51. Create a structured array (★★☆) representing position (x, y) and color (r, g, b, a)
(prompt: 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. Consider the random vector with the shape of (100, 2) and calculate the distance between points (★★☆)
(tip: 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) #Using the scipy library can be faster import scipy.spatial Z = np.random.random((100,2)) D = scipy.spatial.distance.cdist(Z,Z) print(D)
53. How to convert an array type of float(32-bit) to integer(32-bit)? (★★☆)
(prompt: asttype (copy = false))
Z = np.arange(10, dtype=np.int32) Z = Z.astype(np.float32, copy=False) print(Z)
54. How to read the following files? (★★☆)
(tip: NP. Genfromtext)
1, 2, 3, 4, 5
6, , , 7, 8
, , 9,10,11
#First save the above to the file example Txt
#StringIO is not used here because Python 2 ， and python 3 ， have compatibility problems here
Z = np.genfromtxt("example.txt", delimiter=",")
print(Z)55. Equivalent operation of numpy array enumeration? (★★☆)
(prompt: 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. Construct a two-dimensional Gaussian matrix (★★☆)
(tip: 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. How to place p elements at random positions in a two-dimensional array? (★★☆)
(prompt: 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. Subtract the average value of each row of the matrix (★★☆)
(prompt: mean(axis=,keepdims =)
# Author: Warren Weckesser X = np.random.rand(5, 10) #New Y = X - X.mean(axis=1, keepdims=True) #Old Y = X - X.mean(axis=1).reshape(-1, 1) print(Y)
59. How to sort an array by column n? (★★☆)
(prompt: argsort)
# Author: Steve Tjoa Z = np.random.randint(0,10,(3,3)) print(Z) print(Z[ Z[:,1].argsort() ])
60. How to judge that there are empty columns in a given two-dimensional array? (★★☆)
(prompt: any, ~)
# Author: Warren Weckesser Z = np.random.randint(0,3,(3,10)) print((~Z.any(axis=0)).any())
61. Find the value closest to the given value from the array (★★☆)
(prompt: 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. Think about two array shapes with shapes (1,3) and (3,1). How to use iterators to calculate their sum? (★★☆)
(tip: 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. Create an array class with name attribute (★★☆)
(prompt: 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 = NameArray(np.arange(10), "range_10") print (Z.name)
64. Given a vector, how to add 1 to each element of the second vector index (note the repeated index)? (★★★)
(prompt: 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. How to accumulate the elements of vector X to array F according to index list I? (★★★)
(prompt: 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. Think about the (w, h, 3) image of (dtype = ubyte) and calculate the value of unique color (★★★)
(tip: 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. Think about how to find the data sum of the last two axes of a four-dimensional array (★★★)
(prompt: sum(axis=(-2,-1)))
A = np.random.randint(0,10,(3,4,3,4)) #Pass a tuple (numpy# 1.7.0) sum = A.sum(axis=(-2,-1)) print(sum) #Compress the last two dimensions into one #(for functions that do not accept axis tuple parameters) sum = A.reshape(A.shape[:-2] + (-1,)).sum(axis=-1) print(sum)
68. Considering one-dimensional vector D, how to use vector S of the same size to calculate the mean of the subset of D and describe the subset index? (★★★)
(prompt: 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. How to get the diagonal of dot product? (★★★)
(tip: 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. Considering the vector [1,2,3,4,5], how to establish a new vector with three consecutive zeros interleaved between each value? (★★★)
(hint: 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. Consider an array of dimensions (5,5,3). How to multiply it by an array of dimensions (5,5)? (★★★)
(prompt: array [:,:, none])
A = np.ones((5,5,3)) B = 2*np.ones((5,5)) print(A * B[:,:,None])
72. How to exchange any two rows in an array? (★★★)
(prompt: array[[]] = array [[]])
# Author: Eelco Hoogendoorn A = np.arange(25).reshape(5,5) A[[0,1]] = A[[1,0]] print(A)
73. Think about a set of 10 triads describing 10 triangles (shared vertices) and find the unique set of line segments that make up all triangles (★★★)
(Tips: 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. Given a binary array C, how to generate an array a satisfying NP bincount(A)==C? (★★★)
(tip: 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. How to calculate the average of an array through a sliding window? (★★★)
(tip: 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. Think about array Z and build a two-dimensional array. The first line is (Z[0],Z[1],Z[2]), then each line moves one bit, and the last line is (Z[-3],Z[-2],Z[-1]) (★★★★)
(prompt: from numpy.lib import stripe_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. How to negate a Boolean value or change the sign of a floating-point number? (★★★)
(prompt: 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. Consider two sets of point sets P0 and P1 to describe a set of lines (two-dimensional) and a point p. how to calculate the distance from point p to each line i (P0[i],P1[i])? (★★★)
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. Considering two sets of point sets P0 and P1 to describe a set of lines (two-dimensional) and a set of point sets P, how to calculate the distance from each point j(P[j]) to each line i (P0[i],P1[i])? (★★★)
# 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. Think about an arbitrary array and write a function that extracts a sub part with a fixed shape and centers on a given element (fill the value in this part) (★★★★)
(prompt: 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. Consider an array Z = [1,2,3,4,5,6,7,8,9,10,11,12,13,14], how to generate an array r = [[1,2,3,4], [2,3,4,5], [3,4,5,6], [11,12,13,14]]? (★★★)
(prompt: stripe_tricks. As_striped)
# 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. Calculate the rank of the matrix (★★★)
(tip: 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. How to find the most frequent value in the array? (★★★)
(prompt: np.bincount, argmax)
Z = np.random.randint(0,10,50) print(np.bincount(Z).argmax())
84. Extract continuous 3x3 blocks (★★★) from a 10x10 matrix
(prompt: stripe_tricks. As_striped)
# 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. Create a two-dimensional array subclass that satisfies Z[i,j] == Z[j,i] (★★★)
(prompt: 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. Considering p nxn matrices and a set of vectors with shape (n,1), how to directly calculate the product (n,1) of p matrices? (★★★)
(tip: 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. For a 16x16 array, how to get the sum of a region (the region size is 4x4)? (★★★)
(prompt: 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. How to use numpy array to realize Game of Life? (★★★)
(tip: game of life, what graphics does game of life have?)
# 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. How to find the nth maximum value of an array? (★★★)
(prompt: 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]])
★ create any number of Cartesian combinations of each element (★ 90)
(tip: 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. How to create a record array from a regular array? (★★★)
(tip: 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. Think about a large vector Z and calculate its cube in three different ways (★★★)
(Tips: 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. Consider two arrays A and B with shapes (8,3) and (2,2) respectively. How to find A row in array A that satisfies the elements in B? (regardless of the order of elements in each line in B)? (★★★)
(tip: 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. Think about a 10x3 matrix and how to decompose rows with different values (such as [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. Convert an integer vector to a binary matrix (★★★)
(tip: 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. Given a two-dimensional array, how to extract unique rows? (★★★)
(tip: 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. Consider two vectors A and B and write the inner, outer, sum and mul functions corresponding to the einsum equation (★★★★)
(tip: 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. Considering a path (X,Y) described by two vectors, how to sample it with equidistance samples (★★★)?
(prompt: 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. Given an integer n and a two-dimensional array x, select multiple distributed rows from X that can be interpreted as multiple n degrees, that is, these rows contain only the sum of integer pairs n (★★★)
(prompt: 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. For a one-dimensional array X, calculate the average of its 95% confidence interval after bootstrapped (★★★)
(tip: 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)