repo_description: matplotlib: plotting with Python
repo_topics: data-science data-visualization gtk matplotlib plotting python qt tk wx
code: """
  The image module supports basic image loading, rescaling and display
  operations.
  """
  
  import os
  import logging
  from pathlib import Path
  import warnings
  
  import numpy as np
  import PIL.Image
  import PIL.PngImagePlugin
  
  import matplotlib as mpl
  from matplotlib import _api, cbook
  # For clarity, names from _image are given explicitly in this module
  from matplotlib import _image
  # For user convenience, the names from _image are also imported into
  # the image namespace
  from matplotlib._image import *  # noqa: F401, F403
  import matplotlib.artist as martist
  import matplotlib.colorizer as mcolorizer
  from matplotlib.backend_bases import FigureCanvasBase
  import matplotlib.colors as mcolors
  from matplotlib.transforms import (
      Affine2D, BboxBase, Bbox, BboxTransform, BboxTransformTo,
      IdentityTransform, TransformedBbox)
  
  _log = logging.getLogger(__name__)
  
  # map interpolation strings to module constants
  _interpd_ = {
      'auto': _image.NEAREST,  # this will use nearest or Hanning...
      'none': _image.NEAREST,  # fall back to nearest when not supported
      'nearest': _image.NEAREST,
      'bilinear': _image.BILINEAR,
      'bicubic': _image.BICUBIC,
      'spline16': _image.SPLINE16,
      'spline36': _image.SPLINE36,
      'hanning': _image.HANNING,
      'hamming': _image.HAMMING,
      'hermite': _image.HERMITE,
      'kaiser': _image.KAISER,
      'quadric': _image.QUADRIC,
      'catrom': _image.CATROM,
      'gaussian': _image.GAUSSIAN,
      'bessel': _image.BESSEL,
      'mitchell': _image.MITCHELL,
      'sinc': _image.SINC,
      'lanczos': _image.LANCZOS,
      'blackman': _image.BLACKMAN,
      'antialiased': _image.NEAREST,  # this will use nearest or Hanning...
  }
  
  interpolations_names = set(_interpd_)
  
  
  def composite_images(images, renderer, magnification=1.0):
      """
      Composite a number of RGBA images into one.  The images are
      composited in the order in which they appear in the *images* list.
  
      Parameters
      ----------
      images : list of Images
          Each must have a `!make_image` method.  For each image,
          `!can_composite` should return `True`, though this is not
          enforced by this function.  Each image must have a purely
          affine transformation with no shear.
  
      renderer : `.RendererBase`
  
      magnification : float, default: 1
          The additional magnification to apply for the renderer in use.
  
      Returns
      -------
      image : (M, N, 4) `numpy.uint8` array
          The composited RGBA image.
      offset_x, offset_y : float
          The (left, bottom) offset where the composited image should be placed
          in the output figure.
      """
      if len(images) == 0:
          return np.empty((0, 0, 4), dtype=np.uint8), 0, 0
  
      parts = []
      bboxes = []
      for image in images:
          data, x, y, trans = image.make_image(renderer, magnification)
          if data is not None:
              x *= magnification
              y *= magnification
              parts.append((data, x, y, image._get_scalar_alpha()))
              bboxes.append(
                  Bbox([[x, y], [x + data.shape[1], y + data.shape[0]]]))
  
      if len(parts) == 0:
          return np.empty((0, 0, 4), dtype=np.uint8), 0, 0
  
      bbox = Bbox.union(bboxes)
  
      output = np.zeros(
          (int(bbox.height), int(bbox.width), 4), dtype=np.uint8)
  
      for data, x, y, alpha in parts:
          trans = Affine2D().translate(x - bbox.x0, y - bbox.y0)
          _image.resample(data, output, trans, _image.NEAREST,
                          resample=False, alpha=alpha)
  
      return output, bbox.x0 / magnification, bbox.y0 / magnification
  
  
  def _draw_list_compositing_images(
          renderer, parent, artists, suppress_composite=None):
      """
      Draw a sorted list of artists, compositing images into a single
      image where possible.
  
      For internal Matplotlib use only: It is here to reduce duplication
      between `Figure.draw` and `Axes.draw`, but otherwise should not be
      generally useful.
      """
      has_images = any(isinstance(x, _ImageBase) for x in artists)
  
      # override the renderer default if suppressComposite is not None
      not_composite = (suppress_composite if suppress_composite is not None
                       else renderer.option_image_nocomposite())
  
      if not_composite or not has_images:
          for a in artists:
              a.draw(renderer)
      else:
          # Composite any adjacent images together
          image_group = []
          mag = renderer.get_image_magnification()
  
          def flush_images():
              if len(image_group) == 1:
                  image_group[0].draw(renderer)
              elif len(image_group) > 1:
                  data, l, b = composite_images(image_group, renderer, mag)
                  if data.size != 0:
                      gc = renderer.new_gc()
                      gc.set_clip_rectangle(parent.bbox)
                      gc.set_clip_path(parent.get_clip_path())
                      renderer.draw_image(gc, round(l), round(b), data)
                      gc.restore()
              del image_group[:]
  
          for a in artists:
              if (isinstance(a, _ImageBase) and a.can_composite() and
                      a.get_clip_on() and not a.get_clip_path()):
                  image_group.append(a)
              else:
                  flush_images()
                  a.draw(renderer)
          flush_images()
  
