NumPy Basics: Arrays and Vectorized Computation

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import numpy as np
np.random.seed(12345)
import matplotlib.pyplot as plt
plt.rc('figure', figsize=(10, 6))
np.set_printoptions(precision=4, suppress=True)
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import numpy as np
my_arr = np.arange(1000000)
my_list = list(range(1000000))
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%time for _ in range(10): my_arr2 = my_arr * 2
%time for _ in range(10): my_list2 = [x * 2 for x in my_list]

The NumPy ndarray: A Multidimensional Array Object

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import numpy as np
# Generate some random data
data = np.random.randn(2, 3)
data
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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
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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

Arithmetic with NumPy Arrays

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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
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arr2 = np.array([[0., 4., 1.], [7., 2., 12.]])
arr2
arr2 > arr

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
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arr_slice[1] = 12345
arr
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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]
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x = arr3d[1]
x
x[0]

Indexing with slices

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arr
arr[1:6]
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arr2d
arr2d[:2]
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arr2d[:2, 1:]
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arr2d[1, :2]
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arr2d[:2, 2]
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arr2d[:, :1]
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arr2d[:2, 1:] = 0
arr2d

Boolean Indexing

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names = np.array(['Bob', 'Joe', 'Will', 'Bob', 'Will', 'Joe', 'Joe'])
data = np.random.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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cond = names == 'Bob'
data[~cond]
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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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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]]

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)
arr
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)
arr
np.sqrt(arr)
np.exp(arr)
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x = np.random.randn(8)
y = np.random.randn(8)
x
y
np.maximum(x, y)
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arr = np.random.randn(7) * 5
arr
remainder, whole_part = np.modf(arr)
remainder
whole_part
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arr
np.sqrt(arr)
np.sqrt(arr, arr)
arr

Array-Oriented Programming with 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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z = np.sqrt(xs ** 2 + ys ** 2)
z
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import matplotlib.pyplot as plt
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()
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plt.close('all')

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

Mathematical and Statistical Methods

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

Methods for Boolean Arrays

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arr = np.random.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 = np.random.randn(6)
arr
arr.sort()
arr
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arr = np.random.randn(5, 3)
arr
arr.sort(1)
arr
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large_arr = np.random.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

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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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np.savez_compressed('arrays_compressed.npz', a=arr, b=arr)
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!rm some_array.npy
!rm array_archive.npz
!rm arrays_compressed.npz

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)
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np.dot(x, y)
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np.dot(x, np.ones(3))
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x @ np.ones(3)
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from numpy.linalg import inv, qr
X = np.random.randn(5, 5)
mat = X.T.dot(X)
inv(mat)
mat.dot(inv(mat))
q, r = qr(mat)
r

Pseudorandom 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 range(N)]
%timeit np.random.normal(size=N)
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np.random.seed(1234)
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rng = np.random.RandomState(1234)
rng.randn(10)

Example: Random Walks

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import random
position = 0
walk = [position]
steps = 1000
for i in range(steps):
    step = 1 if random.randint(0, 1) else -1
    position += step
    walk.append(position)
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plt.figure()
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plt.plot(walk[:100])
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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))

Conclusion