hp_space.py 14.5 KB
Newer Older
csongor's avatar
csongor committed
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
# 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

import numpy as np
import pylab as pl

from d2o import STRATEGIES as DISTRIBUTION_STRATEGIES

41
from nifty.spaces.lm_space import LMSpace
42

43
from nifty.spaces.space import Space
csongor's avatar
csongor committed
44

Jait Dixit's avatar
Jait Dixit committed
45
from nifty.config import about, nifty_configuration as gc,\
csongor's avatar
csongor committed
46
                         dependency_injector as gdi
theos's avatar
theos committed
47
from hp_space_paradict import HPSpaceParadict
csongor's avatar
csongor committed
48 49 50 51 52 53
from nifty.nifty_random import random

hp = gdi.get('healpy')

HP_DISTRIBUTION_STRATEGIES = DISTRIBUTION_STRATEGIES['global']

54 55

class HPSpace(Space):
csongor's avatar
csongor committed
56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128
    """
        ..        __
        ..      /  /
        ..     /  /___    ______
        ..    /   _   | /   _   |
        ..   /  / /  / /  /_/  /
        ..  /__/ /__/ /   ____/  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']:
Jait Dixit's avatar
Jait Dixit committed
129
            raise ImportError("ERROR: healpy not available.")
csongor's avatar
csongor committed
130

Jait Dixit's avatar
Jait Dixit committed
131 132
        # let the abstract Space class initialize dtype
        super(HPSpace, self).__init__(dtype=np.dtype('float64'))
csongor's avatar
csongor committed
133

Jait Dixit's avatar
Jait Dixit committed
134 135 136 137 138 139
        self.paradict = HPSpaceParadict(nside=nside,
                                        distances=np.float(
                                            4 * np.pi / (12 * nside ** 2))
                                        )
        # HPSpace is never harmonic
        self._harmonic = False
csongor's avatar
csongor committed
140 141

    def copy(self):
142
        return HPSpace(nside=self.paradict['nside'])
csongor's avatar
csongor committed
143 144 145

    @property
    def shape(self):
Jait Dixit's avatar
Jait Dixit committed
146
        return (np.int(12 * self.paradict['nside'] ** 2),)
csongor's avatar
csongor committed
147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176

    @property
    def meta_volume(self):
        """
            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.

            Parameters
            ----------
            total : bool, *optional*
                Whether to return the total meta volume of the space or the
                individual ones of each field component (default: False).

            Returns
            -------
            mol : {numpy.ndarray, float}
                Meta volume of the field components or the complete space.

            Notes
            -----
            For HEALpix discretizations, the meta volumes are the pixel sizes.
        """
        return np.float(4 * np.pi)

    @property
    def meta_volume_split(self):
Jait Dixit's avatar
Jait Dixit committed
177
        pass
csongor's avatar
csongor committed
178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212

    # TODO: Extend to binning/log
    def enforce_power(self, spec, size=None, kindex=None):
        if kindex is None:
            kindex_size = self.paradict['nside'] * 3
            kindex = np.arange(kindex_size,
                               dtype=np.array(self.distances).dtype)
        return self._enforce_power_helper(spec=spec,
                                          size=size,
                                          kindex=kindex)

    def calc_power(self, x, niter=0, **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
            ----------------
            iter : int, *optional*
                Number of iterations performed in the HEALPix basis
                transformation.
        """
        x = self.cast(x)

        nside = self.paradict['nside']
Jait Dixit's avatar
Jait Dixit committed
213
        lmax = 3 * nside - 1
csongor's avatar
csongor committed
214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276
        mmax = lmax

        # if self.datamodel != 'not':
        #     about.warnings.cprint(
        #         "WARNING: Field data is consolidated to all nodes for "
        #         "external smoothalm method!")

        np_x = x.get_full_data()

        # power spectrum
        return hp.anafast(np_x, map2=None, nspec=None, lmax=lmax, mmax=mmax,
                          iter=niter, alm=False, pol=True, use_weights=False,
                          datapath=None)

    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.
        """
277 278
        from nifty.field import Field

csongor's avatar
csongor committed
279 280 281 282 283
        try:
            x = x.get_full_data()
        except AttributeError:
            pass

Jait Dixit's avatar
Jait Dixit committed
284
        if (not pl.isinteractive()) and (not bool(kwargs.get("save", False))):
csongor's avatar
csongor committed
285 286
            about.warnings.cprint("WARNING: interactive mode off.")

