100 numpy exercises

A joint effort of the numpy community

The goal is both to offer a quick reference for new and old users and to provide also a set of exercices for those who teach. If you remember having asked or answered a (short) problem, you can send a pull request. The format is:

#. Find indices of non-zero elements from [1,2,0,0,4,0]
 
   .. code:: python
 
      # Author: Somebody
 
      print(np.nonzero([1,2,0,0,4,0]))

Here is what the page looks like so far: http://www.labri.fr/perso/nrougier/teaching/numpy.100/index.html

Repository is at: https://github.com/rougier/numpy-100

Thanks to Michiaki Ariga, there is now a Julia version.

Import the numpy package under the name np (★☆☆)
```
import numpy as np
```
Print the numpy version and the configuration (★☆☆)
```
print(np.__version__)
np.__config__.show()
```
Create a null vector of size 10 (★☆☆)
```
Z = np.zeros(10)
print(Z)
```
How to get the documentation of the numpy add function from the command line ? (★☆☆)
```
python -c "import numpy; numpy.info(numpy.add)"
```
Create a null vector of size 10 but the fifth value which is 1 (★☆☆)
```
Z = np.zeros(10)
Z[4] = 1
print(Z)
```
Create a vector with values ranging from 10 to 49 (★☆☆)
```
Z = np.arange(10,50)
print(Z)
```
Reverse a vector (first element becomes last) (★☆☆)
```
Z = np.arange(50)
Z = Z[::-1]
```
Create a 3x3 matrix with values ranging from 0 to 8 (★☆☆)
```
Z = np.arange(9).reshape(3,3)
print(Z)
```
Find indices of non-zero elements from [1,2,0,0,4,0] (★☆☆)
```
nz = np.nonzero([1,2,0,0,4,0])
print(nz)
```
Create a 3x3 identity matrix (★☆☆)
```
Z = np.eye(3)
print(Z)
```
Create a 3x3x3 array with random values (★☆☆)
```
Z = np.random.random((3,3,3))
print(Z)
```
Create a 10x10 array with random values and find the minimum and maximum values (★☆☆)
```
Z = np.random.random((10,10))
Zmin, Zmax = Z.min(), Z.max()
print(Zmin, Zmax)
```
Create a random vector of size 30 and find the mean value (★☆☆)
```
Z = np.random.random(30)
m = Z.mean()
print(m)
```
Create a 2d array with 1 on the border and 0 inside (★☆☆)
```
Z = np.ones((10,10))
Z[1:-1,1:-1] = 0
```

What is the result of the following expression ? (★☆☆)

0 * np.nan
np.nan == np.nan
np.inf > np.nan
np.nan - np.nan
0.3 == 3 * 0.1

Create a 5x5 matrix with values 1,2,3,4 just below the diagonal (★☆☆)
```
Z = np.diag(1+np.arange(4),k=-1)
print(Z)
```

Create a 8x8 matrix and fill it with a checkerboard pattern (★☆☆)

Z = np.zeros((8,8),dtype=int)
Z[1::2,::2] = 1
Z[::2,1::2] = 1
print(Z)

Consider a (6,7,8) shape array, what is the index (x,y,z) of the 100th element ?
```
print(np.unravel_index(100,(6,7,8)))
```
Create a checkerboard 8x8 matrix using the tile function (★☆☆)
```
Z = np.tile( np.array([[0,1],[1,0]]), (4,4))
print(Z)
```

Normalize a 5x5 random matrix (★☆☆)

Z = np.random.random((5,5))
Zmax, Zmin = Z.max(), Z.min()
Z = (Z - Zmin)/(Zmax - Zmin)
print(Z)

Multiply a 5x3 matrix by a 3x2 matrix (real matrix product) (★☆☆)
```
Z = np.dot(np.ones((5,3)), np.ones((3,2)))
print(Z)
```
Create a 5x5 matrix with row values ranging from 0 to 4 (★★☆)
```
Z = np.zeros((5,5))
Z += np.arange(5)
print(Z)
```

Consider a generator function that generates 10 integers and use it to build an array (★☆☆)

