Source code for astropy.wcs.wcs

# Licensed under a 3-clause BSD style license - see LICENSE.rst
"""
Under the hood, there are 3 separate classes that perform different
parts of the transformation:

   - `~astropy.wcs.Wcsprm`: Is a direct wrapper of the core WCS
     functionality in `wcslib`_.  (This includes TPV and TPD
     polynomial distortion, but not SIP distortion).

   - `~astropy.wcs.Sip`: Handles polynomial distortion as defined in the
     `SIP`_ convention.

   - `~astropy.wcs.DistortionLookupTable`: Handles `distortion paper`_
     lookup tables.

Additionally, the class `WCS` aggregates all of these transformations
together in a pipeline:

   - Detector to image plane correction (by a pair of
     `~astropy.wcs.DistortionLookupTable` objects).

   - `SIP`_ distortion correction (by an underlying `~astropy.wcs.Sip`
     object)

   - `distortion paper`_ table-lookup correction (by a pair of
     `~astropy.wcs.DistortionLookupTable` objects).

   - `wcslib`_ WCS transformation (by a `~astropy.wcs.Wcsprm` object)

"""

# STDLIB
import copy
import io
import itertools
import os
import re
import textwrap
import warnings
import builtins

# THIRD-PARTY
import numpy as np

# LOCAL
from astropy import log
from astropy.io import fits
from . import docstrings
from . import _wcs

from astropy.utils.compat import possible_filename
from astropy.utils.exceptions import AstropyWarning, AstropyUserWarning, AstropyDeprecationWarning


# Mix-in class that provides the APE 14 API
from .wcsapi.fitswcs import FITSWCSAPIMixin, SlicedFITSWCS

__all__ = ['FITSFixedWarning', 'WCS', 'find_all_wcs',
           'DistortionLookupTable', 'Sip', 'Tabprm', 'Wcsprm',
           'WCSBase', 'validate', 'WcsError', 'SingularMatrixError',
           'InconsistentAxisTypesError', 'InvalidTransformError',
           'InvalidCoordinateError', 'NoSolutionError',
           'InvalidSubimageSpecificationError', 'NoConvergence',
           'NonseparableSubimageCoordinateSystemError',
           'NoWcsKeywordsFoundError', 'InvalidTabularParametersError']


__doctest_skip__ = ['WCS.all_world2pix']

NAXIS_DEPRECATE_MESSAGE = """
Private attributes "_naxis1" and "_naxis2" have been deprecated since v3.1.
Instead use the "pixel_shape" property which returns a list of NAXISj keyword values.
"""

if _wcs is not None:
    _parsed_version = _wcs.__version__.split('.')
    if int(_parsed_version[0]) == 5 and int(_parsed_version[1]) < 8:
        raise ImportError(
            "astropy.wcs is built with wcslib {0}, but only versions 5.8 and "
            "later on the 5.x series are known to work.  The version of wcslib "
            "that ships with astropy may be used.")

    if not _wcs._sanity_check():
        raise RuntimeError(
        "astropy.wcs did not pass its sanity check for your build "
        "on your platform.")

    WCSBase = _wcs._Wcs
    DistortionLookupTable = _wcs.DistortionLookupTable
    Sip = _wcs.Sip
    Wcsprm = _wcs.Wcsprm
    Tabprm = _wcs.Tabprm
    WcsError = _wcs.WcsError
    SingularMatrixError = _wcs.SingularMatrixError
    InconsistentAxisTypesError = _wcs.InconsistentAxisTypesError
    InvalidTransformError = _wcs.InvalidTransformError
    InvalidCoordinateError = _wcs.InvalidCoordinateError
    NoSolutionError = _wcs.NoSolutionError
    InvalidSubimageSpecificationError = _wcs.InvalidSubimageSpecificationError
    NonseparableSubimageCoordinateSystemError = _wcs.NonseparableSubimageCoordinateSystemError
    NoWcsKeywordsFoundError = _wcs.NoWcsKeywordsFoundError
    InvalidTabularParametersError = _wcs.InvalidTabularParametersError

    # Copy all the constants from the C extension into this module's namespace
    for key, val in _wcs.__dict__.items():
        if key.startswith(('WCSSUB', 'WCSHDR', 'WCSHDO')):
            locals()[key] = val
            __all__.append(key)
else:
    WCSBase = object
    Wcsprm = object
    DistortionLookupTable = object
    Sip = object
    Tabprm = object
    WcsError = None
    SingularMatrixError = None
    InconsistentAxisTypesError = None
    InvalidTransformError = None
    InvalidCoordinateError = None
    NoSolutionError = None
    InvalidSubimageSpecificationError = None
    NonseparableSubimageCoordinateSystemError = None
    NoWcsKeywordsFoundError = None
    InvalidTabularParametersError = None


# Additional relax bit flags
WCSHDO_SIP = 0x80000

# Regular expression defining SIP keyword It matches keyword that starts with A
# or B, optionally followed by P, followed by an underscore then a number in
# range of 0-19, followed by an underscore and another number in range of 0-19.
# Keyword optionally ends with a capital letter.
SIP_KW = re.compile('''^[AB]P?_1?[0-9]_1?[0-9][A-Z]?$''')


def _parse_keysel(keysel):
    keysel_flags = 0
    if keysel is not None:
        for element in keysel:
            if element.lower() == 'image':
                keysel_flags |= _wcs.WCSHDR_IMGHEAD
            elif element.lower() == 'binary':
                keysel_flags |= _wcs.WCSHDR_BIMGARR
            elif element.lower() == 'pixel':
                keysel_flags |= _wcs.WCSHDR_PIXLIST
            else:
                raise ValueError(
                    "keysel must be a list of 'image', 'binary' " +
                    "and/or 'pixel'")
    else:
        keysel_flags = -1

