Man and History: Python 量子運算（二一）：張量

Python 量子運算（二一）：張量

2023/02/19

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Fig. 21.1. Tensor.

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純量：秩 0 的張量。

向量：秩 1 的張量。

矩陣：秩 2 的張量。

張量：秩 3 及以上稱為張量。

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代碼 21.1

# Program 21.1：Tensor
import numpy as np
import matplotlib as mpl
import matplotlib.pyplot as plt


class Point:
    def __init__(self, x, y, z):
        self.x = x
        self.y = y
        self.z = z


def Line(ax, A, B):
    ax.plot([A.x, B.x], [A.y, B.y], [A.z, B.z], 'b')
    return


def Cube(ax, P1, P2):

    # parallel to x axis
    for z in range(P1.z, P2.z+1):
        S = Point(P1.x, P1.y, z)
        E = Point(P2.x, P1.y, z)
        Line(ax, S, E)
    for y in range(P1.y, P2.y+1):
        S = Point(P1.x, y, P2.z)
        E = Point(P2.x, y, P2.z)
        Line(ax, S, E)

    # parallel to y axis
    for x in range(P1.x, P2.x+1):
        S = Point(x, P1.y, P2.z)
        E = Point(x, P2.y, P2.z)
        Line(ax, S, E)
    for z in range(P1.z, P2.z+1):
        S = Point(P2.x, P1.y, z)
        E = Point(P2.x, P2.y, z)
        Line(ax, S, E)

    # parallel to z axis
    for x in range(P1.x, P2.x+1):
        S = Point(x, P1.y, P1.z)
        E = Point(x, P1.y, P2.z)
        Line(ax, S, E)
    for y in range(P1.y, P2.y+1):
        S = Point(P2.x, y, P1.z)
        E = Point(P2.x, y, P2.z)
        Line(ax, S, E)

    return


def Set(ax, lim):
    ax.set_xlim([0, lim])
    ax.set_ylim([0, lim])
    ax.set_zlim([0, lim])
    ax.set_axis_off()
    return


def Subplot_1():
    ax = fig.add_subplot(221, projection='3d')  # 3d subplot

    P1 = Point(0, 0, 0)
    P2 = Point(1, 1, 1)
    Cube(ax, P1, P2)
    Set(ax, 6)

    plt.title('Rank 0 Tensor', color='r')
    ax.text(P2.x, P2.y, P2.z, 'scalar')
    ax.text(4, 0, -1, '(a)', fontsize=20)

    return


def Subplot_2():
    ax = fig.add_subplot(222, projection='3d')  # 3d subplot

    P1 = Point(0, 0, 0)
    P2 = Point(4, 1, 1)
    Cube(ax, P1, P2)

    P3 = Point(5, 0, 0)
    P4 = Point(6, 1, 3)
    Cube(ax, P3, P4)

    Set(ax, 6)

    plt.title("Rank 1 Tensor", color='r')
    ax.text(0, 0, 3, 'Row Vecor(shape 1x4)', fontsize=16)
    ax.text(3, 0, 5, 'Column Vector(shape 3x1)', fontsize=16)
    ax.text(P4.x, P4.y, P4.z, 'vector')
    ax.text(4, 0, -1, '(b)', fontsize=20)

    return


def Subplot_3():
    ax = fig.add_subplot(223, projection='3d')  # 3d subplot

    P1 = Point(0, 0, 0)
    P2 = Point(4, 1, 3)
    Cube(ax, P1, P2)
    Set(ax, 6)

    plt.title('Rank 2 Tensor', color='r')
    ax.text(P2.x, P2.y, P2.z, 'matrix')
    ax.text(4, 0, -1, '(c)', fontsize=20)

    return


def Subplot_4():
    ax = fig.add_subplot(224, projection='3d')  # 3d subplot

    P1 = Point(0, 0, 0)
    P2 = Point(4, 5, 3)
    Cube(ax, P1, P2)
    Set(ax, 6)

    plt.title('Rank 3 Tensor', color='r')
    ax.text(P2.x, P2.y, P2.z, 'tensor')
    ax.text(4, 0, -1, '(d)', fontsize=20)

    return


# figure setting
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/0021_001.png')
plt.show()