# NIFTY (Numerical Information Field Theory) has been developed at the
# Max-Planck-Institute for Astrophysics.
##
# Copyright (C) 2013 Max-Planck-Society
##
# Author: Marco Selig
# Project homepage:
##
# 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 .
"""
.. __ ____ __
.. /__/ / _/ / /_
.. __ ___ __ / /_ / _/ __ __
.. / _ | / / / _/ / / / / / /
.. / / / / / / / / / /_ / /_/ /
.. /__/ /__/ /__/ /__/ \___/ \___ / core
.. /______/
.. The NIFTY project homepage is http://www.mpa-garching.mpg.de/ift/nifty/
NIFTY [#]_, "Numerical Information Field Theory", is a versatile
library designed to enable the development of signal inference algorithms
that operate regardless of the underlying spatial grid and its resolution.
Its object-oriented framework is written in Python, although it accesses
libraries written in Cython, C++, and C for efficiency.
NIFTY offers a toolkit that abstracts discretized representations of
continuous spaces, fields in these spaces, and operators acting on fields
into classes. Thereby, the correct normalization of operations on fields is
taken care of automatically without concerning the user. This allows for an
abstract formulation and programming of inference algorithms, including
those derived within information field theory. Thus, NIFTY permits its user
to rapidly prototype algorithms in 1D and then apply the developed code in
higher-dimensional settings of real world problems. The set of spaces on
which NIFTY operates comprises point sets, n-dimensional regular grids,
spherical spaces, their harmonic counterparts, and product spaces
constructed as combinations of those.
References
----------
.. [#] Selig et al., "NIFTY -- Numerical Information Field Theory --
a versatile Python library for signal inference",
`A&A, vol. 554, id. A26 `_,
2013; `arXiv:1301.4499 `_
Class & Feature Overview
------------------------
The NIFTY library features three main classes: **spaces** that represent
certain grids, **fields** that are defined on spaces, and **operators**
that apply to fields.
.. Overview of all (core) classes:
..
.. - switch
.. - notification
.. - _about
.. - random
.. - space
.. - point_space
.. - rg_space
.. - lm_space
.. - gl_space
.. - hp_space
.. - nested_space
.. - field
.. - operator
.. - diagonal_operator
.. - power_operator
.. - projection_operator
.. - vecvec_operator
.. - response_operator
.. - probing
.. - trace_probing
.. - diagonal_probing
Overview of the main classes and functions:
.. automodule:: nifty
- :py:class:`space`
- :py:class:`point_space`
- :py:class:`rg_space`
- :py:class:`lm_space`
- :py:class:`gl_space`
- :py:class:`hp_space`
- :py:class:`nested_space`
- :py:class:`field`
- :py:class:`operator`
- :py:class:`diagonal_operator`
- :py:class:`power_operator`
- :py:class:`projection_operator`
- :py:class:`vecvec_operator`
- :py:class:`response_operator`
.. currentmodule:: nifty.nifty_tools
- :py:class:`invertible_operator`
- :py:class:`propagator_operator`
.. currentmodule:: nifty.nifty_explicit
- :py:class:`explicit_operator`
.. automodule:: nifty
- :py:class:`probing`
- :py:class:`trace_probing`
- :py:class:`diagonal_probing`
.. currentmodule:: nifty.nifty_explicit
- :py:class:`explicit_probing`
.. currentmodule:: nifty.nifty_tools
- :py:class:`conjugate_gradient`
- :py:class:`steepest_descent`
.. currentmodule:: nifty.nifty_explicit
- :py:func:`explicify`
.. currentmodule:: nifty.nifty_power
- :py:func:`weight_power`,
:py:func:`smooth_power`,
:py:func:`infer_power`,
:py:func:`interpolate_power`
"""
from __future__ import division
import numpy as np
import pylab as pl
from d2o import distributed_data_object,\
STRATEGIES as DISTRIBUTION_STRATEGIES
from nifty_paradict import space_paradict,\
point_space_paradict
from nifty.config import about
from nifty_random import random
POINT_DISTRIBUTION_STRATEGIES = DISTRIBUTION_STRATEGIES['global']
class space(object):
"""
.. _______ ______ ____ __ _______ _______
.. / _____/ / _ | / _ / / ____/ / __ /
.. /_____ / / /_/ / / /_/ / / /____ / /____/
.. /_______/ / ____/ \______| \______/ \______/ class
.. /__/
NIFTY base class for spaces and their discretizations.
The base NIFTY space class is an abstract class from which other
specific space subclasses, including those preimplemented in NIFTY
(e.g. the regular grid class) must be derived.
Parameters
----------
dtype : numpy.dtype, *optional*
Data type of the field values for a field defined on this space
(default: numpy.float64).
datamodel :
See Also
--------
point_space : A class for unstructured lists of numbers.
rg_space : A class for regular cartesian grids in arbitrary dimensions.
hp_space : A class for the HEALPix discretization of the sphere
[#]_.
gl_space : A class for the Gauss-Legendre discretization of the sphere
[#]_.
lm_space : A class for spherical harmonic components.
nested_space : A class for product spaces.
