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75854930af
numpy-100/questsions_dict.py
SebastianoF 75854930af dict to 100 questions, hints and answers done
2019-11-18 23:12:56 +00:00

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qha = {
"q1": "Import the numpy package under the name `np` (★☆☆)",
"h1": "hint: import … as ",
"a1":
"""
import numpy as np
""",
"q2": "Print the numpy version and the configuration (★☆☆)",
"h2": "hint: np.__version__, np.show_config)",
"a2":
"""
print(np.__version__)
np.show_config()
""",
"q3": "Create a null vector of size 10 (★☆☆)",
"h3": "hint: np.zeros",
"a3":
"""
Z = np.zeros(10)
print(Z)
""",
"q4": "How to find the memory size of any array (★☆☆)",
"h4": "hint: size, itemsize",
"a4":
"""
Z = np.zeros((10,10))
print("%d bytes" % (Z.size * Z.itemsize))
""",
"q5": "How to get the documentation of the numpy add function from the command line? (★☆☆)",
"h5": "hint: np.info",
"a5":
"""
%run `python -c "import numpy; numpy.info(numpy.add)"`
""",
"q6": "Create a null vector of size 10 but the fifth value which is 1 (★☆☆)",
"h6": "hint: array[4]",
"a6":
"""
Z = np.zeros(10)
Z[4] = 1
print(Z)
""",
"q7": "Create a vector with values ranging from 10 to 49 (★☆☆)",
"h7": "hint: arange",
"a7":
"""
Z = np.arange(10,50)
print(Z)
""",
"q8": "Reverse a vector (first element becomes last) (★☆☆)",
"h8": "hint: array[::-1]",
"a8":
"""
Z = np.arange(50)
Z = Z[::-1]
print(Z)
""",
"q9": "Create a 3x3 matrix with values ranging from 0 to 8 (★☆☆)",
"h9": "hint: reshape",
"a9":
"""
nz = np.nonzero([1,2,0,0,4,0])
print(nz)
""",
"q10": "Find indices of non-zero elements from [1,2,0,0,4,0] (★☆☆)",
"h10": "hint: np.nonzero",
"a10":
"""
nz = np.nonzero([1,2,0,0,4,0])
print(nz)
""",
"q11": "Create a 3x3 identity matrix (★☆☆)",
"h11": "hint: np.eye",
"a11":
"""
Z = np.eye(3)
print(Z)
""",
"q12": "Create a 3x3x3 array with random values (★☆☆)",
"h12": "hint: np.random.random",
"a12":
"""
Z = np.random.random((3,3,3))
print(Z)
""",
"q13": "Create a 10x10 array with random values and find the minimum and maximum values (★☆☆)",
"h13": "hint: min, max",
"a13":
"""
Z = np.random.random((10,10))
Zmin, Zmax = Z.min(), Z.max()
print(Zmin, Zmax)
""",
"q14": "Create a random vector of size 30 and find the mean value (★☆☆)",
"h14": "hint: mean",
"a14":
"""
Z = np.random.random(30)
m = Z.mean()
print(m)
""",
"q15": "Create a 2d array with 1 on the border and 0 inside (★☆☆)",
"h15": "hint: array[1:-1, 1:-1]",
"a15":
"""
Z = np.ones((10,10))
Z[1:-1,1:-1] = 0
print(Z)
""",
"q16": "How to add a border (filled with 0's) around an existing array? (★☆☆)",
"h16": "hint: np.pad",
"a16":
"""
Z = np.ones((5,5))
