Replaced README with index such that page can be read directly from github
−506 · 1 file changed
-
index.rst+0 −506
@@ -1,506 +0,0 @@ -=================== -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]) - - -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) - - - -.. 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 -==========