def solve(A, b):
n = len(A)
L, U = lu(A)
y = []
Lb = append_column(L, b)
for row in xrange(n):
y.append(gk.backward_left(Lb, row))
Uy = append_column(U, [[e] for e in y])
x = []
for row in xrange(n - 1, -1, -1):
x.append(gk.backward_right(Uy, row))
x.reverse()
return x
def main():
from constants import A2, b2
n = len(A2)
L, U = lu(A2)
y = []
Lb = gk.append_column(L, b2)
for row in xrange(n):
y.append(gk.backward_left(Lb, row))
Uy = gk.append_column(U, [[e] for e in y])
x = []
for row in xrange(n - 1, -1, -1):
x.append(gk.backward_right(Uy, row))
x.reverse()
check(A2, x, b2)
def solve(A, b):
n = len(A)
U = getU(A)
gk.print_matrix(U)
Ut = transpose(U)
y = []
Utb = gk.append_column(Ut, b)
for row in xrange(n):
y.append(gk.backward_left(Utb, row))
print(y)
Uy = gk.append_column(U, [[e] for e in y])
x = []
for row in xrange(n - 1, -1, -1):
x.append(gk.backward_right(Uy, row))
x.reverse()
return x, U
for i in xrange(n - 1):
col = transpose([get_row(L, i)[i:]])
H = get_householder_reflection_matrix(col)
if (i != 0):
for j in xrange(i):
H = extend_householder_matrix(H)
L = multiply(L, H)
Q = multiply(H, Q)
householders_reflections.append(H)
params_matrix_list.append(L)
C = []
for i in xrange(len(L)):
C.append(L[i] + [B[i][0]])
print_matrix(C, round_elem=True)
y = transpose([[backward_left(C, i) for i in xrange(len(C))]])
x = multiply(transpose(Q), y)
print_matrix(x)
check_roots(A, [xi[0] for xi in x], B)
print "\ndetA = detQ * detL = " + str(
get_determinant(len(householders_reflections), L))
print "\ninv(A) = inv(L) * inv(Q) = inv(L) * Q' (транспонированая) = "
inversed = get_invariant(L, Q)
print_matrix(inversed)
print("Check inverse matrix:")
print_matrix(multiply(inversed, A))