# Licensed under a 3-clause BSD style license - see LICENSE.rst
from __future__ import absolute_import, division, print_function, unicode_literals
import numpy as np
from astropy.io import fits
from astropy.units import Quantity
from ..utils.units import unit_from_fits_image_hdu
from .geom import MapCoord, pix_tuple_to_idx
from .utils import interp_to_order
from .hpxmap import HpxMap
from .hpx import HpxGeom, HpxToWcsMapping, nside_to_order
__all__ = ["HpxNDMap"]
[docs]class HpxNDMap(HpxMap):
"""Representation of a N+2D map using HEALPix with two spatial
dimensions and N non-spatial dimensions.
This class uses a N+1D numpy array to represent the sequence of
HEALPix image planes. Following the convention of WCS-based maps
this class uses a column-wise ordering for the data array with the
spatial dimension being tied to the last index of the array.
Parameters
----------
geom : `~gammapy.maps.HpxGeom`
HEALPIX geometry object.
data : `~numpy.ndarray`
HEALPIX data array.
If none then an empty array will be allocated.
meta : `~collections.OrderedDict`
Dictionary to store meta data.
unit : str or `~astropy.units.Unit`
The map unit
"""
def __init__(self, geom, data=None, dtype="float32", meta=None, unit=""):
data_shape = geom.data_shape
if data is None:
data = self._make_default_data(geom, data_shape, dtype)
super(HpxNDMap, self).__init__(geom, data, meta, unit)
self._wcs2d = None
self._hpx2wcs = None
@staticmethod
def _make_default_data(geom, shape_np, dtype):
if geom.npix.size > 1:
data = np.full(shape_np, np.nan, dtype=dtype)
idx = geom.get_idx(local=True)
data[idx[::-1]] = 0
else:
data = np.zeros(shape_np, dtype=dtype)
return data
[docs] @classmethod
def from_hdu(cls, hdu, hdu_bands=None):
"""Make a HpxNDMap object from a FITS HDU.
Parameters
----------
hdu : `~astropy.io.fits.BinTableHDU`
The FITS HDU
hdu_bands : `~astropy.io.fits.BinTableHDU`
The BANDS table HDU
"""
hpx = HpxGeom.from_header(hdu.header, hdu_bands)
shape = tuple([ax.nbin for ax in hpx.axes[::-1]])
# shape_data = shape + tuple([np.max(hpx.npix)])
# TODO: Should we support extracting slices?
meta = cls._get_meta_from_header(hdu.header)
unit = unit_from_fits_image_hdu(hdu.header)
map_out = cls(hpx, None, meta=meta, unit=unit)
colnames = hdu.columns.names
cnames = []
if hdu.header.get("INDXSCHM", None) == "SPARSE":
pix = hdu.data.field("PIX")
vals = hdu.data.field("VALUE")
if "CHANNEL" in hdu.data.columns.names:
chan = hdu.data.field("CHANNEL")
chan = np.unravel_index(chan, shape)
idx = chan + (pix,)
else:
idx = (pix,)
map_out.set_by_idx(idx[::-1], vals)
else:
for c in colnames:
if c.find(hpx.hpx_conv.colstring) == 0:
cnames.append(c)
nbin = len(cnames)
if nbin == 1:
map_out.data = hdu.data.field(cnames[0])
else:
for i, cname in enumerate(cnames):
idx = np.unravel_index(i, shape)
map_out.data[idx + (slice(None),)] = hdu.data.field(cname)
return map_out
[docs] def make_wcs_mapping(
self, sum_bands=False, proj="AIT", oversample=2, width_pix=None
):
"""Make a HEALPix to WCS mapping object.
Parameters
----------
sum_bands : bool
sum over non-spatial dimensions before reprojecting
proj : str
WCS-projection
oversample : float
Oversampling factor for WCS map. This will be the
approximate ratio of the width of a HPX pixel to a WCS
pixel. If this parameter is None then the width will be
set from ``width_pix``.
width_pix : int
Width of the WCS geometry in pixels. The pixel size will
be set to the number of pixels satisfying ``oversample``
or ``width_pix`` whichever is smaller. If this parameter
is None then the width will be set from ``oversample``.
