input: Write a class to perform various matrix operations like addition, subtraction, multiplication, and transpose. The class should be capable of initializing a matrix, printing the matrix, and performing the aforementioned operations. Provide appropriate assert tests to validate the functionality of the methods.
  
  ### Input:
  
  ### Output:
  class Matrix:
      def __init__(self, m, n, lst):
          self.m = m
          self.n = n
          self.mat = []
  
          c = 0
          for i in range(self.m):
              a = []
              for j in range(self.n):
                  a.append(lst[c])
                  c += 1
              self.mat.append(a)
  
      def __str__(self):
          output = ""
          for i in self.mat:
              for j in i:
                  output += str(j) + " "
              output += '\n'
          return output
  
      def add(self, mat2):
          for i in range(self.m):
              for j in range(self.n):
                  self.mat[i][j] += mat2.mat[i][j]
  
      def sub(self, mat2):
          for i in range(self.m):
              for j in range(self.n):
                  self.mat[i][j] -= mat2.mat[i][j]
  
      def mul(self, mat2):
          result = []
          for i in range(self.m):
              a = []
              for j in range(mat2.n):
                  s = 0
                  for k in range(self.n):
                      s += self.mat[i][k] * mat2.mat[k][j]
                  a.append(s)
              result.append(a)
          self.mat = result
          self.m = len(result)
          self.n = len(result[0])
  
      def transpose(self):
          result = [[self.mat[j][i] for j in range(len(self.mat))] for i in range(len(self.mat[0]))]
          self.mat = result
          self.m = len(result)
          self.n = len(result[0])
  
  assert str(Matrix(2, 2, [1, 2, 3, 4])) == "1 2 \n3 4 \n"
  assert str(Matrix(2, 2, [1, 2, 3, 4]).transpose()) == "1 3 \n2 4 \n"
  
  mat1 = Matrix(2, 2, [1, 2, 3, 4])
  mat2 = Matrix(2, 2, [2, 3, 4, 5])
  mat1.add(mat2)
  assert str(mat1) == "3 5 \n7 9 \n"
  
  mat1 = Matrix(2, 2, [1, 2, 3, 4])
  mat2 = Matrix(2, 2, [2, 3, 4, 5])
  mat1.sub(mat2)
  assert str(mat1) == "-1 -1 \n-1 -1 \n"
  
  mat1 = Matrix(2, 2, [1, 2, 3, 4])
  mat2 = Matrix(2, 2, [2, 0, 1, 2])
  mat1.mul(mat2)
  assert str(mat1) == "4 4 \n10 8 \n"
  
  assert str(Matrix(1, 3, [1, 2, 3]).transpose()) == "1 \n2 \n3 \n"
output: class Matrix:
      def __init__(self, m, n, lst):
          self.m = m
          self.n = n
          self.mat = []
  
          c = 0
          for i in range(self.m):
              a = []
              for j in range(self.n):
                  a.append(lst[c])
                  c += 1
              self.mat.append(a)
  
      def __str__(self):
          output = ""
          for i in self.mat:
              for j in i:
                  output += str(j) + " "
              output += '\n'
          return output
  
      def add(self, mat2):
          for i in range(self.m):
              for j in range(self.n):
                  self.mat[i][j] += mat2.mat[i][j]
  
      def sub(self, mat2):
          for i in range(self.m):
              for j in range(self.n):
                  self.mat[i][j] -= mat2.mat[i][j]
  
      def mul(self, mat2):
          result = []
          for i in range(self.m):
              a = []
              for j in range(mat2.n):
                  s = 0
                  for k in range(self.n):
                      s += self.mat[i][k] * mat2.mat[k][j]
                  a.append(s)
              result.append(a)
          self.mat = result
          self.m = len(result)
          self.n = len(result[0])
  
      def transpose(self):
          result = [[self.mat[j][i] for j in range(len(self.mat))] for i in range(len(self.mat[0]))]
          self.mat = result
          self.m = len(result)
          self.n = len(result[0])