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nifty_core.py
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nifty_core.py
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## 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: <http://www.mpa-garching.mpg.de/ift/nifty/>
##
## 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 <http://www.gnu.org/licenses/>.
"""
.. __ ____ __
.. /__/ / _/ / /_
.. __ ___ __ / /_ / _/ __ __
.. / _ | / / / _/ / / / / / /
.. / / / / / / / / / /_ / /_/ /
.. /__/ /__/ /__/ /__/ \___/ \___ / 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 <http://dx.doi.org/10.1051/0004-6361/201321236>`_,
2013; `arXiv:1301.4499 <http://www.arxiv.org/abs/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 os
from sys import stdout as so
import numpy as np
import pylab as pl
from multiprocessing import Pool as mp
from multiprocessing import Value as mv
from multiprocessing import Array as ma
__version__ = "1.0.7"
pi = 3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679
##-----------------------------------------------------------------------------
class switch(object):
"""
.. __ __ __
.. /__/ / /_ / /
.. _______ __ __ __ / _/ _______ / /___
.. / _____/ | |/\/ / / / / / / ____/ / _ |
.. /_____ / | / / / / /_ / /____ / / / /
.. /_______/ |__/\__/ /__/ \___/ \______/ /__/ /__/ class
NIFTY support class for switches.
Parameters
----------
default : bool
Default status of the switch (default: False).
See Also
--------
notification : A derived class for displaying notifications.
Examples
--------
>>> option = switch()
>>> option.status
False
>>> option
OFF
>>> print(option)
OFF
>>> option.on()
>>> print(option)
ON
Attributes
----------
status : bool
Status of the switch.
"""
def __init__(self,default=False):
"""
Initilizes the switch and sets the `status`
Parameters
----------
default : bool
Default status of the switch (default: False).
"""
self.status = bool(default)
##+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
def on(self):
"""
Switches the `status` to True.
"""
self.status = True
def off(self):
"""
Switches the `status` to False.
"""
self.status = False
def toggle(self):
"""
Switches the `status`.
"""
self.status = not self.status
##+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
def __repr__(self):
if(self.status):
return "ON"
else:
return "OFF"
##-----------------------------------------------------------------------------
##-----------------------------------------------------------------------------
class notification(switch):
"""
.. __ __ ____ __ __ __
.. / /_ /__/ / _/ /__/ / /_ /__/
.. __ ___ ______ / _/ __ / /_ __ _______ ____ __ / _/ __ ______ __ ___
.. / _ | / _ | / / / / / _/ / / / ____/ / _ / / / / / / _ | / _ |
.. / / / / / /_/ / / /_ / / / / / / / /____ / /_/ / / /_ / / / /_/ / / / / /
.. /__/ /__/ \______/ \___/ /__/ /__/ /__/ \______/ \______| \___/ /__/ \______/ /__/ /__/ class
NIFTY support class for notifications.
Parameters
----------
default : bool
Default status of the switch (default: False).
ccode : string
Color code as string (default: "\033[0m"). The surrounding special
characters are added if missing.
Notes
-----
The color code is a special ANSI escape code, for a list of valid codes
see [#]_. Multiple codes can be combined by seperating them with a
semicolon ';'.
References
----------
.. [#] Wikipedia, `ANSI escape code <http://en.wikipedia.org/wiki/ANSI_escape_code#graphics>`_.
Examples
--------
>>> note = notification()
>>> note.status
True
>>> note.cprint("This is noteworthy.")
This is noteworthy.
>>> note.cflush("12"); note.cflush('3')
123
>>> note.off()
>>> note.cprint("This is noteworthy.")
>>>
Raises
------
TypeError
If `ccode` is no string.
Attributes
----------
status : bool
Status of the switch.
ccode : string
Color code as string.
"""
_code = "\033[0m" ## "\033[39;49m"
def __init__(self,default=True,ccode="\033[0m"):
"""
Initializes the notification and sets `status` and `ccode`
Parameters
----------
default : bool
Default status of the switch (default: False).
ccode : string
Color code as string (default: "\033[0m"). The surrounding
special characters are added if missing.
Raises
------
TypeError
If `ccode` is no string.
