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Corrected recipes and added notebook

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Nicolas Rougier 2014-05-29 21:48:26 +02:00
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README.html
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@ -32,23 +32,8 @@ is:</p>
<p class="last">The level names came from an old-game (Dungeon Master)</p>
</div>
<p>Repository is at: <a class="reference external" href="https://github.com/rougier/numpy-100">https://github.com/rougier/numpy-100</a></p>
<p><strong>Contents</strong></p>
<div class="contents local topic" id="contents">
<ul class="simple">
<li><a class="reference internal" href="#neophyte" id="id1">Neophyte</a></li>
<li><a class="reference internal" href="#novice" id="id2">Novice</a></li>
<li><a class="reference internal" href="#apprentice" id="id3">Apprentice</a></li>
<li><a class="reference internal" href="#journeyman" id="id4">Journeyman</a></li>
<li><a class="reference internal" href="#craftsman" id="id5">Craftsman</a></li>
<li><a class="reference internal" href="#artisan" id="id6">Artisan</a></li>
<li><a class="reference internal" href="#adept" id="id7">Adept</a></li>
<li><a class="reference internal" href="#expert" id="id8">Expert</a></li>
<li><a class="reference internal" href="#master" id="id9">Master</a></li>
<li><a class="reference internal" href="#archmaster" id="id10">Archmaster</a></li>
</ul>
</div>
<div class="section" id="neophyte">
<h1><a class="toc-backref" href="#id1">Neophyte</a></h1>
<h1>Neophyte</h1>
<ol class="arabic">
<li><p class="first">Import the numpy package under the name <tt class="docutils literal">np</tt></p>
<pre class="code python literal-block">
@ -105,7 +90,7 @@ is:</p>
</ol>
</div>
<div class="section" id="novice">
<h1><a class="toc-backref" href="#id2">Novice</a></h1>
<h1>Novice</h1>
<ol class="arabic">
<li><p class="first">Create a 8x8 matrix and fill it with a checkerboard pattern</p>
<pre class="code python literal-block">
@ -170,7 +155,7 @@ is:</p>
</ol>
</div>
<div class="section" id="apprentice">
<h1><a class="toc-backref" href="#id3">Apprentice</a></h1>
<h1>Apprentice</h1>
<ol class="arabic">
<li><p class="first">Make an array immutable (read-only)</p>
<pre class="code python literal-block">
@ -260,7 +245,7 @@ consecutive zeros interleaved between each value ?</p>
</ol>
</div>
<div class="section" id="journeyman">
<h1><a class="toc-backref" href="#id4">Journeyman</a></h1>
<h1>Journeyman</h1>
<ol class="arabic">
<li><p class="first">Consider the following file:</p>
<pre class="literal-block">
@ -336,7 +321,7 @@ using a vector S of same size describing subset indices ?</p>
</ol>
</div>
<div class="section" id="craftsman">
<h1><a class="toc-backref" href="#id5">Craftsman</a></h1>
<h1>Craftsman</h1>
<ol class="arabic">
<li><p class="first">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
@ -378,7 +363,7 @@ np.bincount(A) == C ?</p>
</ol>
</div>
<div class="section" id="artisan">
<h1><a class="toc-backref" href="#id6">Artisan</a></h1>
<h1>Artisan</h1>
<ol class="arabic">
<li><p class="first">Considering a 100x3 matrix, extract rows with unequal values (e.g. [2,2,3])</p>
<pre class="code python literal-block">
@ -406,7 +391,7 @@ np.bincount(A) == C ?</p>
</ol>
</div>
<div class="section" id="adept">
<h1><a class="toc-backref" href="#id7">Adept</a></h1>
<h1>Adept</h1>
<ol class="arabic">
<li><p class="first">Consider an arbitrary array, write a function that extract a subpart with a
fixed shape and centered on a given element (pad with a <tt class="docutils literal">fill</tt> value when
@ -451,7 +436,7 @@ array R = [[1,2,3,4], [2,3,4,5], [3,4,5,6], ..., [11,12,13,14]] ?</p>
</ol>
</div>
<div class="section" id="expert">
<h1><a class="toc-backref" href="#id8">Expert</a></h1>
<h1>Expert</h1>
<ol class="arabic">
<li><p class="first">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
@ -498,7 +483,7 @@ in B ?</p>
</ol>
</div>
<div class="section" id="master">
<h1><a class="toc-backref" href="#id9">Master</a></h1>
<h1>Master</h1>
<ol class="arabic">
<li><p class="first">Given a two dimensional array, how to extract unique rows ?</p>
<div class="note">
@ -517,7 +502,7 @@ in B ?</p>
</ol>
</div>
<div class="section" id="archmaster">
<h1><a class="toc-backref" href="#id10">Archmaster</a></h1>
<h1>Archmaster</h1>
</div>
</div>
</body>

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@ -8,32 +8,33 @@ 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::
is:
#. Find indices of non-zero elements from [1,2,0,0,4,0]
::
.. code:: python
#. Find indices of non-zero elements from [1,2,0,0,4,0]
# Author: Somebody
.. code:: python
print np.nonzero([1,2,0,0,4,0])
# 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 IPython notebook is
available from the github repo, thanks to the `rst2ipynb
<https://github.com/esc/rst2ipynb>`_ conversion tool by `Valentin Haenel
<http://haenel.co>`_
Repository is at: https://github.com/rougier/numpy-100
**Contents**
.. contents::
:local:
:depth: 1
.. **Contents**
.. .. contents::
.. :local:
