100道測試題，輕松玩轉python的Numpy子產品！

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Numpy是Python做資料分析所必須要掌握的基礎庫之一。以下為入門Numpy的100題小練習，原為github上的開源項目，由和鲸社群的小科翻譯并整理（保留了部分原文作為參考）。受限于篇幅，小編在這裡隻提供了部分題目的運作結果。友情提示：代碼雖好，自己動手才算學到。

1. 導入numpy庫并簡寫為 np (★☆☆)

(提示: import … as …)

import numpy as np           

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2. 列印numpy的版本和配置說明 (★☆☆)

(提示: np.version, np.show_config)

print(np.__version__)
np.show_config()           

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3. 建立一個長度為10的空向量 (★☆☆)

(提示: np.zeros)

Z = np.zeros(10)
print(Z)           

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4. 如何找到任何一個數組的記憶體大小？(★☆☆)

(提示: size, itemsize)

Z = np.zeros((10,10))
print("%d bytes" % (Z.size * Z.itemsize))           

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5. 如何從指令行得到numpy中add函數的說明文檔? (★☆☆)

(提示: np.info)

numpy.info(numpy.add)           

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add(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])

6. 建立一個長度為10并且除了第五個值為1的空向量 (★☆☆)

(提示: array[4])

Z = np.zeros(10)
Z[4] = 1
print(Z)           

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7. 建立一個值域範圍從10到49的向量(★☆☆)

(提示: np.arange)

Z = np.arange(10,50)
print(Z)           

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8. 反轉一個向量(第一個元素變為最後一個) (★☆☆)

(提示: array[::-1])

Z = np.arange(50)
Z = Z[::-1]
print(Z)           

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9. 建立一個 3x3 并且值從0到8的矩陣(★☆☆)

(提示: reshape)

Z = np.arange(9).reshape(3,3)
print(Z)           

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10. 找到數組[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)           

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11. 建立一個 3x3 的機關矩陣 (★☆☆)

(提示: np.eye)

Z = np.eye(3)
print(Z)           

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12. 建立一個 3x3x3的随機數組 (★☆☆)

(提示: np.random.random)

Z = np.random.random((3,3,3))
print(Z)           

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13. 建立一個 10x10 的随機數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)           

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14. 建立一個長度為30的随機向量并找到它的平均值 (★☆☆)

(提示: mean)

Z = np.random.random(30)
m = Z.mean()
print(m)           

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15. 建立一個二維數組，其中邊界值為1，其餘值為0 (★☆☆)

(提示: array[1:-1, 1:-1])

Z = np.ones((10,10))
Z[1:-1,1:-1] = 0
print(Z)           

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16. 對于一個存在在數組，如何添加一個用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)           

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17. 以下表達式運作的結果分别是什麼? (★☆☆)

(提示: NaN = not a number, inf = infinity)

0 * np.nan

np.nan == np.nan

np.inf > np.nan

np.nan - np.nan

0.3 == 3 * 0.1

print(0 * np.nan)
print(np.nan == np.nan)
print(np.inf > np.nan)
print(np.nan - np.nan)
print(0.3 == 3 * 0.1)           

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18. 建立一個 5x5的矩陣，并設定值1,2,3,4落在其對角線下方位置 (★☆☆)

(提示: np.diag)

Z = np.diag(1+np.arange(4),k=-1)
print(Z)           

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19. 建立一個8x8 的矩陣，并且設定成棋盤樣式 (★☆☆)

(提示: array[::2])

Z = np.zeros((8,8),dtype=int)
Z[1::2,::2] = 1
Z[::2,1::2] = 1
print(Z)           

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20. 考慮一個 (6,7,8) 形狀的數組，其第100個元素的索引(x,y,z)是什麼?

(提示: np.unravel_index)

print(np.unravel_index(100,(6,7,8)))           

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21. 用tile函數去建立一個 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)           

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22. 對一個5x5的随機矩陣做歸一化(★☆☆)

(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)           

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23. 建立一個将顔色描述為(RGBA)四個無符号位元組的自定義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           

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24. 一個5x3的矩陣與一個3x2的矩陣相乘，實矩陣乘積是什麼？(★☆☆)

(提示: np.dot | @)

Z = np.dot(np.ones((5,3)), np.ones((3,2)))
print(Z)           

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25. 給定一個一維數組，對其在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)           

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26. 下面腳本運作後的結果是什麼? (★☆☆)

