# File: ChapterLists/matrices.py
""" V= [1, 2, 1, 3] [2, 4, 2, 6] [1, 4, 1, 9]
[1, 2, 3]
[4, 5, 6]
[7, 8, 9]

[1, 0, 0]
[0, 1, 0]
[0, 0, 1]

add matrices
[2, 2, 3]
[4, 6, 6]
[7, 8, 10]

multiply matrices
[1, 2, 3]
[4, 5, 6]
[7, 8, 9]
""" 
def addVector(V1,V2):
    return [V1[i] + V2[i] for i in range(len(V1))]

def multVector(V1,V2):
    return [V1[i] * V2[i] for i in range(len(V1))]

def multMatrix(M,N):
    Res=[]  #result
    for i in range(len(M)):
        row=[] #build rows in Res
        for j in range(len(M)):
            col = [ N[k][j]  for k in range(len(M))] #select column j
            r = sum(multVector(M[i],col))   #scalarVector
            row.append(r)   #M[i] row with N[j] column
        Res.append(row)
    return Res

def addMatrix(M,N):
    return [addVector(M[i],N[i]) for i in range(len(M))]

def printMatrix(M):
    for r in M:
        print(r)
    print()
    
def main():
    M1 =  [[1,2,3],[4,5,6],[7,8,9]]
    ID =  [[1,0,0],[0,1,0],[0,0,1]] 
    V = [1,2,1,3]
    print("V=",V,addVector(V,V),multVector(V,V)) # V * V
    printMatrix(M1)
    printMatrix(ID)
    print("add matrices")
    printMatrix(addMatrix(M1,ID))
    print("multiply matrices")
    printMatrix(multMatrix(M1,ID))

main()