nifty_rg.py 56.5 KB
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## NIFTY (Numerical Information Field Theory) has been developed at the
## Max-Planck-Institute for Astrophysics.
##
## Copyright (C) 2015 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/>.

"""
    ..                  __   ____   __
    ..                /__/ /   _/ /  /_
    ..      __ ___    __  /  /_  /   _/  __   __
    ..    /   _   | /  / /   _/ /  /   /  / /  /
    ..   /  / /  / /  / /  /   /  /_  /  /_/  /
    ..  /__/ /__/ /__/ /__/    \___/  \___   /  rg
    ..                               /______/

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    NIFTY submodule for regular Cartesian grids.
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"""
from __future__ import division
#from nifty import *
import os
import numpy as np
import pylab as pl
from matplotlib.colors import LogNorm as ln
from matplotlib.ticker import LogFormatter as lf
from nifty.nifty_core import about,                                          \
                             random,                                         \
                             space,                                          \
                             field
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import nifty.nifty_mpi_data
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import nifty.smoothing as gs
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import powerspectrum as gp
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'''
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try:
    import gfft as gf
except(ImportError):
    about.infos.cprint('INFO: "plain" gfft version 0.1.0')
    import gfft_rg as gf
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'''
import fft_rg
  
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##-----------------------------------------------------------------------------

class rg_space(space):
    """
        ..      _____   _______
        ..    /   __/ /   _   /
        ..   /  /    /  /_/  /
        ..  /__/     \____  /  space class
        ..          /______/

        NIFTY subclass for spaces of regular Cartesian grids.

        Parameters
        ----------
        num : {int, numpy.ndarray}
            Number of gridpoints or numbers of gridpoints along each axis.
        naxes : int, *optional*
            Number of axes (default: None).
        zerocenter : {bool, numpy.ndarray}, *optional*
            Whether the Fourier zero-mode is located in the center of the grid
            (or the center of each axis speparately) or not (default: True).
        hermitian : bool, *optional*
            Whether the fields living in the space follow hermitian symmetry or
            not (default: True).
        purelyreal : bool, *optional*
            Whether the field values are purely real (default: True).
        dist : {float, numpy.ndarray}, *optional*
            Distance between two grid points along each axis (default: None).
        fourier : bool, *optional*
            Whether the space represents a Fourier or a position grid
            (default: False).

        Notes
        -----
        Only even numbers of grid points per axis are supported.
        The basis transformations between position `x` and Fourier mode `k`
        rely on (inverse) fast Fourier transformations using the
        :math:`exp(2 \pi i k^\dagger x)`-formulation.

        Attributes
        ----------
        para : numpy.ndarray
            One-dimensional array containing information on the axes of the
            space in the following form: The first entries give the grid-points
            along each axis in reverse order; the next entry is 0 if the
            fields defined on the space are purely real-valued, 1 if they are
            hermitian and complex, and 2 if they are not hermitian, but
            complex-valued; the last entries hold the information on whether
            the axes are centered on zero or not, containing a one for each
            zero-centered axis and a zero for each other one, in reverse order.
        datatype : numpy.dtype
            Data type of the field values for a field defined on this space,
            either ``numpy.float64`` or ``numpy.complex128``.
        discrete : bool
            Whether or not the underlying space is discrete, always ``False``
            for regular grids.
        vol : numpy.ndarray
            One-dimensional array containing the distances between two grid
            points along each axis, in reverse order. By default, the total
            length of each axis is assumed to be one.
        fourier : bool
            Whether or not the grid represents a Fourier basis.
    """
    epsilon = 0.0001 ## relative precision for comparisons

    def __init__(self,num,naxes=None,zerocenter=True,hermitian=True,purelyreal=True,dist=None,fourier=False):
        """
            Sets the attributes for an rg_space class instance.

            Parameters
            ----------
            num : {int, numpy.ndarray}
                Number of gridpoints or numbers of gridpoints along each axis.
            naxes : int, *optional*
                Number of axes (default: None).
            zerocenter : {bool, numpy.ndarray}, *optional*
                Whether the Fourier zero-mode is located in the center of the
                grid (or the center of each axis speparately) or not
                (default: True).
            hermitian : bool, *optional*
                Whether the fields living in the space follow hermitian
                symmetry or not (default: True).
            purelyreal : bool, *optional*
                Whether the field values are purely real (default: True).
            dist : {float, numpy.ndarray}, *optional*
                Distance between two grid points along each axis
                (default: None).
            fourier : bool, *optional*
                Whether the space represents a Fourier or a position grid
                (default: False).