(提示: np.sum)

print(sum(range(5),-1))

from numpy import *

print(sum(range(5),-1))

print(sum(range(5),-1))
from numpy import *
print(sum(range(5),-1))           

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27. 考慮一個整數向量Z,下清單達合法的是哪個? (★☆☆)

Z**Z

2 << Z >> 2

Z <- Z 1j*Z Z/1/1 ZZ

Z = np.arange(5)
Z ** Z  # legal           

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array([ 1, 1, 4, 27, 256])

Z = np.arange(5)
2 << Z >> 2  # false           

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array([0, 1, 2, 4, 8])

Z = np.arange(5)
Z <- Z   # legal           

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array([False, False, False, False, False])

Z = np.arange(5)
1j*Z   # legal           

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array([0.+0.j, 0.+1.j, 0.+2.j, 0.+3.j, 0.+4.j])

Z = np.arange(5)
Z/1/1   # legal           

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array([0., 1., 2., 3., 4.])

Z = np.arange(5)
Z<Z>Z    # false           

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ValueError: The truth value of an array with more than one element is ambiguous. Use a.any() or a.all()

28. 下清單達式的結果分别是什麼?(★☆☆)

np.array(0) / np.array(0)

np.array(0) // np.array(0)

np.array([np.nan]).astype(int).astype(float)

print(np.array(0) / np.array(0))
print(np.array(0) // np.array(0))
print(np.array([np.nan]).astype(int).astype(float))           

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29. 如何從零位對浮點數組做舍入 ? (★☆☆)

(提示: np.uniform, np.copysign, np.ceil, np.abs)

Z = np.random.uniform(-10,+10,10)
print (np.copysign(np.ceil(np.abs(Z)), Z))           

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30. 如何找到兩個數組中的共同元素? (★☆☆)

(提示: np.intersect1d)

Z1 = np.random.randint(0,10,10)
Z2 = np.random.randint(0,10,10)
print(np.intersect1d(Z1,Z2))           

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31. 如何忽略所有的 numpy 警告(盡管不建議這麼做)? (★☆☆)

(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)           

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An equivalent way, with a context manager:

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

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32. 下面的表達式是正确的嗎? (★☆☆)

(提示: imaginary number)

np.sqrt(-1) == np.emath.sqrt(-1)

np.sqrt(-1) == np.emath.sqrt(-1)             

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False

33. 如何得到昨天，今天，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')
print ("Yesterday is " + str(yesterday))
print ("Today is " + str(today))
print ("Tomorrow is "+ str(tomorrow))           

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34. 如何得到所有與2016年7月對應的日期？(★★☆)

(提示: np.arange(dtype=datetime64['D']))

Z = np.arange('2016-07', '2016-08', dtype='datetime64[D]')
print(Z)           

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35. 如何直接在位計算(A+B)*(-A/2)(不建立副本)? (★★☆)

(提示: np.add(out=), np.negative(out=), np.multiply(out=), np.divide(out=))

A = np.ones(3)*1
B = np.ones(3)*2
C = np.ones(3)*3
np.add(A,B,out=B)
np.divide(A,2,out=A)
np.negative(A,out=A)
np.multiply(A,B,out=A)           

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array([-1.5, -1.5, -1.5])

36. 用五種不同的方法去提取一個随機數組的整數部分(★★☆)

(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.ceil(Z)-1)
print (Z.astype(int))
print (np.trunc(Z))           

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37. 建立一個5x5的矩陣，其中每行的數值範圍從0到4 (★★☆)

(提示: np.arange)

Z = np.zeros((5,5))
Z += np.arange(5)
print (Z)           

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38. 通過考慮一個可生成10個整數的函數，來建構一個數組(★☆☆)

(提示: np.fromiter)

def generate():
    for x in range(10):
        yield x
Z = np.fromiter(generate(),dtype=float,count=-1)
print (Z)           

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[0. 1. 2. 3. 4. 5. 6. 7. 8. 9.]