Returns
-------
hpx2wcs : `~HpxToWcsMapping`
"""
self._wcs2d = self.geom.make_wcs(
proj=proj, oversample=oversample, width_pix=width_pix, drop_axes=True
)
self._hpx2wcs = HpxToWcsMapping.create(self.geom, self._wcs2d)
return self._hpx2wcs
[docs] def to_wcs(
self,
sum_bands=False,
normalize=True,
proj="AIT",
oversample=2,
width_pix=None,
hpx2wcs=None,
):
from .wcsnd import WcsNDMap
if sum_bands and self.geom.nside.size > 1:
map_sum = self.sum_over_axes()
return map_sum.to_wcs(
sum_bands=False,
normalize=normalize,
proj=proj,
oversample=oversample,
width_pix=width_pix,
)
# FIXME: Check whether the old mapping is still valid and reuse it
if hpx2wcs is None:
hpx2wcs = self.make_wcs_mapping(
oversample=oversample, proj=proj, width_pix=width_pix
)
# FIXME: Need a function to extract a valid shape from npix property
if sum_bands:
axes = np.arange(self.data.ndim - 1)
hpx_data = np.apply_over_axes(np.sum, self.data, axes=axes)
hpx_data = np.squeeze(hpx_data)
wcs_shape = tuple([t.flat[0] for t in hpx2wcs.npix])
wcs_data = np.zeros(wcs_shape).T
wcs = hpx2wcs.wcs.to_image()
else:
hpx_data = self.data
wcs_shape = tuple([t.flat[0] for t in hpx2wcs.npix]) + self.geom.shape
wcs_data = np.zeros(wcs_shape).T
wcs = hpx2wcs.wcs.to_cube(self.geom.axes)
# FIXME: Should reimplement instantiating map first and fill data array
hpx2wcs.fill_wcs_map_from_hpx_data(hpx_data, wcs_data, normalize)
return WcsNDMap(wcs, wcs_data, unit=self.unit)
[docs] def sum_over_axes(self):
"""Sum over all non-spatial dimensions.
Returns
-------
map_out : `~HpxNDMap`
Summed map.
"""
geom = self.geom.to_image()
axis = tuple(range(self.data.ndim - 1))
data = np.nansum(self.data, axis=axis)
return self._init_copy(geom=geom, data=data)
def _reproject_to_wcs(self, geom, order=1, mode="interp"):
from reproject import reproject_from_healpix
data = np.empty(geom.data_shape)
coordsys = "galactic" if geom.coordsys == "GAL" else "icrs"
for img, idx in self.iter_by_image():
# TODO: Create WCS object for image plane if
# multi-resolution geom
shape_out = geom.get_image_shape(idx)[::-1]
vals, footprint = reproject_from_healpix(
(img, coordsys),
geom.wcs,
shape_out=shape_out,
nested=self.geom.nest,
order=order,
)
data[idx] = vals
return self._init_copy(geom=geom, data=data)
def _reproject_to_hpx(self):
raise NotImplementedError("Maybe try using Map.interp_by_coord().")
[docs] def pad(self, pad_width, mode="constant", cval=0, order=1):
geom = self.geom.pad(pad_width)
map_out = self._init_copy(geom=geom, data=None)
map_out.coadd(self)
coords = geom.get_coord(flat=True)
m = self.geom.contains(coords)
coords = tuple([c[~m] for c in coords])
if mode == "constant":
map_out.set_by_coord(coords, cval)
elif mode == "interp":
# FIXME: These modes don't work at present because
# interp_by_coord doesn't support extrapolation
vals = self.interp_by_coord(coords, interp=order)
map_out.set_by_coord(coords, vals)
else:
raise ValueError("Unrecognized pad mode: {!r}".format(mode))
return map_out
[docs] def crop(self, crop_width):
geom = self.geom.crop(crop_width)
map_out = self._init_copy(geom=geom, data=None)
map_out.coadd(self)
return map_out
[docs] def upsample(self, factor, preserve_counts=True):
geom = self.geom.upsample(factor)
coords = geom.get_coord()
data = self.get_by_coord(coords)
if preserve_counts:
data /= factor ** 2
return self._init_copy(geom=geom, data=data)
[docs] def downsample(self, factor, preserve_counts=True):
geom = self.geom.downsample(factor)
coords = self.geom.get_coord()
vals = self.get_by_coord(coords)
map_out = self._init_copy(geom=geom, data=None)
map_out.fill_by_coord(coords, vals)
if not preserve_counts:
map_out.data /= factor ** 2
return map_out
[docs] def interp_by_coord(self, coords, interp=1):
# inherited docstring
coords = MapCoord.create(coords, coordsys=self.geom.coordsys)
coords = coords.match_axes_units(self.geom)
order = interp_to_order(interp)
if order == 1:
return self._interp_by_coord(coords, order)
else:
raise ValueError("Invalid interpolation order: {!r}".format(order))
[docs] def interp_by_pix(self, pix, interp=None):
"""Interpolate map values at the given pixel coordinates.
