我是小z之前寫的Pandas系列，已經(jīng)為數(shù)千個(gè)徘徊在pandas大門的小伙伴打開了一條快速上分通道：
最新的一個(gè)百度網(wǎng)盤分享下載量對(duì)于Numpy，我講的不多，因?yàn)楹蚉andas相比，他距離日常的數(shù)據(jù)處理更“遠(yuǎn)”一些。但是，Numpy仍然是Python做數(shù)據(jù)分析所必須要掌握的基礎(chǔ)庫(kù)之一，以下題是github上的開源項(xiàng)目，主要為了檢測(cè)你的Numpy能力，同時(shí)對(duì)你的學(xué)習(xí)作為一個(gè)補(bǔ)充。來(lái)源：https://github.com/rougier/numpy-100
1. 導(dǎo)入numpy庫(kù)并取別名為np (★☆☆)(提示: import … as …)
import numpy as np
2. 打印輸出numpy的版本和配置信息 (★☆☆)(提示: np.version, np.show_config)print(np.__version__)
print(np.show_config())
3. 創(chuàng)建一個(gè)長(zhǎng)度為10的空向量 (★☆☆)(提示: np.zeros)
Z = np.zeros(10)
print(Z)
4. 如何找到任何一個(gè)數(shù)組的內(nèi)存大?。?★☆☆)(提示: size, itemsize)Z = np.zeros((10,10))
print('%d bytes' % (Z.size * Z.itemsize))
5. 如何從命令行得到numpy中add函數(shù)的說(shuō)明文檔? (★☆☆)(提示: np.info)
import numpy
numpy.info(numpy.add)
6. 創(chuàng)建一個(gè)長(zhǎng)度為10并且除了第五個(gè)值為1的空向量 (★☆☆)(提示: array[4])Z = np.zeros(10)
Z[4] = 1
print(Z)
7. 創(chuàng)建一個(gè)值域范圍從10到49的向量(★☆☆)(提示: np.arange)
Z = np.arange(10,50)
print(Z)
8. 反轉(zhuǎn)一個(gè)向量(第一個(gè)元素變?yōu)樽詈笠粋€(gè)) (★☆☆)(提示: array[::-1])Z = np.arange(50)
Z = Z[::-1]
print(Z)
9. 創(chuàng)建一個(gè) 3x3 并且值從0到8的矩陣(★☆☆)(提示: reshape)
Z = np.arange(9).reshape(3,3)
print(Z)
10. 找到數(shù)組[1,2,0,0,4,0]中非0元素的位置索引 (★☆☆)(提示: np.nonzero)nz = np.nonzero([1,2,0,0,4,0])
print(nz)
11. 創(chuàng)建一個(gè) 3x3 的單位矩陣 (★☆☆)(提示: np.eye)
Z = np.eye(3)
print(Z)
12. 創(chuàng)建一個(gè) 3x3x3的隨機(jī)數(shù)組 (★☆☆)(提示: np.random.random)Z = np.random.random((3,3,3))
print(Z)
13. 創(chuàng)建一個(gè) 10x10 的隨機(jī)數(shù)組并找到它的最大值和最小值 (★☆☆)(提示: min, max)
Z = np.random.random((10,10))
Zmin, Zmax = Z.min(), Z.max()
print(Zmin, Zmax)
14. 創(chuàng)建一個(gè)長(zhǎng)度為30的隨機(jī)向量并找到它的平均值 (★☆☆)(提示: mean)Z = np.random.random(30)
m = Z.mean()
print(m)
15. 創(chuàng)建一個(gè)二維數(shù)組，其中邊界值為1，其余值為0 (★☆☆)(提示: array[1:-1, 1:-1])
Z = np.ones((10,10))
Z[1:-1,1:-1] = 0
print(Z)
16. 對(duì)于一個(gè)存在在數(shù)組，如何添加一個(gè)用0填充的邊界? (★☆☆)(提示: np.pad)Z = np.ones((5,5))
Z = np.pad(Z, pad_width=1, mode='constant', constant_values=0)
print(Z)
17. 下面表達(dá)式運(yùn)行的結(jié)果是什么？(★☆☆)(提示: NaN = not a number, inf = infinity)
(提示：NaN : 不是一個(gè)數(shù)，inf : 無(wú)窮)
# 表達(dá)式 # 結(jié)果
0 * np.nan nan
np.nan == np.nan False
np.inf > np.nan False
np.nan - np.nan nan
0.3 == 3 * 0.1 False
18. 創(chuàng)建一個(gè) 5x5的矩陣，并設(shè)置值1,2,3,4落在其對(duì)角線下方位置 (★☆☆)(提示: np.diag)Z = np.diag(1+np.arange(4),k=-1)
print(Z)
