NumPy Basics: Arrays and Vectorized Computation



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%matplotlib inline



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from __future__ import division
from numpy.random import randn
import numpy as np
np.set_printoptions(precision=4, suppress=True)
%cd ../book_scripts

The NumPy ndarray: a multidimensional array object



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data = randn(2, 3)



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data
data * 10
data + data



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data.shape
data.dtype

Creating ndarrays



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data1 = [6, 7.5, 8, 0, 1]
arr1 = np.array(data1)
arr1



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data2 = [[1, 2, 3, 4], [5, 6, 7, 8]]
arr2 = np.array(data2)
arr2
arr2.ndim
arr2.shape



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arr1.dtype
arr2.dtype



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np.zeros(10)
np.zeros((3, 6))
np.empty((2, 3, 2))



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np.arange(15)

Data Types for ndarrays



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arr1 = np.array([1, 2, 3], dtype=np.float64)
arr2 = np.array([1, 2, 3], dtype=np.int32)
arr1.dtype
arr2.dtype



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arr = np.array([1, 2, 3, 4, 5])
arr.dtype
float_arr = arr.astype(np.float64)
float_arr.dtype



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arr = np.array([3.7, -1.2, -2.6, 0.5, 12.9, 10.1])
arr
arr.astype(np.int32)



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numeric_strings = np.array(['1.25', '-9.6', '42'], dtype=np.string_)
numeric_strings.astype(float)



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int_array = np.arange(10)
calibers = np.array([.22, .270, .357, .380, .44, .50], dtype=np.float64)
int_array.astype(calibers.dtype)



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empty_uint32 = np.empty(8, dtype='u4')
empty_uint32

Operations between arrays and scalars



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arr = np.array([[1., 2., 3.], [4., 5., 6.]])
arr
arr * arr
arr - arr



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1 / arr
arr ** 0.5

Basic indexing and slicing



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arr = np.arange(10)
arr
arr[5]
arr[5:8]
arr[5:8] = 12
arr



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arr_slice = arr[5:8]
arr_slice[1] = 12345
arr
arr_slice[:] = 64
arr



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arr2d = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
arr2d[2]



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arr2d[0][2]
arr2d[0, 2]



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arr3d = np.array([[[1, 2, 3], [4, 5, 6]], [[7, 8, 9], [10, 11, 12]]])
arr3d



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arr3d[0]



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old_values = arr3d[0].copy()
arr3d[0] = 42
arr3d
arr3d[0] = old_values
arr3d



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arr3d[1, 0]

Indexing with slices



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arr[1:6]



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arr2d
arr2d[:2]



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arr2d[:2, 1:]



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arr2d[1, :2]
arr2d[2, :1]



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arr2d[:, :1]



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arr2d[:2, 1:] = 0

Boolean indexing



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names = np.array(['Bob', 'Joe', 'Will', 'Bob', 'Will', 'Joe', 'Joe'])
data = randn(7, 4)
names
data



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names == 'Bob'



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data[names == 'Bob']



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data[names == 'Bob', 2:]
data[names == 'Bob', 3]



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names != 'Bob'
data[-(names == 'Bob')]



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mask = (names == 'Bob') | (names == 'Will')
mask
data[mask]



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data[data < 0] = 0
data



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data[names != 'Joe'] = 7
data

Fancy indexing



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arr = np.empty((8, 4))
for i in range(8):
    arr[i] = i
arr



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arr[[4, 3, 0, 6]]



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arr[[-3, -5, -7]]



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# more on reshape in Chapter 12
arr = np.arange(32).reshape((8, 4))
arr
arr[[1, 5, 7, 2], [0, 3, 1, 2]]



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arr[[1, 5, 7, 2]][:, [0, 3, 1, 2]]



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arr[np.ix_([1, 5, 7, 2], [0, 3, 1, 2])]

Transposing arrays and swapping axes



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arr = np.arange(15).reshape((3, 5))
arr
arr.T



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arr = np.random.randn(6, 3)
np.dot(arr.T, arr)



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arr = np.arange(16).reshape((2, 2, 4))
arr
arr.transpose((1, 0, 2))



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arr
arr.swapaxes(1, 2)

Universal Functions: Fast element-wise array functions



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arr = np.arange(10)
np.sqrt(arr)
np.exp(arr)



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x = randn(8)
y = randn(8)
x
y
np.maximum(x, y) # element-wise maximum



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arr = randn(7) * 5
np.modf(arr)

Data processing using arrays



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points = np.arange(-5, 5, 0.01) # 1000 equally spaced points
xs, ys = np.meshgrid(points, points)
ys



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from matplotlib.pyplot import imshow, title