    return keysel_flags


[docs]class NoConvergence(Exception): """ An error class used to report non-convergence and/or divergence of numerical methods. It is used to report errors in the iterative solution used by the :py:meth:`~astropy.wcs.WCS.all_world2pix`. Attributes ---------- best_solution : `numpy.ndarray` Best solution achieved by the numerical method. accuracy : `numpy.ndarray` Accuracy of the ``best_solution``. niter : `int` Number of iterations performed by the numerical method to compute ``best_solution``. divergent : None, `numpy.ndarray` Indices of the points in ``best_solution`` array for which the solution appears to be divergent. If the solution does not diverge, ``divergent`` will be set to `None`. slow_conv : None, `numpy.ndarray` Indices of the solutions in ``best_solution`` array for which the solution failed to converge within the specified maximum number of iterations. If there are no non-converging solutions (i.e., if the required accuracy has been achieved for all input data points) then ``slow_conv`` will be set to `None`. """ def __init__(self, *args, best_solution=None, accuracy=None, niter=None, divergent=None, slow_conv=None, **kwargs): super().__init__(*args) self.best_solution = best_solution self.accuracy = accuracy self.niter = niter self.divergent = divergent self.slow_conv = slow_conv if kwargs: warnings.warn("Function received unexpected arguments ({}) these " "are ignored but will raise an Exception in the " "future.".format(list(kwargs)), AstropyDeprecationWarning)
[docs]class FITSFixedWarning(AstropyWarning): """ The warning raised when the contents of the FITS header have been modified to be standards compliant. """ pass
[docs]class WCS(FITSWCSAPIMixin, WCSBase): """WCS objects perform standard WCS transformations, and correct for `SIP`_ and `distortion paper`_ table-lookup transformations, based on the WCS keywords and supplementary data read from a FITS file. See also: http://docs.astropy.org/en/stable/wcs/ Parameters ---------- header : astropy.io.fits header object, Primary HDU, Image HDU, string, dict-like, or None, optional If *header* is not provided or None, the object will be initialized to default values. fobj : An astropy.io.fits file (hdulist) object, optional It is needed when header keywords point to a `distortion paper`_ lookup table stored in a different extension. key : str, optional The name of a particular WCS transform to use. This may be either ``' '`` or ``'A'``-``'Z'`` and corresponds to the ``\"a\"`` part of the ``CTYPEia`` cards. *key* may only be provided if *header* is also provided. minerr : float, optional The minimum value a distortion correction must have in order to be applied. If the value of ``CQERRja`` is smaller than *minerr*, the corresponding distortion is not applied. relax : bool or int, optional Degree of permissiveness: - `True` (default): Admit all recognized informal extensions of the WCS standard. - `False`: Recognize only FITS keywords defined by the published WCS standard. - `int`: a bit field selecting specific extensions to accept. See :ref:`relaxread` for details. naxis : int or sequence, optional Extracts specific coordinate axes using :meth:`~astropy.wcs.Wcsprm.sub`. If a header is provided, and *naxis* is not ``None``, *naxis* will be passed to :meth:`~astropy.wcs.Wcsprm.sub` in order to select specific axes from the header. See :meth:`~astropy.wcs.Wcsprm.sub` for more details about this parameter. keysel : sequence of flags, optional A sequence of flags used to select the keyword types considered by wcslib. When ``None``, only the standard image header keywords are considered (and the underlying wcspih() C function is called). To use binary table image array or pixel list keywords, *keysel* must be set. Each element in the list should be one of the following strings: - 'image': Image header keywords - 'binary': Binary table image array keywords - 'pixel': Pixel list keywords Keywords such as ``EQUIna`` or ``RFRQna`` that are common to binary table image arrays and pixel lists (including ``WCSNna`` and ``TWCSna``) are selected by both 'binary' and 'pixel'. colsel : sequence of int, optional A sequence of table column numbers used to restrict the WCS transformations considered to only those pertaining to the specified columns. If `None`, there is no restriction. fix : bool, optional When `True` (default), call `~astropy.wcs.Wcsprm.fix` on the resulting object to fix any non-standard uses in the header. `FITSFixedWarning` Warnings will be emitted if any changes were made. translate_units : str, optional Specify which potentially unsafe translations of non-standard unit strings to perform. By default, performs none. See `WCS.fix` for more information about this parameter. Only effective when ``fix`` is `True`. Raises ------ MemoryError Memory allocation failed. ValueError Invalid key. KeyError Key not found in FITS header. ValueError Lookup table distortion present in the header but *fobj* was not provided. Notes ----- 1. astropy.wcs supports arbitrary *n* dimensions for the core WCS (the transformations handled by WCSLIB). However, the `distortion paper`_ lookup table and `SIP`_ distortions must be two dimensional. Therefore, if you try to create a WCS object where the core WCS has a different number of dimensions than 2 and that object also contains a `distortion paper`_ lookup table or `SIP`_ distortion, a `ValueError` exception will be raised. To avoid this, consider using the *naxis* kwarg to select two dimensions from the core WCS. 2. The number of coordinate axes in the transformation is not determined directly from the ``NAXIS`` keyword but instead from the highest of: - ``NAXIS`` keyword - ``WCSAXESa`` keyword - The highest axis number in any parameterized WCS keyword. The keyvalue, as well as the keyword, must be syntactically valid otherwise it will not be considered. If none of these keyword types is present, i.e. if the header only contains auxiliary WCS keywords for a particular coordinate representation, then no coordinate description is constructed for it. The number of axes, which is set as the ``naxis`` member, may differ for different coordinate representations of the same image. 3. When the header includes duplicate keywords, in most cases the last encountered is used. 4. `~astropy.wcs.Wcsprm.set` is called immediately after construction, so any invalid keywords or transformations will be raised by the constructor, not when subsequently calling a transformation method. """ def __init__(self, header=None, fobj=None, key=' ', minerr=0.0, relax=True, naxis=None, keysel=None, colsel=None, fix=True, translate_units='', _do_set=True): close_fds = [] if header is None: if naxis is None: naxis = 2 wcsprm = _wcs.Wcsprm(header=None, key=key, relax=relax, naxis=naxis) self.naxis = wcsprm.naxis # Set some reasonable defaults. det2im = (None, None) cpdis = (None, None) sip = None else: keysel_flags = _parse_keysel(keysel) if isinstance(header, (str, bytes)): try: is_path = (possible_filename(header) and os.path.exists(header)) except (OSError, ValueError): is_path = False if is_path: if fobj is not None: raise ValueError( "Can not provide both a FITS filename to " "argument 1 and a FITS file object to argument 2") fobj = fits.open(header) close_fds.append(fobj) header = fobj[0].header elif isinstance(header, fits.hdu.image._ImageBaseHDU): header = header.header elif not isinstance(header, fits.Header): try: # Accept any dict-like object orig_header = header header = fits.Header() for dict_key in orig_header.keys(): header[dict_key] = orig_header[dict_key] except TypeError: raise TypeError( "header must be a string, an astropy.io.fits.Header " "object, or a dict-like object") if isinstance(header, fits.Header): header_string = header.tostring().rstrip() else: header_string = header # Importantly, header is a *copy* of the passed-in header # because we will be modifying it if isinstance(header_string, str): header_bytes = header_string.encode('ascii') header_string = header_string else: header_bytes = header_string header_string = header_string.decode('ascii') try: tmp_header = fits.Header.fromstring(header_string) self._remove_sip_kw(tmp_header) tmp_header_bytes = tmp_header.tostring().rstrip() if isinstance(tmp_header_bytes, str): tmp_header_bytes = tmp_header_bytes.encode('ascii') tmp_wcsprm = _wcs.Wcsprm(header=tmp_header_bytes, key=key, relax=relax, keysel=keysel_flags, colsel=colsel, warnings=False) except _wcs.NoWcsKeywordsFoundError: est_naxis = 0 else: if naxis is not None: try: tmp_wcsprm.sub(naxis) except ValueError: pass est_naxis = tmp_wcsprm.naxis else: est_naxis = 2 header = fits.Header.fromstring(header_string) if est_naxis == 0: est_naxis = 2 self.naxis = est_naxis det2im = self._read_det2im_kw(header, fobj, err=minerr) cpdis = self._read_distortion_kw( header, fobj, dist='CPDIS', err=minerr) sip = self._read_sip_kw(header, wcskey=key) self._remove_sip_kw(header) header_string = header.tostring() header_string = header_string.replace('END' + ' ' * 77, '') if isinstance(header_string, str): header_bytes = header_string.encode('ascii') header_string = header_string else: header_bytes = header_string header_string = header_string.decode('ascii') try: wcsprm = _wcs.Wcsprm(header=header_bytes, key=key, relax=relax, keysel=keysel_flags, colsel=colsel) except _wcs.NoWcsKeywordsFoundError: # The header may have SIP or distortions, but no core # WCS. That isn't an error -- we want a "default" # (identity) core Wcs transformation in that case. if colsel is None: wcsprm = _wcs.Wcsprm(header=None, key=key, relax=relax, keysel=keysel_flags, colsel=colsel) else: raise if naxis is not None: wcsprm = wcsprm.sub(naxis) self.naxis = wcsprm.naxis if (wcsprm.naxis != 2 and (det2im[0] or det2im[1] or cpdis[0] or cpdis[1] or sip)): raise ValueError( """ FITS WCS distortion paper lookup tables and SIP distortions only work in 2 dimensions. However, WCSLIB has detected {} dimensions in the core WCS keywords. To use core WCS in conjunction with FITS WCS distortion paper lookup tables or SIP distortion, you must select or reduce these to 2 dimensions using the naxis kwarg. """.format(wcsprm.naxis)) header_naxis = header.get('NAXIS', None) if header_naxis is not None and header_naxis < wcsprm.naxis: warnings.warn( "The WCS transformation has more axes ({:d}) than the " "image it is associated with ({:d})".format( wcsprm.naxis, header_naxis), FITSFixedWarning) self._get_naxis(header) WCSBase.__init__(self, sip, cpdis, wcsprm, det2im) if fix: self.fix(translate_units=translate_units) if _do_set: self.wcs.set() for fd in close_fds: fd.close() self._pixel_bounds = None def __copy__(self): new_copy = self.__class__() WCSBase.__init__(new_copy, self.sip, (self.cpdis1, self.cpdis2), self.wcs, (self.det2im1, self.det2im2)) new_copy.__dict__.update(self.__dict__) return new_copy def __deepcopy__(self, memo): from copy import deepcopy new_copy = self.__class__() new_copy.naxis = deepcopy(self.naxis, memo) WCSBase.__init__(new_copy, deepcopy(self.sip, memo), (deepcopy(self.cpdis1, memo), deepcopy(self.cpdis2, memo)), deepcopy(self.wcs, memo), (deepcopy(self.det2im1, memo), deepcopy(self.det2im2, memo))) for key, val in self.__dict__.items(): new_copy.__dict__[key] = deepcopy(val, memo) return new_copy
[docs] def copy(self): """ Return a shallow copy of the object. Convenience method so user doesn't have to import the :mod:`copy` stdlib module. .. warning:: Use `deepcopy` instead of `copy` unless you know why you need a shallow copy. """ return copy.copy(self)
[docs] def deepcopy(self): """ Return a deep copy of the object. Convenience method so user doesn't have to import the :mod:`copy` stdlib module. """ return copy.deepcopy(self)
[docs] def sub(self, axes=None): copy = self.deepcopy() copy.wcs = self.wcs.sub(axes) copy.naxis = copy.wcs.naxis return copy
if _wcs is not None: sub.__doc__ = _wcs.Wcsprm.sub.__doc__ def _fix_scamp(self): """ Remove SCAMP's PVi_m distortion parameters if SIP distortion parameters are also present. Some projects (e.g., Palomar Transient Factory) convert SCAMP's distortion parameters (which abuse the PVi_m cards) to SIP. However, wcslib gets confused by the presence of both SCAMP and SIP distortion parameters. See https://github.com/astropy/astropy/issues/299. """ # Nothing to be done if no WCS attached if self.wcs is None: return # Nothing to be done if no PV parameters attached pv = self.wcs.get_pv() if not pv: return # Nothing to be done if axes don't use SIP distortion parameters if self.sip is None: return # Nothing to be done if any radial terms are present... # Loop over list to find any radial terms. # Certain values of the `j' index are used for storing # radial terms; refer to Equation (1) in # <http://web.ipac.caltech.edu/staff/shupe/reprints/SIP_to_PV_SPIE2012.pdf>. pv = np.asarray(pv) # Loop over distinct values of `i' index for i in set(pv[:, 0]): # Get all values of `j' index for this value of `i' index js = set(pv[:, 1][pv[:, 0] == i]) # Find max value of `j' index max_j = max(js) for j in (3, 11, 23, 39): if j < max_j and j in js: return self.wcs.set_pv([]) warnings.warn("Removed redundant SCAMP distortion parameters " + "because SIP parameters are also present", FITSFixedWarning)