Jait Dixit's avatar
Jait Dixit committed
287
        if (power):
csongor's avatar
csongor committed
288 289
            x = self.calc_power(x, **kwargs)

Jait Dixit's avatar
Jait Dixit committed
290 291 292 293
            fig = pl.figure(num=None, figsize=(6.4, 4.8), dpi=None,
                            facecolor="none",
                            edgecolor="none", frameon=False,
                            FigureClass=pl.Figure)
csongor's avatar
csongor committed
294 295 296
            ax0 = fig.add_axes([0.12, 0.12, 0.82, 0.76])

            xaxes = np.arange(3 * self.para[0], dtype=np.int)
Jait Dixit's avatar
Jait Dixit committed
297
            if (vmin is None):
csongor's avatar
csongor committed
298
                vmin = np.min(x[:mono].tolist(
Jait Dixit's avatar
Jait Dixit committed
299 300 301
                ) + (xaxes * (2 * xaxes + 1) * x)[1:].tolist(), axis=None,
                              out=None)
            if (vmax is None):
csongor's avatar
csongor committed
302
                vmax = np.max(x[:mono].tolist(
Jait Dixit's avatar
Jait Dixit committed
303 304
                ) + (xaxes * (2 * xaxes + 1) * x)[1:].tolist(), axis=None,
                              out=None)
csongor's avatar
csongor committed
305
            ax0.loglog(xaxes[1:], (xaxes * (2 * xaxes + 1) * x)[1:], color=[0.0,
Jait Dixit's avatar
Jait Dixit committed
306 307 308 309 310 311 312 313 314 315 316
                                                                            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)):
csongor's avatar
csongor committed
317 318
                    other = list(other)
                    for ii in xrange(len(other)):
Jait Dixit's avatar
Jait Dixit committed
319
                        if (isinstance(other[ii], Field)):
csongor's avatar
csongor committed
320 321 322
                            other[ii] = other[ii].power(**kwargs)
                        else:
                            other[ii] = self.enforce_power(other[ii])
Jait Dixit's avatar
Jait Dixit committed
323
                elif (isinstance(other, Field)):
csongor's avatar
csongor committed
324 325 326 327 328
                    other = [other.power(**kwargs)]
                else:
                    other = [self.enforce_power(other)]
                imax = max(1, len(other) - 1)
                for ii in xrange(len(other)):
Jait Dixit's avatar
Jait Dixit committed
329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348
                    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 - (
                                   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):
csongor's avatar
csongor committed
349 350 351 352 353 354 355 356 357
                    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:
Jait Dixit's avatar
Jait Dixit committed
358 359 360
            if (norm == "log"):
                if (vmin is not None):
                    if (vmin <= 0):
csongor's avatar
csongor committed
361 362
                        raise ValueError(about._errors.cstring(
                            "ERROR: nonpositive value(s)."))
Jait Dixit's avatar
Jait Dixit committed
363
                elif (np.min(x, axis=None, out=None) <= 0):
csongor's avatar
csongor committed
364 365
                    raise ValueError(about._errors.cstring(
                        "ERROR: nonpositive value(s)."))
Jait Dixit's avatar
Jait Dixit committed
366
            if (cmap is None):
csongor's avatar
csongor committed
367 368
                cmap = pl.cm.jet  # default
            cmap.set_under(color='k', alpha=0.0)  # transparent box
Jait Dixit's avatar
Jait Dixit committed
369 370 371 372 373 374
            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)
csongor's avatar
csongor committed
375 376
            fig = pl.gcf()

Jait Dixit's avatar
Jait Dixit committed
377 378 379 380 381
        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)
csongor's avatar
csongor committed
382 383 384
            pl.close(fig)
        else:
            fig.canvas.draw()