# Licensed under a 3-clause BSD style license - see LICENSE.rst
import functools
import itertools
import warnings
import numpy as np
import numpy.linalg as npla
from scipy import optimize
from astropy.modeling.core import Model # , fix_inputs
from astropy.modeling import utils as mutils
from astropy.modeling.models import (Shift, Polynomial2D, Sky2Pix_TAN,
RotateCelestial2Native, Mapping)
from astropy.modeling.fitting import LinearLSQFitter
import astropy.io.fits as fits
from .api import GWCSAPIMixin
from . import coordinate_frames as cf
from .utils import CoordinateFrameError
from . import utils
from .wcstools import grid_from_bounding_box
try:
from astropy.modeling.core import fix_inputs
HAS_FIX_INPUTS = True
except ImportError:
HAS_FIX_INPUTS = False
__all__ = ['WCS', 'NoConvergence']
_ITER_INV_KWARGS = ['tolerance', 'maxiter', 'adaptive', 'detect_divergence', 'quiet']
[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`
Estimate of the 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):
super().__init__(*args)
self.best_solution = best_solution
self.accuracy = accuracy
self.niter = niter
self.divergent = divergent
self.slow_conv = slow_conv
[docs]class WCS(GWCSAPIMixin):
"""
Basic WCS class.
Parameters
----------
forward_transform : `~astropy.modeling.Model` or a list
The transform between ``input_frame`` and ``output_frame``.
A list of (frame, transform) tuples where ``frame`` is the starting frame and
``transform`` is the transform from this frame to the next one or ``output_frame``.
The last tuple is (transform, None), where None indicates the end of the pipeline.
input_frame : str, `~gwcs.coordinate_frames.CoordinateFrame`
A coordinates object or a string name.
output_frame : str, `~gwcs.coordinate_frames.CoordinateFrame`
A coordinates object or a string name.
name : str
a name for this WCS
"""
def __init__(self, forward_transform=None, input_frame='detector', output_frame=None,
name=""):
#self.low_level_wcs = self
self._approx_inverse = None
self._available_frames = []
self._pipeline = []
self._name = name
self._array_shape = None
self._initialize_wcs(forward_transform, input_frame, output_frame)
self._pixel_shape = None
self._pipeline = [Step(*step) for step in self._pipeline]
def _initialize_wcs(self, forward_transform, input_frame, output_frame):
if forward_transform is not None:
if isinstance(forward_transform, Model):
if output_frame is None:
raise CoordinateFrameError("An output_frame must be specified"
"if forward_transform is a model.")
_input_frame, inp_frame_obj = self._get_frame_name(input_frame)
_output_frame, outp_frame_obj = self._get_frame_name(output_frame)
super(WCS, self).__setattr__(_input_frame, inp_frame_obj)
super(WCS, self).__setattr__(_output_frame, outp_frame_obj)
self._pipeline = [(input_frame, forward_transform.copy()),
(output_frame, None)]
elif isinstance(forward_transform, list):
for item in forward_transform:
name, frame_obj = self._get_frame_name(item[0])
super(WCS, self).__setattr__(name, frame_obj)
#self._pipeline.append((name, item[1]))
self._pipeline = forward_transform
else:
raise TypeError("Expected forward_transform to be a model or a "
"(frame, transform) list, got {0}".format(
type(forward_transform)))
else:
# Initialize a WCS without a forward_transform - allows building a WCS programmatically.
if output_frame is None:
raise CoordinateFrameError("An output_frame must be specified"
"if forward_transform is None.")
_input_frame, inp_frame_obj = self._get_frame_name(input_frame)
_output_frame, outp_frame_obj = self._get_frame_name(output_frame)
super(WCS, self).__setattr__(_input_frame, inp_frame_obj)
super(WCS, self).__setattr__(_output_frame, outp_frame_obj)
self._pipeline = [(_input_frame, None),
(_output_frame, None)]
@property
def forward_transform(self):
"""
Return the total forward transform - from input to output coordinate frame.
"""
if self._pipeline:
#return functools.reduce(lambda x, y: x | y, [step[1] for step in self._pipeline[: -1]])
return functools.reduce(lambda x, y: x | y, [step.transform for step in self._pipeline[:-1]])
else:
return None
@property
def backward_transform(self):
"""
Return the total backward transform if available - from output to input coordinate system.
Raises
------
NotImplementedError :
An analytical inverse does not exist.
"""
try:
backward = self.forward_transform.inverse
except NotImplementedError as err:
raise NotImplementedError("Could not construct backward transform. \n{0}".format(err))
return backward
def _get_frame_index(self, frame):
"""
Return the index in the pipeline where this frame is locate.
"""
if isinstance(frame, cf.CoordinateFrame):
frame = frame.name
#frame_names = [getattr(item[0], "name", item[0]) for item in self._pipeline]
frame_names = [step.frame if isinstance(step.frame, str) else step.frame.name for step in self._pipeline]
return frame_names.index(frame)
def _get_frame_name(self, frame):
"""
Return the name of the frame and a ``CoordinateFrame`` object.
Parameters
----------
frame : str, `~gwcs.coordinate_frames.CoordinateFrame`
Coordinate frame.
Returns
-------
name : str
The name of the frame
frame_obj : `~gwcs.coordinate_frames.CoordinateFrame`
Frame instance or None (if `frame` is str)
"""
if isinstance(frame, str):
name = frame
frame_obj = None
else:
name = frame.name
frame_obj = frame
return name, frame_obj
[docs] def __call__(self, *args, **kwargs):
"""
Executes the forward transform.
args : float or array-like
Inputs in the input coordinate system, separate inputs
for each dimension.
with_units : bool
If ``True`` returns a `~astropy.coordinates.SkyCoord` or
`~astropy.units.Quantity` object, by using the units of
the output cooridnate frame.
Optional, default=False.
with_bounding_box : bool, optional
If True(default) values in the result which correspond to
any of the inputs being outside the bounding_box are set
to ``fill_value``.
fill_value : float, optional
Output value for inputs outside the bounding_box
(default is np.nan).
