.. _using_wcs_examples: Using the WCS object ==================== This section uses the ``imaging_wcs_wdist.asdf`` created in :ref:`imaging_example` to read in a WCS object and demo its methods. .. doctest-skip:: >>> import asdf >>> asdf_file = asdf.open("imaging_wcs_wdist.asdf") >>> wcsobj = asdf_file.tree["wcs"] >>> print(wcsobj) # doctest: +SKIP From Transform ----------------- ---------------- detector distortion undistorted_frame linear_transform icrs None Inspecting Available Coordinate Frames -------------------------------------- To see what frames are defined: .. doctest-skip:: >>> print(wcsobj.available_frames) ['detector', 'undistorted_frame', 'icrs'] >>> wcsobj.input_frame >>> wcsobj.output_frame )> Because the ``output_frame`` is a `~gwcs.coordinate_frames.CoordinateFrame` object we can get the result of the WCS transform as an `~astropy.coordinates.SkyCoord` object and transform them to other standard coordinate frames supported by `astropy.coordinates`. .. doctest-skip:: >>> skycoord = wcsobj(1, 2, with_units=True) >>> print(skycoord) >>> print(skycoord.transform_to("galactic")) Using Bounding Box ------------------ The WCS object has an attribute :attr:`~gwcs.WCS.bounding_box` (default value of ``None``) which describes the range of acceptable values for each input axis. .. doctest-skip:: >>> wcsobj.bounding_box = ((0, 2048), (0, 1000)) >>> wcsobj((2,3), (1020, 980)) [array([ nan, 5.54527989]), array([ nan, -72.06454341])] The WCS object accepts a boolean flag called ``with_bounding_box`` with default value of ``True``. Output values which are outside the ``bounding_box`` are set to ``NaN``. There are cases when this is not desirable and ``with_bounding_box=False`` should be passes. Calling the :meth:`~gwcs.WCS.footprint` returns the footprint on the sky. .. doctest-skip:: >>> wcsobj.footprint() Manipulating Transforms ----------------------- Some methods allow managing the transforms in a more detailed manner. Transforms between frames can be retrieved and evaluated separately. .. doctest-skip:: >>> dist = wcsobj.get_transform('detector', 'undistorted_frame') >>> dist(1, 2) # doctest: +FLOAT_CMP (-292.4150238489997, -616.8680129899999) Transforms in the pipeline can be replaced by new transforms. .. doctest-skip:: >>> new_transform = models.Shift(1) & models.Shift(1.5) | distortion >>> wcsobj.set_transform('detector', 'undistorted_frame', new_transform) >>> wcsobj(1, 2) # doctest: +FLOAT_CMP (5.501064280097802, -72.04557376712566) A transform can be inserted before or after a frame in the pipeline. .. doctest-skip:: >>> scale = models.Scale(2) & models.Scale(1) >>> wcsobj.insert_transform('icrs', scale, after=False) >>> wcsobj(1, 2) # doctest: +FLOAT_CMP (11.002128560195604, -72.04557376712566) Inverse Transformations ----------------------- Often, it is useful to be able to compute inverse transformation that converts coordinates from the output frame back to the coordinates in the input frame. Note. the ``backward_transform`` attribute is equivalent to ``forward_transform.inverse``. In this section, for illustration purpose, we will be using the same 2D imaging WCS from ``imaging_wcs_wdist.asdf`` created in :ref:`imaging_example` whose forward transformation converts image coordinates to world coordinates and inverse transformation converts world coordinates back to image coordinates. .. doctest-skip:: >>> wcsobj = asdf.open(get_pkg_data_filename('imaging_wcs_wdist.asdf')).tree['wcs'] The most general method available for computing inverse coordinate transformation is the `WCS.invert() ` method. This method uses automatic or user-supplied analytical inverses whenever available to convert coordinates from the output frame to the input frame. When analytical inverse is not available as is the case for the ``wcsobj`` above, a numerical solution will be attempted using `WCS.numerical_inverse() `. Default parameters used by `WCS.numerical_inverse() ` or `WCS.invert() ` methods should be acceptable in most situations: .. doctest-skip:: >>> world = wcsobj(350, 200) >>> print(wcsobj.invert(*world)) # convert a single point (349.9999994163172, 200.00000017679295) >>> world = wcsobj([2, 350, -5000], [2, 200, 6000]) >>> print(wcsobj.invert(*world)) # convert multiple points at once (array([ 2.00000000e+00, 3.49999999e+02, -5.00000000e+03]), array([1.99999972e+00, 2.00000002e+02, 6.00000000e+03]) By default, parameter ``quiet`` is set to `True` in `WCS.numerical_inverse() ` and so it will return results "as is" without warning us about possible loss of accuracy or about divergence of the iterative process. In order to catch these kind of errors that can occur during numerical inversion, we need to turn off ``quiet`` mode and be prepared to catch `gwcs.wcs.NoConvergence` exceptions. In the next example, let's also add a point far away from the image for which numerical inverse fails. .. doctest-skip:: >>> from gwcs import NoConvergence >>> world = wcsobj([-85000, 2, 350, 3333, -5000], [-55000, 2, 200, 1111, 6000], ... with_bounding_box=False) >>> try: ... x, y = wcsobj.invert(*world, quiet=False, maxiter=40, ... detect_divergence=True, with_bounding_box=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: [0] Indices of poorly converging points: [4] Best solution: [[ 1.38600585e+11 6.77595594e+11] [ 2.00000000e+00 1.99999972e+00] [ 3.49999999e+02 2.00000002e+02] [ 3.33300000e+03 1.11100000e+03] [-4.99999985e+03 5.99999985e+03]] Achieved accuracy: [[8.56497375e+02 5.09216089e+03] [6.57962988e-06 3.70445289e-07] [5.31656943e-06 2.72052603e-10] [6.81557583e-06 1.06560533e-06] [3.96365344e-04 6.41822468e-05]]