.. :depth: 1
Neophyte
@ -41,14 +42,14 @@ Neophyte
1. Import the numpy package under the name ``np``
.. code:: python
.. code-block:: python
import numpy as np
2. Print the numpy version and the configuration.
.. code:: python
.. code-block:: python
print np.__version__
np.__config__.show()
@ -56,129 +57,160 @@ Neophyte
3. Create a null vector of size 10
.. code:: python
.. code-block:: python
Z = np.zeros(10)
print Z
4. Create a null vector of size 10 but the fifth value which is 1
.. code:: python
.. code-block:: python
Z = np.zeros(10)
Z[4] = 1
print Z
5. Create a vector with values ranging from 10 to 99
.. code:: python
5. Create a vector with values ranging from 10 to 49
.. code-block:: python
Z = np.arange(10,50)
print Z
Z = np.arange(10,100)
6. Create a 3x3 matrix with values ranging from 0 to 8
.. code:: python
.. code-block:: python
Z = np.arange(9).reshape(3,3)
print Z
7. Find indices of non-zero elements from [1,2,0,0,4,0]
.. code:: python
.. code-block:: python
nz = np.nonzero([1,2,0,0,4,0])
print nz
8. Create a 3x3 identity matrix
.. code:: python
.. code-block:: python
Z = np.eye(3)
print Z
9. Create a 5x5 matrix with values 1,2,3,4 just below the diagonal
.. code:: python
.. code-block:: python
Z = np.diag(1+np.arange(4),k=-1)
print Z
10. Create a 10x10x10 array with random values
10. Create a 3x3x3 array with random values
.. code:: python
.. code-block:: python
Z = np.random.random((3,3,3))
print Z
Z = np.random.random((10,10,10))
Novice
======
1. Create a 8x8 matrix and fill it with a checkerboard pattern
.. code:: python
.. code-block:: python
Z = np.zeros((8,8))
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
.. code:: python
.. code-block:: python
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
.. code:: python
.. code-block:: python
Z = np.tile( np.array([[0,1],[1,0]]), (4,4))
print Z
4. Normalize a 5x5 random matrix (between 0 and 1)
.. code:: python
.. code-block:: python
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)
.. code:: python
.. code-block:: python
Z = np.dot(np.ones((5,3)), np.ones((3,2)))
print Z
6. Create a 10x10 matrix with row values ranging from 0 to 9
6. Create a 5x5 matrix with row values ranging from 0 to 4
.. code:: python
.. code-block:: python
Z = np.zeros((10,10))
Z += np.arange(10)
Z = np.zeros((5,5))
Z += np.arange(5)
print Z
7. Create a vector of size 1000 with values ranging from 0 to 1, both excluded
.. code:: python
7. Create a vector of size 10 with values ranging from 0 to 1, both excluded
Z = np.random.linspace(0,1,1002,endpoint=True)[1:-1]
.. code-block:: python
8. Create a random vector of size 100 and sort it
Z = np.linspace(0,1,12,endpoint=True)[1:-1]
print Z
.. code:: python
Z = np.random.random(100)
8. Create a random vector of size 10 and sort it
.. code-block:: python
Z = np.random.random(10)
Z.sort()
print Z
9. Consider two random matrices A anb B, check if they are equal.
.. code:: python
9. Consider two random array A anb B, check if they are equal.
A = np.random.randint(0,2,(2,2))
B = np.random.randint(0,2,(2,2))
.. code-block:: python
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 1000 and find the mean value
.. code:: python
10. Create a random vector of size 30 and find the mean value
Z = np.random.random(1000)
.. code-block:: python
Z = np.random.random(30)
m = Z.mean()
print m
@ -188,43 +220,49 @@ Apprentice
1. Make an array immutable (read-only)
.. code:: python
.. code-block:: python
Z = np.zeros(10)
Z.flags.writeable = False
Z[0] = 1
2. Consider a random 100x2 matrix representing cartesian coordinates, convert
2. Consider a random 10x2 matrix representing cartesian coordinates, convert
them to polar coordinates
.. code:: python
.. code-block:: python
Z = np.random.random((100,2))
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 100 and replace the maximum value by 0
3. Create random vector of size 10 and replace the maximum value by 0
.. code:: python
.. code-block:: python
Z = np.random.random(100)
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.