"""
transform = self.forward_transform
if transform is None:
raise NotImplementedError("WCS.forward_transform is not implemented.")
with_units = kwargs.pop("with_units", False)
if 'with_bounding_box' not in kwargs:
kwargs['with_bounding_box'] = True
if 'fill_value' not in kwargs:
kwargs['fill_value'] = np.nan
if self.bounding_box is not None:
# Currently compound models do not attempt to combine individual model
# bounding boxes. Get the forward transform and assign the bounding_box to it
# before evaluating it. The order Model.bounding_box is reversed.
axes_ind = self._get_axes_indices()
if transform.n_inputs > 1:
transform.bounding_box = [self.bounding_box[ind] for ind in axes_ind][::-1]
else:
transform.bounding_box = self.bounding_box
result = transform(*args, **kwargs)
if with_units:
if self.output_frame.naxes == 1:
result = self.output_frame.coordinates(result)
else:
result = self.output_frame.coordinates(*result)
return result
[docs] def in_image(self, *args, **kwargs):
"""
This method tests if one or more of the input world coordinates are
contained within forward transformation's image and that it maps to
the domain of definition of the forward transformation.
In practical terms, this function tests
that input world coordinate(s) can be converted to input frame and that
it is within the forward transformation's ``bounding_box`` when
defined.
Parameters
----------
args : float, array like, `~astropy.coordinates.SkyCoord` or
`~astropy.units.Unit` coordinates to be inverted
kwargs : dict
keyword arguments to be passed either to ``backward_transform``
(when defined) or to the iterative invert method.
Returns
-------
result : bool, numpy.ndarray
A single boolean value or an array of boolean values with `True`
indicating that the WCS footprint contains the coordinate
and `False` if input is outside the footprint.
"""
kwargs['with_bounding_box'] = True
kwargs['fill_value'] = np.nan
coords = self.invert(*args, **kwargs)
result = np.isfinite(coords)
if self.input_frame.naxes > 1:
result = np.all(result, axis=0)
if self.bounding_box is None or not np.any(result):
return result
if self.input_frame.naxes == 1:
x1, x2 = self.bounding_box
if len(np.shape(args[0])) > 0:
result[result] = (coords[result] >= x1) & (coords[result] <= x2)
elif result:
result = (coords >= x1) and (coords <= x2)
else:
if len(np.shape(args[0])) > 0:
for c, (x1, x2) in zip(coords, self.bounding_box):
result[result] = (c[result] >= x1) & (c[result] <= x2)
elif result:
result = all([(c >= x1) and (c <= x2) for c, (x1, x2) in zip(coords, self.bounding_box)])
return result
[docs] def invert(self, *args, **kwargs):
"""
Invert coordinates from output frame to input frame using analytical or
user-supplied inverse. When neither analytical nor user-supplied
inverses are defined, a numerical solution will be attempted using
:py:meth:`numerical_inverse`.
.. note::
Currently numerical inverse is implemented only for 2D imaging WCS.
Parameters
----------
args : float, array like, `~astropy.coordinates.SkyCoord` or `~astropy.units.Unit`
Coordinates to be inverted. The number of arguments must be equal
to the number of world coordinates given by ``world_n_dim``.
with_bounding_box : bool, optional
If `True` (default) values in the result which correspond to any
of the inputs being outside the bounding_box are set to
``fill_value``.
fill_value : float, optional
Output value for inputs outside the bounding_box (default is ``np.nan``).
with_units : bool, optional
If ``True`` returns a `~astropy.coordinates.SkyCoord` or
`~astropy.units.Quantity` object, by using the units of
the output cooridnate frame. Default is `False`.
Other Parameters
----------------
kwargs : dict
Keyword arguments to be passed to :py:meth:`numerical_inverse`
(when defined) or to the iterative invert method.
Returns
-------
result : tuple
Returns a tuple of scalar or array values for each axis.
"""
with_units = kwargs.pop('with_units', False)
if not utils.isnumerical(args[0]):
args = self.output_frame.coordinate_to_quantity(*args)
if self.output_frame.naxes == 1:
args = [args]
try:
if not self.backward_transform.uses_quantity:
args = utils.get_values(self.output_frame.unit, *args)
except (NotImplementedError, KeyError):
args = utils.get_values(self.output_frame.unit, *args)
if 'with_bounding_box' not in kwargs:
kwargs['with_bounding_box'] = True
if 'fill_value' not in kwargs:
kwargs['fill_value'] = np.nan
try:
# remove iterative inverse-specific keyword arguments:
akwargs = {k: v for k, v in kwargs.items() if k not in _ITER_INV_KWARGS}
result = self.backward_transform(*args, **akwargs)
except (NotImplementedError, KeyError):
result = self.numerical_inverse(*args, **kwargs, with_units=with_units)
if with_units and self.input_frame:
if self.input_frame.naxes == 1:
return self.input_frame.coordinates(result)
else:
return self.input_frame.coordinates(*result)
else:
return result
[docs] def numerical_inverse(self, *args, **kwargs):
"""
Invert coordinates from output frame to input frame using numerical
inverse.
.. note::
Currently numerical inverse is implemented only for 2D imaging WCS.
.. note::
This method uses a combination of vectorized fixed-point
iterations algorithm and `scipy.optimize.root`. The later is used
for input coordinates for which vectorized algorithm diverges.
Parameters
----------
args : float, array like, `~astropy.coordinates.SkyCoord` or `~astropy.units.Unit`
Coordinates to be inverted. The number of arguments must be equal
to the number of world coordinates given by ``world_n_dim``.
with_bounding_box : bool, optional
If `True` (default) values in the result which correspond to any
of the inputs being outside the bounding_box are set to
``fill_value``.
fill_value : float, optional
Output value for inputs outside the bounding_box (default is ``np.nan``).
with_units : bool, optional
If ``True`` returns a `~astropy.coordinates.SkyCoord` or
`~astropy.units.Quantity` object, by using the units of
the output cooridnate frame. Default is `False`.
tolerance : float, optional
*Absolute 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``.
Default ``tolerance`` is 1.0e-5.
maxiter : int, optional
Maximum number of iterations allowed to reach a solution.
Default is 50.
quiet : bool, optional
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. Default is `True`.
Other Parameters
----------------
adaptive : bool, optional
Specifies whether to adaptively select only points that
did not converge to a solution within the required
accuracy for the next iteration. Default (`True`) is recommended.
.. note::
The :py:meth:`numerical_inverse` 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:`numerical_inverse` will continue
iterating *only* over the points that have not yet
converged to the required accuracy.
