Corrected recipes and added notebook

2014-05-29 21:48:26 +02:00
parent 6d55b8bcac
commit 4cef439df0
3 changed files with 2411 additions and 137 deletions
--- a/README.html
+++ b/README.html
@@ -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>
--- a/README.ipynb
+++ b/README.ipynb
--- a/README.rst
+++ b/README.rst
@@ -8,7 +8,9 @@ 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]
@@ -22,18 +24,17 @@ is::
 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:
-**Contents**
+..     :depth: 1
 .. 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.zeros((5,5))
-    Z += np.arange(10)
+    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))
+   .. code-block:: python
-      B = np.random.randint(0,2,(2,2))
+
      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
+    .. code-block:: python
       Z.flat[np.abs(Z - z).argmin()]
       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))
-
+      print np.unique(I)
      np.unique(I)
 6. Considering a four dimensions array, how to get sum over the last two axis at once ?
-
+   .. code-block:: python
   .. code:: 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))
+      Z = np.random.randint(0,10,(10,10))
-      shape = (3,3)
+      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)
+      Z = np.arange(1,15,dtype=uint32)
-      R = as_strided(Z,(11,4),(4,4))
+      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