  
  def _resample(
          image_obj, data, out_shape, transform, *, resample=None, alpha=1):
      """
      Convenience wrapper around `._image.resample` to resample *data* to
      *out_shape* (with a third dimension if *data* is RGBA) that takes care of
      allocating the output array and fetching the relevant properties from the
      Image object *image_obj*.
      """
      # AGG can only handle coordinates smaller than 24-bit signed integers,
      # so raise errors if the input data is larger than _image.resample can
      # handle.
      msg = ('Data with more than {n} cannot be accurately displayed. '
             'Downsampling to less than {n} before displaying. '
             'To remove this warning, manually downsample your data.')
      if data.shape[1] > 2**23:
          warnings.warn(msg.format(n='2**23 columns'))
          step = int(np.ceil(data.shape[1] / 2**23))
          data = data[:, ::step]
          transform = Affine2D().scale(step, 1) + transform
      if data.shape[0] > 2**24:
          warnings.warn(msg.format(n='2**24 rows'))
          step = int(np.ceil(data.shape[0] / 2**24))
          data = data[::step, :]
          transform = Affine2D().scale(1, step) + transform
      # decide if we need to apply anti-aliasing if the data is upsampled:
      # compare the number of displayed pixels to the number of
      # the data pixels.
      interpolation = image_obj.get_interpolation()
      if interpolation in ['antialiased', 'auto']:
          # don't antialias if upsampling by an integer number or
          # if zooming in more than a factor of 3
          pos = np.array([[0, 0], [data.shape[1], data.shape[0]]])
          disp = transform.transform(pos)
          dispx = np.abs(np.diff(disp[:, 0]))
          dispy = np.abs(np.diff(disp[:, 1]))
          if ((dispx > 3 * data.shape[1] or
                  dispx == data.shape[1] or
                  dispx == 2 * data.shape[1]) and
              (dispy > 3 * data.shape[0] or
                  dispy == data.shape[0] or
                  dispy == 2 * data.shape[0])):
              interpolation = 'nearest'
          else:
              interpolation = 'hanning'
      out = np.zeros(out_shape + data.shape[2:], data.dtype)  # 2D->2D, 3D->3D.
      if resample is None:
          resample = image_obj.get_resample()
  
      # When an output pixel falls exactly on the edge between two input pixels, the Agg
      # resampler will use the right input pixel as the nearest neighbor.  We want the
      # left input pixel to be chosen instead, so we flip the input data and the supplied
      # transform.  If origin != 'upper', the transform will already include a flip in the
      # vertical direction.
      if interpolation == 'nearest':
          transform = Affine2D().translate(-data.shape[1], 0).scale(-1, 1) + transform
          data = np.flip(data, axis=1)
          if image_obj.origin == 'upper':
              transform = Affine2D().translate(0, -data.shape[0]).scale(1, -1) + transform
              data = np.flip(data, axis=0)
  
      _image.resample(data, out, transform,
                      _interpd_[interpolation],
                      resample,
                      alpha,
                      image_obj.get_filternorm(),
                      image_obj.get_filterrad())
  
      return out
  
  
  def _rgb_to_rgba(A):
      """
      Convert an RGB image to RGBA, as required by the image resample C++
      extension.
      """
      rgba = np.zeros((A.shape[0], A.shape[1], 4), dtype=A.dtype)
      rgba[:, :, :3] = A
      if rgba.dtype == np.uint8:
          rgba[:, :, 3] = 255
      else:
          rgba[:, :, 3] = 1.0
      return rgba
  
  
  class _ImageBase(mcolorizer.ColorizingArtist):
      """
      Base class for images.
  
      *interpolation* and *cmap* default to their rc settings.
  
      *cmap* is a `.colors.Colormap` instance.
      *norm* is a `.colors.Normalize` instance to map luminance to 0-1.
  
      *extent* is a ``(left, right, bottom, top)`` tuple in data coordinates, for
      making image plots registered with data plots; the default is to label the
      pixel centers with the zero-based row and column indices.
  
      Additional kwargs are `.Artist` properties.
      """
  
      zorder = 0
  
      def __init__(self, ax,
                   cmap=None,
                   norm=None,
                   colorizer=None,
                   interpolation=None,
                   origin=None,
                   filternorm=True,
                   filterrad=4.0,
                   resample=False,
                   *,
                   interpolation_stage=None,
                   **kwargs
                   ):
          super().__init__(self._get_colorizer(cmap, norm, colorizer))
          origin = mpl._val_or_rc(origin, 'image.origin')
          _api.check_in_list(["upper", "lower"], origin=origin)
          self.origin = origin
          self.set_filternorm(filternorm)
          self.set_filterrad(filterrad)
          self.set_interpolation(interpolation)
          self.set_interpolation_stage(interpolation_stage)
          self.set_resample(resample)
          self.axes = ax
  
          self._imcache = None
  
          self._internal_update(kwargs)
  
      def __str__(self):
          try:
              shape = self.get_shape()
              return f"{type(self).__name__}(shape={shape!r})"
          except RuntimeError:
              return type(self).__name__
  
      def __getstate__(self):
          # Save some space on the pickle by not saving the cache.
          return {**super().__getstate__(), "_imcache": None}
  
      def get_size(self):
          """Return the size of the image as tuple (numrows, numcols)."""
          return self.get_shape()[:2]
  
      def get_shape(self):
          """
          Return the shape of the image as tuple (numrows, numcols, channels).
          """
          if self._A is None:
              raise RuntimeError('You must first set the image array')
  
          return self._A.shape
  
      def set_alpha(self, alpha):
          """
          Set the alpha value used for blending - not supported on all backends.
  
