用 python 解决线性代数中的矩阵运算

用 python 解决线性代数中的矩阵运算

• 矩阵叉乘
• 矩阵求逆
• 矩阵转置
• 假定AX=B，求解未知矩阵X
• 矩阵的行列式值|matrix|
• 未完待续。。。。。
  

import sys
from PyQt5.QtWidgets import *
import numpy as np

class Form(QDialog):
    def __init__(self, parent=None):
        super().__init__(parent)
        grid = QGridLayout()

        self.setWindowTitle("矩阵行列式计算器")

        self.Title = QLabel("矩阵行列式计算器")
        grid.addWidget(self.Title, 0, 1)
        self.Title = QLabel("作者：小潘")
        grid.addWidget(self.Title, 0, 2)
        titles = ['计算两矩阵叉乘', '矩阵求逆', '矩阵转置', '假定AX=B，求解未知矩阵X', '求矩阵的行列式值', '清空']
        func = [self.multiplication_cross, self.cal_inverse, self.cal_transposition, self.solve_equations, self.cal_value, self.clear]
        for index, title in enumerate(titles):
            self.set_button(title, 1, index, grid, func[index])

        self.textTitle1 = QLabel("第一个矩阵的行数：")
        grid.addWidget(self.textTitle1, 3, 0)
        self.hang1 = QLineEdit(self)
        grid.addWidget(self.hang1, 3, 1)
        self.textTitle1 = QLabel("第一个矩阵的列数：")
        grid.addWidget(self.textTitle1, 3, 2)
        self.lie1 = QLineEdit(self)
        grid.addWidget(self.lie1, 3, 3)
        self.texts1 = [self.set_text(i, 4, grid) for i in range(36)]

        self.textTitle2 = QLabel("第二个矩阵的行数：")
        grid.addWidget(self.textTitle2, 10, 0)
        self.hang2 = QLineEdit(self)
        grid.addWidget(self.hang2, 10, 1)
        self.textTitle2 = QLabel("第二个矩阵的列数：")
        grid.addWidget(self.textTitle2, 10, 2)
        self.lie2 = QLineEdit(self)
        grid.addWidget(self.lie2, 10, 3)
        self.texts2 = [self.set_text(i, 11, grid) for i in range(36)]
        self.setLayout(grid)

    def set_button(self, title, x, y, grid, cal):
        bt = QPushButton(title)
        bt.setParent(self)
        grid.addWidget(bt, x, y)
        bt.clicked.connect(cal)

    def set_text(self, i, y, grid):
        text = QLineEdit(self)
        grid.addWidget(text, y + i // 6, 0 + i % 6)
        return text

    def clear(self):
        self.hang1.setText('')
        self.lie1.setText('')
        self.hang2.setText('')
        self.lie2.setText('')
        for i in range(36):
                self.texts1[i].setText('')
                self.texts2[i].setText('')

    def get_matrix(self):
        hang1 = int(self.hang1.text() if self.hang1.text() != '' else 0)
        lie1 = int(self.lie1.text() if self.lie1.text() != '' else 0)
        hang2 = int(self.hang2.text() if self.hang2.text() != '' else 0)
        lie2 = int(self.lie2.text() if self.lie2.text() != '' else 0)
        # , lie1, hang2, lie2 = , int(self.lie1.text()), int(self.hang2.text()), int(self.lie2.text())
        matrix1, matrix2 = [[] for i in range(hang1)], [[] for i in range(hang2)]
        for i in range(hang1):
            for j in range(lie1):
                matrix1[i].append(eval(self.texts1[i*6+j].text()))
        for i in range(hang2):
            for j in range(lie2):
                matrix2[i].append(eval(self.texts2[i*6+j].text()))
        return matrix1, matrix2

    '''
    description: 矩阵叉乘 matrix1 左乘 matrix2
    param {matrix1, matrix2} 多维数组
    return {matrix} 叉乘后的矩阵
    Date Changed:
    '''
    def multiplication_cross(self):
        matrix1, matrix2 = self.get_matrix()
        pass
        a, b = np.mat(matrix1), np.mat(matrix2)
        print('叉乘后的矩阵的矩阵为：')
        print(a * b)
    '''
    description: 矩阵求逆
    param {matrix} 多维数组
    return {matrix} 逆矩阵
    Date Changed:
    '''
    def cal_inverse(self, matrix):
        matrix1, matrix2 = self.get_matrix()
        print('逆矩阵为：')
        print(np.mat(matrix1).I)

    '''
    description: 矩阵转置
    param {matrix} 多维数组
    return {matrix} 转置矩阵
    Date Changed:
    '''
    def cal_transposition(self, matrix):
        matrix1, matrix2 = self.get_matrix()
        print('转置矩阵为：')
        print(np.mat(matrix1).T)

    '''
    description: 假定AX=B，求解未知矩阵X
    param {A, B} 多维数组
    return {X} 矩阵X
    Date Changed:
    '''
    def solve_equations (self):
        A, B = self.get_matrix()
        print('解得X矩阵为：')
        print(np.linalg.solve(A, B))

    '''
    description: 矩阵的行列式值|matrix|
    param {matrix} 多维数组
    return {number} 矩阵的行列式值
    Date Changed:
    '''
    def cal_value(self, matrix):
        matrix1, matrix2 = self.get_matrix()
        print('矩阵行列式的值为：')
        print(np.linalg.det(matrix1))

if __name__ == '__main__':
    # 每一个PyQt5程序都需要有一个QApplication对象。sys.argv是从命令行传入的参数列表。Python脚本可以从shell中运行。这是一种通过参数来选择启动脚本的方式。
    app = QApplication(sys.argv)
    # 创建一个 Form 对象
    form = Form()
    # 将控件展示出来
    form.show()
    #退出中使用的消息循环，结束消息循环时就退出程序
    app.exec_()