19. 創(chuàng)建一個(gè)8x8 的矩陣，并且設(shè)置成棋盤樣式 (★☆☆)(提示: array[::2])
Z = np.zeros((8,8),dtype=int)
Z[1::2,::2] = 1
Z[::2,1::2] = 1
print(Z)
20. 考慮一個(gè) (6,7,8) 形狀的數(shù)組，其第100個(gè)元素的索引(x,y,z)是什么?(提示: np.unravel_index)print(np.unravel_index(100,(6,7,8)))
21. 用tile函數(shù)去創(chuàng)建一個(gè) 8x8的棋盤樣式矩陣(★☆☆)(提示: np.tile)
Z = np.tile( np.array([[0,1],[1,0]]), (4,4))
print(Z)
22. 對(duì)一個(gè)5x5的隨機(jī)矩陣做歸一化(★☆☆)(提示: (x - min) / (max - min))Z = np.random.random((5,5))
Zmax, Zmin = Z.max(), Z.min()
Z = (Z - Zmin)/(Zmax - Zmin)
print(Z)
23. 創(chuàng)建一個(gè)將顏色描述為(RGBA)四個(gè)無(wú)符號(hào)字節(jié)的自定義dtype？(★☆☆)(提示: np.dtype)
color = np.dtype([('r', np.ubyte, 1),
('g', np.ubyte, 1),
('b', np.ubyte, 1),
('a', np.ubyte, 1)])
color
24. 一個(gè)5x3的矩陣與一個(gè)3x2的矩陣相乘，實(shí)矩陣乘積是什么？(★☆☆)(提示: np.dot | @)Z = np.dot(np.ones((5,3)), np.ones((3,2)))
print(Z)
25. 給定一個(gè)一維數(shù)組，對(duì)其在3到8之間的所有元素取反 (★☆☆)(提示: >, <=)
Z = np.arange(11)
Z[(3 < Z) & (Z <= 8)] *= -1
print(Z)
26. 下面腳本運(yùn)行后的結(jié)果是什么? (★☆☆)(提示: np.sum)# Author: Jake VanderPlas # 結(jié)果
print(sum(range(5),-1)) 9
from numpy import *
print(sum(range(5),-1)) 10 #numpy.sum(a, axis=None)
27. 考慮一個(gè)整數(shù)向量Z,下列表達(dá)合法的是哪個(gè)? (★☆☆)（提示：這里還有“位運(yùn)算符”）
Z**Z True
2 << Z >> 2 False
Z <- Z True
1j*Z True #復(fù)數(shù)
Z/1/1 True
ZZ False
28. 下面表達(dá)式的結(jié)果分別是什么？(★☆☆)np.array(0) / np.array(0) nan
np.array(0) // np.array(0) 0
np.array([np.nan]).astype(int).astype(float) -2.14748365e+09
29. 如何從零位開始舍入浮點(diǎn)數(shù)組？(★☆☆)(提示: np.uniform, np.copysign, np.ceil, np.abs)
# Author: Charles R Harris
Z = np.random.uniform(-10,+10,10)
print (np.copysign(np.ceil(np.abs(Z)), Z))
30. 如何找出兩個(gè)數(shù)組公共的元素? (★☆☆)(提示: np.intersect1d)Z1 = np.random.randint(0, 10, 10)
Z2 = np.random.randint(0, 10, 10)
print (np.intersect1d(Z1, Z2))
31. 如何忽略所有的 numpy 警告(盡管不建議這么做)? (★☆☆)(提示: np.seterr, np.errstate)
# Suicide mode on
defaults = np.seterr(all='ignore')
Z = np.ones(1) / 0
# Back to sanity
_ = np.seterr(**defaults)
# 另一個(gè)等價(jià)的方式， 使用上下文管理器（context manager）
with np.errstate(divide='ignore'):
Z = np.ones(1) / 0
32. 下面的表達(dá)式是否為真? (★☆☆)(提示: 虛數(shù))np.sqrt(-1) == np.emath.sqrt(-1) Faslse
33. 如何獲得昨天，今天和明天的日期? (★☆☆)(提示: np.datetime64, np.timedelta64)
yesterday = np.datetime64('today', 'D') - np.timedelta64(1, 'D')
today = np.datetime64('today', 'D')
tomorrow = np.datetime64('today', 'D') + np.timedelta64(1, 'D')