          Parameters
          ----------
          alpha : float or 2D array-like or None
          """
          martist.Artist._set_alpha_for_array(self, alpha)
          if np.ndim(alpha) not in (0, 2):
              raise TypeError('alpha must be a float, two-dimensional '
                              'array, or None')
          self._imcache = None
  
      def _get_scalar_alpha(self):
          """
          Get a scalar alpha value to be applied to the artist as a whole.
  
          If the alpha value is a matrix, the method returns 1.0 because pixels
          have individual alpha values (see `~._ImageBase._make_image` for
          details). If the alpha value is a scalar, the method returns said value
          to be applied to the artist as a whole because pixels do not have
          individual alpha values.
          """
          return 1.0 if self._alpha is None or np.ndim(self._alpha) > 0 \
              else self._alpha
  
      def changed(self):
          """
          Call this whenever the mappable is changed so observers can update.
          """
          self._imcache = None
          super().changed()
  
      def _make_image(self, A, in_bbox, out_bbox, clip_bbox, magnification=1.0,
                      unsampled=False, round_to_pixel_border=True):
          """
          Normalize, rescale, and colormap the image *A* from the given *in_bbox*
          (in data space), to the given *out_bbox* (in pixel space) clipped to
          the given *clip_bbox* (also in pixel space), and magnified by the
          *magnification* factor.
  
          Parameters
          ----------
          A : ndarray
  
              - a (M, N) array interpreted as scalar (greyscale) image,
                with one of the dtypes `~numpy.float32`, `~numpy.float64`,
                `~numpy.float128`, `~numpy.uint16` or `~numpy.uint8`.
              - (M, N, 4) RGBA image with a dtype of `~numpy.float32`,
                `~numpy.float64`, `~numpy.float128`, or `~numpy.uint8`.
  
          in_bbox : `~matplotlib.transforms.Bbox`
  
          out_bbox : `~matplotlib.transforms.Bbox`
  
          clip_bbox : `~matplotlib.transforms.Bbox`
  
          magnification : float, default: 1
  
          unsampled : bool, default: False
              If True, the image will not be scaled, but an appropriate
              affine transformation will be returned instead.
  
          round_to_pixel_border : bool, default: True
              If True, the output image size will be rounded to the nearest pixel
              boundary.  This makes the images align correctly with the Axes.
              It should not be used if exact scaling is needed, such as for
              `.FigureImage`.
  
          Returns
          -------
          image : (M, N, 4) `numpy.uint8` array
              The RGBA image, resampled unless *unsampled* is True.
          x, y : float
              The upper left corner where the image should be drawn, in pixel
              space.
          trans : `~matplotlib.transforms.Affine2D`
              The affine transformation from image to pixel space.
          """
          if A is None:
              raise RuntimeError('You must first set the image '
                                 'array or the image attribute')
          if A.size == 0:
              raise RuntimeError("_make_image must get a non-empty image. "
                                 "Your Artist's draw method must filter before "
                                 "this method is called.")
  
          clipped_bbox = Bbox.intersection(out_bbox, clip_bbox)
  
          if clipped_bbox is None:
              return None, 0, 0, None
  
          # Define the magnified bbox after clipping
          magnified_extents = clipped_bbox.extents * magnification
          if ((not unsampled) and round_to_pixel_border):
              # Round to the nearest output pixel
              # Add a tiny fudge amount to account for numerical precision loss
              # on the two sides away from the Agg anchor point (x0, y1)
              x0 = np.floor(magnified_extents[0] + 0.5)  # round half up
              y0 = np.ceil(magnified_extents[1] - 0.5 - 1e-8)  # round half down
              x1 = np.floor(magnified_extents[2] + 0.5 + 1e-8)  # round half up
              y1 = np.ceil(magnified_extents[3] - 0.5)  # round half down
              magnified_bbox = Bbox.from_extents([x0, y0, x1, y1])
          else:
              magnified_bbox = Bbox.from_extents(magnified_extents)
  
          if magnified_bbox.width == 0 or magnified_bbox.height == 0:
              return None, 0, 0, None
  
          if self.origin == 'upper':
              # Flip the input image using a transform.  This avoids the
              # problem with flipping the array, which results in a copy
              # when it is converted to contiguous in the C wrapper
              t0 = Affine2D().translate(0, -A.shape[0]).scale(1, -1)
          else:
              t0 = IdentityTransform()
  
          t0 += (
              Affine2D()
              .scale(
                  in_bbox.width / A.shape[1],
                  in_bbox.height / A.shape[0])
              .translate(in_bbox.x0, in_bbox.y0)
              + self.get_transform())
  
          t = (t0
               + (Affine2D()
                  .scale(magnification)
                  .translate(-magnified_bbox.x0, -magnified_bbox.y0)))
  
          out_shape = (int(magnified_bbox.height), int(magnified_bbox.width))
  
          if not unsampled:
              if not (A.ndim == 2 or A.ndim == 3 and A.shape[-1] in (3, 4)):
                  raise ValueError(f"Invalid shape {A.shape} for image data")
  
              float_rgba_in = A.ndim == 3 and A.shape[-1] == 4 and A.dtype.kind == 'f'
  
