# Licensed under a 3-clause BSD style license - see LICENSE.rst """ This module includes helper functions for array operations. """ from copy import deepcopy import numpy as np from astropy import units as u from astropy.coordinates import SkyCoord from astropy.utils import lazyproperty from astropy.wcs.utils import skycoord_to_pixel, proj_plane_pixel_scales from astropy.wcs import Sip __all__ = ['extract_array', 'add_array', 'subpixel_indices', 'overlap_slices', 'NoOverlapError', 'PartialOverlapError', 'Cutout2D'] class NoOverlapError(ValueError): '''Raised when determining the overlap of non-overlapping arrays.''' pass class PartialOverlapError(ValueError): '''Raised when arrays only partially overlap.''' pass def overlap_slices(large_array_shape, small_array_shape, position, mode='partial'): """ Get slices for the overlapping part of a small and a large array. Given a certain position of the center of the small array, with respect to the large array, tuples of slices are returned which can be used to extract, add or subtract the small array at the given position. This function takes care of the correct behavior at the boundaries, where the small array is cut of appropriately. Integer positions are at the pixel centers. Parameters ---------- large_array_shape : tuple of int or int The shape of the large array (for 1D arrays, this can be an `int`). small_array_shape : int or tuple thereof The shape of the small array (for 1D arrays, this can be an `int`). See the ``mode`` keyword for additional details. position : number or tuple thereof The position of the small array's center with respect to the large array. The pixel coordinates should be in the same order as the array shape. Integer positions are at the pixel centers. For any axis where ``small_array_shape`` is even, the position is rounded up, e.g. extracting two elements with a center of ``1`` will define the extracted region as ``[0, 1]``. mode : {'partial', 'trim', 'strict'}, optional In ``'partial'`` mode, a partial overlap of the small and the large array is sufficient. The ``'trim'`` mode is similar to the ``'partial'`` mode, but ``slices_small`` will be adjusted to return only the overlapping elements. In the ``'strict'`` mode, the small array has to be fully contained in the large array, otherwise an `~astropy.nddata.utils.PartialOverlapError` is raised. In all modes, non-overlapping arrays will raise a `~astropy.nddata.utils.NoOverlapError`. Returns ------- slices_large : tuple of slice A tuple of slice objects for each axis of the large array, such that ``large_array[slices_large]`` extracts the region of the large array that overlaps with the small array. slices_small : tuple of slice A tuple of slice objects for each axis of the small array, such that ``small_array[slices_small]`` extracts the region that is inside the large array. """ if mode not in ['partial', 'trim', 'strict']: raise ValueError('Mode can be only "partial", "trim", or "strict".') if np.isscalar(small_array_shape): small_array_shape = (small_array_shape, ) if np.isscalar(large_array_shape): large_array_shape = (large_array_shape, ) if np.isscalar(position): position = (position, ) if any(~np.isfinite(position)): raise ValueError('Input position contains invalid values (NaNs or ' 'infs).') if len(small_array_shape) != len(large_array_shape): raise ValueError('"large_array_shape" and "small_array_shape" must ' 'have the same number of dimensions.') if len(small_array_shape) != len(position): raise ValueError('"position" must have the same number of dimensions ' 'as "small_array_shape".') # define the min/max pixel indices indices_min = [int(np.ceil(pos - (small_shape / 2.))) for (pos, small_shape) in zip(position, small_array_shape)] indices_max = [int(np.ceil(pos + (small_shape / 2.))) for (pos, small_shape) in zip(position, small_array_shape)] for e_max in indices_max: if e_max < 0: raise NoOverlapError('Arrays do not overlap.') for e_min, large_shape in zip(indices_min, large_array_shape): if e_min >= large_shape: raise NoOverlapError('Arrays do not overlap.') if mode == 'strict': for e_min in indices_min: if e_min < 0: raise PartialOverlapError('Arrays overlap only partially.') for e_max, large_shape in