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.

Contents

Neophyte

  1. Import the numpy package under the name np

    import numpy as np
    
  2. Print the numpy version and the configuration.

    print np.__version__
    np.__config__.show()
    
  3. Create a null vector of size 10

    Z = np.zeros(10)
    print Z
    
  4. Create a null vector of size 10 but the fifth value which is 1

    Z = np.zeros(10)
    Z[4] = 1
    print Z
    
  5. Create a vector with values ranging from 10 to 49

    Z = np.arange(10,50)
    print Z
    
  6. Create a 3x3 matrix with values ranging from 0 to 8

    Z = np.arange(9).reshape(3,3)
    print Z
    
  7. Find indices of non-zero elements from [1,2,0,0,4,0]

    nz = np.nonzero([1,2,0,0,4,0])
    print nz
    
  8. Create a 3x3 identity matrix

    Z = np.eye(3)
    print Z
    
  9. 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
    
  10. Create a 3x3x3 array with random values

    Z = np.random.random((3,3,3))
    print Z
    

Novice

  1. 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
    
  2. 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
    
  3. Create a checkerboard 8x8 matrix using the tile function

    Z = np.tile( np.array([[0,1],[1,0]]), (4,4))
    print Z
    
  4. 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
    
  5. Multiply a 5x3 matrix by a 3x2 matrix (real matrix product)

    Z = np.dot(np.ones((5,3)), np.ones((3,2)))
    print Z
    
  6. Create a 5x5 matrix with row values ranging from 0 to 4

    Z = np.zeros((5,5))
    Z += np.arange(5)
    print Z
    
  7. 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
    
  8. Create a random vector of size 10 and sort it

    Z = np.random.random(10)
    Z.sort()
    print Z
    
  9. 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
    
  10. Create a random vector of size 30 and find the mean value

    Z = np.random.random(30)
    m = Z.mean()
    print m
    

Apprentice

  1. Make an array immutable (read-only)

    Z = np.zeros(10)
    Z.flags.writeable = False
    Z[0] = 1
    
  2. 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
    
  3. Create random vector of size 10 and replace the maximum value by 0

    Z = np.random.random(10)
    Z[Z.argmax()] = 0
    print Z
    
  4. 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
    
  5. 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
    
  6. 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
    
  7. 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
    
  8. 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
    
  9. 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
    
  10. 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

  1. 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=",")
    
  2. 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
    
  3. 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
    
  4. 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
    
  5. 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)
    
  6. 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
    
  7. 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
    

Craftsman

  1. 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
    
  2. 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
    
  3. 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
    
  4. 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

  1. 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
    
  2. 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)
    

Adept

  1. 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
    
  2. 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

  1. 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
    
  2. 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
    
  3. 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
    
  4. 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

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

    Note

    See stackoverflow for explanations.

    # 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
    

Archmaster