# 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.
from __future__ import division
from builtins import range
import numpy as np
from .domain_object import DomainObject
from .spaces.power_space import PowerSpace
from . import nifty_utilities as utilities
from .random import Random
from functools import reduce
class Field(object):
""" The discrete representation of a continuous field over multiple spaces.
In NIFTY, Fields are used to store data arrays and carry all the needed
metainformation (i.e. the domain) for operators to be able to work on them.
In addition, Field has methods to work with power spectra.
Parameters
----------
domain : DomainObject
One of the space types NIFTY supports. RGSpace, GLSpace, HPSpace,
LMSpace or PowerSpace. It might also be a FieldArray, which is
an unstructured domain.
val : scalar, numpy.ndarray, Field
The values the array should contain after init. A scalar input will
fill the whole array with this scalar. If an array is provided the
array's dimensions must match the domain's.
dtype : type
A numpy.type. Most common are float and complex.
copy: boolean
Attributes
----------
val : numpy.ndarray
domain : DomainObject
See Parameters.
domain_axes : tuple of tuples
Enumerates the axes of the Field
dtype : type
Contains the datatype stored in the Field.
Raise
-----
TypeError
Raised if
*the given domain contains something that is not a DomainObject
instance
*val is an array that has a different dimension than the domain
"""
# ---Initialization methods---
def __init__(self, domain=None, val=None, dtype=None, copy=False):
self.domain = self._parse_domain(domain=domain, val=val)
self.domain_axes = self._get_axes_tuple(self.domain)
shape_tuple = tuple(sp.shape for sp in self.domain)
if len(shape_tuple) == 0:
global_shape = ()
else:
global_shape = reduce(lambda x, y: x + y, shape_tuple)
dtype = self._infer_dtype(dtype=dtype, val=val)
if isinstance(val, Field):
if self.domain != val.domain:
raise ValueError("Domain mismatch")
self._val = np.array(val.val, dtype=dtype, copy=copy)
elif (np.isscalar(val)):
self._val = np.full(global_shape, dtype=dtype, fill_value=val)
elif isinstance(val, np.ndarray):
if global_shape == val.shape:
self._val = np.array(val, dtype=dtype, copy=copy)
else:
raise ValueError("Shape mismatch")
elif val is None:
self._val = np.empty(global_shape, dtype=dtype)
else:
raise TypeError("unknown source type")
def _parse_domain(self, domain, val=None):
if domain is None:
if isinstance(val, Field):
return val.domain
if np.isscalar(val):
return () # empty domain tuple
raise TypeError("could not infer domain from value")
if isinstance(domain, DomainObject):
return (domain,)
if not isinstance(domain, tuple):
domain = tuple(domain)
for d in domain:
if not isinstance(d, DomainObject):
raise TypeError(
"Given domain contains something that is not a "
"DomainObject instance.")
return domain
def _get_axes_tuple(self, things_with_shape):
i = 0
axes_list = []
for thing in things_with_shape:
nax = len(thing.shape)
axes_list += [tuple(range(i, i+nax))]
i += nax
return tuple(axes_list)
def _infer_dtype(self, dtype, val):
if val is None:
return np.float64 if dtype is None else dtype
if dtype is None:
if isinstance(val, Field):
return val.dtype
return np.result_type(val)
# ---Factory methods---
@classmethod
def from_random(cls, random_type, domain=None, dtype=None, **kwargs):
""" Draws a random field with the given parameters.
Parameters
----------
cls : class
random_type : String
'pm1', 'normal', 'uniform' are the supported arguments for this
method.
domain : DomainObject
The domain of the output random field
dtype : type
The datatype of the output random field
Returns
-------
out : Field
The output object.
See Also
--------
power_synthesize
"""
f = cls(domain=domain, dtype=dtype)
generator_function = getattr(Random, random_type)
f.val = generator_function(dtype=f.dtype, shape=f.shape, **kwargs)
return f
# ---Powerspectral methods---
def power_analyze(self, spaces=None, binbounds=None,
keep_phase_information=False):
""" Computes the square root power spectrum for a subspace of `self`.
Creates a PowerSpace for the space addressed by `spaces` with the given
binning and computes the power spectrum as a Field over this
PowerSpace. This can only be done if the subspace to be analyzed is a
harmonic space. The resulting field has the same units as the initial
field, corresponding to the square root of the power spectrum.
Parameters
----------
spaces : int *optional*
The subspace for which the powerspectrum shall be computed
(default : None).
binbounds : array-like *optional*
Inner bounds of the bins (default : None).
if binbounds==None : bins are inferred.
keep_phase_information : boolean, *optional*
If False, return a real-valued result containing the power spectrum
of the input Field.
