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
Contents
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)
Create a null vector of size 10 but the fifth value which is 1
Z = np.zeros(10) Z[4] = 1
Create a vector with values ranging from 10 to 99
Z = np.arange(10,100)
Create a 3x3 matrix with values ranging from 0 to 8
Z = np.arange(9).reshape(3,3)
Find indices of non-zero elements from [1,2,0,0,4,0]
nz = np.nonzero([1,2,0,0,4,0])
Create a 3x3 identity matrix
Z = np.eye(3)
Create a 5x5 matrix with values 1,2,3,4 just below the diagonal
Z = np.diag(1+np.arange(4),k=-1)
Create a 10x10x10 array with random values
Z = np.random.random((10,10,10))
Create a 8x8 matrix and fill it with a checkerboard pattern
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
Z = np.random.random((10,10)) Zmin, Zmax = Z.min(), Z.max()
Create a checkerboard 8x8 matrix using the tile function
Z = np.tile( np.array([[0,1],[1,0]]), (4,4))
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)
Multiply a 5x3 matrix by a 3x2 matrix (real matrix product)
Z = np.dot(np.ones((5,3)), np.ones((3,2)))
Create a 10x10 matrix with row values ranging from 0 to 9
Z = np.zeros((10,10)) Z += np.arange(10)
Create a vector of size 1000 with values ranging from 0 to 1, both excluded
Z = np.random.linspace(0,1,1002,endpoint=True)[1:-1]
Create a random vector of size 100 and sort it
Z = np.random.random(100) Z.sort()
Consider two random matrices A anb B, check if they are equal.
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
Z = np.random.random(1000) m = Z.mean()
Make an array immutable (read-only)
Z = np.zeros(10) Z.flags.writeable = False
Consider a random 100x2 matrix representing cartesian coordinates, convert them to polar coordinates
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
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.
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
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)])])
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) # Much faster with scipy Z = np.random.random((10,2)) D = scipy.spatial.distance.cdist(Z,Z)
Generate a generic 2D Gaussian-like array
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 ?
# 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
Z.flat[np.abs(Z - z).argmin()]
Consider the following file:
1,2,3,4,5 6,,,7,8 ,,9,10,11
How to read it ?
Z = 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)
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))
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)
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)) 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)
Considering a one-dimensional vector D, how to compute means of subsets of D using a vector S of same size describing subset indices ?
# 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
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 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.
# 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 ?
# Jaime Fernández del Río C = np.bincount([1,1,2,3,4,4,6]) A = np.repeat(np.arange(len(C)), C)
Considering a 100x3 matrix, extract rows with unequal values (e.g. [2,2,3])
# 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.
# 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)
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.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 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]
Extract all the contiguous 3x3 blocks from a random 10x10 matrix.
# 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)
Create a 2D array subclass such that Z[i,j] == Z[j,i]
# 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