Python程序检查对合矩阵

# input no of rows
rows = 3
# creating a function to perform matrix multiplication
def multiplyMatrix(inputMatrix, output):
   # traversing through the rows of a matrix
      for p in range(rows):
         # traversing through all the columns of a current row
         for q in range(rows):
            # assuming the current element is 0
               output[p][q] = 0
               for x in range(rows):
                  # performing matrix multiplication
                  output[p][q] += inputMatrix[p][x] * inputMatrix[x][q]
      # returning the resultant matrix multiplication output
      return output
# creating a function to check whether the input matrix
# is an involuntary  matrix by accepting matrix as an argument
def checkInvolutoryMat(inputMatrix):
   # Creating a rows*rows size matrix with all elements as 0
      output = [[0 for p in range(rows)]
              for q in range(rows)]
      # calling the above multiplyMatrix() function
      output = multiplyMatrix(inputMatrix, output)
   # Iterating in the rows of the output matrix
      for p in range(rows):
         # Iterating in the diagonals of the output matrix
            for q in range(rows):
               # If it is a diagonal element and if it is not 1 then return False(Not Involuntary)
               if (p == q and output[p][q] != 1):
                  return False
               # If it is a non-diagonal element and if it is not 1 then return False(Not Involuntary)
               if (p != q and output[p][q] != 0):
                  return False
      # It is an involuntary matrix so return True
      return True
# input matrix
inputMatrix = [[1, 0, 0], [0, -1, 0], [0, 0, -1]]
# checking whether the above checkInvolutoryMat() function returns true
# by passing the input matrix as an argument
if (checkInvolutoryMat(inputMatrix)):
   # printing involuntary matrix if the condition is true
      print("The input matrix is an Involutory matrix")
else:
   # else printing NOT involuntary matrix
      print("The input matrix is NOT an Involutory matrix")

# using the numpy module
import numpy as np
# creating a function to check whether the input matrix
# is an involuntary  matrix by accepting matrix as an argument
def checkInvolutoryMat(inputMatrix):
   # Getting the inverse of an input matrix using the numpy linalg module
      inverseMat = np.linalg.inv(inputMatrix)
      # checking whether the input matrix is equal to its inverse matrix
      # using the numpy.allclose() function and returning the result
      return np.allclose(inputMatrix, inverseMat)
# input matrix
inputMatrix = [[1, 0, 0], [0, -1, 0], [0, 0, -1]]
# calling the checkInvolutoryMat() function by passing the input matrix as an argument
# The output True indicates an INVOLUNTARY matrix
print(checkInvolutoryMat(inputMatrix))