Z = np.pad(Z, pad_width=1, mode='constant', constant_values=0)
print(Z)
""",
"q17": """
What is the result of the following expression? (★☆☆)"
```python
0 * np.nan
np.nan == np.nan
np.inf > np.nan
np.nan - np.nan
np.nan in set([np.nan])
# 0.3 == 3 * 0.1
# ```""",
"h17": "hint: NaN = not a number, inf = infinity",
"a17":
"""
print(0 * np.nan)
print(np.nan == np.nan)
print(np.inf > np.nan)
print(np.nan - np.nan)
print(np.nan in set([np.nan]))
print(0.3 == 3 * 0.1)
""",
"q18": "Create a 5x5 matrix with values 1,2,3,4 just below the diagonal (★☆☆)",
"h18": "hint: np.diag",
"a18":
"""
Z = np.diag(1+np.arange(4),k=-1)
print(Z)
""",
"q19": "Create a 8x8 matrix and fill it with a checkerboard pattern (★☆☆)",
"h19": "hint: array[::2]",
"a19":
"""
Z = np.zeros((8,8),dtype=int)
Z[1::2,::2] = 1
Z[::2,1::2] = 1
print(Z)
""",
"q20": "Consider a (6,7,8) shape array, what is the index (x,y,z) of the 100th element?",
"h20": "hint: np.unravel_index",
"a20":
"""
print(np.unravel_index(99,(6,7,8)))
""",
"q21": "Create a checkerboard 8x8 matrix using the tile function (★☆☆)",
"h21": "hint: np.tile",
"a21":
"""
Z = np.tile( np.array([[0,1],[1,0]]), (4,4))
print(Z)
""",
"q22": "Normalize a 5x5 random matrix (★☆☆)",
"h22": "hint: (x -mean)/std",
"a22":
"""
Z = np.random.random((5,5))
Z = (Z - np.mean (Z)) / (np.std (Z))
print(Z)
""",
"q23": "Create a custom dtype that describes a color as four unsigned bytes (RGBA) (★☆☆)",
"h23": "hint: np.dtype",
"a23":
"""
color = np.dtype([("r", np.ubyte, 1),
("g", np.ubyte, 1),
("b", np.ubyte, 1),
("a", np.ubyte, 1)])
""",
"q24": "Multiply a 5x3 matrix by a 3x2 matrix (real matrix product) (★☆☆)",
"h24": "hint: ",
"a24":
"""
Z = np.dot(np.ones((5,3)), np.ones((3,2)))
print(Z)
# Alternative solution, in Python 3.5 and above
Z = np.ones((5,3)) @ np.ones((3,2))
print(Z)
""",
"q25": "Given a 1D array, negate all elements which are between 3 and 8, in place. (★☆☆)",
"h25": "hint: >, <=",
"a25":
"""
# Author: Evgeni Burovski
Z = np.arange(11)
Z[(3 < Z) & (Z <= 8)] *= -1
print(Z)
""",
"q26": """
What is the output of the following script? (★☆☆)
```python
# Author: Jake VanderPlas
print(sum(range(5),-1))
from numpy import *
print(sum(range(5),-1))
```
""",
"h26": "hint: np.sum",
"a26":
"""
# Author: Jake VanderPlas
print(sum(range(5),-1))
from numpy import *
print(sum(range(5),-1))
""",
"q27": """
Consider an integer vector Z, which of these expressions are legal? (★☆☆)
```python
Z**Z
2 << Z >> 2
Z <- Z
1j*Z
Z/1/1
Z<Z>Z
```""",
"h27": "No hints provided...",
"a27":
"""
Z**Z
2 << Z >> 2
Z <- Z
1j*Z
Z/1/1
Z<Z>Z
""",
"q28": """
What are the result of the following expressions?
