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    別整天 “學妹/前女友”了,花2小時整理了Numpy測試習題100道,做個測驗吧!

    前面,已經為大家發布了Numpy系列的十篇文章,這里暫時告一段落,現為大家提供100道Numpy練習題,算是作為一個查漏補缺吧!

    前面我為大家總結了Numpy中的常用函數,但是沒有舉例子解釋說明。那么,今天的這100道題目是個很好的鍛煉。
    在這里插入圖片描述

    來源:https://github.com/rougier/numpy-100

    Numpy是Python做數據分析所必須要掌握的基礎庫之一,以下題是github上的開源項目,主要為了檢測你的Numpy能力,同時對你的學習作為一個補充。黃同學花了2小時為大家整理出來了,希望對你有幫助。

    1. 導入numpy庫并取別名為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內存大小?(★☆☆)

    (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)

    import numpy
    numpy.info(numpy.add)
    

    6. 創建一個長度為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)
    

    7. 創建一個值域范圍從10到49的向量(★☆☆)

    (提示: np.arange)

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

    8. 反轉一個向量(第一個元素變為最后一個) (★☆☆)

    (提示: array[::-1])

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

    9. 創建一個 3x3 并且值從0到8的矩陣(★☆☆)

    (提示: reshape)

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

    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 3x3 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 10x10 的隨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)
    

    14. 創建一個長度為30的隨機向量并找到它的平均值 (★☆☆)

    (提示: mean)

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

    15. 創建一個二維數組,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)
    

    17. 下面表達式運行的結果是什么?(★☆☆)

    (提示: NaN = not a number, inf = infinity)
    (提示:NaN : 不是一個數,inf : 無窮)

    # 表達式                           # 結果
    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. 創建一個 5x5的矩陣,并設置值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8x8 的矩陣,并且設置成棋盤樣式 (★☆☆)

    (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)是什么?

    (提示: np.unravel_index)

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

    21. 用tile函數去創建一個 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)
    

    22. 對一個5x5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)四個無符號字節的自定義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5x3的矩陣與一個3x2的矩陣相乘,實矩陣乘積是什么?(★☆☆)

    (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. 下面腳本運行后的結果是什么? (★☆☆)

    (提示: np.sum)

    # Author: Jake VanderPlas               # 結果
    
    print(sum(range(5),-1))                 9
    from numpy import *                     
    print(sum(range(5),-1))                 10    #numpy.sum(a, axis=None)
    

    27. 考慮一個整數向量Z,下列表達合法的是哪個? (★☆☆)

    (提示:這里還有“位運算符”)

    Z**Z                        True
    2 << Z >> 2                 False
    Z <- Z                      True
    1j*Z                        True  #復數           
    Z/1/1                       True
    Z<Z>Z                       False
    

    28. 下面表達式的結果分別是什么? (★☆☆)

    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數組? (★☆☆)

    (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. 如何找出兩個數組公共的元素? (★☆☆)

    (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)
    
    # 另一個等價的方式, 使用上下文管理器(context manager)
    with np.errstate(divide='ignore'):
        Z = np.ones(1) / 0
    

    32. 下面的表達式是否為真? (★☆☆)

    (提示: 虛數)

    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數組中的整數部分 (★★☆)

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

    37. 創建一個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. 如何用一個生成10個整數的函數來構建數組 (★☆☆)

    (提示: np.fromiter)

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

    39. 創建一個大小為10的向量, 值域為0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. 創建一個大小為10的隨機向量,并把它排序 (★★☆)

    (提示: sort)

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

    41. 對一個小數組進行求和有沒有辦法比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ufunc(universal function)函數,C語言實現
    

    42. 如何判斷兩和隨機數組相等 (★★☆)

    (提示: np.allclose, np.array_equal)

    A = np.random.randint(0, 2, 5)
    B = np.random.randint(0, 2, 5)
    
    # 假設array的形狀(shape)相同和一個誤差容限(tolerance)
    equal = np.allclose(A,B)
    print(equal)
    
    # 檢查形狀和元素值,沒有誤差容限(值必須完全相等)
    equal = np.array_equal(A,B)
    print(equal)
    

    43. 把數組變為只讀 (★★☆)

    (提示: flags.writeable)