If True, return a complex-valued result whose real component
contains the power spectrum computed from the real part of the
input Field, and whose imaginary component contains the power
spectrum computed from the imaginary part of the input Field.
The absolute value of this result should be identical to the output
of power_analyze with keep_phase_information=False.
(default : False).
Raise
-----
ValueError
Raised if
*len(domain) is != 1 when spaces==None
*len(spaces) is != 1 if not None
*the analyzed space is not harmonic
Returns
-------
out : Field
The output object. Its domain is a PowerSpace and it contains
the power spectrum of 'self's field.
See Also
--------
power_synthesize, PowerSpace
"""
# check if all spaces in `self.domain` are either harmonic or
# power_space instances
for sp in self.domain:
if not sp.harmonic and not isinstance(sp, PowerSpace):
raise TypeError(
"Field has a space in `domain` which is neither "
"harmonic nor a PowerSpace.")
# check if the `spaces` input is valid
spaces = utilities.cast_axis_to_tuple(spaces, len(self.domain))
if spaces is None:
spaces = list(range(len(self.domain)))
if len(spaces) == 0:
raise ValueError("No space for analysis specified.")
if keep_phase_information:
parts_val = self._hermitian_decomposition(
val=self.val,
preserve_gaussian_variance=False)
parts = [Field(self.domain, part_val, self.dtype, copy=False)
for part_val in parts_val]
else:
parts = [self]
parts = [abs(part)**2 for part in parts]
for space_index in spaces:
parts = [self._single_power_analyze(
work_field=part,
space_index=space_index,
binbounds=binbounds)
for part in parts]
if keep_phase_information:
return parts[0] + 1j*parts[1]
else:
return parts[0]
@classmethod
def _single_power_analyze(cls, work_field, space_index, binbounds):
if not work_field.domain[space_index].harmonic:
raise ValueError(
"The analyzed space must be harmonic.")
# Create the target PowerSpace instance:
# If the associated signal-space field was real, we extract the
# hermitian and anti-hermitian parts of `self` and put them
# into the real and imaginary parts of the power spectrum.
# If it was complex, all the power is put into a real power spectrum.
harmonic_domain = work_field.domain[space_index]
power_domain = PowerSpace(harmonic_partner=harmonic_domain,
binbounds=binbounds)
power_spectrum = cls._calculate_power_spectrum(
field_val=work_field.val,
pdomain=power_domain,
axes=work_field.domain_axes[space_index])
# create the result field and put power_spectrum into it
result_domain = list(work_field.domain)
result_domain[space_index] = power_domain
return Field(domain=result_domain, val=power_spectrum,
dtype=power_spectrum.dtype)
@classmethod
def _calculate_power_spectrum(cls, field_val, pdomain, axes=None):
pindex = pdomain.pindex
if axes is not None:
pindex = cls._shape_up_pindex(
pindex=pindex,
target_shape=field_val.shape,
axes=axes)
power_spectrum = utilities.bincount_axis(pindex, weights=field_val,
axis=axes)
rho = pdomain.rho
if axes is not None:
new_rho_shape = [1, ] * len(power_spectrum.shape)
new_rho_shape[axes[0]] = len(rho)
rho = rho.reshape(new_rho_shape)
power_spectrum /= rho
return power_spectrum
@staticmethod
def _shape_up_pindex(pindex, target_shape, axes):
semiscaled_local_shape = [1] * len(target_shape)
for i in range(len(axes)):
semiscaled_local_shape[axes[i]] = pindex.shape[i]
semiscaled_local_data = pindex.reshape(semiscaled_local_shape)
result_obj = np.empty(target_shape, dtype=pindex.dtype)
result_obj[()] = semiscaled_local_data
return result_obj
def power_synthesize(self, spaces=None, real_power=True, real_signal=True,
mean=None, std=None):
""" Yields a sampled field with `self`**2 as its power spectrum.
This method draws a Gaussian random field in the harmonic partner
domain of this field's domains, using this field as power spectrum.
Parameters
----------
spaces : {tuple, int, None} *optional*
Specifies the subspace containing all the PowerSpaces which
should be converted (default : None).
if spaces==None : Tries to convert the whole domain.
real_power : boolean *optional*
Determines whether the power spectrum is treated as intrinsically
real or complex (default : True).
real_signal : boolean *optional*
True will result in a purely real signal-space field
(default : True).
mean : float *optional*
The mean of the Gaussian noise field which is used for the Field
synthetization (default : None).
if mean==None : mean will be set to 0
std : float *optional*
The standard deviation of the Gaussian noise field which is used
for the Field synthetization (default : None).
if std==None : std will be set to 1
Returns
-------
out : Field
The output object. A random field created with the power spectrum
stored in the `spaces` in `self`.
