From 3a048024493689fb785d6f62964c7b0a245e842b Mon Sep 17 00:00:00 2001 From: Nicolas Rougier Date: Sun, 22 Jun 2014 17:01:01 +0200 Subject: [PATCH] Added link to Julia version --- README.html | 189 ++++++++++++++++++++++++++++++++++++--------------- README.ipynb | 26 ++++--- README.rst | 3 + 3 files changed, 154 insertions(+), 64 deletions(-) diff --git a/README.html b/README.html index 8caf239..ec1eb4c 100644 --- a/README.html +++ b/README.html @@ -32,6 +32,9 @@ is:

The level names came from an old-game (Dungeon Master)

Repository is at: https://github.com/rougier/numpy-100

+

The corresponding IPython notebook is available +from the github repo, thanks to the rst2ipynb conversion tool by Valentin Haenel

+

Thanks to Michiaki Ariga, there is now a Julia version.

Neophyte

    @@ -49,42 +52,50 @@ is:

  1. Create a null vector of size 10

     Z = np.zeros(10)
+print Z

  2. Create a null vector of size 10 but the fifth value which is 1

     Z = np.zeros(10)
 Z[4] = 1
+print Z
    3. -

  3. Create a vector with values ranging from 10 to 99

    +

  4. Create a vector with values ranging from 10 to 49

    -Z = np.arange(10,100)
+Z = np.arange(10,50)
+print Z

  5. Create a 3x3 matrix with values ranging from 0 to 8

     Z = np.arange(9).reshape(3,3)
+print Z

  6. Find indices of non-zero elements from [1,2,0,0,4,0]

     nz = np.nonzero([1,2,0,0,4,0])
+print nz

  7. Create a 3x3 identity matrix

     Z = np.eye(3)
+print Z

  8. Create a 5x5 matrix with values 1,2,3,4 just below the diagonal

     Z = np.diag(1+np.arange(4),k=-1)
+print Z
    9. -

  9. Create a 10x10x10 array with random values

    +

  10. Create a 3x3x3 array with random values

    -Z = np.random.random((10,10,10))
+Z = np.random.random((3,3,3))
+print Z
@@ -94,20 +105,23 @@ is:

  1. Create a 8x8 matrix and fill it with a checkerboard pattern

    -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

     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

     Z = np.tile( np.array([[0,1],[1,0]]), (4,4))
+print Z

  4. Normalize a 5x5 random matrix (between 0 and 1)

    @@ -115,41 +129,48 @@ is:

    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)

     Z = np.dot(np.ones((5,3)), np.ones((3,2)))
+print Z
    6. -

  6. Create a 10x10 matrix with row values ranging from 0 to 9

    +

  7. Create a 5x5 matrix with row values ranging from 0 to 4

    -Z = np.zeros((10,10))
-Z += np.arange(10)
+Z = np.zeros((5,5))
+Z += np.arange(5)
+print Z
    8. -

  8. Create a vector of size 1000 with values ranging from 0 to 1, both excluded

    +

  9. 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]
+Z = np.linspace(0,1,12,endpoint=True)[1:-1]
+print Z
    10. -

  10. Create a random vector of size 100 and sort it

    +

  11. Create a random vector of size 10 and sort it

    -Z = np.random.random(100)
+Z = np.random.random(10)
 Z.sort()
+print Z
    12. -

  12. Consider two random matrices A anb B, check if they are equal.

    +

  13. 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))
+A = np.random.randint(0,2,5)
+B = np.random.randint(0,2,5)
 equal = np.allclose(A,B)
+print equal
    14. -

  14. Create a random vector of size 1000 and find the mean value

    +

  15. Create a random vector of size 30 and find the mean value

    -Z = np.random.random(1000)
+Z = np.random.random(30)
 m = Z.mean()
+print m
@@ -161,21 +182,25 @@ is:

 Z = np.zeros(10)
 Z.flags.writeable = False
+Z[0] = 1
-

  • Consider a random 100x2 matrix representing cartesian coordinates, convert +

  • Consider a random 10x2 matrix representing cartesian coordinates, convert them to polar coordinates

    -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
    • -

  • Create random vector of size 100 and replace the maximum value by 0

    +

  • Create random vector of size 10 and replace the maximum value by 0

    -Z = np.random.random(100)
+Z = np.random.random(10)
 Z[Z.argmax()] = 0
+print Z

  • Create a structured array with x and y coordinates covering the @@ -184,6 +209,7 @@ them to polar coordinates

