Matrix operations in Python with a functional style

matrix.py

#!/usr/bin/python3

'''
Copyright (c) 2014 Douglas Vaz

Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in
all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
THE SOFTWARE.
'''


from functools import reduce
class Matrix:
    def __init__(self, args):
        self.__n__ = (len(args), len(args[0]))
        self.__matrix__ = args
        self.__square__ = False;

        #Validate
        for i in args:
            assert(len(i) == self.__n__[1])

        if self.__n__[0] == self.__n__[1]:
            self.__square__ = True

    def row(self, i):
        assert(i < self.__n__[0])
        return self.__matrix__[i]

    def column(self, j):
        assert(j < self.__n__[1])
        return [col[j] for col in self.__matrix__]

    def __add__(self, b):
        assert(self.__n__ == b.__n__)
        return Matrix([[i+j for i,j in zip(ai,bi)] for ai, bi in zip(self.__matrix__, b.__matrix__)])

    def __sub__(self, b):
        assert(self.__n__ == b.__n__)
        return Matrix([[i-j for i,j in zip(ai,bi)] for ai, bi in zip(self.__matrix__, b.__matrix__)])

    def __mul__(self, b):
        assert(self.__n__[1] == b.__n__[0])
        sum = lambda x,y: x + y
        return Matrix([[reduce(sum, [aik*bkj for aik, bkj in zip(self.row(i),b.column(j)) ]) for j in range(b.__n__[1])] for i in range(self.__n__[0])])

    def __truediv__(self, b):
        return Matrix([[e/b for e in row] for row in self.__matrix__])
        

    def transpose(self):
        return Matrix([self.column(i) for i in range(self.__n__[0])])

    def minor(self,i,j):
        assert(i < self.__n__[0] and j < self.__n__[0])
        mat = []
        for m, row in enumerate(self.__matrix__):
            r = [e for n,e in enumerate(row) if m != i and n != j]
            if len(r) > 0:
                mat.append(r)
        return Matrix(mat)

    def __str__(self):
        return str(self.__matrix__)

    def dimensions(self):
        return self.__n__

    def determinant(self):
        assert(self.__square__)
        if self.__n__[0] == 1:
            return self.row(0)[0]
        elif self.__n__[0] == 2:
            return self.row(0)[0] * self.row(1)[1] - self.row(0)[1] * self.row(1)[0]
        else:
            sum = 0
            for j,n in enumerate(self.row(0)):
                sum = sum + pow(-1,j+2) * n * self.minor(0,j).determinant()
            return sum

    def cofactor(self):
        assert(self.__square__)
        m = []
        for i,row in enumerate(self.__matrix__):
            m.append([pow(-1,i+j+2) * self.minor(i,j).determinant() for j in range(self.__n__[0])])
        return Matrix(m)

    def adjoint(self):
        assert(self.__square__)
        return self.cofactor().transpose()

    def inverse(self):
        d = self.determinant()
        assert(self.__square__ and d != 0)
        return self.adjoint()/d

if __name__ == "__main__":
    a = Matrix((( 5, 6,-1, 4),
                ( 3, 5, 2, 1),
                (-1, 0, 3, 6)))
    b = Matrix((( 2, 1),
                ( 4,-2),
                ( 7, 5),
                ( 3,-8)))
    c = a * b

    d = Matrix((( 2, 3, 1),
          ( 4, 5,-3),
          (-1, 6, 7)))

    print("A * B = C = ")
    print(c)
    print('\n')

    print("C / 2 = ")
    print(str(c/2))
    print('\n')

    print("Adj D = ")
    print(d.adjoint())
    print('\n')

    print("|D| = ")
    print(d.determinant())
    print('\n')

    print("Inverse D = ")
    print(d.inverse())