    Z = np.zeros(5)
    Z.flags.writeable = False
    Z[0] = 1
    

    44. 將一個10x2的笛卡爾坐標矩陣轉換為極坐標 (★★☆)

    (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. 創建一個大小為10的隨機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. 創建一個結構化數組,其中x和y坐標覆蓋[0, 1]x[1, 0]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,構造柯西(Cauchy)矩陣C ( C i j = 1 x i ? y j C_{ij}=\frac{1}{x_i-y_j} Cij?=xi??yj?1?) (★★☆)

    (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)) # 計算行列式
    

    48. 打印每個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. 如何在數組中找到與給定標量接近的值? (★★☆)

    (提示: argmin)

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

    51. 創建表示位置(x, y)和顏色(r, g, b, a)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. 思考形狀為(100, 2)的隨機向量,求出點與點之間的距離 (★★☆)

    (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)的數組類型轉換位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, 因為Python2 和Python3 在這個地方有兼容性問題
    Z = np.genfromtxt("example.txt", delimiter=",")  
    print(Z)
    

    55. numpy數組枚舉(enumerate)的等價操作? (★★☆)

    (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. 構造一個二維高斯矩陣(★★☆)

    (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. 如何在二維數組的隨機位置放置p個元素? (★★☆)

    (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. 如何對數組通過第n列進行排序? (★★☆)

    (提示: argsort)

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

    60. 如何判斷一個給定的二維數組存在空列? (★★☆)

    (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)的兩個數組形狀,如何使用迭代器計算它們的和? (★★☆)

    (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. 創建一個具有name屬性的數組類 (★★☆)

    (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 = NamedArray(np.arange(10), "range_10")
    print (Z.name)
    

    64. 給定一個向量,如何讓在第二個向量索引的每個元素加1(注意重復索引)? (★★★)

    (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. 如何根據索引列表I將向量X的元素累加到數組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. 思考如何求一個四維數組最后兩個軸的數據和(★★★)

    (提示: sum(axis=(-2,-1)))

    A = np.random.randint(0,10,(3,4,3,4))
    # 傳遞一個元組(numpy 1.7.0)
    sum = A.sum(axis=(-2,-1))
    print(sum)
    
    # 將最后兩個維度壓縮為一個
    # (適用于不接受軸元組參數的函數)
    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來計算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. 如何獲得點積的對角線? (★★★)

    (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],如何建立一個新的向量,在每個值之間交錯有3個連續的零? (★★★)

    (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[[]])

    # Author: Eelco Hoogendoorn
    
    A = np.arange(25).reshape(5,5)
    A[[0,1]] = A[[1,0]]
    print(A)
    

    73. 思考描述10個三角形(共享頂點)的一組10個三元組,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. 給定一個二進制的數組C,如何生成一個數組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. 如何通過滑動窗口計算一個數組的平均數? (★★★)

    (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. 思考以為數組Z,構建一個二維數組,其第一行是(Z[0],Z[1],Z[2]), 然后每一行移動一位,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. 如何對布爾值取反,或改變浮點數的符號(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? (★★★)

    # 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. 思考一個任意的數組,編寫一個函數,該函數提取一個具有固定形狀的子部分,并以一個給定的元素為中心(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)

    # 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())
    

    84. 從一個10x10的矩陣中提取出連續的3x3區塊(★★★)

    (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.創建一個滿足 Z[i,j] == Z[j,i]的二維數組子類 (★★★)

    (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 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)

    # 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. 對于一個16x16的數組,如何得到一個區域的和(區域大小為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數組實現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:]])
    
    # Fast
    print (Z[np.argpartition(-Z,n)[:n]])
    

    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)

    # 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. 如何從一個常規數組中創建記錄數組(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)
    

    92. 思考一個大向量Z, 用三種不同的方法計算它的立方 (★★★)

    (提示: np.power, *, np.einsum)

    # 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)

    # 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. 將一個整數向量轉換為二進制矩陣 (★★★)

    (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. 給定一個二維數組,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. 考慮兩個向量A和B,寫出用einsum等式對應的inner, outer, sum, mul函數 (★★★)

    (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)(★★★)?

    (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. 給定一個整數n 和一個二維數組X,從X中選擇可以被解釋為從多n度的多項分布式的行,即這些行只包含整數對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. 對于一個一維數組X,計算它boostrapped之后的95%置信區間的平均值. (★★★)

    (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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