    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

  • Print the minimum and maximum representable value for each numpy scalar type

    @@ -199,11 +225,12 @@ them to polar coordinates

  • 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)])])
+ Z = np.zeros(10, [ ('position', [ ('x', float, 1),
+                                   ('y', float, 1)]),
+                    ('color',    [ ('r', float, 1),
+                                   ('g', float, 1),
+                                   ('b', float, 1)])])
+print Z

  • Consider a random vector with shape (100,2) representing coordinates, find @@ -212,18 +239,22 @@ 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) +print D # Much faster with scipy +import scipy Z = np.random.random((10,2)) D = scipy.spatial.distance.cdist(Z,Z) +print D

  • Generate a generic 2D Gaussian-like array

    -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

  • Consider the vector [1, 2, 3, 4, 5], how to build a new vector with 3 @@ -235,11 +266,15 @@ consecutive zeros interleaved between each value ?

    nz = 3 Z0 = np.zeros(len(Z) + (len(Z)-1)*(nz)) Z0[::nz+1] = Z +print Z0

  • Find the nearest value from a given value in an array

    -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
    • @@ -255,7 +290,7 @@ consecutive zeros interleaved between each value ?

    How to read it ?

    -Z = genfromtxt("missing.dat", delimiter=",")
+Z = np.genfromtxt("missing.dat", delimiter=",")

  • Consider a generator function that generates 10 integers and use it to build an @@ -265,6 +300,7 @@ array

    for x in xrange(10): yield x Z = np.fromiter(generate(),dtype=float,count=-1) +print Z

  • Consider a given vector, how to add 1 to each element indexed by a second @@ -275,6 +311,7 @@ vector (be careful with repeated indices) ?

    Z = np.ones(10) I = np.random.randint(0,len(Z),20) Z += np.bincount(I, minlength=len(Z)) +print Z

  • How to accumulate elements of a vector (X) to an array (F) based on an index @@ -285,6 +322,7 @@ list (I) ?

    X = [1,2,3,4,5,6] I = [1,3,9,3,4,1] F = np.bincount(I,X) +print F

  • Considering a (w,h,3) image of (dtype=ubyte), compute the number of unique @@ -296,26 +334,27 @@ colors

    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)

  • 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)
+print

  • 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
+# Author: 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
+print D_means
    • @@ -328,36 +367,50 @@ 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
+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)
-
-Z = rolling(np.arange(100), 3)
+    return stride_tricks.as_strided(a, shape=shape, strides=strides)
+Z = rolling(np.arange(10), 3)
+print Z
    -

  • Consider a set of 100 triplets describing 100 triangles (with shared +

  • Consider a set of 10 triplets describing 10 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))
+# Author: Nicolas P. Rougier
 
+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

  • Given an array C that is a bincount, how to produce an array A such that np.bincount(A) == C ?

    -# Jaime Fernández del Río
+# Author: Jaime Fernández del Río
 
 C = np.bincount([1,1,2,3,4,4,6])
 A = np.repeat(np.arange(len(C)), C)
+print A
+
    +
    • +

  • How to compute averages using a sliding window over an array ?

    +
    +# Author: Jaime Fernández del Río
+
+def moving_average(a, n=3) :
+    ret = np.cumsum(a, dtype=float)
+    ret[n:] = ret[n:] - ret[:-n]
+    return ret[n - 1:] / n
+Z = np.arange(20)
+print moving_average(Z, n=3)
    • @@ -365,13 +418,15 @@ np.bincount(A) == C ?

    Artisan

      -

    1. Considering a 100x3 matrix, extract rows with unequal values (e.g. [2,2,3])

      +

    2. Considering a 10x3 matrix, extract rows with unequal values (e.g. [2,2,3])

       # 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

    3. Convert a vector of ints into a matrix binary representation.

      @@ -380,12 +435,12 @@ np.bincount(A) == C ?

      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)
    @@ -399,10 +454,10 @@ necessary)

     # 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)
@@ -422,15 +477,18 @@ necessary)
    
 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

  • 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]] ?

    -# Stéfan van der Walt
+# Author: 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
    • @@ -449,22 +507,24 @@ in B ?

    C = (A[..., np.newaxis, np.newaxis] == B) rows = (C.sum(axis=(1,2,3)) >= B.shape[1]).nonzero()[0] +print rows

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

    -# Chris Barker
+# Author: 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)
+print C

  • Create a 2D array subclass such that Z[i,j] == Z[j,i]

    -# Eric O. Lebigot
+# Author: Eric O. Lebigot
 # Note: only works for 2d array and value setting using indices
 
 class Symetric(np.ndarray):
@@ -475,11 +535,29 @@ in B ?
    
