Replaced README with index such that page can be read directly from github
This commit is contained in:
Nicolas Rougier
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index.rst
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index.rst
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===================
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100 numpy exercises
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===================
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A joint effort of the numpy community
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-------------------------------------
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The goal is both to offer a quick reference for new and old users and to
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provide also a set of exercices for those who teach.
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If you remember having asked or answered a (short) problem, you can send a pull
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request. The format is:
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#. Find indices of non-zero elements from [1,2,0,0,4,0]
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.. code:: python
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# Author: Somebody
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print np.nonzero([1,2,0,0,4,0])
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If you can provide the assumed level of the answer, that would be even better.
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Here is what the page looks like so far:
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http://www.loria.fr/~rougier/teaching/numpy.100/index.html
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(The level names came from an old-game: Dungeon Master)
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.. contents::
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:local:
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:depth: 1
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Neophyte
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========
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1. Import the numpy package under the name ``np``
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.. code:: python
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import numpy as np
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#. Print the numpy version and the configuration.
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.. code:: python
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print np.__version__
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np.__config__.show()
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#. Create a null vector of size 10
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.. code:: python
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Z = np.zeros(10)
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#. Create a null vector of size 10 but the fifth value which is 1
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.. code:: python
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Z = np.zeros(10)
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Z[4] = 1
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#. Create a vector with values ranging from 10 to 99
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.. code:: python
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Z = np.arange(10,100)
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#. Create a 3x3 matrix with values ranging from 0 to 8
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.. code:: python
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Z = np.arange(9).reshape(3,3)
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#. Find indices of non-zero elements from [1,2,0,0,4,0]
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.. code:: python
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nz = np.nonzero([1,2,0,0,4,0])
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#. Declare a 3x3 identity matrix
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.. code:: python
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Z = np.eye(3)
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#. Declare a 5x5 matrix with values 1,2,3,4 just below the diagonal
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.. code:: python
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Z = np.diag(1+np.arange(4),k=-1)
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#. Declare a 10x10x10 array with random values
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.. code:: python
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Z = np.random.random((10,10,10))
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Novice
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======
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#. Declare a 8x8 matrix and fill it with a checkerboard pattern
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.. code:: python
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Z = np.zeros((8,8))
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Z[1::2,::2] = 1
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Z[::2,1::2] = 1
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#. Declare a 10x10 array with random values and find the minimum and maximum values
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.. code:: python
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Z = np.random.random((10,10))
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Zmin, Zmax = Z.min(), Z.max()
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#. Create a checkerboard 8x8 matrix using the tile function
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.. code:: python
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Z = np.tile( np.array([[0,1],[1,0]]), (4,4))
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#. Normalize a 5x5 random matrix (between 0 and 1)
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.. code:: python
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Z = np.random.random((5,5))
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Zmax,Zmin = Z.max(), Z.min()
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Z = (Z - Zmin)/(Zmax - Zmin)
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#. Multiply a 5x3 matrix by a 3x2 matrix (real matrix product)
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.. code:: python
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Z = np.dot(np.ones((5,3)), np.ones((3,2)))
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#. Create a 10x10 matrix with row values ranging from 0 to 9
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.. code:: python
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Z = np.zeros((10,10))
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Z += np.arange(10)
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#. Create a vector of size 1000 with values ranging from 0 to 1, both excluded
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.. code:: python
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Z = np.random.linspace(0,1,1002,endpoint=True)[1:-1]
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#. Create a random vector of size 100 and sort it
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.. code:: python
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Z = np.random.random(100)
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Z.sort()
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#. Consider two random matrices A anb B, check if they are equal.
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.. code:: python
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A = np.random.randint(0,2,(2,2))
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B = np.random.randint(0,2,(2,2))
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equal = np.allclose(A,B)
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#. Create a random vector of size 1000 and find the mean value
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.. code:: python
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Z = np.random.random(1000)
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m = Z.mean()
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Apprentice
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==========
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#. Make an array immutable
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.. code:: python
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Z = np.zeros(10)
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Z.flags.writeable = False
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#. Consider a random 100x2 matrix representing cartesian coordinates, convert
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them to polar coordinates
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.. code:: python
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Z = np.random.random((100,2))
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X,Y = Z[:,0], Z[:,1]
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R = np.sqrt(X**2+Y**2)
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T = np.arctan2(Y,X)
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#. Create random vector of size 100 and replace the maximum value by 0
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.. code:: python
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Z = np.random.random(100)
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Z[Z.argmax()] = 0
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#. Declare a structured array with ``x`` and ``y`` coordinates covering the
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[0,1]x[0,1] area.