References
----------
.. [#] K.M. Gorski et al., 2005, "HEALPix: A Framework for
High-Resolution Discretization and Fast Analysis of Data
Distributed on the Sphere", *ApJ* 622..759G.
.. [#] M. Reinecke and D. Sverre Seljebotn, 2013, "Libsharp - spherical
harmonic transforms revisited";
`arXiv:1303.4945 `_
Attributes
----------
para : {single object, list of objects}
This is a freeform list of parameters that derivatives of the space
class can use.
dtype : numpy.dtype
Data type of the field values for a field defined on this space.
discrete : bool
Whether the space is inherently discrete (true) or a discretization
of a continuous space (false).
vol : numpy.ndarray
An array of pixel volumes, only one component if the pixels all
have the same volume.
"""
def __init__(self):
"""
Sets the attributes for a space class instance.
Parameters
----------
dtype : numpy.dtype, *optional*
Data type of the field values for a field defined on this space
(default: numpy.float64).
datamodel :
Returns
-------
None
"""
self.paradict = space_paradict()
@property
def para(self):
return self.paradict['default']
@para.setter
def para(self, x):
self.paradict['default'] = x
def __hash__(self):
return hash(())
def _identifier(self):
"""
_identiftier returns an object which contains all information needed
to uniquely idetnify a space. It returns a (immutable) tuple which
therefore can be compared.
"""
return tuple(sorted(vars(self).items()))
def __eq__(self, x):
if isinstance(x, type(self)):
return self._identifier() == x._identifier()
else:
return False
def __ne__(self, x):
return not self.__eq__(x)
def __len__(self):
return int(self.get_dim())
def copy(self):
return space(para=self.para,
dtype=self.dtype)
def getitem(self, data, key):
raise NotImplementedError(about._errors.cstring(
"ERROR: no generic instance method 'getitem'."))
def setitem(self, data, update, key):
raise NotImplementedError(about._errors.cstring(
"ERROR: no generic instance method 'getitem'."))
def apply_scalar_function(self, x, function, inplace=False):
raise NotImplementedError(about._errors.cstring(
"ERROR: no generic instance method 'apply_scalar_function'."))
def unary_operation(self, x, op=None):
raise NotImplementedError(about._errors.cstring(
"ERROR: no generic instance method 'unary_operation'."))
def binary_operation(self, x, y, op=None):
raise NotImplementedError(about._errors.cstring(
"ERROR: no generic instance method 'binary_operation'."))
def get_shape(self):
raise NotImplementedError(about._errors.cstring(
"ERROR: no generic instance method 'shape'."))
def get_dim(self):
"""
Computes the dimension of the space, i.e.\ the number of pixels.
Parameters
----------
split : bool, *optional*
Whether to return the dimension split up, i.e. the numbers of
pixels in each direction, or not (default: False).
Returns
-------
dim : {int, numpy.ndarray}
Dimension(s) of the space.
"""
raise NotImplementedError(about._errors.cstring(
"ERROR: no generic instance method 'dim'."))
def get_dof(self):
"""
Computes the number of degrees of freedom of the space.
Returns
-------
dof : int
Number of degrees of freedom of the space.
"""
raise NotImplementedError(about._errors.cstring(
"ERROR: no generic instance method 'dof'."))
def _complement_cast(self, x, axis=None):
return x
# TODO: Move enforce power into power_indices class
def enforce_power(self, spec, **kwargs):
"""
Provides a valid power spectrum array from a given object.
Parameters
----------
spec : {scalar, list, numpy.ndarray, nifty.field, function}
Fiducial power spectrum from which a valid power spectrum is to
be calculated. Scalars are interpreted as constant power
spectra.
Returns
-------
spec : numpy.ndarray
Valid power spectrum.
Other parameters
----------------
size : int, *optional*
Number of bands the power spectrum shall have (default: None).
kindex : numpy.ndarray, *optional*
Scale of each band.
codomain : nifty.space, *optional*
A compatible codomain for power indexing (default: None).
log : bool, *optional*
Flag specifying if the spectral binning is performed on
logarithmic
scale or not; if set, the number of used bins is set
automatically (if not given otherwise); by default no binning
is done (default: None).
nbin : integer, *optional*
Number of used spectral bins; if given `log` is set to
``False``;
integers below the minimum of 3 induce an automatic setting;
by default no binning is done (default: None).
binbounds : {list, array}, *optional*
User specific inner boundaries of the bins, which are preferred
over the above parameters; by default no binning is done
(default: None).
vmin : {scalar, list, ndarray, field}, *optional*
Lower limit of the uniform distribution if ``random == "uni"``
(default: 0).
"""
raise NotImplementedError(about._errors.cstring(
"ERROR: no generic instance method 'enforce_power'."))
def check_codomain(self, codomain):
"""
Checks whether a given codomain is compatible to the space or not.
Parameters
----------
codomain : nifty.space
Space to be checked for compatibility.
Returns
-------
check : bool
Whether or not the given codomain is compatible to the space.
"""
if codomain is None:
return False
else:
raise NotImplementedError(about._errors.cstring(
"ERROR: no generic instance method 'check_codomain'."))
def get_codomain(self, **kwargs):
"""
Generates a compatible codomain to which transformations are
reasonable, usually either the position basis or the basis of
harmonic eigenmodes.