34. 怎么獲得所有與2016年7月的所有日期? (★★☆)(提示: np.arange(dtype=datetime64['D']))Z = np.arange('2016-07', '2016-08', dtype='datetime64[D]')
print (Z)
35. 如何計(jì)算 ((A+B)*(-A/2)) (不使用中間變量)? (★★☆)(提示: np.add(out=), np.negative(out=), np.multiply(out=), np.divide(out=))
A = np.ones(3) * 1
B = np.ones(3) * 1
C = np.ones(3) * 1
np.add(A, B, out=B)
np.divide(A, 2, out=A)
np.negative(A, out=A)
np.multiply(A, B, out=A)
36. 用5種不同的方法提取隨機(jī)數(shù)組中的整數(shù)部分 (★★☆)(提示: %, np.floor, np.ceil, astype, np.trunc)Z = np.random.uniform(0, 10, 10)
print (Z - Z % 1)
print (np.floor(Z))
print (np.cell(Z)-1)
print (Z.astype(int))
print (np.trunc(Z))
37. 創(chuàng)建一個(gè)5x5的矩陣且每一行的值范圍為從0到4 (★★☆)(提示: np.arange)
Z = np.zeros((5, 5))
Z += np.arange(5)
print (Z)
38. 如何用一個(gè)生成10個(gè)整數(shù)的函數(shù)來(lái)構(gòu)建數(shù)組 (★☆☆)(提示: np.fromiter)def generate():
for x in range(10):
yield x
Z = np.fromiter(generate(), dtype=float, count=-1)
print (Z)
39. 創(chuàng)建一個(gè)大小為10的向量， 值域?yàn)?到1，不包括0和1 (★★☆)(提示: np.linspace)
Z = np.linspace(0, 1, 12, endpoint=True)[1: -1]
print (Z)
40. 創(chuàng)建一個(gè)大小為10的隨機(jī)向量，并把它排序 (★★☆)(提示: sort)Z = np.random.random(10)
Z.sort()
print (Z)
41. 對(duì)一個(gè)小數(shù)組進(jìn)行求和有沒(méi)有辦法比np.sum更快? (★★☆)(提示: np.add.reduce)
# Author: Evgeni Burovski
Z = np.arange(10)
np.add.reduce(Z)
# np.add.reduce 是numpy.add模塊中的一個(gè)ufunc(universal function)函數(shù),C語(yǔ)言實(shí)現(xiàn)
42. 如何判斷兩和隨機(jī)數(shù)組相等 (★★☆)(提示: np.allclose, np.array_equal)A = np.random.randint(0, 2, 5)
B = np.random.randint(0, 2, 5)
# 假設(shè)array的形狀(shape)相同和一個(gè)誤差容限（tolerance）
equal = np.allclose(A,B)
print(equal)
# 檢查形狀和元素值，沒(méi)有誤差容限（值必須完全相等）
equal = np.array_equal(A,B)
print(equal)
43. 把數(shù)組變?yōu)橹蛔x (★★☆)(提示: flags.writeable)
Z = np.zeros(5)
Z.flags.writeable = False
Z[0] = 1
44. 將一個(gè)10x2的笛卡爾坐標(biāo)矩陣轉(zhuǎn)換為極坐標(biāo) (★★☆)(提示: np.sqrt, np.arctan2)Z = np.random.random((10, 2))
X, Y = Z[:, 0], Z[:, 1]
R = np.sqrt(X**2 + Y**2)
T = np.arctan2(Y, X)
print (R)
print (T)
45. 創(chuàng)建一個(gè)大小為10的隨機(jī)向量并且將該向量中最大的值替換為0(★★☆)(提示: argmax)
Z = np.random.random(10)
Z[Z.argmax()] = 0
print (Z)
46. 創(chuàng)建一個(gè)結(jié)構(gòu)化數(shù)組，其中x和y坐標(biāo)覆蓋[0, 1]x[1, 0]區(qū)域 (★★☆)(提示: np.meshgrid)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)
47. 給定兩個(gè)數(shù)組X和Y，構(gòu)造柯西(Cauchy)矩陣C () (★★☆)(提示: np.subtract.outer)
# Author: Evgeni Burovski
X = np.arange(8)
Y = X + 0.5
C = 1.0 / np.subtract.outer(X, Y)
print (C)
print(np.linalg.det(C)) # 計(jì)算行列式
