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Prog09_Doolittle.py
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Prog09_Doolittle.py
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__author__ = 'jboris'
from numpy import array, identity
from Prog07_Gauss import leer_matriz_cuadrada, leer_vector, sustitucion as sustitucion_regresiva
def calcular_u_ii(matriz, L, U, i):
u_ii = matriz[i][i]
k = 0
while k <= i-1:
u_ii -= U[k][i] * L[i][k]
k += 1
U[i][i] = u_ii
return U
def calcular_l_ij(matriz, L, U, i, j):
l_ij = matriz[i][j]
k = 0
while k <= j-1:
l_ij -= U[k][j] * L[i][k]
k += 1
L[i][j] = l_ij / U[j][j]
return L
def calcular_u_ij(matriz, L, U, i, j):
u_ij = matriz[i][j]
k = 0
while k <= i-1:
u_ij -= U[k][j] * L[i][k]
k += 1
U[i][j] = u_ij
return U
def doolittle(matriz):
n = len(matriz)
L = identity(n)
U = identity(n)
i = 0
while i < n:
j = 0
while j < n:
if i == j:
U = calcular_u_ii(matriz, L, U, i)
if i > j:
L = calcular_l_ij(matriz, L, U, i, j)
if i < j:
U = calcular_u_ij(matriz, L, U, i, j)
j += 1
i += 1
return L, U
def sustitucion_progresiva(matriz, vector):
n = len(matriz)
x = range(n)
i = 0
while i < n:
suma = vector[i]
j = 0
while j < i:
suma -= x[j] * matriz[i][j]
j += 1
x[i] = suma / matriz[i][i]
i += 1
return x
def main():
n = int(raw_input('Grado del sistema: '))
if n > 1:
print 'Matriz A'
A = array(leer_matriz_cuadrada(n))
print 'Vector b'
b = array(leer_vector(n))
L, U = doolittle(A)
z = sustitucion_progresiva(L, b)
x = sustitucion_regresiva(U, z)
print 'Raices'
print x
if __name__ == '__main__':
main()