[docs] def fix(self, translate_units='', naxis=None): """ Perform the fix operations from wcslib, and warn about any changes it has made. Parameters ---------- translate_units : str, optional Specify which potentially unsafe translations of non-standard unit strings to perform. By default, performs none. Although ``"S"`` is commonly used to represent seconds, its translation to ``"s"`` is potentially unsafe since the standard recognizes ``"S"`` formally as Siemens, however rarely that may be used. The same applies to ``"H"`` for hours (Henry), and ``"D"`` for days (Debye). This string controls what to do in such cases, and is case-insensitive. - If the string contains ``"s"``, translate ``"S"`` to ``"s"``. - If the string contains ``"h"``, translate ``"H"`` to ``"h"``. - If the string contains ``"d"``, translate ``"D"`` to ``"d"``. Thus ``''`` doesn't do any unsafe translations, whereas ``'shd'`` does all of them. naxis : int array[naxis], optional Image axis lengths. If this array is set to zero or ``None``, then `~astropy.wcs.Wcsprm.cylfix` will not be invoked. """ if self.wcs is not None: self._fix_scamp() fixes = self.wcs.fix(translate_units, naxis) for key, val in fixes.items(): if val != "No change": warnings.warn( ("'{0}' made the change '{1}'."). format(key, val), FITSFixedWarning)
[docs] def calc_footprint(self, header=None, undistort=True, axes=None, center=True): """ Calculates the footprint of the image on the sky. A footprint is defined as the positions of the corners of the image on the sky after all available distortions have been applied. Parameters ---------- header : `~astropy.io.fits.Header` object, optional Used to get ``NAXIS1`` and ``NAXIS2`` header and axes are mutually exclusive, alternative ways to provide the same information. undistort : bool, optional If `True`, take SIP and distortion lookup table into account axes : length 2 sequence ints, optional If provided, use the given sequence as the shape of the image. Otherwise, use the ``NAXIS1`` and ``NAXIS2`` keywords from the header that was used to create this `WCS` object. center : bool, optional If `True` use the center of the pixel, otherwise use the corner. Returns ------- coord : (4, 2) array of (*x*, *y*) coordinates. The order is clockwise starting with the bottom left corner. """ if axes is not None: naxis1, naxis2 = axes else: if header is None: try: # classes that inherit from WCS and define naxis1/2 # do not require a header parameter naxis1, naxis2 = self.pixel_shape except (AttributeError, TypeError): warnings.warn("Need a valid header in order to calculate footprint\n", AstropyUserWarning) return None else: naxis1 = header.get('NAXIS1', None) naxis2 = header.get('NAXIS2', None) if naxis1 is None or naxis2 is None: raise ValueError( "Image size could not be determined.") if center: corners = np.array([[1, 1], [1, naxis2], [naxis1, naxis2], [naxis1, 1]], dtype=np.float64) else: corners = np.array([[0.5, 0.5], [0.5, naxis2 + 0.5], [naxis1 + 0.5, naxis2 + 0.5], [naxis1 + 0.5, 0.5]], dtype=np.float64) if undistort: return self.all_pix2world(corners, 1) else: return self.wcs_pix2world(corners, 1)
def _read_det2im_kw(self, header, fobj, err=0.0): """ Create a `distortion paper`_ type lookup table for detector to image plane correction. """ if fobj is None: return (None, None) if not isinstance(fobj, fits.HDUList): return (None, None) try: axiscorr = header['AXISCORR'] d2imdis = self._read_d2im_old_format(header, fobj, axiscorr) return d2imdis except KeyError: pass dist = 'D2IMDIS' d_kw = 'D2IM' err_kw = 'D2IMERR' tables = {} for i in range(1, self.naxis + 1): d_error = header.get(err_kw + str(i), 0.0) if d_error < err: tables[i] = None continue distortion = dist + str(i) if distortion in header: dis = header[distortion].lower() if dis == 'lookup': del header[distortion] assert isinstance(fobj, fits.HDUList), ('An astropy.io.fits.HDUList' 'is required for Lookup table distortion.') dp = (d_kw + str(i)).strip() dp_extver_key = dp + '.EXTVER' if dp_extver_key in header: d_extver = header[dp_extver_key] del header[dp_extver_key] else: d_extver = 1 dp_axis_key = dp + f'.AXIS.{i:d}' if i == header[dp_axis_key]: d_data = fobj['D2IMARR', d_extver].data else: d_data = (fobj['D2IMARR', d_extver].data).transpose() del header[dp_axis_key] d_header = fobj['D2IMARR', d_extver].header d_crpix = (d_header.get('CRPIX1', 0.0), d_header.get('CRPIX2', 0.0)) d_crval = (d_header.get('CRVAL1', 0.0), d_header.get('CRVAL2', 0.0)) d_cdelt = (d_header.get('CDELT1', 1.0), d_header.get('CDELT2', 1.0)) d_lookup = DistortionLookupTable(d_data, d_crpix, d_crval, d_cdelt) tables[i] = d_lookup else: warnings.warn('Polynomial distortion is not implemented.\n', AstropyUserWarning) for key in set(header): if key.startswith(dp + '.'): del header[key] else: tables[i] = None if not tables: return (None, None) else: return (tables.get(1), tables.get(2)) def _read_d2im_old_format(self, header, fobj, axiscorr): warnings.warn("The use of ``AXISCORR`` for D2IM correction has been deprecated." "`~astropy.wcs` will read in files with ``AXISCORR`` but ``to_fits()`` will write " "out files without it.", AstropyDeprecationWarning) cpdis = [None, None] crpix = [0., 0.] crval = [0., 0.] cdelt = [1., 1.] try: d2im_data = fobj[('D2IMARR', 1)].data except KeyError: return (None, None) except AttributeError: return (None, None) d2im_data = np.array([d2im_data]) d2im_hdr = fobj[('D2IMARR', 1)].header naxis = d2im_hdr['NAXIS'] for i in range(1, naxis + 1): crpix[i - 1] = d2im_hdr.get('CRPIX' + str(i), 0.0) crval[i - 1] = d2im_hdr.get('CRVAL' + str(i), 0.0) cdelt[i - 1] = d2im_hdr.get('CDELT' + str(i), 1.0) cpdis = DistortionLookupTable(d2im_data, crpix, crval, cdelt) if axiscorr == 1: return (cpdis, None) elif axiscorr == 2: return (None, cpdis) else: warnings.warn("Expected AXISCORR to be 1 or 2", AstropyUserWarning) return (None, None) def _write_det2im(self, hdulist): """ Writes a `distortion paper`_ type lookup table to the given `astropy.io.fits.HDUList`. """ if self.det2im1 is None and self.det2im2 is None: return dist = 'D2IMDIS' d_kw = 'D2IM' err_kw = 'D2IMERR' def write_d2i(num, det2im): if det2im is None: return f'{dist}{num:d}', hdulist[0].header[f'{dist}{num:d}'] = ( 'LOOKUP', 'Detector to image correction type') hdulist[0].header[f'{d_kw}{num:d}.EXTVER'] = ( num, 'Version number of WCSDVARR extension') hdulist[0].header[f'{d_kw}{num:d}.NAXES'] = ( len(det2im.data.shape), 'Number of independent variables in d2im function') for i in range(det2im.data.ndim): hdulist[0].header['{}{:d}.AXIS.{:d}'.format(d_kw, num, i + 1)] = ( i + 1, 'Axis number of the jth independent variable in a d2im function') image = fits.ImageHDU(det2im.data, name='D2IMARR') header = image.header header['CRPIX1'] = (det2im.crpix[0], 'Coordinate system reference pixel') header['CRPIX2'] = (det2im.crpix[1], 'Coordinate system reference pixel') header['CRVAL1'] = (det2im.crval[0], 'Coordinate system value at reference pixel') header['CRVAL2'] = (det2im.crval[1], 'Coordinate system value at reference pixel') header['CDELT1'] = (det2im.cdelt[0], 'Coordinate increment along axis') header['CDELT2'] = (det2im.cdelt[1], 'Coordinate increment along axis') image.ver = int(hdulist[0].header[f'{d_kw}{num:d}.EXTVER']) hdulist.append(image) write_d2i(1, self.det2im1) write_d2i(2, self.det2im2) def _read_distortion_kw(self, header, fobj, dist='CPDIS', err=0.0): """ Reads `distortion paper`_ table-lookup keywords and data, and returns a 2-tuple of `~astropy.wcs.DistortionLookupTable` objects. If no `distortion paper`_ keywords are found, ``(None, None)`` is returned. """ if isinstance(header, (str, bytes)): return (None, None) if dist == 'CPDIS': d_kw = 'DP' err_kw = 'CPERR' else: d_kw = 'DQ' err_kw = 'CQERR' tables = {} for i in range(1, self.naxis + 1): d_error_key = err_kw + str(i) if d_error_key in header: d_error = header[d_error_key] del header[d_error_key] else: d_error = 0.0 if d_error < err: tables[i] = None continue distortion = dist + str(i) if distortion in header: dis = header[distortion].lower() del header[distortion] if dis == 'lookup': if not isinstance(fobj, fits.HDUList): raise ValueError('an astropy.io.fits.HDUList is ' 'required for Lookup table distortion.') dp = (d_kw + str(i)).strip() dp_extver_key = dp + '.EXTVER' if dp_extver_key in header: d_extver = header[dp_extver_key] del header[dp_extver_key] else: d_extver = 1 dp_axis_key = dp + f'.AXIS.{i:d}' if i == header[dp_axis_key]: d_data = fobj['WCSDVARR', d_extver].data else: d_data = (fobj['WCSDVARR', d_extver].data).transpose() del header[dp_axis_key] d_header = fobj['WCSDVARR', d_extver].header d_crpix = (d_header.get('CRPIX1', 0.0), d_header.get('CRPIX2', 0.0)) d_crval = (d_header.get('CRVAL1', 0.0), d_header.get('CRVAL2', 0.0)) d_cdelt = (d_header.get('CDELT1', 1.0), d_header.get('CDELT2', 1.0)) d_lookup = DistortionLookupTable(d_data, d_crpix, d_crval, d_cdelt) tables[i] = d_lookup for key in set(header): if key.startswith(dp + '.'): del header[key] else: warnings.warn('Polynomial distortion is not implemented.\n', AstropyUserWarning) else: tables[i] = None if not tables: return (None, None) else: return (tables.get(1), tables.get(2)) def _write_distortion_kw(self, hdulist, dist='CPDIS'): """ Write out `distortion paper`_ keywords to the given `fits.HDUList`. """ if self.cpdis1 is None and self.cpdis2 is None: return if dist == 'CPDIS': d_kw = 'DP' err_kw = 'CPERR' else: d_kw = 'DQ' err_kw = 'CQERR' def write_dist(num, cpdis): if cpdis is None: return hdulist[0].header[f'{dist}{num:d}'] = ( 'LOOKUP', 'Prior distortion function type') hdulist[0].header[f'{d_kw}{num:d}.EXTVER'] = ( num, 'Version number of WCSDVARR extension') hdulist[0].header[f'{d_kw}{num:d}.NAXES'] = ( len(cpdis.data.shape), 'Number of independent variables in distortion function') for i in range(cpdis.data.ndim): hdulist[0].header['{}{:d}.AXIS.{:d}'.format(d_kw, num, i + 1)] = ( i + 1, 'Axis number of the jth independent variable in a distortion function') image = fits.ImageHDU(cpdis.data, name='WCSDVARR') header = image.header header['CRPIX1'] = (cpdis.crpix[0], 'Coordinate system reference pixel') header['CRPIX2'] = (cpdis.crpix[1], 'Coordinate system reference pixel') header['CRVAL1'] = (cpdis.crval[0], 'Coordinate system value at reference pixel') header['CRVAL2'] = (cpdis.crval[1], 'Coordinate system value at reference pixel') header['CDELT1'] = (cpdis.cdelt[0], 'Coordinate increment along axis') header['CDELT2'] = (cpdis.cdelt[1], 'Coordinate increment along axis') image.ver = int(hdulist[0].header[f'{d_kw}{num:d}.EXTVER']) hdulist.append(image) write_dist(1, self.cpdis1) write_dist(2, self.cpdis2) def _remove_sip_kw(self, header): """ Remove SIP information from a header. """ # Never pass SIP coefficients to wcslib # CTYPE must be passed with -SIP to wcslib for key in set(m.group() for m in map(SIP_KW.match, list(header)) if m is not None): del header[key] def _read_sip_kw(self, header, wcskey=""): """ Reads `SIP`_ header keywords and returns a `~astropy.wcs.Sip` object. If no `SIP`_ header keywords are found, ``None`` is returned. """ if isinstance(header, (str, bytes)): # TODO: Parse SIP from a string without pyfits around return None if "A_ORDER" in header and header['A_ORDER'] > 1: if "B_ORDER" not in header: raise ValueError( "A_ORDER provided without corresponding B_ORDER " "keyword for SIP distortion") m = int(header["A_ORDER"]) a = np.zeros((m + 1, m + 1), np.double) for i in range(m + 1): for j in range(m - i + 1): key = f"A_{i}_{j}" if key in header: a[i, j] = header[key] del header[key] m = int(header["B_ORDER"]) if m > 1: b = np.zeros((m + 1, m + 1), np.double) for i in range(m + 1): for j in range(m - i + 1): key = f"B_{i}_{j}" if key in header: b[i, j] = header[key] del header[key] else: a = None b = None del header['A_ORDER'] del header['B_ORDER'] ctype = [header[f'CTYPE{nax}{wcskey}'] for nax in range(1, self.naxis + 1)] if any(not ctyp.endswith('-SIP') for ctyp in ctype): message = """ Inconsistent SIP distortion information is present in the FITS header and the WCS object: SIP coefficients were detected, but CTYPE is missing a "-SIP" suffix. astropy.wcs is using the SIP distortion