39. 建立一個長度為10的随機向量，其值域範圍從0到1，但是不包括0和1 (★★☆)

(提示: np.linspace)

Z = np.linspace(0,1,11,endpoint=False)[1:]
print (Z)           

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40. 建立一個長度為10的随機向量，并将其排序 (★★☆)

(提示: sort)

Z = np.random.random(10)
Z.sort()
print (Z)           

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41.對于一個小數組，如何用比 np.sum更快的方式對其求和？(★★☆)

(提示: np.add.reduce)

Z = np.arange(10)
np.add.reduce(Z)           

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42. 對于兩個随機數組A和B，檢查它們是否相等(★★☆)

(提示: np.allclose, np.array_equal)

A = np.random.randint(0,2,5)
B = np.random.randint(0,2,5)
# Assuming identical shape of the arrays and a tolerance for the comparison of values
equal = np.allclose(A,B)
print(equal)           

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False

# 方法2
# Checking both the shape and the element values, no tolerance (values have to be exactly equal)
equal = np.array_equal(A,B)
print(equal)           

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False

43. 建立一個隻讀數組(read-only) (★★☆)

(提示: flags.writeable)

# 使用如下過程實作
Z = np.zeros(10)
Z.flags.writeable = False
Z[0] = 1           

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44. 将笛卡爾坐标下的一個10x2的矩陣轉換為極坐标形式(★★☆)

(hint: 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)           

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45. 建立一個長度為10的向量，并将向量中最大值替換為1 (★★☆)

(提示: argmax)

Z = np.random.random(10)
Z[Z.argmax()] = 0
print (Z)           

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46. 建立一個結構化數組，并實作 x 和 y 坐标覆寫 [0,1]x[0,1] 區域 (★★☆)

(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)           

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47. 給定兩個數組X和Y，構造Cauchy矩陣C (Cij =1/(xi - yj))

(提示: np.subtract.outer)

X = np.arange(8)
Y = X + 0.5
C = 1.0 / np.subtract.outer(X, Y)
print(np.linalg.det(C))           

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48. 列印每個numpy标量類型的最小值和最大值？(★★☆)

(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)           

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49. 如何列印一個數組中的所有數值? (★★☆)

(提示: np.set_printoptions)

np.set_printoptions(threshold=np.nan)
Z = np.zeros((16,16))
print (Z)           

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50. 給定标量時，如何找到數組中最接近标量的值？(★★☆)

(提示: argmin)

Z = np.arange(100)
v = np.random.uniform(0,100)
index = (np.abs(Z-v)).argmin()
print (Z[index])           

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51. 建立一個表示位置(x,y)和顔色(r,g,b)的結構化數組(★★☆)

(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)           

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52. 對一個表示坐标形狀為(100,2)的随機向量，找到點與點的距離(★★☆)

(提示: np.atleast_2d, T, np.sqrt)

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)           

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# 方法2
# Much faster with scipy
import scipy
# Thanks Gavin Heverly-Coulson (#issue 1)
import scipy.spatial
D = scipy.spatial.distance.cdist(Z,Z)
print (D)           

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53. 如何将32位的浮點數(float)轉換為對應的整數(integer)?

(提示: astype(copy=False))

Z = np.arange(10, dtype=np.int32)
Z = Z.astype(np.float32, copy=False)
print (Z)           

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54. 如何讀取以下檔案? (★★☆)

(提示: np.genfromtxt)

1, 2, 3, 4, 5
6,  ,  , 7, 8
 ,  , 9,10,11           

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參考連結：https://docs.scipy.org/doc/numpy-1.13.0/reference/generated/numpy.genfromtxt.html

55. 對于numpy數組，enumerate的等價操作是什麼？(★★☆)

(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])           

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56. 生成一個通用的二維Gaussian-like數組 (★★☆)

(提示: np.meshgrid, np.exp)

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)           

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57. 對一個二維數組，如何在其内部随機放置p個元素? (★★☆)

(提示: np.put, np.random.choice)

n = 10
p = 3
Z = np.zeros((n,n))
np.put(Z, np.random.choice(range(n*n), p, replace=False),1)
print (Z)           

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58. 減去一個矩陣中的每一行的平均值 (★★☆)

(提示: mean(axis=,keepdims=))

X = np.random.rand(5, 10)
# Recent versions of numpy
Y = X - X.mean(axis=1, keepdims=True)
print(Y)           

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# 方法2
# Older versions of numpy
Y = X - X.mean(axis=1).reshape(-1, 1)
print (Y)           

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59. 如何通過第n列對一個數組進行排序? (★★☆)

(提示: argsort)

Z = np.random.randint(0,10,(3,3))
print (Z)
print (Z[Z[:,1].argsort()])           

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60. 如何檢查一個二維數組是否有空列？(★★☆)

(提示: any, ~)

Z = np.random.randint(0,3,(3,10))
print ((~Z.any(axis=0)).any())           

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True

61. 從數組中的給定值中找出最近的值 (★★☆)

(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)           

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0.5531249196891759

62. 如何用疊代器(iterator)計算兩個分别具有形狀(1,3)和(3,1)的數組? (★★☆)

(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])           

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63. 建立一個具有name屬性的數組類(★★☆)

(提示: class方法)

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)           

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range_10

64. 考慮一個給定的向量，如何對由第二個向量索引的每個元素加1(小心重複的索引)? (★★★)

(提示: np.bincount | np.add.at)

Z = np.ones(10)
I = np.random.randint(0,len(Z),20)
Z += np.bincount(I, minlength=len(Z))
print(Z)           

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[3. 1. 5. 4. 3. 4. 2. 1. 4. 3.]

