def Doolittle(mat, b, n, option):
lower = [[0 for x in range(n)] for y in range(n)]
upper = [[0 for x in range(n)] for y in range(n)]
# Decomposing matrix into Upper
# and Lower triangular matrix
for i in range(n):
# Upper Triangular
for k in range(i, n):
# Summation of L(i, j) * U(j, k)
sum = 0
for j in range(i):
sum += (lower[i][j] * upper[j][k])
# Evaluating U(i, k)
upper[i][k] = mat[i][k] - sum
# Lower Triangular
for k in range(i, n):
if (i == k):
lower[i][i] = 1 # Diagonal as 1
else:
# Summation of L(k, j) * U(j, i)
sum = 0
for j in range(i):
sum += (lower[k][j] * upper[j][i])
# Evaluating L(k, i)
lower[k][i] = int((mat[k][i] - sum) / upper[i][i])
# setw is for displaying nicely
print("Lower Triangular matrix:")
Services.PrintArray(lower)
print("Upper Triangular matrix:")
Services.PrintArray(upper)
if option.lower() == 'y':
Services.solveDecompositon(lower, upper, b, 'a')
import numpy as np
import scipy.linalg as la
import sys
sys.path.append("../")
import services as Services
option = input("Do you want to find solution also? y or n : ")
A = np.array([[4, -1, 1], [-1, 4.25, 2.75], [1, 2.75, 3.5]])
b = np.array([1, 0, 0])
print("Given Matrix=>")
Services.PrintArray(A)
L, D, P = la.ldl(A)
Lt = np.transpose(L)
print("L:")
Services.PrintArray(L)
print("D:")
Services.PrintArray(D)
print("Lt:")
Services.PrintArray(Lt)
if option.lower() == 'y':
Services.solveLDLt(L, D, Lt, b)
# Lower Triangular
for k in range(i, n):
# Summation of L(k, j) * U(j, i)
sum = 0
for j in range(i):
sum += (lower[k][j] * upper[j][i])
# Evaluating L(k, i)
lower[k][i] = int((mat[k][i] - sum) / upper[i][i])
# setw is for displaying nicely
print("Lower Triangular matrix:")
Services.PrintArray(lower)
print("Upper Triangular matrix:")
Services.PrintArray(upper)
if option.lower() == 'y':
Services.solveDecompositon(lower, upper, b, 'a')
option = input("Do you want to find solution also? y or n : ")
# Driver code
mat = [[1, 2, 3], [2, -4, 6], [3, -9, -3]]
b = [5, 18, 6]
print("Given matrix=> ")
Services.PrintArray(mat)
Crouts(mat, b, len(mat), option)
# This code is contributed by mits
from math import sqrt
from pprint import pprint
import numpy as np
import scipy.linalg as la
import sys
sys.path.append("../")
import services as Services
option = input("Do you want to find solution also? y or n : ")
A = np.array([[4, 2, 14], [2, 17, -5], [14, -5, 83]])
b = np.array([14, -101, 155])
print("Given Matrix=>")
Services.PrintArray(A)
try:
Lt = la.cholesky(A)
L = np.transpose(Lt)
except RuntimeError as identifier:
print(identifier)
print("L:")
for i in range(0, len(L)):
for j in range(0, len(L)):
print("{:15.3f}".format(L[i][j]), end=" ")
print("")
print("Lt:")
for i in range(0, len(Lt)):
for j in range(0, len(Lt)):
print("{:15.3f}".format(Lt[i][j]), end=" ")
print("")
if option.lower() == "y":
Services.solveDecompositon(L, Lt, b, 'b')
for i in range(N):
x = (b - dot(R, x)) / D
print("Iteratin: ", i + 1)
for k in range(0, len(x)):
print("x(", k + 1, ") = ", round(x[k], 6), end=", ")
print("\n")
return x
# enter your arguments:
A = [[1, 2, 1], [3, 1, 1], [1, -1, 4]]
b = array([0, 0, 3])
print("Equations given =>")
Services.PrintArray(A)
print("Checking Condition =>")
print("")
arranged = copy(A)
conditon = Services.CheckCondition(A)
if conditon == False:
arranged = Services.Arrange(arranged)
if Services.isEqual(A, arranged):
print(
"It isn't a diagnolly dominent, Therefore solution will be diverged"
)
print("")
else:
print("Rearranging equaitions =>")