## Numpy personal tips

numpy is one of the essential tools for data analysis and numerical computation. It is a library that is always needed when implementing machine learning, etc. I’ll leave a memo as a personal reminder. For details, please refer to the following official page.

### github

• The file in jupyter notebook format on github is here .

### Author’s environment

The author’s environment and import method are as follows.

!sw_vers
ProductName: Mac OS X
ProductVersion: 10.14.6
BuildVersion: 18G2022
Python -V
Python 3.5.5 :: Anaconda, Inc.
%matplotlib inline
%config InlineBackend.figure_format = 'svg'

import numpy as np
import matplotlib
import matplotlib.pyplot as plt

print(np.__version__)
print(matplotlib.__version__)
1.18.1
2.2.2

## Trigonometric functions

### np.sin(x)

$\sin x$

print(np.sin(0))
print(np.sin(np.pi / 2))
print(np.sin(np.pi))
0.0
1.0
1.2246467991473532e-16
x = np.linspace(-2 * np.pi, 2 * np.pi, 100)
y = np.sin(x)

plt.grid()
plt.title('$y = \sin x$', fontsize=16)
plt.ylabel('$\sin x$')
plt.plot(x,y)
[<matplotlib.lines.Line2D at 0x114397588>]

### np.cos(x)

$\cos x$

print(np.cos(0))
print(np.cos(np.pi / 2))
print(np.cos(np.pi))
1.0
6.123233995736766e-17
-1.0
x = np.linspace(-2 * np.pi, 2 * np.pi, 100)
y = np.cos(x)

plt.grid()
plt.title('$y = \cos x$', fontsize=16)
plt.ylabel('$\cos x$')
plt.plot(x,y)
[<matplotlib.lines.Line2D at 0x1144e8fd0>]

### np.tan(x).

$\tan x$

print(np.tan(0))
print(np.tan(np.pi / 4))
print(np.tan(np.pi))
0.0
0.999999999999999
-1.2246467991473532e-16
x = np.linspace(-2 * np.pi, 2 * np.pi, 100)
y = np.tan(x)

plt.grid()
plt.title('$y = \\tan x$', fontsize=16)
plt.ylabel('$\tan x$')
plt.ylim(-5,5)
plt.plot(x,y)
[<matplotlib.lines.Line2D at 0x1145def98>]

Inverse function of sin x$’'. print(np.arcsin(0)) print(np.arcsin(1)) print(np.arcsin(-1)) 0.0 1.5707963267948966 -1.5707963267948966 x = np.linspace(-1, 1, 100) y = np.arcsin(x) plt.grid() plt.title('$y = \arcsin x$', fontsize=16) plt.plot(x,y) [<matplotlib.line.Line2D at 0x11e48cef0>] }}. ### np.arccos(x) Inverse function of$cos x$. print(np.arccos(0)) print(np.arccos(1)) print(np.arccos(-1)) 1.5707963267948966 0.0 3.141592653589793 x = np.linspace(-1, 1, 100) y = np.arccos(x) plt.grid() plt.title('$y = \arccos x$', fontsize=16) plt.plot(x,y) <matplotlib.line.Line2D at 0x11e4a4b00>] }}. ### np.arctan(x) The inverse function of$tan x$. print(np.arctan(0)) print(np.arctan(1)) print(np.arctan(-1)) 0.0 0.7853981633974483 -0.7853981633974483 x = np.linspace(-np.pi, np.pi, 100) y = np.arctan(x) plt.grid() plt.title('$y = \arctan x$', fontsize=16) plt.plot(x,y) <matplotlib.line.Line2D at 0x11e55ee10>] }}. ### np.sinh(x) Hyperbolic sine function.$ \displaystyle \sinh x = \frac{e^x - e^{-x}}{2} $. print(np.sinh(0)) print(np.sinh(-1)) print(np.sinh(1)) 0.0 -1.1752011936438014 1.1752011936438014 x = np.linspace(-np.pi, np.pi, 100) y = np.sinh(x) plt.grid() plt.title('$y = \sinh x$', fontsize=16) plt.plot(x,y) [<matplotlib.lines.Line2D at 0x11e6dcf60>] ### np.cosh(x) Hyperbolic cosine function.$ \displaystyle \cosh x = \frac{e^x + e^{-x}}{2} $print(np.cosh(0)) print(np.cosh(-1)) print(np.cosh(1)) 1.0 1.5430806348152437 1.5430806348152437 x = np.linspace(-np.pi, np.pi, 100) y = np.cosh(x) plt.grid() plt.title('$y = \cosh x$', fontsize=16) plt.plot(x,y) [<matplotlib.lines.Line2D at 0x1142c8860>] ### np.tanh(x) Hyperbolic tangent function.$ \displaystyle \tanh x = \frac{\sinh x}{\cosh x} $This is sometimes used for activation functions in deep learning. print(np.tanh(0)) print(np.tanh(-1)) print(np.tanh(1)) 0.0 -0.7615941559557649 0.761594155955557649 x = np.linspace(-np.pi, np.pi, 100) y = np.tanh(x) plt.grid() plt.title('$y = \\tanh x$', fontsize=16) plt.plot(x,y) [<matplotlib.lines.Line2D at 0x11e4a8a90>] ### np.arcsinh(x) Inverse function of$\sinh x$. print(np.arcsinh(0)) print(np.arcsinh(1)) print(np.arcsinh(-1)) 0.0 0.881373587019543 -0.881373587019543 x = np.linspace(-np.pi, np.pi, 100) y = np.arcsinh(x) plt.grid() plt.title('$y = \\arcsinh x$', fontsize=16) plt.plot(x,y) [<matplotlib.lines.Line2D at 0x11e7d2588>] ### np.arccosh(x) Inverse function of$\cosh x$. print(np.arccosh(1)) 0.0 x = np.linspace(1, np.pi, 100) y = np.arccosh(x) plt.grid() plt.title('$y = \\arccosh x$', fontsize=16) plt.plot(x,y) [<matplotlib.lines.Line2D at 0x11e917438>] ### np.arctanh(x) Inverse function of$\tanh x$. print(np.arctanh(0)) print(np.arctanh(0.5)) print(np.arctanh(-0.5)) 0.0 0.5493061443340549 -0.0 0.5493061443340549 x = np.linspace(-0.99, 0.99, 100) y = np.arctanh(x) plt.grid() plt.title('$y = \\arctanh x\$', fontsize=16)
plt.plot(x,y)
[<matplotlib.lines.Line2D at 0x11e9e4278>]