def solve_upper_sys(up_matrix: Matrix, vector: Vector) -> Vector:
"""
Given an upper triangular matrix `up_matrix` [U] and a vector
`vector` [b], computes the [U][x] = [b] system solution,
[x], by backward substitution.
:param up_matrix: upper triangular `Matrix` [U]
:param vector: system's `Vector` [b]
:return: solution vector [x]
"""
size = vector.length
last_index = size - 1
solution = Vector(size)
for i in range(last_index, -1, -1):
_sum = 0.0
for j in range(i + 1, size):
u_ij = up_matrix.value_at(i, j)
x_j = solution.value_at(j)
_sum += u_ij * x_j
y_i = vector.value_at(i)
u_ii = up_matrix.value_at(i, i)
solution_val = (y_i - _sum) / u_ii
solution.set_value(solution_val, i)
return solution
def test_add_to_value(self):
vector = Vector(2).set_data([1, 2]).add_to_value(10, 0)
self.assertEqual(11, vector.value_at(0))
self.assertEqual(2, vector.value_at(1))
def test_set_get_value(self):
value = 10.0
vector = Vector(2).set_value(value, 1)
self.assertEqual(0.0, vector.value_at(0))
self.assertEqual(value, vector.value_at(1))
def test_unset_value_is_zero(self):
vector = Vector(2)
self.assertEqual(0.0, vector.value_at(0))
self.assertEqual(0.0, vector.value_at(1))