用 python 解决线性代数中的矩阵运算

向右看齐 2022-12-19 15:25 221阅读 0赞

# 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。。。。。  
    ![1][]

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_()

[1]: /images/20221120/73e24b36bf58414496cb715756ac09b8.png