coefficients, therefore the coordinates calculated here might be incorrect. If you do not want to apply the SIP distortion coefficients, please remove the SIP coefficients from the FITS header or the WCS object. As an example, if the image is already distortion-corrected (e.g., drizzled) then distortion components should not apply and the SIP coefficients should be removed. While the SIP distortion coefficients are being applied here, if that was indeed the intent, for consistency please append "-SIP" to the CTYPE in the FITS header or the WCS object. """ log.info(message) elif "B_ORDER" in header and header['B_ORDER'] > 1: raise ValueError( "B_ORDER provided without corresponding A_ORDER " + "keyword for SIP distortion") else: a = None b = None if "AP_ORDER" in header and header['AP_ORDER'] > 1: if "BP_ORDER" not in header: raise ValueError( "AP_ORDER provided without corresponding BP_ORDER " "keyword for SIP distortion") m = int(header["AP_ORDER"]) ap = np.zeros((m + 1, m + 1), np.double) for i in range(m + 1): for j in range(m - i + 1): key = f"AP_{i}_{j}" if key in header: ap[i, j] = header[key] del header[key] m = int(header["BP_ORDER"]) if m > 1: bp = np.zeros((m + 1, m + 1), np.double) for i in range(m + 1): for j in range(m - i + 1): key = f"BP_{i}_{j}" if key in header: bp[i, j] = header[key] del header[key] else: ap = None bp = None del header['AP_ORDER'] del header['BP_ORDER'] elif "BP_ORDER" in header and header['BP_ORDER'] > 1: raise ValueError( "BP_ORDER provided without corresponding AP_ORDER " "keyword for SIP distortion") else: ap = None bp = None if a is None and b is None and ap is None and bp is None: return None if f"CRPIX1{wcskey}" not in header or f"CRPIX2{wcskey}" not in header: raise ValueError( "Header has SIP keywords without CRPIX keywords") crpix1 = header.get(f"CRPIX1{wcskey}") crpix2 = header.get(f"CRPIX2{wcskey}") return Sip(a, b, ap, bp, (crpix1, crpix2)) def _write_sip_kw(self): """ Write out SIP keywords. Returns a dictionary of key-value pairs. """ if self.sip is None: return {} keywords = {} def write_array(name, a): if a is None: return size = a.shape[0] keywords[f'{name}_ORDER'] = size - 1 for i in range(size): for j in range(size - i): if a[i, j] != 0.0: keywords[ f'{name}_{i:d}_{j:d}'] = a[i, j] write_array('A', self.sip.a) write_array('B', self.sip.b) write_array('AP', self.sip.ap) write_array('BP', self.sip.bp) return keywords def _denormalize_sky(self, sky): if self.wcs.lngtyp != 'RA': raise ValueError( "WCS does not have longitude type of 'RA', therefore " + "(ra, dec) data can not be used as input") if self.wcs.lattyp != 'DEC': raise ValueError( "WCS does not have longitude type of 'DEC', therefore " + "(ra, dec) data can not be used as input") if self.wcs.naxis == 2: if self.wcs.lng == 0 and self.wcs.lat == 1: return sky elif self.wcs.lng == 1 and self.wcs.lat == 0: # Reverse the order of the columns return sky[:, ::-1] else: raise ValueError( "WCS does not have longitude and latitude celestial " + "axes, therefore (ra, dec) data can not be used as input") else: if self.wcs.lng < 0 or self.wcs.lat < 0: raise ValueError( "WCS does not have both longitude and latitude " "celestial axes, therefore (ra, dec) data can not be " + "used as input") out = np.zeros((sky.shape[0], self.wcs.naxis)) out[:, self.wcs.lng] = sky[:, 0] out[:, self.wcs.lat] = sky[:, 1] return out def _normalize_sky(self, sky): if self.wcs.lngtyp != 'RA': raise ValueError( "WCS does not have longitude type of 'RA', therefore " + "(ra, dec) data can not be returned") if self.wcs.lattyp != 'DEC': raise ValueError( "WCS does not have longitude type of 'DEC', therefore " + "(ra, dec) data can not be returned") if self.wcs.naxis == 2: if self.wcs.lng == 0 and self.wcs.lat == 1: return sky elif self.wcs.lng == 1 and self.wcs.lat == 0: # Reverse the order of the columns return sky[:, ::-1] else: raise ValueError( "WCS does not have longitude and latitude celestial " "axes, therefore (ra, dec) data can not be returned") else: if self.wcs.lng < 0 or self.wcs.lat < 0: raise ValueError( "WCS does not have both longitude and latitude celestial " "axes, therefore (ra, dec) data can not be returned") out = np.empty((sky.shape[0], 2)) out[:, 0] = sky[:, self.wcs.lng] out[:, 1] = sky[:, self.wcs.lat] return out def _array_converter(self, func, sky, *args, ra_dec_order=False): """ A helper function to support reading either a pair of arrays or a single Nx2 array. """ def _return_list_of_arrays(axes, origin): if any([x.size == 0 for x in axes]): return axes try: axes = np.broadcast_arrays(*axes) except ValueError: raise ValueError( "Coordinate arrays are not broadcastable to each other") xy = np.hstack([x.reshape((x.size, 1)) for x in axes]) if ra_dec_order and sky == 'input': xy = self._denormalize_sky(xy) output = func(xy, origin) if ra_dec_order and sky == 'output': output = self._normalize_sky(output) return (output[:, 0].reshape(axes[0].shape), output[:, 1].reshape(axes[0].shape)) return [output[:, i].reshape(axes[0].shape) for i in range(output.shape[1])] def _return_single_array(xy, origin): if xy.shape[-1] != self.naxis: raise ValueError( "When providing two arguments, the array must be " "of shape (N, {})".format(self.naxis)) if 0 in xy.shape: return xy if ra_dec_order and sky == 'input': xy = self._denormalize_sky(xy) result = func(xy, origin) if ra_dec_order and sky == 'output': result = self._normalize_sky(result) return result if len(args) == 2: try: xy, origin = args xy = np.asarray(xy) origin = int(origin) except Exception: raise TypeError( "When providing two arguments, they must be " "(coords[N][{}], origin)".format(self.naxis)) if xy.shape == () or len(xy.shape) == 1: return _return_list_of_arrays([xy], origin) return _return_single_array(xy, origin) elif len(args) == self.naxis + 1: axes = args[:-1] origin = args[-1] try: axes = [np.asarray(x) for x in axes] origin = int(origin) except Exception: raise TypeError( "When providing more than two arguments, they must be " + "a 1-D array for each axis, followed by an origin.") return _return_list_of_arrays(axes, origin) raise TypeError( "WCS projection has {0} dimensions, so expected 2 (an Nx{0} array " "and the origin argument) or {1} arguments (the position in each " "dimension, and the origin argument). Instead, {2} arguments were " "given.".format( self.naxis, self.naxis + 1, len(args)))
[docs] def all_pix2world(self, *args, **kwargs): return self._array_converter( self._all_pix2world, 'output', *args, **kwargs)
all_pix2world.__doc__ = """ Transforms pixel coordinates to world coordinates. Performs all of the following in series: - Detector to image plane correction (if present in the FITS file) - `SIP`_ distortion correction (if present in the FITS file) - `distortion paper`_ table-lookup correction (if present in the FITS file) - `wcslib`_ "core" WCS transformation Parameters ---------- {} For a transformation that is not two-dimensional, the two-argument form must be used. {} Returns ------- {} Notes ----- The order of the axes for the result is determined by the ``CTYPEia`` keywords in the FITS header, therefore it may not always be of the form (*ra*, *dec*). The `~astropy.wcs.Wcsprm.lat`, `~astropy.wcs.Wcsprm.lng`, `~astropy.wcs.Wcsprm.lattyp` and `~astropy.wcs.Wcsprm.lngtyp` members can be used to determine the order of the axes. Raises ------ MemoryError Memory allocation failed. SingularMatrixError Linear transformation matrix is singular. InconsistentAxisTypesError Inconsistent or unrecognized coordinate axis types. ValueError Invalid parameter value. ValueError Invalid coordinate transformation parameters. ValueError x- and y-coordinate arrays are not the same size. InvalidTransformError Invalid coordinate transformation parameters. InvalidTransformError Ill-conditioned coordinate transformation parameters. """.format(docstrings.TWO_OR_MORE_ARGS('naxis', 8), docstrings.RA_DEC_ORDER(8), docstrings.RETURNS('sky coordinates, in degrees', 8))
[docs] def wcs_pix2world(self, *args, **kwargs): if self.wcs is None: raise ValueError("No basic WCS settings were created.") return self._array_converter( lambda xy, o: self.wcs.p2s(xy, o)['world'], 'output', *args, **kwargs)
wcs_pix2world.__doc__ = """ Transforms pixel coordinates to world coordinates by doing only the basic `wcslib`_ transformation. No `SIP`_ or `distortion paper`_ table lookup correction is applied. To perform distortion correction, see `~astropy.wcs.WCS.all_pix2world`, `~astropy.wcs.WCS.sip_pix2foc`, `~astropy.wcs.WCS.p4_pix2foc`, or `~astropy.wcs.WCS.pix2foc`. Parameters ---------- {} For a transformation that is not two-dimensional, the two-argument form must be used. {} Returns ------- {} Raises ------ MemoryError Memory allocation failed. SingularMatrixError Linear transformation matrix is singular. InconsistentAxisTypesError Inconsistent or unrecognized coordinate axis types. ValueError Invalid parameter value. ValueError Invalid coordinate transformation parameters. ValueError x- and y-coordinate arrays are not the same size. InvalidTransformError Invalid coordinate transformation parameters. InvalidTransformError Ill-conditioned coordinate transformation parameters. Notes ----- The order of the axes for the result is determined by the ``CTYPEia`` keywords in the FITS header, therefore it may not always be of the form (*ra*, *dec*). The `~astropy.wcs.Wcsprm.lat`, `~astropy.wcs.Wcsprm.lng`, `~astropy.wcs.Wcsprm.lattyp` and `~astropy.wcs.Wcsprm.lngtyp` members can be used to determine the order of the axes. """.format(docstrings.TWO_OR_MORE_ARGS('naxis', 8), docstrings.RA_DEC_ORDER(8), docstrings.RETURNS('world coordinates, in degrees', 8)) def _all_world2pix(self, world, origin, tolerance, maxiter, adaptive, detect_divergence, quiet): # ############################################################ # # DESCRIPTION OF THE NUMERICAL METHOD ## # ############################################################ # In this section I will outline the method of solving # the inverse problem of converting world coordinates to # pixel coordinates (*inverse* of the direct transformation # `all_pix2world`) and I will summarize some of the aspects # of the method proposed here and some of the issues of the # original `all_world2pix` (in relation to this method) # discussed in https://github.com/astropy/astropy/issues/1977 # A more detailed discussion can be found here: # https://github.com/astropy/astropy/pull/2373 # # # ### Background ### # # # I will refer here to the [SIP Paper] # (http://fits.gsfc.nasa.gov/registry/sip/SIP_distortion_v1_0.pdf). # According to this paper, the effect of distortions as # described in *their* equation (1) is: # # (1) x = CD*(u+f(u)), # # where `x` is a *vector* of "intermediate spherical # coordinates" (equivalent to (x,y) in the paper) and `u` # is a *vector* of "pixel coordinates", and `f` is a vector # function describing geometrical distortions # (see equations 2 and 3 in SIP Paper. # However, I prefer to use `w` for "intermediate world # coordinates", `x` for pixel coordinates, and assume that # transformation `W` performs the **linear** # (CD matrix + projection onto celestial sphere) part of the # conversion from pixel coordinates to world coordinates. # Then we can re-write (1) as: # # (2) w = W*(x+f(x)) = T(x) # # In `astropy.wcs.WCS` transformation `W` is represented by # the `wcs_pix2world` member, while the combined ("total") # transformation (linear part + distortions) is performed by # `all_pix2world`. Below I summarize the notations and their # equivalents in `astropy.wcs.WCS`: # # | Equation term | astropy.WCS/meaning | # | ------------- | ---------------------------- | # | `x` | pixel coordinates | # | `w` | world coordinates | # | `W` | `wcs_pix2world()` | # | `W^{-1}` | `wcs_world2pix()` | # | `T` | `all_pix2world()` | # | `x+f(x)` | `pix2foc()` | # # # ### Direct Solving of Equation (2) ### # # # In order to find the pixel coordinates that correspond to # given world coordinates `w`, it is necessary to invert # equation (2): `x=T^{-1}(w)`, or solve equation `w==T(x)` # for `x`. However, this approach has the following # disadvantages: # 1. It requires unnecessary transformations (see next # section). # 2. It is prone to "RA wrapping" issues as described in # https://github.com/astropy/astropy/issues/1977 # (essentially because `all_pix2world` may return points with # a different phase than user's input `w`). # # # ### Description of the Method Used here ### # # # By applying inverse linear WCS transformation (`W^{-1}`) # to both sides of equation (2) and introducing notation `x'` # (prime) for the pixels coordinates obtained from the world # coordinates by applying inverse *linear* WCS transformation # ("focal