Parameters
----------
coname : string, *optional*
String specifying a desired codomain (default: None).
cozerocenter : {bool, numpy.ndarray}, *optional*
Whether or not the grid is zerocentered for each axis or not
(default: None).
conest : list, *optional*
List of nested spaces of the codomain (default: None).
coorder : list, *optional*
Permutation of the list of nested spaces (default: None).
Returns
-------
codomain : nifty.space
A compatible codomain.
"""
raise NotImplementedError(about._errors.cstring(
"ERROR: no generic instance method 'get_codomain'."))
def get_random_values(self, **kwargs):
"""
Generates random field values according to the specifications given
by the parameters.
Returns
-------
x : numpy.ndarray
Valid field values.
Other parameters
----------------
random : string, *optional*
Specifies the probability distribution from which the random
numbers are to be drawn.
Supported distributions are:
- "pm1" (uniform distribution over {+1,-1} or {+1,+i,-1,-i}
- "gau" (normal distribution with zero-mean and a given
standard deviation or variance)
- "syn" (synthesizes from a given power spectrum)
- "uni" (uniform distribution over [vmin,vmax[)
(default: None).
dev : float, *optional*
Standard deviation (default: 1).
var : float, *optional*
Variance, overriding `dev` if both are specified
(default: 1).
spec : {scalar, list, numpy.ndarray, nifty.field, function},
*optional*
Power spectrum (default: 1).
pindex : numpy.ndarray, *optional*
Indexing array giving the power spectrum index of each band
(default: None).
kindex : numpy.ndarray, *optional*
Scale of each band (default: None).
codomain : nifty.space, *optional*
A compatible codomain with power indices (default: None).
log : bool, *optional*
Flag specifying if the spectral binning is performed on
logarithmic
scale or not; if set, the number of used bins is set
automatically (if not given otherwise); by default no binning
is done (default: None).
nbin : integer, *optional*
Number of used spectral bins; if given `log` is set to
``False``;
integers below the minimum of 3 induce an automatic setting;
by default no binning is done (default: None).
binbounds : {list, array}, *optional*
User specific inner boundaries of the bins, which are preferred
over the above parameters; by default no binning is done
(default: None).
vmin : {scalar, list, ndarray, field}, *optional*
Lower limit of the uniform distribution if ``random == "uni"``
(default: 0).
vmin : float, *optional*
Lower limit for a uniform distribution (default: 0).
vmax : float, *optional*
Upper limit for a uniform distribution (default: 1).
"""
raise NotImplementedError(about._errors.cstring(
"ERROR: no generic instance method 'get_random_values'."))
def calc_weight(self, x, power=1):
"""
Weights a given array of field values with the pixel volumes (not
the meta volumes) to a given power.
Parameters
----------
x : numpy.ndarray
Array to be weighted.
power : float, *optional*
Power of the pixel volumes to be used (default: 1).
Returns
-------
y : numpy.ndarray
Weighted array.
"""
raise NotImplementedError(about._errors.cstring(
"ERROR: no generic instance method 'calc_weight'."))
def get_weight(self, power=1):
raise NotImplementedError(about._errors.cstring(
"ERROR: no generic instance method 'get_weight'."))
def calc_norm(self, x, q):
raise NotImplementedError(about._errors.cstring(
"ERROR: no generic instance method 'norm'."))
def calc_dot(self, x, y):
"""
Computes the discrete inner product of two given arrays of field
values.
Parameters
----------
x : numpy.ndarray
First array
y : numpy.ndarray
Second array
Returns
-------
dot : scalar
Inner product of the two arrays.
"""
raise NotImplementedError(about._errors.cstring(
"ERROR: no generic instance method 'dot'."))
def calc_transform(self, x, codomain=None, **kwargs):
"""
Computes the transform of a given array of field values.
Parameters
----------
x : numpy.ndarray
Array to be transformed.
codomain : nifty.space, *optional*
codomain space to which the transformation shall map
(default: self).
Returns
-------
Tx : numpy.ndarray
Transformed array
Other parameters
----------------
iter : int, *optional*
Number of iterations performed in specific transformations.
"""
raise NotImplementedError(about._errors.cstring(
"ERROR: no generic instance method 'calc_transform'."))
def calc_smooth(self, x, sigma=0, **kwargs):
"""
Smoothes an array of field values by convolution with a Gaussian
kernel.
Parameters
----------
x : numpy.ndarray
Array of field values to be smoothed.
sigma : float, *optional*
Standard deviation of the Gaussian kernel, specified in units
of length in position space (default: 0).
Returns
-------
Gx : numpy.ndarray
Smoothed array.
Other parameters
----------------
iter : int, *optional*
Number of iterations (default: 0).
"""
raise NotImplementedError(about._errors.cstring(
"ERROR: no generic instance method 'calc_smooth'."))
def calc_power(self, x, **kwargs):
"""
Computes the power of an array of field values.
Parameters
----------
x : numpy.ndarray
Array containing the field values of which the power is to be
calculated.
Returns
-------
spec : numpy.ndarray
Power contained in the input array.
