Man and History: Python 量子運算（一四）：點積

Python 量子運算（一四）：點積

2023/01/03

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Fig. 14.1. Dot product.

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代碼 14.1

# Program 14.1：Dot product
import numpy as np
import matplotlib as mpl
import matplotlib.pyplot as plt


def Subplot_1():
    ax = plt.subplot(221)

    # basic setting
    theta = np.linspace(0, np.pi/2, 100)
    axis = np.linspace(0, 1, 100)
    zero = axis * 0
    radius = 0.7
    x1 = radius * np.cos(theta)
    y1 = radius * np.sin(theta)

    # basic plotting
    ax.plot(axis, zero, 'k')  # y = 0(x_axis)
    ax.plot(zero, axis, 'k')  # x = 0(y_axis)
    ax.plot(x1, y1, 'k')      # cicle

    # vector setting
    coordinates = [0, 0]      # original point
    splt_radian = np.pi / 4   # subplot

    # vector plotting
    v_p1 = splt_radian
    v_p2 = 0
    vector_1 = [radius*np.cos(v_p1), radius*np.sin(v_p1)]  # direction
    vector_2 = [radius*np.cos(v_p2), radius*np.sin(v_p2)]  # direction
    plt.quiver(coordinates[0], coordinates[1], vector_1[0], vector_1[1],
               scale=1.15, color='r')
    plt.quiver(coordinates[0], coordinates[1], vector_2[0], vector_2[1],
               scale=1.1, color='b')
    plt.quiver(coordinates[0], coordinates[1]-0.05, vector_1[0], vector_2[1],
               scale=1.15, color='k')

    # red line
    r_line_y = np.linspace(0, radius*np.sin(1.05*splt_radian), 100)
    r_line_x = r_line_y * 0 + radius * np.cos(1.05*splt_radian)
    ax.plot(r_line_x, r_line_y, 'r', linestyle=':')

    # red arc
    phi = np.linspace(0, splt_radian, 100)
    x2 = 0.2 * np.cos(phi)
    y2 = 0.2 * np.sin(phi)
    ax.plot(x2, y2, 'r')

    ax.text(0.25, 0.1, r"$\theta=45^{\circ}$", fontsize='20')
    ax.text(radius+0.1, 0.05, r"$\vec u=(1,0)$", color='b')
    ax.text(radius*np.cos(v_p1)+0.1, radius*np.sin(v_p1),
            r"$\vec v=(\frac{\sqrt 2}{2},\frac{\sqrt 2}{2})$", color='r')
    ax.text(radius*np.cos(v_p1)+0.1, -0.15,
            r"$\vec w=(\frac{\sqrt 2}{2},0)$", color='k')
    ax.text(0.5, -0.28, '(a)', fontsize=20)
    ax.set_axis_off()

    return


def Subplot_2():
    ax = plt.subplot(222)

    # string setting
    s1 = r'${\rm cos}\ \theta=\frac{\vert \vec w\vert}{\vert \vec v\vert}$'
    s2 = r'${\vert \vec w\vert}={\vert \vec v\vert}{\rm cos}\ \theta$'
    s3 = r'$\vec u \cdot \vec v={\vert \vec u\vert}{\vert \vec w\vert}=$'\
         r'${\vert \vec u\vert}{\vert \vec v\vert}{\rm cos}\ \theta$'

    # string output
    ax.text(0.10, 0.75, s1)
    ax.text(0.10, 0.45, s2)
    ax.text(0.10, 0.15, s3)
    ax.text(0.5, -0.15, '(b)', fontsize=20)
    ax.set_axis_off()

    return


def Subplot_3():
    ax = plt.subplot(223)

    # string setting
    s1_1 = r'$\vec v\cdot \vec u$'
    s1_2 = r'$=\begin{bmatrix}\sqrt2/2\quad \sqrt2/2\end{bmatrix}$'\
           r'$\begin{bmatrix}1\\0\end{bmatrix}$'
    s2 = r'$=\frac{\sqrt 2}{2}*1+\frac{\sqrt 2}{2}*0$'
    s3 = r'$=\frac{\sqrt 2}{2}$'

    # string output
    ax.text(0.10, 0.75, s1_1)
    ax.text(0.30, 0.75, s1_2)
    ax.text(0.30, 0.45, s2)
    ax.text(0.30, 0.15, s3)
    ax.text(0.5, -0.15, '(c)', fontsize=20)
    ax.set_axis_off()

    return


def Subplot_4():
    ax = plt.subplot(224)

    # string setting
    s1_1 = r'$\vec u\cdot \vec v$'
    s1_2 = r'$=\begin{bmatrix}1\quad 0\end{bmatrix}$'\
           r'$\begin{bmatrix}\sqrt2/2\\\sqrt2/2\end{bmatrix}$'
    s2 = r'$=1*\frac{\sqrt 2}{2}+0*\frac{\sqrt 2}{2}$'
    s3 = r'$=\frac{\sqrt 2}{2}$'

    # string output
    ax.text(0.10, 0.75, s1_1)
    ax.text(0.30, 0.75, s1_2)
    ax.text(0.30, 0.45, s2)
    ax.text(0.30, 0.15, s3)
    ax.text(0.5, -0.15, '(d)', fontsize=20)
    ax.set_axis_off()

    return


mpl.rcParams['text.usetex'] = True
mpl.rcParams['text.latex.preamble'] = r'\usepackage{{amsmath}}'
mpl.rcParams['font.size'] = 40
fig = plt.figure(figsize=(16, 16))

Subplot_1()
Subplot_2()
Subplot_3()
Subplot_4()

# plt.savefig('/content/drive/My Drive/pqc/0014_001.png')
plt.show()