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@@ -12,6 +12,27 @@ <h1 class="title">100 numpy exercises</h1> <h2 class="subtitle" id="a-joint-effort-of-the-numpy-community">A joint effort of the numpy community</h2> +<p>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:</p> +<pre class="literal-block"> +#. Find indices of non-zero elements from [1,2,0,0,4,0] + + .. code:: python + + # Author: Somebody + + print np.nonzero([1,2,0,0,4,0]) +</pre> +<p>Here is what the page looks like so far: +<a class="reference external" href="http://www.loria.fr/~rougier/teaching/numpy.100/index.html">http://www.loria.fr/~rougier/teaching/numpy.100/index.html</a></p> +<div class="note"> +<p class="first admonition-title">Note</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> @@ -290,6 +311,8 @@ colors</p> <span class="name">I</span> <span class="operator">=</span> <span class="name">np</span><span class="operator">.</span><span class="name">random</span><span class="operator">.</span><span class="name">randint</span><span class="punctuation">(</span><span class="literal number integer">0</span><span class="punctuation">,</span><span class="literal number integer">2</span><span class="punctuation">,(</span><span class="name">h</span><span class="punctuation">,</span><span class="name">w</span><span class="punctuation">,</span><span class="literal number integer">3</span><span class="punctuation">))</span><span class="operator">.</span><span class="name">astype</span><span class="punctuation">(</span><span class="name">np</span><span class="operator">.</span><span class="name">ubyte</span><span class="punctuation">)</span> <span class="name">F</span> <span class="operator">=</span> <span class="name">I</span><span class="punctuation">[</span><span class="operator">...</span><span class="punctuation">,</span><span class="literal number integer">0</span><span class="punctuation">]</span><span class="operator">*</span><span class="literal number integer">256</span><span class="operator">*</span><span class="literal number integer">256</span> <span class="operator">+</span> <span class="name">I</span><span class="punctuation">[</span><span class="operator">...</span><span class="punctuation">,</span><span class="literal number integer">1</span><span class="punctuation">]</span><span class="operator">*</span><span class="literal number integer">256</span> <span class="operator">+</span><span class="name">I</span><span class="punctuation">[</span><span class="operator">...</span><span class="punctuation">,</span><span class="literal number integer">2</span><span class="punctuation">]</span> <span class="name">n</span> <span class="operator">=</span> <span class="name builtin">len</span><span class="punctuation">(</span><span class="name">np</span><span class="operator">.</span><span class="name">unique</span><span class="punctuation">(</span><span class="name">F</span><span class="punctuation">))</span> + +<span class="name">np</span><span class="operator">.</span><span class="name">unique</span><span class="punctuation">(</span><span class="name">I</span><span class="punctuation">)</span> </pre> </li> <li><p class="first">Considering a four dimensions array, how to get sum over the last two axis at once ?</p> @@ -0,0 +1,506 @@ +=================== +100 numpy exercises +=================== + +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:: + + #. Find indices of non-zero elements from [1,2,0,0,4,0] + + .. code:: python + + # 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 + + +**Contents** + +.. contents:: + :local: + :depth: 1 + + +Neophyte +======== + +1. Import the numpy package under the name ``np`` + + .. code:: python + + import numpy as np + + +#. Print the numpy version and the configuration. + + .. code:: python + + print np.__version__ + np.__config__.show() + + +#. Create a null vector of size 10 + + .. code:: python + + Z = np.zeros(10) + +#. Create a null vector of size 10 but the fifth value which is 1 + + .. code:: python + + Z = np.zeros(10) + Z[4] = 1 + +#. Create a vector with values ranging from 10 to 99 + + .. code:: python + + Z = np.arange(10,100) + +#. Create a 3x3 matrix with values ranging from 0 to 8 + + .. code:: python + + Z = np.arange(9).reshape(3,3) + +#. Find indices of non-zero elements from [1,2,0,0,4,0] + + .. code:: python + + nz = np.nonzero([1,2,0,0,4,0]) + + +#. Declare a 3x3 identity matrix + + .. code:: python + + Z = np.eye(3) + +#. Declare a 5x5 matrix with values 1,2,3,4 just below the diagonal + + .. code:: python + + Z = np.diag(1+np.arange(4),k=-1) + + +#. Declare a 10x10x10 array with random values + + .. code:: python + + Z = np.random.random((10,10,10)) + +Novice +====== + +#. Declare a 8x8 matrix and fill it with a checkerboard pattern + + .. code:: python + + 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 + + .. code:: python + + Z = np.random.random((10,10)) + Zmin, Zmax = Z.min(), Z.max() + +#. Create a checkerboard 8x8 matrix using the tile function + + .. code:: python + + Z = np.tile( np.array([[0,1],[1,0]]), (4,4)) + +#. Normalize a 5x5 random matrix (between 0 and 1) + + .. code:: python + + 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) + + .. code:: python + + Z = np.dot(np.ones((5,3)), np.ones((3,2))) + + +#. Create a 10x10 matrix with row values ranging from 0 to 9 + + .. code:: python + + Z = np.zeros((10,10)) + Z += np.arange(10) + +#. Create a vector of size 1000 with values ranging from 0 to 1, both excluded + + .. code:: python + + Z = np.random.linspace(0,1,1002,endpoint=True)[1:-1] + +#. Create a random vector of size 100 and sort it + + .. code:: python + + Z = np.random.random(100) + Z.sort() + +#. Consider two random matrices A anb B, check if they are equal. + + .. code:: python + + 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 + + .. code:: python + + Z = np.random.random(1000) + m = Z.mean() + + + +Apprentice +========== + + +#. Make an array immutable + + .. code:: python + + Z = np.zeros(10) + Z.flags.writeable = False + + +#. Consider a random 100x2 matrix representing cartesian coordinates, convert + them to polar coordinates + + .. code:: python + + 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 + + .. code:: python + + 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. + + .. code:: 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 the minimum and maximum representable value for each numpy scalar type + + .. code:: python + + 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) + + .. code:: python + + 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 + + .. code:: 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) + + # Much faster with scipy + Z = np.random.random((10,2)) + D = scipy.spatial.distance.cdist(Z,Z) + + + +#. Generate a generic 2D Gaussian-like array + + .. code:: python + + 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 ? + + .. code:: python + + # 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 + + .. code:: python + + 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 ? + + .. code:: python + + Z = genfromtxt("missing.dat", delimiter=",") + + +#. Consider a generator function that generates 10 integers and use it to build an + array + + .. code:: python + + 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) ? + + .. code:: python + + # 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) ? + + .. code:: python + + # 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 + + .. code:: python + + # 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)) + + np.unique(I) + +#. Considering a four dimensions array, how to get sum over the last two axis at once ? + + + .. code:: python + + 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]) + + .. code:: python + + # 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. + + .. code:: python + + # 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]) + + .. code:: python + + # 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. + + .. code:: 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] + + # 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) + + .. code :: python + + # 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 ? + + .. code:: python + + # 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. + + .. code:: python + + 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) + + +Master +====== + +Archmaster +========== @@ -1,26 +0,0 @@ -100 Numpy exercices -=================== - -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: - - -#. Find indices of non-zero elements from [1,2,0,0,4,0] - - .. code:: python - - # Author: Somebody - - print np.nonzero([1,2,0,0,4,0]) - - -If you can provide the assumed level of the answer, that would be even better. - -Here is what the page looks like so far: - -http://www.loria.fr/~rougier/teaching/numpy.100/index.html - -(The level names came from an old-game: Dungeon Master)