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.. code:: python
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Z = np.zeros((10,10), [('x',float),('y',float)])
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Z['x'], Z['y'] = np.meshgrid(np.linspace(0,1,10),
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np.linspace(0,1,10))
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#. Print the minimum and maximum representable value for each numpy scalar type
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.. code:: python
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for dtype in [np.int8, np.int32, np.int64]:
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print np.iinfo(dtype).min
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print np.iinfo(dtype).max
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for dtype in [np.float32, np.float64]:
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print np.finfo(dtype).min
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print np.finfo(dtype).max
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print np.finfo(dtype).eps
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#. Create a structured array representing a position (x,y) and a color (r,g,b)
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.. code:: python
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Z = np.zeros(10, [ ('position', [ ('x', float, 1),
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('y', float, 1)]),
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('color', [ ('r', float, 1),
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('g', float, 1),
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('b', float, 1)])])
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#. Consider a random vector with shape (100,2) representing coordinates, find
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point by point distances
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.. code:: python
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Z = np.random.random((10,2))
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X,Y = np.atleast_2d(Z[:,0]), np.atleast_2d(Z[:,1])
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D = np.sqrt( (X-X.T)**2 + (Y-Y.T)**2)
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# Much faster with scipy
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Z = np.random.random((10,2))
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D = scipy.spatial.distance.cdist(Z,Z)
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#. Generate a generic 2D Gaussian-like array
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.. code:: python
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X, Y = np.meshgrid(np.linspace(-1,1,100), np.linspace(-1,1,100))
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D = np.sqrt(X*X+Y*Y)
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sigma, mu = 1.0, 0.0
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G = np.exp(-( (D-mu)**2 / ( 2.0 * sigma**2 ) ) )
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#. Consider the vector [1, 2, 3, 4, 5], how to build a new vector with 3
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consecutive zeros interleaved between each value ?
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.. code:: python
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# Author: Warren Weckesser
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Z = np.array([1,2,3,4,5])
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nz = 3
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Z0 = np.zeros(len(Z) + (len(Z)-1)*(nz))
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Z0[::nz+1] = Z
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#. Find the nearest value from a given value in an array
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.. code:: python
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Z.flat[np.abs(Z - z).argmin()]
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Journeyman
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==========
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#. Consider the following file::
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1,2,3,4,5
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6,,,7,8
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,,9,10,11
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How to read it ?
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.. code:: python
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Z = genfromtxt("missing.dat", delimiter=",")
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#. Consider a generator function that generates 10 integers and use it to build an
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array
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.. code:: python
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def generate():
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for x in xrange(10):
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yield x
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Z = np.fromiter(generate(),dtype=float,count=-1)
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#. Consider a given vector, how to add 1 to each element indexed by a second
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vector (be careful with repeated indices) ?
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.. code:: python
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# Author: Brett Olsen
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Z = np.ones(10)
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I = np.random.randint(0,len(Z),20)
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Z += np.bincount(I, minlength=len(Z))
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#. How to accumulate elements of a vector (X) to an array (F) based on an index
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list (I) ?
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.. code:: python
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# Author: Alan G Isaac
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X = [1,2,3,4,5,6]
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I = [1,3,9,3,4,1]
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F = np.bincount(I,X)
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#. Considering a (w,h,3) image of (dtype=ubyte), compute the number of unique
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colors
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.. code:: python
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# Author: Nadav Horesh
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w,h = 16,16
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I = np.random.randint(0,2,(h,w,3)).astype(np.ubyte)
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F = I[...,0]*256*256 + I[...,1]*256 +I[...,2]
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n = len(np.unique(F))
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np.unique(I)
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#. Considering a four dimensions array, how to get sum over the last two axis at once ?
