Gram-Schimdt-Modificado-Columnas

import math
m = int(raw_input())
n = int(raw_input())

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



#leemos la matriz A y b, inicializamos E en 0
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)


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

###fin de lectura



#inicializamos las matrices necesarias
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 i in range(n):
    B.append(0.0)

E=a

####    Fin de inicializacion


###############################################
#### ACA COMIENZA EL ALGORITMO
###############################################

for j in range(n):
    for k in range(m):
        E[k][j] = a[k][j]

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

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

###############################################
#### termina EL ALGORITMO
###############################################

#hallamos la transpuesta
for i in range(m):
    for j in range(n):
        Et[j][i] = E[i][j]


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


#Resolvemos x por regresion
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
    j-=1


#imprimimos las matrices
print 'matriz A:'
for i in range(m):
    print A[i]
print'\n'

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

print 'matriz B:'
print B
print'\n'

print 'matriz x:'
print x
print'\n'