"""
self.status = bool(default)
## check colour code
if(not isinstance(ccode,str)):
raise TypeError(about._errors.cstring("ERROR: invalid input."))
if(ccode[0]!="\033"):
ccode = "\033"+ccode
if(ccode[1]!='['):
ccode = ccode[0]+'['+ccode[1:]
if(ccode[-1]!='m'):
ccode = ccode+'m'
self.ccode = ccode
##+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
def set_ccode(self,newccode=None):
"""
Resets the the `ccode` string.
Parameters
----------
newccode : string
Color code as string (default: "\033[0m"). The surrounding
characters "\033", '[', and 'm' are added if missing.
Returns
-------
None
Raises
------
TypeError
If `ccode` is no string.
Examples
--------
>>> note = notification()
>>> note.set_ccode("31;1") ## "31;1" corresponds to red and bright
"""
if(newccode is None):
newccode = self._code
else:
## check colour code
if(not isinstance(newccode,str)):
raise TypeError(about._errors.cstring("ERROR: invalid input."))
if(newccode[0]!="\033"):
newccode = "\033"+newccode
if(newccode[1]!='['):
newccode = newccode[0]+'['+newccode[1:]
if(newccode[-1]!='m'):
newccode = newccode+'m'
self.ccode = newccode
##+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
def cstring(self,subject):
"""
Casts an object to a string and augments that with a colour code.
Parameters
----------
subject : {string, object}
String to be augmented with a color code. A given object is
cast to its string representation by :py:func:`str`.
Returns
-------
cstring : string
String augmented with a color code.
"""
return self.ccode+str(subject)+self._code
def cflush(self,subject):
"""
Flushes an object in its colour coded sting representation to the
standard output (*without* line break).
Parameters
----------
subject : {string, object}
String to be flushed. A given object is
cast to a string by :py:func:`str`.
Returns
-------
None
"""
if(self.status):
so.write(self.cstring(subject))
so.flush()
def cprint(self,subject):
"""
Flushes an object in its colour coded sting representation to the
standard output (*with* line break).
Parameters
----------
subject : {string, object}
String to be flushed. A given object is
cast to a string by :py:func:`str`.
Returns
-------
None
"""
if(self.status):
so.write(self.cstring(subject)+"\n")
so.flush()
##+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
def __repr__(self):
if(self.status):
return self.cstring("ON")
else:
return self.cstring("OFF")
##-----------------------------------------------------------------------------
##-----------------------------------------------------------------------------
class _about(object): ## nifty support class for global settings
"""
NIFTY support class for global settings.
.. warning::
Turning off the `_error` notification will suppress all NIFTY error
strings (not recommended).
Examples
--------
>>> from nifty import *
>>> about
nifty version 0.2.0
>>> print(about)
nifty version 0.2.0
- errors = ON (immutable)
- warnings = ON
- infos = OFF
- multiprocessing = ON
- hermitianize = ON
- lm2gl = ON
>>> about.infos.on()
>>> about.about.save_config()
>>> from nifty import *
INFO: nifty version 0.2.0
>>> print(about)
nifty version 0.2.0
- errors = ON (immutable)
- warnings = ON
- infos = ON
- multiprocessing = ON
- hermitianize = ON
- lm2gl = ON
Attributes
----------
warnings : notification
Notification instance controlling whether warings shall be printed.
infos : notification
Notification instance controlling whether information shall be
printed.
multiprocessing : switch
Switch instance controlling whether multiprocessing might be
performed.
hermitianize : switch
Switch instance controlling whether hermitian symmetry for certain
:py:class:`rg_space` instances is inforced.
lm2gl : switch
Switch instance controlling whether default target of a
:py:class:`lm_space` instance is a :py:class:`gl_space` or a
:py:class:`hp_space` instance.
"""
def __init__(self):
"""
Initializes the _about and sets the attributes.
"""
## version
self._version = str(__version__)
## switches and notifications
self._errors = notification(default=True,ccode=notification._code)
self.warnings = notification(default=True,ccode=notification._code)
self.infos = notification(default=False,ccode=notification._code)
self.multiprocessing = switch(default=True)
self.hermitianize = switch(default=True)
self.lm2gl = switch(default=True)
##+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
def load_config(self,force=True):
"""
Reads the configuration file "~/.nifty/nifty_config".
Parameters
----------
force : bool
Whether to cause an error if the file does not exsist or not.
Returns
-------
None
Raises
------
ValueError
If the configuration file is malformed.
OSError
If the configuration file does not exist.