              # if antialiased, this needs to change as window sizes
              # change:
              interpolation_stage = self._interpolation_stage
              if interpolation_stage in ['antialiased', 'auto']:
                  pos = np.array([[0, 0], [A.shape[1], A.shape[0]]])
                  disp = t.transform(pos)
                  dispx = np.abs(np.diff(disp[:, 0])) / A.shape[1]
                  dispy = np.abs(np.diff(disp[:, 1])) / A.shape[0]
                  if (dispx < 3) or (dispy < 3):
                      interpolation_stage = 'rgba'
                  else:
                      interpolation_stage = 'data'
  
              if A.ndim == 2 and interpolation_stage == 'data':
                  # if we are a 2D array, then we are running through the
                  # norm + colormap transformation.  However, in general the
                  # input data is not going to match the size on the screen so we
                  # have to resample to the correct number of pixels
  
                  if A.dtype.kind == 'f':  # Float dtype: scale to same dtype.
                      scaled_dtype = np.dtype("f8" if A.dtype.itemsize > 4 else "f4")
                      if scaled_dtype.itemsize < A.dtype.itemsize:
                          _api.warn_external(f"Casting input data from {A.dtype}"
                                             f" to {scaled_dtype} for imshow.")
                  else:  # Int dtype, likely.
                      # TODO slice input array first
                      # Scale to appropriately sized float: use float32 if the
                      # dynamic range is small, to limit the memory footprint.
                      da = A.max().astype("f8") - A.min().astype("f8")
                      scaled_dtype = "f8" if da > 1e8 else "f4"
  
                  # resample the input data to the correct resolution and shape
                  A_resampled = _resample(self, A.astype(scaled_dtype), out_shape, t)
  
                  # if using NoNorm, cast back to the original datatype
                  if isinstance(self.norm, mcolors.NoNorm):
                      A_resampled = A_resampled.astype(A.dtype)
  
                  # Compute out_mask (what screen pixels include "bad" data
                  # pixels) and out_alpha (to what extent screen pixels are
                  # covered by data pixels: 0 outside the data extent, 1 inside
                  # (even for bad data), and intermediate values at the edges).
                  mask = (np.where(A.mask, np.float32(np.nan), np.float32(1))
                          if A.mask.shape == A.shape  # nontrivial mask
                          else np.ones_like(A, np.float32))
                  # we always have to interpolate the mask to account for
                  # non-affine transformations
                  out_alpha = _resample(self, mask, out_shape, t, resample=True)
                  del mask  # Make sure we don't use mask anymore!
                  out_mask = np.isnan(out_alpha)
                  out_alpha[out_mask] = 1
                  # Apply the pixel-by-pixel alpha values if present
                  alpha = self.get_alpha()
                  if alpha is not None and np.ndim(alpha) > 0:
                      out_alpha *= _resample(self, alpha, out_shape, t, resample=True)
                  # mask and run through the norm
                  resampled_masked = np.ma.masked_array(A_resampled, out_mask)
                  res = self.norm(resampled_masked)
              else:
                  if A.ndim == 2:  # interpolation_stage = 'rgba'
                      self.norm.autoscale_None(A)
                      A = self.to_rgba(A)
                  if A.dtype == np.uint8:
                      # uint8 is too imprecise for premultiplied alpha roundtrips.
                      A = np.divide(A, 0xff, dtype=np.float32)
                  alpha = self.get_alpha()
                  post_apply_alpha = False
                  if alpha is None:  # alpha parameter not specified
                      if A.shape[2] == 3:  # image has no alpha channel
                          A = np.dstack([A, np.ones(A.shape[:2])])
                  elif np.ndim(alpha) > 0:  # Array alpha
                      if A.shape[2] == 3:  # RGB: use array alpha directly
                          A = np.dstack([A, alpha])
                      else:  # RGBA: multiply existing alpha by array alpha
                          A = np.dstack([A[..., :3], A[..., 3] * alpha])
                  else:  # Scalar alpha
                      if A.shape[2] == 3:  # broadcast scalar alpha
                          A = np.dstack([A, np.full(A.shape[:2], alpha, np.float32)])
                      else:  # or apply scalar alpha to existing alpha channel
                          post_apply_alpha = True
                  # Resample in premultiplied alpha space.  (TODO: Consider
                  # implementing premultiplied-space resampling in
                  # span_image_resample_rgba_affine::generate?)
                  if float_rgba_in and np.ndim(alpha) == 0 and np.any(A[..., 3] < 1):
                      # Do not modify original RGBA input
                      A = A.copy()
                  A[..., :3] *= A[..., 3:]
                  res = _resample(self, A, out_shape, t)
                  np.divide(res[..., :3], res[..., 3:], out=res[..., :3],
                              where=res[..., 3:] != 0)
                  if post_apply_alpha:
                      res[..., 3] *= alpha
  
              # res is now either a 2D array of normed (int or float) data
              # or an RGBA array of re-sampled input
              output = self.to_rgba(res, bytes=True, norm=False)
              # output is now a correctly sized RGBA array of uint8
  
