首页
学习
活动
专区
工具
TVP
发布
社区首页 >专栏 >100个Numpy练习【5】

100个Numpy练习【5】

原创
作者头像
YingJoy_
发布2018-03-01 13:58:08
1.5K0
发布2018-03-01 13:58:08
举报
文章被收录于专栏:应兆康的专栏应兆康的专栏

Numpy是Python做数据分析必须掌握的基础库之一,非常适合刚学习完Numpy基础的同学,完成以下习题可以帮助你更好的掌握这个基础库。

Python版本:Python 3.6.2

Numpy版本:Numpy 1.13.1

81. 考虑一个数组Z = [1,2,3,4,5,6,7,8,9,10,11,12,13,14],如何生成一个数组R = [[1,2,3,4], [2,3,4,5], [3,4,5,6], ...,[11,12,13,14]]? (★★★)

(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. 计算矩阵的秩 (★★★)

(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. 如何找出数组中出现频率最高的值?(★★★)

(提示: np.bincount, argmax)

Z = np.random.randint(0,10,50)
print(np.bincount(Z).argmax())
84. 从一个10x10的矩阵中提取出连续的3x3区块(★★★)

(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.创建一个满足 Z[i,j] == Z[j,i]的二维数组子类 (★★★)

(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. 考虑p个 nxn 矩阵和一组形状为(n,1)的向量,如何直接计算p个矩阵的乘积(n,1)? (★★★)

(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. 对于一个16x16的数组,如何得到一个区域的和(区域大小为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数组实现Game of Life? (★★★)

(提示: Game of Life , Game of Life有哪些图形?)

# 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. 如何找到一个数组的第n个最大值? (★★★)

(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. 给定任意个数向量,创建笛卡尔积(每一个元素的每一种组合) (★★★)

(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. 如何从一个常规数组中创建记录数组(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. 思考一个大向量Z, 用三种不同的方法计算它的立方 (★★★)

(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. 考虑两个形状分别为(8,3) (2,2)的数组AB. 如何在数组A中找到满足包含B中元素的行?(不考虑B中每行元素顺序)? (★★★)

(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. 思考一个10x3的矩阵,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. 将一个整数向量转换为二进制矩阵 (★★★)

(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. 给定一个二维数组,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. 考虑两个向量AB,写出用einsum等式对应的inner, outer, sum, mul函数 (★★★)

(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. 考虑一个由两个向量描述的路径(X,Y),如何用等距样例(equidistant samples)对其进行采样(sample)(★★★)?

(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. 给定一个整数n 和一个二维数组X,从X中选择可以被解释为从多n度的多项分布式的行,即这些行只包含整数对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. 对于一个一维数组X,计算它boostrapped之后的95%置信区间的平均值. (★★★)

(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)

原创声明:本文系作者授权腾讯云开发者社区发表,未经许可,不得转载。

如有侵权,请联系 cloudcommunity@tencent.com 删除。

原创声明:本文系作者授权腾讯云开发者社区发表,未经许可,不得转载。

如有侵权,请联系 cloudcommunity@tencent.com 删除。

评论
登录后参与评论
0 条评论
热度
最新
推荐阅读
目录
  • 82. 计算矩阵的秩 (★★★)
  • 83. 如何找出数组中出现频率最高的值?(★★★)
  • 84. 从一个10x10的矩阵中提取出连续的3x3区块(★★★)
  • 85.创建一个满足 Z[i,j] == Z[j,i]的二维数组子类 (★★★)
  • 86. 考虑p个 nxn 矩阵和一组形状为(n,1)的向量,如何直接计算p个矩阵的乘积(n,1)? (★★★)
  • 87. 对于一个16x16的数组,如何得到一个区域的和(区域大小为4x4)? (★★★)
  • 88. 如何利用numpy数组实现Game of Life? (★★★)
  • 89. 如何找到一个数组的第n个最大值? (★★★)
  • 90. 给定任意个数向量,创建笛卡尔积(每一个元素的每一种组合) (★★★)
  • 91. 如何从一个常规数组中创建记录数组(record array)? (★★★)
  • 92. 思考一个大向量Z, 用三种不同的方法计算它的立方 (★★★)
  • 93. 考虑两个形状分别为(8,3) 和(2,2)的数组A和B. 如何在数组A中找到满足包含B中元素的行?(不考虑B中每行元素顺序)? (★★★)
  • 94. 思考一个10x3的矩阵,如何分解出有不全相同值的行 (如 [2,2,3]) (★★★)
  • 95. 将一个整数向量转换为二进制矩阵 (★★★)
  • 96. 给定一个二维数组,如何提取出唯一的行?(★★★)
  • 97. 考虑两个向量A和B,写出用einsum等式对应的inner, outer, sum, mul函数 (★★★)
  • 98. 考虑一个由两个向量描述的路径(X,Y),如何用等距样例(equidistant samples)对其进行采样(sample)(★★★)?
  • 99. 给定一个整数n 和一个二维数组X,从X中选择可以被解释为从多n度的多项分布式的行,即这些行只包含整数对n的和. (★★★)
  • 100. 对于一个一维数组X,计算它boostrapped之后的95%置信区间的平均值. (★★★)
领券
问题归档专栏文章快讯文章归档关键词归档开发者手册归档开发者手册 Section 归档