            Returns
            -------
            None
        """
        ## check parameters
        para = np.array([],dtype=np.int)
        if(np.isscalar(num)):
            num = np.array([num],dtype=np.int)
        else:
            num = np.array(num,dtype=np.int)
        if(np.any(num%2)): ## module restriction
            raise ValueError(about._errors.cstring("ERROR: unsupported odd number of grid points."))
        if(naxes is None):
            naxes = np.size(num)
        elif(np.size(num)==1):
            num = num*np.ones(naxes,dtype=np.int,order='C')
        elif(np.size(num)!=naxes):
            raise ValueError(about._errors.cstring("ERROR: size mismatch ( "+str(np.size(num))+" <> "+str(naxes)+" )."))
        para = np.append(para,num[::-1],axis=None)
        para = np.append(para,2-(bool(hermitian) or bool(purelyreal))-bool(purelyreal),axis=None) ## {0,1,2}
        if(np.isscalar(zerocenter)):
            zerocenter = bool(zerocenter)*np.ones(naxes,dtype=np.int,order='C')
        else:
            zerocenter = np.array(zerocenter,dtype=np.bool)
            if(np.size(zerocenter)==1):
                zerocenter = zerocenter*np.ones(naxes,dtype=np.int,order='C')
            elif(np.size(zerocenter)!=naxes):
                raise ValueError(about._errors.cstring("ERROR: size mismatch ( "+str(np.size(zerocenter))+" <> "+str(naxes)+" )."))
        para = np.append(para,zerocenter[::-1]*-1,axis=None) ## -1 XOR 0 (centered XOR not)

        self.para = para

        ## set data type
        if(not self.para[naxes]):
            self.datatype = np.float64
        else:
            self.datatype = np.complex128

        self.discrete = False

        ## set volume
        if(dist is None):
            dist = 1/num.astype(self.datatype)
        elif(np.isscalar(dist)):
            dist = self.datatype(dist)*np.ones(naxes,dtype=self.datatype,order='C')
        else:
            dist = np.array(dist,dtype=self.datatype)
            if(np.size(dist)==1):
                dist = dist*np.ones(naxes,dtype=self.datatype,order='C')
            if(np.size(dist)!=naxes):
                raise ValueError(about._errors.cstring("ERROR: size mismatch ( "+str(np.size(dist))+" <> "+str(naxes)+" )."))
        if(np.any(dist<=0)):
            raise ValueError(about._errors.cstring("ERROR: nonpositive distance(s)."))
        self.vol = np.real(dist)[::-1]

        self.fourier = bool(fourier)
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        ## Initializes the fast-fourier-transform machine, which will be used 
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        ## to transform the space
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        self.fft_machine = fft_rg.fft_factory()
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    ##+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

    def naxes(self):
        """
            Returns the number of axes of the grid.

            Returns
            -------
            naxes : int
                Number of axes of the regular grid.
        """
        return (np.size(self.para)-1)//2

    def zerocenter(self):
        """
            Returns information on the centering of the axes.

            Returns
            -------
            zerocenter : numpy.ndarray
                Whether the grid is centered on zero for each axis or not.
        """
        return self.para[-(np.size(self.para)-1)//2:][::-1].astype(np.bool)

    def dist(self):
        """
            Returns the distances between grid points along each axis.

            Returns
            -------
            dist : np.ndarray
                Distances between two grid points on each axis.
        """
        return self.vol[::-1]

    def dim(self,split=False):
        """
            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 along each axis, or their product (default: False).

            Returns
            -------
            dim : {int, numpy.ndarray}
                Dimension(s) of the space. If ``split==True``, a
                one-dimensional array with an entry for each axis is returned.
        """
        ## dim = product(n)
        if(split):
            return self.para[:(np.size(self.para)-1)//2]
        else:
            return np.prod(self.para[:(np.size(self.para)-1)//2],axis=0,dtype=None,out=None)

    ##+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

    def dof(self):
        """
            Computes the number of degrees of freedom of the space, i.e.\  the
            number of grid points multiplied with one or two, depending on
            complex-valuedness and hermitian symmetry of the fields.

            Returns
            -------
            dof : int
                Number of degrees of freedom of the space.
        """
        ## dof ~ dim
        if(self.para[(np.size(self.para)-1)//2]<2):
            return np.prod(self.para[:(np.size(self.para)-1)//2],axis=0,dtype=None,out=None)
        else:
            return 2*np.prod(self.para[:(np.size(self.para)-1)//2],axis=0,dtype=None,out=None)

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    ##+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

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    def enforce_power(self,spec,size=None,**kwargs):
        """
            Provides a valid power spectrum array from a given object.

            Parameters
            ----------
            spec : {float, 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).

        """
        if(size is None)or(callable(spec)):
            ## explicit kindex
            kindex = kwargs.get("kindex",None)
            if(kindex is None):
                ## quick kindex
                if(self.fourier)and(not hasattr(self,"power_indices"))and(len(kwargs)==0):
                    kindex = gp.nklength(gp.nkdict_fast(self.para[:(np.size(self.para)-1)//2],self.vol,fourier=True))
                ## implicit kindex
                else:
                    try:
                        self.set_power_indices(**kwargs)
                    except:
                        codomain = kwargs.get("codomain",self.get_codomain())
                        codomain.set_power_indices(**kwargs)
                        kindex = codomain.power_indices.get("kindex")
                    else:
                        kindex = self.power_indices.get("kindex")
            size = len(kindex)

        if(isinstance(spec,field)):
            spec = spec.val.astype(self.datatype)
        elif(callable(spec)):
            try:
                spec = np.array(spec(kindex),dtype=self.datatype)
            except:
                raise TypeError(about._errors.cstring("ERROR: invalid power spectra function.")) ## exception in ``spec(kindex)``
        elif(np.isscalar(spec)):
            spec = np.array([spec],dtype=self.datatype)
        else:
            spec = np.array(spec,dtype=self.datatype)

        ## drop imaginary part
        spec = np.real(spec)
        ## 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)."))
        elif(np.any(spec==0)):
            about.warnings.cprint("WARNING: nonpositive value(s).")

