100 numpy exercises

A joint effort of the numpy community

+ +

Neophyte
Novice
Apprentice
Journeyman
Craftsman
Artisan
Adept
Expert
Master
Archmaster

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)
+
```
+
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])
+
```
+
Declare a 3x3 identity matrix
+
```
+Z = np.eye(3)
+
```
+
Declare a 5x5 matrix with values 1,2,3,4 just below the diagonal
+
```
+Z = np.diag(1+np.arange(4),k=-1)
+
```
+
Declare a 10x10x10 array with random values
+
```
+Z = np.random.random((10,10,10))
+
```
+

Novice

Declare 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
+

Declare 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()
+
```
+

Apprentice

Make an array immutable

+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
+
```
+

Declare 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()]
+
```
+

Journeyman

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))
+

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)
+

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
+
+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)
+

Artisan

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)
+

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.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]
+

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]
+

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

+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)
+