# 方法2
np.add.at(Z, I, 1)
print(Z)           

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[5. 1. 9. 7. 5. 7. 3. 1. 7. 5.]

65. 根據索引清單(I)，如何将向量(X)的元素累加到數組(F)? (★★★)

(提示: np.bincount)

X = [1,2,3,4,5,6]
I = [1,3,9,3,4,1]
F = np.bincount(I,X)
print (F)           

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[0. 7. 0. 6. 5. 0. 0. 0. 0. 3.]

66. 考慮一個(dtype=ubyte) 的 (w,h,3)圖像，計算其唯一顔色的數量(★★★)

(提示: np.unique)

w,h = 16,16
I = np.random.randint(0,2,(h,w,3)).astype(np.ubyte)
#Note that we should compute 256*256 first. 
#Otherwise numpy will only promote F.dtype to 'uint16' and overfolw will occur
F = I[...,0]*(256*256) + I[...,1]*256 +I[...,2]
n = len(np.unique(F))
print (n)           

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8

67. 考慮一個四維數組，如何一次性計算出最後兩個軸(axis)的和？(★★★)

(提示: sum(axis=(-2,-1)))

A = np.random.randint(0,10,(3,4,3,4))
# solution by passing a tuple of axes (introduced in numpy 1.7.0)
sum = A.sum(axis=(-2,-1))
print (sum)

# 方法2
sum = A.reshape(A.shape[:-2] + (-1,)).sum(axis=-1)
print (sum)           

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68. 考慮一個一維向量D，如何使用相同大小的向量S來計算D子集的均值？(★★★)

(提示: np.bincount)

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)           

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# 方法2
import pandas as pd
print(pd.Series(D).groupby(S).mean())           

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69. 如何獲得點積 dot prodcut的對角線? (★★★)

(提示: np.diag)

A = np.random.uniform(0,1,(5,5))
B = np.random.uniform(0,1,(5,5))
# slow version
np.diag(np.dot(A, B))

# 方法2
# Fast version
np.sum(A * B.T, axis=1)

# 方法3
# Faster version
np.einsum("ij,ji->i", A, B)           

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70. 考慮一個向量[1,2,3,4,5],如何建立一個新的向量，在這個新向量中每個值之間有3個連續的零？(★★★)

(提示: array[::4])

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)           

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[1. 0. 0. 0. 2. 0. 0. 0. 3. 0. 0. 0. 4. 0. 0. 0. 5.]

71. 考慮一個次元(5,5,3)的數組，如何将其與一個(5,5)的數組相乘？(★★★)

(提示: array[:, :, None])

A = np.ones((5,5,3))
B = 2*np.ones((5,5))
print (A * B[:,:,None])           

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72. 如何對一個數組中任意兩行做交換? (★★★)

(提示: array[[]] = array[[]])

A = np.arange(25).reshape(5,5)
A[[0,1]] = A[[1,0]]
print (A)           

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73. 考慮一個可以描述10個三角形的triplets，找到可以分割全部三角形的line segment

Consider a set of 10 triplets describing 10 triangles (with shared vertices), find the set of unique line segments composing all the triangles (★★★)

(提示: repeat, np.roll, np.sort, view, np.unique)

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)           

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74. 給定一個二進制的數組C，如何産生一個數組A滿足np.bincount(A)==C(★★★)

(提示: np.repeat)

C = np.bincount([1,1,2,3,4,4,6])
A = np.repeat(np.arange(len(C)), C)
print (A)           

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[1 1 2 3 4 4 6]

75. 如何通過滑動視窗計算一個數組的平均數? (★★★)

(提示: 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))           

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[ 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18.]