plane coordinates"): # # (3) x' = W^{-1}(w) # # we obtain the following equation: # # (4) x' = x+f(x), # # or, # # (5) x = x'-f(x) # # This equation is well suited for solving using the method # of fixed-point iterations # (http://en.wikipedia.org/wiki/Fixed-point_iteration): # # (6) x_{i+1} = x'-f(x_i) # # As an initial value of the pixel coordinate `x_0` we take # "focal plane coordinate" `x'=W^{-1}(w)=wcs_world2pix(w)`. # We stop iterations when `|x_{i+1}-x_i|<tolerance`. We also # consider the process to be diverging if # `|x_{i+1}-x_i|>|x_i-x_{i-1}|` # **when** `|x_{i+1}-x_i|>=tolerance` (when current # approximation is close to the true solution, # `|x_{i+1}-x_i|>|x_i-x_{i-1}|` may be due to rounding errors # and we ignore such "divergences" when # `|x_{i+1}-x_i|<tolerance`). It may appear that checking for # `|x_{i+1}-x_i|<tolerance` in order to ignore divergence is # unnecessary since the iterative process should stop anyway, # however, the proposed implementation of this iterative # process is completely vectorized and, therefore, we may # continue iterating over *some* points even though they have # converged to within a specified tolerance (while iterating # over other points that have not yet converged to # a solution). # # In order to efficiently implement iterative process (6) # using available methods in `astropy.wcs.WCS`, we add and # subtract `x_i` from the right side of equation (6): # # (7) x_{i+1} = x'-(x_i+f(x_i))+x_i = x'-pix2foc(x_i)+x_i, # # where `x'=wcs_world2pix(w)` and it is computed only *once* # before the beginning of the iterative process (and we also # set `x_0=x'`). By using `pix2foc` at each iteration instead # of `all_pix2world` we get about 25% increase in performance # (by not performing the linear `W` transformation at each # step) and we also avoid the "RA wrapping" issue described # above (by working in focal plane coordinates and avoiding # pix->world transformations). # # As an added benefit, the process converges to the correct # solution in just one iteration when distortions are not # present (compare to # https://github.com/astropy/astropy/issues/1977 and # https://github.com/astropy/astropy/pull/2294): in this case # `pix2foc` is the identical transformation # `x_i=pix2foc(x_i)` and from equation (7) we get: # # x' = x_0 = wcs_world2pix(w) # x_1 = x' - pix2foc(x_0) + x_0 = x' - pix2foc(x') + x' = x' # = wcs_world2pix(w) = x_0 # => # |x_1-x_0| = 0 < tolerance (with tolerance > 0) # # However, for performance reasons, it is still better to # avoid iterations altogether and return the exact linear # solution (`wcs_world2pix`) right-away when non-linear # distortions are not present by checking that attributes # `sip`, `cpdis1`, `cpdis2`, `det2im1`, and `det2im2` are # *all* `None`. # # # ### Outline of the Algorithm ### # # # While the proposed code is relatively long (considering # the simplicity of the algorithm), this is due to: 1) # checking if iterative solution is necessary at all; 2) # checking for divergence; 3) re-implementation of the # completely vectorized algorithm as an "adaptive" vectorized # algorithm (for cases when some points diverge for which we # want to stop iterations). In my tests, the adaptive version # of the algorithm is about 50% slower than non-adaptive # version for all HST images. # # The essential part of the vectorized non-adaptive algorithm # (without divergence and other checks) can be described # as follows: # # pix0 = self.wcs_world2pix(world, origin) # pix = pix0.copy() # 0-order solution # # for k in range(maxiter): # # find correction to the previous solution: # dpix = self.pix2foc(pix, origin) - pix0 # # # compute norm (L2) of the correction: # dn = np.linalg.norm(dpix, axis=1) # # # apply correction: # pix -= dpix # # # check convergence: # if np.max(dn) < tolerance: # break # # return pix # # Here, the input parameter `world` can be a `MxN` array # where `M` is the number of coordinate axes in WCS and `N` # is the number of points to be converted simultaneously to # image coordinates. # # # ### IMPORTANT NOTE: ### # # If, in the future releases of the `~astropy.wcs`, # `pix2foc` will not apply all the required distortion # corrections then in the code below, calls to `pix2foc` will # have to be replaced with # wcs_world2pix(all_pix2world(pix_list, origin), origin) # # ############################################################ # # INITIALIZE ITERATIVE PROCESS: ## # ############################################################ # initial approximation (linear WCS based only) pix0 = self.wcs_world2pix(world, origin) # Check that an iterative solution is required at all # (when any of the non-CD-matrix-based corrections are # present). If not required return the initial # approximation (pix0). if not self.has_distortion: # No non-WCS corrections detected so # simply return initial approximation: return pix0 pix = pix0.copy() # 0-order solution # initial correction: dpix = self.pix2foc(pix, origin) - pix0 # Update initial solution: pix -= dpix # Norm (L2) squared of the correction: dn = np.sum(dpix*dpix, axis=1) dnprev = dn.copy() # if adaptive else dn tol2 = tolerance**2 # Prepare for iterative process k = 1 ind = None inddiv = None # Turn off numpy runtime warnings for 'invalid' and 'over': old_invalid = np.geterr()['invalid'] old_over = np.geterr()['over'] np.seterr(invalid='ignore', over='ignore') # ############################################################ # # NON-ADAPTIVE ITERATIONS: ## # ############################################################ if not adaptive: # Fixed-point iterations: while (np.nanmax(dn) >= tol2 and k < maxiter): # Find correction to the previous solution: dpix = self.pix2foc(pix, origin) - pix0 # Compute norm (L2) squared of the correction: dn = np.sum(dpix*dpix, axis=1) # Check for divergence (we do this in two stages # to optimize performance for the most common # scenario when successive approximations converge): if detect_divergence: divergent = (dn >= dnprev) if np.any(divergent): # Find solutions that have not yet converged: slowconv = (dn >= tol2) inddiv, = np.where(divergent & slowconv) if inddiv.shape[0] > 0: # Update indices of elements that # still need correction: conv = (dn < dnprev) iconv = np.where(conv) # Apply correction: dpixgood = dpix[iconv] pix[iconv] -= dpixgood dpix[iconv] = dpixgood # For the next iteration choose # non-divergent points that have not yet # converged to the requested accuracy: ind, = np.where(slowconv & conv) pix0 = pix0[ind] dnprev[ind] = dn[ind] k += 1 # Switch to adaptive iterations: adaptive = True break # Save current correction magnitudes for later: dnprev = dn # Apply correction: pix -= dpix k += 1 # ############################################################ # # ADAPTIVE ITERATIONS: ## # ############################################################ if adaptive: if ind is None: ind, = np.where(np.isfinite(pix).all(axis=1)) pix0 = pix0[ind] # "Adaptive" fixed-point iterations: while (ind.shape[0] > 0 and k < maxiter): # Find correction to the previous solution: dpixnew = self.pix2foc(pix[ind], origin) - pix0 # Compute norm (L2) of the correction: dnnew = np.sum(np.square(dpixnew), axis=1) # Bookeeping of corrections: dnprev[ind] = dn[ind].copy() dn[ind] = dnnew if detect_divergence: # Find indices of pixels that are converging: conv = (dnnew < dnprev[ind]) iconv = np.where(conv) iiconv = ind[iconv] # Apply correction: dpixgood = dpixnew[iconv] pix[iiconv] -= dpixgood dpix[iiconv] = dpixgood # Find indices of solutions that have not yet # converged to the requested accuracy # AND that do not diverge: subind, = np.where((dnnew >= tol2) & conv) else: # Apply correction: pix[ind] -= dpixnew dpix[ind] = dpixnew # Find indices of solutions that have not yet # converged to the requested accuracy: subind, = np.where(dnnew >= tol2) # Choose solutions that need more iterations: ind = ind[subind] pix0 = pix0[subind] k += 1 # ############################################################ # # FINAL DETECTION OF INVALID, DIVERGING, ## # # AND FAILED-TO-CONVERGE POINTS ## # ############################################################ # Identify diverging and/or invalid points: invalid = ((~np.all(np.isfinite(pix), axis=1)) & (np.all(np.isfinite(world), axis=1))) # When detect_divergence==False, dnprev is outdated # (it is the norm of the very first correction). # Still better than nothing... inddiv, = np.where(((dn >= tol2) & (dn >= dnprev)) | invalid) if inddiv.shape[0] == 0: inddiv = None # Identify points that did not converge within 'maxiter' # iterations: if k >= maxiter: ind, = np.where((dn >= tol2) & (dn < dnprev) & (~invalid)) if ind.shape[0] == 0: ind = None else: ind = None # Restore previous numpy error settings: np.seterr(invalid=old_invalid, over=old_over) # ############################################################ # # RAISE EXCEPTION IF DIVERGING OR TOO SLOWLY CONVERGING ## # # DATA POINTS HAVE BEEN DETECTED: ## # ############################################################ if (ind is not None or inddiv is not None) and not quiet: if inddiv is None: raise NoConvergence( "'WCS.all_world2pix' failed to " "converge to the requested accuracy after {:d} " "iterations.".format(k), best_solution=pix, accuracy=np.abs(dpix), niter=k, slow_conv=ind, divergent=None) else: raise NoConvergence( "'WCS.all_world2pix' failed to " "converge to the requested accuracy.\n" "After {:d} iterations, the solution is diverging " "at least for one input point." .format(k), best_solution=pix, accuracy=np.abs(dpix), niter=k, slow_conv=ind, divergent=inddiv) return pix
[docs] def all_world2pix(self, *args, tolerance=1e-4, maxiter=20, adaptive=False, detect_divergence=True, quiet=False, **kwargs): if self.wcs is None: raise ValueError("No basic WCS settings were created.") return self._array_converter( lambda *args, **kwargs: self._all_world2pix( *args, tolerance=tolerance, maxiter=maxiter, adaptive=adaptive, detect_divergence=detect_divergence, quiet=quiet), 'input', *args, **kwargs )
all_world2pix.__doc__ = """ all_world2pix(*arg, accuracy=1.0e-4, maxiter=20, adaptive=False, detect_divergence=True, quiet=False) Transforms world coordinates to pixel coordinates, using numerical iteration to invert the full forward transformation `~astropy.wcs.WCS.all_pix2world` with complete distortion model. Parameters ---------- {0} For a transformation that is not two-dimensional, the two-argument form must be used. {1} tolerance : float, optional (Default = 1.0e-4) Tolerance of solution. Iteration terminates when the iterative solver estimates that the "true solution" is within this many pixels current estimate, more specifically, when the correction to the solution found during the previous iteration is smaller (in the sense of the L2 norm) than ``tolerance``. maxiter : int, optional (Default = 20) Maximum number of iterations allowed to reach a solution. quiet : bool, optional (Default = False) Do not throw :py:class:`NoConvergence` exceptions when the method does not converge to a solution with the required accuracy within a specified number of maximum iterations set by ``maxiter`` parameter. Instead, simply return the found solution. Other Parameters ---------------- adaptive : bool, optional (Default = False) Specifies whether to adaptively select only points that did not converge to a solution within the required accuracy for the next iteration. Default is recommended for HST as well as most other instruments. .. note:: The :py:meth:`all_world2pix` uses a vectorized implementation of the method of consecutive approximations (see ``Notes`` section below) in which it iterates over *all* input points *regardless* until the required accuracy has been reached for *all* input points. In some cases it may be possible that *almost all* points have reached the required accuracy but there are only a few of input data points for which additional iterations may be needed (this depends mostly on the characteristics of the geometric distortions for a given instrument). In this situation it may be advantageous to set ``adaptive`` = `True` in which case :py:meth:`all_world2pix` will continue iterating *only* over the points that have not yet converged to the required accuracy. However, for the HST's ACS/WFC detector, which has the strongest distortions of all HST instruments, testing has shown that enabling this option would lead to a about 50-100% penalty in computational time (depending on specifics of the image, geometric distortions, and number of input points to be converted). Therefore, for HST and possibly instruments, it is recommended to set ``adaptive`` = `False`. The only danger in getting this setting wrong will be a performance penalty. .. note:: When ``detect_divergence`` is `True`, :py:meth:`all_world2pix` will automatically switch to the adaptive algorithm once divergence has been detected. detect_divergence : bool, optional (Default = True) Specifies whether to perform a more detailed analysis of the convergence to a solution. Normally :py:meth:`all_world2pix` may not achieve the required accuracy if either the ``tolerance`` or ``maxiter`` arguments are too low. However, it may happen that for some geometric distortions the conditions of convergence for the the method of consecutive approximations used by :py:meth:`all_world2pix` may not be satisfied, in which case consecutive approximations to the solution will diverge regardless of the ``tolerance`` or ``maxiter`` settings. When ``detect_divergence`` is `False`, these divergent points will be detected as not having achieved the required accuracy (without further details). In addition, if ``adaptive`` is `False` then the algorithm will not know that the solution (for specific points) is diverging and will continue iterating and trying to "improve" diverging solutions. This may result in ``NaN`` or ``Inf`` values in the return results (in addition to a performance penalties). Even when ``detect_divergence`` is `False`, :py:meth:`all_world2pix`, at the end of the iterative process, will identify invalid results (``NaN`` or ``Inf``) as "diverging" solutions and will raise :py:class:`NoConvergence` unless the ``quiet`` parameter is set to `True`. When ``detect_divergence`` is `True`, :py:meth:`all_world2pix` will detect points for which current correction to the coordinates is larger than the correction applied during the previous iteration **if** the requested accuracy **has not yet been achieved**. In this case, if ``adaptive`` is `True`, these points will be excluded from further iterations and if ``adaptive`` is `False`, :py:meth:`all_world2pix` will automatically switch to the adaptive algorithm. Thus, the reported divergent solution will be the latest converging solution computed immediately *before* divergence has been detected. .. note:: When accuracy has been achieved, small increases in current corrections may be possible due to rounding errors (when ``adaptive`` is `False`) and such increases will be ignored. .. note:: Based on our testing using HST ACS/WFC images, setting ``detect_divergence`` to `True` will incur about 5-20% performance penalty with the larger penalty corresponding to ``adaptive`` set to `True`. Because the benefits of enabling this feature outweigh the small performance penalty, especially when ``adaptive`` = `False`, it is recommended to set ``detect_divergence`` to `True`, unless extensive testing of the distortion models for images from specific instruments show a good stability of the numerical method for a wide range of coordinates (even outside the image itself). .. note:: Indices of the diverging inverse solutions will be reported in the ``divergent`` attribute of the raised :py:class:`NoConvergence` exception object. Returns ------- {2} Notes ----- The order of the axes for the input world array is determined by the ``CTYPEia`` keywords in the FITS header, therefore it may not always be of the form (*ra*, *dec*). The `~astropy.wcs.Wcsprm.lat`, `~astropy.wcs.Wcsprm.lng`, `~astropy.wcs.Wcsprm.lattyp`, and `~astropy.wcs.Wcsprm.lngtyp` members can be used to determine the order of the axes. Using the method of fixed-point iterations approximations we iterate starting with the initial approximation, which is computed using the non-distortion-aware :py:meth:`wcs_world2pix` (or equivalent). The :py:meth:`all_world2pix` function uses a vectorized implementation of the method of consecutive approximations and therefore it is highly efficient (>30x) when *all* data points that need to be converted from sky coordinates to image coordinates are passed at *once*. Therefore, it is advisable, whenever possible, to pass as input a long array of all points that need to be converted to :py:meth:`all_world2pix` instead of calling :py:meth:`all_world2pix` for each data point. Also see the note to the ``adaptive`` parameter. Raises ------ NoConvergence The method did not converge to a solution to the required accuracy within a specified number of maximum iterations set by the ``maxiter`` parameter. To turn off this exception, set ``quiet`` to `True`. Indices of the points for which the requested accuracy was not achieved (if any) will be listed in the ``slow_conv`` attribute of the raised :py:class:`NoConvergence` exception object. See :py:class:`NoConvergence` documentation for more details. MemoryError Memory allocation failed. SingularMatrixError Linear transformation matrix is singular. InconsistentAxisTypesError Inconsistent or unrecognized coordinate axis types. ValueError Invalid parameter value. ValueError Invalid coordinate transformation parameters. ValueError x- and y-coordinate arrays are not the same size. InvalidTransformError Invalid coordinate transformation parameters. InvalidTransformError Ill-conditioned coordinate transformation parameters. Examples -------- >>> import astropy.io.fits as fits >>> import astropy.wcs as wcs >>> import numpy as np >>> import os >>> filename = os.path.join(wcs.__path__[0], 'tests/data/j94f05bgq_flt.fits') >>> hdulist = fits.open(filename) >>> w = wcs.WCS(hdulist[('sci',1)].header, hdulist) >>> hdulist.close() >>> ra, dec = w.all_pix2world([1,2,3], [1,1,1], 1) >>> print(ra) # doctest: +FLOAT_CMP [ 5.52645627 5.52649663 5.52653698] >>> print(dec) # doctest: +FLOAT_CMP [-72.05171757 -72.05171276 -72.05170795] >>> radec = w.all_pix2world([[1,1], [2,1], [3,1]], 1) >>> print(radec) # doctest: +FLOAT_CMP [[ 5.52645627 -72.05171757] [ 5.52649663 -72.05171276] [ 5.52653698 -72.05170795]] >>> x, y = w.all_world2pix(ra, dec, 1) >>> print(x) # doctest: +FLOAT_CMP [ 1.00000238 2.00000237 3.00000236] >>> print(y) # doctest: +FLOAT_CMP [ 0.99999996 0.99999997 0.99999997] >>> xy = w.all_world2pix(radec, 1) >>> print(xy) # doctest: +FLOAT_CMP [[ 1.00000238 0.99999996] [ 2.00000237 0.99999997] [ 3.00000236 0.99999997]] >>> xy = w.all_world2pix(radec, 1, maxiter=3, ... tolerance=1.0e-10, quiet=False) Traceback (most recent call last): ... NoConvergence: 'WCS.all_world2pix' failed to converge to the requested accuracy. After 3 iterations, the solution is diverging at least for one input point. >>> # Now try to use some diverging data: >>> divradec = w.all_pix2world([[1.0, 1.0], ... [10000.0, 50000.0], ... [3.0, 1.0]], 1) >>> print(divradec) # doctest: +FLOAT_CMP [[ 5.52645627 -72.05171757] [ 7.15976932 -70.8140779 ] [ 5.52653698 -72.05170795]] >>> # First, turn detect_divergence on: >>> try: # doctest: +FLOAT_CMP ... xy = w.all_world2pix(divradec, 1, maxiter=20, ... tolerance=1.0e-4, adaptive=False, ... detect_divergence=True, ... quiet=False) ... except wcs.wcs.NoConvergence as e: ... print("Indices of diverging points: {{0}}" ... .format(e.divergent)) ... print("Indices of poorly converging points: {{0}}" ... .format(e.slow_conv)) ... print("Best solution:\\n{{0}}".format(e.best_solution)) ... print("Achieved accuracy:\\n{{0}}".format(e.accuracy)) Indices of diverging points: [1] Indices of poorly converging points: None Best solution: [[ 1.00000238e+00 9.99999965e-01] [ -1.99441636e+06 1.44309097e+06] [ 3.00000236e+00 9.99999966e-01]] Achieved accuracy: [[ 6.13968380e-05 8.59638593e-07] [ 8.59526812e+11 6.61713548e+11] [ 6.09398446e-05 8.38759724e-07]] >>> raise e Traceback (most recent call last): ... NoConvergence: 'WCS.all_world2pix' failed to converge to the requested accuracy. After 5 iterations, the solution is diverging at least for one input point. >>> # This time turn detect_divergence off: >>> try: # doctest: +FLOAT_CMP ... xy = w.all_world2pix(divradec, 1, maxiter=20, ... tolerance=1.0e-4, adaptive=False, ... detect_divergence=False, ... quiet=False) ... except wcs.wcs.NoConvergence as e: ... print("Indices of diverging points: {{0}}" ... .format(e.divergent)) ... print("Indices of poorly converging points: {{0}}" ... .format(e.slow_conv)) ... print("Best solution:\\n{{0}}".format(e.best_solution)) ... print("Achieved accuracy:\\n{{0}}".format(e.accuracy)) Indices of diverging points: [1] Indices of poorly converging points: None Best solution: [[ 1.00000009 1. ] [ nan nan] [ 3.00000009 1. ]] Achieved accuracy: [[ 2.29417358e-06 3.21222995e-08] [ nan nan] [ 2.27407877e-06 3.13005639e-08]] >>> raise e Traceback (most recent call last): ... NoConvergence: 'WCS.all_world2pix' failed to converge to the requested accuracy. After 6 iterations, the solution is diverging at least for one input point. """.format(docstrings.TWO_OR_MORE_ARGS('naxis', 8), docstrings.RA_DEC_ORDER(8), docstrings.RETURNS('pixel coordinates', 8))
[docs] def wcs_world2pix(self, *args, **kwargs): if self.wcs is None: raise ValueError("No basic WCS settings were created.") return self._array_converter( lambda xy, o: self.wcs.s2p(xy, o)['pixcrd'], 'input', *args, **kwargs)
wcs_world2pix.__doc__ = """ Transforms world coordinates to pixel coordinates, using only the basic `wcslib`_ WCS transformation. No `SIP`_ or `distortion paper`_ table lookup transformation is applied. Parameters ---------- {} For a transformation that is not two-dimensional, the two-argument form must be used. {} Returns ------- {} Notes ----- The order of the axes for the input world array is determined by the ``CTYPEia`` keywords in the FITS header, therefore it may not always be of the form (*ra*, *dec*). The `~astropy.wcs.Wcsprm.lat`, `~astropy.wcs.Wcsprm.lng`, `~astropy.wcs.Wcsprm.lattyp` and `~astropy.wcs.Wcsprm.lngtyp` members can be used to determine the order of the axes. Raises ------ MemoryError Memory allocation failed. SingularMatrixError Linear transformation matrix is singular. InconsistentAxisTypesError Inconsistent or unrecognized coordinate axis types. ValueError Invalid parameter value. ValueError Invalid coordinate transformation parameters. ValueError x- and y-coordinate arrays are not the same size. InvalidTransformError Invalid coordinate transformation parameters. InvalidTransformError Ill-conditioned coordinate transformation parameters. """.format(docstrings.TWO_OR_MORE_ARGS('naxis', 8), docstrings.RA_DEC_ORDER(8), docstrings.RETURNS('pixel coordinates', 8))
[docs] def pix2foc(self, *args): return self._array_converter(self._pix2foc, None, *args)
pix2foc.__doc__ = """ Convert pixel coordinates to focal plane coordinates using the `SIP`_ polynomial distortion convention and `distortion paper`_ table-lookup correction. The output is in absolute pixel coordinates, not relative to ``CRPIX``. Parameters ---------- {} Returns ------- {} Raises ------ MemoryError Memory allocation failed. ValueError Invalid coordinate transformation parameters. """.format(docstrings.TWO_OR_MORE_ARGS('2', 8), docstrings.RETURNS('focal coordinates', 8))
[docs] def p4_pix2foc(self, *args): return self._array_converter(self._p4_pix2foc, None, *args)
p4_pix2foc.__doc__ = """ Convert pixel coordinates to focal plane coordinates using `distortion paper`_ table-lookup correction. The output is in absolute pixel coordinates, not relative to ``CRPIX``. Parameters ---------- {} Returns ------- {} Raises ------ MemoryError Memory allocation failed. ValueError Invalid coordinate transformation parameters. """.format(docstrings.TWO_OR_MORE_ARGS('2', 8), docstrings.RETURNS('focal coordinates', 8))
[docs] def det2im(self, *args): return self._array_converter(self._det2im, None, *args)
det2im.__doc__ = """ Convert detector coordinates to image plane coordinates using `distortion paper`_ table-lookup correction. The output is in absolute pixel coordinates, not relative to ``CRPIX``. Parameters ---------- {} Returns ------- {} Raises ------ MemoryError Memory allocation failed. ValueError Invalid coordinate transformation parameters. """.format(docstrings.TWO_OR_MORE_ARGS('2', 8), docstrings.RETURNS('pixel coordinates', 8))
[docs] def sip_pix2foc(self, *args): if self.sip is None: if len(args) == 2: return args[0] elif len(args) == 3: return args[:2] else: raise TypeError("Wrong number of arguments") return self._array_converter(self.sip.pix2foc, None, *args)
sip_pix2foc.__doc__ = """ Convert pixel coordinates to focal plane coordinates using the `SIP`_ polynomial distortion convention. The output is in pixel coordinates, relative to ``CRPIX``. FITS WCS `distortion paper`_ table lookup correction is not applied, even if that information existed in the FITS file that initialized this :class:`~astropy.wcs.WCS` object. To correct for that, use `~astropy.wcs.WCS.pix2foc` or `~astropy.wcs.WCS.p4_pix2foc`. Parameters ---------- {} Returns ------- {} Raises ------ MemoryError Memory allocation failed. ValueError Invalid coordinate transformation parameters. """.format(docstrings.TWO_OR_MORE_ARGS('2', 8), docstrings.RETURNS('focal coordinates', 8))
