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 solve(Q, R, b):
y = multiply(transpose(Q), b)
print_matrix(R, round_elem=True)
C = append_column(R, y)
x = [backward_right(C, i) for i in xrange(len(C) - 1, -1, -1)]
x.reverse()
return x
def solve(A, b):
n = len(A)
U = getU(A)
print_matrix(U)
Ut = transpose(U)
y = []
Utb = append_column(Ut, b)
for row in xrange(n):
y.append(gk.backward_left(Utb, row))
print(y)
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, U
def solve(A, b):
S = append_column(A, b)
for i in xrange(len(S)):
forward(S, i, verbose=False)
roots = []
for i in xrange(len(S) - 1, -1, -1):
roots.append(backward_right(S, i))
roots.reverse()
return roots
def solve(A, b):
S = append_column(A, b)
for i in xrange(len(S)):
print("Choosing main for iteration #{}".format(i))
choose_main(S, i)
gk.forward(S, i)
roots = []
for i in xrange(len(S) - 1, -1, -1):
roots.append(gk.backward_right(S, i))
roots.reverse()
return roots
def inverse(A):
n = len(A)
m = len(A[0])
I = eye(n)
AE = append_column(A, I)
for row in xrange(n):
forward(AE, row, verbose=False)
print("Forward pass:"******"Backward pass:")
print_matrix(AE)
print()
E = []
for i in xrange(n):
E.append(AE[i][n:])
return E