Question

我正在尝试使用递归函数来计算矩阵的行列式。我有一个具有 getitem ， setitem ，...的Matrix类。.eliminated（i，j）方法将返回一个新的矩阵，该矩阵将从第i行，第j列中删除。

这是Matrix类，我之前也创建了Array，Array_2D类，它们都很好：

class Matrix:
    def __init__(self, numRows, numCols):
        self.grid = Array_2D(numRows,numCols)
        self.grid.clear(0)
    def __getitem__(self, tuple):
        return self.grid[tuple[0],tuple[1]]
    def numRows(self):
        return self.grid.numRows()
    def numCols(self):
        return self.grid.numCols()
    def __add__(self, other):
        assert other.numRows() == self.numRows() and\
            other.numCols == self.numCols() , "Matrix sizes not compatible"
        newMatrix = Matrix(self.numRows(),self.numCols())
        for r in range(self.numRows()):
            for c in range(self.numCols()):
                newMatrix[r,c]=self[r,c]+other[r,c]
        return  newMatrix

    def __setitem__(self, tuple, value):
        self.grid[tuple[0],tuple[1]]=value

    def scaleBy(self,scalar):
        for r in range(self.numRows()):
            for c in range(self.numCols()):
                self[r,c]=self[r,c]*scalar

    def tranpose(self):
        newMatrix = Matrix(self.numCols(),self.numRows())
        for r in range(newMatrix.numRows()):
            for c in range(newMatrix.numCols()):
                newMatrix[r,c]=self[c,r]
        return newMatrix

    def __sub__(self, other):
        assert other.numRows() == self.numRows() and \
               other.numCols == self.numCols(), "Matrix sizes not compatible"
        newMatrix = Matrix(self.numRows(), self.numCols())
        for r in range(self.numRows()):
            for c in range(self.numCols()):
                newMatrix[r, c] = self[r, c] - other[r, c]
        return newMatrix

    def __mul__(self, other):
        assert other.numRows() == self.numCols(), "Matrix sizes not compatible"
        newMatrix = Matrix(self.numRows(),other.numCols())
        for r in range(newMatrix.numRows()):
            for c in range(newMatrix.numCols()):
                newMatrix[r,c] = 0
                for i in range(self.numCols()):
                    newMatrix[r,c]+=self[r,i]*other[i,c]
        return newMatrix

    def determinant(self):
        assert self.numCols()==self.numRows(), "Must be a square matrix"
        assert self.numCols() > 0
        if self.numCols() == 1:
            return self[0,0]
        if self.numCols() == 2:
            return self[0,0]*self[1,1]-self[0,1]*self[1,0]
        det = 0
        if self.numCols() >=2:
            for c in range(self.numCols()):
                det+=((-1) ** c) * self[0, c] * self.eliminated(0, c).determinant()
            return det

    def eliminated(self,row,col):
        assert row >=0 and row < self.numRows(), "Invalid row"
        assert col >=0 and col < self.numCols(), "Invalid column"
        assert self.numCols() >1 and self.numRows()>1
        entry_list = []
        for r in range(self.numRows()):
            for c in range(self.numCols()):
                self[r, col] = None
                self[row,c]=None
                if self[r,c] != None:
                    entry_list.append(self[r,c])
        new_matrix  = Matrix(self.numRows()-1, self.numCols()-1)
        for r in range(new_matrix.numRows()):
            for c in range(new_matrix.numCols()):
                new_matrix[r,c] = entry_list[c + r*new_matrix.numCols()]
        return new_matrix

对于3x3矩阵，我一直收到此错误，2x2和1x1很好：

Traceback (most recent call last):
  File "E:/DataStructures/matrix.py", line 100, in <module>
    print(ma4.determinant())
  File "E:/DataStructures/matrix.py", line 67, in determinant
    det+=((-1) ** c) * self[0, c] * self.eliminated(0, c).determinant()
TypeError: unsupported operand type(s) for *: 'int' and 'NoneType'

我知道我的递归函数会一直删除行和列，直到到达NoneType为止，但是不知道如何解决

Answer 1

您好，请查看以下内容：

matrix=[]
def det(IC,i):
    global matrix,row
    determinent=0
    m=1
    for j in range(len(matrix)):
        if j not in IC:
            m+=1
            if i == row-1:
                determinent = matrix[i][j]
            else:
                determinent+=(-1)**(m)*matrix[i][j]*det(IC+[j],i+1)
    return determinent
row=int(input("enter order:"))
for i in range(row):
    rowEntry=[int(x) for x in input().split(' ')]

    matrix.append(rowEntry)
print(matrix)
print(det([],0))

请仔细输入信息，例如：输入订单：3

2 3 4

1 2 3

3 4 5

递归计算矩阵的行列式

1 个答案: