Detailed code example of how Python implements matrix class

This article mainly introduces the matrix class implemented in Python, and analyzes the definition, calculation, conversion and other related operation skills of Python matrices in the form of complete examples. Friends in need can refer to the following

The examples in this article describe Matrix class implemented in Python. Share it with everyone for your reference, the details are as follows:

Scientific calculation is inseparable from matrix operations. Of course, python already has a very good ready-made library: numpy(Simple installation and use of numpy

I wrote this matrix class, not intending to recreate it The wheel is just an exercise, recorded here.

Note: All functions of this class have not been implemented yet, and they will be improved slowly.

Full code:

import copy
class Matrix:
  '''矩阵类'''
  def __init__(self, row, column, fill=0.0):
    self.shape = (row, column)
    self.row = row
    self.column = column
    self._matrix = [[fill]*column for i in range(row)]
  # 返回元素m(i, j)的值: m[i, j]
  def __getitem__(self, index):
    if isinstance(index, int):
      return self._matrix[index-1]
    elif isinstance(index, tuple):
      return self._matrix[index[0]-1][index[1]-1]
  # 设置元素m(i,j)的值为s: m[i, j] = s
  def __setitem__(self, index, value):
    if isinstance(index, int):
      self._matrix[index-1] = copy.deepcopy(value)
    elif isinstance(index, tuple):
      self._matrix[index[0]-1][index[1]-1] = value
  def __eq__(self, N):
    '''相等'''
    # A == B
    assert isinstance(N, Matrix), "类型不匹配，不能比较"
    return N.shape == self.shape # 比较维度，可以修改为别的
  def __add__(self, N):
    '''加法'''
    # A + B
    assert N.shape == self.shape, "维度不匹配，不能相加"
    M = Matrix(self.row, self.column)
    for r in range(self.row):
      for c in range(self.column):
        M[r, c] = self[r, c] + N[r, c]
    return M
  def __sub__(self, N):
    '''减法'''
    # A - B
    assert N.shape == self.shape, "维度不匹配，不能相减"
    M = Matrix(self.row, self.column)
    for r in range(self.row):
      for c in range(self.column):
        M[r, c] = self[r, c] - N[r, c]
    return M
  def __mul__(self, N):
    '''乘法'''
    # A * B (或：A * 2.0)
    if isinstance(N, int) or isinstance(N,float):
      M = Matrix(self.row, self.column)
      for r in range(self.row):
        for c in range(self.column):
          M[r, c] = self[r, c]*N
    else:
      assert N.row == self.column, "维度不匹配，不能相乘"
      M = Matrix(self.row, N.column)
      for r in range(self.row):
        for c in range(N.column):
          sum = 0
          for k in range(self.column):
            sum += self[r, k] * N[k, r]
          M[r, c] = sum
    return M
  def __p__(self, N):
    '''除法'''
    # A / B
    pass
  def __pow__(self, k):
    '''乘方'''
    # A**k
    assert self.row == self.column, "不是方阵，不能乘方"
    M = copy.deepcopy(self)
    for i in range(k):
      M = M * self
    return M
  def rank(self):
    '''矩阵的秩'''
    pass
  def trace(self):
    '''矩阵的迹'''
    pass
  def adjoint(self):
    '''伴随矩阵'''
    pass
  def invert(self):
    '''逆矩阵'''
    assert self.row == self.column, "不是方阵"
    M = Matrix(self.row, self.column*2)
    I = self.identity() # 单位矩阵
    I.show()#############################
    # 拼接
    for r in range(1,M.row+1):
      temp = self[r]
      temp.extend(I[r])
      M[r] = copy.deepcopy(temp)
    M.show()#############################
    # 初等行变换
    for r in range(1, M.row+1):
      # 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
      if M[r, r] == 0:
        for rr in range(r+1, M.row+1):
          if M[rr, r] != 0:
            M[r],M[rr] = M[rr],M[r] # 交换两行
          break
      assert M[r, r] != 0, '矩阵不可逆'
      # 本行首元素(M[r, r])化为 1
      temp = M[r,r] # 缓存
      for c in range(r, M.column+1):
        M[r, c] /= temp
        print("M[{0}, {1}] /= {2}".format(r,c,temp))
      M.show()
      # 本列上、下方的所有元素化为 0
      for rr in range(1, M.row+1):
        temp = M[rr, r] # 缓存
        for c in range(r, M.column+1):
          if rr == r:
            continue
          M[rr, c] -= temp * M[r, c]
          print("M[{0}, {1}] -= {2} * M[{3}, {1}]".format(rr, c, temp,r))
        M.show()
    # 截取逆矩阵
    N = Matrix(self.row,self.column)
    for r in range(1,self.row+1):
      N[r] = M[r][self.row:]
    return N
  def jieti(self):
    '''行简化阶梯矩阵'''
    pass
  def transpose(self):
    '''转置'''
    M = Matrix(self.column, self.row)
    for r in range(self.column):
      for c in range(self.row):
        M[r, c] = self[c, r]
    return M
  def cofactor(self, row, column):
    '''代数余子式（用于行列式展开）'''
    assert self.row == self.column, "不是方阵，无法计算代数余子式"
    assert self.row >= 3, "至少是3*3阶方阵"
    assert row <= self.row and column <= self.column, "下标超出范围"
    M = Matrix(self.column-1, self.row-1)
    for r in range(self.row):
      if r == row:
        continue
      for c in range(self.column):
        if c == column:
          continue
        rr = r-1 if r > row else r
        cc = c-1 if c > column else c
        M[rr, cc] = self[r, c]
    return M
  def det(self):
    &#39;&#39;&#39;计算行列式(determinant)&#39;&#39;&#39;
    assert self.row == self.column,"非行列式，不能计算"
    if self.shape == (2,2):
      return self[1,1]*self[2,2]-self[1,2]*self[2,1]
    else:
      sum = 0.0
      for c in range(self.column+1):
        sum += (-1)**(c+1)*self[1,c]*self.cofactor(1,c).det()
      return sum
  def zeros(self):
    &#39;&#39;&#39;全零矩阵&#39;&#39;&#39;
    M = Matrix(self.column, self.row, fill=0.0)
    return M
  def ones(self):
    &#39;&#39;&#39;全1矩阵&#39;&#39;&#39;
    M = Matrix(self.column, self.row, fill=1.0)
    return M
  def identity(self):
    &#39;&#39;&#39;单位矩阵&#39;&#39;&#39;
    assert self.row == self.column, "非n*n矩阵，无单位矩阵"
    M = Matrix(self.column, self.row)
    for r in range(self.row):
      for c in range(self.column):
        M[r, c] = 1.0 if r == c else 0.0
    return M
  def show(self):
    &#39;&#39;&#39;打印矩阵&#39;&#39;&#39;
    for r in range(self.row):
      for c in range(self.column):
        print(self[r+1, c+1],end=&#39; &#39;)
      print()
if __name__ == &#39;__main__&#39;:
  m = Matrix(3,3,fill=2.0)
  n = Matrix(3,3,fill=3.5)
  m[1] = [1.,1.,2.]
  m[2] = [1.,2.,1.]
  m[3] = [2.,1.,1.]
  p = m * n
  q = m*2.1
  r = m**3
  #r.show()
  #q.show()
  #print(p[1,1])
  #r = m.invert()
  #s = r*m
  print()
  m.show()
  print()
  #r.show()
  print()
  #s.show()
  print()
  print(m.det())

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