```python
np.array(0) / np.array(0)
np.array(0) // np.array(0)
np.array([np.nan]).astype(int).astype(float)
```
""",
"h28": "No hints provided... ",
"a28":
"""
print(np.array(0) / np.array(0))
print(np.array(0) // np.array(0))
print(np.array([np.nan]).astype(int).astype(float))
""",
"q29": "How to round away from zero a float array ? (★☆☆)",
"h29": "hint: np.uniform, np.copysign, np.ceil, np.abs",
"a29":
"""
# Author: Charles R Harris
Z = np.random.uniform(-10,+10,10)
print (np.copysign(np.ceil(np.abs(Z)), Z))
""",
"q30": "How to find common values between two arrays? (★☆☆)",
"h30": "hint: np.intersect1d",
"a30":
"""
Z1 = np.random.randint(0,10,10)
Z2 = np.random.randint(0,10,10)
print(np.intersect1d(Z1,Z2))
""",
"q31": "How to ignore all numpy warnings (not recommended)? (★☆☆)",
"h31": "hint: np.seterr, np.errstate",
"a31":
"""
# Suicide mode on
defaults = np.seterr(all="ignore")
Z = np.ones(1) / 0
# Back to sanity
_ = np.seterr(**defaults)
# Equivalently with a context manager
nz = np.nonzero([1,2,0,0,4,0])
print(nz)
""",
"q32": """
Is the following expressions true? (★☆☆)
```python
np.sqrt(-1) == np.emath.sqrt(-1)
```
""",
"h32": "hint: imaginary number",
"a32":
"""
np.sqrt(-1) == np.emath.sqrt(-1)
""",
"q33": "How to get the dates of yesterday, today and tomorrow? (★☆☆)",
"h33": "hint: np.datetime64, np.timedelta64",
"a33":
"""
yesterday = np.datetime64('today', 'D') - np.timedelta64(1, 'D')
today = np.datetime64('today', 'D')
tomorrow = np.datetime64('today', 'D') + np.timedelta64(1, 'D')
""",
"q34": "How to get all the dates corresponding to the month of July 2016? (★★☆)",
"h34": "hint: np.arange(dtype=datetime64['D'])",
"a34":
"""
Z = np.arange('2016-07', '2016-08', dtype='datetime64[D]')
print(Z)
""",
"q35": "How to compute ((A+B)*(-A/2)) in place (without copy)? (★★☆)",
"h35": "hint: np.add(out=), np.negative(out=), np.multiply(out=), np.divide(out=)",
"a35":
"""
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)
""",
"q36": "Extract the integer part of a random array using 5 different methods (★★☆)",
"h36": "hint: %, np.floor, np.ceil, astype, np.trunc",
"a36":
"""
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))
""",
"q37": "Create a 5x5 matrix with row values ranging from 0 to 4 (★★☆)",
"h37": "hint: np.arange",
"a37":
"""
Z = np.zeros((5,5))
Z += np.arange(5)
print(Z)
""",
"q38": "Consider a generator function that generates 10 integers and use it to build an array (★☆☆)",
"h38": "hint: np.fromiter",
"a38":
"""
def generate():
for x in range(10):
yield x
Z = np.fromiter(generate(),dtype=float,count=-1)
print(Z)
""",
"q39": "Create a vector of size 10 with values ranging from 0 to 1, both excluded (★★☆)",
"h39": "hint: np.linspace",
"a39":
"""
Z = np.linspace(0,1,11,endpoint=False)[1:]
print(Z)
""",
"q40": "Create a random vector of size 10 and sort it (★★☆)",
"h40": "hint: sort",
"a40":
"""
Z = np.random.random(10)
Z.sort()
print(Z)
""",
"q41": "How to sum a small array faster than np.sum? (★★☆)",
"h41": "hint: np.add.reduce",
"a41":
"""
# Author: Evgeni Burovski
Z = np.arange(10)
np.add.reduce(Z)
""",
"q42": "Consider two random array A and B, check if they are equal (★★☆)",
"h42": "hint: np.allclose, np.array_equal",
"a42":
"""
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)
# Checking both the shape and the element values, no tolerance (values have to be exactly equal)
equal = np.array_equal(A,B)
print(equal)
""",
"q43": "Make an array immutable (read-only) (★★☆)",
"h43": "hint: flags.writeable",
"a43":
"""
Z = np.zeros(10)
Z.flags.writeable = False
Z[0] = 1
""",
"q44": "Consider a random 10x2 matrix representing cartesian coordinates, convert them to polar coordinates (★★☆)",
"h44": "hint: np.sqrt, np.arctan2",
"a44":
"""
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)
""",
"q45": "Create random vector of size 10 and replace the maximum value by 0 (★★☆)",
"h45": "hint: argmax",
"a45":
"""
Z = np.random.random(10)
Z[Z.argmax()] = 0
print(Z)
""",
"q46": "Create a structured array with `x` and `y` coordinates covering the [0,1]x[0,1] area (★★☆)",
