# 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 nifty.config import about
from space_paradict import SpaceParadict
class Space(object):
"""
.. __ __
.. /__/ / /_
.. ______ ______ __ __ ___ / _/
.. / _ | / _ | / / / _ | / /
.. / /_/ / / /_/ / / / / / / / / /_
.. / ____/ \______/ /__/ /__/ /__/ \___/ 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, dtype=np.dtype('float'), **kwargs):
"""
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.paradict = SpaceParadict(**kwargs)
# parse dtype
dtype = np.dtype(dtype)
self.dtype = dtype
self._harmonic = None
@property
def harmonic(self):
return self._harmonic
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 []:
continue
result_hash ^= item.__hash__() ^ int(hash(key)/117)
return result_hash
def __eq__(self, x):
if isinstance(x, type(self)):
return hash(self) == hash(x)
else:
return False
def copy(self):
return self.__class__(dtype=self.dtype, **self.paradict.parameters)
@property
def shape(self):
raise NotImplementedError(about._errors.cstring(
"ERROR: There is no generic shape for the Space base class."))
@property
def dim(self):
raise NotImplementedError(about._errors.cstring(
"ERROR: There is no generic dim for the Space base class."))
@property
def dof(self):
"""
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.
"""
dof = self.dim
if issubclass(self.dtype.type, np.complexfloating):
dof = dof * 2
return dof
@property
def total_volume(self):
raise NotImplementedError(about._errors.cstring(
"ERROR: There is no generic volume for the Space base class."))
def complement_cast(self, x, axes=None):
return x
def weight(self, x, power=1, axes=None):
"""
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
def dot_contraction(self, x, axes):
"""
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.
"""
return x.sum(axis=axes)
def compute_k_array(self, distribution_strategy):
raise NotImplementedError(about._errors.cstring(
"ERROR: There is no generic k_array for Space base class."))
def smooth(self, x, **kwargs):
raise AttributeError(about._errors.cstring(
"ERROR: There is no generic smoothing for Space base class."))
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 += "harmonic: " + str(self.harmonic) + "\n"
return string