48. 打印每個(gè)numpy 類型的最小和最大可表示值 (★★☆)(提示: np.iinfo, np.finfo, eps)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)
49. 如何打印數(shù)組中所有的值？(★★☆)(提示: np.set_printoptions)
np.set_printoptions(threshold=np.nan)
Z = np.zeros((16,16))
print(Z)
50. 如何在數(shù)組中找到與給定標(biāo)量接近的值? (★★☆)(提示: argmin)Z = np.arange(100)
v = np.random.uniform(0, 100)
index = (np.abs(Z-v)).argmin()
print(Z[index])
51. 創(chuàng)建表示位置(x, y)和顏色(r, g, b, a)的結(jié)構(gòu)化數(shù)組 (★★☆)(提示: dtype)
Z = np.zeros(10, [('position', [('x', float, 1),
('y', float, 1)]),
('color', [('r', float, 1),
('g', float, 1),
('b', float, 1)])])
print (Z)
52. 思考形狀為(100, 2)的隨機(jī)向量，求出點(diǎn)與點(diǎn)之間的距離 (★★☆)(提示: np.atleast_2d, T, np.sqrt)Z = np.random.random((100, 2))
X, Y = np.atleast_2d(Z[:, 0], Z[:, 1])
D = np.sqrt((X-X.T)**2 + (Y-Y.T)**2)
print (D)
# 使用scipy庫(kù)可以更快
import scipy.spatial
Z = np.random.random((100,2))
D = scipy.spatial.distance.cdist(Z,Z)
print(D)
53. 如何將類型為float(32位)的數(shù)組類型轉(zhuǎn)換位integer(32位)? (★★☆)(提示: astype(copy=False))
Z = np.arange(10, dtype=np.int32)
Z = Z.astype(np.float32, copy=False)
print(Z)
54. 如何讀取下面的文件? (★★☆)(提示: np.genfromtxt)1, 2, 3, 4, 5
6, , , 7, 8
, , 9,10,11
# 先把上面保存到文件example.txt中
# 這里不使用StringIO， 因?yàn)镻ython2 和Python3 在這個(gè)地方有兼容性問(wèn)題
Z = np.genfromtxt('example.txt', delimiter=',')
print(Z)
55. numpy數(shù)組枚舉(enumerate)的等價(jià)操作? (★★☆)(提示: np.ndenumerate, np.ndindex)
Z = np.arange(9).reshape(3,3)
for index, value in np.ndenumerate(Z):
print(index, value)
for index in np.ndindex(Z.shape):
print(index, Z[index])
56. 構(gòu)造一個(gè)二維高斯矩陣(★★☆)(提示: np.meshgrid, np.exp)X, Y = np.meshgrid(np.linspace(-1, 1, 10), np.linspace(-1, 1, 10))
D = np.sqrt(X**2 + Y**2)
sigma, mu = 1.0, 0.0
G = np.exp(-( (D-mu)**2 / (2.0*sigma**2) ))
print (G)
57. 如何在二維數(shù)組的隨機(jī)位置放置p個(gè)元素? (★★☆)(提示: np.put, np.random.choice)
# Author: Divakar
n = 10
p = 3
Z = np.zeros((n,n))
np.put(Z, np.random.choice(range(n*n), p, replace=False),1)
print(Z)
58. 減去矩陣每一行的平均值 (★★☆)(提示: mean(axis=,keepdims=))# Author: Warren Weckesser
X = np.random.rand(5, 10)
# 新
Y = X - X.mean(axis=1, keepdims=True)
# 舊
Y = X - X.mean(axis=1).reshape(-1, 1)
print(Y)
59. 如何對(duì)數(shù)組通過(guò)第n列進(jìn)行排序? (★★☆)(提示: argsort)
# Author: Steve Tjoa
Z = np.random.randint(0,10,(3,3))
print(Z)
print(Z[ Z[:,1].argsort() ])
60. 如何判斷一個(gè)給定的二維數(shù)組存在空列? (★★☆)(提示: any, ~)# Author: Warren Weckesser
Z = np.random.randint(0,3,(3,10))
