def compute_hyperbolic_level_indices(num_dims, level, p=1.0):
if level == 0:
return numpy.zeros((num_dims), numpy.int32)
indices = []
for d in xrange(num_dims):
index = numpy.zeros((num_dims), numpy.int32)
index[d] = level
indices.append(index)
for d in xrange(2, min(level + 1, num_dims + 1)):
level_comb = compute_hyperbolic_level_subdim_indices(num_dims, level, d, p)
if level_comb.shape[0] == 0:
break
dim_indices = []
dims_comb = compute_combinations(num_dims, d)
for i in xrange(dims_comb.shape[0]):
if numpy.count_nonzero(dims_comb[i, :]) == d:
dim_indices.append(dims_comb[i, :])
for dim_index in dim_indices:
I = numpy.nonzero(dim_index)
for level_index in level_comb:
index = numpy.zeros((num_dims), numpy.int32)
index[I] = level_index
indices.append(index)
return numpy.asarray(indices)
def compute_hyperbolic_level_subdim_indices(num_dims, level, num_active_dims, p=1.0):
eps = 100 * numpy.finfo(numpy.double).eps
indices = []
l = num_active_dims
while True:
level_data = compute_combinations(num_active_dims, l)
found = False
for i in xrange(level_data.shape[0]):
if numpy.count_nonzero(level_data[i, :]) == num_active_dims:
if (p_norm(level_data[i, :], p) > level - 1 + eps) and (p_norm(level_data[i, :], p) < level + eps):
indices.append(level_data[i, :])
l += 1
if l > level:
break
return numpy.asarray(indices)
for l in xrange(1, level + 1):
indices = numpy.vstack((indices, compute_hyperbolic_level_indices(num_dims, l, p)))
return numpy.asarray(indices)
if "__main__" in __name__:
from math_tools_cpp import (
compute_combinations,
compute_hyperbolic_level_subdim_indices,
compute_hyperbolic_level_indices,
compute_hyperbolic_indices,
)
num_dims = 2
level = 0
print compute_combinations(num_dims, level)
num_dims = 2
level = 3
print compute_combinations(num_dims, level)
num_dims = 3
level = 2
print compute_combinations(num_dims, level)
num_dims = 2
level = 4
p = 0.5
print compute_hyperbolic_indices(num_dims, level, p)
num_dims = 3