.. note::
When ``detect_divergence`` is `True`,
:py:meth:`numerical_inverse` will automatically switch
to the adaptive algorithm once divergence has been
detected.
detect_divergence : bool, optional
Specifies whether to perform a more detailed analysis
of the convergence to a solution. Normally
:py:meth:`numerical_inverse` 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:`numerical_inverse` 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:`numerical_inverse`, 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` (default),
:py:meth:`numerical_inverse` 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:`numerical_inverse` 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 JWST NIRCAM images, setting
``detect_divergence`` to `True` will incur about 5-10%
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
-------
result : tuple
Returns a tuple of scalar or array values for each axis.
Raises
------
NoConvergence
The iterative 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.
NotImplementedError
Numerical inverse has not been implemented for this WCS.
ValueError
Invalid argument values.
Examples
--------
>>> from astropy.utils.data import get_pkg_data_filename
>>> from gwcs import NoConvergence
>>> import asdf
>>> import numpy as np
>>> filename = get_pkg_data_filename('data/nircamwcs.asdf', package='gwcs.tests')
>>> w = asdf.open(filename).tree['wcs']
>>> ra, dec = w([1,2,3], [1,1,1])
>>> print(ra) # doctest: +FLOAT_CMP
[5.927628 5.92757069 5.92751337]
>>> print(dec) # doctest: +FLOAT_CMP
[-72.01341247 -72.01341273 -72.013413 ]
>>> x, y = w.numerical_inverse(ra, dec)
>>> print(x) # doctest: +FLOAT_CMP
[1.00000005 2.00000005 3.00000006]
>>> print(y) # doctest: +FLOAT_CMP
[1.00000004 0.99999979 1.00000015]
>>> x, y = w.numerical_inverse(ra, dec, maxiter=3, tolerance=1.0e-10, quiet=False)
Traceback (most recent call last):
...
gwcs.wcs.NoConvergence: 'WCS.numerical_inverse' failed to converge to the
requested accuracy after 3 iterations.
>>> w.numerical_inverse(
... *w([1, 300000, 3], [2, 1000000, 5], with_bounding_box=False),
... adaptive=False,
... detect_divergence=True,
... quiet=False,
... with_bounding_box=False
... )
Traceback (most recent call last):
...
gwcs.wcs.NoConvergence: 'WCS.numerical_inverse' failed to converge to the
requested accuracy. After 4 iterations, the solution is diverging at
least for one input point.
>>> # Now try to use some diverging data:
>>> divradec = w([1, 300000, 3], [2, 1000000, 5], with_bounding_box=False)
>>> print(divradec) # doctest: +FLOAT_CMP
(array([ 5.92762673, 148.21600848, 5.92750827]),
array([-72.01339464, -7.80968079, -72.01334172]))
>>> try: # doctest: +SKIP
... x, y = w.numerical_inverse(*divradec, maxiter=20,
... tolerance=1.0e-4, adaptive=True,
... detect_divergence=True,
... quiet=False)
... except NoConvergence as e:
... print(f"Indices of diverging points: {e.divergent}")
... print(f"Indices of poorly converging points: {e.slow_conv}")
... print(f"Best solution:\\n{e.best_solution}")
... print(f"Achieved accuracy:\\n{e.accuracy}")
Indices of diverging points: None
Indices of poorly converging points: [1]
Best solution:
[[1.00000040e+00 1.99999841e+00]
[6.33507833e+17 3.40118820e+17]
[3.00000038e+00 4.99999841e+00]]
Achieved accuracy:
[[2.75925982e-05 1.18471543e-05]
[3.65405005e+04 1.31364188e+04]
[2.76552923e-05 1.14789013e-05]]
"""
tolerance = kwargs.get('tolerance', 1e-5)
maxiter = kwargs.get('maxiter', 50)
adaptive = kwargs.get('adaptive', True)
detect_divergence = kwargs.get('detect_divergence', True)
quiet = kwargs.get('quiet', True)
with_bounding_box = kwargs.get('with_bounding_box', True)
fill_value = kwargs.get('fill_value', np.nan)
with_units = kwargs.pop('with_units', False)
if not utils.isnumerical(args[0]):
args = self.output_frame.coordinate_to_quantity(*args)
if self.output_frame.naxes == 1:
args = [args]
args = utils.get_values(self.output_frame.unit, *args)
args_shape = np.shape(args)
nargs = args_shape[0]
arg_dim = len(args_shape) - 1
if nargs != self.world_n_dim:
raise ValueError("Number of input coordinates is different from "
"the number of defined world coordinates in the "
f"WCS ({self.world_n_dim:d})")
if self.world_n_dim != self.pixel_n_dim:
raise NotImplementedError(
"Support for iterative inverse for transformations with "
"different number of inputs and outputs was not implemented."