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.. code:: python
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A = np.random.randint(0,10,(3,4,3,4))
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sum = A.reshape(A.shape[:-2] + (-1,)).sum(axis=-1)
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Craftsman
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=========
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#. Consider a one-dimensional array Z, build a two-dimensional array whose
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first row is (Z[0],Z[1],Z[2]) and each subsequent row is shifted by 1 (last
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row should be (Z[-3],Z[-2],Z[-1])
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.. code:: python
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# Author: Joe Kington / Erik Rigtorp
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def rolling(a, window):
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shape = (a.size - window + 1, window)
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strides = (a.itemsize, a.itemsize)
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return np.lib.stride_tricks.as_strided(a, shape=shape, strides=strides)
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Z = rolling(np.arange(100), 3)
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#. Consider a set of 100 triplets describing 100 triangles (with shared
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vertices), find the set of unique line segments composing all the triangles.
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.. code:: python
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# Author: Nicolas Rougier
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faces = np.random.randint(0,100,(100,3))
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F = np.roll(faces.repeat(2,axis=1),-1,axis=1)
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F = F.reshape(len(F)*3,2)
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F = np.sort(F,axis=1)
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G = F.view( dtype=[('p0',F.dtype),('p1',F.dtype)] )
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G = np.unique(G)
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Artisan
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=======
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#. Considering a 100x3 matrix, extract rows with unequal values (e.g. [2,2,3])
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.. code:: python
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# Author: Robert Kern
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Z = np.random.randint(0,5,(100,3))
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E = np.logical_and.reduce(Z[:,1:] == Z[:,:-1], axis=1)
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U = Z[~E]
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#. Convert a vector of ints into a matrix binary representation.
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.. code:: python
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# Author: Warren Weckesser
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I = np.array([0, 1, 2, 3, 15, 16, 32, 64, 128])
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B = ((I.reshape(-1,1) & (2**np.arange(8))) != 0).astype(int)
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B = B[:,::-1]
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# Author: Daniel T. McDonald
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I = np.array([0, 1, 2, 3, 15, 16, 32, 64, 128], dtype=np.uint8)
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np.unpackbits(I[:, np.newaxis], axis=1)
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Adept
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=====
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#. Consider an arbitrary array, write a function that extract a subpart with a
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fixed shape and centered on a given element (pad with a ``fill`` value when
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necessary)
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.. code :: python
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# Author: Nicolas Rougier
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Z = np.random.random((25,25))
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shape = (3,3)
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fill = 0
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position = (0,0)
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R = np.ones(shape, dtype=Z.dtype)*fill
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P = np.array(list(position)).astype(int)
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Rs = np.array(list(R.shape)).astype(int)
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Zs = np.array(list(Z.shape)).astype(int)
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R_start = np.zeros((len(shape),)).astype(int)
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R_stop = np.array(list(shape)).astype(int)
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Z_start = (P-Rs//2)
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Z_stop = (P+Rs//2)+Rs%2
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R_start = (R_start - np.minimum(Z_start,0)).tolist()
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Z_start = (np.maximum(Z_start,0)).tolist()
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R_stop = np.maximum(R_start, (R_stop - np.maximum(Z_stop-Zs,0))).tolist()
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Z_stop = (np.minimum(Z_stop,Zs)).tolist()
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r = [slice(start,stop) for start,stop in zip(R_start,R_stop)]
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z = [slice(start,stop) for start,stop in zip(Z_start,Z_stop)]
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R[r] = Z[z]
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Expert
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======
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#. Consider two arrays A and B of shape (8,3) and (2,2). How to find rows of A
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that contain elements of each row of B regardless of the order of the elements
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in B ?
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.. code:: python
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# Author: Gabe Schwartz
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A = np.random.randint(0,5,(8,3))
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B = np.random.randint(0,5,(2,2))
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C = (A[..., np.newaxis, np.newaxis] == B)
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rows = (C.sum(axis=(1,2,3)) >= B.shape[1]).nonzero()[0]
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#. Extract all the contiguous 3x3 blocks from a random 10x10 matrix.
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.. code:: python
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Z = np.random.randint(0,5,(10,10))
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n = 3
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i = 1 + (Z.shape[0]-3)
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j = 1 + (Z.shape[1]-3)
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C = stride_tricks.as_strided(Z, shape=(i, j, n, n), strides=Z.strides + Z.strides)
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Master
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======
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Archmaster
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==========
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Reference in New Issue
Block a user