def transform(m, e=0.001):
m = [[e / row[i] for e in row]for i, row in enumerate(m)]
a = [[-e for e in row[:-1]] for row in m]
b = [row[-1] for row in m]
a = [row[:i] + [0] + row[i+1:]for i, row in enumerate(a)]
print_m(a)
return a, b
def solution(A):
n = len(A)
for k in range(1, n):
for j in range(k, n):
m = A[j][k-1] / A[k-1][k-1]
for i in range(n+1):
A[j][i] = A[j][i] - m*A[k-1][i]
print(f"----------{k:} step ---------------")
print_m(A)
print("-------------------------------")
print()
x = [0]*n
for i in reversed(range(n)):
x[i] = A[i][n] / A[i][i]
for c in reversed(range(i + 1, n)):
x[i] -= A[i][c]*x[c]/A[i][i]
return x
print("-------------------------------")
print()
x = [0]*n
for i in reversed(range(n)):
x[i] = A[i][n] / A[i][i]
for c in reversed(range(i + 1, n)):
x[i] -= A[i][c]*x[c]/A[i][i]
return x
A = testMatrix
a = [row[:-1] for row in A]
b = [row[-1] for row in A]
A_1 = linalg.inv(a)
print("Your matrix:")
print_m(testMatrix)
print()
print(solution(testMatrix))
print()
print("pow(Matrix,-1)")
print_m(A_1)
print()
A_max = max([sum(row)] for row in A)
Inv_max = max([sum(row)] for row in A_1)
B_max = max(b)
d_x = Inv_max[0] * 0.001
_d_x = A_max[0] * Inv_max[0] * 0.001 / B_max
print("absolute and relative error")
print(d_x)
print(_d_x)
while diff >= acc:
temp = px[:]
cx = [0.0] * len(b)
for i,row in enumerate(a):
for j,e in enumerate(row):
cx[i] += e * px[j]
cx[i] += b[i]
px[i] = cx[i]
diff = max([abs(e-temp[i]) for i, e in enumerate(cx)])
px = cx
print(px,diff)
return diff, px
print("Your matrix")
print_m(testMatrix)
print("------------")
a, b = transform(testMatrix)
print("Transformed matrix :")
print_m(a)
print(np.matrix(b))
print("------------")
print("Seidel method:")
max_val, result = seidel(a, b)
print(f"Max value is {max_val}")
print("Result:")
print(result)
print("------------")
res = []
for n in range(len(u)):
ort = [0 for i in range(len(u) - 1)]
ort.insert(n, 1)
y = lower(u_t, ort)
x = upper(u, y)
res.append(x)
res = np.array(list(zip(*res[:])))
return np.array(res)
if np.linalg.det(A) == 0:
raise ValueError(" det A == 0 ")
ASymmetrized, BSymmetrized = symmetrize(A, B)
print("Symmetrized matrix :")
print_m(ASymmetrized)
print()
print(BSymmetrized)
print("------------------")
U, U_T = U(ASymmetrized, BSymmetrized)
print()
print_m(U)
print()
print_m(U_T)
print("------------------")
print("Y-vect :")
AnswerY = lower(U_T, BSymmetrized)
print(AnswerY)
print("------------------")
print("X-vect :")
AnswerX = upper(U, AnswerY)