)
# initial guess:
if nargs == 2 and self._approx_inverse is None:
self._calc_approx_inv(max_inv_pix_error=5, inv_degree=None)
if self._approx_inverse is None:
if self.bounding_box is None:
x0 = np.ones(self.pixel_n_dim)
else:
x0 = np.mean(self.bounding_box, axis=-1)
if arg_dim == 0:
argsi = args
if nargs == 2 and self._approx_inverse is not None:
x0 = self._approx_inverse(*argsi)
if not np.all(np.isfinite(x0)):
return [np.array(np.nan) for _ in range(nargs)]
result = tuple(self._vectorized_fixed_point(
x0, argsi,
tolerance=tolerance,
maxiter=maxiter,
adaptive=adaptive,
detect_divergence=detect_divergence,
quiet=quiet,
with_bounding_box=with_bounding_box,
fill_value=fill_value
).T.ravel().tolist())
else:
arg_shape = args_shape[1:]
nelem = np.prod(arg_shape)
args = np.reshape(args, (nargs, nelem))
if self._approx_inverse is None:
x0 = np.full((nelem, nargs), x0)
else:
x0 = np.array(self._approx_inverse(*args)).T
result = self._vectorized_fixed_point(
x0, args.T,
tolerance=tolerance,
maxiter=maxiter,
adaptive=adaptive,
detect_divergence=detect_divergence,
quiet=quiet,
with_bounding_box=with_bounding_box,
fill_value=fill_value
).T
result = tuple(np.reshape(result, args_shape))
if with_units and self.input_frame:
if self.input_frame.naxes == 1:
return self.input_frame.coordinates(result)
else:
return self.input_frame.coordinates(*result)
else:
return result
def _vectorized_fixed_point(self, pix0, world, tolerance, maxiter,
adaptive, detect_divergence, quiet,
with_bounding_box, fill_value):
# ############################################################
# # INITIALIZE ITERATIVE PROCESS: ##
# ############################################################
# make a copy of the initial approximation
pix0 = np.atleast_2d(np.array(pix0)) # 0-order solution
pix = np.array(pix0)
world0 = np.atleast_2d(np.array(world))
world = np.array(world0)
# estimate pixel scale using approximate algorithm
# from https://trs.jpl.nasa.gov/handle/2014/40409
if self.bounding_box is None:
crpix = np.ones(self.pixel_n_dim)
else:
crpix = np.mean(self.bounding_box, axis=-1)
l1, phi1 = np.deg2rad(self.__call__(*(crpix - 0.5)))
l2, phi2 = np.deg2rad(self.__call__(*(crpix + [-0.5, 0.5])))
l3, phi3 = np.deg2rad(self.__call__(*(crpix + 0.5)))
l4, phi4 = np.deg2rad(self.__call__(*(crpix + [0.5, -0.5])))
area = np.abs(0.5 * ((l4 - l2) * np.sin(phi1) +
(l1 - l3) * np.sin(phi2) +
(l2 - l4) * np.sin(phi3) +
(l3 - l2) * np.sin(phi4)))
inv_pscale = 1 / np.rad2deg(np.sqrt(area))
# form equation:
def f(x):
w = np.array(self.__call__(*(x.T), with_bounding_box=False)).T
dw = np.mod(np.subtract(w, world) - 180.0, 360.0) - 180.0
return np.add(inv_pscale * dw, x)
def froot(x):
return np.mod(np.subtract(self.__call__(*x, with_bounding_box=False), worldi) - 180.0, 360.0) - 180.0
# compute correction:
def correction(pix):
p1 = f(pix)
p2 = f(p1)
d = p2 - 2.0 * p1 + pix
idx = np.where(d != 0)
corr = pix - p2
corr[idx] = np.square(p1[idx] - pix[idx]) / d[idx]
return corr
# initial iteration:
dpix = correction(pix)
# 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 = correction(pix)
# 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)
world = world[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))
world = world[ind]
# "Adaptive" fixed-point iterations:
while (ind.shape[0] > 0 and k < maxiter):
# Find correction to the previous solution:
dpixnew = correction(pix[ind])
# Compute norm (L2) of the correction:
dnnew = np.sum(np.square(dpixnew), axis=1)
# Bookkeeping of corrections:
dnprev[ind] = dn[ind].copy()
dn[ind] = dnnew
if detect_divergence:
# Find indices of pixels that are converging:
conv = np.logical_or(dnnew < dnprev[ind], dnnew < tol2)
if not np.all(conv):
conv = np.ones_like(dnnew, dtype=np.bool)
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]
world = world[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(world0), axis=1)))
# When detect_divergence is 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
# If there are divergent points, attempt to find a solution using
# scipy's 'hybr' method:
if detect_divergence and inddiv is not None and inddiv.size:
bad = []
for idx in inddiv:
worldi = world0[idx]
result = optimize.root(
froot,
pix0[idx],
method='hybr',
tol=tolerance / (np.linalg.norm(pix0[idx]) + 1),
options={'maxfev': 2 * maxiter}
)
if result['success']:
pix[idx, :] = result['x']
invalid[idx] = False
else:
bad.append(idx)
if bad:
inddiv = np.array(bad, dtype=np.int)
else:
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.numerical_inverse' 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.numerical_inverse' 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)
if with_bounding_box and self.bounding_box is not None:
# find points outside the bounding box and replace their values
# with fill_value
valid = np.logical_not(invalid)
in_bb = np.ones_like(invalid, dtype=np.bool_)
for c, (x1, x2) in zip(pix[valid].T, self.bounding_box):
in_bb[valid] &= (c >= x1) & (c <= x2)
pix[np.logical_not(in_bb)] = fill_value
return pix
@property
def available_frames(self):
"""
List all frames in this WCS object.
Returns
-------
available_frames : dict
{frame_name: frame_object or None}
"""
if self._pipeline:
#return [getattr(frame[0], "name", frame[0]) for frame in self._pipeline]
return [step.frame if isinstance(step.frame, str) else step.frame.name for step in self._pipeline ]
else:
return None
[docs] def insert_frame(self, input_frame, transform, output_frame):
"""
Insert a new frame into an existing pipeline. This frame must be
anchored to a frame already in the pipeline by a transform. This
existing frame is identified solely by its name, although an entire
`~gwcs.coordinate_frame.CoordinateFrame` can be passed (e.g., the
`input_frame` or `output_frame` attribute). This frame is never
modified.
Parameters
----------
input_frame : str or `~gwcs.coordinate_frame.CoordinateFrame`
Coordinate frame at start of new transform
transform : `~astropy.modeling.Model`
New transform to be inserted in the pipeline
output_frame: str or `~gwcs.coordinate_frame.CoordinateFrame`
Coordinate frame at end of new transform
"""
input_name, input_frame_obj = self._get_frame_name(input_frame)
output_name, output_frame_obj = self._get_frame_name(output_frame)
try:
input_index = self._get_frame_index(input_frame)
except ValueError:
input_index = None
if input_frame_obj is None:
raise ValueError(f"New coordinate frame {input_name} must "
"be defined")
try:
output_index = self._get_frame_index(output_frame)
except ValueError:
output_index = None
if output_frame_obj is None:
raise ValueError(f"New coordinate frame {output_name} must "
"be defined")
new_frames = [input_index, output_index].count(None)
if new_frames == 0:
raise ValueError("Could not insert frame as both frames "
f"{input_name} and {output_name} already exist")
elif new_frames == 2:
raise ValueError("Could not insert frame as neither frame "
f"{input_name} nor {output_name} exists")
if input_index is None:
self._pipeline = (self._pipeline[:output_index] +
[Step(input_frame_obj, transform)] +
self._pipeline[output_index:])
super(WCS, self).__setattr__(input_name, input_frame_obj)
else:
split_step = self._pipeline[input_index]
self._pipeline = (self._pipeline[:input_index] +
[Step(split_step.frame, transform),
Step(output_frame_obj, split_step.transform)] +
self._pipeline[input_index + 1:])
super(WCS, self).__setattr__(output_name, output_frame_obj)
@property
def unit(self):
"""The unit of the coordinates in the output coordinate system."""