[docs] def sip_foc2pix(self, *args): if self.sip is None: if len(args) == 2: return args[0] elif len(args) == 3: return args[:2] else: raise TypeError("Wrong number of arguments") return self._array_converter(self.sip.foc2pix, None, *args)
sip_foc2pix.__doc__ = """ Convert focal plane coordinates to pixel coordinates using the `SIP`_ polynomial distortion convention. FITS WCS `distortion paper`_ table lookup distortion correction is not applied, even if that information existed in the FITS file that initialized this `~astropy.wcs.WCS` object. Parameters ---------- {} Returns ------- {} Raises ------ MemoryError Memory allocation failed. ValueError Invalid coordinate transformation parameters. """.format(docstrings.TWO_OR_MORE_ARGS('2', 8), docstrings.RETURNS('pixel coordinates', 8))
[docs] def to_fits(self, relax=False, key=None): """ Generate an `astropy.io.fits.HDUList` object with all of the information stored in this object. This should be logically identical to the input FITS file, but it will be normalized in a number of ways. See `to_header` for some warnings about the output produced. Parameters ---------- relax : bool or int, optional Degree of permissiveness: - `False` (default): Write all extensions that are considered to be safe and recommended. - `True`: Write all recognized informal extensions of the WCS standard. - `int`: a bit field selecting specific extensions to write. See :ref:`relaxwrite` for details. key : str The name of a particular WCS transform to use. This may be either ``' '`` or ``'A'``-``'Z'`` and corresponds to the ``"a"`` part of the ``CTYPEia`` cards. Returns ------- hdulist : `astropy.io.fits.HDUList` """ header = self.to_header(relax=relax, key=key) hdu = fits.PrimaryHDU(header=header) hdulist = fits.HDUList(hdu) self._write_det2im(hdulist) self._write_distortion_kw(hdulist) return hdulist
[docs] def to_header(self, relax=None, key=None): """Generate an `astropy.io.fits.Header` object with the basic WCS and SIP information stored in this object. This should be logically identical to the input FITS file, but it will be normalized in a number of ways. .. warning:: This function does not write out FITS WCS `distortion paper`_ information, since that requires multiple FITS header data units. To get a full representation of everything in this object, use `to_fits`. Parameters ---------- relax : bool or int, optional Degree of permissiveness: - `False` (default): Write all extensions that are considered to be safe and recommended. - `True`: Write all recognized informal extensions of the WCS standard. - `int`: a bit field selecting specific extensions to write. See :ref:`relaxwrite` for details. If the ``relax`` keyword argument is not given and any keywords were omitted from the output, an `~astropy.utils.exceptions.AstropyWarning` is displayed. To override this, explicitly pass a value to ``relax``. key : str The name of a particular WCS transform to use. This may be either ``' '`` or ``'A'``-``'Z'`` and corresponds to the ``"a"`` part of the ``CTYPEia`` cards. Returns ------- header : `astropy.io.fits.Header` Notes ----- The output header will almost certainly differ from the input in a number of respects: 1. The output header only contains WCS-related keywords. In particular, it does not contain syntactically-required keywords such as ``SIMPLE``, ``NAXIS``, ``BITPIX``, or ``END``. 2. Deprecated (e.g. ``CROTAn``) or non-standard usage will be translated to standard (this is partially dependent on whether ``fix`` was applied). 3. Quantities will be converted to the units used internally, basically SI with the addition of degrees. 4. Floating-point quantities may be given to a different decimal precision. 5. Elements of the ``PCi_j`` matrix will be written if and only if they differ from the unit matrix. Thus, if the matrix is unity then no elements will be written. 6. Additional keywords such as ``WCSAXES``, ``CUNITia``, ``LONPOLEa`` and ``LATPOLEa`` may appear. 7. The original keycomments will be lost, although `to_header` tries hard to write meaningful comments. 8. Keyword order may be changed. """ # default precision for numerical WCS keywords precision = WCSHDO_P14 display_warning = False if relax is None: display_warning = True relax = False if relax not in (True, False): do_sip = relax & WCSHDO_SIP relax &= ~WCSHDO_SIP else: do_sip = relax relax = WCSHDO_all if relax is True else WCSHDO_safe relax = precision | relax if self.wcs is not None: if key is not None: orig_key = self.wcs.alt self.wcs.alt = key header_string = self.wcs.to_header(relax) header = fits.Header.fromstring(header_string) keys_to_remove = ["", " ", "COMMENT"] for kw in keys_to_remove: if kw in header: del header[kw] else: header = fits.Header() if do_sip and self.sip is not None: if self.wcs is not None and any(not ctyp.endswith('-SIP') for ctyp in self.wcs.ctype): self._fix_ctype(header, add_sip=True) for kw, val in self._write_sip_kw().items(): header[kw] = val if not do_sip and self.wcs is not None and any(self.wcs.ctype) and self.sip is not None: # This is called when relax is not False or WCSHDO_SIP # The default case of ``relax=None`` is handled further in the code. header = self._fix_ctype(header, add_sip=False) if display_warning: full_header = self.to_header(relax=True, key=key) missing_keys = [] for kw, val in full_header.items(): if kw not in header: missing_keys.append(kw) if len(missing_keys): warnings.warn( "Some non-standard WCS keywords were excluded: {} " "Use the ``relax`` kwarg to control this.".format( ', '.join(missing_keys)), AstropyWarning) # called when ``relax=None`` # This is different from the case of ``relax=False``. if any(self.wcs.ctype) and self.sip is not None: header = self._fix_ctype(header, add_sip=False, log_message=False) # Finally reset the key. This must be called after ``_fix_ctype``. if key is not None: self.wcs.alt = orig_key return header
def _fix_ctype(self, header, add_sip=True, log_message=True): """ Parameters ---------- header : `~astropy.io.fits.Header` FITS header. add_sip : bool Flag indicating whether "-SIP" should be added or removed from CTYPE keywords. Remove "-SIP" from CTYPE when writing out a header with relax=False. This needs to be done outside ``to_header`` because ``to_header`` runs twice when ``relax=False`` and the second time ``relax`` is set to ``True`` to display the missing keywords. If the user requested SIP distortion to be written out add "-SIP" to CTYPE if it is missing. """ _add_sip_to_ctype = """ Inconsistent SIP distortion information is present in the current WCS: SIP coefficients were detected, but CTYPE is missing "-SIP" suffix, therefore the current WCS is internally inconsistent. Because relax has been set to True, the resulting output WCS will have "-SIP" appended to CTYPE in order to make the header internally consistent. However, this may produce incorrect astrometry in the output WCS, if in fact the current WCS is already distortion-corrected. Therefore, if current WCS is already distortion-corrected (eg, drizzled) then SIP distortion components should not apply. In that case, for a WCS that is already distortion-corrected, please remove the SIP coefficients from the header. """ if log_message: if add_sip: log.info(_add_sip_to_ctype) for i in range(1, self.naxis+1): # strip() must be called here to cover the case of alt key= " " kw = f'CTYPE{i}{self.wcs.alt}'.strip() if kw in header: if add_sip: val = header[kw].strip("-SIP") + "-SIP" else: val = header[kw].strip("-SIP") header[kw] = val else: continue return header
[docs] def to_header_string(self, relax=None): """ Identical to `to_header`, but returns a string containing the header cards. """ return str(self.to_header(relax))
[docs] def footprint_to_file(self, filename='footprint.reg', color='green', width=2, coordsys=None): """ Writes out a `ds9`_ style regions file. It can be loaded directly by `ds9`_. Parameters ---------- filename : str, optional Output file name - default is ``'footprint.reg'`` color : str, optional Color to use when plotting the line. width : int, optional Width of the region line. coordsys : str, optional Coordinate system. If not specified (default), the ``radesys`` value is used. For all possible values, see http://ds9.si.edu/doc/ref/region.html#RegionFileFormat """ comments = ('# Region file format: DS9 version 4.0 \n' '# global color=green font="helvetica 12 bold ' 'select=1 highlite=1 edit=1 move=1 delete=1 ' 'include=1 fixed=0 source\n') coordsys = coordsys or self.wcs.radesys if coordsys not in ('PHYSICAL', 'IMAGE', 'FK4', 'B1950', 'FK5', 'J2000', 'GALACTIC', 'ECLIPTIC', 'ICRS', 'LINEAR', 'AMPLIFIER', 'DETECTOR'): raise ValueError("Coordinate system '{}' is not supported. A valid" " one can be given with the 'coordsys' argument." .format(coordsys)) with open(filename, mode='w') as f: f.write(comments) f.write(f'{coordsys}\n') f.write('polygon(') ftpr = self.calc_footprint() if ftpr is not None: ftpr.tofile(f, sep=',') f.write(f') # color={color}, width={width:d} \n')
@property def _naxis1(self): warnings.warn(NAXIS_DEPRECATE_MESSAGE, AstropyDeprecationWarning) return self._naxis[0] @_naxis1.setter def _naxis1(self, value): warnings.warn(NAXIS_DEPRECATE_MESSAGE, AstropyDeprecationWarning) self._naxis[0] = value @property def _naxis2(self): warnings.warn(NAXIS_DEPRECATE_MESSAGE, AstropyDeprecationWarning) return self._naxis[1] @_naxis2.setter def _naxis2(self, value): warnings.warn(NAXIS_DEPRECATE_MESSAGE, AstropyDeprecationWarning) self._naxis[1] = value def _get_naxis(self, header=None): _naxis = [] if (header is not None and not isinstance(header, (str, bytes))): for naxis in itertools.count(1): try: _naxis.append(header[f'NAXIS{naxis}']) except KeyError: break if len(_naxis) == 0: _naxis = [0, 0] elif len(_naxis) == 1: _naxis.append(0) self._naxis = _naxis
[docs] def printwcs(self): print(repr(self))
def __repr__(self): ''' Return a short description. Simply porting the behavior from the `printwcs()` method. ''' description = ["WCS Keywords\n", f"Number of WCS axes: {self.naxis!r}"] sfmt = ' : ' + "".join(["{"+f"{i}"+"!r} " for i in range(self.naxis)]) keywords = ['CTYPE', 'CRVAL', 'CRPIX'] values = [self.wcs.ctype, self.wcs.crval, self.wcs.crpix] for keyword, value in zip(keywords, values): description.append(keyword+sfmt.format(*value)) if hasattr(self.wcs, 'pc'): for i in range(self.naxis): s = '' for j in range(self.naxis): s += ''.join(['PC', str(i+1), '_', str(j+1), ' ']) s += sfmt description.append(s.format(*self.wcs.pc[i])) s = 'CDELT' + sfmt description.append(s.format(*self.wcs.cdelt)) elif hasattr(self.wcs, 'cd'): for i in range(self.naxis): s = '' for j in range(self.naxis): s += "".join(['CD', str(i+1), '_', str(j+1), ' ']) s += sfmt description.append(s.format(*self.wcs.cd[i])) description.append('NAXIS : {}'.format(' '.join(map(str, self._naxis)))) return '\n'.join(description)
[docs] def get_axis_types(self): """ Similar to `self.wcsprm.axis_types <astropy.wcs.Wcsprm.axis_types>` but provides the information in a more Python-friendly format. Returns ------- result : list of dicts Returns a list of dictionaries, one for each axis, each containing attributes about the type of that axis. Each dictionary has the following keys: - 'coordinate_type': - None: Non-specific coordinate type. - 'stokes': Stokes coordinate. - 'celestial': Celestial coordinate (including ``CUBEFACE``). - 'spectral': Spectral coordinate. - 'scale': - 'linear': Linear axis. - 'quantized': Quantized axis (``STOKES``, ``CUBEFACE``). - 'non-linear celestial': Non-linear celestial axis. - 'non-linear spectral': Non-linear spectral axis. - 'logarithmic': Logarithmic axis. - 'tabular': Tabular axis. - 'group' - Group number, e.g. lookup table number - 'number' - For celestial axes: - 0: Longitude coordinate. - 1: Latitude coordinate. - 2: ``CUBEFACE`` number. - For lookup tables: - the axis number in a multidimensional table. ``CTYPEia`` in ``"4-3"`` form with unrecognized algorithm code will generate an error. """ if self.wcs is None: raise AttributeError( "This WCS object does not have a wcsprm object.") coordinate_type_map = { 0: None, 1: 'stokes', 2: 'celestial', 3: 'spectral'} scale_map = { 0: 'linear', 1: 'quantized', 2: 'non-linear celestial', 3: 'non-linear spectral', 4: 'logarithmic', 5: 'tabular'} result = [] for axis_type in self.wcs.axis_types: subresult = {} coordinate_type = (axis_type // 1000) % 10 subresult['coordinate_type'] = coordinate_type_map[coordinate_type] scale = (axis_type // 100) % 10 subresult['scale'] = scale_map[scale] group = (axis_type // 10) % 10 subresult['group'] = group number = axis_type % 10 subresult['number'] = number result.append(subresult) return result