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

Create a vector of size 10 with values ranging from 0 to 1, both excluded (★★☆)
```
Z = np.linspace(0,1,12,endpoint=True)[1:-1]
print(Z)
```
Create a random vector of size 10 and sort it (★★☆)
```
Z = np.random.random(10)
Z.sort()
print(Z)
```

Consider two random array A anb B, check if they are equal (★★☆)

A = np.random.randint(0,2,5)
B = np.random.randint(0,2,5)
equal = np.allclose(A,B)
print(equal)

Make an array immutable (read-only) (★★☆)

Z = np.zeros(10)
Z.flags.writeable = False
Z[0] = 1

Consider a random 10x2 matrix representing cartesian coordinates, convert them to polar coordinates (★★☆)

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)

Create random vector of size 10 and replace the maximum value by 0 (★★☆)
```
Z = np.random.random(10)
Z[Z.argmax()] = 0
print(Z)
```

Create a structured array with x and y coordinates covering the [0,1]x[0,1] area (★★☆)

Z = np.zeros((10,10), [('x',float),('y',float)])
Z['x'], Z['y'] = np.meshgrid(np.linspace(0,1,10),
                             np.linspace(0,1,10))
print(Z)

Print the minimum and maximum representable value for each numpy scalar type (★★☆)

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)

How to print all the values of an array ? (★★☆)

np.set_printoptions(threshold=np.nan)
Z = np.zeros((25,25))
print(Z)

How to print all the values of an array ? (★★☆)

np.set_printoptions(threshold=np.nan)
Z = np.zeros((25,25))
print(Z)

How to find the closest value (to a given scalar) in an array ? (★★☆)

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

Create a structured array representing a position (x,y) and a color (r,g,b) (★★☆)

 Z = np.zeros(10, [ ('position', [ ('x', float, 1),
                                   ('y', float, 1)]),
                    ('color',    [ ('r', float, 1),
                                   ('g', float, 1),
                                   ('b', float, 1)])])
print(Z)

Consider a random vector with shape (100,2) representing coordinates, find point by point distances (★★☆)

Z = np.random.random((10,2))
X,Y = np.atleast_2d(Z[:,0]), np.atleast_2d(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)

How to convert a float (32 bits) array into an integer (32 bits) in place ?

Z = np.arange(10, dtype=np.int32)
Z = Z.astype(np.float32, copy=False)

Consider the following file:

1,2,3,4,5
6,,,7,8
,,9,10,11

How to read it ? (★★☆)

Z = np.genfromtxt("missing.dat", delimiter=",")

What is the equivalent of enumerate for numpy arrays ? (★★☆)

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])

Generate a generic 2D Gaussian-like array (★★☆)

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)

How to randomly place p elements in a 2D array ? (★★☆)

# Author: Divakar
 
n = 10
p = 3
Z = np.zeros((n,n))
np.put(Z, np.random.choice(range(n*n), p, replace=False),1)

Subtract the mean of each row of a matrix (★★☆)

# 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)

How to I sort an array by the nth column ? (★★☆)

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

How to tell if a given 2D array has null columns ? (★★☆)

# Author: Warren Weckesser
 
Z = np.random.randint(0,3,(3,10))
print((~Z.any(axis=0)).any())

Find the nearest value from a given value in an array (★★☆)

Z = np.random.uniform(0,1,10)
z = 0.5
m = Z.flat[np.abs(Z - z).argmin()]
print(m)

Consider a given vector, how to add 1 to each element indexed by a second vector (be careful with repeated indices) ? (★★★)
```
# Author: Brett Olsen
 
Z = np.ones(10)
I = np.random.randint(0,len(Z),20)
Z += np.bincount(I, minlength=len(Z))
print(Z)
```
How to accumulate elements of a vector (X) to an array (F) based on an index list (I) ? (★★★)
```
# 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)
```

Considering a (w,h,3) image of (dtype=ubyte), compute the number of unique colors (★★★)

# 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))

Considering a four dimensions array, how to get sum over the last two axis at once ? (★★★)

A = np.random.randint(0,10,(3,4,3,4))
sum = A.reshape(A.shape[:-2] + (-1,)).sum(axis=-1)
print(sum)