if self._pipeline:
try:
#return getattr(self, self._pipeline[-1][0].name).unit
return self._pipeline[-1].frame.unit
except AttributeError:
return None
else:
return None
@property
def output_frame(self):
"""Return the output coordinate frame."""
if self._pipeline:
frame = self._pipeline[-1].frame
if not isinstance(frame, str):
frame = frame.name
return getattr(self, frame)
else:
return None
@property
def input_frame(self):
"""Return the input coordinate frame."""
if self._pipeline:
frame = self._pipeline[0].frame
if not isinstance(frame, str):
frame = frame.name
return getattr(self, frame)
else:
return None
@property
def name(self):
"""Return the name for this WCS."""
return self._name
@name.setter
def name(self, value):
"""Set the name for the WCS."""
self._name = value
@property
def pipeline(self):
"""Return the pipeline structure."""
return self._pipeline
@property
def bounding_box(self):
"""
Return the range of acceptable values for each input axis.
The order of the axes is `~gwcs.coordinate_frames.CoordinateFrame.axes_order`.
"""
frames = self.available_frames
transform_0 = self.get_transform(frames[0], frames[1])
try:
bb = transform_0.bounding_box
except NotImplementedError:
return None
if transform_0.n_inputs == 1:
return bb
try:
axes_order = self.input_frame.axes_order
except AttributeError:
axes_order = np.arange(transform_0.n_inputs)
# Model.bounding_box is in python order, need to reverse it first.
return tuple(bb[::-1][i] for i in axes_order)
@bounding_box.setter
def bounding_box(self, value):
"""
Set the range of acceptable values for each input axis.
The order of the axes is `~gwcs.coordinate_frames.CoordinateFrame.axes_order`.
For two inputs and axes_order(0, 1) the bounding box is ((xlow, xhigh), (ylow, yhigh)).
Parameters
----------
value : tuple or None
Tuple of tuples with ("low", high") values for the range.
"""
frames = self.available_frames
transform_0 = self.get_transform(frames[0], frames[1])
if value is None:
transform_0.bounding_box = value
else:
try:
# Make sure the dimensions of the new bbox are correct.
mutils._BoundingBox.validate(transform_0, value)
except Exception:
raise
# get the sorted order of axes' indices
axes_ind = self._get_axes_indices()
if transform_0.n_inputs == 1:
transform_0.bounding_box = value
else:
# The axes in bounding_box in modeling follow python order
#transform_0.bounding_box = np.array(value)[axes_ind][::-1]
transform_0.bounding_box = [value[ind] for ind in axes_ind][::-1]
self.set_transform(frames[0], frames[1], transform_0)
def _get_axes_indices(self):
try:
axes_ind = np.argsort(self.input_frame.axes_order)
except AttributeError:
# the case of a frame being a string
axes_ind = np.arange(self.forward_transform.n_inputs)
return axes_ind
def __str__(self):
from astropy.table import Table
#col1 = [item[0] for item in self._pipeline]
col1 = [step.frame for step in self._pipeline]
col2 = []
for item in self._pipeline[: -1]:
#model = item[1]
model = item.transform
if model.name is not None:
col2.append(model.name)
else:
col2.append(model.__class__.__name__)
col2.append(None)
t = Table([col1, col2], names=['From', 'Transform'])
return str(t)
def __repr__(self):
fmt = "<WCS(output_frame={0}, input_frame={1}, forward_transform={2})>".format(
self.output_frame, self.input_frame, self.forward_transform)
return fmt
[docs] def to_fits_sip(self, bounding_box=None, max_pix_error=0.25, degree=None,
max_inv_pix_error=0.25, inv_degree=None,
npoints=32, crpix=None, verbose=False):
"""
Construct a SIP-based approximation to the WCS in the form of a FITS header
This assumes a tangent projection.
The default mode in using this attempts to achieve roughly 0.25 pixel
accuracy over the whole image.
Parameters
----------
bounding_box : tuple, optional
A pair of tuples, each consisting of two numbers
Represents the range of pixel values in both dimensions
((xmin, xmax), (ymin, ymax))
max_pix_error : float, optional
Maximum allowed error over the domain of the pixel array. This
error is the equivalent pixel error that corresponds to the maximum
error in the output coordinate resulting from the fit based on
a nominal plate scale.
degree : int, iterable, None, optional
Degree of the SIP polynomial. Default value `None` indicates that
all allowed degree values (``[1...9]``) will be considered and
the lowest degree that meets accuracy requerements set by
``max_pix_error`` will be returned. Alternatively, ``degree`` can be
an iterable containing allowed values for the SIP polynomial degree.
This option is similar to default `None` but it allows caller to
restrict the range of allowed SIP degrees used for fitting.
Finally, ``degree`` can be an integer indicating the exact SIP degree
to be fit to the WCS transformation. In this case
``max_pixel_error`` is ignored.
max_inv_error : float, optional
Maximum allowed inverse error over the domain of the pixel array
in pixel units. If None, no inverse is generated.
inv_degree : int, iterable, None, optional
Degree of the SIP polynomial. Default value `None` indicates that
all allowed degree values (``[1...9]``) will be considered and
the lowest degree that meets accuracy requerements set by
``max_pix_error`` will be returned. Alternatively, ``degree`` can be
an iterable containing allowed values for the SIP polynomial degree.
This option is similar to default `None` but it allows caller to
restrict the range of allowed SIP degrees used for fitting.
Finally, ``degree`` can be an integer indicating the exact SIP degree
to be fit to the WCS transformation. In this case
``max_inv_pixel_error`` is ignored.
npoints : int, optional
The number of points in each dimension to sample the bounding box
for use in the SIP fit. Minimum number of points is 3.
crpix : list of float, None, optional
Coordinates (1-based) of the reference point for the new FITS WCS.
When not provided, i.e., when set to `None` (default) the reference
pixel will be chosen near the center of the bounding box.
verbose : bool, optional
Print progress of fits.