.. code:: python
.. code-block:: python
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
.. code:: python
.. code-block:: python
for dtype in [np.int8, np.int32, np.int64]:
print np.iinfo(dtype).min
@ -237,43 +275,48 @@ Apprentice
6. Create a structured array representing a position (x,y) and a color (r,g,b)
.. code:: python
.. code-block:: python
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
.. code:: python
.. code-block:: python
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
.. code:: python
.. code-block:: python
X, Y = np.meshgrid(np.linspace(-1,1,100), np.linspace(-1,1,100))
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 ?
.. code:: python
.. code-block:: python
# Author: Warren Weckesser
@ -281,14 +324,17 @@ Apprentice
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
.. code:: python
Z.flat[np.abs(Z - z).argmin()]
.. code-block:: python
Z = np.random.uniform(0,1,10)
z = 0.5
m = Z.flat[np.abs(Z - z).argmin()]
print m
Journeyman
@ -302,49 +348,53 @@ Journeyman
How to read it ?
.. code:: python
.. code-block:: python
Z = genfromtxt("missing.dat", delimiter=",")
Z = np.genfromtxt("missing.dat", delimiter=",")
2. Consider a generator function that generates 10 integers and use it to build an
array
.. code:: python
.. code-block:: python
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) ?
.. code:: python
.. code-block:: python
# 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) ?
.. code:: python
.. code-block:: python
# 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
.. code:: python
.. code-block:: python
# Author: Nadav Horesh
@ -352,23 +402,22 @@ Journeyman
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)
print np.unique(I)
6. Considering a four dimensions array, how to get sum over the last two axis at once ?
.. code:: python
.. code-block:: python
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 ?
.. code:: python
.. code-block:: python
# Jaime Fernández del Río
@ -377,8 +426,7 @@ Journeyman
D_sums = np.bincount(S, weights=D)
D_counts = np.bincount(S)
D_means = D_sums / D_counts
print D_means
@ -389,72 +437,77 @@ Craftsman
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])
.. code:: python
.. code-block:: python
# 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 np.lib.stride_tricks.as_strided(a, shape=shape, strides=strides)
return stride_tricks.as_strided(a, shape=shape, strides=strides)
Z = rolling(np.arange(10), 3)
print Z
Z = rolling(np.arange(100), 3)
2. Consider a set of 100 triplets describing 100 triangles (with shared
2. Consider a set of 10 triplets describing 10 triangles (with shared
vertices), find the set of unique line segments composing all the triangles.
.. code:: python
.. code-block:: python
# Author: Nicolas Rougier
faces = np.random.randint(0,100,(100,3))
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 ?
.. code:: python
.. code-block:: python
# Jaime Fernández del Río
C = np.bincount([1,1,2,3,4,4,6])
A = np.repeat(np.arange(len(C)), C)
print A
Artisan
=======
1. Considering a 100x3 matrix, extract rows with unequal values (e.g. [2,2,3])
1. Considering a 10x3 matrix, extract rows with unequal values (e.g. [2,2,3])
.. code:: python
.. code-block:: python
# Author: Robert Kern
Z = np.random.randint(0,5,(100,3))
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.
.. code:: python
.. code-block:: python
# 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]
print 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)
print np.unpackbits(I[:, np.newaxis], axis=1)
@ -465,14 +518,14 @@ Adept
fixed shape and centered on a given element (pad with a ``fill`` value when
necessary)
.. code :: python
.. code:: python
# Author: Nicolas Rougier
Z = np.random.random((25,25))
shape = (3,3)
Z = np.random.randint(0,10,(10,10))
shape = (5,5)
fill = 0
position = (0,0)
position = (1,1)
R = np.ones(shape, dtype=Z.dtype)*fill
P = np.array(list(position)).astype(int)
@ -492,20 +545,20 @@ Adept
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]] ?
.. code:: python
.. code-block:: python
# Stéfan van der Walt
Z = np.arange(1,15)
R = as_strided(Z,(11,4),(4,4))
Z = np.arange(1,15,dtype=uint32)
R = stride_tricks.as_strided(Z,(11,4),(4,4))
print R
Expert
@ -515,7 +568,7 @@ Expert
that contain elements of each row of B regardless of the order of the elements
in B ?
.. code:: python
.. code-block:: python
# Author: Gabe Schwartz
@ -524,11 +577,12 @@ Expert
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.
.. code:: python
.. code-block:: python
# Chris Barker
@ -537,11 +591,12 @@ Expert
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]
.. code:: python
.. code-block:: python
# Eric O. Lebigot
# Note: only works for 2d array and value setting using indices
@ -554,7 +609,7 @@ Expert
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 = symetric(np.random.randint(0,10,(5,5)))
S[2,3] = 42
print S
@ -566,14 +621,15 @@ Master
.. note:: See `stackoverflow <http://stackoverflow.com/questions/16970982/find-unique-rows-in-numpy-array/>`_ for explanations.
.. code:: python
.. code-block:: python
# Jaime Fernández del Río
Z = np.random.randint(0,2,(6,6))
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