Source code for gwcs.wcs

# 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 astropy.modeling.core import Model # , fix_inputs
from astropy.modeling import utils as mutils
from astropy.modeling.models import (Shift, Polynomial2D, Sky2Pix_TAN,
                                     RotateCelestial2Native)
from astropy.modeling.fitting import LinearLSQFitter
import astropy.io.fits as fits

from .api import GWCSAPIMixin
from . import coordinate_frames
from .utils import CoordinateFrameError
from .utils import _toindex
from . import utils
from gwcs import coordinate_frames as cf


HAS_FIX_INPUTS = True

try:
    from astropy.modeling.core import fix_inputs
except ImportError:
    HAS_FIX_INPUTS = False


__all__ = ['WCS']


[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._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)]
[docs] def get_transform(self, from_frame, to_frame): """ Return a transform between two coordinate frames. Parameters ---------- from_frame : str or `~gwcs.coordinate_frame.CoordinateFrame` Initial coordinate frame name of object. to_frame : str, or instance of `~gwcs.cordinate_frames.CoordinateFrame` End coordinate frame name or object. Returns ------- transform : `~astropy.modeling.Model` Transform between two frames. """ if not self._pipeline: return None try: from_ind = self._get_frame_index(from_frame) except ValueError: raise CoordinateFrameError("Frame {0} is not in the available " "frames".format(from_frame)) try: to_ind = self._get_frame_index(to_frame) except ValueError: raise CoordinateFrameError("Frame {0} is not in the available frames".format(to_frame)) if to_ind < from_ind: #transforms = np.array(self._pipeline[to_ind: from_ind], dtype="object")[:, 1].tolist() transforms = [step.transform for step in self._pipeline[to_ind: from_ind]] transforms = [tr.inverse for tr in transforms[::-1]] elif to_ind == from_ind: return None else: #transforms = np.array(self._pipeline[from_ind: to_ind], dtype="object")[:, 1].copy() transforms = [step.transform for step in self._pipeline[from_ind: to_ind]] return functools.reduce(lambda x, y: x | y, transforms)
[docs] def set_transform(self, from_frame, to_frame, transform): """ Set/replace the transform between two coordinate frames. Parameters ---------- from_frame : str or `~gwcs.coordinate_frame.CoordinateFrame` Initial coordinate frame. to_frame : str, or instance of `~gwcs.cordinate_frames.CoordinateFrame` End coordinate frame. transform : `~astropy.modeling.Model` Transform between ``from_frame`` and ``to_frame``. """ from_name, from_obj = self._get_frame_name(from_frame) to_name, to_obj = self._get_frame_name(to_frame) if not self._pipeline: if from_name != self._input_frame: raise CoordinateFrameError( "Expected 'from_frame' to be {0}".format(self._input_frame)) if to_frame != self._output_frame: raise CoordinateFrameError( "Expected 'to_frame' to be {0}".format(self._output_frame)) try: from_ind = self._get_frame_index(from_name) except ValueError: raise CoordinateFrameError("Frame {0} is not in the available frames".format(from_name)) try: to_ind = self._get_frame_index(to_name) except ValueError: raise CoordinateFrameError("Frame {0} is not in the available frames".format(to_name)) if from_ind + 1 != to_ind: raise ValueError("Frames {0} and {1} are not in sequence".format(from_name, to_name)) self._pipeline[from_ind].transform = transform
@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, coordinate_frames.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 ounding_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 = np.array(self.bounding_box)[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 invert(self, *args, **kwargs): """ Invert coordinates. The analytical inverse of the forward transform is used, if available. If not an iterative method is used. Parameters ---------- args : float, array like, `~astropy.coordinates.SkyCoord` or `~astropy.units.Unit` coordinates to be inverted kwargs : dict keyword arguments to be passed to the iterative invert method. 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). """ if not utils.isnumerical(args[0]): args = self.output_frame.coordinate_to_quantity(*args) if self.output_frame.naxes == 1: args = [args] if not self.backward_transform.uses_quantity: args = utils.get_values(self.output_frame.unit, *args) 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 try: result = self.backward_transform(*args, **kwargs) except (NotImplementedError, KeyError): result = self._invert(*args, **kwargs) 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 _invert(self, *args, **kwargs): """ Implement iterative inverse here. """ raise NotImplementedError
[docs] def transform(self, from_frame, to_frame, *args, **kwargs): """ Transform positions between two frames. Parameters ---------- from_frame : str or `~gwcs.coordinate_frames.CoordinateFrame` Initial coordinate frame. to_frame : str, or instance of `~gwcs.cordinate_frames.CoordinateFrame` Coordinate frame into which to transform. args : float or array-like Inputs in ``from_frame``, separate inputs for each dimension. output_with_units : bool If ``True`` - returns a `~astropy.coordinates.SkyCoord` or `~astropy.units.Quantity` object. 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.get_transform(from_frame, to_frame) if not utils.isnumerical(args[0]): inp_frame = getattr(self, from_frame) args = inp_frame.coordinate_to_quantity(*args) if not transform.uses_quantity: args = utils.get_values(inp_frame.unit, *args) 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 result = transform(*args, **kwargs) if with_units: to_frame_name, to_frame_obj = self._get_frame_name(to_frame) if to_frame_obj is not None: if to_frame_obj.naxes == 1: result = to_frame_obj.coordinates(result) else: result = to_frame_obj.coordinates(*result) else: raise TypeError("Coordinate objects could not be created because" "frame {0} is not defined.".format(to_frame_name)) return result