        ## extend
        if(np.size(spec)==1):
            spec = spec*np.ones(size,dtype=spec.dtype,order='C')
        ## size check
        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 set_power_indices(self,**kwargs):
        """
            Sets the (un)indexing objects for spectral indexing internally.

            Parameters
            ----------
            log : bool
                Flag specifying if the 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
                Number of used 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}
                User specific inner boundaries of the bins, which are preferred
                over the above parameters; by default no binning is done
                (default: None).

            Returns
            -------
            None

            See Also
            --------
            get_power_indices

            Raises
            ------
            AttributeError
                If ``self.fourier == False``.
            ValueError
                If the binning leaves one or more bins empty.

        """
        if(not self.fourier):
            raise AttributeError(about._errors.cstring("ERROR: power spectra indexing ill-defined."))
        ## check storage
        if(hasattr(self,"power_indices")):
            config = self.power_indices.get("config")
            ## check configuration
            redo = False
            if(config.get("log")!=kwargs.get("log",config.get("log"))):
                config["log"] = kwargs.get("log")
                redo = True
            if(config.get("nbin")!=kwargs.get("nbin",config.get("nbin"))):
                config["nbin"] = kwargs.get("nbin")
                redo = True
            if(np.any(config.get("binbounds")!=kwargs.get("binbounds",config.get("binbounds")))):
                config["binbounds"] = kwargs.get("binbounds")
                redo = True
            if(not redo):
                return None
        else:
            config = {"binbounds":kwargs.get("binbounds",None),"log":kwargs.get("log",None),"nbin":kwargs.get("nbin",None)}
        ## power indices
        about.infos.cflush("INFO: setting power indices ...")
        pindex,kindex,rho = gp.get_power_indices2(self.para[:(np.size(self.para)-1)//2],self.vol,self.para[-((np.size(self.para)-1)//2):].astype(np.bool),fourier=True)
        ## bin if ...
        if(config.get("log") is not None)or(config.get("nbin") is not None)or(config.get("binbounds") is not None):
            pindex,kindex,rho = gp.bin_power_indices(pindex,kindex,rho,**config)
            ## check binning
            if(np.any(rho==0)):
                raise ValueError(about._errors.cstring("ERROR: empty bin(s).")) ## binning too fine
        ## power undex
        pundex = np.unique(pindex,return_index=True,return_inverse=False)[1]
        ## storage
        self.power_indices = {"config":config,"kindex":kindex,"pindex":pindex,"pundex":pundex,"rho":rho} ## alphabetical
        about.infos.cprint(" done.")
        return None

    ##+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

    def enforce_values(self,x,extend=True):
        """
            Computes valid field values from a given object, taking care of
            data types, shape, and symmetry.

            Parameters
            ----------
            x : {float, numpy.ndarray, nifty.field}
                Object to be transformed into an array of valid field values.

            Returns
            -------
            x : numpy.ndarray
                Array containing the valid field values.

            Other parameters
            ----------------
            extend : bool, *optional*
                Whether a scalar is extented to a constant array or not
                (default: True).
        """
        if(isinstance(x,field)):
            if(self==x.domain):
                if(self.datatype is not x.domain.datatype):
                    raise TypeError(about._errors.cstring("ERROR: inequal data types ( '"+str(np.result_type(self.datatype))+"' <> '"+str(np.result_type(x.domain.datatype))+"' )."))
                else:
                    x = np.copy(x.val)
            else:
                raise ValueError(about._errors.cstring("ERROR: inequal domains."))
        else:
            if(np.size(x)==1):
                if(extend):
                    x = self.datatype(x)*np.ones(self.dim(split=True),dtype=self.datatype,order='C')
                else:
                    if(np.isscalar(x)):
                        x = np.array([x],dtype=self.datatype)
                    else:
                        x = np.array(x,dtype=self.datatype)
            else:
                x = self.enforce_shape(np.array(x,dtype=self.datatype))

        ## hermitianize if ...
        if(about.hermitianize.status)and(np.size(x)!=1)and(self.para[(np.size(self.para)-1)//2]==1):
            x = gp.nhermitianize_fast(x,self.para[-((np.size(self.para)-1)//2):].astype(np.bool),special=False)

        ## check finiteness
        if(not np.all(np.isfinite(x))):
            about.warnings.cprint("WARNING: infinite value(s).")

        return x

    ##+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

    def get_random_values(self,**kwargs):
        """
            Generates random field values according to the specifications given
            by the parameters, taking into account possible complex-valuedness
            and hermitian symmetry.