Other parameters
----------------
pindex : numpy.ndarray, *optional*
Indexing array assigning the input array components to
components of the power spectrum (default: None).
kindex : numpy.ndarray, *optional*
Scale corresponding to each band in the power spectrum
(default: None).
rho : numpy.ndarray, *optional*
Number of degrees of freedom per band (default: None).
codomain : nifty.space, *optional*
A compatible codomain for power indexing (default: None).
log : bool, *optional*
Flag specifying if the spectral binning is performed on
logarithmic
scale or not; if set, the number of used bins is set
automatically (if not given otherwise); by default no binning
is done (default: None).
nbin : integer, *optional*
Number of used spectral bins; if given `log` is set to
``False``;
integers below the minimum of 3 induce an automatic setting;
by default no binning is done (default: None).
binbounds : {list, array}, *optional*
User specific inner boundaries of the bins, which are preferred
over the above parameters; by default no binning is done
(default: None).
vmin : {scalar, list, ndarray, field}, *optional*
Lower limit of the uniform distribution if ``random == "uni"``
(default: 0).
"""
raise NotImplementedError(about._errors.cstring(
"ERROR: no generic instance method 'calc_power'."))
def calc_real_Q(self, x):
raise NotImplementedError(about._errors.cstring(
"ERROR: no generic instance method 'calc_real_Q'."))
def calc_bincount(self, x, weights=None, minlength=None):
raise NotImplementedError(about._errors.cstring(
"ERROR: no generic instance method 'calc_bincount'."))
def get_plot(self, x, **kwargs):
"""
Creates a plot of field values according to the specifications
given by the parameters.
Parameters
----------
x : numpy.ndarray
Array containing the field values.
Returns
-------
None
Other parameters
----------------
title : string, *optional*
Title of the plot (default: "").
vmin : float, *optional*
Minimum value to be displayed (default: ``min(x)``).
vmax : float, *optional*
Maximum value to be displayed (default: ``max(x)``).
power : bool, *optional*
Whether to plot the power contained in the field or the field
values themselves (default: False).
unit : string, *optional*
Unit of the field values (default: "").
norm : string, *optional*
Scaling of the field values before plotting (default: None).
cmap : matplotlib.colors.LinearSegmentedColormap, *optional*
Color map to be used for two-dimensional plots (default: None).
cbar : bool, *optional*
Whether to show the color bar or not (default: True).
other : {single object, tuple of objects}, *optional*
Object or tuple of objects to be added, where objects can be
scalars, arrays, or fields (default: None).
legend : bool, *optional*
Whether to show the legend or not (default: False).
mono : bool, *optional*
Whether to plot the monopole or not (default: True).
save : string, *optional*
Valid file name where the figure is to be stored, by default
the figure is not saved (default: False).
error : {float, numpy.ndarray, nifty.field}, *optional*
Object indicating some confidence interval to be plotted
(default: None).
kindex : numpy.ndarray, *optional*
Scale corresponding to each band in the power spectrum
(default: None).
codomain : nifty.space, *optional*
A compatible codomain for power indexing (default: None).
log : bool, *optional*
Flag specifying if the spectral binning is performed on
logarithmic
scale or not; if set, the number of used bins is set
automatically (if not given otherwise); by default no binning
is done (default: None).
nbin : integer, *optional*
Number of used spectral bins; if given `log` is set to
``False``;
integers below the minimum of 3 induce an automatic setting;
by default no binning is done (default: None).
binbounds : {list, array}, *optional*
User specific inner boundaries of the bins, which are preferred
over the above parameters; by default no binning is done
(default: None).
vmin : {scalar, list, ndarray, field}, *optional*
Lower limit of the uniform distribution if ``random == "uni"``
(default: 0).
iter : int, *optional*
Number of iterations (default: 0).
"""
raise NotImplementedError(about._errors.cstring(
"ERROR: no generic instance method 'get_plot'."))
def __repr__(self):
string = ""
string += str(type(self)) + "\n"
string += "paradict: " + str(self.paradict) + "\n"
return string
def __str__(self):
return self.__repr__()
class point_space(space):
"""
.. __ __
.. /__/ / /_
.. ______ ______ __ __ ___ / _/
.. / _ | / _ | / / / _ | / /
.. / /_/ / / /_/ / / / / / / / / /_
.. / ____/ \______/ /__/ /__/ /__/ \___/ space class
.. /__/
NIFTY subclass for unstructured spaces.
Unstructured spaces are lists of values without any geometrical
information.
Parameters
----------
num : int
Number of points.
dtype : numpy.dtype, *optional*
Data type of the field values (default: None).
Attributes
----------
para : numpy.ndarray
Array containing the number of points.
dtype : numpy.dtype
Data type of the field values.
discrete : bool
Parameter captioning the fact that a :py:class:`point_space` is
always discrete.
vol : numpy.ndarray
Pixel volume of the :py:class:`point_space`, which is always 1.
"""
def __init__(self, num, dtype=np.dtype('float')):
"""
Sets the attributes for a point_space class instance.
Parameters
----------
num : int
Number of points.
dtype : numpy.dtype, *optional*
Data type of the field values (default: numpy.float64).