def __reduce__(self): """ Support pickling of WCS objects. This is done by serializing to an in-memory FITS file and dumping that as a string. """ hdulist = self.to_fits(relax=True) buffer = io.BytesIO() hdulist.writeto(buffer) return (__WCS_unpickle__, (self.__class__, self.__dict__, buffer.getvalue(),))
[docs] def dropaxis(self, dropax): """ Remove an axis from the WCS. Parameters ---------- wcs : `~astropy.wcs.WCS` The WCS with naxis to be chopped to naxis-1 dropax : int The index of the WCS to drop, counting from 0 (i.e., python convention, not FITS convention) Returns ------- A new `~astropy.wcs.WCS` instance with one axis fewer """ inds = list(range(self.wcs.naxis)) inds.pop(dropax) # axis 0 has special meaning to sub # if wcs.wcs.ctype == ['RA','DEC','VLSR'], you want # wcs.sub([1,2]) to get 'RA','DEC' back return self.sub([i+1 for i in inds])
[docs] def swapaxes(self, ax0, ax1): """ Swap axes in a WCS. Parameters ---------- wcs : `~astropy.wcs.WCS` The WCS to have its axes swapped ax0 : int ax1 : int The indices of the WCS to be swapped, counting from 0 (i.e., python convention, not FITS convention) Returns ------- A new `~astropy.wcs.WCS` instance with the same number of axes, but two swapped """ inds = list(range(self.wcs.naxis)) inds[ax0], inds[ax1] = inds[ax1], inds[ax0] return self.sub([i+1 for i in inds])
[docs] def reorient_celestial_first(self): """ Reorient the WCS such that the celestial axes are first, followed by the spectral axis, followed by any others. Assumes at least celestial axes are present. """ return self.sub([WCSSUB_CELESTIAL, WCSSUB_SPECTRAL, WCSSUB_STOKES])
[docs] def slice(self, view, numpy_order=True): """ Slice a WCS instance using a Numpy slice. The order of the slice should be reversed (as for the data) compared to the natural WCS order. Parameters ---------- view : tuple A tuple containing the same number of slices as the WCS system. The ``step`` method, the third argument to a slice, is not presently supported. numpy_order : bool Use numpy order, i.e. slice the WCS so that an identical slice applied to a numpy array will slice the array and WCS in the same way. If set to `False`, the WCS will be sliced in FITS order, meaning the first slice will be applied to the *last* numpy index but the *first* WCS axis. Returns ------- wcs_new : `~astropy.wcs.WCS` A new resampled WCS axis """ if hasattr(view, '__len__') and len(view) > self.wcs.naxis: raise ValueError("Must have # of slices <= # of WCS axes") elif not hasattr(view, '__len__'): # view MUST be an iterable view = [view] if not all(isinstance(x, slice) for x in view): # We need to drop some dimensions, but this may not always be # possible with .sub due to correlated axes, so instead we use the # generalized slicing infrastructure from astropy.wcs.wcsapi. return SlicedFITSWCS(self, view) # NOTE: we could in principle use SlicedFITSWCS as above for all slicing, # but in the simple case where there are no axes dropped, we can just # create a full WCS object with updated WCS parameters which is faster # for this specific case and also backward-compatible. wcs_new = self.deepcopy() if wcs_new.sip is not None: sip_crpix = wcs_new.sip.crpix.tolist() for i, iview in enumerate(view): if iview.step is not None and iview.step < 0: raise NotImplementedError("Reversing an axis is not " "implemented.") if numpy_order: wcs_index = self.wcs.naxis - 1 - i else: wcs_index = i if iview.step is not None and iview.start is None: # Slice from "None" is equivalent to slice from 0 (but one # might want to downsample, so allow slices with # None,None,step or None,stop,step) iview = slice(0, iview.stop, iview.step) if iview.start is not None: if iview.step not in (None, 1): crpix = self.wcs.crpix[wcs_index] cdelt = self.wcs.cdelt[wcs_index] # equivalently (keep this comment so you can compare eqns): # wcs_new.wcs.crpix[wcs_index] = # (crpix - iview.start)*iview.step + 0.5 - iview.step/2. crp = ((crpix - iview.start - 1.)/iview.step + 0.5 + 1./iview.step/2.) wcs_new.wcs.crpix[wcs_index] = crp if wcs_new.sip is not None: sip_crpix[wcs_index] = crp wcs_new.wcs.cdelt[wcs_index] = cdelt * iview.step else: wcs_new.wcs.crpix[wcs_index] -= iview.start if wcs_new.sip is not None: sip_crpix[wcs_index] -= iview.start try: # range requires integers but the other attributes can also # handle arbitrary values, so this needs to be in a try/except. nitems = len(builtins.range(self._naxis[wcs_index])[iview]) except TypeError as exc: if 'indices must be integers' not in str(exc): raise warnings.warn("NAXIS{} attribute is not updated because at " "least one index ('{}') is no integer." "".format(wcs_index, iview), AstropyUserWarning) else: wcs_new._naxis[wcs_index] = nitems if wcs_new.sip is not None: wcs_new.sip = Sip(self.sip.a, self.sip.b, self.sip.ap, self.sip.bp, sip_crpix) return wcs_new
def __getitem__(self, item): # "getitem" is a shortcut for self.slice; it is very limited # there is no obvious and unambiguous interpretation of wcs[1,2,3] # We COULD allow wcs[1] to link to wcs.sub([2]) # (wcs[i] -> wcs.sub([i+1]) return self.slice(item) def __iter__(self): # Having __getitem__ makes Python think WCS is iterable. However, # Python first checks whether __iter__ is present, so we can raise an # exception here. raise TypeError(f"'{self.__class__.__name__}' object is not iterable") @property def axis_type_names(self): """ World names for each coordinate axis Returns ------- A list of names along each axis """ names = list(self.wcs.cname) types = self.wcs.ctype for i in range(len(names)): if len(names[i]) > 0: continue names[i] = types[i].split('-')[0] return names @property def celestial(self): """ A copy of the current WCS with only the celestial axes included """ return self.sub([WCSSUB_CELESTIAL]) @property def is_celestial(self): return self.has_celestial and self.naxis == 2 @property def has_celestial(self): try: return self.wcs.lng >= 0 and self.wcs.lat >= 0 except InconsistentAxisTypesError: return False @property def has_distortion(self): """ Returns `True` if any distortion terms are present. """ return (self.sip is not None or self.cpdis1 is not None or self.cpdis2 is not None or self.det2im1 is not None and self.det2im2 is not None) @property def pixel_scale_matrix(self): try: cdelt = np.diag(self.wcs.get_cdelt()) pc = self.wcs.get_pc() except InconsistentAxisTypesError: try: # for non-celestial axes, get_cdelt doesn't work cdelt = np.dot(self.wcs.cd, np.diag(self.wcs.cdelt)) except AttributeError: cdelt = np.diag(self.wcs.cdelt) try: pc = self.wcs.pc except AttributeError: pc = 1 pccd = np.array(np.dot(cdelt, pc)) return pccd def _as_mpl_axes(self): """ Compatibility hook for Matplotlib and WCSAxes. With this method, one can do: from astropy.wcs import WCS import matplotlib.pyplot as plt wcs = WCS('filename.fits') fig = plt.figure() ax = fig.add_axes([0.15, 0.1, 0.8, 0.8], projection=wcs) ... and this will generate a plot with the correct WCS coordinates on the axes. """ from astropy.visualization.wcsaxes import WCSAxes return WCSAxes, {'wcs': self}
[docs] def footprint_contains(self, coord, **kwargs): """ Determines if a given SkyCoord is contained in the wcs footprint. Parameters ---------- coord : `~astropy.coordinates.SkyCoord` The coordinate to check if it is within the wcs coordinate. **kwargs : Additional arguments to pass to `~astropy.coordinates.SkyCoord.to_pixel` Returns ------- response : bool True means the WCS footprint contains the coordinate, False means it does not. """ return coord.contained_by(self, **kwargs)
def __WCS_unpickle__(cls, dct, fits_data): """ Unpickles a WCS object from a serialized FITS string. """ self = cls.__new__(cls) self.__dict__.update(dct) buffer = io.BytesIO(fits_data) hdulist = fits.open(buffer) WCS.__init__(self, hdulist[0].header, hdulist) return self
[docs]def find_all_wcs(header, relax=True, keysel=None, fix=True, translate_units='', _do_set=True): """ Find all the WCS transformations in the given header. Parameters ---------- header : str or astropy.io.fits header object. relax : bool or int, optional Degree of permissiveness: - `True` (default): Admit all recognized informal extensions of the WCS standard. - `False`: Recognize only FITS keywords defined by the published WCS standard. - `int`: a bit field selecting specific extensions to accept. See :ref:`relaxread` for details. keysel : sequence of flags, optional A list of flags used to select the keyword types considered by wcslib. When ``None``, only the standard image header keywords are considered (and the underlying wcspih() C function is called). To use binary table image array or pixel list keywords, *keysel* must be set. Each element in the list should be one of the following strings: - 'image': Image header keywords - 'binary': Binary table image array keywords - 'pixel': Pixel list keywords Keywords such as ``EQUIna`` or ``RFRQna`` that are common to binary table image arrays and pixel lists (including ``WCSNna`` and ``TWCSna``) are selected by both 'binary' and 'pixel'. fix : bool, optional When `True` (default), call `~astropy.wcs.Wcsprm.fix` on the resulting objects to fix any non-standard uses in the header. `FITSFixedWarning` warnings will be emitted if any changes were made. translate_units : str, optional Specify which potentially unsafe translations of non-standard unit strings to perform. By default, performs none. See `WCS.fix` for more information about this parameter. Only effective when ``fix`` is `True`. Returns ------- wcses : list of `WCS` objects """ if isinstance(header, (str, bytes)): header_string = header elif isinstance(header, fits.Header): header_string = header.tostring() else: raise TypeError( "header must be a string or astropy.io.fits.Header object") keysel_flags = _parse_keysel(keysel) if isinstance(header_string, str): header_bytes = header_string.encode('ascii') else: header_bytes = header_string wcsprms = _wcs.find_all_wcs(header_bytes, relax, keysel_flags) result = [] for wcsprm in wcsprms: subresult = WCS(fix=False, _do_set=False) subresult.wcs = wcsprm result.append(subresult) if fix: subresult.fix(translate_units) if _do_set: subresult.wcs.set() return result
[docs]def validate(source): """ Prints a WCS validation report for the given FITS file. Parameters ---------- source : str path, readable file-like object or `astropy.io.fits.HDUList` object The FITS file to validate. Returns ------- results : WcsValidateResults instance The result is returned as nested lists. The first level corresponds to the HDUs in the given file. The next level has an entry for each WCS found in that header. The special subclass of list will pretty-print the results as a table when printed. """ class _WcsValidateWcsResult(list): def __init__(self, key): self._key = key def __repr__(self): result = [" WCS key '{}':".format(self._key or ' ')] if len(self): for entry in self: for i, line in enumerate(entry.splitlines()): if i == 0: initial_indent = ' - ' else: initial_indent = ' ' result.extend( textwrap.wrap( line, initial_indent=initial_indent, subsequent_indent=' ')) else: result.append(" No issues.") return '\n'.join(result) class _WcsValidateHduResult(list): def __init__(self, hdu_index, hdu_name): self._hdu_index = hdu_index self._hdu_name = hdu_name list.__init__(self) def __repr__(self): if len(self): if self._hdu_name: hdu_name = f' ({self._hdu_name})' else: hdu_name = '' result = [f'HDU {self._hdu_index}{hdu_name}:'] for wcs in self: result.append(repr(wcs)) return '\n'.join(result) return '' class _WcsValidateResults(list): def __repr__(self): result = [] for hdu in self: content = repr(hdu) if len(content): result.append(content) return '\n\n'.join(result) global __warningregistry__ if isinstance(source, fits.HDUList): hdulist = source else: hdulist = fits.open(source) results = _WcsValidateResults() for i, hdu in enumerate(hdulist): hdu_results = _WcsValidateHduResult(i, hdu.name) results.append(hdu_results) with warnings.catch_warnings(record=True) as warning_lines: wcses = find_all_wcs( hdu.header, relax=_wcs.WCSHDR_reject, fix=False, _do_set=False) for wcs in wcses: wcs_results = _WcsValidateWcsResult(wcs.wcs.alt) hdu_results.append(wcs_results) try: del __warningregistry__ except NameError: pass with warnings.catch_warnings(record=True) as warning_lines: warnings.resetwarnings() warnings.simplefilter( "always", FITSFixedWarning, append=True) try: WCS(hdu.header, key=wcs.wcs.alt or ' ', relax=_wcs.WCSHDR_reject, fix=True, _do_set=False) except WcsError as e: wcs_results.append(str(e)) wcs_results.extend([str(x.message) for x in warning_lines]) return results