            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.rg_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.arguments(self,**kwargs)

        if(arg is None):
            return np.zeros(self.dim(split=True),dtype=self.datatype,order='C')

        elif(arg[0]=="pm1"):
            if(about.hermitianize.status)and(self.para[(np.size(self.para)-1)//2]==1):
                return gp.random_hermitian_pm1(self.datatype,self.para[-((np.size(self.para)-1)//2):].astype(np.bool),self.dim(split=True)) ## special case
            else:
                x = random.pm1(datatype=self.datatype,shape=self.dim(split=True))

        elif(arg[0]=="gau"):
            x = random.gau(datatype=self.datatype,shape=self.dim(split=True),mean=None,dev=arg[2],var=arg[3])

        elif(arg[0]=="syn"):
            naxes = (np.size(self.para)-1)//2
            x = gp.draw_vector_nd(self.para[:naxes],self.vol,arg[1],symtype=self.para[naxes],fourier=self.fourier,zerocentered=self.para[-naxes:].astype(np.bool),kpack=arg[2])
            ## correct for 'ifft'
            if(not self.fourier):
                x = self.calc_weight(x,power=-1)
            return x

        elif(arg[0]=="uni"):
            x = random.uni(datatype=self.datatype,shape=self.dim(split=True),vmin=arg[1],vmax=arg[2])

        else:
            raise KeyError(about._errors.cstring("ERROR: unsupported random key '"+str(arg[0])+"'."))

        ## hermitianize if ...
        if(about.hermitianize.status)and(self.para[(np.size(self.para)-1)//2]==1):
            x = gp.nhermitianize_fast(x,self.para[-((np.size(self.para)-1)//2):].astype(np.bool),special=(arg[0] in ["gau","pm1"]))

        return x

    ##+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

    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(not isinstance(codomain,space)):
            raise TypeError(about._errors.cstring("ERROR: invalid input."))

        elif(isinstance(codomain,rg_space)):
            ##                       naxes==naxes
            if((np.size(codomain.para)-1)//2==(np.size(self.para)-1)//2):
                naxes = (np.size(self.para)-1)//2
                ##                            num'==num
                if(np.all(codomain.para[:naxes]==self.para[:naxes])):
                    ##                 typ'==typ             ==2
                    if(codomain.para[naxes]==self.para[naxes]==2):
                        ##                                         dist'~=1/(num*dist)
                        if(np.all(np.absolute(self.para[:naxes]*self.vol*codomain.vol-1)<self.epsilon)):
                            return True
                        ##           fourier'==fourier
                        elif(codomain.fourier==self.fourier):
                            ##                           dist'~=dist
                            if(np.all(np.absolute(codomain.vol/self.vol-1)<self.epsilon)):
                                return True
                            else:
                                about.warnings.cprint("WARNING: unrecommended codomain.")
                    ##   2!=                typ'!=typ             !=2                                             dist'~=1/(num*dist)
                    elif(2!=codomain.para[naxes]!=self.para[naxes]!=2)and(np.all(np.absolute(self.para[:naxes]*self.vol*codomain.vol-1)<self.epsilon)):
                        return True
                    ##                   typ'==typ             !=2
                    elif(codomain.para[naxes]==self.para[naxes]!=2)and(codomain.fourier==self.fourier):
                        ##                           dist'~=dist
                        if(np.all(np.absolute(codomain.vol/self.vol-1)<self.epsilon)):
                            return True
                        else:
                            about.warnings.cprint("WARNING: unrecommended codomain.")

        return False

    ##+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

    def get_codomain(self,coname=None,cozerocenter=None,**kwargs):
        """
            Generates a compatible codomain to which transformations are
            reasonable, i.e.\  either a shifted grid or a Fourier conjugate
            grid.

            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).

            Returns
            -------
            codomain : nifty.rg_space
                A compatible codomain.

            Notes
            -----
            Possible arguments for `coname` are ``'f'`` in which case the
            codomain arises from a Fourier transformation, ``'i'`` in which case
            it arises from an inverse Fourier transformation, and ``'?'`` in
            which case it arises from a simple shift. If no `coname` is given,
            the Fourier conjugate grid is produced.
        """
        naxes = (np.size(self.para)-1)//2
        if(cozerocenter is None):
            cozerocenter = self.para[-naxes:][::-1]
        elif(np.isscalar(cozerocenter)):
            cozerocenter = bool(cozerocenter)
        else:
            cozerocenter = np.array(cozerocenter,dtype=np.bool)
            if(np.size(cozerocenter)==1):
                cozerocenter = np.asscalar(cozerocenter)
            elif(np.size(cozerocenter)!=naxes):
                raise ValueError(about._errors.cstring("ERROR: size mismatch ( "+str(np.size(cozerocenter))+" <> "+str(naxes)+" )."))