"h46": "hint: np.meshgrid",
"a46":
"""
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)
""",
"q47": "Given two arrays, X and Y, construct the Cauchy matrix C (Cij =1/(xi - yj))",
"h47": "hint: np.subtract.outer",
"a47":
"""
# Author: Evgeni Burovski
X = np.arange(8)
Y = X + 0.5
C = 1.0 / np.subtract.outer(X, Y)
print(np.linalg.det(C))
""",
"q48": "Print the minimum and maximum representable value for each numpy scalar type (★★☆)",
"h48": "hint: np.iinfo, np.finfo, eps",
"a48":
"""
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)
""",
"q49": "How to print all the values of an array? (★★☆)",
"h49": "hint: np.set_printoptions",
"a49":
"""
np.set_printoptions(threshold=np.nan)
Z = np.zeros((16,16))
print(Z)
""",
"q50": "How to find the closest value (to a given scalar) in a vector? (★★☆)",
"h50": "hint: argmin",
"a50":
"""
Z = np.arange(100)
v = np.random.uniform(0,100)
index = (np.abs(Z-v)).argmin()
print(Z[index])
""",
"q51": "Create a structured array representing a position (x,y) and a color (r,g,b) (★★☆)",
"h51": "hint: dtype",
"a51":
"""
Z = np.zeros(10, [ ('position', [ ('x', float, 1),
('y', float, 1)]),
('color', [ ('r', float, 1),
('g', float, 1),
('b', float, 1)])])
print(Z)
""",
"q52": "Consider a random vector with shape (100,2) representing coordinates, find point by point distances (★★☆)",
"h52": "hint: np.atleast_2d, T, np.sqrt",
"a52":
"""
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)
# Much faster with scipy
import scipy
# Thanks Gavin Heverly-Coulson (#issue 1)
import scipy.spatial
Z = np.random.random((10,2))
D = scipy.spatial.distance.cdist(Z,Z)
print(D)
""",
"q53": "How to convert a float (32 bits) array into an integer (32 bits) in place?",
"h53": "hint: astype(copy=False)",
"a53":
"""
Z = np.arange(10, dtype=np.float32)
Z = Z.astype(np.int32, copy=False)
print(Z)
""",
"q54": """
How to read the following file? (★★☆)
```
1, 2, 3, 4, 5
6, , , 7, 8
, , 9,10,11
```
""",
"h54": "hint: np.genfromtxt",
"a54":
"""
from io import StringIO
# Fake file
s = StringIO('''1, 2, 3, 4, 5\n
6, , , 7, 8\n
, , 9,10,11\n''')
Z = np.genfromtxt(s, delimiter=",", dtype=np.int)
print(Z)
""",
"q55": "What is the equivalent of enumerate for numpy arrays? (★★☆)",
"h55": "hint: np.ndenumerate, np.ndindex",
"a55":
"""
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])
""",
"q56": "Generate a generic 2D Gaussian-like array (★★☆)",
"h56": "hint: np.meshgrid, np.exp",
"a56":
"""
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)
""",
"q57": "How to randomly place p elements in a 2D array? (★★☆)",
"h57": "hint: np.put, np.random.choice",
"a57":
"""
# 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)
""",
"q58": "Subtract the mean of each row of a matrix (★★☆)",
"h58": "hint: mean(axis=,keepdims=)",
"a58":
"""
# Author: Warren Weckesser
X = np.random.rand(5, 10)
# Recent versions of numpy
Y = X - X.mean(axis=1, keepdims=True)
# Older versions of numpy
Y = X - X.mean(axis=1).reshape(-1, 1)
print(Y)
""",
"q59": "How to sort an array by the nth column? (★★☆)",
"h59": "hint: argsort",
"a59":
"""
# Author: Steve Tjoa
Z = np.random.randint(0,10,(3,3))
print(Z)
print(Z[Z[:,1].argsort()])
""",
"q60": "How to tell if a given 2D array has null columns? (★★☆)",
"h60": "hint: any, ~",
"a60":
"""
# Author: Warren Weckesser
Z = np.random.randint(0,3,(3,10))
print((~Z.any(axis=0)).any())
""",
"q61": "Find the nearest value from a given value in an array (★★☆)",
"h61": "hint: np.abs, argmin, flat",
"a61":
"""
Z = np.random.uniform(0,1,10)
z = 0.5
m = Z.flat[np.abs(Z - z).argmin()]
print(m)
""",
"q62": "Considering two arrays with shape (1,3) and (3,1), how to compute their sum using an iterator? (★★☆)",
"h62": "hint: np.nditer",
"a62":
"""
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])
""",
"q63": "Create an array class that has a name attribute (★★☆)",
"h63": "hint: class method",
"a63":
"""
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)
""",