Returns
-------
None.
"""
self._cache_dict = {'check_codomain': {}}
self.paradict = point_space_paradict(num=num)
# parse dtype
dtype = np.dtype(dtype)
if dtype not in [np.dtype('bool'),
np.dtype('int16'),
np.dtype('int32'),
np.dtype('int64'),
np.dtype('float32'),
np.dtype('float64'),
np.dtype('complex64'),
np.dtype('complex128')]:
raise ValueError(about._errors.cstring(
"WARNING: incompatible dtype: " + str(dtype)))
self.dtype = dtype
self.discrete = True
# self.harmonic = False
self.distances = (np.float(1),)
@property
def para(self):
temp = np.array([self.paradict['num']], dtype=int)
return temp
@para.setter
def para(self, x):
self.paradict['num'] = x[0]
def __hash__(self):
# Extract the identifying parts from the vars(self) dict.
result_hash = 0
for (key, item) in vars(self).items():
if key in ['_cache_dict']:
continue
result_hash ^= item.__hash__() * hash(key)
return result_hash
def _identifier(self):
# Extract the identifying parts from the vars(self) dict.
temp = [(ii[0],
((lambda x: x[1].__hash__() if x[0] == 'comm' else x)(ii)))
for ii in vars(self).iteritems()
if ii[0] not in ['_cache_dict']
]
# Return the sorted identifiers as a tuple.
return tuple(sorted(temp))
def copy(self):
return point_space(num=self.paradict['num'],
dtype=self.dtype)
def getitem(self, data, key):
return data[key]
def setitem(self, data, update, key):
data[key] = update
def apply_scalar_function(self, x, function, inplace=False):
return x.apply_scalar_function(function, inplace=inplace)
def unary_operation(self, x, op='None', axis=None, **kwargs):
"""
x must be a numpy array which is compatible with the space!
Valid operations are
"""
translation = {'pos': lambda y: getattr(y, '__pos__')(),
'neg': lambda y: getattr(y, '__neg__')(),
'abs': lambda y: getattr(y, '__abs__')(),
'real': lambda y: getattr(y, 'real'),
'imag': lambda y: getattr(y, 'imag'),
'nanmin': lambda y: getattr(y, 'nanmin')(axis=axis),
'amin': lambda y: getattr(y, 'amin')(axis=axis),
'nanmax': lambda y: getattr(y, 'nanmax')(axis=axis),
'amax': lambda y: getattr(y, 'amax')(axis=axis),
'median': lambda y: getattr(y, 'median')(axis=axis),
'mean': lambda y: getattr(y, 'mean')(axis=axis),
'std': lambda y: getattr(y, 'std')(axis=axis),
'var': lambda y: getattr(y, 'var')(axis=axis),
'argmin_nonflat': lambda y: getattr(y, 'argmin_nonflat')(
axis=axis),
'argmin': lambda y: getattr(y, 'argmin')(axis=axis),
'argmax_nonflat': lambda y: getattr(y, 'argmax_nonflat')(
axis=axis),
'argmax': lambda y: getattr(y, 'argmax')(axis=axis),
'conjugate': lambda y: getattr(y, 'conjugate')(),
'sum': lambda y: getattr(y, 'sum')(axis=axis),
'prod': lambda y: getattr(y, 'prod')(axis=axis),
'unique': lambda y: getattr(y, 'unique')(),
'copy': lambda y: getattr(y, 'copy')(),
'copy_empty': lambda y: getattr(y, 'copy_empty')(),
'isnan': lambda y: getattr(y, 'isnan')(),
'isinf': lambda y: getattr(y, 'isinf')(),
'isfinite': lambda y: getattr(y, 'isfinite')(),
'nan_to_num': lambda y: getattr(y, 'nan_to_num')(),
'all': lambda y: getattr(y, 'all')(axis=axis),
'any': lambda y: getattr(y, 'any')(axis=axis),
'None': lambda y: y}
return translation[op](x, **kwargs)
def binary_operation(self, x, y, op='None', cast=0):
translation = {'add': lambda z: getattr(z, '__add__'),
'radd': lambda z: getattr(z, '__radd__'),
'iadd': lambda z: getattr(z, '__iadd__'),
'sub': lambda z: getattr(z, '__sub__'),
'rsub': lambda z: getattr(z, '__rsub__'),
'isub': lambda z: getattr(z, '__isub__'),
'mul': lambda z: getattr(z, '__mul__'),
'rmul': lambda z: getattr(z, '__rmul__'),
'imul': lambda z: getattr(z, '__imul__'),
'div': lambda z: getattr(z, '__div__'),
'rdiv': lambda z: getattr(z, '__rdiv__'),
'idiv': lambda z: getattr(z, '__idiv__'),
'pow': lambda z: getattr(z, '__pow__'),
'rpow': lambda z: getattr(z, '__rpow__'),
'ipow': lambda z: getattr(z, '__ipow__'),
'ne': lambda z: getattr(z, '__ne__'),
'lt': lambda z: getattr(z, '__lt__'),
'le': lambda z: getattr(z, '__le__'),
'eq': lambda z: getattr(z, '__eq__'),
'ge': lambda z: getattr(z, '__ge__'),
'gt': lambda z: getattr(z, '__gt__'),
'None': lambda z: lambda u: u}
if (cast & 1) != 0:
x = self.cast(x)
if (cast & 2) != 0:
y = self.cast(y)
return translation[op](x)(y)
def get_shape(self):
return (self.paradict['num'],)
def get_dim(self):
"""
Computes the dimension of the space, i.e.\ the number of points.