        if(coname is None):
            return rg_space(self.para[:naxes][::-1],naxes=naxes,zerocenter=cozerocenter,hermitian=bool(self.para[naxes]<2),purelyreal=bool(self.para[naxes]==1),dist=1/(self.para[:naxes]*self.vol)[::-1],fourier=bool(not self.fourier)) ## dist',fourier' = 1/(num*dist),NOT fourier

        elif(coname[0]=='f'):
            return rg_space(self.para[:naxes][::-1],naxes=naxes,zerocenter=cozerocenter,hermitian=bool(self.para[naxes]<2),purelyreal=bool(self.para[naxes]==1),dist=1/(self.para[:naxes]*self.vol)[::-1],fourier=True) ## dist',fourier' = 1/(num*dist),True

        elif(coname[0]=='i'):
            return rg_space(self.para[:naxes][::-1],naxes=naxes,zerocenter=cozerocenter,hermitian=bool(self.para[naxes]<2),purelyreal=bool(self.para[naxes]==1),dist=1/(self.para[:naxes]*self.vol)[::-1],fourier=False) ## dist',fourier' = 1/(num*dist),False

        else:
            return rg_space(self.para[:naxes][::-1],naxes=naxes,zerocenter=cozerocenter,hermitian=bool(self.para[naxes]<2),purelyreal=bool(not self.para[naxes]),dist=self.vol[::-1],fourier=self.fourier) ## dist',fourier' = dist,fourier

    ##+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

    def get_meta_volume(self,total=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(total):
            return self.dim(split=False)*np.prod(self.vol,axis=0,dtype=None,out=None)
        else:
            mol = np.ones(self.dim(split=True),dtype=self.vol.dtype,order='C')
            return self.calc_weight(mol,power=1)

    ##+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

    def calc_weight(self,x,power=1):
        """
            Weights a given array with the pixel 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.
        """
        x = self.enforce_shape(np.array(x,dtype=self.datatype))
        ## weight
        return x*np.prod(self.vol,axis=0,dtype=None,out=None)**power

    ##+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

    def calc_dot(self,x,y):
        """
            Computes the discrete inner product of two given arrays.

            Parameters
            ----------
            x : numpy.ndarray
                First array
            y : numpy.ndarray
                Second array

            Returns
            -------
            dot : scalar
                Inner product of the two arrays.
        """
        x = self.enforce_shape(np.array(x,dtype=self.datatype))
        y = self.enforce_shape(np.array(y,dtype=self.datatype))
        ## inner product
        dot = np.dot(np.conjugate(x.flatten(order='C')),y.flatten(order='C'),out=None)
        if(np.isreal(dot)):
            return np.asscalar(np.real(dot))
        elif(self.para[(np.size(self.para)-1)//2]!=2):
                ## check imaginary part
                if(np.absolute(dot.imag)>self.epsilon**2*np.absolute(dot.real)):
                    about.warnings.cprint("WARNING: discarding considerable imaginary part.")
                return np.asscalar(np.real(dot))
        else:
            return 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.rg_space, *optional*
                Target space to which the transformation shall map
                (default: None).

            Returns
            -------
            Tx : numpy.ndarray
                Transformed array
        """
        x = self.enforce_shape(np.array(x,dtype=self.datatype))

        if(codomain is None):
            return x ## T == id

        ## mandatory(!) codomain check
        if(isinstance(codomain,rg_space))and(self.check_codomain(codomain)):
            naxes = (np.size(self.para)-1)//2
            ## select machine
            if(np.all(np.absolute(self.para[:naxes]*self.vol*codomain.vol-1)<self.epsilon)):
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                ## Use the codomain information here only for the rescaling. The direction
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                ## of transformation is infered from the fourier attribute of the 
                ## supplied space
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                if(codomain.fourier):
                    ## correct for 'fft'
                    x = self.calc_weight(x,power=1)
                else:
                    ## correct for 'ifft'
                    x = self.calc_weight(x,power=1)
                    x *= self.dim(split=False)
            else:
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                ## TODO: Is this error correct?                
                raise ValueError(about._errors.cstring("ERROR: unsupported transformation."))                
                #ftmachine = "none"
            
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            ## transform
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            Tx = self.fft_machine.transform(x,self,codomain,**kwargs)            
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            ## check complexity
            if(not codomain.para[naxes]): ## purely real
                ## check imaginary part
                if(np.any(Tx.imag!=0))and(np.dot(Tx.imag.flatten(order='C'),Tx.imag.flatten(order='C'),out=None)>self.epsilon**2*np.dot(Tx.real.flatten(order='C'),Tx.real.flatten(order='C'),out=None)):
                    about.warnings.cprint("WARNING: discarding considerable imaginary part.")
                Tx = np.real(Tx)

        else:
            raise ValueError(about._errors.cstring("ERROR: unsupported transformation."))

        return Tx.astype(codomain.datatype)

    ##+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

    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; for testing: a sigma of -1 will be
                reset to a reasonable value (default: 0).