Returns
-------
FITS header with all SIP WCS keywords
Raises
------
ValueError
If the WCS is not 2D, an exception will be raised. If the specified accuracy
(both forward and inverse, both rms and maximum) is not achieved an exception
will be raised.
Notes
-----
Use of this requires a judicious choice of required accuracies. Attempts to use
higher degrees (~7 or higher) will typically fail due floating point problems
that arise with high powers.
"""
if not isinstance(self.output_frame, cf.CelestialFrame):
raise ValueError(
"The to_fits_sip method only works with celestial frame transforms")
if npoints < 8:
raise ValueError("Number of sampling points is too small. 'npoints' must be >= 8.")
transform = self.forward_transform
# Determine reference points.
if bounding_box is None and self.bounding_box is None:
raise ValueError("A bounding_box is needed to proceed.")
if bounding_box is None:
bounding_box = self.bounding_box
(xmin, xmax), (ymin, ymax) = bounding_box
if crpix is None:
crpix1 = round((xmax + xmin) / 2, 1)
crpix2 = round((ymax + ymin) / 2, 1)
else:
crpix1 = crpix[0] - 1
crpix2 = crpix[1] - 1
# check that the bounding box has some reasonable size:
if (xmax - xmin) < 1 or (ymax - ymin) < 1:
raise ValueError("Bounding box is too small for fitting a SIP polynomial")
crval1, crval2 = transform(crpix1, crpix2)
hdr = fits.Header()
hdr['naxis'] = 2
hdr['naxis1'] = int(xmax) + 1
hdr['naxis2'] = int(ymax) + 1
hdr['ctype1'] = 'RA---TAN-SIP'
hdr['ctype2'] = 'DEC--TAN-SIP'
hdr['CRPIX1'] = crpix1 + 1
hdr['CRPIX2'] = crpix2 + 1
hdr['CRVAL1'] = crval1
hdr['CRVAL2'] = crval2
hdr['cd1_1'] = 1 # Placeholders for FITS card order, all will change.
hdr['cd1_2'] = 0
hdr['cd2_1'] = 0
hdr['cd2_2'] = 1
# Now rotate to native system and deproject. Recall that transform
# expects pixels in the original coordinate system, but the SIP
# transform is relative to crpix coordinates, thus the initial shift.
ntransform = ((Shift(crpix1) & Shift(crpix2)) | transform
| RotateCelestial2Native(crval1, crval2, 180)
| Sky2Pix_TAN())
# standard sampling:
u, v = _make_sampling_grid(npoints, bounding_box, crpix=[crpix1, crpix2])
undist_x, undist_y = ntransform(u, v)
# Double sampling to check if sampling is sufficient.
ud, vd = _make_sampling_grid(2 * npoints, bounding_box, crpix=[crpix1, crpix2])
undist_xd, undist_yd = ntransform(ud, vd)
# Determine approximate pixel scale in order to compute error threshold
# from the specified pixel error. Computed at the center of the array.
x0, y0 = ntransform(0, 0)
xx, xy = ntransform(1, 0)
yx, yy = ntransform(0, 1)
pixarea = np.abs((xx - x0) * (yy - y0) - (xy - y0) * (yx - x0))
plate_scale = np.sqrt(pixarea)
max_error = max_pix_error * plate_scale
# The fitting section.
fit_poly_x, fit_poly_y, max_resid = _fit_2D_poly(
ntransform, npoints,
degree, max_error,
u, v, undist_x, undist_y,
ud, vd, undist_xd, undist_yd,
verbose=verbose
)
# The following is necessary to put the fit into the SIP formalism.
cdmat, sip_poly_x, sip_poly_y = _reform_poly_coefficients(fit_poly_x, fit_poly_y)
# cdmat = np.array([[fit_poly_x.c1_0.value, fit_poly_x.c0_1.value],
# [fit_poly_y.c1_0.value, fit_poly_y.c0_1.value]])
det = cdmat[0][0] * cdmat[1][1] - cdmat[0][1] * cdmat[1][0]
U = ( cdmat[1][1] * undist_x - cdmat[0][1] * undist_y) / det
V = (-cdmat[1][0] * undist_x + cdmat[0][0] * undist_y) / det
detd = cdmat[0][0] * cdmat[1][1] - cdmat[0][1] * cdmat[1][0]
Ud = ( cdmat[1][1] * undist_xd - cdmat[0][1] * undist_yd) / detd
Vd = (-cdmat[1][0] * undist_xd + cdmat[0][0] * undist_yd) / detd
if max_inv_pix_error:
fit_inv_poly_u, fit_inv_poly_v, max_inv_resid = _fit_2D_poly(ntransform,
npoints, inv_degree,
max_inv_pix_error,
U, V, u-U, v-V,
Ud, Vd, ud-Ud, vd-Vd,
verbose=verbose)
pdegree = fit_poly_x.degree
if pdegree > 1:
hdr['a_order'] = pdegree
hdr['b_order'] = pdegree
_store_2D_coefficients(hdr, sip_poly_x, 'A')
_store_2D_coefficients(hdr, sip_poly_y, 'B')
hdr['sipmxerr'] = (max_resid * plate_scale, 'Max diff from GWCS (equiv pix).')
if max_inv_pix_error:
hdr['sipiverr'] = (max_inv_resid, 'Max diff for inverse (pixels)')
_store_2D_coefficients(hdr, fit_inv_poly_u, 'AP', keeplinear=True)
_store_2D_coefficients(hdr, fit_inv_poly_v, 'BP', keeplinear=True)
if max_inv_pix_error:
ipdegree = fit_inv_poly_u.degree
hdr['ap_order'] = ipdegree
hdr['bp_order'] = ipdegree
else:
hdr['ctype1'] = 'RA---TAN'
hdr['ctype2'] = 'DEC--TAN'
hdr['cd1_1'] = cdmat[0][0]
hdr['cd1_2'] = cdmat[0][1]
hdr['cd2_1'] = cdmat[1][0]
hdr['cd2_2'] = cdmat[1][1]
return hdr
[docs] def to_fits_tab(self, bounding_box=None, bin_ext_name='WCS-TABLE',
coord_col_name='coordinates', sampling=1):
"""
Construct a FITS WCS ``-TAB``-based approximation to the WCS
in the form of a FITS header and a binary table extension. For the
description of the FITS WCS ``-TAB`` convention, see
"Representations of spectral coordinates in FITS" in
`Greisen, E. W. et al. A&A 446 (2) 747-771 (2006)
<https://doi.org/10.1051/0004-6361:20053818>`_ .