print((~Z.any(axis=0)).any())
61. 從數(shù)組中找出與給定值最接近的值 (★★☆)(提示: np.abs, argmin, flat)
Z = np.random.uniform(0,1,10)
z = 0.5
m = Z.flat[np.abs(Z - z).argmin()]
print(m)
62. 思考形狀為(1, 3)和(3, 1)的兩個(gè)數(shù)組形狀，如何使用迭代器計(jì)算它們的和? (★★☆)(提示: np.nditer)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])
63. 創(chuàng)建一個(gè)具有name屬性的數(shù)組類 (★★☆)(提示: class method)
class NameArray(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 = NameArray(np.arange(10), 'range_10')
print (Z.name)
64. 給定一個(gè)向量，如何讓在第二個(gè)向量索引的每個(gè)元素加1(注意重復(fù)索引)? (★★★)(提示: np.bincount | np.add.at)# Author: Brett Olsen
Z = np.ones(10)
I = np.random.randint(0,len(Z),20)
Z += np.bincount(I, minlength=len(Z))
print(Z)
# Another solution
# Author: Bartosz Telenczuk
np.add.at(Z, I, 1)
print(Z)
65. 如何根據(jù)索引列表I將向量X的元素累加到數(shù)組F? (★★★)(提示: np.bincount)
# Author: Alan G Isaac
X = [1,2,3,4,5,6]
I = [1,3,9,3,4,1]
F = np.bincount(I,X)
print(F)
66. 思考(dtype = ubyte)的(w, h, 3)圖像，計(jì)算唯一顏色的值(★★★)(提示: np.unique)# Author: Nadav Horesh
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(np.unique(I))
67. 思考如何求一個(gè)四維數(shù)組最后兩個(gè)軸的數(shù)據(jù)和(★★★)(提示: sum(axis=(-2,-1)))
A = np.random.randint(0,10,(3,4,3,4))
# 傳遞一個(gè)元組(numpy 1.7.0)
sum = A.sum(axis=(-2,-1))
print(sum)
# 將最后兩個(gè)維度壓縮為一個(gè)
# (適用于不接受軸元組參數(shù)的函數(shù))
sum = A.reshape(A.shape[:-2] + (-1,)).sum(axis=-1)
print(sum)
68. 考慮一維向量D，如何使用相同大小的向量S來(lái)計(jì)算D的子集的均值，其描述子集索引？(★★★)(提示: np.bincount)# Author: Jaime Fernández del Río
D = np.random.uniform(0,1,100)
S = np.random.randint(0,10,100)
D_sums = np.bincount(S, weights=D)
D_counts = np.bincount(S)
D_means = D_sums / D_counts
print(D_means)
# Pandas solution as a reference due to more intuitive code
import pandas as pd
print(pd.Series(D).groupby(S).mean())
69. 如何獲得點(diǎn)積的對(duì)角線？(★★★)(提示: np.diag)
# Author: Mathieu Blondel
A = np.random.uniform(0,1,(5,5))
B = np.random.uniform(0,1,(5,5))
# Slow version
np.diag(np.dot(A, B))
# Fast version
np.sum(A * B.T, axis=1)
# Faster version
np.einsum('ij,ji->i', A, B)
70.考慮向量[1,2,3,4,5]，如何建立一個(gè)新的向量，在每個(gè)值之間交錯(cuò)有3個(gè)連續(xù)的零？(★★★)(提示: array[::4])# Author: Warren Weckesser
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)
71. 考慮一個(gè)維度(5,5,3)的數(shù)組，如何將其與一個(gè)(5,5)的數(shù)組相乘？(★★★)(提示: array[:, :, None])
A = np.ones((5,5,3))
B = 2*np.ones((5,5))
print(A * B[:,:,None])
72. 如何對(duì)一個(gè)數(shù)組中任意兩行做交換? (★★★)(提示: array[[]] = array[[]])# Author: Eelco Hoogendoorn
