hp_space.py 12.9 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/>.

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

    NIFTY submodule for grids on the two-sphere.

"""
from __future__ import division

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import itertools
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import numpy as np
import pylab as pl

from d2o import STRATEGIES as DISTRIBUTION_STRATEGIES

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from nifty.spaces.lm_space import LMSpace
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from nifty.spaces.space import Space
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from nifty.config import about, nifty_configuration as gc, \
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                         dependency_injector as gdi
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from hp_space_paradict import HPSpaceParadict
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from nifty.nifty_random import random

hp = gdi.get('healpy')

HP_DISTRIBUTION_STRATEGIES = DISTRIBUTION_STRATEGIES['global']

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class HPSpace(Space):
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    """
        ..        __
        ..      /  /
        ..     /  /___    ______
        ..    /   _   | /   _   |
        ..   /  / /  / /  /_/  /
        ..  /__/ /__/ /   ____/  space class
        ..           /__/

        NIFTY subclass for HEALPix discretizations of the two-sphere [#]_.

        Parameters
        ----------
        nside : int
            Resolution parameter for the HEALPix discretization, resulting in
            ``12*nside**2`` pixels.

        See Also
        --------
        gl_space : A class for the Gauss-Legendre discretization of the
            sphere [#]_.
        lm_space : A class for spherical harmonic components.

        Notes
        -----
        Only powers of two are allowed for `nside`.

        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 : numpy.ndarray
            Array containing the number `nside`.
        dtype : numpy.dtype
            Data type of the field values, which is always numpy.float64.
        discrete : bool
            Whether or not the underlying space is discrete, always ``False``
            for spherical spaces.
        vol : numpy.ndarray
            An array with one element containing the pixel size.
    """

    def __init__(self, nside):
        """
            Sets the attributes for a hp_space class instance.

            Parameters
            ----------
            nside : int
                Resolution parameter for the HEALPix discretization, resulting
                in ``12*nside**2`` pixels.

            Returns
            -------
            None

            Raises
            ------
            ImportError
                If the healpy module is not available.
            ValueError
                If input `nside` is invaild.

        """
        # check imports
        if not gc['use_healpy']:
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            raise ImportError("ERROR: healpy not available.")
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        # setup paradict
        self.paradict = HPSpaceParadict(nside=nside)
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        # setup dtype
        self.dtype = np.dtype('float64')
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        # HPSpace is never harmonic
        self._harmonic = False
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    def copy(self):
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        return HPSpace(nside=self.paradict['nside'])
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    @property
    def shape(self):
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        return (np.int(12 * self.paradict['nside'] ** 2),)
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    @property
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    def dim(self):
        return np.int(12 * self.paradict['nside'] ** 2)
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    def weight(self, x, power=1, axes=None, inplace=False):
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        # check if the axes provided are valid given the input shape
        if axes is not None and \
                not all(axis in range(len(x.shape)) for axis in axes):
            raise ValueError("ERROR: Provided axes does not match array shape")

        weight = np.array(list(
            itertools.chain.from_iterable(
                itertools.repeat(
                    (4 * np.pi / 12 * self.paradict['nside'] ** 2) ** power,
                    12 * self.paradict['nside'] ** 2
                )
            )
        ))

        if axes is not None:
            # reshape the weight array to match the input shape
            new_shape = np.ones(x.shape)
            for index in range(len(axes)):
                new_shape[index] = len(weight)
            weight = weight.reshape(new_shape)

        if inplace:
            x *= weight
            result_x = x
        else:
            result_x = x * weight

        return result_x
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    def get_plot(self, x, title="", vmin=None, vmax=None, power=False, 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).
            iter : int, *optional*
                Number of iterations performed in the HEALPix basis
                transformation.
        """
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        from nifty.field import Field

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        try:
            x = x.get_full_data()
        except AttributeError:
            pass

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

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

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            fig = pl.figure(num=None, figsize=(6.4, 4.8), dpi=None,
                            facecolor="none",
                            edgecolor="none", frameon=False,
                            FigureClass=pl.Figure)
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            ax0 = fig.add_axes([0.12, 0.12, 0.82, 0.76])

            xaxes = np.arange(3 * self.para[0], dtype=np.int)
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            if (vmin is None):
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                vmin = np.min(x[:mono].tolist(
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                ) + (xaxes * (2 * xaxes + 1) * x)[1:].tolist(), axis=None,
                              out=None)
            if (vmax is None):
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                vmax = np.max(x[:mono].tolist(
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                ) + (xaxes * (2 * xaxes + 1) * x)[1:].tolist(), axis=None,
                              out=None)
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            ax0.loglog(xaxes[1:], (xaxes * (2 * xaxes + 1) * x)[1:], color=[0.0,
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                                                                            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)):
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                    other = list(other)
                    for ii in xrange(len(other)):
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                        if (isinstance(other[ii], Field)):
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                            other[ii] = other[ii].power(**kwargs)
                        else:
                            other[ii] = self.enforce_power(other[ii])
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                elif (isinstance(other, Field)):
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                    other = [other.power(**kwargs)]
                else:
                    other = [self.enforce_power(other)]
                imax = max(1, len(other) - 1)
                for ii in xrange(len(other)):
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                    ax0.loglog(xaxes[1:],
                               (xaxes * (2 * xaxes + 1) * 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 - (
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                                       2 * (ii - imax) / imax) ** 2)],
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                               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 - (
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                                                   2 * (
                                                   ii - imax) / imax) ** 2)],
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                                    marker='o', cmap=None, norm=None, vmin=None,
                                    vmax=None, alpha=None, linewidths=None,
                                    verts=None, zorder=-ii)
                if (legend):
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                    ax0.legend()

            ax0.set_xlim(xaxes[1], xaxes[-1])
            ax0.set_xlabel(r"$\ell$")
            ax0.set_ylim(vmin, vmax)
            ax0.set_ylabel(r"$\ell(2\ell+1) C_\ell$")
            ax0.set_title(title)

        else:
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            if (norm == "log"):
                if (vmin is not None):
                    if (vmin <= 0):
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                        raise ValueError(about._errors.cstring(
                            "ERROR: nonpositive value(s)."))
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                elif (np.min(x, axis=None, out=None) <= 0):
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                    raise ValueError(about._errors.cstring(
                        "ERROR: nonpositive value(s)."))
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            if (cmap is None):
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                cmap = pl.cm.jet  # default
            cmap.set_under(color='k', alpha=0.0)  # transparent box
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            hp.mollview(x, fig=None, rot=None, coord=None, unit=unit, xsize=800,
                        title=title, nest=False, min=vmin, max=vmax,
                        flip="astro", remove_dip=False,
                        remove_mono=False, gal_cut=0, format="%g", format2="%g",
                        cbar=cbar, cmap=cmap, notext=False, norm=norm,
                        hold=False, margins=None, sub=None)
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            fig = pl.gcf()

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        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)
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            pl.close(fig)
        else:
            fig.canvas.draw()