Parameters
----------
split : bool, *optional*
Whether to return the dimension as an array with one component
or as a scalar (default: False).
Returns
-------
dim : {int, numpy.ndarray}
Dimension(s) of the space.
"""
return np.prod(self.get_shape())
def get_dof(self, split=False):
"""
Computes the number of degrees of freedom of the space, i.e./ the
number of points for real-valued fields and twice that number for
complex-valued fields.
Returns
-------
dof : int
Number of degrees of freedom of the space.
"""
if split:
dof = self.get_shape()
if issubclass(self.dtype.type, np.complexfloating):
dof = tuple(np.array(dof)*2)
else:
dof = self.get_dim()
if issubclass(self.dtype.type, np.complexfloating):
dof = dof * 2
return dof
def get_vol(self, split=False):
if split:
return self.distances
else:
return np.prod(self.distances)
def get_meta_volume(self, split=False):
"""
Calculates the meta volumes.
The meta volumes are the volumes associated with each component of
a field, taking into account field components that are not
explicitly included in the array of field values but are determined
by symmetry conditions. In the case of an :py:class:`rg_space`, the
meta volumes are simply the pixel volumes.
Parameters
----------
total : bool, *optional*
Whether to return the total meta volume of the space or the
individual ones of each pixel (default: False).
Returns
-------
mol : {numpy.ndarray, float}
Meta volume of the pixels or the complete space.
"""
if not split:
return self.get_dim() * self.get_vol()
else:
mol = self.cast(1, dtype=np.dtype('float'))
return self.calc_weight(mol, power=1)
def enforce_power(self, spec, **kwargs):
"""
Raises an error since the power spectrum is ill-defined for point
spaces.
"""
raise AttributeError(about._errors.cstring(
"ERROR: the definition of power spectra is ill-defined for " +
"(unstructured) point spaces."))
def _enforce_power_helper(self, spec, size, kindex):
# Now it's about to extract a powerspectrum from spec
# First of all just extract a numpy array. The shape is cared about
# later.
dtype = np.dtype('float')
# Case 1: spec is a function
if callable(spec):
# Try to plug in the kindex array in the function directly
try:
spec = np.array(spec(kindex), dtype=dtype)
except:
# Second try: Use a vectorized version of the function.
# This is slower, but better than nothing
try:
spec = np.array(np.vectorize(spec)(kindex),
dtype=dtype)
except:
raise TypeError(about._errors.cstring(
"ERROR: invalid power spectra function."))
# Case 2: spec is a field:
elif isinstance(spec, field):
try:
spec = spec.val.get_full_data()
except AttributeError:
spec = spec.val
spec = spec.astype(dtype).flatten()
# Case 3: spec is a scalar or something else:
else:
spec = np.array(spec, dtype=dtype).flatten()
# Make some sanity checks
# check finiteness
if not np.all(np.isfinite(spec)):
about.warnings.cprint("WARNING: infinite value(s).")
# check positivity (excluding null)
if np.any(spec < 0):
raise ValueError(about._errors.cstring(
"ERROR: nonpositive value(s)."))
if np.any(spec == 0):
about.warnings.cprint("WARNING: nonpositive value(s).")
# Set the size parameter
if size is None:
size = len(kindex)
# Fix the size of the spectrum
# If spec is singlevalued, expand it
if np.size(spec) == 1:
spec = spec * np.ones(size, dtype=spec.dtype)
# If the size does not fit at all, throw an exception
elif np.size(spec) < size:
raise ValueError(about._errors.cstring("ERROR: size mismatch ( " +
str(np.size(spec)) + " < " +
str(size) + " )."))
elif np.size(spec) > size:
about.warnings.cprint("WARNING: power spectrum cut to size ( == " +
str(size) + " ).")
spec = spec[:size]
return spec
def check_codomain(self, codomain):
check_dict = self._cache_dict['check_codomain']
temp_id = id(codomain)
if temp_id in check_dict:
return check_dict[temp_id]
else:
temp_result = self._check_codomain(codomain)
check_dict[temp_id] = temp_result
return temp_result
def _check_codomain(self, codomain):
"""
Checks whether a given codomain is compatible to the space or not.
Parameters
----------
codomain : nifty.space
Space to be checked for compatibility.
Returns
-------
check : bool
Whether or not the given codomain is compatible to the space.
"""
if codomain is None:
return False
if not isinstance(codomain, space):
raise TypeError(about._errors.cstring(
"ERROR: invalid input. The given input is not a nifty space."))
if codomain == self:
return True
else:
return False
def get_codomain(self, **kwargs):
"""
Generates a compatible codomain to which transformations are
reasonable, in this case another instance of
:py:class:`point_space` with the same properties.