"q64": "Consider a given vector, how to add 1 to each element indexed by a second vector "
"(be careful with repeated indices)? (★★★)",
"h64": "hint: np.bincount | np.add.at",
"a64":
"""
# 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)
""",
"q65": "How to accumulate elements of a vector (X) to an array (F) based on an index list (I)? (★★★)",
"h65": "hint: np.bincount",
"a65":
"""
# 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)
""",
"q66": "Considering a (w,h,3) image of (dtype=ubyte), compute the number of unique colors (★★★)",
"h66": "hint: np.unique",
"a66":
"""
# 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))
""",
"q67": "Considering a four dimensions array, how to get sum over the last two axis at once? (★★★)",
"h67": "hint: sum(axis=(-2,-1))",
"a67":
"""
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)
# solution by flattening the last two dimensions into one
# (useful for functions that don't accept tuples for axis argument)
sum = A.reshape(A.shape[:-2] + (-1,)).sum(axis=-1)
print(sum)
""",
"q68": "Considering a one-dimensional vector D, how to compute means of subsets of D using a vector S "
"of same size describing subset indices? (★★★)",
"h68": "hint: np.bincount",
"a68":
"""
# 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())
""",
"q69": "How to get the diagonal of a dot product? (★★★)",
"h69": "hint: np.diag",
"a69":
"""
# 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)
""",
"q70": "Consider the vector [1, 2, 3, 4, 5], how to build a new vector with 3 consecutive "
"zeros interleaved between each value? (★★★)",
"h70": "hint: array[::4]",
"a70":
"""
# 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)
""",
"q71": "Consider an array of dimension (5,5,3), how to mulitply it by an array with dimensions (5,5)? (★★★)",
"h71": "hint: array[:, :, None]",
"a71":
"""
A = np.ones((5,5,3))
B = 2*np.ones((5,5))
print(A * B[:,:,None])
""",
"q72": "How to swap two rows of an array? (★★★)",
"h72": "hint: array[[]] = array[[]]",
"a72":
"""
# Author: Eelco Hoogendoorn
A = np.arange(25).reshape(5,5)
A[[0,1]] = A[[1,0]]
print(A)
""",
"q73": "Consider a set of 10 triplets describing 10 triangles (with shared vertices), find the "
"set of unique line segments composing all the triangles (★★★)",
"h73": "hint: repeat, np.roll, np.sort, view, np.unique",
"a73":
"""
# 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)
""",
"q74": "Given an array C that is a bincount, how to produce an array A such that np.bincount(A) == C? (★★★)",
"h74": "hint: np.repeat",
"a74":
"""
# 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)
""",
"q75": "How to compute averages using a sliding window over an array? (★★★)",
"h75": "hint: np.cumsum",
"a75":
"""
# 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))
""",
"q76": "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]) (★★★)",
"h76": "hint: from numpy.lib import stride_tricks",
"a76":
"""
# 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)
""",
"q77": "How to negate a boolean, or to change the sign of a float inplace? (★★★)",
"h77": "hint: np.logical_not, np.negative",
"a77":
"""
# 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)
""",
"q78": "Consider 2 sets of points P0,P1 describing lines (2d) and a point p, how to compute "
"distance from p to each line i (P0[i],P1[i])? (★★★)",
"h78": "No hints provided...",
"a78":
"""
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))
""",
"q79": "Consider 2 sets of points P0,P1 describing lines (2d) and a set of points P, how to "
"compute distance from each point j (P[j]) to each line i (P0[i],P1[i])? (★★★)",
"h79": "No hints provided...",
"a79":
"""
# 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]))
""",
"q80": "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) (★★★)",
"h80": "hint: minimum maximum",
"a80":
"""
# 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)
""",
"q81": "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]]? (★★★)",
"h81": "hint: stride_tricks.as_strided",
"a81":
"""