A = np.arange(25).reshape(5,5)
A[[0,1]] = A[[1,0]]
print(A)
73. 思考描述10個(gè)三角形（共享頂點(diǎn)）的一組10個(gè)三元組，找到組成所有三角形的唯一線段集 (★★★)(提示: repeat, np.roll, np.sort, view, np.unique)
# Author: Nicolas P. Rougier
faces = np.random.randint(0,100,(10,3))
F = np.roll(faces.repeat(2,axis=1),-1,axis=1)
F = F.reshape(len(F)*3,2)
F = np.sort(F,axis=1)
G = F.view( dtype=[('p0',F.dtype),('p1',F.dtype)] )
G = np.unique(G)
print(G)
74. 給定一個(gè)二進(jìn)制的數(shù)組C，如何生成一個(gè)數(shù)組A滿足np.bincount(A)==C? (★★★)(提示: np.repeat)# Author: Jaime Fernández del Río
C = np.bincount([1,1,2,3,4,4,6])
A = np.repeat(np.arange(len(C)), C)
print(A)
75. 如何通過(guò)滑動(dòng)窗口計(jì)算一個(gè)數(shù)組的平均數(shù)? (★★★)(提示: np.cumsum)
# Author: Jaime Fernández del Río
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))
76. 思考以為數(shù)組Z，構(gòu)建一個(gè)二維數(shù)組，其第一行是(Z[0],Z[1],Z[2])， 然后每一行移動(dòng)一位，最后一行為 (Z[-3],Z[-2],Z[-1]) (★★★)(提示: from numpy.lib import stride_tricks)# Author: Joe Kington / Erik Rigtorp
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)
77. 如何對(duì)布爾值取反，或改變浮點(diǎn)數(shù)的符號(hào)(sign)? (★★★)(提示: np.logical_not, np.negative)
# Author: Nathaniel J. Smith
Z = np.random.randint(0,2,100)
np.logical_not(Z, out=Z)
Z = np.random.uniform(-1.0,1.0,100)
np.negative(Z, out=Z)
78. 思考兩組點(diǎn)集P0和P1去描述一組線(二維)和一個(gè)點(diǎn)p,如何計(jì)算點(diǎn)p到每一條線 i (P0[i],P1[i])的距離？(★★★)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))
79. 考慮兩組點(diǎn)集P0和P1去描述一組線(二維)和一組點(diǎn)集P，如何計(jì)算每一個(gè)點(diǎn) j(P[j]) 到每一條線 i (P0[i],P1[i])的距離? (★★★)
# Author: Italmassov Kuanysh
# based on distance function from previous question
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]))
80. 思考一個(gè)任意的數(shù)組，編寫一個(gè)函數(shù)，該函數(shù)提取一個(gè)具有固定形狀的子部分，并以一個(gè)給定的元素為中心(在該部分填充值) (★★★)(提示: minimum, maximum)# Author: Nicolas Rougier
Z = np.random.randint(0,10,(10,10))
shape = (5,5)
fill = 0
position = (1,1)
R = np.ones(shape, dtype=Z.dtype)*fill
P = np.array(list(position)).astype(int)
Rs = np.array(list(R.shape)).astype(int)
Zs = np.array(list(Z.shape)).astype(int)R_start = np.zeros((len(shape),)).astype(int)
R_stop = np.array(list(shape)).astype(int)
Z_start = (P-Rs//2)
Z_stop = (P+Rs//2)+Rs%2
R_start = (R_start - np.minimum(Z_start,0)).tolist()
Z_start = (np.maximum(Z_start,0)).tolist()
R_stop = np.maximum(R_start, (R_stop - np.maximum(Z_stop-Zs,0))).tolist()
Z_stop = (np.minimum(Z_stop,Zs)).tolist()
