def gaussElemination(n, matrix):
sol = [0] * n
print("matrix : ")
printAB(matrix)
for x in range(n):
print("==========")
print("fixing a", x + 1)
for y in range(x + 1, n):
axy = matrix[y][x]
axx = matrix[x][x]
print("transformation :", "R", y, "->", axx, "*R" + str(y), "-",
axy, "*R" + str(x))
for z in range(n + 1):
matrix[y][z] = Fraction((axx * matrix[y][z]) -
(axy *
matrix[x][z])).limit_denominator()
printAB(matrix)
for y in range(n - 1, -1, -1):
extra = 0
for x in range(y + 1, n):
extra = extra + (matrix[y][x] * sol[x])
sol[y] = (matrix[y][n] - extra) / matrix[y][y]
print("solution :")
printArr(sol)
return sol
def dominantEigen(A, B=[1, 0, 0]):
n = 4 # number of iterations
E = 0
for i in range(n):
print("iteration :", i + 1)
B = multiply(A, B)
E, B = extractMax(B, checkSign(E))
print("eigen value:", E)
print("eigen vector:")
printArr(B)
def gaussJordan(n, matrix):
sol = []
print("matrix : ")
printAB(matrix)
for x in range(n):
print("==========")
print("fixing a", x + 1)
for y in range(n):
if x == y or matrix[y][x] == 0:
continue
axy = matrix[y][x]
axx = matrix[x][x]
print("transformation :", "R", y, "->", axx, "*R" + str(y), "-",
axy, "*R" + str(x))
for z in range(n + 1):
matrix[y][z] = Fraction((axx * matrix[y][z]) -
(axy *
matrix[x][z])).limit_denominator()
printAB(matrix)
for y in range(n):
sol.append(matrix[y][n] / matrix[y][y])
print("solution :")
printArr(sol)
return sol
if x == y:
U[y][x] = 1
print("U", y, x, "=",
Fraction(U[y][x]).limit_denominator())
else: # set U
sub = 0
for i in range(y):
sub = sub + (L[y][i] * U[i][x])
U[y][x] = (A[y][x] - sub) / L[y][y]
print("U", y, x, "=", Fraction(U[y][x]).limit_denominator())
return L, U
if __name__ == "__main__":
A = [[5, 1, 3], [4, -3, 1], [3, -2, -1]]
B = [10, 18, 11]
n = len(A)
L, U = crout(n, A)
print()
print("L :")
printA(L)
print("U :")
printA(U)
Y = solveLower(n, L, B)
print("Y :", end=" ")
printArr(Y)
X = solveUpper(n, U, Y)
print("X :", end=" ")
printArr(X)
sys.path.append(parentdir)
from print_matrix import printArr
def gaussJacobi(AB):
n = 6 # number of iterations
o = len(AB)
sol = [0]* o
for i in range(n):
tempsol = sol.copy()
print("iteration :",i+1)
for j in range(o):
sub = 0
for k in range(o):
if k == j:
continue
sub = sub + (AB[j][k] * tempsol[k])
sol[j] = (AB[j][o] - sub)/AB[j][j]
print("sol",j,"=",sol[j])
return sol
if __name__ == "__main__":
AB = [ # enter in diagnal dominant manner
[20,2,1,104],
[5,25,3,56],
[6,2,30,92]
]
X = gaussJacobi(AB)
print("solution :")
printArr(X)