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.loria.fr/~rougier/teaching/numpy.100/index.html

Note

The level names came from an old-game (Dungeon Master)

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

The corresponding IPython notebook is available from the github repo, thanks to the rst2ipynb conversion tool by Valentin Haenel

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

Neophyte

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
```
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
```
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 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 3x3x3 array with random values
```
Z = np.random.random((3,3,3))
print Z
```

Novice

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

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 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 (between 0 and 1)

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
```
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

Create a random vector of size 30 and find the mean value
```
Z = np.random.random(30)
m = Z.mean()
print m
```

Apprentice

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

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
Z = np.random.random((10,2))
D = scipy.spatial.distance.cdist(Z,Z)
print D

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 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

Journeyman

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=",")

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

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

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

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

Craftsman

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

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)

Artisan

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)

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 point P, how to compute distance from each point j (P[j]) to each line i (P0[i],P1[i]) ?
```
Answer needed actually
```

Adept

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: Stéfan van der Walt

Z = np.arange(1,15,dtype=uint32)
R = stride_tricks.as_strided(Z,(11,4),(4,4))
print R
```

Expert

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

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: Stéfan 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.

Master

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