zip(indices_max, large_array_shape): if e_max > large_shape: raise PartialOverlapError('Arrays overlap only partially.') # Set up slices slices_large = tuple(slice(max(0, indices_min), min(large_shape, indices_max)) for (indices_min, indices_max, large_shape) in zip(indices_min, indices_max, large_array_shape)) if mode == 'trim': slices_small = tuple(slice(0, slc.stop - slc.start) for slc in slices_large) else: slices_small = tuple(slice(max(0, -indices_min), min(large_shape - indices_min, indices_max - indices_min)) for (indices_min, indices_max, large_shape) in zip(indices_min, indices_max, large_array_shape)) return slices_large, slices_small def extract_array(array_large, shape, position, mode='partial', fill_value=np.nan, return_position=False): """ Extract a smaller array of the given shape and position from a larger array. Parameters ---------- array_large : ndarray The array from which to extract the small array. shape : int or tuple thereof The shape of the extracted array (for 1D arrays, this can be an `int`). See the ``mode`` keyword for additional details. position : number or tuple thereof The position of the small array's center with respect to the large array. The pixel coordinates should be in the same order as the array shape. Integer positions are at the pixel centers (for 1D arrays, this can be a number). mode : {'partial', 'trim', 'strict'}, optional The mode used for extracting the small array. For the ``'partial'`` and ``'trim'`` modes, a partial overlap of the small array and the large array is sufficient. For the ``'strict'`` mode, the small array has to be fully contained within the large array, otherwise an `~astropy.nddata.utils.PartialOverlapError` is raised. In all modes, non-overlapping arrays will raise a `~astropy.nddata.utils.NoOverlapError`. In ``'partial'`` mode, positions in the small array that do not overlap with the large array will be filled with ``fill_value``. In ``'trim'`` mode only the overlapping elements are returned, thus the resulting small array may be smaller than the requested ``shape``. fill_value : number, optional If ``mode='partial'``, the value to fill pixels in the extracted small array that do not overlap with the input ``array_large``. ``fill_value`` will be changed to have the same ``dtype`` as the ``array_large`` array, with one exception. If ``array_large`` has integer type and ``fill_value`` is ``np.nan``, then a `ValueError` will be raised. return_position : bool, optional If `True`, return the coordinates of ``position`` in the coordinate system of the returned array. Returns ------- array_small : ndarray The extracted array. new_position : tuple If ``return_position`` is true, this tuple will contain the coordinates of the input ``position`` in the coordinate system of ``array_small``. Note that for partially overlapping arrays, ``new_position`` might actually be outside of the ``array_small``; ``array_small[new_position]`` might give wrong results if any element in ``new_position`` is negative. Examples -------- We consider a large array with the shape 11x10, from which we extract a small array of shape 3x5: >>> import numpy as np >>> from astropy.nddata.utils import extract_array >>> large_array = np.arange(110).reshape((11, 10)) >>> extract_array(large_array, (3, 5), (7, 7)) array([[65, 66, 67, 68, 69], [75, 76, 77, 78, 79], [85, 86, 87, 88, 89]]) """ if np.isscalar(shape): shape = (shape, ) if np.isscalar(position): position = (position, ) if mode not in ['partial', 'trim', 'strict']: raise ValueError("Valid modes are 'partial', 'trim', and 'strict'.") large_slices, small_slices = overlap_slices(array_large.shape, shape, position, mode=mode) extracted_array = array_large[large_slices] if return_position: new_position = [i - s.start for i, s in zip(position, large_slices)] # Extracting on the edges is presumably a rare case, so treat special here if (extracted_array.shape != shape) and (mode == 'partial'): extracted_array = np.zeros(shape, dtype=array_large.dtype) try: extracted_array[:] = fill_value except ValueError as exc: exc.args += ('fill_value is inconsistent with the data type of ' 'the input array (e.g., fill_value cannot be set to ' 'np.nan if the input array has integer type). Please ' 'change either the input array dtype or the ' 'fill_value.',) raise exc extracted_array[small_slices] = array_large[large_slices] if return_position: new_position = [i + s.start for i, s in zip(new_position, small_slices)] if return_position: return extracted_array, tuple(new_position) else: return extracted_array def add_array(array_large, array_small, position): """ Add a smaller array at a given position in a larger array. Parameters ---------- array_large : ndarray Large array. array_small : ndarray Small array to add. Can be equal to ``array_large`` in size in a given dimension, but not larger. position : tuple Position of the small array's center, with respect to the large array. Coordinates should be in the same order as the array shape. Returns ------- new_array : ndarray The new array formed from the sum of ``array_large`` and ``array_small``. Notes ----- The addition is done in-place. Examples -------- We consider a large array of zeros with the shape 5x5 and a small array of ones with a shape of 3x3: >>> import numpy as np >>> from astropy.nddata.utils import add_array >>> large_array = np.zeros((5, 5)) >>> small_array = np.ones((3, 3)) >>> add_array(large_array, small_array, (1, 2)) # doctest: +FLOAT_CMP array([[0., 1., 1., 1., 0.], [0., 1., 1., 1., 0.], [0., 1., 1., 1., 0.], [0., 0., 0., 0., 0.], [0., 0., 0., 0., 0.]]) """ # Check if large array is not smaller if all(large_shape >= small_shape for (large_shape, small_shape) in zip(array_large.shape, array_small.shape)): large_slices, small_slices = overlap_slices(array_large.shape, array_small.shape, position) array_large[large_slices] += array_small[small_slices] return array_large else: raise ValueError("Can't add array. Small array too large.") def subpixel_indices(position, subsampling): """ Convert decimal points to indices, given a subsampling factor. This discards the integer part of the position and uses only the decimal place, and converts this to a subpixel position depending on the subsampling specified. The center of a pixel corresponds to an integer position. Parameters ---------- position : ndarray or array-like Positions in pixels. subsampling : int Subsampling factor per pixel. Returns ------- indices : ndarray The integer subpixel indices corresponding to the input positions. Examples -------- If no subsampling is used, then the subpixel indices returned are always 0: >>> from astropy.nddata.utils import subpixel_indices >>> subpixel_indices([1.2, 3.4, 5.6], 1) # doctest: +FLOAT_CMP array([0., 0., 0.]) If instead we use a subsampling of 2, we see that for the two first values (1.1 and 3.4) the subpixel position is 1, while for 5.6 it is 0. This is because the values of 1, 3, and 6 lie in the center of pixels, and 1.1 and 3.4 lie in the left part of the pixels and 5.6 lies in the right part. >>> subpixel_indices([1.2, 3.4, 5.5], 2) # doctest: +FLOAT_CMP array([1., 1., 0.]) """ # Get decimal points fractions = np.modf(np.asanyarray(position) + 0.5)[0] return np.floor(fractions * subsampling) class Cutout2D: """ Create a cutout object from a 2D array. The returned object will contain a 2D cutout array. If ``copy=False`` (default), the cutout array is a view into the original ``data`` array, otherwise the cutout array will contain a copy of the original data. If a `~astropy.wcs.WCS` object is input, then the returned object will also contain a copy of the original WCS, but updated for the cutout array. For example usage, see :ref:`astropy:cutout_images`. .. warning:: The cutout WCS object does not currently handle cases where the input WCS object contains distortion lookup tables described in the `FITS WCS distortion paper `__. Parameters ---------- data : ndarray The 2D data array from which to extract the cutout array. position : tuple or `~astropy.coordinates.SkyCoord` The position of the cutout array's center with respect to the ``data`` array. The position can be specified either as a ``(x, y)`` tuple of pixel coordinates or a `~astropy.coordinates.SkyCoord`, in which case ``wcs`` is a required input. size : int, array-like, or `~astropy.units.Quantity` The size of the cutout array along each axis. If ``size`` is a scalar number or a scalar `~astropy.units.Quantity`, then a square cutout of ``size`` will be created. If ``size`` has two elements, they should be in ``(ny, nx)`` order. Scalar numbers in ``size`` are assumed to be in units of pixels. ``size`` can also be a `~astropy.units.Quantity` object or contain `~astropy.units.Quantity` objects. Such `~astropy.units.Quantity` objects must be in pixel or angular units. For all cases, ``size`` will be converted to an integer number of pixels, rounding the the nearest integer. See the ``mode`` keyword for additional details on the final cutout size. .. note:: If ``size`` is in angular units, the cutout size is converted to pixels using the pixel scales along each axis of the image at the ``CRPIX`` location. Projection and other non-linear distortions are not taken into account. wcs : `~astropy.wcs.WCS`, optional A WCS object associated with the input ``data`` array. If ``wcs`` is not `None`, then the returned cutout object will contain a copy of the updated WCS for the cutout data array. mode : {'trim', 'partial', 'strict'}, optional The mode used for creating the cutout data array. For the ``'partial'`` and ``'trim'`` modes, a partial overlap of the cutout array and the input ``data`` array is sufficient. For the ``'strict'`` mode, the cutout array has to be fully contained within the ``data`` array, otherwise an `~astropy.nddata.utils.PartialOverlapError` is raised. In all modes, non-overlapping arrays will raise a `~astropy.nddata.utils.NoOverlapError`. In ``'partial'`` mode, positions in the cutout array that do not overlap with the ``data`` array will be filled with ``fill_value``. In ``'trim'`` mode only the overlapping elements are returned, thus the resulting cutout array may be smaller than the requested ``shape``. fill_value : float or int, optional If ``mode='partial'``, the value to fill pixels in the cutout array that do not overlap with the input ``data``. ``fill_value`` must have the same ``dtype`` as the input ``data`` array. copy : bool, optional If `False` (default), then the cutout data will be a view into the original ``data`` array. If `True`, then the cutout data will hold a copy of the original ``data`` array. Attributes ---------- data : 2D `~numpy.ndarray` The 2D cutout array. shape : (2,) tuple The ``(ny, nx)`` shape of the cutout array. shape_input : (2,) tuple The ``(ny, nx)`` shape of the input (original) array. input_position_cutout : (2,) tuple The (unrounded) ``(x, y)`` position with respect to the cutout array. input_position_original : (2,) tuple The original (unrounded) ``(x, y)`` input position (with respect to the original array). slices_original : (2,) tuple of slice object A tuple of slice objects for the minimal bounding box of the cutout with respect to the original array. For ``mode='partial'``, the slices are for the valid (non-filled) cutout values. slices_cutout : (2,) tuple of slice object A tuple of slice objects for the minimal bounding box of the cutout with respect to the cutout array. For ``mode='partial'``, the slices are for the valid (non-filled) cutout values. xmin_original, ymin_original, xmax_original, ymax_original : float The minimum and maximum ``x`` and ``y`` indices of the minimal rectangular region of the cutout array with respect to the original array. For ``mode='partial'``, the bounding box indices are for the valid (non-filled) cutout values. These values are the same as those in `bbox_original`. xmin_cutout, ymin_cutout, xmax_cutout, ymax_cutout : float The minimum and maximum ``x`` and ``y`` indices of the minimal rectangular region of the cutout array with respect to the cutout array. For ``mode='partial'``, the bounding box indices are for the valid (non-filled) cutout values. These values are the same as those in `bbox_cutout`. wcs : `~astropy.wcs.WCS` or None A WCS object associated with the cutout array if a ``wcs`` was input. Examples -------- >>> import numpy as np >>> from astropy.nddata.utils import Cutout2D >>> from astropy import units as u >>> data = np.arange(20.).reshape(5, 4) >>> cutout1 = Cutout2D(data, (2, 2), (3, 3)) >>> print(cutout1.data) # doctest: +FLOAT_CMP [[ 5. 6. 7.] [ 9. 10. 11.] [13. 14. 