import numpy as np
import pandas as pdOverview of linear algebra operations in python
The numpy library is the main tool for linear algebra in python.
Creating and shaping arrays
m = np.array([1, 2, 3, 4, 5, 6, 7, 8])
print("Array {} with shape {} (a row vector)".format(m, m.shape))
print("Reshaped array to shape (2,4):\n {}".format(m.reshape((2, 4))))
print("Reshaped array to column vector:\n {}".format(m.reshape(8, 1)))Array [1 2 3 4 5 6 7 8] with shape (8,) (a row vector)
Reshaped array to shape (2,4):
[[1 2 3 4]
[5 6 7 8]]
Reshaped array to column vector:
[[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]]Some special arrays
one = np.ones(shape=(3, 4))
print(one)
zero = np.zeros(shape=(3, 3))
print(zero)
d = np.diag([1, 2, 3, 4])
print(d)[[1. 1. 1. 1.]
[1. 1. 1. 1.]
[1. 1. 1. 1.]]
[[0. 0. 0.]
[0. 0. 0.]
[0. 0. 0.]]
[[1 0 0 0]
[0 2 0 0]
[0 0 3 0]
[0 0 0 4]]Addition and scalar multiplication
x = np.random.normal(size=(4,))
y = np.random.normal(size=(4,))
print(x + y)
u = np.random.normal(size=(2,))
try:
print(x + u)
except:
print("Cant Mix These")[-0.80263053 0.2517913 1.11840438 -0.72227525]
Cant Mix TheseBroadcasting
x = np.array([[1, 2], [3, 4]])
print("x={}".format(x))
print("x-1={}".format(x - 1))
z = np.array([1, 2])
print("z={}".format(z))
print("x-z={}".format(x - z))
z = np.array([[3], [4]])
print("z={}".format(z))
print("x-z={}".format(x - z))x=[[1 2]
[3 4]]
x-1=[[0 1]
[2 3]]
z=[1 2]
x-z=[[0 0]
[2 2]]
z=[[3]
[4]]
x-z=[[-2 -1]
[-1 0]]Element by Element
x = np.array([[1, 2, 3], [2, 3, 4], [4, 5, 6]])
print(1 / x)
print(np.log(x))[[1. 0.5 0.33333333]
[0.5 0.33333333 0.25 ]
[0.25 0.2 0.16666667]]
[[0. 0.69314718 1.09861229]
[0.69314718 1.09861229 1.38629436]
[1.38629436 1.60943791 1.79175947]]Multiplication
x = np.random.normal(size=(3, 4))
print(x)
y = np.random.normal(size=(4, 1))
print(y)
print(x @ y)[[-0.38282693 0.56666355 -1.23844588 0.28654749]
[ 0.64545868 1.18922632 -0.52113292 0.16461292]
[-0.54573844 0.82154508 1.10311255 0.20158659]]
[[ 0.85713165]
[-0.41036715]
[ 0.06549535]
[-0.7014138 ]]
[[-0.84277399]
[-0.08436991]
[-0.87405168]]Transpose
x = np.array([[1, 2, 3], [2, 3, 4], [3, 4, 5]])
print(x)
print(x.transpose())[[1 2 3]
[2 3 4]
[3 4 5]]
[[1 2 3]
[2 3 4]
[3 4 5]]Norm
x = np.array([[1, 2], [3, 4]])
print(x)
y = np.linalg.norm(x)
print(y)
y = np.linalg.norm(x, axis=0)
print("axis=0 yields row norms: {}".format(y))
y = np.linalg.norm(x, axis=1)
print("axis=1 yields column norms: {}".format(y))[[1 2]
[3 4]]
5.477225575051661
axis=0 yields row norms: [3.16227766 4.47213595]
axis=1 yields column norms: [2.23606798 5. ]Rank
x = np.array([[1,2],[3,4]])
np.linalg.matrix_rank(x)2Dataframes and matrices
data = pd.read_csv("data/penguins-raw.csv")
print(data[["Body Mass (g)"]])
print(data[["Body Mass (g)"]].values) Body Mass (g)
0 3750.0
1 3800.0
2 3250.0
3 NaN
4 3450.0
.. ...
339 4000.0
340 3400.0
341 3775.0
342 4100.0
343 3775.0
[344 rows x 1 columns]
[[3750.]
[3800.]
[3250.]
[ nan]
[3450.]
[3650.]
[3625.]
[4675.]
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[4250.]
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[3775.]]Datatypes
x = np.array([[1, 2, 3], [2, 3, 4]], dtype=int)
print(x)
y = np.array([[1, 2, 3], [2, 3, 4]], dtype=float)
print(y)
print(x + y)[[1 2 3]
[2 3 4]]
[[1. 2. 3.]
[2. 3. 4.]]
[[2. 4. 6.]
[4. 6. 8.]]