Notes
-----
For this the spaces specified by `spaces` must be a PowerSpace.
This expects this field to be the square root of a power spectrum, i.e.
to have the unit of the field to be sampled.
See Also
--------
power_analyze
Raises
------
ValueError : If domain specified by `spaces` is not a PowerSpace.
"""
# check if the `spaces` input is valid
spaces = utilities.cast_axis_to_tuple(spaces, len(self.domain))
if spaces is None:
spaces = list(range(len(self.domain)))
for power_space_index in spaces:
power_space = self.domain[power_space_index]
if not isinstance(power_space, PowerSpace):
raise ValueError("A PowerSpace is needed for field "
"synthetization.")
# create the result domain
result_domain = list(self.domain)
for power_space_index in spaces:
power_space = self.domain[power_space_index]
harmonic_domain = power_space.harmonic_partner
result_domain[power_space_index] = harmonic_domain
# create random samples: one or two, depending on whether the
# power spectrum is real or complex
result_list = [self.__class__.from_random(
'normal',
mean=mean,
std=std,
domain=result_domain,
dtype=np.complex)
for x in range(1 if real_power else 2)]
# from now on extract the values from the random fields for further
# processing without killing the fields.
# if the signal-space field should be real, hermitianize the field
# components
spec = np.sqrt(self.val)
for power_space_index in spaces:
spec = self._spec_to_rescaler(spec, power_space_index)
# apply the rescaler to the random fields
result_list[0].val *= spec.real
if not real_power:
result_list[1].val *= spec.imag
if real_signal:
result_list = [Field(i.domain, self._hermitian_decomposition(
i.val,
preserve_gaussian_variance=True)[0])
for i in result_list]
if real_power:
result = result_list[0]
if not issubclass(result_list[0].dtype.type,
np.complexfloating):
result = result.real
else:
result = result_list[0] + 1j*result_list[1]
return result
@staticmethod
def _hermitian_decomposition(val, preserve_gaussian_variance=False):
if preserve_gaussian_variance:
if not issubclass(val.dtype.type, np.complexfloating):
raise TypeError("complex input field is needed here")
return (val.real*np.sqrt(2.), val.imag*np.sqrt(2.))
else:
return (val.real.copy(), val.imag.copy())
def _spec_to_rescaler(self, spec, power_space_index):
power_space = self.domain[power_space_index]
local_blow_up = [slice(None)]*len(spec.shape)
# it is important to count from behind, since spec potentially grows
# with every iteration
index = self.domain_axes[power_space_index][0]-len(self.shape)
local_blow_up[index] = power_space.pindex
# here, the power_spectrum is distributed into the new shape
return spec[local_blow_up]
# ---Properties---
def set_val(self, new_val=None, copy=False):
""" Sets the field's data object.
Parameters
----------
new_val : scalar, array-like, Field, None *optional*
The values to be stored in the field.
{default : None}
copy : boolean, *optional*
If False, Field tries to not copy the input data but use it
directly.
{default : False}
See Also
--------
val
"""
if new_val is None:
pass
elif isinstance(new_val, Field):
if self.domain != new_val.domain:
raise ValueError("Domain mismatch")
if copy:
self._val[()] = new_val.val
else:
self._val = np.array(new_val.val, dtype=self.dtype, copy=False)
elif (np.isscalar(new_val)):
self._val[()] = new_val
elif isinstance(new_val, np.ndarray):
if copy:
self._val[()] = new_val
else:
if self.shape != new_val.shape:
raise ValueError("Shape mismatch")
self._val = np.array(new_val, dtype=self.dtype, copy=False)
else:
raise TypeError("unknown source type")
return self
def get_val(self, copy=False):
""" Returns the data object associated with this Field.
Parameters
----------
copy : boolean
If true, a copy of the Field's underlying data object
is returned.
Returns
-------
out : numpy.ndarray
See Also
--------
val
"""
return self._val.copy() if copy else self._val
@property
def val(self):
""" Returns the data object associated with this Field.
No copy is made.
Returns
-------
out : numpy.ndarray
See Also
--------
get_val
"""
return self._val
@val.setter
def val(self, new_val):
self.set_val(new_val=new_val, copy=False)
@property
def dtype(self):
return self._val.dtype
@property
def shape(self):
""" Returns the total shape of the Field's data array.
