Write a python function which takes input matrix A and applies gaussian elimination with pivoting strategy...

Write a python function which takes input matrix A and applies gaussian elimination with pivoting strategy which returns P,Q (permutation matrices) L (lower triangular matrix with 1's on the diagonal) and U (upper triangular matrix) such that (P^t)(A)(Q)=LU is correct,

Expert Solution

`Hey,

Note: If you have any queries related to the answer please do comment. I would be very happy to resolve all your queries.

from pprint import pprint

def matrixMul(A, B):
TB = zip(*B)
return [[sum(ea*eb for ea,eb in zip(a,b)) for b in TB] for a in A]

def pivotize(m):
"""Creates the pivoting matrix for m."""
n = len(m)
ID = [[float(i == j) for i in xrange(n)] for j in xrange(n)]
for j in xrange(n):
row = max(xrange(j, n), key=lambda i: abs(m[i][j]))
if j != row:
ID[j], ID[row] = ID[row], ID[j]
return ID

def lu(A):
"""Decomposes a nxn matrix A by PA=LU and returns L, U and P."""
n = len(A)
L = [[0.0] * n for i in xrange(n)]
U = [[0.0] * n for i in xrange(n)]
P = pivotize(A)
A2 = matrixMul(P, A)
for j in xrange(n):
L[j][j] = 1.0
for i in xrange(j+1):
s1 = sum(U[k][j] * L[i][k] for k in xrange(i))
U[i][j] = A2[i][j] - s1
for i in xrange(j, n):
s2 = sum(U[k][j] * L[i][k] for k in xrange(j))
L[i][j] = (A2[i][j] - s2) / U[j][j]
return (L, U, P)

a = [[1, 3, 5], [2, 4, 7], [1, 1, 0]]
for part in lu(a):
pprint(part, width=19)
print
print
b = [[11,9,24,2],[1,5,2,6],[3,17,18,1],[2,5,7,1]]
for part in lu(b):
pprint(part)
print

Kindly revert for any queries

Thanks.

venereology answered 3 months ago

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