 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
    • +

  • Consider a set of p matrices wich shape (n,n) and a set of p vectors with shape (n,1). +How to compute the sum of of the p matrix products at once ? (result has shape (n,1))

    +
    +# Author: Stéfan van der Walt
+
+p, n = 10, 20
+M = np.ones((p,n,n))
+V = np.ones((p,n,1))
+S = np.tensordot(M, V, axes=[[0, 2], [0, 1]])
+print S
+
+# It works, because:
+# M is (p,n,n)
+# V is (p,n,1)
+# Thus, summing over the paired axes 0 and 0 (of M and V independently),
+# and 2 and 1, to remain with a (n,1) vector.
+
    +
    • @@ -491,12 +569,13 @@ in B ?

    See stackoverflow for explanations.

    -# Jaime Fernández del Río
+# Author: 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
    diff --git a/README.ipynb b/README.ipynb index 64db89e..061f47a 100644 --- a/README.ipynb +++ b/README.ipynb @@ -77,6 +77,14 @@ "[Valentin Haenel](http://haenel.co)\n" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Thanks to Michiaki Ariga, there is now a [Julia\n", + "version](https://github.com/chezou/julia-100-exercises).\n" + ] + }, { "cell_type": "heading", "level": 2, @@ -859,7 +867,7 @@ "cell_type": "code", "collapsed": false, "input": [ - "# Jaime Fern\u00e1ndez del R\u00edo\n", + "# Author: Jaime Fern\u00e1ndez del R\u00edo\n", "\n", "D = np.random.uniform(0,1,100)\n", "S = np.random.randint(0,10,100)\n", @@ -920,7 +928,7 @@ "cell_type": "code", "collapsed": false, "input": [ - "# Author: Nicolas Rougier\n", + "# Author: Nicolas P. Rougier\n", "\n", "faces = np.random.randint(0,100,(10,3))\n", "F = np.roll(faces.repeat(2,axis=1),-1,axis=1)\n", @@ -946,7 +954,7 @@ "cell_type": "code", "collapsed": false, "input": [ - "# Jaime Fern\u00e1ndez del R\u00edo\n", + "# Author: Jaime Fern\u00e1ndez del R\u00edo\n", "\n", "C = np.bincount([1,1,2,3,4,4,6])\n", "A = np.repeat(np.arange(len(C)), C)\n", @@ -1180,7 +1188,7 @@ "cell_type": "code", "collapsed": false, "input": [ - "# Eric O. Lebigot\n", + "# Author: Eric O. Lebigot\n", "# Note: only works for 2d array and value setting using indices\n", "\n", "class Symetric(np.ndarray):\n", @@ -1212,7 +1220,7 @@ "cell_type": "code", "collapsed": false, "input": [ - "# St\u00e9fan van der Walt\n", + "# Author: St\u00e9fan van der Walt\n", "\n", "p, n = 10, 20\n", "M = np.ones((p,n,n))\n", @@ -1221,10 +1229,10 @@ "print S\n", "\n", "# It works, because:\n", - "# M is (P, N, N)\n", - "# V is (P, N, 1)\n", + "# M is (p,n,n)\n", + "# V is (p,n,1)\n", "# Thus, summing over the paired axes 0 and 0 (of M and V independently),\n", - "# and 2 and 1, to remain with a Mx1 vector." + "# and 2 and 1, to remain with a (n,1) vector." ], "language": "python", "metadata": {}, @@ -1266,7 +1274,7 @@ "cell_type": "code", "collapsed": false, "input": [ - "# Jaime Fern\u00e1ndez del R\u00edo\n", + "# Author: Jaime Fern\u00e1ndez del R\u00edo\n", "\n", "Z = np.random.randint(0,2,(6,3))\n", "T = np.ascontiguousarray(Z).view(np.dtype((np.void, Z.dtype.itemsize * Z.shape[1])))\n", diff --git a/README.rst b/README.rst index 601568a..f063b9c 100644 --- a/README.rst +++ b/README.rst @@ -34,6 +34,9 @@ from the github repo, thanks to the `rst2ipynb `_ conversion tool by `Valentin Haenel `_ +Thanks to Michiaki Ariga, there is now a `Julia version `_. + + .. **Contents** .. .. contents:: .. :local: