2. 線形空間と線形写像

code: vec2d.py

from numpy import array

import matplotlib.pyplot as plt

arrows = [(o, x + y, 'b'), (o, x, 'r'), (x, y, 'g'),

(o, y, 'g'), (y, x, 'r')]

for p, v, c in arrows:

color=c, units='xy', scale=1)

plt.axis('scaled'), plt.xlim(0, 5), plt.ylim(0, 5), plt.show()

https://gyazo.com/69620cb24986d53a4b0f6d0ecaab5c88

code: vec3d.py

from vpython import vec, arrow, mag

o = vec(0, 0, 0)

x, y, z = vec(1, 0, 0), vec(0, 1, 0), vec(0, 0, 1)

arrows = [(o, x + y), (x, y + z), (o, x + y + z), (o, x), (y, x),

(z, x), (y + z, x), (o, y), (x, y), (z, y), (x + z, y),

(o, z), (x, z), (y, z), (x + y, z)]

for p, v in arrows:

arrow(pos=p, axis=v, color=v, shaftwidth=mag(v) / 50)

https://gyazo.com/b593db758d033459dd118c1db26428d9

code: func.py

from numpy import pi, sin, cos, linspace

import matplotlib.pyplot as plt

f = lambda x: x**2 + x + 1

g = lambda x: 3 * sin(x) + 4 * cos(x)

x = linspace(-pi, pi, 101)

plt.plot(x, y)

plt.show()

code: comp.py

from numpy import exp, pi, linspace

import matplotlib.pyplot as plt

from mpl_toolkits.mplot3d import Axes3D

f = lambda n, x: exp(1j * n * x)

x = linspace(0, 2 * pi, 1001)

ax = Axes3D(plt.figure())

for n in range(-2, 3):

ax.plot(x, f(n, x).real, f(n, x).imag)

plt.show()

https://gyazo.com/a893e20bbd0e93692fdc3e07c10483a9

code: sound2.py

import scipy.io.wavfile as wav

import numpy as np

import matplotlib.pyplot as plt

rate, Data = wav.read('mono.wav')

print(rate, Data.shape)

t = len(Data) / rate

dt = 1 / rate

print(t, dt)

x = np.arange(0, t, dt)

y = Data / 32768

if len(Data.shape) == 1:

plt.plot(x, y)

plt.xlim(0, t), plt.ylim(-1, 1), plt.show()

elif len(Data.shape) == 2:

fig, ax = plt.subplots(2)

for i in range(2):

plt.show()

code: chord.py

from numpy import arange, pi, sin

import scipy.io.wavfile as wav

import matplotlib.pyplot as plt

xmax, rate = 2, 22050

x = arange(0, xmax, 1 / rate)

def f(hz):

A = f(440.000000) # ラ

B = f(493.883301) # シ

C = f(523.251131) # ド

D = f(587.329536) # レ

E = f(659.255114) # ミ

F = f(698.456463) # ファ

G = f(783.990872) # ソ

Data = (CEG * 32768).astype('int16')

wav.write('CEG.wav', rate, Data)

plt.plot(x, y)

plt.xlim(1, 1.01), plt.show()

https://gyazo.com/1b412ddd691dd474da4713883396c0a1