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) 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)？ (★★★)
(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A和B，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)
