clasico gram

import math
m = int(raw_input("Ingrese m: "))
n = int(raw_input("Ingrese n: "))

a = []          # m*n
A = []          # m*n
b = []          # m*1
U = []          # n*n
E = []          # m*n
Et = []         # n*m
x = []          # n*1

for i in range (m):
    A.append([])
    a.append([])
    E.append([])
    for j in range (n):
        A[i].append(float(raw_input()))
        a[i].append(float(A[i][j]))
        E[i].append(0.0)
#       if i == j:
#           E[i].append(1.0)
#       else:
#           E[i].append(0.0)

print 'matriz E:'
for i in range(m):
    print E[i]
print'\n'


for i in range(m):
    b.append(float(raw_input()))

for i in range(n):
    U.append([])
    for j in range(n):
        U[i].append(0.0)

for i in range(n):
    Et.append([])
    x.append(0.0)
    for j in range(m):
        Et[i].append(0.0)


for j in range(n):
    for i in range(j):
        prod_int = 0.0      #producto interno de ET[][].A[][]
        for k in range(m):
            prod_int += E[k][i]*a[k][j]
        U[i][j] = prod_int

        for k in range (m):
            E[k][j] = a[k][j] - U[i][j]*E[k][i]

        suma=0.0
        for k in range(m):
            suma += E[k][j]*E[k][j]
        U[j][j] = math.sqrt(suma)

        for k in range(m):
            E[k][j] = E[k][j]/U[j][j]

for i in range(m):
    for j in range(n):
        Et[j][i] = E[i][j]

B = []

for i in range(n):
    B.append(0.0)

for i in range(n):
    for j in range(m):
        B[i] = B[i]+ Et[i][j]*b[j]


print 'matriz A:'
for i in range(m):
    print a[i]
print'\n'

print 'matriz b:'
for i in range(m):
    print b[i]
print'\n'

print 'matriz U:'
for i in range(n):
    print U[i]
print'\n'

print 'matriz E:'
for i in range(m):
    print E[i]
print'\n'

print 'matriz B:'
for i in range(n):
    print B[i]
print'\n'

j = n-1
while j>=0:
    res = B[j]
    for k in range (j+1, n):
        res -= U[j][k] *x[k]
    res /= float(U[j][j])
    x[j] = res
    print j, res
    j-=1

print 'matriz x:'
for i in range(n):
    print x[i]
print'\n'