              # Apply alpha *after* if the input was greyscale without a mask
              if A.ndim == 2:
                  alpha = self._get_scalar_alpha()
                  alpha_channel = output[:, :, 3]
                  alpha_channel[:] = (  # Assignment will cast to uint8.
                      alpha_channel.astype(np.float32) * out_alpha * alpha)
  
          else:
              if self._imcache is None:
                  self._imcache = self.to_rgba(A, bytes=True, norm=(A.ndim == 2))
              output = self._imcache
  
              # Subset the input image to only the part that will be displayed.
              subset = TransformedBbox(clip_bbox, t0.inverted()).frozen()
              output = output[
                  int(max(subset.ymin, 0)):
                  int(min(subset.ymax + 1, output.shape[0])),
                  int(max(subset.xmin, 0)):
                  int(min(subset.xmax + 1, output.shape[1]))]
  
              t = Affine2D().translate(
                  int(max(subset.xmin, 0)), int(max(subset.ymin, 0))) + t
  
          return (output,
                  magnified_bbox.x0 / magnification,
                  magnified_bbox.y0 / magnification,
                  t)
  
      def make_image(self, renderer, magnification=1.0, unsampled=False):
          """
          Normalize, rescale, and colormap this image's data for rendering using
          *renderer*, with the given *magnification*.
  
          If *unsampled* is True, the image will not be scaled, but an
          appropriate affine transformation will be returned instead.
  
          Returns
          -------
          image : (M, N, 4) `numpy.uint8` array
              The RGBA image, resampled unless *unsampled* is True.
          x, y : float
              The upper left corner where the image should be drawn, in pixel
              space.
          trans : `~matplotlib.transforms.Affine2D`
              The affine transformation from image to pixel space.
          """
          raise NotImplementedError('The make_image method must be overridden')
  
      def _check_unsampled_image(self):
          """
          Return whether the image is better to be drawn unsampled.
  
          The derived class needs to override it.
          """
          return False
  
      @martist.allow_rasterization
      def draw(self, renderer):
          # if not visible, declare victory and return
          if not self.get_visible():
              self.stale = False
              return
          # for empty images, there is nothing to draw!
          if self.get_array().size == 0:
              self.stale = False
              return
          # actually render the image.
          gc = renderer.new_gc()
          self._set_gc_clip(gc)
          gc.set_alpha(self._get_scalar_alpha())
          gc.set_url(self.get_url())
          gc.set_gid(self.get_gid())
          if (renderer.option_scale_image()  # Renderer supports transform kwarg.
                  and self._check_unsampled_image()
                  and self.get_transform().is_affine):
              im, l, b, trans = self.make_image(renderer, unsampled=True)
              if im is not None:
                  trans = Affine2D().scale(im.shape[1], im.shape[0]) + trans
                  renderer.draw_image(gc, l, b, im, trans)
          else:
              im, l, b, trans = self.make_image(
                  renderer, renderer.get_image_magnification())
              if im is not None:
                  renderer.draw_image(gc, l, b, im)
          gc.restore()
          self.stale = False
  
      def contains(self, mouseevent):
          """Test whether the mouse event occurred within the image."""
          if (self._different_canvas(mouseevent)
                  # This doesn't work for figimage.
                  or not self.axes.contains(mouseevent)[0]):
              return False, {}
          # TODO: make sure this is consistent with patch and patch
          # collection on nonlinear transformed coordinates.
          # TODO: consider returning image coordinates (shouldn't
          # be too difficult given that the image is rectilinear
          trans = self.get_transform().inverted()
          x, y = trans.transform([mouseevent.x, mouseevent.y])
          xmin, xmax, ymin, ymax = self.get_extent()
          # This checks xmin <= x <= xmax *or* xmax <= x <= xmin.
          inside = (x is not None and (x - xmin) * (x - xmax) <= 0
                    and y is not None and (y - ymin) * (y - ymax) <= 0)
          return inside, {}
  
      def write_png(self, fname):
          """Write the image to png file *fname*."""
          im = self.to_rgba(self._A[::-1] if self.origin == 'lower' else self._A,
                            bytes=True, norm=True)
          PIL.Image.fromarray(im).save(fname, format="png")
  
      @staticmethod
      def _normalize_image_array(A):
          """
          Check validity of image-like input *A* and normalize it to a format suitable for
          Image subclasses.
          """
          A = cbook.safe_masked_invalid(A, copy=True)
          if A.dtype != np.uint8 and not np.can_cast(A.dtype, float, "same_kind"):
              raise TypeError(f"Image data of dtype {A.dtype} cannot be "
                              f"converted to float")
          if A.ndim == 3 and A.shape[-1] == 1:
              A = A.squeeze(-1)  # If just (M, N, 1), assume scalar and apply colormap.
          if not (A.ndim == 2 or A.ndim == 3 and A.shape[-1] in [3, 4]):
              raise TypeError(f"Invalid shape {A.shape} for image data")
          if A.ndim == 3:
              # If the input data has values outside the valid range (after
              # normalisation), we issue a warning and then clip X to the bounds
              # - otherwise casting wraps extreme values, hiding outliers and
              # making reliable interpretation impossible.
              high = 255 if np.issubdtype(A.dtype, np.integer) else 1
              if A.min() < 0 or high < A.max():
                  _log.warning(
                      'Clipping input data to the valid range for imshow with '
                      'RGB data ([0..1] for floats or [0..255] for integers). '
                      'Got range [%s..%s].',
                      A.min(), A.max()
                  )
                  A = np.clip(A, 0, high)
              # Cast unsupported integer types to uint8
              if A.dtype != np.uint8 and np.issubdtype(A.dtype, np.integer):
                  A = A.astype(np.uint8)
          return A
  
      def set_data(self, A):
          """
          Set the image array.
  