@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_transform(self, frame, transform, after=False): """ Insert a transform before (default) or after a coordinate frame. Append (or prepend) a transform to the transform connected to frame. Parameters ---------- frame : str or `~gwcs.coordinate_frame.CoordinateFrame` Coordinate frame which sets the point of insertion. transform : `~astropy.modeling.Model` New transform to be inserted in the pipeline after : bool If True, the new transform is inserted in the pipeline immediately after ``frame``. """ name, _ = self._get_frame_name(frame) frame_ind = self._get_frame_index(name) if not after: current_transform = self._pipeline[frame_ind - 1].transform self._pipeline[frame_ind - 1].transform = current_transform | transform else: current_transform = self._pipeline[frame_ind].transform self._pipeline[frame_ind].transform = transform | current_transform
@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][0] 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][0] 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. bb = np.array(bb[::-1])[np.array(axes_order)] return tuple(tuple(item) for item in bb) @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] 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 footprint(self, bounding_box=None, center=False, axis_type="all"): """ Return the footprint in world coordinates. Parameters ---------- bounding_box : tuple of floats: (start, stop) `prop: bounding_box` center : bool If `True` use the center of the pixel, otherwise use the corner. axis_type : str A supported ``output_frame.axes_type`` or "all" (default). One of ['spatial', 'spectral', 'temporal'] or a custom type. Returns ------- coord : ndarray Array of coordinates in the output_frame mapping corners to the output frame. For spatial coordinates the order is clockwise, starting from the bottom left corner. """ def _order_clockwise(v): return np.asarray([[v[0][0], v[1][0]], [v[0][0], v[1][1]], [v[0][1], v[1][1]], [v[0][1], v[1][0]]]).T if bounding_box is None: if self.bounding_box is None: raise TypeError("Need a valid bounding_box to compute the footprint.") bb = self.bounding_box else: bb = bounding_box all_spatial = all([t.lower() == "spatial" for t in self.output_frame.axes_type]) if all_spatial: vertices = _order_clockwise(bb) else: vertices = np.array(list(itertools.product(*bb))).T if center: vertices = _toindex(vertices) result = np.asarray(self.__call__(*vertices, **{'with_bounding_box': False})) axis_type = axis_type.lower() if axis_type == 'spatial' and all_spatial: return result.T if axis_type != "all": axtyp_ind = np.array([t.lower() for t in self.output_frame.axes_type]) == axis_type if not axtyp_ind.any(): raise ValueError('This WCS does not have axis of type "{}".'.format(axis_type)) result = np.asarray([(r.min(), r.max()) for r in result[axtyp_ind]]) if axis_type == "spatial": result = _order_clockwise(result) else: result.sort() result = np.squeeze(result) return result.T
[docs] def fix_inputs(self, fixed): """ Return a new unique WCS by fixing inputs to constant values. Parameters ---------- fixed : dict Keyword arguments with fixed values corresponding to `self.selector`. Returns ------- new_wcs : `WCS` A new unique WCS corresponding to the values in `fixed`. Examples -------- >>> w = WCS(pipeline, selector={"spectral_order": [1, 2]}) # doctest: +SKIP >>> new_wcs = w.set_inputs(spectral_order=2) # doctest: +SKIP >>> new_wcs.inputs # doctest: +SKIP ("x", "y") """ if not HAS_FIX_INPUTS: raise ImportError('"fix_inputs" needs astropy version >= 4.0.') new_pipeline = [] step0 = self.pipeline[0] new_transform = fix_inputs(step0[1], fixed) new_pipeline.append((step0[0], new_transform)) new_pipeline.extend(self.pipeline[1:]) return self.__class__(new_pipeline)
[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, 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, optional Degree of the SIP polynomial. If supplied, 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, optional Degree of the inverse SIP polynomial. If supplied 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. 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") 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 crpix1 = (xmax - xmin) // 2 crpix2 = (ymax - ymin) // 2 crval1, crval2 = transform(crpix1, crpix2) hdr = fits.Header() hdr['naxis'] = 2 hdr['naxis1'] = xmax hdr['naxis2'] = ymax 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()) u, v = _make_sampling_grid(npoints, bounding_box) undist_x, undist_y = ntransform(u, v) # Double sampling to check if sampling is sufficient. ud, vd = _make_sampling_grid(2 * npoints, bounding_box) 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, None, 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
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: deglist = [degree] else: deglist = range(10) 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): (xmin, xmax), (ymin, ymax) = bounding_box xsize = xmax - xmin ysize = ymax - ymin crpix1 = int(xsize / 2) crpix2 = int(ysize / 2) stepsize_x = int(xsize / npoints) stepsize_y = int(ysize / npoints) # Ensure last row and column are part of the evaluation grid. y, x = np.mgrid[: ymax + 1: stepsize_y, : xmax + 1: stepsize_x] x[:, -1] = xsize - 1 y[-1, :] = ysize - 1 u = x - crpix1 v = y - crpix2 return u, v 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__})"