Returns
-------
codomain : nifty.point_space
A compatible codomain.
"""
return self.copy()
def get_random_values(self, **kwargs):
"""
Generates random field values according to the specifications given
by the parameters.
Returns
-------
x : numpy.ndarray
Valid field values.
Other parameters
----------------
random : string, *optional*
Specifies the probability distribution from which the random
numbers are to be drawn.
Supported distributions are:
- "pm1" (uniform distribution over {+1,-1} or {+1,+i,-1,-i}
- "gau" (normal distribution with zero-mean and a given
standard
deviation or variance)
- "syn" (synthesizes from a given power spectrum)
- "uni" (uniform distribution over [vmin,vmax[)
(default: None).
dev : float, *optional*
Standard deviation (default: 1).
var : float, *optional*
Variance, overriding `dev` if both are specified
(default: 1).
spec : {scalar, list, numpy.ndarray, nifty.field, function},
*optional*
Power spectrum (default: 1).
pindex : numpy.ndarray, *optional*
Indexing array giving the power spectrum index of each band
(default: None).
kindex : numpy.ndarray, *optional*
Scale of each band (default: None).
codomain : nifty.space, *optional*
A compatible codomain with power indices (default: None).
log : bool, *optional*
Flag specifying if the spectral binning is performed on
logarithmic
scale or not; if set, the number of used bins is set
automatically (if not given otherwise); by default no binning
is done (default: None).
nbin : integer, *optional*
Number of used spectral bins; if given `log` is set to
``False``;
integers below the minimum of 3 induce an automatic setting;
by default no binning is done (default: None).
binbounds : {list, array}, *optional*
User specific inner boundaries of the bins, which are preferred
over the above parameters; by default no binning is done
(default: None).
vmin : {scalar, list, ndarray, field}, *optional*
Lower limit of the uniform distribution if ``random == "uni"``
(default: 0).
vmin : float, *optional*
Lower limit for a uniform distribution (default: 0).
vmax : float, *optional*
Upper limit for a uniform distribution (default: 1).
"""
arg = random.parse_arguments(self, **kwargs)
if arg is None:
return self.cast(0)
# Prepare the empty distributed_data_object
sample = distributed_data_object(
global_shape=self.get_shape(),
dtype=self.dtype)
# Case 1: uniform distribution over {-1,+1}/{1,i,-1,-i}
if arg['random'] == 'pm1':
sample.apply_generator(lambda s: random.pm1(dtype=self.dtype,
shape=s))
# Case 2: normal distribution with zero-mean and a given standard
# deviation or variance
elif arg['random'] == 'gau':
std = arg['std']
if np.isscalar(std) or std is None:
processed_std = std
else:
try:
processed_std = sample.distributor. \
extract_local_data(std)
except(AttributeError):
processed_std = std
sample.apply_generator(lambda s: random.gau(dtype=self.dtype,
shape=s,
mean=arg['mean'],
std=processed_std))
# Case 3: uniform distribution
elif arg['random'] == 'uni':
sample.apply_generator(lambda s: random.uni(dtype=self.dtype,
shape=s,
vmin=arg['vmin'],
vmax=arg['vmax']))
return sample
def calc_weight(self, x, power=1):
"""
Weights a given array of field values with the pixel volumes (not
the meta volumes) to a given power.
Parameters
----------
x : numpy.ndarray
Array to be weighted.
power : float, *optional*
Power of the pixel volumes to be used (default: 1).
Returns
-------
y : numpy.ndarray
Weighted array.
"""
# weight
return x * self.get_weight(power=power)
def get_weight(self, power=1, split=False):
splitted_weight = tuple(np.array(self.distances)**np.array(power))
if not split:
return np.prod(splitted_weight)
else:
return splitted_weight
def calc_norm(self, x, q=2):
"""
Computes the Lq-norm of field values.
Parameters
----------
x : np.ndarray
The data array
q : scalar
Parameter q of the Lq-norm (default: 2).
Returns
-------
norm : scalar
The Lq-norm of the field values.
"""
if q == 2:
result = self.calc_dot(x, x)
else:
y = x**(q - 1)
result = self.calc_dot(x, y)
result = result**(1. / q)
return result
def calc_dot(self, x, y):
"""
Computes the discrete inner product of two given arrays of field
values.
Parameters
----------
x : numpy.ndarray
First array
y : numpy.ndarray
Second array
Returns
-------
dot : scalar
Inner product of the two arrays.
"""
x = self.cast(x)
y = self.cast(y)
result = x.vdot(y)
if np.isreal(result):
result = np.asscalar(np.real(result))
return result
def calc_transform(self, x, codomain=None, **kwargs):
"""
Computes the transform of a given array of field values.
Parameters
----------
x : numpy.ndarray
Array to be transformed.
codomain : nifty.space, *optional*
codomain space to which the transformation shall map
(default: self).
Returns
-------
Tx : numpy.ndarray
Transformed array
Other parameters
----------------
iter : int, *optional*
Number of iterations performed in specific transformations.
"""
raise AttributeError(about._errors.cstring(
"ERROR: fourier-transformation is ill-defined for " +
"(unstructured) point space."))
def calc_smooth(self, x, **kwargs):
"""
Raises an error since smoothing is ill-defined on an unstructured
space.