76. 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]) (★★★)

(提示: from numpy.lib import stride_tricks)

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)           

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77. 如何對布爾值取反，或者原位(in-place)改變浮點數的符号(sign)？(★★★)

(提示: np.logical_not, np.negative)

Z = np.random.randint(0,2,100)
np.logical_not(Z, out=Z)           

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Z = np.random.uniform(-1.0,1.0,100)
np.negative(Z, out=Z)           

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78. 考慮兩組點集P0和P1去描述一組線(二維)和一個點p,如何計算點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))           

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79.考慮兩組點集P0和P1去描述一組線(二維)和一組點集P，如何計算每一個點 j(P[j]) 到每一條線 i (P0[i],P1[i])的距離？(★★★)

# 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]))           

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80.Consider an arbitrary array, write a function that extract a subpart with a fixed shape and centered on a given element (pad with a fill value when necessary) (★★★)

(hint: minimum, maximum)

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)           

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81. 考慮一個數組Z = [1,2,3,4,5,6,7,8,9,10,11,12,13,14],如何生成一個數組R = [[1,2,3,4], [2,3,4,5], [3,4,5,6], …,[11,12,13,14]]? (★★★)

(提示: stride_tricks.as_strided)

Z = np.arange(1,15,dtype=np.uint32)
R = stride_tricks.as_strided(Z,(11,4),(4,4))
print (R)           

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82. 計算一個矩陣的秩(★★★)

(提示: np.linalg.svd)

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)           

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83. 如何找到一個數組中出現頻率最高的值？

(提示: np.bincount, argmax)

Z = np.random.randint(0,10,50)
print (np.bincount(Z).argmax()           

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84. 從一個10x10的矩陣中提取出連續的3x3區塊(★★★)

(提示: 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)           

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85. 建立一個滿足 Z[i,j] == Z[j,i]的子類 (★★★)

(提示: class 方法)

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)           

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86. 考慮p個 nxn 矩陣和一組形狀為(n,1)的向量，如何直接計算p個矩陣的乘積(n,1)？(★★★)

(提示: 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)           

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87. 對于一個16x16的數組，如何得到一個區域(block-sum)的和(區域大小為4x4)? (★★★)

(提示: 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)           

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88. 如何利用numpy數組實作Game of Life? (★★★)

(提示: 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)           

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89. 如何找到一個數組的第n個最大值? (★★★)

(提示: np.argsort | np.argpartition)

Z = np.arange(10000)
np.random.shuffle(Z)
n = 5

# Slow
print (Z[np.argsort(Z)[-n:]])           

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[9995 9996 9997 9998 9999]

# 方法2
# Fast
print (Z[np.argpartition(-Z,n)[:n]])           

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[9999 9997 9998 9996 9995]

90. 給定任意個數向量，建立笛卡爾積(每一個元素的每一種組合)(★★★)

(提示: 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])))           

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91. 如何從一個正常數組建立記錄數組(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)           

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[(b'Hello', 2.5, 3) (b'World', 3.6, 2)]

92. 考慮一個大向量Z, 用三種不同的方法計算它的立方(★★★)

(提示: np.power, *, np.einsum)

x = np.random.rand()
np.power(x,3)

# 方法2
x*x*x

# 方法3
np.einsum('i,i,i->i',x,x,x)           

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93. 考慮兩個形狀分别為(8,3) 和(2,2)的數組A和B. 如何在數組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)

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)           

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[0 1 4 5 6 7]

94. 考慮一個10x3的矩陣，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)

# 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)           

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# 方法2
# 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)           

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95. 将一個整數向量轉換為matrix binary的表現形式 (★★★)

(提示: np.unpackbits)

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])           

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# 方法2
print (np.unpackbits(I[:, np.newaxis], axis=1))           

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96. 給定一個二維數組，如何提取出唯一的(unique)行?(★★★)

(提示: 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)           

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97. 考慮兩個向量A和B，寫出用einsum等式對應的inner, outer, sum, mul函數(★★★)

(提示: 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)           

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98. 考慮一個由兩個向量描述的路徑(X,Y)，如何用等距樣例(equidistant samples)對其進行采樣(sample)? (★★★)

Considering a path described by two vectors (X,Y), how to sample it using equidistant samples

(提示: 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)           

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99. Given an integer n and a 2D array X, select from X the rows which can be interpreted as draws from a multinomial distribution with n degrees, i.e., the rows which only contain integers and which sum to n. (★★★)

(提示: np.logical_and.reduce, np.mod)

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])           

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[[2. 0. 1. 1.]]

100. 對于一個一維數組X，計算它boostrapped之後的95%置信區間的平均值。

(Compute bootstrapped 95% confidence intervals for the mean of a 1D array X，i.e. resample the elements of an array with replacement N times, compute the mean of each sample, and then compute percentiles over the means). (★★★)

(提示: 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)           

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