"""
nconfig = os.path.expanduser('~')+"/.nifty/nifty_config"
if(os.path.isfile(nconfig)):
rawconfig = []
with open(nconfig,'r') as configfile:
for ll in configfile:
if(not ll.startswith('#')):
rawconfig += ll.split()
try:
self._errors = notification(default=True,ccode=rawconfig[0])
self.warnings = notification(default=int(rawconfig[1]),ccode=rawconfig[2])
self.infos = notification(default=int(rawconfig[3]),ccode=rawconfig[4])
self.multiprocessing = switch(default=int(rawconfig[5]))
self.hermitianize = switch(default=int(rawconfig[6]))
self.lm2gl = switch(default=int(rawconfig[7]))
except(IndexError):
raise ValueError(about._errors.cstring("ERROR: '"+nconfig+"' damaged."))
elif(force):
raise OSError(about._errors.cstring("ERROR: '"+nconfig+"' nonexisting."))
def save_config(self):
"""
Writes to the configuration file "~/.nifty/nifty_config".
Returns
-------
None
"""
rawconfig = [self._errors.ccode[2:-1],str(int(self.warnings.status)),self.warnings.ccode[2:-1],str(int(self.infos.status)),self.infos.ccode[2:-1],str(int(self.multiprocessing.status)),str(int(self.hermitianize.status)),str(int(self.lm2gl.status))]
nconfig = os.path.expanduser('~')+"/.nifty/nifty_config"
if(os.path.isfile(nconfig)):
rawconfig = [self._errors.ccode[2:-1],str(int(self.warnings.status)),self.warnings.ccode[2:-1],str(int(self.infos.status)),self.infos.ccode[2:-1],str(int(self.multiprocessing.status)),str(int(self.hermitianize.status)),str(int(self.lm2gl.status))]
nconfig = os.path.expanduser('~')+"/.nifty/nifty_config"
with open(nconfig,'r') as sourcefile:
with open(nconfig+"_",'w') as targetfile:
for ll in sourcefile:
if(ll.startswith('#')):
targetfile.write(ll)
else:
ll = ll.replace(ll.split()[0],rawconfig[0]) ## one(!) per line
rawconfig = rawconfig[1:]
targetfile.write(ll)
os.rename(nconfig+"_",nconfig) ## overwrite old congiguration
else:
if(not os.path.exists(os.path.expanduser('~')+"/.nifty")):
os.makedirs(os.path.expanduser('~')+"/.nifty")
with open(nconfig,'w') as targetfile:
for rr in rawconfig:
targetfile.write(rr+"\n") ## one(!) per line
##+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
def __repr__(self):
return "nifty version "+self._version
def __str__(self):
return "nifty version "+self._version+"\n- errors = "+self._errors.cstring("ON")+" (immutable)\n- warnings = "+str(self.warnings)+"\n- infos = "+str(self.infos)+"\n- multiprocessing = "+str(self.multiprocessing)+"\n- hermitianize = "+str(self.hermitianize)+"\n- lm2gl = "+str(self.lm2gl)
##-----------------------------------------------------------------------------
## set global instance
about = _about()
about.load_config(force=False)
about.infos.cprint("INFO: "+about.__repr__())
##-----------------------------------------------------------------------------
class random(object):
"""
.. __
.. / /
.. _____ ____ __ __ ___ ____/ / ______ __ ____ ___
.. / __/ / _ / / _ | / _ / / _ | / _ _ |
.. / / / /_/ / / / / / / /_/ / / /_/ / / / / / / /
.. /__/ \______| /__/ /__/ \______| \______/ /__/ /__/ /__/ class
NIFTY (static) class for pseudo random number generators.
"""
__init__ = None
##+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
@staticmethod
def arguments(domain,**kwargs):
"""
Analyses the keyword arguments for supported or necessary ones.
Parameters
----------
domain : space
Space wherein the random field values live.
random : string, *optional*
Specifies a certain distribution to be drwan from using a
pseudo random number generator. 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[)
dev : {scalar, list, ndarray, field}, *optional*
Standard deviation of the normal distribution if
``random == "gau"`` (default: None).
var : {scalar, list, ndarray, field}, *optional*
Variance of the normal distribution (outranks the standard
deviation) if ``random == "gau"`` (default: None).
spec : {scalar, list, array, field, function}, *optional*
Power spectrum for ``random == "syn"`` (default: 1).
size : integer, *optional*
Number of irreducible bands for ``random == "syn"``
(default: None).
pindex : numpy.ndarray, *optional*
Indexing array giving the power spectrum index of each band
(default: None).
kindex : numpy.ndarray, *optional*
Scale of each irreducible band (default: None).
vmax : {scalar, list, ndarray, field}, *optional*
Upper limit of the uniform distribution if ``random == "uni"``
(default: 1).