15.]] >>> print(cutout1.center_original) (2.0, 2.0) >>> print(cutout1.center_cutout) (1.0, 1.0) >>> print(cutout1.origin_original) (1, 1) >>> cutout2 = Cutout2D(data, (2, 2), 3) >>> print(cutout2.data) # doctest: +FLOAT_CMP [[ 5. 6. 7.] [ 9. 10. 11.] [13. 14. 15.]] >>> size = u.Quantity([3, 3], u.pixel) >>> cutout3 = Cutout2D(data, (0, 0), size) >>> print(cutout3.data) # doctest: +FLOAT_CMP [[0. 1.] [4. 5.]] >>> cutout4 = Cutout2D(data, (0, 0), (3 * u.pixel, 3)) >>> print(cutout4.data) # doctest: +FLOAT_CMP [[0. 1.] [4. 5.]] >>> cutout5 = Cutout2D(data, (0, 0), (3, 3), mode='partial') >>> print(cutout5.data) # doctest: +FLOAT_CMP [[nan nan nan] [nan 0. 1.] [nan 4. 5.]] """ def __init__(self, data, position, size, wcs=None, mode='trim', fill_value=np.nan, copy=False): if wcs is None: wcs = getattr(data, 'wcs', None) if isinstance(position, SkyCoord): if wcs is None: raise ValueError('wcs must be input if position is a ' 'SkyCoord') position = skycoord_to_pixel(position, wcs, mode='all') # (x, y) if np.isscalar(size): size = np.repeat(size, 2) # special handling for a scalar Quantity if isinstance(size, u.Quantity): size = np.atleast_1d(size) if len(size) == 1: size = np.repeat(size, 2) if len(size) > 2: raise ValueError('size must have at most two elements') shape = np.zeros(2).astype(int) pixel_scales = None # ``size`` can have a mixture of int and Quantity (and even units), # so evaluate each axis separately for axis, side in enumerate(size): if not isinstance(side, u.Quantity): shape[axis] = int(np.round(size[axis])) # pixels else: if side.unit == u.pixel: shape[axis] = int(np.round(side.value)) elif side.unit.physical_type == 'angle': if wcs is None: raise ValueError('wcs must be input if any element ' 'of size has angular units') if pixel_scales is None: pixel_scales = u.Quantity( proj_plane_pixel_scales(wcs), wcs.wcs.cunit[axis]) shape[axis] = int(np.round( (side / pixel_scales[axis]).decompose())) else: raise ValueError('shape can contain Quantities with only ' 'pixel or angular units') data = np.asanyarray(data) # reverse position because extract_array and overlap_slices # use (y, x), but keep the input position pos_yx = position[::-1] cutout_data, input_position_cutout = extract_array( data, tuple(shape), pos_yx, mode=mode, fill_value=fill_value, return_position=True) if copy: cutout_data = np.copy(cutout_data) self.data = cutout_data self.input_position_cutout = input_position_cutout[::-1] # (x, y) slices_original, slices_cutout = overlap_slices( data.shape, shape, pos_yx, mode=mode) self.slices_original = slices_original self.slices_cutout = slices_cutout self.shape = self.data.shape self.input_position_original = position self.shape_input = shape ((self.ymin_original, self.ymax_original), (self.xmin_original, self.xmax_original)) = self.bbox_original ((self.ymin_cutout, self.ymax_cutout), (self.xmin_cutout, self.xmax_cutout)) = self.bbox_cutout # the true origin pixel of the cutout array, including any # filled cutout values self._origin_original_true = ( self.origin_original[0] - self.slices_cutout[1].start, self.origin_original[1] - self.slices_cutout[0].start) if wcs is not None: self.wcs = deepcopy(wcs) self.wcs.wcs.crpix -= self._origin_original_true self.wcs.array_shape = self.data.shape if wcs.sip is not None: self.wcs.sip = Sip(wcs.sip.a, wcs.sip.b, wcs.sip.ap, wcs.sip.bp, wcs.sip.crpix - self._origin_original_true) else: self.wcs = None def to_original_position(self, cutout_position): """ Convert an ``(x, y)`` position in the cutout array to the original ``(x, y)`` position in the original large array. Parameters ---------- cutout_position : tuple The ``(x, y)`` pixel position in the cutout array. Returns ------- original_position : tuple The corresponding ``(x, y)`` pixel position in the original large array. """ return tuple(cutout_position[i] + self.origin_original[i] for i in [0, 1]) def to_cutout_position(self, original_position): """ Convert an ``(x, y)`` position in the original large array to the ``(x, y)`` position in the cutout array. Parameters ---------- original_position : tuple The ``(x, y)`` pixel position in the original large array. Returns ------- cutout_position : tuple The corresponding ``(x, y)`` pixel position in the cutout array. """ return tuple(original_position[i] - self.origin_original[i] for