# 100 numpy exercises¶

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-block:: 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)

Contents

## Neophyte¶

Import the numpy package under the name np

In :
import numpy as np


Print the numpy version and the configuration.

In :
print np.__version__
np.__config__.show()

1.8.0
NOT AVAILABLE
blas_opt_info:
libraries = ['f77blas', 'cblas', 'atlas']
library_dirs = ['/home/esc/anaconda/lib']
define_macros = [('ATLAS_INFO', '"\\"3.8.4\\""')]
language = c
NOT AVAILABLE
openblas_info:
NOT AVAILABLE
lapack_opt_info:
libraries = ['lapack', 'f77blas', 'cblas', 'atlas']
library_dirs = ['/home/esc/anaconda/lib']
define_macros = [('ATLAS_INFO', '"\\"3.8.4\\""')]
language = f77
atlas_info:
libraries = ['lapack', 'f77blas', 'cblas', 'atlas']
library_dirs = ['/home/esc/anaconda/lib']
define_macros = [('ATLAS_INFO', '"\\"3.8.4\\""')]
language = f77
lapack_mkl_info:
NOT AVAILABLE
blas_mkl_info:
NOT AVAILABLE
atlas_blas_info:
libraries = ['f77blas', 'cblas', 'atlas']
library_dirs = ['/home/esc/anaconda/lib']
define_macros = [('ATLAS_INFO', '"\\"3.8.4\\""')]
language = c
mkl_info:
NOT AVAILABLE


Create a null vector of size 10

In :
Z = np.zeros(10)


Create a null vector of size 10 but the fifth value which is 1

In :
Z = np.zeros(10)
Z = 1


Create a vector with values ranging from 10 to 99

In :
Z = np.arange(10,100)


Create a 3x3 matrix with values ranging from 0 to 8

In :
Z = np.arange(9).reshape(3,3)


Find indices of non-zero elements from [1,2,0,0,4,0]

In :
nz = np.nonzero([1,2,0,0,4,0])


Create a 3x3 identity matrix

In :
Z = np.eye(3)


Create a 5x5 matrix with values 1,2,3,4 just below the diagonal

In :
Z = np.diag(1+np.arange(4),k=-1)


Create a 10x10x10 array with random values

In :
Z = np.random.random((10,10,10))


## Novice¶

Create a 8x8 matrix and fill it with a checkerboard pattern

In :
Z = np.zeros((8,8))
Z[1::2,::2] = 1
Z[::2,1::2] = 1


Create a 10x10 array with random values and find the minimum and maximum values

In :
Z = np.random.random((10,10))
Zmin, Zmax = Z.min(), Z.max()


Create a checkerboard 8x8 matrix using the tile function

In :
Z = np.tile( np.array([[0,1],[1,0]]), (4,4))


Normalize a 5x5 random matrix (between 0 and 1)

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


Multiply a 5x3 matrix by a 3x2 matrix (real matrix product)

In :
Z = np.dot(np.ones((5,3)), np.ones((3,2)))


Create a 10x10 matrix with row values ranging from 0 to 9

In :
Z = np.zeros((10,10))
Z += np.arange(10)


Create a vector of size 1000 with values ranging from 0 to 1, both excluded

In :
Z = np.random.linspace(0,1,1002,endpoint=True)[1:-1]

---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
<ipython-input-17-e5d39b8d39cb> in <module>()
----> 1 Z = np.random.linspace(0,1,1002,endpoint=True)[1:-1]

AttributeError: 'module' object has no attribute 'linspace'

Create a random vector of size 100 and sort it

In :
Z = np.random.random(100)
Z.sort()


Consider two random matrices A anb B, check if they are equal.

In :
A = np.random.randint(0,2,(2,2))
B = np.random.randint(0,2,(2,2))
equal = np.allclose(A,B)


Create a random vector of size 1000 and find the mean value

In :
Z = np.random.random(1000)
m = Z.mean()


## Apprentice¶

In :
Z = np.zeros(10)
Z.flags.writeable = False


Consider a random 100x2 matrix representing cartesian coordinates, convert them to polar coordinates

In :
Z = np.random.random((100,2))
X,Y = Z[:,0], Z[:,1]
R = np.sqrt(X**2+Y**2)
T = np.arctan2(Y,X)


Create random vector of size 100 and replace the maximum value by 0

In :
Z = np.random.random(100)
Z[Z.argmax()] = 0


Create a structured array with x and y coordinates covering the [0,1]x[0,1] area.

In :
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 the minimum and maximum representable value for each numpy scalar type

In :
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

-128
127
-2147483648
2147483647
-9223372036854775808
9223372036854775807
-3.40282e+38
3.40282e+38
1.19209e-07
-1.79769313486e+308
1.79769313486e+308
2.22044604925e-16


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

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


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

In :
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)

# Much faster with scipy
Z = np.random.random((10,2))
D = scipy.spatial.distance.cdist(Z,Z)

---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
<ipython-input-27-bc6bf442f025> in <module>()
5 # Much faster with scipy
6 Z = np.random.random((10,2))
----> 7 D = scipy.spatial.distance.cdist(Z,Z)

