In case you are interested in reading through a list of problems in numerical methods you can do so in the following blog post Here.
The following code from this site implements Gauss elimination method to solve a system of linear equations. While the author is brilliant in her coding, something missing is a way of executing the python code.(I am reproducing the code here.....find the input at the end)
The following code from this site implements Gauss elimination method to solve a system of linear equations. While the author is brilliant in her coding, something missing is a way of executing the python code.(I am reproducing the code here.....find the input at the end)
def pprint(A):
n = len(A)
for i in range(0, n):
line = ""
for j in range(0, n+1):
line += str(A[i][j]) + "\t"
if j == n-1:
line += "| "
print(line)
print("")
def gauss(A):
n = len(A)
for i in range(0, n):
# Search for maximum in this column
maxEl = abs(A[i][i])
maxRow = i
for k in range(i+1, n):
if abs(A[k][i]) > maxEl:
maxEl = abs(A[k][i])
maxRow = k
# Swap maximum row with current row (column by column)
for k in range(i, n+1):
tmp = A[maxRow][k]
A[maxRow][k] = A[i][k]
A[i][k] = tmp
# Make all rows below this one 0 in current column
for k in range(i+1, n):
c = -A[k][i]/A[i][i]
for j in range(i, n+1):
if i == j:
A[k][j] = 0
else:
A[k][j] += c * A[i][j]
# Solve equation Ax=b for an upper triangular matrix A
x = [0 for i in range(n)]
for i in range(n-1, -1, -1):
x[i] = A[i][n]/A[i][i]
for k in range(i-1, -1, -1):
A[k][n] -= A[k][i] * x[i]
return x
if __name__ == "__main__":
from fractions import Fraction
n = input()
A = [[0 for j in range(n+1)] for i in range(n)]
# Read input data
for i in range(0, n):
line = map(Fraction, raw_input().split(" "))
for j, el in enumerate(line):
A[i][j] = el
raw_input()
line = raw_input().split(" ")
lastLine = map(Fraction, line)
for i in range(0, n):
A[i][n] = lastLine[i]
# Print input
pprint(A)
# Calculate solution
x = gauss(A)
# Print result
line = "Result:\t"
for i in range(0, n):
line += str(x[i]) + "\t"
print(line)
Input:
E:\python\Workspace>python gauss.py
3
1 2 5
6 2 1
5 4 3
(a blank line afterwards enter the b(column) matrix)
2 70 3
1 2 5 | 2
6 2 1 | 70
5 4 3 | 3
Result: 480/23 -1479/46 209/23