Returns
-------
out : tuple
The output object. The tuple contains the dimensions of the spaces
in domain.
"""
return self._val.shape
@property
def dim(self):
""" Returns the total number of pixel-dimensions the field has.
Effectively, all values from shape are multiplied.
Returns
-------
out : int
The dimension of the Field.
"""
return self._val.size
@property
def total_volume(self):
""" Returns the total volume of all spaces in the domain.
"""
volume_tuple = tuple(sp.total_volume for sp in self.domain)
try:
return reduce(lambda x, y: x * y, volume_tuple)
except TypeError:
return 0.
@property
def real(self):
""" The real part of the field (data is not copied).
"""
return Field(self.domain, self.val.real)
@property
def imag(self):
""" The imaginary part of the field (data is not copied).
"""
return Field(self.domain, self.val.imag)
# ---Special unary/binary operations---
def copy(self, domain=None, dtype=None):
""" Returns a full copy of the Field.
If no keyword arguments are given, the returned object will be an
identical copy of the original Field. By explicit specification one is
able to define the domain and the dtype of the returned Field.
Parameters
----------
domain : DomainObject
The new domain the Field shall have.
dtype : type
The new dtype the Field shall have.
Returns
-------
out : Field
The output object. An identical copy of 'self'.
"""
if domain is None:
domain = self.domain
return Field(domain=domain, val=self._val, dtype=dtype, copy=True)
def scalar_weight(self, spaces=None):
if np.isscalar(spaces):
return self.domain[spaces].scalar_weight()
if spaces is None:
spaces = range(len(self.domain))
res = 1.
for i in spaces:
tmp = self.domain[i].scalar_weight()
if tmp is None:
return None
res *= tmp
return res
def weight(self, power=1, inplace=False, spaces=None):
""" Weights the pixels of `self` with their invidual pixel-volume.
Parameters
----------
power : number
The pixels get weighted with the volume-factor**power.
inplace : boolean
If True, `self` will be weighted and returned. Otherwise, a copy
is made.
spaces : tuple of ints
Determines on which subspace the operation takes place.
Returns
-------
out : Field
The weighted field.
"""
new_val = self.get_val(copy=not inplace)
spaces = utilities.cast_axis_to_tuple(spaces, len(self.domain))
if spaces is None:
spaces = list(range(len(self.domain)))
fct = 1.
for ind in spaces:
wgt = self.domain[ind].weight()
if np.isscalar(wgt):
fct *= wgt
else:
new_shape = np.ones(len(self.shape), dtype=np.int)
new_shape[self.domain_axes[ind][0]:self.domain_axes[ind][-1]+1]=wgt.shape
wgt = wgt.reshape(new_shape)
new_val *= wgt**power
fct = fct**power
if fct != 1.:
new_val *= fct
return Field(self.domain, new_val, self.dtype)
def vdot(self, x=None, spaces=None, bare=False):
""" Computes the volume-factor-aware dot product of 'self' with x.
Parameters
----------
x : Field
The domain of x must contain `self.domain`
spaces : tuple of ints
If the domain of `self` and `x` are not the same, `spaces` specfies
the mapping.
bare : boolean
If true, no volume factors will be included in the computation.
Returns
-------
out : float, complex
"""
if not isinstance(x, Field):
raise ValueError("The dot-partner must be an instance of " +
"the NIFTy field class")
# Compute the dot respecting the fact of discrete/continuous spaces
fct = 1.
if bare:
y = self
else:
tmp = self.scalar_weight(spaces)
if tmp is None:
y = self.weight(power=1)
else:
y = self
fct = tmp
if spaces is None:
return fct*np.vdot(y.val.ravel(), x.val.ravel())
else:
# create a diagonal operator which is capable of taking care of the
# axes-matching
from .operators.diagonal_operator import DiagonalOperator
diagonal = y.val.conjugate()
diagonalOperator = DiagonalOperator(domain=y.domain,
diagonal=diagonal,
copy=False)
dotted = diagonalOperator(x, spaces=spaces)
return fct*dotted.sum(spaces=spaces)
def norm(self):
""" Computes the L2-norm of the field values.
Returns
-------
norm : float
The L2-norm of the field values.
"""
return np.sqrt(np.abs(self.vdot(x=self)))
def conjugate(self, inplace=False):
""" Retruns the complex conjugate of the field.
Parameters
----------
inplace : boolean
Decides whether the conjugation should be performed inplace.