r = [slice(start,stop) for start,stop in zip(R_start,R_stop)]
z = [slice(start,stop) for start,stop in zip(Z_start,Z_stop)]
R[r] = Z[z]
print(Z)
print(R)
81. 考慮一個(gè)數(shù)組Z = [1,2,3,4,5,6,7,8,9,10,11,12,13,14],如何生成一個(gè)數(shù)組R = [[1,2,3,4], [2,3,4,5], [3,4,5,6], ...,[11,12,13,14]]? (★★★)(提示: stride_tricks.as_strided)
# Author: Stefan van der Walt
Z = np.arange(1,15,dtype=np.uint32)
R = stride_tricks.as_strided(Z,(11,4),(4,4))
print(R)
82. 計(jì)算矩陣的秩 (★★★)(提示: np.linalg.svd)# Author: Stefan van der Walt
Z = np.random.uniform(0,1,(10,10))
U, S, V = np.linalg.svd(Z) # Singular Value Decomposition
rank = np.sum(S > 1e-10)
print(rank)
83. 如何找出數(shù)組中出現(xiàn)頻率最高的值?(★★★)(提示: np.bincount, argmax)
Z = np.random.randint(0,10,50)
print(np.bincount(Z).argmax())
84. 從一個(gè)10x10的矩陣中提取出連續(xù)的3x3區(qū)塊(★★★)(提示: stride_tricks.as_strided)# Author: Chris Barker
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)
85.創(chuàng)建一個(gè)滿足 Z[i,j] == Z[j,i]的二維數(shù)組子類 (★★★)(提示: class method)
# Author: Eric O. Lebigot
# Note: only works for 2d array and value setting using indices
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)
86. 考慮p個(gè) nxn 矩陣和一組形狀為(n,1)的向量，如何直接計(jì)算p個(gè)矩陣的乘積(n,1)? (★★★)(提示: np.tensordot)# Author: Stefan van der Walt
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)
# It works, because:
# M is (p,n,n)
# V is (p,n,1)
# Thus, summing over the paired axes 0 and 0 (of M and V independently),
# and 2 and 1, to remain with a (n,1) vector.
87. 對(duì)于一個(gè)16x16的數(shù)組，如何得到一個(gè)區(qū)域的和(區(qū)域大小為4x4)? (★★★)(提示: np.add.reduceat)
# Author: Robert Kern
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)
88. 如何利用numpy數(shù)組實(shí)現(xiàn)Game of Life? (★★★)(提示: Game of Life , Game of Life有哪些圖形？)# Author: Nicolas Rougier
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)
89. 如何找到一個(gè)數(shù)組的第n個(gè)最大值? (★★★)(提示: np.argsort | np.argpartition)
Z = np.arange(10000)
np.random.shuffle(Z)
n = 5
# Slow
print (Z[np.argsort(Z)[-n:]])
# Fast
print (Z[np.argpartition(-Z,n)[:n]])
90. 給定任意個(gè)數(shù)向量，創(chuàng)建笛卡爾積(每一個(gè)元素的每一種組合) (★★★)(提示: np.indices)# Author: Stefan Van der Walt
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])))
91. 如何從一個(gè)常規(guī)數(shù)組中創(chuàng)建記錄數(shù)組(record array)? (★★★)(提示: 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)
92. 思考一個(gè)大向量Z, 用三種不同的方法計(jì)算它的立方 (★★★)(提示: np.power, *, np.einsum)# Author: Ryan G.