            Returns
            -------
            Gx : numpy.ndarray
                Smoothed array.
        """
        x = self.enforce_shape(np.array(x,dtype=self.datatype))
        naxes = (np.size(self.para)-1)//2

        ## check sigma
        if(sigma==0):
            return x
        elif(sigma==-1):
            about.infos.cprint("INFO: invalid sigma reset.")
            if(self.fourier):
                sigma = 1.5/np.min(self.para[:naxes]*self.vol) ## sqrt(2)*max(dist)
            else:
                sigma = 1.5*np.max(self.vol) ## sqrt(2)*max(dist)
        elif(sigma<0):
            raise ValueError(about._errors.cstring("ERROR: invalid sigma."))
        ## smooth
        Gx = gs.smooth_field(x,self.fourier,self.para[-naxes:].astype(np.bool).tolist(),bool(self.para[naxes]==1),self.vol,smooth_length=sigma)
        ## check complexity
        if(not self.para[naxes]): ## purely real
            ## check imaginary part
            if(np.any(Gx.imag!=0))and(np.dot(Gx.imag.flatten(order='C'),Gx.imag.flatten(order='C'),out=None)>self.epsilon**2*np.dot(Gx.real.flatten(order='C'),Gx.real.flatten(order='C'),out=None)):
                about.warnings.cprint("WARNING: discarding considerable imaginary part.")
            Gx = np.real(Gx)
        return Gx

    ##+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

    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).

        """
        x = self.enforce_shape(np.array(x,dtype=self.datatype))
        ## correct for 'fft'
        if(not self.fourier):
            x = self.calc_weight(x,power=1)
        ## explicit power indices
        pindex,kindex,rho = kwargs.get("pindex",None),kwargs.get("kindex",None),kwargs.get("rho",None)
        ## implicit power indices
        if(pindex is None)or(kindex is None)or(rho is None):
            try:
                self.set_power_indices(**kwargs)
            except:
                codomain = kwargs.get("codomain",self.get_codomain())
                codomain.set_power_indices(**kwargs)
                pindex,kindex,rho = codomain.power_indices.get("pindex"),codomain.power_indices.get("kindex"),codomain.power_indices.get("rho")
            else:
                pindex,kindex,rho = self.power_indices.get("pindex"),self.power_indices.get("kindex"),self.power_indices.get("rho")
        ## power spectrum
        return gp.calc_ps_fast(x,self.para[:(np.size(self.para)-1)//2],self.vol,self.para[-((np.size(self.para)-1)//2):].astype(np.bool),fourier=self.fourier,pindex=pindex,kindex=kindex,rho=rho)

    ##+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

    def get_plot(self,x,title="",vmin=None,vmax=None,power=None,unit="",norm=None,cmap=None,cbar=True,other=None,legend=False,mono=True,**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).

        """
        if(not pl.isinteractive())and(not bool(kwargs.get("save",False))):
            about.warnings.cprint("WARNING: interactive mode off.")

        naxes = (np.size(self.para)-1)//2
        if(power is None):
            power = bool(self.para[naxes])

        if(power):
            x = self.calc_power(x,**kwargs)

            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])

            ## explicit kindex
            xaxes = kwargs.get("kindex",None)
            ## implicit kindex
            if(xaxes is None):
                try:
                    self.set_power_indices(**kwargs)
                except:
                    codomain = kwargs.get("codomain",self.get_codomain())
                    codomain.set_power_indices(**kwargs)
                    xaxes = codomain.power_indices.get("kindex")
                else:
                    xaxes = self.power_indices.get("kindex")

            if(norm is None)or(not isinstance(norm,int)):
                norm = naxes
            if(vmin is None):
                vmin = np.min(x[:mono].tolist()+(xaxes**norm*x)[1:].tolist(),axis=None,out=None)
            if(vmax is None):
                vmax = np.max(x[:mono].tolist()+(xaxes**norm*x)[1:].tolist(),axis=None,out=None)
            ax0.loglog(xaxes[1:],(xaxes**norm*x)[1:],color=[0.0,0.5,0.0],label="graph 0",linestyle='-',linewidth=2.0,zorder=1)
            if(mono):
                ax0.scatter(0.5*(xaxes[1]+xaxes[2]),x[0],s=20,color=[0.0,0.5,0.0],marker='o',cmap=None,norm=None,vmin=None,vmax=None,alpha=None,linewidths=None,verts=None,zorder=1)

            if(other is not None):
                if(isinstance(other,tuple)):
                    other = list(other)
                    for ii in xrange(len(other)):
                        if(isinstance(other[ii],field)):
                            other[ii] = other[ii].power(**kwargs)
                        else:
                            other[ii] = self.enforce_power(other[ii],size=np.size(xaxes),kindex=xaxes)
                elif(isinstance(other,field)):
                    other = [other.power(**kwargs)]
                else:
                    other = [self.enforce_power(other,size=np.size(xaxes),kindex=xaxes)]
                imax = max(1,len(other)-1)
                for ii in xrange(len(other)):
                    ax0.loglog(xaxes[1:],(xaxes**norm*other[ii])[1:],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)],label="graph "+str(ii+1),linestyle='-',linewidth=1.0,zorder=-ii)
                    if(mono):
                        ax0.scatter(0.5*(xaxes[1]+xaxes[2]),other[ii][0],s=20,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',cmap=None,norm=None,vmin=None,vmax=None,alpha=None,linewidths=None,verts=None,zorder=-ii)
                if(legend):
                    ax0.legend()