Parameters
----------
bounding_box : tuple, optional
Specifies the range of acceptable values for each input axis.
The order of the axes is
`~gwcs.coordinate_frames.CoordinateFrame.axes_order`.
For two image axes ``bounding_box`` is of the form
``((xmin, xmax), (ymin, ymax))``.
bin_ext_name : str, optional
Extension name for the `~astropy.io.fits.BinTableHDU` extension.
coord_col_name : str, optional
Field name of the coordinate array in the structured array
stored in `~astropy.io.fits.BinTableHDU` data. This corresponds to
``TTYPEi`` field in the FITS header of the binary table extension.
sampling : float, tuple, optional
The target "density" of grid nodes per pixel to be used when
creating the coordinate array for the ``-TAB`` FITS WCS convention.
It is equal to ``1/step`` where ``step`` is the distance between
grid nodes in pixels. ``sampling`` can be specified as a single
number to be used for all axes or as a `tuple` of numbers
that specify the sampling for each image axis.
Returns
-------
hdr : `~astropy.io.fits.Header`
Header with WCS-TAB information associated (to be used) with image
data.
bin_table : `~astropy.io.fits.BinTableHDU`
Binary table extension containing the coordinate array.
Raises
------
ValueError
When ``bounding_box`` is not defined either through the input
``bounding_box`` parameter or this object's ``bounding_box``
property.
ValueError
When ``sampling`` is a `tuple` of length larger than 1 that
does not match the number of image axes.
RuntimeError
If the number of image axes (`~gwcs.WCS.pixel_n_dim`) is larger
than the number of world axes (`~gwcs.WCS.world_n_dim`).
"""
if bounding_box is None:
if self.bounding_box is None:
raise ValueError(
"Need a valid bounding_box to compute the footprint."
)
bounding_box = self.bounding_box
else:
# validate user-supplied bounding box:
frames = self.available_frames
transform_0 = self.get_transform(frames[0], frames[1])
mutils._BoundingBox.validate(transform_0, bounding_box)
if self.pixel_n_dim > self.world_n_dim:
raise RuntimeError(
"The case when the number of input axes is larger than the "
"number of output axes is not supported."
)
try:
sampling = np.broadcast_to(sampling, (self.pixel_n_dim, ))
except ValueError:
raise ValueError("Number of sampling values either must be 1 "
"or it must match the number of pixel axes.")
# 1D grid coordinates:
gcrds = []
cdelt = []
for (xmin, xmax), s in zip(bounding_box, sampling):
npix = max(2, 1 + int(np.ceil(abs((xmax - xmin) / s))))
gcrds.append(np.linspace(xmin, xmax, npix))
cdelt.append((npix - 1) / (xmax - xmin) if xmin != xmax else 1)
# n-dim coordinate arrays:
coord = np.stack(
self(*np.meshgrid(*gcrds[::-1], indexing='ij')[::-1]),
axis=-1
)
# create header with WCS info:
hdr = fits.Header()
for k in range(self.world_n_dim):
k1 = k + 1
ct = cf.get_ctype_from_ucd(self.world_axis_physical_types[k])
if len(ct) > 4:
raise ValueError("Axis type name too long.")
hdr['CTYPE{:d}'.format(k1)] = ct + (4 - len(ct)) * '-' + '-TAB'
hdr['CUNIT{:d}'.format(k1)] = self.world_axis_units[k]
hdr['PS{:d}_0'.format(k1)] = bin_ext_name
hdr['PS{:d}_1'.format(k1)] = coord_col_name
hdr['PV{:d}_3'.format(k1)] = k1
hdr['CRVAL{:d}'.format(k1)] = 1
if k < self.pixel_n_dim:
hdr['CRPIX{:d}'.format(k1)] = gcrds[k][0] + 1
hdr['PC{0:d}_{0:d}'.format(k1)] = 1.0
hdr['CDELT{:d}'.format(k1)] = cdelt[k]
else:
hdr['CRPIX{:d}'.format(k1)] = 1
coord = coord[None, :]
# structured array (data) for binary table HDU:
arr = np.array(
[(coord, )],
dtype=[
(coord_col_name, np.float64, coord.shape),
]
)
# create binary table HDU:
bin_tab = fits.BinTableHDU(arr)
bin_tab.header['EXTNAME'] = bin_ext_name
return hdr, bin_tab
def _calc_approx_inv(self, max_inv_pix_error=5, inv_degree=None, npoints=16):
"""
Compute polynomial fit for the inverse transformation to be used as
initial aproximation/guess for the iterative solution.
"""
self._approx_inverse = None
try:
# try to use analytic inverse if available:
self._approx_inverse = functools.partial(self.backward_transform,
with_bounding_box=False)
return
except (NotImplementedError, KeyError):
pass
if not isinstance(self.output_frame, cf.CelestialFrame):
# The _calc_approx_inv method only works with celestial frame transforms
return
# Determine reference points.
if self.bounding_box is None:
# A bounding_box is needed to proceed.
return
crpix = np.mean(self.bounding_box, axis=1)
crval1, crval2 = self.forward_transform(*crpix)
# Rotate to native system and deproject. Set center of the projection
# transformation to the middle of the bounding box ("image") in order
# to minimize projection effects across the entire image,
# thus the initial shift.
ntransform = ((Shift(crpix[0]) & Shift(crpix[1])) | self.forward_transform
| RotateCelestial2Native(crval1, crval2, 180)
| Sky2Pix_TAN())
# standard sampling:
u, v = _make_sampling_grid(npoints, self.bounding_box, crpix=crpix)
undist_x, undist_y = ntransform(u, v)
# Double sampling to check if sampling is sufficient.
ud, vd = _make_sampling_grid(2 * npoints, self.bounding_box, crpix=crpix)
undist_xd, undist_yd = ntransform(ud, vd)
fit_inv_poly_u, fit_inv_poly_v, max_inv_resid = _fit_2D_poly(
ntransform,
npoints, None,
max_inv_pix_error,
undist_x, undist_y, u, v,
undist_xd, undist_yd, ud, vd,
verbose=True
)
self._approx_inverse = (RotateCelestial2Native(crval1, crval2, 180) |
Sky2Pix_TAN() | Mapping((0, 1, 0, 1)) |
(fit_inv_poly_u & fit_inv_poly_v) |
(Shift(crpix[0]) & Shift(crpix[1])))
def _fit_2D_poly(ntransform, npoints, degree, max_error,
xin, yin, xout, yout,
xind, yind, xoutd, youtd,
verbose=False):
"""
Fit a pair of ordinary 2D polynomials to the supplied transform.