NameError: name 'scipy' is not defined

Generate a generic 2D Gaussian-like array

In :
X, Y = np.meshgrid(np.linspace(-1,1,100), np.linspace(-1,1,100))
D = np.sqrt(X*X+Y*Y)
sigma, mu = 1.0, 0.0
G = np.exp(-( (D-mu)**2 / ( 2.0 * sigma**2 ) ) )


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

In :
# 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


Find the nearest value from a given value in an array

In :
Z.flat[np.abs(Z - z).argmin()]

---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
<ipython-input-30-1fd90557d1cc> in <module>()
----> 1 Z.flat[np.abs(Z - z).argmin()]

NameError: name 'z' is not defined

## Journeyman¶

Consider the following file::

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

In :
Z = genfromtxt("missing.dat", delimiter=",")

---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
<ipython-input-31-ec7cc23ee08d> in <module>()
----> 1 Z = genfromtxt("missing.dat", delimiter=",")

NameError: name 'genfromtxt' is not defined

Consider a generator function that generates 10 integers and use it to build an array

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


Consider a given vector, how to add 1 to each element indexed by a second vector (be careful with repeated indices) ?

In :
# Author: Brett Olsen

Z = np.ones(10)
I = np.random.randint(0,len(Z),20)
Z += np.bincount(I, minlength=len(Z))


How to accumulate elements of a vector (X) to an array (F) based on an index list (I) ?

In :
# Author: Alan G Isaac

X = [1,2,3,4,5,6]
I = [1,3,9,3,4,1]
F = np.bincount(I,X)


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

In :
# 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))

np.unique(I)

Out:
array([0, 1], dtype=uint8)

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

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


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

In :
# 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


## Craftsman¶

Consider a one-dimensional array Z, build a two-dimensional array whose first row is (Z,Z,Z) and each subsequent row is shifted by 1 (last row should be (Z[-3],Z[-2],Z[-1])

In :
# Author: Joe Kington / Erik Rigtorp

def rolling(a, window):
shape = (a.size - window + 1, window)
strides = (a.itemsize, a.itemsize)
return np.lib.stride_tricks.as_strided(a, shape=shape, strides=strides)

Z = rolling(np.arange(100), 3)


Consider a set of 100 triplets describing 100 triangles (with shared vertices), find the set of unique line segments composing all the triangles.

In :
# Author: Nicolas Rougier

faces = np.random.randint(0,100,(100,3))

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)


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

In :
# Jaime Fernández del Río

C = np.bincount([1,1,2,3,4,4,6])
A = np.repeat(np.arange(len(C)), C)


## Artisan¶

Considering a 100x3 matrix, extract rows with unequal values (e.g. [2,2,3])

In :
# Author: Robert Kern

Z = np.random.randint(0,5,(100,3))
E = np.logical_and.reduce(Z[:,1:] == Z[:,:-1], axis=1)
U = Z[~E]


Convert a vector of ints into a matrix binary representation.

In :
# 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)
B = B[:,::-1]

# Author: Daniel T. McDonald

I = np.array([0, 1, 2, 3, 15, 16, 32, 64, 128], dtype=np.uint8)
np.unpackbits(I[:, np.newaxis], axis=1)

Out:
array([[0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 1],
[0, 0, 0, 0, 0, 0, 1, 0],
[0, 0, 0, 0, 0, 0, 1, 1],
[0, 0, 0, 0, 1, 1, 1, 1],
[0, 0, 0, 1, 0, 0, 0, 0],
[0, 0, 1, 0, 0, 0, 0, 0],
[0, 1, 0, 0, 0, 0, 0, 0],
[1, 0, 0, 0, 0, 0, 0, 0]], dtype=uint8)

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)

In :
# Author: Nicolas Rougier

Z = np.random.random((25,25))
shape = (3,3)
fill  = 0
position = (0,0)

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]


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]] ?

In :
# Stéfan van der Walt

Z = np.arange(1,15)
R = as_strided(Z,(11,4),(4,4))

---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
<ipython-input-44-372239c684a6> in <module>()
2
3 Z = np.arange(1,15)
----> 4 R = as_strided(Z,(11,4),(4,4))

NameError: name 'as_strided' is not defined

## 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 ?

In :
# 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).nonzero()


Extract all the contiguous 3x3 blocks from a random 10x10 matrix.

In :
# Chris Barker

Z = np.random.randint(0,5,(10,10))
n = 3
i = 1 + (Z.shape-3)
j = 1 + (Z.shape-3)
C = stride_tricks.as_strided(Z, shape=(i, j, n, n), strides=Z.strides + Z.strides)

---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
<ipython-input-46-be634ecf5686> in <module>()
5 i = 1 + (Z.shape-3)
6 j = 1 + (Z.shape-3)
----> 7 C = stride_tricks.as_strided(Z, shape=(i, j, n, n), strides=Z.strides + Z.strides)

NameError: name 'stride_tricks' is not defined

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

In :
# 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

  File "<ipython-input-47-e55f32d39787>", line 13
S[2,3] = 42
^
SyntaxError: invalid syntax


## Master¶

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

## Note¶

See stackoverflow for explanations.

In :
# Jaime Fernández del Río

Z = np.random.randint(0,2,(6,6))
T = np.ascontiguousarray(Z).view(np.dtype((np.void, Z.dtype.itemsize * Z.shape)))
_, idx = np.unique(T, return_index=True)
uZ = Z[idx]