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,

Solutions

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 2 days ago

Next > < Previous

Related Solutions

A. Write a function in MATLAB called findTranspose that takes in as input any matrix or...

A. Write a function in MATLAB called findTranspose that takes in as input any matrix or any vector and simply returns back the transpose of that input. You can always verify your answer by using the inbuilt transpose function in MATLAB, however, you cannot use the transpose function directly when writing your code. Here is the starter code that we are providing to help you get started %x is the input vector or matrix. You can find the %size that...

Can you explain in detail what Gaussian Elimination with pivoting is? and how is it different...

Can you explain in detail what Gaussian Elimination with pivoting is? and how is it different from Gaussian Elimination without pivoting?

USING PYTHON, write a function that takes a list of integers as input and returns a...

USING PYTHON, write a function that takes a list of integers as input and returns a list with only the even numbers in descending order (Largest to smallest) Example: Input list: [1,6,3,8,2,5] List returned: [8, 6, 2]. DO NOT use any special or built in functions like append, reverse etc.

Write a Python function that takes as input parameters base_cost (a float) and customer_type and prints...

Write a Python function that takes as input parameters base_cost (a float) and customer_type and prints a message with information about the total amount owed and how much the tip was. As a reminder, the tip amounts are 10%, 15% and 20% for stingy, regular, and generous customers. And the tax amount should be 7%. The total amount is calculated as the sum of two amounts: check_amount = base_cost*1.07 tip_amount = tip_percentage*check_amount To receive full credit, you must use string...

B. Write a function in MATLAB called findInverseOf2x2Matrix that takes in as input any square matrix...

B. Write a function in MATLAB called findInverseOf2x2Matrix that takes in as input any square matrix of size 2 × 2 and returns back the inverse of that matrix if one exists. If no inverse exists, print back a suitable error message. You can safely assume that we will test your code on square matrices of size 2 × 2 only. You can always verify your answer by using the inbuilt inverse function in MATLAB, however, you cannot use the...

Write a PYTHON function CommonLetters(mystring) that takes mystring as input and returns the number of letters...

Write a PYTHON function CommonLetters(mystring) that takes mystring as input and returns the number of letters in mystring that also occur in the string ‘Python’. Using above function, write a program that repeatedly prompts the user for a string and then prints the number of letters in the string that are also in string ‘Python’. The program terminates when the user types an empty string.

All functions are written in python Write a function cube_evens_lc(values) that takes as input a list...

All functions are written in python Write a function cube_evens_lc(values) that takes as input a list of numbers called values, and that uses a list comprehension to create and return a list containing the cubes of the even numbers in values (i.e., the even numbers raised to the third power). For example: >>> cube_evens_lc([2, 5, 6, 4, 1]) result: [8, 216, 64] This version of the function may not use recursion. Write a function cube_evens_rec(values) that takes as input a...

Question