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import matplotlib.pyplot as plt
z = np.sqrt(xs ** 2 + ys ** 2)
z
plt.imshow(z, cmap=plt.cm.gray); plt.colorbar()
plt.title("Image plot of $\sqrt{x^2 + y^2}$ for a grid of values")



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plt.draw()

Expressing conditional logic as array operations



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xarr = np.array([1.1, 1.2, 1.3, 1.4, 1.5])
yarr = np.array([2.1, 2.2, 2.3, 2.4, 2.5])
cond = np.array([True, False, True, True, False])



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result = [(x if c else y)
          for x, y, c in zip(xarr, yarr, cond)]
result



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result = np.where(cond, xarr, yarr)
result



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arr = randn(4, 4)
arr
np.where(arr > 0, 2, -2)
np.where(arr > 0, 2, arr) # set only positive values to 2



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# Not to be executed

result = []
for i in range(n):
    if cond1[i] and cond2[i]:
        result.append(0)
    elif cond1[i]:
        result.append(1)
    elif cond2[i]:
        result.append(2)
    else:
        result.append(3)



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# Not to be executed

np.where(cond1 & cond2, 0,
         np.where(cond1, 1,
                  np.where(cond2, 2, 3)))



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# Not to be executed

result = 1 * cond1 + 2 * cond2 + 3 * -(cond1 | cond2)

Mathematical and statistical methods



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arr = np.random.randn(5, 4) # normally-distributed data
arr.mean()
np.mean(arr)
arr.sum()



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arr.mean(axis=1)
arr.sum(0)



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arr = np.array([[0, 1, 2], [3, 4, 5], [6, 7, 8]])
arr.cumsum(0)
arr.cumprod(1)

Methods for boolean arrays



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arr = randn(100)
(arr > 0).sum() # Number of positive values



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bools = np.array([False, False, True, False])
bools.any()
bools.all()

Sorting



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arr = randn(8)
arr
arr.sort()
arr



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arr = randn(5, 3)
arr
arr.sort(1)
arr



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large_arr = randn(1000)
large_arr.sort()
large_arr[int(0.05 * len(large_arr))] # 5% quantile

Unique and other set logic



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names = np.array(['Bob', 'Joe', 'Will', 'Bob', 'Will', 'Joe', 'Joe'])
    np.unique(names)
ints = np.array([3, 3, 3, 2, 2, 1, 1, 4, 4])
np.unique(ints)



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sorted(set(names))



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values = np.array([6, 0, 0, 3, 2, 5, 6])
np.in1d(values, [2, 3, 6])

File input and output with arrays

Storing arrays on disk in binary format



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arr = np.arange(10)
np.save('some_array', arr)



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np.load('some_array.npy')



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np.savez('array_archive.npz', a=arr, b=arr)



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arch = np.load('array_archive.npz')
arch['b']



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!rm some_array.npy
!rm array_archive.npz

Saving and loading text files



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!cat array_ex.txt



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arr = np.loadtxt('array_ex.txt', delimiter=',')
arr

Linear algebra



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x = np.array([[1., 2., 3.], [4., 5., 6.]])
y = np.array([[6., 23.], [-1, 7], [8, 9]])
x
y
x.dot(y)  # equivalently np.dot(x, y)



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np.dot(x, np.ones(3))



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np.random.seed(12345)



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from numpy.linalg import inv, qr
X = randn(5, 5)
mat = X.T.dot(X)
inv(mat)
mat.dot(inv(mat))
q, r = qr(mat)
r

Random number generation



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samples = np.random.normal(size=(4, 4))
samples



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from random import normalvariate
N = 1000000
%timeit samples = [normalvariate(0, 1) for _ in xrange(N)]
%timeit np.random.normal(size=N)

Example: Random Walks

import random position = 0 walk = [position] steps = 1000 for i in xrange(steps): step = 1 if random.randint(0, 1) else -1 position += step walk.append(position)



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np.random.seed(12345)



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nsteps = 1000
draws = np.random.randint(0, 2, size=nsteps)
steps = np.where(draws > 0, 1, -1)
walk = steps.cumsum()



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walk.min()
walk.max()



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(np.abs(walk) >= 10).argmax()

Simulating many random walks at once



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nwalks = 5000
nsteps = 1000
draws = np.random.randint(0, 2, size=(nwalks, nsteps)) # 0 or 1
steps = np.where(draws > 0, 1, -1)
walks = steps.cumsum(1)
walks



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walks.max()
walks.min()



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hits30 = (np.abs(walks) >= 30).any(1)
hits30
hits30.sum() # Number that hit 30 or -30



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crossing_times = (np.abs(walks[hits30]) >= 30).argmax(1)
crossing_times.mean()



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steps = np.random.normal(loc=0, scale=0.25,
                         size=(nwalks, nsteps))