"""
raise NotImplementedError
[docs] def get_by_idx(self, idx):
# inherited docstring
idx = pix_tuple_to_idx(idx)
idx = self.geom.global_to_local(idx)
return self.data.T[idx]
def _get_interp_weights(self, coords, idxs=None):
import healpy as hp
if idxs is None:
idxs = self.geom.coord_to_idx(coords, clip=True)[1:]
theta, phi = coords.theta, coords.phi
m = ~np.isfinite(theta)
theta[m] = 0
phi[m] = 0
if not self.geom.is_regular:
nside = self.geom.nside[tuple(idxs)]
else:
nside = self.geom.nside
pix, wts = hp.get_interp_weights(nside, theta, phi, nest=self.geom.nest)
wts[:, m] = 0
pix[:, m] = -1
if not self.geom.is_regular:
pix_local = [self.geom.global_to_local([pix] + list(idxs))[0]]
else:
pix_local = [self.geom[pix]]
# If a pixel lies outside of the geometry set its index to the center pixel
m = pix_local[0] == -1
if m.any():
coords_ctr = [coords.lon, coords.lat]
coords_ctr += [ax.pix_to_coord(t) for ax, t in zip(self.geom.axes, idxs)]
idx_ctr = self.geom.coord_to_idx(coords_ctr)
idx_ctr = self.geom.global_to_local(idx_ctr)
pix_local[0][m] = (idx_ctr[0] * np.ones(pix.shape, dtype=int))[m]
pix_local += [np.broadcast_to(t, pix_local[0].shape) for t in idxs]
return pix_local, wts
def _interp_by_coord(self, coords, order):
"""Linearly interpolate map values."""
pix, wts = self._get_interp_weights(coords)
if self.geom.is_image:
return np.sum(self.data.T[tuple(pix)] * wts, axis=0)
val = np.zeros(pix[0].shape[1:])
# Loop over function values at corners
for i in range(2 ** len(self.geom.axes)):
pix_i = []
wt = np.ones(pix[0].shape[1:])[np.newaxis, ...]
