def solve(A, b, pivoting):
# No pivoting
if pivoting == 0:
L, U = lu.lu_out_of_place(A)
z = forward_substitution(L, b)
x = back_substitution(U, z)
return x
# Partial pivoting
if pivoting == 1:
P, L, U = lu.lu_partial_pivot(A)
z = forward_substitution(L, np.dot(P.transpose(), b))
x = back_substitution(U, z)
return x
# Complete pivoting
if pivoting == 2:
P, Q, L, U = lu.lu_complete_pivot(A)
z = forward_substitution(L, np.dot(P.transpose(), b))
x = np.dot(Q.transpose(), back_substitution(U, z))
return x
# Rook pivoting
if pivoting == 3:
P, Q, L, U = lu.lu_rook_pivot(A)
z = forward_substitution(L, np.dot(P.transpose(), b))
x = np.dot(Q.transpose(), back_substitution(U, z))
return x
# Blok PP
if pivoting == 4:
P, L, U = lu_block.lu_partial_block(A, 32)
z = forward_substitution(L, np.dot(P.transpose(), b))
x = back_substitution(U, z)
return x
def inverse(A, pivoting):
(m, n) = A.shape
A_inverse = np.zeros((m, m))
b = np.identity(m)
# No pivot
if pivoting == 0:
L, U = lu.lu_out_of_place(A)
for k in range(m):
z = forward_substitution(L, b[:, k])
x = back_substitution(U, z)
A_inverse[:, k, np.newaxis] = x
return A_inverse
# Partial pivot
if pivoting == 1:
P, L, U = lu.lu_partial_pivot(A)
for k in range(m):
z = forward_substitution(L, np.dot(P.transpose(), b[:, k]))
x = back_substitution(U, z)
A_inverse[:, k, np.newaxis] = x
return A_inverse
# Complete pivot
if pivoting == 2:
P, Q, L, U = lu.lu_complete_pivot(A)
for k in range(m):
z = forward_substitution(L, np.dot(P.transpose(), b[:, k]))
x = np.dot(Q.transpose(), back_substitution(U, z))
A_inverse[:, k, np.newaxis] = x
return A_inverse
# Rook pivot
if pivoting == 3:
P, Q, L, U = lu.lu_rook_pivot(A)
for k in range(m):
z = forward_substitution(L, np.dot(P.transpose(), b[:, k]))
x = np.dot(Q.transpose(), back_substitution(U, z))
A_inverse[:, k, np.newaxis] = x
return A_inverse
# PP block
if pivoting == 4:
P, L, U = lu_block.lu_partial_block(A, 32)
for k in range(m):
z = forward_substitution(L, np.dot(P.transpose(), b[:, k]))
x = back_substitution(U, z)
A_inverse[:, k, np.newaxis] = x
return A_inverse
