Question

Gauss elimination using python without using any libraries for a 2d list (n x n) .

Thanks

Answer 1

CODE

def gaussElimination(A, b, n):

l = [0 for x in range(n)]

s = [0.0 for x in range(n)]

for i in range(n):

l[i] = i

max1 = 0.0

for j in range(n):

if abs(A[i][j]) > max1:

max1 = abs(A[i][j])

s[i] = max1

for i in range(n - 1):

max2 = 0.0

for j in range(i, n):

ratio = abs(A[l[j]][i]) / s[l[j]]

if ratio > max2:

max2 = ratio

rindex = j

temp = l[i]

l[i] = l[rindex]

l[rindex] = temp

for j in range(i + 1, n):

multiplier = A[l[j]][i] / A[l[i]][i]

for k in range(i, n):

A[l[j]][k] = A[l[j]][k] - multiplier * A[l[i]][k]

b[l[j]] = b[l[j]] - multiplier * b[l[i]]

x = [0.0 for y in range(n)]

x[n - 1] = b[l[n - 1]] / A[l[n - 1]][n - 1]

for j in range(n - 2, -1, -1):

summ = 0.0

for k in range(j + 1, n):

summ = summ + A[l[j]][k] * x[k]

x[j] = (b[l[j]] - summ) / A[l[j]][j]

print("\nResult = ")

for i in range(n):

print(x[i], end=" ")

matrix = [[11.0, -3.0, 5.0, 2.0], [4.0, 14.0, -1.0, -8.0], [5.0, -2.0, 4.0, 2.0], [1.0, -7.0, 5.0, 19.0]]

vector = [-13.0, -27.0, 20.0, 18.0]

gaussElimination(matrix, vector, 4)

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