for j, ax in enumerate(self.geom.axes):
idx = ax.coord_to_idx(coords[ax.name])
idx = np.clip(idx, 0, len(ax.center) - 2)
w = ax.center[idx + 1] - ax.center[idx]
if i & (1 << j):
wt *= (coords[ax.name] - ax.center[idx]) / w
pix_i += [idx + 1]
else:
wt *= 1.0 - (coords[ax.name] - ax.center[idx]) / w
pix_i += [idx]
if not self.geom.is_regular:
pix, wts = self._get_interp_weights(coords, pix_i)
wts[pix[0] == -1] = 0
wt[~np.isfinite(wt)] = 0
val += np.nansum(wts * wt * self.data.T[tuple(pix[:1] + pix_i)], axis=0)
return val
[docs] def fill_by_idx(self, idx, weights=None):
idx = pix_tuple_to_idx(idx)
msk = np.all(np.stack([t != -1 for t in idx]), axis=0)
if weights is not None:
weights = weights[msk]
idx = [t[msk] for t in idx]
idx_local = list(self.geom.global_to_local(idx))
msk = idx_local[0] >= 0
idx_local = [t[msk] for t in idx_local]
if weights is not None:
if isinstance(weights, Quantity):
weights = weights.to(self.unit).value
weights = weights[msk]
idx_local = np.ravel_multi_index(idx_local, self.data.T.shape)
idx_local, idx_inv = np.unique(idx_local, return_inverse=True)
weights = np.bincount(idx_inv, weights=weights)
self.data.T.flat[idx_local] += weights
[docs] def set_by_idx(self, idx, vals):
idx = pix_tuple_to_idx(idx)
idx_local = self.geom.global_to_local(idx)
self.data.T[idx_local] = vals
def _make_cols(self, header, conv):
shape = self.data.shape
cols = []
if header["INDXSCHM"] == "SPARSE":
data = self.data.copy()
data[~np.isfinite(data)] = 0
nonzero = np.where(data > 0)
value = data[nonzero].astype(float)
pix = self.geom.local_to_global(nonzero[::-1])[0]
if len(shape) == 1:
cols.append(fits.Column("PIX", "J", array=pix))
cols.append(fits.Column("VALUE", "E", array=value))
else:
channel = np.ravel_multi_index(nonzero[:-1], shape[:-1])
cols.append(fits.Column("PIX", "J", array=pix))
cols.append(fits.Column("CHANNEL", "I", array=channel))
cols.append(fits.Column("VALUE", "E", array=value))
elif len(shape) == 1:
name = conv.colname(indx=conv.firstcol)
array = self.data.astype(float)
cols.append(fits.Column(name, "E", array=array))
else:
for i, idx in enumerate(np.ndindex(shape[:-1])):
name = conv.colname(indx=i + conv.firstcol)
array = self.data[idx].astype(float)
cols.append(fits.Column(name, "E", array=array))
return cols
[docs] def to_swapped(self):
import healpy as hp
hpx_out = self.geom.to_swapped()
map_out = self._init_copy(geom=hpx_out, data=None)
idx = self.geom.get_idx(flat=True)
vals = self.get_by_idx(idx)
if self.geom.nside.size > 1:
nside = self.geom.nside[idx[1:]]
else:
nside = self.geom.nside
if self.geom.nest:
idx_new = tuple([hp.nest2ring(nside, idx[0])]) + idx[1:]
else:
idx_new = tuple([hp.ring2nest(nside, idx[0])]) + idx[1:]
map_out.set_by_idx(idx_new, vals)
return map_out
[docs] def to_ud_graded(self, nside, preserve_counts=False):
# FIXME: Should we remove/deprecate this method?
order = nside_to_order(nside)
new_hpx = self.geom.to_ud_graded(order)
map_out = self._init_copy(geom=new_hpx, data=None)
if np.all(order <= self.geom.order):
# Downsample
idx = self.geom.get_idx(flat=True)
coords = self.geom.pix_to_coord(idx)
vals = self.get_by_idx(idx)
map_out.fill_by_coord(coords, vals)
else:
# Upsample
idx = new_hpx.get_idx(flat=True)
coords = new_hpx.pix_to_coord(idx)
vals = self.get_by_coord(coords)
m = np.isfinite(vals)
map_out.fill_by_coord([c[m] for c in coords], vals[m])
if not preserve_counts:
fact = (2 ** order) ** 2 / (2 ** self.geom.order) ** 2
if self.geom.nside.size > 1:
fact = fact[..., None]
map_out.data *= fact
return map_out
[docs] def plot(
self,
method="raster",
ax=None,
normalize=False,
proj="AIT",
oversample=2,
width_pix=1000,
**kwargs
):
"""Quickplot method.
This will generate a visualization of the map by converting to
a rasterized WCS image (method='raster') or drawing polygons
for each pixel (method='poly').
Parameters
----------
method : {'raster','poly'}
Method for mapping HEALPix pixels to a two-dimensional
image. Can be set to 'raster' (rasterization to cartesian
image plane) or 'poly' (explicit polygons for each pixel).