          Note that this function does *not* update the normalization used.
  
          Parameters
          ----------
          A : array-like or `PIL.Image.Image`
          """
          if isinstance(A, PIL.Image.Image):
              A = pil_to_array(A)  # Needed e.g. to apply png palette.
          self._A = self._normalize_image_array(A)
          self._imcache = None
          self.stale = True
  
      def set_array(self, A):
          """
          Retained for backwards compatibility - use set_data instead.
  
          Parameters
          ----------
          A : array-like
          """
          # This also needs to be here to override the inherited
          # cm.ScalarMappable.set_array method so it is not invoked by mistake.
          self.set_data(A)
  
      def get_interpolation(self):
          """
          Return the interpolation method the image uses when resizing.
  
          One of 'auto', 'antialiased', 'nearest', 'bilinear', 'bicubic',
          'spline16', 'spline36', 'hanning', 'hamming', 'hermite', 'kaiser',
          'quadric', 'catrom', 'gaussian', 'bessel', 'mitchell', 'sinc', 'lanczos',
          or 'none'.
          """
          return self._interpolation
  
      def set_interpolation(self, s):
          """
          Set the interpolation method the image uses when resizing.
  
          If None, use :rc:`image.interpolation`. If 'none', the image is
          shown as is without interpolating. 'none' is only supported in
          agg, ps and pdf backends and will fall back to 'nearest' mode
          for other backends.
  
          Parameters
          ----------
          s : {'auto', 'nearest', 'bilinear', 'bicubic', 'spline16', \
  'spline36', 'hanning', 'hamming', 'hermite', 'kaiser', 'quadric', 'catrom', \
  'gaussian', 'bessel', 'mitchell', 'sinc', 'lanczos', 'none'} or None
          """
          s = mpl._val_or_rc(s, 'image.interpolation').lower()
          _api.check_in_list(interpolations_names, interpolation=s)
          self._interpolation = s
          self.stale = True
  
      def get_interpolation_stage(self):
          """
          Return when interpolation happens during the transform to RGBA.
  
          One of 'data', 'rgba', 'auto'.
          """
          return self._interpolation_stage
  
      def set_interpolation_stage(self, s):
          """
          Set when interpolation happens during the transform to RGBA.
  
          Parameters
          ----------
          s : {'data', 'rgba', 'auto'}, default: :rc:`image.interpolation_stage`
              Whether to apply resampling interpolation in data or RGBA space.
              If 'auto', 'rgba' is used if the upsampling rate is less than 3,
              otherwise 'data' is used.
          """
          s = mpl._val_or_rc(s, 'image.interpolation_stage')
          _api.check_in_list(['data', 'rgba', 'auto'], s=s)
          self._interpolation_stage = s
          self.stale = True
  
      def can_composite(self):
          """Return whether the image can be composited with its neighbors."""
          trans = self.get_transform()
          return (
              self._interpolation != 'none' and
              trans.is_affine and
              trans.is_separable)
  
      def set_resample(self, v):
          """
          Set whether image resampling is used.
  
          Parameters
          ----------
          v : bool, default: :rc:`image.resample`
          """
          v = mpl._val_or_rc(v, 'image.resample')
          self._resample = v
          self.stale = True
  
      def get_resample(self):
          """Return whether image resampling is used."""
          return self._resample
  
      def set_filternorm(self, filternorm):
          """
          Set whether the resize filter normalizes the weights.
  
          See help for `~.Axes.imshow`.
  
          Parameters
          ----------
          filternorm : bool
          """
          self._filternorm = bool(filternorm)
          self.stale = True
  
      def get_filternorm(self):
          """Return whether the resize filter normalizes the weights."""
          return self._filternorm
  
      def set_filterrad(self, filterrad):
          """
          Set the resize filter radius (only applicable to some
          interpolation schemes).
  
          See help for `~.Axes.imshow`.
  
          Parameters
          ----------
          filterrad : positive float
          """
          r = float(filterrad)
          if r <= 0:
              raise ValueError("The filter radius must be a positive number")
          self._filterrad = r
          self.stale = True
  
      def get_filterrad(self):
          """Return the filterrad setting."""
          return self._filterrad
  
  
  class AxesImage(_ImageBase):
      """
      An image with pixels on a regular grid, attached to an Axes.
  