Returns
-------
arg : list
Ordered list of arguments (to be processed in
``get_random_values`` of the domain).
Other Parameters
----------------
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).
Raises
------
KeyError
If the `random` key is not supporrted.
"""
if("random" in kwargs):
key = kwargs.get("random")
else:
return None
if(key=="pm1"):
return [key]
elif(key=="gau"):
if("mean" in kwargs):
mean = domain.enforce_values(kwargs.get("mean"),extend=False)
else:
mean = None
if("dev" in kwargs):
dev = domain.enforce_values(kwargs.get("dev"),extend=False)
else:
dev = None
if("var" in kwargs):
var = domain.enforce_values(kwargs.get("var"),extend=False)
else:
var = None
return [key,mean,dev,var]
elif(key=="syn"):
## explicit power indices
if("pindex" in kwargs)and("kindex" in kwargs):
kindex = kwargs.get("kindex")
if(kindex is None):
spec = domain.enforce_power(kwargs.get("spec",1),size=kwargs.get("size",None))
kpack = None
else:
spec = domain.enforce_power(kwargs.get("spec",1),size=len(kindex),kindex=kindex)
pindex = kwargs.get("pindex",None)
if(pindex is None):
kpack = None
else:
kpack = [pindex,kindex]
## implicit power indices
else:
try:
domain.set_power_indices(**kwargs)
except:
codomain = kwargs.get("codomain",None)
if(codomain is None):
spec = domain.enforce_power(kwargs.get("spec",1),size=kwargs.get("size",None))
kpack = None
else:
domain.check_codomain(codomain)
codomain.set_power_indices(**kwargs)
kindex = codomain.power_indices.get("kindex")
spec = domain.enforce_power(kwargs.get("spec",1),size=len(kindex),kindex=kindex,codomain=codomain)
kpack = [codomain.power_indices.get("pindex"),kindex]
else:
kindex = domain.power_indices.get("kindex")
spec = domain.enforce_power(kwargs.get("spec",1),size=len(kindex),kindex=kindex)
kpack = [domain.power_indices.get("pindex"),kindex]
return [key,spec,kpack]
elif(key=="uni"):
if("vmin" in kwargs):
vmin = domain.enforce_values(kwargs.get("vmin"),extend=False)
else:
vmin = 0
if("vmax" in kwargs):
vmax = domain.enforce_values(kwargs.get("vmax"),extend=False)
else:
vmax = 1
return [key,vmin,vmax]
else:
raise KeyError(about._errors.cstring("ERROR: unsupported random key '"+str(key)+"'."))
##+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
@staticmethod
def pm1(datatype=np.int,shape=1):
"""
Generates random field values according to an uniform distribution
over {+1,-1} or {+1,+i,-1,-i}, respectively.
Parameters
----------
datatype : type, *optional*
Data type of the field values (default: np.int).
shape : {integer, tuple, list, ndarray}, *optional*
Split up dimension of the space (default: 1).
Returns
-------
x : ndarray
Random field values (with correct dtype and shape).
"""
size = np.prod(shape,axis=0,dtype=np.int,out=None)
if(issubclass(datatype,np.complexfloating)):
x = np.array([1+0j,0+1j,-1+0j,0-1j],dtype=datatype)[np.random.randint(4,high=None,size=size)]
else:
x = 2*np.random.randint(2,high=None,size=size)-1
return x.astype(datatype).reshape(shape,order='C')
##+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
@staticmethod
def gau(datatype=np.float64,shape=1,mean=None,dev=None,var=None):
"""
Generates random field values according to a normal distribution.
Parameters
----------
datatype : type, *optional*
Data type of the field values (default: np.float64).
shape : {integer, tuple, list, ndarray}, *optional*
Split up dimension of the space (default: 1).
mean : {scalar, ndarray}, *optional*
Mean of the normal distribution (default: 0).
dev : {scalar, ndarray}, *optional*
Standard deviation of the normal distribution (default: 1).
var : {scalar, ndarray}, *optional*
Variance of the normal distribution (outranks the standard
deviation) (default: None).