"""
raise AttributeError(about._errors.cstring(
"ERROR: smoothing ill-defined for (unstructured) point space."))
def calc_power(self, x, **kwargs):
"""
Raises an error since the power spectrum is ill-defined for point
spaces.
"""
raise AttributeError(about._errors.cstring(
"ERROR: power spectra ill-defined for (unstructured) " +
"point space."))
def calc_real_Q(self, x):
try:
return x.isreal().all()
except AttributeError:
return np.all(np.isreal(x))
def calc_bincount(self, x, weights=None, minlength=None):
try:
complex_weights_Q = issubclass(weights.dtype.type,
np.complexfloating)
except AttributeError:
complex_weights_Q = False
if complex_weights_Q:
real_bincount = x.bincount(weights=weights.real,
minlength=minlength)
imag_bincount = x.bincount(weights=weights.imag,
minlength=minlength)
return real_bincount + imag_bincount
else:
return x.bincount(weights=weights, minlength=minlength)
def get_plot(self, x, title="", vmin=None, vmax=None, unit=None,
norm=None, other=None, legend=False, save=None, **kwargs):
"""
Creates a plot of field values according to the specifications
given by the parameters.
Parameters
----------
x : numpy.ndarray
Array containing the field values.
Returns
-------
None
Other parameters
----------------
title : string, *optional*
Title of the plot (default: "").
vmin : float, *optional*
Minimum value to be displayed (default: ``min(x)``).
vmax : float, *optional*
Maximum value to be displayed (default: ``max(x)``).
unit : string, *optional*
Unit of the field values (default: "").
norm : string, *optional*
Scaling of the field values before plotting (default: None).
other : {single object, tuple of objects}, *optional*
Object or tuple of objects to be added, where objects can be
scalars, arrays, or fields (default: None).
legend : bool, *optional*
Whether to show the legend or not (default: False).
save : string, *optional*
Valid file name where the figure is to be stored, by default
the figure is not saved (default: False).
"""
if not pl.isinteractive() and save is not None:
about.warnings.cprint("WARNING: interactive mode off.")
x = self.cast(x)
fig = pl.figure(num=None,
figsize=(6.4, 4.8),
dpi=None,
facecolor="none",
edgecolor="none",
frameon=False,
FigureClass=pl.Figure)
ax0 = fig.add_axes([0.12, 0.12, 0.82, 0.76])
xaxes = np.arange(self.para[0], dtype=np.dtype('int'))
if (norm == "log") and (vmin <= 0):
raise ValueError(about._errors.cstring(
"ERROR: nonpositive value(s)."))
if issubclass(self.dtype.type, np.complexfloating):
if vmin is None:
vmin = min(x.real.min(), x.imag.min(), abs(x).min())
if vmax is None:
vmax = min(x.real.max(), x.imag.max(), abs(x).max())
else:
if vmin is None:
vmin = x.min()
if vmax is None:
vmax = x.max()
ax0.set_xlim(xaxes[0], xaxes[-1])
ax0.set_xlabel("index")
ax0.set_ylim(vmin, vmax)
if(norm == "log"):
ax0.set_yscale('log')
if issubclass(self.dtype.type, np.complexfloating):
ax0.scatter(xaxes, self.unary_operation(x, op='abs'),
color=[0.0, 0.5, 0.0], marker='o',
label="graph (absolute)", facecolor="none", zorder=1)
ax0.scatter(xaxes, self.unary_operation(x, op='real'),
color=[0.0, 0.5, 0.0], marker='s',
label="graph (real part)", facecolor="none", zorder=1)
ax0.scatter(xaxes, self.unary_operation(x, op='imag'),
color=[0.0, 0.5, 0.0], marker='D',
label="graph (imaginary part)", facecolor="none",
zorder=1)
else:
ax0.scatter(xaxes, x, color=[0.0, 0.5, 0.0], marker='o',
label="graph 0", zorder=1)
if other is not None:
if not isinstance(other, tuple):
other = (other, )
imax = max(1, len(other) - 1)
for ii in xrange(len(other)):
ax0.scatter(xaxes, self.dtype(other[ii]),
color=[max(0.0, 1.0 - (2 * ii / imax)**2),
0.5 * ((2 * ii - imax) / imax)**2,
max(0.0, 1.0 -
(2 * (ii - imax) / imax)**2)],
marker='o', label="'other' graph " + str(ii),
zorder=-ii)
if legend:
ax0.legend()
if unit is not None:
unit = " [" + unit + "]"
else:
unit = ""
ax0.set_ylabel("values" + unit)
ax0.set_title(title)
if save is not None:
fig.savefig(str(save), dpi=None,
facecolor="none", edgecolor="none")
pl.close(fig)
else:
fig.canvas.draw()
def __repr__(self):
string = ""
string += str(type(self)) + "\n"
string += "paradict: " + str(self.paradict) + "\n"
string += 'dtype: ' + str(self.dtype) + "\n"
string += 'discrete: ' + str(self.discrete) + "\n"
string += 'distances: ' + str(self.distances) + "\n"
return string