x = np.random.rand(5e7)
%timeit np.power(x,3)
%timeit x*x*x
%timeit np.einsum('i,i,i->i',x,x,x)
93. 考慮兩個(gè)形狀分別為(8,3) 和(2,2)的數(shù)組A和B. 如何在數(shù)組A中找到滿足包含B中元素的行？(不考慮B中每行元素順序)？(★★★)(提示: np.where)
# Author: Gabe Schwartz
A = np.random.randint(0,5,(8,3))
B = np.random.randint(0,5,(2,2))
C = (A[..., np.newaxis, np.newaxis] == B)
rows = np.where(C.any((3,1)).all(1))[0]
print(rows)
94. 思考一個(gè)10x3的矩陣，如何分解出有不全相同值的行 (如 [2,2,3]) (★★★)# Author: Robert Kern
Z = np.random.randint(0,5,(10,3))
print(Z)
# solution for arrays of all dtypes (including string arrays and record arrays)
E = np.all(Z[:,1:] == Z[:,:-1], axis=1)
U = Z[~E]
print(U)
# soluiton for numerical arrays only, will work for any number of columns in Z
U = Z[Z.max(axis=1) != Z.min(axis=1),:]
print(U)
95. 將一個(gè)整數(shù)向量轉(zhuǎn)換為二進(jìn)制矩陣 (★★★)(提示: np.unpackbits)
# Author: Warren Weckesser
I = np.array([0, 1, 2, 3, 15, 16, 32, 64, 128])
B = ((I.reshape(-1,1) & (2**np.arange(8))) != 0).astype(int)
print(B[:,::-1])
# Author: Daniel T. McDonald
I = np.array([0, 1, 2, 3, 15, 16, 32, 64, 128], dtype=np.uint8)
print(np.unpackbits(I[:, np.newaxis], axis=1))
96. 給定一個(gè)二維數(shù)組，如何提取出唯一的行?(★★★)(提示: np.ascontiguousarray)# Author: Jaime Fernández del Río
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)
97. 考慮兩個(gè)向量A和B，寫出用einsum等式對(duì)應(yīng)的inner, outer, sum, mul函數(shù) (★★★)(提示: np.einsum)
# Author: Alex Riley
# Make sure to read: http://ajcr.net/Basic-guide-to-einsum/
A = np.random.uniform(0,1,10)
B = np.random.uniform(0,1,10)
np.einsum('i->', A) # np.sum(A)
np.einsum('i,i->i', A, B) # A * B
np.einsum('i,i', A, B) # np.inner(A, B)
np.einsum('i,j->ij', A, B) # np.outer(A, B)
98. 考慮一個(gè)由兩個(gè)向量描述的路徑(X,Y)，如何用等距樣例(equidistant samples)對(duì)其進(jìn)行采樣(sample)(★★★)?(提示: np.cumsum, np.interp)# Author: Bas Swinckels
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)
99. 給定一個(gè)整數(shù)n 和一個(gè)二維數(shù)組X，從X中選擇可以被解釋為從多n度的多項(xiàng)分布式的行，即這些行只包含整數(shù)對(duì)n的和. (★★★)(提示: np.logical_and.reduce, np.mod)
# Author: Evgeni Burovski
X = np.asarray([[1.0, 0.0, 3.0, 8.0],
[2.0, 0.0, 1.0, 1.0],
[1.5, 2.5, 1.0, 0.0]])
n = 4
M = np.logical_and.reduce(np.mod(X, 1) == 0, axis=-1)
M &= (X.sum(axis=-1) == n)
print(X[M])
100. 對(duì)于一個(gè)一維數(shù)組X，計(jì)算它boostrapped之后的95%置信區(qū)間的平均值. (★★★)(提示: np.percentile)# Author: Jessica B. Hamrick
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)
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