i in [0, 1]) def plot_on_original(self, ax=None, fill=False, **kwargs): """ Plot the cutout region on a matplotlib Axes instance. Parameters ---------- ax : `matplotlib.axes.Axes` instance, optional If `None`, then the current `matplotlib.axes.Axes` instance is used. fill : bool, optional Set whether to fill the cutout patch. The default is `False`. kwargs : optional Any keyword arguments accepted by `matplotlib.patches.Patch`. Returns ------- ax : `matplotlib.axes.Axes` instance The matplotlib Axes instance constructed in the method if ``ax=None``. Otherwise the output ``ax`` is the same as the input ``ax``. """ import matplotlib.pyplot as plt import matplotlib.patches as mpatches kwargs['fill'] = fill if ax is None: ax = plt.gca() height, width = self.shape hw, hh = width / 2., height / 2. pos_xy = self.position_original - np.array([hw, hh]) patch = mpatches.Rectangle(pos_xy, width, height, 0., **kwargs) ax.add_patch(patch) return ax @staticmethod def _calc_center(slices): """ Calculate the center position. The center position will be fractional for even-sized arrays. For ``mode='partial'``, the central position is calculated for the valid (non-filled) cutout values. """ return tuple(0.5 * (slices[i].start + slices[i].stop - 1) for i in [1, 0]) @staticmethod def _calc_bbox(slices): """ Calculate a minimal bounding box in the form ``((ymin, ymax), (xmin, xmax))``. Note these are pixel locations, not slice indices. For ``mode='partial'``, the bounding box indices are for the valid (non-filled) cutout values. """ # (stop - 1) to return the max pixel location, not the slice index return ((slices[0].start, slices[0].stop - 1), (slices[1].start, slices[1].stop - 1)) @lazyproperty def origin_original(self): """ The ``(x, y)`` index of the origin pixel of the cutout with respect to the original array. For ``mode='partial'``, the origin pixel is calculated for the valid (non-filled) cutout values. """ return (self.slices_original[1].start, self.slices_original[0].start) @lazyproperty def origin_cutout(self): """ The ``(x, y)`` index of the origin pixel of the cutout with respect to the cutout array. For ``mode='partial'``, the origin pixel is calculated for the valid (non-filled) cutout values. """ return (self.slices_cutout[1].start, self.slices_cutout[0].start) @staticmethod def _round(a): """ Round the input to the nearest integer. If two integers are equally close, the value is rounded up. Note that this is different from `np.round`, which rounds to the nearest even number. """ return int(np.floor(a + 0.5)) @lazyproperty def position_original(self): """ The ``(x, y)`` position index (rounded to the nearest pixel) in the original array. """ return (self._round(self.input_position_original[0]), self._round(self.input_position_original[1])) @lazyproperty def position_cutout(self): """ The ``(x, y)`` position index (rounded to the nearest pixel) in the cutout array. """ return (self._round(self.input_position_cutout[0]), self._round(self.input_position_cutout[1])) @lazyproperty def center_original(self): """ The central ``(x, y)`` position of the cutout array with respect to the original array. For ``mode='partial'``, the central position is calculated for the valid (non-filled) cutout values. """ return self._calc_center(self.slices_original) @lazyproperty def center_cutout(self): """ The central ``(x, y)`` position of the cutout array with respect to the cutout array. For ``mode='partial'``, the central position is calculated for the valid (non-filled) cutout values. """ return self._calc_center(self.slices_cutout) @lazyproperty def bbox_original(self): """ The bounding box ``((ymin, ymax), (xmin, xmax))`` of the minimal rectangular region of the cutout array with respect to the original array. For ``mode='partial'``, the bounding box indices are for the valid (non-filled) cutout values. """ return self._calc_bbox(self.slices_original) @lazyproperty def bbox_cutout(self): """ The bounding box ``((ymin, ymax), (xmin, xmax))`` of the minimal rectangular region of the cutout array with respect to the cutout array. For ``mode='partial'``, the bounding box indices are for the valid (non-filled) cutout values. """ return self._calc_bbox(self.slices_cutout)