def cs_hdmr_expansion(inputs, outputs, basis_dict):
print "Validating hierarchical orthogonality of basis:", sym_poly_utils.validate_sample_basis_ho(inputs, basis_dict)
print "Validating normality of basis:", sym_poly_utils.validate_sample_basis_n(inputs, basis_dict)
sensing_columns = []
basis_polys = []
basis_poly_syms = []
for syms, poly_list in basis_dict.items():
_, values = zip(*[(x.poly, x.vals) for x in poly_list])
values = list(values)
sensing_columns += values
basis_polys += poly_list
basis_poly_syms += [syms]*len(poly_list)
# Construct sensing matrix
# astype fixes speed issue
A = np.column_stack(sensing_columns).astype(float)
# coeffs = basis_pursuit.l1m(A, outputs, e=0)
coeffs = list(meridian_cs.mbcs(A, outputs, 0.1))
d = defaultdict(list)
for syms, p, c in zip(basis_poly_syms, basis_polys, coeffs):
d[syms] += [(p, c)]
return BasisExpansion(d, inputs)
def cs_expansion_correlated(inputs, outputs, deg_cap=3, ord_cap=3):
# Construct polynomial basis
space = linalg.SampledPolynomialSpace(inputs, 2.0**inputs.shape[0])
print "Constructing basis..."
# basis = linalg.get_basis(space, ord_cap, deg_cap)
basis_dict = linalg.get_basis_qr(space, ord_cap, deg_cap)
sensing_columns = []
basis_polys = []
zipped_basis = []
for syms, syms_zipped_basis in basis_dict.items():
polys, values = zip(*syms_zipped_basis)
polys = list(polys)
values = list(values)
sensing_columns += values
zipped_basis += syms_zipped_basis
basis_polys += [(p, syms) for p in polys]
print "done.\n"
# Construct sensing matrix
print "Constructing sensing matrix..."
A = np.column_stack(sensing_columns)
print "Solving for compressed coefficients..."
# coeffs = basis_pursuit.l1m(A, outputs, e=0)
coeffs = list(meridian_cs.mbcs(A, outputs, 0.1))
print "done.\n"
return zip(zipped_basis, coeffs)
