矩阵类的python实现

1 import copy

2

3 class Matrix:

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'''矩阵类'''

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def __init__(self, row, column, fill=0.0):

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self.shape = (row, column)

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self.row = row

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self.column = column

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self._matrix = [[fill]*column for i in range(row)]
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# 返回元素m(i, j)的值:
m[i, j]
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def __getitem__(self, index):
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if isinstance(index, int):
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return self._matrix[index-1]
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elif isinstance(index, tuple):
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return self._matrix[index[0]-1][index[1]-1]
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# 设置元素m(i,j)的值为s:
m[i, j] = s
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def __setitem__(self, index, value):
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if isinstance(index, int):
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self._matrix[index-1] = copy.deepcopy(value)
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elif isinstance(index, tuple):
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self._matrix[index[0]-1][index[1]-1] = value
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def __eq__(self, N):
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'''相等'''
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# A == B
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assert isinstance(N, Matrix), "类型不匹配，不能比较"
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return N.shape == self.shape
# 比较维度，可以修改为别的
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def __add__(self, N):
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'''加法'''
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# A + B
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assert N.shape == self.shape, "维度不匹配，不能相加"
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M = Matrix(self.row, self.column)
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for r in range(self.row):
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for c in range(self.column):
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M[r, c] = self[r, c] + N[r, c]
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return M
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def __sub__(self, N):
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'''减法'''
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# A - B
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assert N.shape == self.shape, "维度不匹配，不能相减"
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M = Matrix(self.row, self.column)
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for r in range(self.row):
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for c in range(self.column):
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M[r, c] = self[r, c] - N[r, c]
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return M
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def __mul__(self, N):
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'''乘法'''
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# A * B (或：A * 2.0)
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if isinstance(N, int) or isinstance(N,float):
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M = Matrix(self.row, self.column)
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for r in range(self.row):
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for c in range(self.column):
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M[r, c] = self[r, c]*N
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else:
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assert N.row == self.column, "维度不匹配，不能相乘"
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M = Matrix(self.row, N.column)
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for r in range(self.row):
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for c in range(N.column):
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sum = 0
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for k in range(self.column):
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sum += self[r, k] * N[k, r]
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M[r, c] = sum
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return M
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def __div__(self, N):
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'''除法'''
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# A / B
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pass
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def __pow__(self, k):
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'''乘方'''
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# A**k
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assert self.row == self.column, "不是方阵，不能乘方"
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M = copy.deepcopy(self)
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for i in range(k):
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M = M * self
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return M
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def rank(self):
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'''矩阵的秩'''
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pass
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def trace(self):
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'''矩阵的迹'''
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pass
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def adjoint(self):
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'''伴随矩阵'''
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pass
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def invert(self):
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'''逆矩阵'''
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assert self.row == self.column, "不是方阵"
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M = Matrix(self.row, self.column*2)
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I = self.identity() # 单位矩阵
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I.show()#############################
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# 拼接
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for r in range(1,M.row+1):
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temp = self[r]
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temp.extend(I[r])
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M[r] = copy.deepcopy(temp)
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M.show()#############################
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# 初等行变换
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for r in range(1, M.row+1):
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# 本行首元素(M[r, r])若为 0，则向下交换最近的当前列元素非零的行
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if M[r, r] == 0:
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for rr in range(r+1, M.row+1):
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if M[rr, r] != 0:
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M[r],M[rr] = M[rr],M[r] # 交换两行
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break
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assert M[r, r] != 0, '矩阵不可逆'
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# 本行首元素(M[r, r])化为 1
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temp = M[r,r] # 缓存
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for c in range(r, M.column+1):
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M[r, c] /= temp
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print("M[{0}, {1}] /=
{2}".format(r,c,temp))
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M.show()
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# 本列上、下方的所有元素化为 0
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for rr in range(1, M.row+1):
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temp = M[rr, r] # 缓存
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for c in range(r, M.column+1):
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if rr == r:
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continue
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M[rr, c] -= temp * M[r, c]
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print("M[{0}, {1}] -= {2} * M[{3}, {1}]".format(rr, c, temp,r))
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M.show()
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# 截取逆矩阵
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N = Matrix(self.row,self.column)
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for r in range(1,self.row+1):
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N[r] = M[r][self.row:]
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return N
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def jieti(self):
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'''行简化阶梯矩阵'''
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pass
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def transpose(self):
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'''转置'''
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M = Matrix(self.column, self.row)
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for r in range(self.column):
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for c in range(self.row):
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M[r, c] = self[c, r]
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return M
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def cofactor(self, row, column):
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'''代数余子式（用于行列式展开）'''
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assert self.row == self.column, "不是方阵，无法计算代数余子式"
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assert self.row >= 3, "至少是3*3阶方阵"
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assert row <= self.row and column <= self.column, "下标超出范围"
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M = Matrix(self.column-1, self.row-1)
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for r in range(self.row):
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if r == row:
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continue
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for c in range(self.column):
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if c == column:
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continue
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rr = r-1 if r > row else r
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cc = c-1 if c > column else c
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M[rr, cc] = self[r, c]
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return M
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def det(self):
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'''计算行列式(determinant)'''
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assert self.row == self.column,"非行列式，不能计算"
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if self.shape == (2,2):
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return self[1,1]*self[2,2]-self[1,2]*self[2,1]
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else:
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sum = 0.0
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for c in range(self.column+1):
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sum += (-1)**(c+1)*self[1,c]*self.cofactor(1,c).det()
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return sum
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def zeros(self):
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'''全零矩阵'''
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M = Matrix(self.column, self.row, fill=0.0)
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return M
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def ones(self):
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'''全1矩阵'''
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M = Matrix(self.column, self.row, fill=1.0)
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return M
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def identity(self):
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'''单位矩阵'''
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assert self.row == self.column, "非n*n矩阵，无单位矩阵"
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M = Matrix(self.column, self.row)
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for r in range(self.row):
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for c in range(self.column):
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M[r, c] = 1.0 if r == c else 0.0
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return M
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def show(self):
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'''打印矩阵'''
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for r in range(self.row):
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for c in range(self.column):
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print(self[r+1, c+1],end='
')
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print()
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212 if __name__ == '__main__':
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m = Matrix(3,3,fill=2.0)
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n = Matrix(3,3,fill=3.5)
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m[1] = [1.,1.,2.]
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m[2] = [1.,2.,1.]
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m[3] = [2.,1.,1.]
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p = m * n
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q = m*2.1
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r = m**3
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#r.show()
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#q.show()
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#print(p[1,1])
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#r = m.invert()
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#s = r*m
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print()
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m.show()
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print()
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#r.show()
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print()
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#s.show()
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print()
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print(m.det())