      Parameters
      ----------
      ax : `~matplotlib.axes.Axes`
          The Axes the image will belong to.
      cmap : str or `~matplotlib.colors.Colormap`, default: :rc:`image.cmap`
          The Colormap instance or registered colormap name used to map scalar
          data to colors.
      norm : str or `~matplotlib.colors.Normalize`
          Maps luminance to 0-1.
      interpolation : str, default: :rc:`image.interpolation`
          Supported values are 'none', 'auto', 'nearest', 'bilinear',
          'bicubic', 'spline16', 'spline36', 'hanning', 'hamming', 'hermite',
          'kaiser', 'quadric', 'catrom', 'gaussian', 'bessel', 'mitchell',
          'sinc', 'lanczos', 'blackman'.
      interpolation_stage : {'data', 'rgba'}, default: 'data'
          If 'data', interpolation
          is carried out on the data provided by the user.  If 'rgba', the
          interpolation is carried out after the colormapping has been
          applied (visual interpolation).
      origin : {'upper', 'lower'}, default: :rc:`image.origin`
          Place the [0, 0] index of the array in the upper left or lower left
          corner of the Axes. The convention 'upper' is typically used for
          matrices and images.
      extent : tuple, optional
          The data axes (left, right, bottom, top) for making image plots
          registered with data plots.  Default is to label the pixel
          centers with the zero-based row and column indices.
      filternorm : bool, default: True
          A parameter for the antigrain image resize filter
          (see the antigrain documentation).
          If filternorm is set, the filter normalizes integer values and corrects
          the rounding errors. It doesn't do anything with the source floating
          point values, it corrects only integers according to the rule of 1.0
          which means that any sum of pixel weights must be equal to 1.0. So,
          the filter function must produce a graph of the proper shape.
      filterrad : float > 0, default: 4
          The filter radius for filters that have a radius parameter, i.e. when
          interpolation is one of: 'sinc', 'lanczos' or 'blackman'.
      resample : bool, default: False
          When True, use a full resampling method. When False, only resample when
          the output image is larger than the input image.
      **kwargs : `~matplotlib.artist.Artist` properties
      """
  
      def __init__(self, ax,
                   *,
                   cmap=None,
                   norm=None,
                   colorizer=None,
                   interpolation=None,
                   origin=None,
                   extent=None,
                   filternorm=True,
                   filterrad=4.0,
                   resample=False,
                   interpolation_stage=None,
                   **kwargs
                   ):
  
          self._extent = extent
  
          super().__init__(
              ax,
              cmap=cmap,
              norm=norm,
              colorizer=colorizer,
              interpolation=interpolation,
              origin=origin,
              filternorm=filternorm,
              filterrad=filterrad,
              resample=resample,
              interpolation_stage=interpolation_stage,
              **kwargs
          )
  
      def get_window_extent(self, renderer=None):
          x0, x1, y0, y1 = self._extent
          bbox = Bbox.from_extents([x0, y0, x1, y1])
          return bbox.transformed(self.get_transform())
  
      def make_image(self, renderer, magnification=1.0, unsampled=False):
          # docstring inherited
          trans = self.get_transform()
          # image is created in the canvas coordinate.
          x1, x2, y1, y2 = self.get_extent()
          bbox = Bbox(np.array([[x1, y1], [x2, y2]]))
          transformed_bbox = TransformedBbox(bbox, trans)
          clip = ((self.get_clip_box() or self.axes.bbox) if self.get_clip_on()
                  else self.get_figure(root=True).bbox)
          return self._make_image(self._A, bbox, transformed_bbox, clip,
                                  magnification, unsampled=unsampled)
  
      def _check_unsampled_image(self):
          """Return whether the image would be better drawn unsampled."""
          return self.get_interpolation() == "none"
  
      def set_extent(self, extent, **kwargs):
          """
          Set the image extent.
  
          Parameters
          ----------
          extent : 4-tuple of float
              The position and size of the image as tuple
              ``(left, right, bottom, top)`` in data coordinates.
          **kwargs
              Other parameters from which unit info (i.e., the *xunits*,
              *yunits*, *zunits* (for 3D Axes), *runits* and *thetaunits* (for
              polar Axes) entries are applied, if present.
  
          Notes
          -----
          This updates `.Axes.dataLim`, and, if autoscaling, sets `.Axes.viewLim`
          to tightly fit the image, regardless of `~.Axes.dataLim`.  Autoscaling
          state is not changed, so a subsequent call to `.Axes.autoscale_view`
          will redo the autoscaling in accord with `~.Axes.dataLim`.
          """
          (xmin, xmax), (ymin, ymax) = self.axes._process_unit_info(
              [("x", [extent[0], extent[1]]),
               ("y", [extent[2], extent[3]])],
              kwargs)
          if kwargs:
              raise _api.kwarg_error("set_extent", kwargs)
          xmin = self.axes._validate_converted_limits(
              xmin, self.convert_xunits)
          xmax = self.axes._validate_converted_limits(
              xmax, self.convert_xunits)
          ymin = self.axes._validate_converted_limits(
              ymin, self.convert_yunits)
          ymax = self.axes._validate_converted_limits(
              ymax, self.convert_yunits)
          extent = [xmin, xmax, ymin, ymax]
  
          self._extent = extent
          corners = (xmin, ymin), (xmax, ymax)
          self.axes.update_datalim(corners)
          self.sticky_edges.x[:] = [xmin, xmax]
          self.sticky_edges.y[:] = [ymin, ymax]
          if self.axes.get_autoscalex_on():
              self.axes.set_xlim(xmin, xmax, auto=None)
          if self.axes.get_autoscaley_on():
              self.axes.set_ylim(ymin, ymax, auto=None)
          self.stale = True
  
      def get_extent(self):
          """Return the image extent as tuple (left, right, bottom, top)."""
          if self._extent is not None:
              return self._extent
          else:
              sz = self.get_size()
              numrows, numcols = sz
              if self.origin == 'upper':
                  return (-0.5, numcols-0.5, numrows-0.5, -0.5)
              else:
                  return (-0.5, numcols-0.5, -0.5, numrows-0.5)
  
      def get_cursor_data(self, event):
          """
          Return the image value at the event position or *None* if the event is
          outside the image.
  
