#!/usr/bin/python
# Import required libraries
from __future__ import division
import sys
import numpy as np


def matrixTranspose(M):
    answer = [];
    answer = [ [row[n] for row in M] for n in range(len(M[0])) ]
    return answer;

def identityMatrix(n):
    answer = [];
    answer = [ [int(i==j) for j in range(n)] for i in range(n) ];
    return answer;

def vectorMatrixMultiplication(M,V):
    """
    Function multiplies a Matrix and a Vector
    Inputs:
    M: A matrix of length m x n (m rows, n columns)
    V: A vector of length n
    Output:
    answer: A vector of length m
    """
    answer = [];
    mLen = len(M);
    vLen = len(V);

    if ( (mLen == 0) or (vLen == 0) ) :
        raise ValueError("Matrix and Vector cannot be empty");
    elif ( len(M[0]) != vLen ) :
        raise ValueError("Number of columns of matrix M should equal length of vector V")

    answer = [ sum(row[n]*V[n] for n in range(vLen) )  for row in M]

    return answer



def matrixMultiplication(M1, M2):
    """
    Function multiplies a Matrix and a Vector
    Inputs:
    M1: A matrix of length m x n (m rows, n columns)
    M2: A matrix of length n x p (n rows, p columns)
    Output:
    answer: A matrix of length m x p (m rows, p columns)
    """
    answer = [];

    m = len(M1);
    n = len(M2);
    p = len(M2[0]);

    if ( (m == 0) or (n == 0) ) :
        raise ValueError("Matrices cannot be empty");
    elif ( len(M1[0]) != n ) :
        raise ValueError("Number of columns of matrix M1 should equal number of rows of matrix M2")

    for n in range(p):
        vector = [ row[n] for row in M2];
        answer.append(vectorMatrixMultiplication(M1, vector) );

    return matrixTranspose(answer);



matrix = [[1, 2, 3, 4], [10, 11, 12, 13]];
vector = [5, 6, 7, 9];

print "========= test vectorMatrixMultiplication =========";
print "matrix: \n", np.matrix(matrix);
print "vector: \n", vector;
print "vectorMatrixMultiplication:";
print vectorMatrixMultiplication(matrix,vector);


matrix1 = [[1, 2, 3, 4], [10, 11, 12, 13]];
matrix2 = [ [5,10], [6,11], [7,12], [9,13] ];

print "========= test matrixMultiplication =========";
print "matrix: \n", np.matrix(matrix1);
print "matrix: \n", np.matrix(matrix2);
print "matrixMultiplication:";
print np.matrix(matrixMultiplication(matrix1, matrix2));

print "========= test identityMatrix =========";
print np.matrix(identityMatrix(4));