# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program. If not, see .
#
# Copyright(C) 2013-2017 Max-Planck-Society
#
# NIFTy is being developed at the Max-Planck-Institut fuer Astrophysik
# and financially supported by the Studienstiftung des deutschen Volkes.
import numpy as np
from .structured_domain import StructuredDomain
from .. import dobj
class PowerSpace(StructuredDomain):
"""NIFTy class for spaces of power spectra.
A power space is the result of a projection of a harmonic domain where
k-modes of equal length get mapped to one power index.
Parameters
----------
harmonic_partner : StructuredDomain
The harmonic domain of which this is the power space.
binbounds : None, or tuple of float (default: None)
if None:
There will be as many bins as there are distinct k-vector lengths
in the harmonic partner space.
The `binbounds` property of the PowerSpace will also be None.
else:
the bin bounds requested for this PowerSpace. The array
must be sorted and strictly ascending. The first entry is the right
boundary of the first bin, and the last entry is the left boundary
of the last bin, i.e. thee will be `len(binbounds)+1` bins in
total, with the first and last bins reaching to -+infinity,
respectively.
"""
_powerIndexCache = {}
@staticmethod
def linear_binbounds(nbin, first_bound, last_bound):
"""Produces linearly spaced bin bounds.
This will produce a binbounds array with nbin-1 entries with
binbounds[0]=first_bound and binbounds[-1]=last_bound and the remaining
values equidistantly spaced (in linear scale) between these two.
nbin : int
the number of bins
first_bound, last_bound : float
the k values for the right boundary of the first bin and the left
boundary of the last bin, respectively. They are given in length
units of the harmonic partner space.
"""
nbin = int(nbin)
if nbin < 3:
raise ValueError("nbin must be at least 3")
return np.linspace(float(first_bound), float(last_bound), nbin-1)
@staticmethod
def logarithmic_binbounds(nbin, first_bound, last_bound):
"""Produces logarithmically spaced bin bounds.
This will produce a binbounds array with nbin-1 entries with
binbounds[0]=first_bound and binbounds[-1]=last_bound and the remaining
values equidistantly spaced (in natural logarithmic scale)
between these two.
nbin : int
the number of bins
first_bound, last_bound : float
the k values for the right boundary of the first bin and the left
boundary of the last bin, respectively. They are given in length
units of the harmonic partner space.
"""
nbin = int(nbin)
if nbin < 3:
raise ValueError("nbin must be at least 3")
return np.logspace(np.log(float(first_bound)),
np.log(float(last_bound)),
nbin-1, base=np.e)
@staticmethod
def useful_binbounds(space, logarithmic, nbin=None):
"""Produces bin bounds suitable for a given domain.
This will produce a binbounds array with `nbin-1` entries, if `nbin` is
supplied, or the maximum number of entries that does not produce empty
bins, if `nbin` is not supplied.
The first and last bin boundary are inferred from `space`.
space : StructuredDomain
the domain for which the binbounds will be computed.
logarithmic : bool
If True bins will have equal size in linear space; otherwise they
will have equali size in logarithmic space.
nbin : int, optional
the number of bins
If None, the highest possible number of bins will be used
"""
if not (isinstance(space, StructuredDomain) and space.harmonic):
raise ValueError("first argument must be a harmonic space.")
if logarithmic is None and nbin is None:
return None
nbin = None if nbin is None else int(nbin)
logarithmic = bool(logarithmic)
dists = space.get_unique_k_lengths()
if len(dists) < 3:
raise ValueError("Space does not have enough unique k lengths")
lbound = 0.5*(dists[0]+dists[1])
rbound = 0.5*(dists[-2]+dists[-1])
dists[0] = lbound
dists[-1] = rbound
if logarithmic:
dists = np.log(dists)
binsz_min = np.max(np.diff(dists))
nbin_max = int((dists[-1]-dists[0])/binsz_min)+2
if nbin is None:
nbin = nbin_max
if nbin < 3:
raise ValueError("nbin must be at least 3")
if nbin > nbin_max:
raise ValueError("nbin is too large")
if logarithmic:
return PowerSpace.logarithmic_binbounds(nbin, lbound, rbound)
else:
return PowerSpace.linear_binbounds(nbin, lbound, rbound)
def __init__(self, harmonic_partner, binbounds=None):
super(PowerSpace, self).__init__()
self._needed_for_hash += ['_harmonic_partner', '_binbounds']
if not (isinstance(harmonic_partner, StructuredDomain) and
harmonic_partner.harmonic):
raise ValueError("harmonic_partner must be a harmonic space.")
if harmonic_partner.scalar_dvol() is None:
raise ValueError("harmonic partner must have "
"scalar volume factors")
self._harmonic_partner = harmonic_partner
pdvol = harmonic_partner.scalar_dvol()
if binbounds is not None:
binbounds = tuple(binbounds)
key = (harmonic_partner, binbounds)
if self._powerIndexCache.get(key) is None:
k_length_array = self.harmonic_partner.get_k_length_array()
if binbounds is None:
tmp = harmonic_partner.get_unique_k_lengths()
tbb = 0.5*(tmp[:-1]+tmp[1:])
else:
tbb = binbounds
locdat = np.searchsorted(tbb, dobj.local_data(k_length_array.val))
temp_pindex = dobj.from_local_data(
k_length_array.val.shape, locdat,
dobj.distaxis(k_length_array.val))
nbin = len(tbb)+1
temp_rho = np.bincount(dobj.local_data(temp_pindex).ravel(),
minlength=nbin)
temp_rho = dobj.np_allreduce_sum(temp_rho)
if (temp_rho == 0).any():
raise ValueError("empty bins detected")
# The explicit conversion to float64 is necessary because bincount
# sometimes returns its result as an integer array, even when
# floating-point weights are present ...
temp_k_lengths = np.bincount(
dobj.local_data(temp_pindex).ravel(),
weights=dobj.local_data(k_length_array.val).ravel(),
minlength=nbin).astype(np.float64, copy=False)
temp_k_lengths = dobj.np_allreduce_sum(temp_k_lengths) / temp_rho
temp_dvol = temp_rho*pdvol
self._powerIndexCache[key] = (binbounds, temp_pindex,
temp_k_lengths, temp_dvol)
(self._binbounds, self._pindex, self._k_lengths, self._dvol) = \
self._powerIndexCache[key]
def __repr__(self):
return ("PowerSpace(harmonic_partner=%r, binbounds=%r)"
% (self.harmonic_partner, self._binbounds))
@property
def harmonic(self):
"""bool : Always False for this class."""
return False
@property
def shape(self):
return self.k_lengths.shape
@property
def size(self):
return self.shape[0]
def scalar_dvol(self):
return None
def dvol(self):
return self._dvol
@property
def harmonic_partner(self):
"""StructuredDomain : the harmonic domain associated with `self`."""
return self._harmonic_partner
@property
def binbounds(self):
"""None or tuple of float : inner bin boundaries
The boundaries between bins, starting with the right boundary of the
first bin, up to the left boundary of the last bin.
`None` is used to indicate natural binning.
"""
return self._binbounds
@property
def pindex(self):
"""data_object : bin indices
Bin index for every pixel in the harmonic partner.
"""
return self._pindex
@property
def k_lengths(self):
"""numpy.ndarray(float) : sorted array of all k-vector lengths."""
return self._k_lengths