def multiply_multivariate_orthonormal_polynomial_expansions(
product_coefs_1d, poly_indices1, poly_coefficients1, poly_indices2,
poly_coefficients2):
num_indices1 = poly_indices1.shape[1]
num_indices2 = poly_indices2.shape[1]
assert num_indices2 <= num_indices1
assert poly_coefficients1.shape[0] == num_indices1
assert poly_coefficients2.shape[0] == num_indices2
# following assumes the max degrees were used to create product_coefs_1d
max_degrees1 = poly_indices1.max(axis=1)
max_degrees2 = poly_indices2.max(axis=1)
basis_coefs, basis_indices = [], []
for ii in range(num_indices1):
poly_index_ii = poly_indices1[:, ii]
for jj in range(num_indices2):
poly_index_jj = poly_indices2[:, jj]
product_indices, product_coefs = \
compute_multivariate_orthonormal_basis_product(
product_coefs_1d, poly_index_ii, poly_index_jj,
max_degrees1, max_degrees2)
# print(ii,jj,product_coefs,poly_index_ii,poly_index_jj)
# TODO for unique polynomials the product_coefs and indices
# of [0,1,2] is the same as [2,1,0] so perhaps store
# sorted active indices and look up to reuse computations
product_coefs_iijj = product_coefs*poly_coefficients1[ii, :] *\
poly_coefficients2[jj, :]
basis_coefs.append(product_coefs_iijj)
basis_indices.append(product_indices)
assert basis_coefs[-1].shape[0] == basis_indices[-1].shape[1]
indices, coefs = add_polynomials(basis_indices, basis_coefs)
return indices, coefs
def __sub__(self, other):
indices_list = [self.indices, other.indices]
coefs_list = [self.coefficients, -other.coefficients]
indices, coefs = add_polynomials(indices_list, coefs_list)
poly = get_polynomial_from_variable(self.var_trans.variable)
poly.set_indices(indices)
poly.set_coefficients(coefs)
return poly