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Matrix.py

+import copy
+
+class Matrix:
+    def __init__(self, matrix):
+        # 列表类型检查
+        assert isinstance(matrix, list), "参数必须为二维列表！"
+        for row in matrix:
+            assert isinstance(row, list), "参数必须为二维列表！"
+        for row in matrix:
+            assert len(row) == len(matrix[0]), "参数第二维度不一致！"
+        for row in matrix:
+            for each in row:
+                assert isinstance(each, (int, float, complex)), "元素类型只能为int, float或complex！"
+        self.__matrix = matrix
+        self.__row = len(matrix)
+        self.__col = len(matrix[0])
+
+    # 矩阵间加法 +
+    def __add__(self, other):
+        assert isinstance(other, Matrix), "加数必须是 Matrix 类"
+        if self.__row != other.__row or self.__col != other.__col:
+                raise ValueError("两矩阵维度不一致！")
+        result = Matrix( [[0 for i in range(self.__col)]  for i in range( self.__row ) ] )
+        for i in range(self.__row):
+            for j in range(self.__col):
+                result.__matrix[i][j] = self.__matrix[i][j] + other.__matrix[i][j]
+        return result
+
+    # 矩阵间减法 -
+    def __sub__(self, other):
+        assert isinstance(other, Matrix), "加数必须是 Matrix 类"
+        if self.__row != other.__row or self.__col != other.__col:
+            raise ValueError("两矩阵维度不一致！")
+        result = Matrix([[0 for i in range(self.__col)] for i in range(self.__row)])
+        for i in range(self.__row):
+            for j in range(self.__col):
+                result.__matrix[i][j] = self.__matrix[i][j] - other.__matrix[i][j]
+        return result
+    # 矩阵乘矩阵 *
+    def __mul__(self, other):
+        assert isinstance(other, Matrix), "右乘数必须是 Matrix 类"
+        if self.__col != other.__row:
+            raise ValueError("两矩阵维度不一致！")
+        result = Matrix([[0 for i in range(other.__col)] for i in range(self.__row)])
+        for i in range(self.__row):
+            for j in range(other.__col):
+                for m in range(self.__col):
+                    result.__matrix[i][j] += self.__matrix[i][m] * other.__matrix[m][j]
+        return result
+    # 数与矩阵乘 *
+    def __rmul__(self, other):
+        assert isinstance(other, (int, float, complex)), "左乘系数类型错误"
+        result = Matrix([[0 for i in range(self.__col)] for i in range(self.__row)])
+        for i in range(self.__row):
+            for j in range(self.__col):
+                result.__matrix[i][j] = self.__matrix[i][j] * other
+        return result
+    # 矩阵除以数
+    def __truediv__(self, other):
+        assert isinstance(other, (int, float, complex)), "被除数系数类型错误"
+        result = Matrix([[0 for i in range(self.__col)] for i in range(self.__row)])
+        for i in range(self.__row):
+            for j in range(self.__col):
+                result.__matrix[i][j] = self.__matrix[i][j] / other
+        return result
+    # 数除以矩阵
+    def __rtruediv__(self, other):
+        assert isinstance(other, (int, float, complex)), "除数系数类型错误"
+        result = Matrix([[0 for i in range(self.__col)] for i in range(self.__row)])
+        for i in range(self.__row):
+            for j in range(self.__col):
+                result.__matrix[i][j] = other / self.__matrix[i][j]
+        return result
+    # 矩阵与矩阵元素是否相等
+    def __eq__(self, other):
+        assert isinstance(other, Matrix), "必须是 Matrix 类"
+        for i in range(self.__row):
+            for j in range(self.__col):
+                if self.__matrix[i][j] != other.__matrix[i][j]:
+                    return False
+        return True
+    # 矩阵字符化
+    def __str__(self):
+        return '\n'.join(list(map(str, self.__matrix)))
+    # 行迭代器
+    def __iter__(self):
+        return self.__matrix.__iter__()
+    # 元素获取，看齐numpy
+    def __getitem__(self, item):
+        if isinstance(item, int):
+            return self.__matrix[item]
+        if isinstance(item, tuple):
+            row, col = item[0], item[1]
+            if isinstance(row, int) and isinstance(col, int):
+                return self.__matrix[row][col]
+            if isinstance(row, slice) and isinstance(col, int):
+                return Matrix( [ [ line[col] ] for line in self.__matrix[row]] )
+            if isinstance(row, int) and isinstance(col, slice):
+                return Matrix( [self.__matrix[row][col]] )
+            if isinstance(row, slice) and isinstance(col, slice):
+                return Matrix( [ line[col] for line in self.__matrix[row] ] )
+    # len()
+    def __len__(self):
+        return (self.__row)*(self.__col)
+
+    # 析构函数
+    def __del__(self):
+        del self.__matrix
+    # def __copy__(self):
+    # 元素和
+    def sum(self):
+        value = 0
+        for i in range(self.__row):
+            for j in range(self.__col):
+                value += self.__matrix[i][j]
+        return value
+
+    # 某行某列的代数余子式
+    def cofacor(self, row, col):
+        assert self.__row == self.__col, "必须是方阵"
+        mat_1 = copy.deepcopy(self)
+        temp_mat = []
+        # 删除对应行和列
+        for row_index, line in enumerate(mat_1):
+            if row_index == row:
+                continue
+            line.pop(col)
+            temp_mat.append(line)
+        return pow(-1, row+col+2) * Matrix(temp_mat).det()
+
+    # 定义法迭代法行列式
+    def det(self):
+        assert  self.__row == self.__col, "必须是方阵"
+        if self.__row == 1 and self.__col == 1:
+            return self.__matrix[0][0]
+        if self.__row == 2 and self.__col == 2:
+            return self.__matrix[0][0]*self.__matrix[1][1] - self.__matrix[0][1]*self.__matrix[1][0]
+        # 取出第一行与之代数余子式相乘
+        value = 0
+        for col_index, m in enumerate(self.__matrix[0]):
+            value += m * copy.deepcopy(self).cofacor(0, col_index)
+        return value
+    # 当前矩阵的伴随矩阵
+    def adj(self):
+        assert self.__row == self.__col, "必须是方阵"
+        result = [[0 for i in range(self.__col)] for i in range(self.__row)]
+        for i in range(self.__row):
+            for j in range(self.__col):
+                result[i][j] = self.cofacor(j,i)
+        return Matrix(result)
+    # 矩阵的逆
+    def inv(self):
+        assert self.__row == self.__col, "必须是方阵"
+        det = self.det()
+        assert det != 0, "矩阵必须非奇异"
+        return self.adj() / det
+    # 矩阵转置
+    def transpose(self):
+        return Matrix(list(map(list, zip(*self.__matrix))))
+
+    # 矩阵的秩
+    def rank(self):
+        def col_sort(mat, col_index = 0):
+            assert isinstance(mat, Matrix), "对象必须为矩阵"
+            temp_mat = Matrix( sorted(mat.__matrix, key=lambda x:abs(x[col_index]), reverse=True) )
+            return temp_mat
+        def cal_col_k(mat, col_index=0):
+            assert isinstance(mat, Matrix), "对象必须为矩阵"
+            k = [[0] for i in range(mat.__row)]
+            if abs(mat.__matrix[0][col_index]) < 1e-9:
+                return 0, None
+            for i in range(1,mat.__row):
+                k[i][0] = mat.__matrix[i][col_index] / mat.__matrix[0][col_index]
+            return 1, Matrix(k)
+        def elimination(mat, k):
+            assert isinstance(mat, Matrix), "对象必须为矩阵"
+            temp_mat = [[0 for col in range(mat.__col)] for j in range(mat.__row) ]
+            for i in range(mat.__row):
+                for j in range(mat.__col):
+                    temp_mat[i][j] = mat.__matrix[i][j] -( mat.__matrix[0][j] * k[i][0])
+            return Matrix(temp_mat)
+        
+        mat = copy.deepcopy(self)
+        # 列排序
+        mat = col_sort(mat, col_index=0)
+        if mat.__col == 1 or mat.__row == 1:
+                return int(bool(abs(mat.sum())))
+        # 列比例
+        ret, K = cal_col_k(mat, col_index=0)
+        if ret == 0:
+            return mat[1:,1:].rank()
+        # 消源
+        mat = elimination(mat, K)
+        return 1 + mat[1:,1:].rank()

