100道測試題，帶你玩轉Numpy模組！
- 2020 年 2 月 25 日
- 筆記
題圖：Photo by Tobias Bjørkli from Pexels
Numpy是Python做數據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，由和鯨社區的小科翻譯並整理（保留了部分原文作為參考）。受限於篇幅，小編在這裡只提供了部分題目的運行結果。友情提示：程式碼雖好，自己動手才算學到。
1. 導入numpy庫並簡寫為 np (★☆☆)
(提示: import … as …)
import numpy as np
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()
3. 創建一個長度為10的空向量 (★☆☆)
(提示: np.zeros)
Z = np.zeros(10) print(Z)
4. 如何找到任何一個數組的記憶體大小？(★☆☆)
(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函數的說明文檔? (★☆☆)
(提示: np.info)
numpy.info(numpy.add)
add(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])
6. 創建一個長度為10並且除了第五個值為1的空向量 (★☆☆)
(提示: array[4])
Z = np.zeros(10) Z[4] = 1 print(Z)
7. 創建一個值域範圍從10到49的向量(★☆☆)
(提示: np.arange)
Z = np.arange(10,50) print(Z)
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)
9. 創建一個 3×3 並且值從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. 創建一個 3×3 的單位矩陣 (★☆☆)
(提示: np.eye)
Z = np.eye(3) print(Z)
12. 創建一個 3x3x3的隨機數組 (★☆☆)
(提示: np.random.random)
Z = np.random.random((3,3,3)) print(Z)
13. 創建一個 10×10 的隨機數組並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. 創建一個長度為30的隨機向量並找到它的平均值 (★☆☆)
(提示: mean)
Z = np.random.random(30) m = Z.mean() print(m)
15. 創建一個二維數組，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)
16. 對於一個存在在數組，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)
17. 以下表達式運行的結果分別是什麼? (★☆☆)
(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)
18. 創建一個 5×5的矩陣，並設置值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)
19. 創建一個8×8 的矩陣，並且設置成棋盤樣式 (★☆☆)
(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 (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)))
21. 用tile函數去創建一個 8×8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. 對一個5×5的隨機矩陣做歸一化(★☆☆)
(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)
23. 創建一個將顏色描述為(RGBA)四個無符號位元組的自定義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
24. 一個5×3的矩陣與一個3×2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)
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)
26. 下面腳本運行後的結果是什麼? (★☆☆)
(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))
27. 考慮一個整數向量Z,下列表達合法的是哪個? (★☆☆)
Z**Z 2 << Z >> 2 Z <- Z 1j*Z Z/1/1 ZZ
Z = np.arange(5) Z ** Z # legal
array([ 1, 1, 4, 27, 256])
Z = np.arange(5) 2 << Z >> 2 # false
array([0, 1, 2, 4, 8])
Z = np.arange(5) Z <- Z # legal
array([False, False, False, False, False])
Z = np.arange(5) 1j*Z # legal
array([0.+0.j, 0.+1.j, 0.+2.j, 0.+3.j, 0.+4.j])
Z = np.arange(5) Z/1/1 # legal
array([0., 1., 2., 3., 4.])
Z = np.arange(5) Z<Z>Z # false
ValueError: The truth value of an array with more than one element is ambiguous. Use a.any() or a.all()
28. 下列表達式的結果分別是什麼?(★☆☆)
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))
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))
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))
31. 如何忽略所有的 numpy 警告(儘管不建議這麼做)? (★☆☆)
(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)
An equivalent way, with a context manager:
with np.errstate(divide='ignore'): Z = np.ones(1) / 0
32. 下面的表達式是正確的嗎? (★☆☆)
(提示: imaginary number)
np.sqrt(-1) == np.emath.sqrt(-1)
np.sqrt(-1) == np.emath.sqrt(-1)
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))
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)
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)
array([-1.5, -1.5, -1.5])
36. 用五種不同的方法去提取一個隨機數組的整數部分(★★☆)
(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))
37. 創建一個5×5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)
38. 通過考慮一個可生成10個整數的函數，來構建一個數組(★☆☆)
(提示: np.fromiter)
def generate(): for x in range(10): yield x Z = np.fromiter(generate(),dtype=float,count=-1) print (Z)
[0. 1. 2. 3. 4. 5. 6. 7. 8. 9.]