WARNING: The 'poly' method is much slower than 'raster'
and only suitable for maps with less than ~10k pixels.
proj : string, optional
Any valid WCS projection type.
oversample : float
Oversampling factor for WCS map. This will be the
approximate ratio of the width of a HPX pixel to a WCS
pixel. If this parameter is None then the width will be
set from ``width_pix``.
width_pix : int
Width of the WCS geometry in pixels. The pixel size will
be set to the number of pixels satisfying ``oversample``
or ``width_pix`` whichever is smaller. If this parameter
is None then the width will be set from ``oversample``.
**kwargs : dict
Keyword arguments passed to `~matplotlib.pyplot.imshow`.
Returns
-------
fig : `~matplotlib.figure.Figure`
Figure object.
ax : `~astropy.visualization.wcsaxes.WCSAxes`
WCS axis object
im : `~matplotlib.image.AxesImage` or `~matplotlib.collections.PatchCollection`
Image object.
"""
if method == "raster":
m = self.to_wcs(
sum_bands=True,
normalize=normalize,
proj=proj,
oversample=oversample,
width_pix=width_pix,
)
return m.plot(ax, **kwargs)
elif method == "poly":
return self._plot_poly(proj=proj, ax=ax)
else:
raise ValueError("Invalid method: {!r}".format(method))
def _plot_poly(self, proj="AIT", step=1, ax=None):
"""Plot the map using a collection of polygons.
Parameters
----------
proj : string, optional
Any valid WCS projection type.
step : int
Set the number vertices that will be computed for each
pixel in multiples of 4.
"""
# FIXME: At the moment this only works for all-sky maps if the
# projection is centered at (0,0)
# FIXME: Figure out how to force a square aspect-ratio like imshow
import matplotlib.pyplot as plt
from matplotlib.patches import Polygon
from matplotlib.collections import PatchCollection
import healpy as hp
wcs = self.geom.make_wcs(proj=proj, oversample=1)
if ax is None:
fig = plt.gcf()
ax = fig.add_subplot(111, projection=wcs.wcs, aspect="equal")
wcs_lonlat = wcs.center_coord[:2]
idx = self.geom.get_idx()
vtx = hp.boundaries(self.geom.nside, idx[0], nest=self.geom.nest, step=step)
theta, phi = hp.vec2ang(np.rollaxis(vtx, 2))
theta = theta.reshape((4 * step, -1)).T
phi = phi.reshape((4 * step, -1)).T
patches = []
data = []
def get_angle(x, t):
return 180. - (180. - x + t) % 360.
for i, (x, y) in enumerate(zip(phi, theta)):
lon, lat = np.degrees(x), np.degrees(np.pi / 2. - y)
# Add a small ofset to avoid vertices wrapping to the
# other size of the projection
if get_angle(np.median(lon), wcs_lonlat[0]) > 0:
idx = wcs.coord_to_pix((lon - 1E-4, lat))
else:
idx = wcs.coord_to_pix((lon + 1E-4, lat))
dist = np.max(np.abs(idx[0][0] - idx[0]))
# Split pixels that wrap around the edges of the projection
if dist > wcs.npix[0] / 1.5:
lon, lat = np.degrees(x), np.degrees(np.pi / 2. - y)
lon0 = lon - 1E-4
lon1 = lon + 1E-4
pix0 = wcs.coord_to_pix((lon0, lat))
pix1 = wcs.coord_to_pix((lon1, lat))
idx0 = np.argsort(pix0[0])
idx1 = np.argsort(pix1[0])
pix0 = (pix0[0][idx0][:3], pix0[1][idx0][:3])
pix1 = (pix1[0][idx1][1:], pix1[1][idx1][1:])
patches.append(Polygon(np.vstack((pix0[0], pix0[1])).T, True))
patches.append(Polygon(np.vstack((pix1[0], pix1[1])).T, True))
data.append(self.data[i])
data.append(self.data[i])
else:
polygon = Polygon(np.vstack((idx[0], idx[1])).T, True)
patches.append(polygon)
data.append(self.data[i])
p = PatchCollection(patches, linewidths=0, edgecolors="None")
p.set_array(np.array(data))
ax.add_collection(p)
ax.autoscale_view()
ax.coords.grid(color="w", linestyle=":", linewidth=0.5)
return fig, ax, p