main.py

+from Matrix import Matrix
+
+
+
+
 print('欢迎来到 InsCode')
+print('以下为矩阵实现演示...')
+
+
+
+
+print('矩阵变量'.center(50,'-'))
+A = Matrix( [ [1, 2, 2],
+              [2, 3, 2],
+              [2, 2, 3]])
+
+M = Matrix([    [0],
+                [0],
+                [2]])
+
+B = Matrix( [ [1, 2, 3],
+              [3, 2, -1],
+              [2, 2, 2]] )
+print("A:")
+print(A)
+print("M:")
+print(M)
+print("B:")
+print(B)
+
+
+# 加法
+print("矩阵加法:A+B".center(50, '-'))
+print(A + B)
+print("矩阵减法:A-B".center(50,'-'))
+print(A - B)
+print("矩阵乘法:A*B".center(50, '-'))
+print(A * B)
+print("数乘矩阵:10*B".center(50, '-'))
+print(10 * B)
+print("矩阵除以数:A/10".center(50, '-'))
+print(A / 10)
+print("数除以矩阵（元素）:10/B".center(50, '-'))
+print(10 / B)
+print("矩阵元素访问(副本):A[1:, 1:]".center(50,'-'))
+print(A[1:, 1:])
+
+print("代数余子式:A.cofacor(0, 0)".center(50, '-'))
+print(A.cofacor(0, 0))
+print("行列式:A.det()".center(50, '-'))
+print(A.det())
+print("伴随矩阵:A.adj()".center(50, '-'))
+print(A.adj())
+print("矩阵逆:A.inv()".center(50, '-'))
+print(A.inv())
+print("矩阵转置:A.transpose()".center(50, '-'))
+print(A.transpose())
+print("矩阵秩:A.rank()".center(50, '-'))
+print(A.rank())
+
+
+