"""
llsqfitter = LinearLSQFitter()
# The case of one pass with the specified polynomial degree
if degree is None:
deglist = range(1, 10)
elif hasattr(degree, '__iter__'):
deglist = sorted(map(int, degree))
if set(deglist).difference(range(1, 10)):
raise ValueError("Allowed values for SIP degree are [1...9]")
else:
degree = int(degree)
if degree < 1 or degree > 9:
raise ValueError("Allowed values for SIP degree are [1...9]")
deglist = [degree]
prev_max_error = float(np.inf)
if verbose:
print(f'maximum_specified_error: {max_error}')
for deg in deglist:
poly_x = Polynomial2D(degree=deg)
poly_y = Polynomial2D(degree=deg)
fit_poly_x = llsqfitter(poly_x, xin, yin, xout)
fit_poly_y = llsqfitter(poly_y, xin, yin, yout)
max_resid = _compute_distance_residual(xout, yout,
fit_poly_x(xin, yin),
fit_poly_y(xin, yin))
if max_resid > prev_max_error:
raise RuntimeError('Failed to achieve required error tolerance')
if verbose:
print(f'Degree = {deg}, max_resid = {max_resid}')
if max_resid < max_error:
# Check to see if double sampling meets error requirement.
max_resid = _compute_distance_residual(xoutd, youtd,
fit_poly_x(xind, yind),
fit_poly_y(xind, yind))
if verbose:
print(f'Double sampling check: maximum residual={max_resid}')
if max_resid < max_error:
if verbose:
print('terminating condition met')
break
return fit_poly_x, fit_poly_y, max_resid
def _make_sampling_grid(npoints, bounding_box, crpix):
step = np.subtract.reduce(bounding_box, axis=1) / (1.0 - npoints)
crpix = np.asanyarray(crpix)[:, None, None]
return grid_from_bounding_box(bounding_box, step=step, center=False) - crpix
def _compute_distance_residual(undist_x, undist_y, fit_poly_x, fit_poly_y):
"""
Compute the distance residuals and return the rms and maximum values.
"""
dist = np.sqrt((undist_x - fit_poly_x)**2 + (undist_y - fit_poly_y)**2)
max_resid = dist.max()
return max_resid
def _reform_poly_coefficients(fit_poly_x, fit_poly_y):
"""
The fit polynomials must be recombined to align with the SIP decomposition
The result is the f(u,v) and g(u,v) polynomials, and the CD matrix.
"""
# Extract values for CD matrix and recombining
c11 = fit_poly_x.c1_0.value
c12 = fit_poly_x.c0_1.value
c21 = fit_poly_y.c1_0.value
c22 = fit_poly_y.c0_1.value
sip_poly_x = fit_poly_x.copy()
sip_poly_y = fit_poly_y.copy()
# Force low order coefficients to be 0 as defined in SIP
sip_poly_x.c0_0 = 0
sip_poly_y.c0_0 = 0
sip_poly_x.c1_0 = 0
sip_poly_x.c0_1 = 0
sip_poly_y.c1_0 = 0
sip_poly_y.c0_1 = 0
cdmat = ((c11, c12), (c21, c22))
invcdmat = npla.inv(np.array(cdmat))
degree = fit_poly_x.degree
# Now loop through all remaining coefficients
for i in range(0, degree + 1):
for j in range(0, degree + 1):
if (i + j > 1) and (i + j < degree + 1):
old_x = getattr(fit_poly_x, f'c{i}_{j}').value
old_y = getattr(fit_poly_y, f'c{i}_{j}').value
newcoeff = np.dot(invcdmat, np.array([[old_x], [old_y]]))
setattr(sip_poly_x, f'c{i}_{j}', newcoeff[0, 0])
setattr(sip_poly_y, f'c{i}_{j}', newcoeff[1, 0])
return cdmat, sip_poly_x, sip_poly_y
def _store_2D_coefficients(hdr, poly_model, coeff_prefix, keeplinear=False):
"""
Write the polynomial model coefficients to the header.
"""
mindeg = int(not keeplinear)
degree = poly_model.degree
for i in range(0, degree + 1):
for j in range(0, degree + 1):
if (i + j) > mindeg and (i + j < degree + 1):
hdr[f'{coeff_prefix}_{i}_{j}'] = getattr(poly_model, f'c{i}_{j}').value
class Step:
"""
Represents a ``step`` in the WCS pipeline.
Parameters
----------
frame : `~gwcs.coordinate_frames.CoordinateFrame`
A gwcs coordinate frame object.
transform : `~astropy.modeling.core.Model` or None
A transform from this step's frame to next step's frame.
The transform of the last step should be ``None``.
"""
def __init__(self, frame, transform=None):
self.frame = frame
self.transform = transform
@property
def frame(self):
return self._frame
@frame.setter
def frame(self, val):
if not isinstance(val, (cf.CoordinateFrame, str)):
raise TypeError('"frame" should be an instance of CoordinateFrame or a string.')
self._frame = val
@property
def transform(self):
return self._transform
@transform.setter
def transform(self, val):
if val is not None and not isinstance(val, (Model)):
raise TypeError('"transform" should be an instance of astropy.modeling.Model.')
self._transform = val
@property
def frame_name(self):
if isinstance(self.frame, str):
return self.frame
return self.frame.name
def __getitem__(self, ind):
warnings.warn("Indexing a WCS.pipeline step is deprecated. "
"Use the `frame` and `transform` attributes instead.", DeprecationWarning)
if ind not in (0, 1):
raise IndexError("Allowed inices are 0 (frame) and 1 (transform).")
if ind == 0:
return self.frame
return self.transform
def __str__(self):
return f"{self.frame_name}\t {getattr(self.transform, 'name', 'None') or self.transform.__class__.__name__}"
def __repr__(self):
return f"Step(frame={self.frame_name}, \
transform={getattr(self.transform, 'name', 'None') or self.transform.__class__.__name__})"