39. 創建一個長度為10的隨機向量，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)
40. 創建一個長度為10的隨機向量，並將其排序 (★★☆)
(提示: sort)
Z = np.random.random(10) Z.sort() print (Z)
41.對於一個小數組，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)
42. 對於兩個隨機數組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)
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)
False
43. 創建一個只讀數組(read-only) (★★☆)
(提示: flags.writeable)
# 使用如下過程實現 Z = np.zeros(10) Z.flags.writeable = False Z[0] = 1
44. 將笛卡爾坐標下的一個10×2的矩陣轉換為極坐標形式(★★☆)
(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)
45. 創建一個長度為10的向量，並將向量中最大值替換為1 (★★☆)
(提示: argmax)
Z = np.random.random(10) Z[Z.argmax()] = 0 print (Z)
46. 創建一個結構化數組，並實現 x 和 y 坐標覆蓋 [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)
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))
48. 列印每個numpy標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)
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)
50. 給定標量時，如何找到數組中最接近標量的值？(★★☆)
(提示: argmin)
Z = np.arange(100) v = np.random.uniform(0,100) index = (np.abs(Z-v)).argmin() print (Z[index])
51. 創建一個表示位置(x,y)和顏色(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)
52. 對一個表示坐標形狀為(100,2)的隨機向量，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)
# 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)
53. 如何將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)
54. 如何讀取以下文件? (★★☆)
(提示: np.genfromtxt)
1, 2, 3, 4, 5 6, , , 7, 8 , , 9,10,11
參考鏈接：https://docs.scipy.org/doc/numpy-1.13.0/reference/generated/numpy.genfromtxt.html
55. 對於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])
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)
57. 對一個二維數組，如何在其內部隨機放置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)
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)
# 方法2 # Older versions of numpy Y = X - X.mean(axis=1).reshape(-1, 1) print (Y)
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()])
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())
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)
0.5531249196891759
62. 如何用迭代器(iterator)計算兩個分別具有形狀(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])
63. 創建一個具有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)
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)
[3. 1. 5. 4. 3. 4. 2. 1. 4. 3.]
# 方法2 np.add.at(Z, I, 1) print(Z)
[5. 1. 9. 7. 5. 7. 3. 1. 7. 5.]
65. 根據索引列表(I)，如何將向量(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)
[0. 7. 0. 6. 5. 0. 0. 0. 0. 3.]
66. 考慮一個(dtype=ubyte) 的 (w,h,3)影像，計算其唯一顏色的數量(★★★)
(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)
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)
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)
# 方法2 import pandas as pd print(pd.Series(D).groupby(S).mean())
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)
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)
[1. 0. 0. 0. 2. 0. 0. 0. 3. 0. 0. 0. 4. 0. 0. 0. 5.]
71. 考慮一個維度(5,5,3)的數組，如何將其與一個(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])
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)
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)
74. 給定一個二進位的數組C，如何產生一個數組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)
[1 1 2 3 4 4 6]
75. 如何通過滑動窗口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))
[ 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)
77. 如何對布爾值取反，或者原位(in-place)改變浮點數的符號(sign)？(★★★)
(提示: np.logical_not, np.negative)
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. 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))
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]))
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)
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)
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)
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())
1
84. 從一個10×10的矩陣中提取出連續的3×3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)
85. 創建一個滿足 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)
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)
87. 對於一個16×16的數組，如何得到一個區域(block-sum)的和(區域大小為4×4)? (★★★)
(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)
88. 如何利用numpy數組實現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)
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:]])
[9995 9996 9997 9998 9999]
# 方法2 # Fast print (Z[np.argpartition(-Z,n)[:n]])
[9999 9997 9998 9996 9995]
90. 給定任意個數向量，創建笛卡爾積(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])))
91. 如何從一個正常數組創建記錄數組(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)
[(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)
93. 考慮兩個形狀分別為(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)
[0 1 4 5 6 7]
94. 考慮一個10×3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)
# 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)
95. 將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])
# 方法2 print (np.unpackbits(I[:, np.newaxis], axis=1))
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)
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)
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)對其進行取樣(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)
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])
[[2. 0. 1. 1.]]
100. 對於一個一維數組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)