# 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)
""",
"q82": "Compute a matrix rank (★★★) ",
"h82": "hint: np.linalg.svd",
"a82":
"""
# 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)
""",
"q83": "How to find the most frequent value in an array?",
"h83": "hint: np.bincount, argmax",
"a83":
"""
Z = np.random.randint(0,10,50)
print(np.bincount(Z).argmax())
""",
"q84": "Extract all the contiguous 3x3 blocks from a random 10x10 matrix (★★★)",
"h84": "hint: stride_tricks.as_strided",
"a84":
"""
# 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)
""",
"q85": "Create a 2D array subclass such that Z[i,j] == Z[j,i] (★★★)",
"h85": "hint: class method",
"a85":
"""
# 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)
""",
"q86": "Consider a set of p matrices wich shape (n,n) and a set of p vectors with shape (n,1). "
"How to compute the sum of of the p matrix products at once? (result has shape (n,1)) (★★★)",
"h86": "hint: np.tensordot",
"a86":
"""
# 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.
""",
"q87": "Consider a 16x16 array, how to get the block-sum (block size is 4x4)? (★★★)",
"h87": "hint: np.add.reduceat",
"a87":
"""
# 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)
""",
"q88": "How to implement the Game of Life using numpy arrays? (★★★)",
"h88": "No hints provided... ",
"a88":
"""
# 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)
""",
"q89": "How to get the n largest values of an array (★★★)",
"h89": "hint: np.argsort | np.argpartition",
"a89":
"""
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]])
""",
"q90": "Given an arbitrary number of vectors, build the cartesian product "
"(every combinations of every item) (★★★)",
"h90": "hint: np.indices",
"a90":
"""
# 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])))
""",
"q91": "How to create a record array from a regular array? (★★★)",
"h91": "hint: np.core.records.fromarrays",
"a91":
"""
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)
""",
"q92": "Consider a large vector Z, compute Z to the power of 3 using 3 different methods (★★★)",
"h92": "hint: np.power, *, np.einsum",
"a92":
"""
# Author: Ryan G.
x = np.random.rand(int(5e7))
%timeit np.power(x,3)
%timeit x*x*x
%timeit np.einsum('i,i,i->i',x,x,x)
""",
"q93": "Consider two arrays A and B of shape (8,3) and (2,2). How to find rows of A "
"that contain elements of each row of B regardless of the order of the elements in B? (★★★)",
"h93": "hint: np.where",
"a93":
"""
# 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)
""",
"q94": "Considering a 10x3 matrix, extract rows with unequal values (e.g. [2,2,3]) (★★★)",
"h94": "No hints provided...",
"a94":
"""
# 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)
""",
"q95": "Convert a vector of ints into a matrix binary representation (★★★)",
"h95": "hint: np.unpackbits",
"a95":
"""
# 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))
""",
"q96": "Given a two dimensional array, how to extract unique rows? (★★★)",
"h96": "hint: np.ascontiguousarray | np.unique",
"a96":
"""
# 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)
# Author: Andreas Kouzelis
# NumPy >= 1.13
uZ = np.unique(Z, axis=0)
print(uZ)
""",
"q97": "Considering 2 vectors A & B, write the einsum equivalent of inner, outer, sum, and mul function (★★★)",
"h97": "hint: np.einsum",
"a97":
"""
# 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)
""",
"q98": "Considering a path described by two vectors (X,Y), how to sample it using equidistant samples (★★★)?",
"h98": "hint: np.cumsum, np.interp ",
"a98":
"""
# 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)
""",
"q99": "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. (★★★)",
"h99": "hint: np.logical_and.reduce, np.mod",
"a99":
"""
# 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])
""",
"q100": "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). (★★★)",
"h100": "hint: np.percentile",
"a100":
"""
# 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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