Returns
-------
x : ndarray
Random field values (with correct dtype and shape).
Raises
------
ValueError
If the array dimension of `mean`, `dev` or `var` mismatch with
`shape`.
"""
size = np.prod(shape,axis=0,dtype=np.int,out=None)
if(issubclass(datatype,np.complexfloating)):
x = np.empty(size,dtype=datatype,order='C')
x.real = np.random.normal(loc=0,scale=np.sqrt(0.5),size=size)
x.imag = np.random.normal(loc=0,scale=np.sqrt(0.5),size=size)
else:
x = np.random.normal(loc=0,scale=1,size=size)
if(var is not None):
if(np.size(var)==1):
x *= np.sqrt(np.abs(var))
elif(np.size(var)==size):
x *= np.sqrt(np.absolute(var).flatten(order='C'))
else:
raise ValueError(about._errors.cstring("ERROR: dimension mismatch ( "+str(np.size(var))+" <> "+str(size)+" )."))
elif(dev is not None):
if(np.size(dev)==1):
x *= np.abs(dev)
elif(np.size(dev)==size):
x *= np.absolute(dev).flatten(order='C')
else:
raise ValueError(about._errors.cstring("ERROR: dimension mismatch ( "+str(np.size(dev))+" <> "+str(size)+" )."))
if(mean is not None):
if(np.size(mean)==1):
x += mean
elif(np.size(mean)==size):
x += np.array(mean).flatten(order='C')
else:
raise ValueError(about._errors.cstring("ERROR: dimension mismatch ( "+str(np.size(mean))+" <> "+str(size)+" )."))
return x.astype(datatype).reshape(shape,order='C')
##+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
@staticmethod
def uni(datatype=np.float64,shape=1,vmin=0,vmax=1):
"""
Generates random field values according to an uniform distribution
over [vmin,vmax[.
Parameters
----------
datatype : type, *optional*
Data type of the field values (default: np.float64).
shape : {integer, tuple, list, ndarray}, *optional*
Split up dimension of the space (default: 1).
vmin : {scalar, list, ndarray, field}, *optional*
Lower limit of the uniform distribution (default: 0).
vmax : {scalar, list, ndarray, field}, *optional*
Upper limit of the uniform distribution (default: 1).
Returns
-------
x : ndarray
Random field values (with correct dtype and shape).
"""
size = np.prod(shape,axis=0,dtype=np.int,out=None)
if(np.size(vmin)>1):
vmin = np.array(vmin).flatten(order='C')
if(np.size(vmax)>1):
vmax = np.array(vmax).flatten(order='C')
if(datatype in [np.complex64,np.complex128]):
x = np.empty(size,dtype=datatype,order='C')
x.real = (vmax-vmin)*np.random.random(size=size)+vmin
x.imag = (vmax-vmin)*np.random.random(size=size)+vmin
elif(datatype in [np.int8,np.int16,np.int32,np.int64]):
x = np.random.randint(min(vmin,vmax),high=max(vmin,vmax),size=size)
else:
x = (vmax-vmin)*np.random.random(size=size)+vmin
return x.astype(datatype).reshape(shape,order='C')
##+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
def __repr__(self):
return "<nifty_core.random>"
##-----------------------------------------------------------------------------
##=============================================================================
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
----------
para : {single object, list of objects}, *optional*
This is a freeform list of parameters that derivatives of the space
class can use (default: 0).
datatype : numpy.dtype, *optional*
Data type of the field values for a field defined on this space
(default: numpy.float64).
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 <http://www.arxiv.org/abs/1303.4945>`_
Attributes
----------
para : {single object, list of objects}
This is a freeform list of parameters that derivatives of the space class can use.
datatype : 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,para=0,datatype=None):
"""
Sets the attributes for a space class instance.
Parameters
----------
para : {single object, list of objects}, *optional*
This is a freeform list of parameters that derivatives of the
space class can use (default: 0).
datatype : numpy.dtype, *optional*
Data type of the field values for a field defined on this space
(default: numpy.float64).
Returns
-------
None
"""
if(np.isscalar(para)):
para = np.array([para],dtype=np.int)