Returns
-------
cc : field
The complex conjugated field.
"""
if inplace:
self.imag *= -1
return self
else:
return Field(self.domain, np.conj(self.val), self.dtype)
# ---General unary/contraction methods---
def __pos__(self):
return self.copy()
def __neg__(self):
return Field(self.domain, -self.val, self.dtype)
def __abs__(self):
return Field(self.domain, np.abs(self.val), self.dtype)
def _contraction_helper(self, op, spaces):
if spaces is None:
return getattr(self.val, op)()
# build a list of all axes
spaces = utilities.cast_axis_to_tuple(spaces, len(self.domain))
axes_list = tuple(self.domain_axes[sp_index] for sp_index in spaces)
try:
axes_list = reduce(lambda x, y: x+y, axes_list)
except TypeError:
axes_list = ()
# perform the contraction on the data
data = self.get_val(copy=False)
data = getattr(data, op)(axis=axes_list)
# check if the result is scalar or if a result_field must be constr.
if np.isscalar(data):
return data
else:
return_domain = tuple(self.domain[i]
for i in range(len(self.domain))
if i not in spaces)
return Field(domain=return_domain, val=data, copy=False)
def sum(self, spaces=None):
return self._contraction_helper('sum', spaces)
def prod(self, spaces=None):
return self._contraction_helper('prod', spaces)
def all(self, spaces=None):
return self._contraction_helper('all', spaces)
def any(self, spaces=None):
return self._contraction_helper('any', spaces)
def min(self, spaces=None):
return self._contraction_helper('min', spaces)
def nanmin(self, spaces=None):
return self._contraction_helper('nanmin', spaces)
def max(self, spaces=None):
return self._contraction_helper('max', spaces)
def nanmax(self, spaces=None):
return self._contraction_helper('nanmax', spaces)
def mean(self, spaces=None):
return self._contraction_helper('mean', spaces)
def var(self, spaces=None):
return self._contraction_helper('var', spaces)
def std(self, spaces=None):
return self._contraction_helper('std', spaces)
# ---General binary methods---
def _binary_helper(self, other, op):
# if other is a field, make sure that the domains match
if isinstance(other, Field):
if other.domain != self.domain:
raise ValueError("domains are incompatible.")
return Field(self.domain, getattr(self.val, op)(other.val))
return Field(self.domain, getattr(self.val, op)(other))
def __add__(self, other):
return self._binary_helper(other, op='__add__')
def __radd__(self, other):
return self._binary_helper(other, op='__radd__')
def __iadd__(self, other):
return self._binary_helper(other, op='__iadd__')
def __sub__(self, other):
return self._binary_helper(other, op='__sub__')
def __rsub__(self, other):
return self._binary_helper(other, op='__rsub__')
def __isub__(self, other):
return self._binary_helper(other, op='__isub__')
def __mul__(self, other):
return self._binary_helper(other, op='__mul__')
def __rmul__(self, other):
return self._binary_helper(other, op='__rmul__')
def __imul__(self, other):
return self._binary_helper(other, op='__imul__')
def __div__(self, other):
return self._binary_helper(other, op='__div__')
def __truediv__(self, other):
return self._binary_helper(other, op='__truediv__')
def __rdiv__(self, other):
return self._binary_helper(other, op='__rdiv__')
def __rtruediv__(self, other):
return self._binary_helper(other, op='__rtruediv__')
def __idiv__(self, other):
return self._binary_helper(other, op='__idiv__')
def __pow__(self, other):
return self._binary_helper(other, op='__pow__')
def __rpow__(self, other):
return self._binary_helper(other, op='__rpow__')
def __ipow__(self, other):
return self._binary_helper(other, op='__ipow__')
def __lt__(self, other):
return self._binary_helper(other, op='__lt__')
def __le__(self, other):
return self._binary_helper(other, op='__le__')
def __ne__(self, other):
if other is None:
return True
else:
return self._binary_helper(other, op='__ne__')
def __eq__(self, other):
if other is None:
return False
else:
return self._binary_helper(other, op='__eq__')
def __ge__(self, other):
return self._binary_helper(other, op='__ge__')
def __gt__(self, other):
return self._binary_helper(other, op='__gt__')
def __repr__(self):
return ""
def __str__(self):
minmax = [self.min(), self.max()]
mean = self.mean()
return "nifty_core.field instance\n- domain = " + \
repr(self.domain) + \
"\n- val = " + repr(self.get_val()) + \
"\n - min.,max. = " + str(minmax) + \
"\n - mean = " + str(mean)