Considering a one-dimensional vector D, how to compute means of subsets of D using a vector S of same size describing subset indices ? (★★★)

# 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)

How to get the diagonal of a dot product ? (★★★)

# Author: Mathieu Blondel
 
# 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).

Consider the vector [1, 2, 3, 4, 5], how to build a new vector with 3 consecutive zeros interleaved between each value ? (★★★)

# 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)

Consider an array of dimension (5,5,3), how to mulitply it by an array with dimensions (5,5) ? (★★★)
```
A = np.ones((5,5,3))
B = 2*np.ones((5,5))
print(A * B[:,:,None])
```

How to swap two rows of an array ? (★★★)

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

Consider a set of 10 triplets describing 10 triangles (with shared vertices), find the set of unique line segments composing all the triangles (★★★)

# 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)

Given an array C that is a bincount, how to produce an array A such that np.bincount(A) == C ? (★★★)

# 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)

How to compute averages using a sliding window over an array ? (★★★)

# 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))

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]) (★★★)

# 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)

How to negate a boolean, or to change the sign of a float inplace ? (★★★)

# Author: Nathaniel J. Smith
 
Z = np.random.randint(0,2,100)
np.logical_not(arr, out=arr)
 
Z = np.random.uniform(-1.0,1.0,100)
np.negative(arr, out=arr)

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]) ? (★★★)

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))

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]) ? (★★★)

# 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])

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) (★★★)

# 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)

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]] ? (★★★)
```
# Author: Stefan van der Walt
 
Z = np.arange(1,15,dtype=uint32)
R = stride_tricks.as_strided(Z,(11,4),(4,4))
print(R)
```

Compute a matrix rank (★★★)

# 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)

How to find the most frequent value in an array ?

Z = np.random.randint(0,10,50)
print(np.bincount(Z).argmax())

Extract all the contiguous 3x3 blocks from a random 10x10 matrix (★★★)

# 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)

Create a 2D array subclass such that Z[i,j] == Z[j,i] (★★★)

# Author: Eric O. Lebigot
# Note: only works for 2d array and value setting using indices
 
class Symetric(np.ndarray):
    def __setitem__(self, (i,j), value):
        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)

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)) (★★★)

# 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.

Consider a 16x16 array, how to get the block-sum (block size is 4x4) ? (★★★)

# 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)

How to implement the Game of Life using numpy arrays ? (★★★)

# 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)

How to get the n largest values of an array (★★★)

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]])

Given an arbitrary number of vectors, build the cartesian product (every combinations of every item) (★★★)

# 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])))

How to create a record array from a regular array ? (★★★)

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')

Comsider a large vector Z, compute Z to the power of 3 using 3 different methods (★★★)

Author: Ryan G.
 
x = np.random.rand(5e7)
 
%timeit np.power(x,3)
1 loops, best of 3: 574 ms per loop
 
%timeit x*x*x
1 loops, best of 3: 429 ms per loop
 
%timeit np.einsum('i,i,i->i',x,x,x)
1 loops, best of 3: 244 ms per loop

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 ? (★★★)

# 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 = (C.sum(axis=(1,2,3)) >= B.shape[1]).nonzero()[0]
print(rows)

Considering a 10x3 matrix, extract rows with unequal values (e.g. [2,2,3]) (★★★)

# Author: Robert Kern
 
Z = np.random.randint(0,5,(10,3))
E = np.logical_and.reduce(Z[:,1:] == Z[:,:-1], axis=1)
U = Z[~E]
print(Z)
print(U)

Convert a vector of ints into a matrix binary representation (★★★)

# 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))

Given a two dimensional array, how to extract unique rows ? (★★★)

# 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)

Considering 2 vectors A & B, write the einsum equivalent of inner, outer, sum, and mul function (★★★)

# Author: Alex Riley
# Make sure to read: http://ajcr.net/Basic-guide-to-einsum/
 
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', A, B)    # np.outer(A, B)

Considering a path described by two vectors (X,Y), how to sample it using equidistant samples (★★★) ?

# 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)