Jacobian -Introduce-

ProjectionFunc.py

import matplotlib.pyplot as plt
import mpl_toolkits.mplot3d as Axes3D
import matplotlib.animation as anim
from matplotlib.animation import PillowWriter
import numpy as np
from numpy import sin, cos, pi


def ExFunc(v):
    A = np.array([[1, 0, 0], [0, 1, 0], [0, 0, 0]])
    v_out = A @ v
    return v_out


def Pole2Car(r, theta, phi):
    x = r*cos(theta)*cos(phi)
    y = r*sin(theta)*cos(phi)
    z = r*sin(phi)
    return np.array([[x], [y], [z]])


r = 1
phi = pi/6
T = np.linspace(0, 2, 120)
X_zero = (0, 0)
Y_zero = (0, 0)
Z_zero = (0, 0)

fig = plt.figure(figsize=(6, 6))
ax = fig.add_subplot(111, projection='3d')
ax.set_title("Projection Func")
ax.set_xlabel("x", size=14)
ax.set_ylabel("y", size=14)
ax.set_zlabel("z", size=14)
ax.set_xlim(-1.1, 1.1)
ax.set_ylim(-1.1, 1.1)
ax.set_zlim(-0.1, 1.1)

imgs = []

for t in T:
    theta = 2*pi*(t/2)
    V_in = Pole2Car(r, theta, phi)
    v_in = V_in.flatten()
    V_out = ExFunc(V_in)
    v_out = V_out.flatten()
    X = (v_in[0], v_out[0])
    Y = (v_in[1], v_out[1])
    Z = (v_in[2], v_out[2])
    im = ax.quiver(X_zero, Y_zero, Z_zero, X, Y,  Z,
                   length=r, arrow_length_ratio=0.1,
                   color=('blue', 'red'))
    imgs.append([im])

ani = anim.ArtistAnimation(fig, imgs, interval=66)
plt.show()

ani.save("PeojectionFuncEx.gif", writer="pillow")

SpiralFunc.py

import matplotlib.pyplot as plt
import mpl_toolkits.mplot3d as Axes3D
import matplotlib.animation as anim
from matplotlib.animation import PillowWriter
import numpy as np
from numpy import sin, cos, pi


def ExFunc(t):
    return p_x(t), p_y(t), p_z(t)


def p_x(t):
    return cos(2*pi*0.2*t)


def p_y(t):
    return sin(2*pi*0.2*t)


def p_z(t):
    return t


T_end = np.linspace(0, 10, 100)

fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.set_title("Spiral Func")
ax.set_xlabel("x", size=14)
ax.set_ylabel("y", size=14)
ax.set_zlabel("z", size=14)

imgs = []

for t_end in T_end:
    t = np.linspace(0, t_end, t_end*10)
    im = ax.plot(*ExFunc(t), color="blue")
    imgs.append(im)

ani = anim.ArtistAnimation(fig, imgs, interval=100)
# plt.show()

# 保存用に使用
#ani.save("VectorFuncEx.gif", writer="pillow")

TwoVariableFunc.py

import matplotlib.pyplot as plt
import numpy as np
from mpl_toolkits.mplot3d import Axes3D


def ExFunc(x, y):
    return -x ** 2-y ** 2+1


def FuncPlot2(f, x, y):
    out = np.zeros((len(x), len(y)))
    for i_y, p_y in enumerate(y):
        for i_x, p_x in enumerate(x):
            out[i_x, i_y] = f(p_x, p_y)
    return out


Interval = np.array([-5, 5])
Nsamp = 100
x = np.linspace(-5, 5, Nsamp)
y = np.linspace(-5, 5, Nsamp)
h = FuncPlot2(ExFunc, x, y)

X, Y = np.meshgrid(x, y)

figure = plt.figure()
ax = figure.add_subplot(111, projection='3d')
ax.set_xlabel("x", size=14)
ax.set_ylabel("y", size=14)
ax.set_zlabel("h", size=14)
surf = ax.plot_surface(X, Y, h, cmap="bwr", linewidth=0)
figure.colorbar(surf)
ax.set_title("TwoVariableFunc")
plt.show()