            ax0.set_xlim(xaxes[1],xaxes[-1])
            ax0.set_xlabel(r"$|k|$")
            ax0.set_ylim(vmin,vmax)
            ax0.set_ylabel(r"$|k|^{%i} P_k$"%norm)
            ax0.set_title(title)

        else:
            x = self.enforce_shape(np.array(x))

            if(naxes==1):
                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.int)+self.para[2]*(self.para[0]//2))*self.vol
                if(vmin is None):
                    if(np.iscomplexobj(x)):
                        vmin = min(np.min(np.absolute(x),axis=None,out=None),np.min(np.real(x),axis=None,out=None),np.min(np.imag(x),axis=None,out=None))
                    else:
                        vmin = np.min(x,axis=None,out=None)
                if(vmax is None):
                    if(np.iscomplexobj(x)):
                        vmax = max(np.max(np.absolute(x),axis=None,out=None),np.max(np.real(x),axis=None,out=None),np.max(np.imag(x),axis=None,out=None))
                    else:
                        vmax = np.max(x,axis=None,out=None)
                if(norm=="log"):
                    ax0graph = ax0.semilogy
                    if(vmin<=0):
                        raise ValueError(about._errors.cstring("ERROR: nonpositive value(s)."))
                else:
                    ax0graph = ax0.plot

                if(np.iscomplexobj(x)):
                    ax0graph(xaxes,np.absolute(x),color=[0.0,0.5,0.0],label="graph (absolute)",linestyle='-',linewidth=2.0,zorder=1)
                    ax0graph(xaxes,np.real(x),color=[0.0,0.5,0.0],label="graph (real part)",linestyle="--",linewidth=1.0,zorder=0)
                    ax0graph(xaxes,np.imag(x),color=[0.0,0.5,0.0],label="graph (imaginary part)",linestyle=':',linewidth=1.0,zorder=0)
                    if(legend):
                        ax0.legend()
                elif(other is not None):
                    ax0graph(xaxes,x,color=[0.0,0.5,0.0],label="graph 0",linestyle='-',linewidth=2.0,zorder=1)
                    if(isinstance(other,tuple)):
                        other = [self.enforce_values(xx,extend=True) for xx in other]
                    else:
                        other = [self.enforce_values(other,extend=True)]
                    imax = max(1,len(other)-1)
                    for ii in xrange(len(other)):
                        ax0graph(xaxes,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)],label="graph "+str(ii+1),linestyle='-',linewidth=1.0,zorder=-ii)
                    if("error" in kwargs):
                        error = self.enforce_values(np.absolute(kwargs.get("error")),extend=True)
                        ax0.fill_between(xaxes,x-error,x+error,color=[0.8,0.8,0.8],label="error 0",zorder=-len(other))
                    if(legend):
                        ax0.legend()
                else:
                    ax0graph(xaxes,x,color=[0.0,0.5,0.0],label="graph 0",linestyle='-',linewidth=2.0,zorder=1)
                    if("error" in kwargs):
                        error = self.enforce_values(np.absolute(kwargs.get("error")),extend=True)
                        ax0.fill_between(xaxes,x-error,x+error,color=[0.8,0.8,0.8],label="error 0",zorder=0)

                ax0.set_xlim(xaxes[0],xaxes[-1])
                ax0.set_xlabel("coordinate")
                ax0.set_ylim(vmin,vmax)
                if(unit):
                    unit = " ["+unit+"]"
                ax0.set_ylabel("values"+unit)
                ax0.set_title(title)

            elif(naxes==2):
                if(np.iscomplexobj(x)):
                    about.infos.cprint("INFO: absolute values and phases are plotted.")
                    if(title):
                        title += " "
                    if(bool(kwargs.get("save",False))):
                        save_ = os.path.splitext(os.path.basename(str(kwargs.get("save"))))
                        kwargs.update(save=save_[0]+"_absolute"+save_[1])
                    self.get_plot(np.absolute(x),title=title+"(absolute)",vmin=vmin,vmax=vmax,power=False,unit=unit,norm=norm,cmap=cmap,cbar=cbar,other=None,legend=False,**kwargs)
#                    self.get_plot(np.real(x),title=title+"(real part)",vmin=vmin,vmax=vmax,power=False,unit=unit,norm=norm,cmap=cmap,cbar=cbar,other=None,legend=False,**kwargs)
#                    self.get_plot(np.imag(x),title=title+"(imaginary part)",vmin=vmin,vmax=vmax,power=False,unit=unit,norm=norm,cmap=cmap,cbar=cbar,other=None,legend=False,**kwargs)
                    if(unit):
                        unit = "rad"
                    if(cmap is None):
                        cmap = pl.cm.hsv_r
                    if(bool(kwargs.get("save",False))):
                        kwargs.update(save=save_[0]+"_phase"+save_[1])
                    self.get_plot(np.angle(x,deg=False),title=title+"(phase)",vmin=-3.1416,vmax=3.1416,power=False,unit=unit,norm=None,cmap=cmap,cbar=cbar,other=None,legend=False,**kwargs) ## values in [-pi,pi]
                    return None ## leave method
                else:
                    if(vmin is None):
                        vmin = np.min(x,axis=None,out=None)
                    if(vmax is None):
                        vmax = np.max(x,axis=None,out=None)
                    if(norm=="log")and(vmin<=0):
                        raise ValueError(about._errors.cstring("ERROR: nonpositive value(s)."))

