def add_to_Nk(Nk0: np.array, binom_table: np.ndarray, binom_index: int)->np.array:
"""
Дополняет индексы положительных базисных векторов так, чтобы составленная из них матрица была квадратной
:param Nk0: массив индексов положительных переменных
:param binom_table: биномиальная таблица, созданная функцией `utils.binomial_grid`
:param binom_index: номер итерации смены базиса от 0 до C[|Nk_plus|,m-|Nk0|]
:return: индексы из `Nk0`, которые надо добавить к `Nk_plus`, чтобы получить квадратную матрицу
"""
return subset_by_index(Nk0, binom_table, binom_index)
def add_to_Nk(Nk0: np.array, binom_table: np.ndarray,
binom_index: int) -> np.array:
"""
Augments indices of positive basis vectors so that they form
a square matrix when put together
:param Nk0: an array of indices of positive vectors
:param binom_table: binomial table created by `utils.binomial_grid` method
:param binom_index: iteration of basis change (0 to C[|Nk_plus|,m-|Nk0|])
:return: indices from `Nk0` that should be added to `Nk_plus` in order to
make a square matrix from vectors with those indices
"""
return subset_by_index(Nk0, binom_table, binom_index)
def find_all_svs(cf: NpCanonicalForm):
binom_table = binomial_grid(cf.n, cf.m)
N = np.array(list(range(cf.n)))
for idx in range(binom_table[-1, -1]):
Nk = subset_by_index(N, binom_table, idx)
AMNk = np.array([cf.A[:, i] for i in Nk]).T
if np.abs(np.linalg.det(AMNk)) > 1e-3:
xNk = np.matmul(np.linalg.inv(AMNk), cf.b)
if np.min(xNk) < 0:
continue
xN = np.zeros(cf.n)
for i in range(len(Nk)):
xN[Nk[i]] = xNk[i]
yield xN
def starting_vector(cf: CanonicalForm) -> np.array:
binom_table = binomial_grid(cf.n, cf.m)
N = np.array(list(range(cf.n)))
for idx in range(binom_table[-1, -1]):
Nk = subset_by_index(N, binom_table, idx)
AMNk = np.array([cf.A[:, i] for i in Nk]).T
if np.linalg.det(AMNk) != 0:
xNk = np.matmul(np.linalg.inv(AMNk), cf.b)
if np.min(xNk) < 0:
continue # we need only vectors with all positive components
xN = np.zeros(cf.n)
for i in range(len(Nk)):
xN[Nk[i]] = xNk[i]
return xN
logging.info("error, initial vector not found!")
return np.zeros(cf.n)
def find_min_sv(cf: CanonicalForm,
target_function: Callable[[np.array], float],
abs_tolerance: float = 1e-3) -> BruteForceResult:
binom_table = binomial_grid(cf.n, cf.m)
N = np.array(list(range(cf.n)))
min_sv, inv_AMNk_min, Nk_min = None, None, None
for idx in range(binom_table[-1, -1]):
Nk = subset_by_index(N, binom_table, idx)
AMNk = np.array([cf.A[:, i] for i in Nk]).T
if np.abs(np.linalg.det(AMNk)) > abs_tolerance:
inv_AMNk = np.linalg.inv(AMNk)
xNk = np.matmul(inv_AMNk, cf.b)
if np.min(xNk) < 0:
continue
xN = np.zeros(cf.n)
for i in range(len(Nk)):
xN[Nk[i]] = xNk[i]
if min_sv is None or target_function(xN) < target_function(min_sv):
min_sv, inv_AMNk_min, Nk_min = xN, inv_AMNk, Nk
return BruteForceResult(min_sv, inv_AMNk_min, Nk_min)