np.ones((p,n,1))
S = np.tensordot(M,V,axes=[[0,2],[0,1]])
print S 

# 79.对于一个16x16的数组，如何得到一个区域(block-sum)的和(区域大小为4x4)?
# np.add.reduceat
Z = np.ones((16,16))
k = 4
S = np.add.reduceat(np.add.reduceat(Z, np.arange(0, Z.shape[0], k), axis=0),
                                        np.arange(0, Z.shape[1], k), axis=1)
print (S)

# 80.如何利用numpy数组实现Game of Life
def iterate(Z):
    # Count neighbours
    N = (Z[0:-2,0:-2] + Z[0:-2,1:-1] + Z[0:-2,2:] +
         Z[1:-1,0:-2]                + Z[1:-1,2:] +
         Z[2:  ,0:-2] + Z[2:  ,1:-1] + Z[2:  ,2:])

    # Apply rules
    birth = (N==3) & (Z[1:-1,1:-1]==0)
    survive = ((N==2) | (N==3)) & (Z[1:-1,1:-1]==1)
    Z[...] = 0
    Z[1:-1,1:-1][birth | survive] = 1
    return Z

Z = np.random.randint(0,2,(50,50))
for i in range(100): Z = iterate(Z)
print (Z)

# 81.如何找到一个数组的第n个最大值?
# np.argsort
# numpy.random.shuffle():通过随机播放其内容来修改序列
Z = np.arange(10000)
np.random.shuffle(Z)
n = 5
print (Z[np.argsort(Z)[-n:]])

# 82.给定任意个数向量，创建笛卡尔积(每一个元素的每一种组合)(
# np.indices
def cartesian(arrays):
    arrays = [np.asarray(a) for a in arrays]
    shape = (len(x) for x in arrays)

    ix = np.indices(shape, dtype=int)
    ix = ix.reshape(len(arrays), -1).T

    for n, arr in enumerate(arrays):
        ix[:, n] = arrays[n][ix[:, n]]

    return ix

print (cartesian(([1, 2, 3], [4, 5], [6, 7])))

# 82.如何从一个正常数组创建记录数组(record array)?
np.core.records.fromarrays
Z = np.array([("Hello", 2.5, 3),
              ("World", 3.6, 2)])
R = np.core.records.fromarrays(Z.T, 
                               names='col1, col2, col3',
                               formats = 'S8, f8, i8')
print (R)

# 83.考虑一个大向量Z, 用三种不同的方法计算它的立方
# np.power:第一个数组元素从第二个数组提升到权力，逐元素
x = np.random.rand()
print np.power(x,3)

# 84. 考虑一个10x3的矩阵，分解出有不全相同值的行 (如 [2,2,3]) 
Z = np.random.randint(0,5,(10,3))
print Z 
E = np.all(Z[:,1:] == Z[:,:-1], axis=1)
U = Z[~E]
print (U)

U = Z[Z.max(axis=1) != Z.min(axis=1),:]
print (U)

# 85.将一个整数向量转换为matrix binary的表现形式
print (np.unpackbits(I[:, np.newaxis], axis=1))

# 86.给定一个二维数组，如何提取出唯一的(unique)行?
# np.ascontiguousarray
Z = np.random.randint(0,2,(6,3))
T = np.ascontiguousarray(Z).view(np.dtype((np.void, Z.dtype.itemsize * Z.shape[1])))
_, idx = np.unique(T, return_index=True)
uZ = Z[idx]
print (uZ)

# 87.考虑两个向量A和B，写出用einsum等式对应的inner, outer, sum, mul函数
# np.einsum
A = np.random.uniform(0,1,10)
B = np.random.uniform(0,1,10)
print ('sum')
print (np.einsum('i->', A))# np.sum(A)

print ('A * B')
print (np.einsum('i,i->i', A, B)) # A * B

print ('inner')
print (np.einsum('i,i', A, B))    # np.inner(A, B)

print ('outer')
print (np.einsum('i,j->ij', A, B))    # np.outer(A, B)

# 88. 考虑一个由两个向量描述的路径(X,Y)，如何用等距样例(equidistant samples)对其进行采样(sample)?
# Considering a path described by two vectors (X,Y), how to sample it using equidistant samples
np.cumsum, np.interp)
phi = np.arange(0, 10*np.pi, 0.1)
a = 1
x = a*phi*np.cos(phi)
y = a*phi*np.sin(phi)

dr = (np.diff(x)**2 + np.diff(y)**2)**.5 # segment lengths
r = np.zeros_like(x)
r[1:] = np.cumsum(dr)                # integrate path
r_int = np.linspace(0, r.max(), 200) # regular spaced path
x_int = np.interp(r_int, r, x)       # integrate path
y_int = np.interp(r_int, r, y)

# 89.对于一个一维数组X，计算它boostrapped之后的95%置信区间的平均
# np.percentile
X = np.random.randn(100) # random 1D array
N = 1000 # number of bootstrap samples
idx = np.random.randint(0, X.size, (N, X.size))
means = X[idx].mean(axis=1)
confint = np.percentile(means, [2.5, 97.5])
print (confint)

Reference

这100道练习，带你玩转Numpy

100 numpy exercises