                    s_ = np.array([self.para[1]*self.vol[1]/np.max(self.para[:naxes]*self.vol,axis=None,out=None),self.para[0]*self.vol[0]/np.max(self.para[:naxes]*self.vol,axis=None,out=None)*(1.0+0.159*bool(cbar))])
                    fig = pl.figure(num=None,figsize=(6.4*s_[0],6.4*s_[1]),dpi=None,facecolor="none",edgecolor="none",frameon=False,FigureClass=pl.Figure)
                    ax0 = fig.add_axes([0.06/s_[0],0.06/s_[1],1.0-0.12/s_[0],1.0-0.12/s_[1]])

                    xaxes = (np.arange(self.para[1]+1,dtype=np.int)-0.5+self.para[4]*(self.para[1]//2))*self.vol[1]
                    yaxes = (np.arange(self.para[0]+1,dtype=np.int)-0.5+self.para[3]*(self.para[0]//2))*self.vol[0]
                    if(norm=="log"):
                        n_ = ln(vmin=vmin,vmax=vmax)
                    else:
                        n_ = None
                    sub = ax0.pcolormesh(xaxes,yaxes,x,cmap=cmap,norm=n_,vmin=vmin,vmax=vmax)
                    ax0.set_xlim(xaxes[0],xaxes[-1])
                    ax0.set_xticks([0],minor=False)
                    ax0.set_ylim(yaxes[0],yaxes[-1])
                    ax0.set_yticks([0],minor=False)
                    ax0.set_aspect("equal")
                    if(cbar):
                        if(norm=="log"):
                            f_ = lf(10,labelOnlyBase=False)
                            b_ = sub.norm.inverse(np.linspace(0,1,sub.cmap.N+1))
                            v_ = np.linspace(sub.norm.vmin,sub.norm.vmax,sub.cmap.N)
                        else:
                            f_ = None
                            b_ = None
                            v_ = None
                        cb0 = fig.colorbar(sub,ax=ax0,orientation="horizontal",fraction=0.1,pad=0.05,shrink=0.75,aspect=20,ticks=[vmin,vmax],format=f_,drawedges=False,boundaries=b_,values=v_)
                        cb0.ax.text(0.5,-1.0,unit,fontdict=None,withdash=False,transform=cb0.ax.transAxes,horizontalalignment="center",verticalalignment="center")
                    ax0.set_title(title)

            else:
                raise ValueError(about._errors.cstring("ERROR: unsupported number of axes ( "+str(naxes)+" > 2 )."))

        if(bool(kwargs.get("save",False))):
            fig.savefig(str(kwargs.get("save")),dpi=None,facecolor="none",edgecolor="none",orientation="portrait",papertype=None,format=None,transparent=False,bbox_inches=None,pad_inches=0.1)
            pl.close(fig)
        else:
            fig.canvas.draw()

    ##+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

    def __repr__(self):
        return "<nifty_rg.rg_space>"

    def __str__(self):
        naxes = (np.size(self.para)-1)//2
        num = self.para[:naxes][::-1].tolist()
        zerocenter = self.para[-naxes:][::-1].astype(np.bool).tolist()
        dist = self.vol[::-1].tolist()
        return "nifty_rg.rg_space instance\n- num        = "+str(num)+"\n- naxes      = "+str(naxes)+"\n- hermitian  = "+str(bool(self.para[naxes]<2))+"\n- purelyreal = "+str(bool(not self.para[naxes]))+"\n- zerocenter = "+str(zerocenter)+"\n- dist       = "+str(dist)+"\n- fourier    = "+str(self.fourier)
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    ##+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

    ## __identiftier__ returns an object which contains all information needed 
    ## to uniquely idetnify a space. It returns a (immutable) tuple which therefore
    ## can be compored. 
    ## The rg_space version of __identifier__ filters out the vars-information
    ## which is describing the rg_space's structure
    def __identifier__(self):
        ## Extract the identifying parts from the vars(self) dict.
        temp = [(ii[0],((lambda x: tuple(x) if isinstance(x,np.ndarray) else x)(ii[1]))) for ii in vars(self).iteritems() if ii[0] not in ["fft_machine","power_indices"]]
        ## Return the sorted identifiers as a tuple.
        return tuple(sorted(temp))
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##-----------------------------------------------------------------------------