          See Also
          --------
          matplotlib.artist.Artist.get_cursor_data
          """
          xmin, xmax, ymin, ymax = self.get_extent()
          if self.origin == 'upper':
              ymin, ymax = ymax, ymin
          arr = self.get_array()
          data_extent = Bbox([[xmin, ymin], [xmax, ymax]])
          array_extent = Bbox([[0, 0], [arr.shape[1], arr.shape[0]]])
          trans = self.get_transform().inverted()
          trans += BboxTransform(boxin=data_extent, boxout=array_extent)
          point = trans.transform([event.x, event.y])
          if any(np.isnan(point)):
              return None
          j, i = point.astype(int)
          # Clip the coordinates at array bounds
          if not (0 <= i < arr.shape[0]) or not (0 <= j < arr.shape[1]):
              return None
          else:
              return arr[i, j]
  
  
  class NonUniformImage(AxesImage):
      """
      An image with pixels on a rectilinear grid.
  
      In contrast to `.AxesImage`, where pixels are on a regular grid,
      NonUniformImage allows rows and columns with individual heights / widths.
  
      See also :doc:`/gallery/images_contours_and_fields/image_nonuniform`.
      """
  
      def __init__(self, ax, *, interpolation='nearest', **kwargs):
          """
          Parameters
          ----------
          ax : `~matplotlib.axes.Axes`
              The Axes the image will belong to.
          interpolation : {'nearest', 'bilinear'}, default: 'nearest'
              The interpolation scheme used in the resampling.
          **kwargs
              All other keyword arguments are identical to those of `.AxesImage`.
          """
          super().__init__(ax, **kwargs)
          self.set_interpolation(interpolation)
  
      def _check_unsampled_image(self):
          """Return False. Do not use unsampled image."""
          return False
  
      def make_image(self, renderer, magnification=1.0, unsampled=False):
          # docstring inherited
          if self._A is None:
              raise RuntimeError('You must first set the image array')
          if unsampled:
              raise ValueError('unsampled not supported on NonUniformImage')
          A = self._A
          if A.ndim == 2:
              if A.dtype != np.uint8:
                  A = self.to_rgba(A, bytes=True)
              else:
                  A = np.repeat(A[:, :, np.newaxis], 4, 2)
                  A[:, :, 3] = 255
          else:
              if A.dtype != np.uint8:
                  A = (255*A).astype(np.uint8)
              if A.shape[2] == 3:
                  B = np.zeros(tuple([*A.shape[0:2], 4]), np.uint8)
                  B[:, :, 0:3] = A
                  B[:, :, 3] = 255
                  A = B
          magnified_extents = (self.axes.bbox.extents * magnification + 0.5).astype(int)
          l, b, r, t = magnified_extents / magnification
          width = int((r - l) * magnification)
          height = int((t - b) * magnification)
  
          invertedTransform = self.axes.transData.inverted()
          x_pix_edges = invertedTransform.transform(
              [(x, b) for x in np.linspace(l, r, width + 1)])[:, 0]
          y_pix_edges = invertedTransform.transform(
              [(l, y) for y in np.linspace(b, t, height + 1)])[:, 1]
          x_pix_centers = (x_pix_edges[:-1] + x_pix_edges[1:]) / 2
          y_pix_centers = (y_pix_edges[:-1] + y_pix_edges[1:]) / 2
  
          if self._interpolation == "nearest":
              x_mid = (self._Ax[:-1] + self._Ax[1:]) / 2
              y_mid = (self._Ay[:-1] + self._Ay[1:]) / 2
              x_int = x_mid.searchsorted(x_pix_centers)
              y_int = y_mid.searchsorted(y_pix_centers)
              # The following is equal to `A[y_int[:, None], x_int[None, :]]`,
              # but many times faster.  Both casting to uint32 (to have an
              # effectively 1D array) and manual index flattening matter.
              im = (
                  np.ascontiguousarray(A).view(np.uint32).ravel()[
                      np.add.outer(y_int * A.shape[1], x_int)]
                  .view(np.uint8).reshape((height, width, 4)))
          else:  # self._interpolation == "bilinear"
              # Use np.interp to compute x_int/x_float has similar speed.
              x_int = np.clip(
                  self._Ax.searchsorted(x_pix_centers) - 1, 0, len(self._Ax) - 2)
              y_int = np.clip(
                  self._Ay.searchsorted(y_pix_centers) - 1, 0, len(self._Ay) - 2)
              idx_int = np.add.outer(y_int * A.shape[1], x_int)
              x_frac = np.clip(
                  np.divide(x_pix_centers - self._Ax[x_int], np.diff(self._Ax)[x_int],
                            dtype=np.float32),  # Downcasting helps with speed.
                  0, 1)
              y_frac = np.clip(
                  np.divide(y_pix_centers - self._Ay[y_int], np.diff(self._Ay)[y_int],
                            dtype=np.float32),
                  0, 1)
              f00 = np.outer(1 - y_frac, 1 - x_frac)
              f10 = np.outer(y_frac, 1 - x_frac)
              f01 = np.outer(1 - y_frac, x_frac)
              f11 = np.outer(y_frac, x_frac)
              im = np.empty((height, width, 4), np.uint8)
              for chan in range(4):
                  ac = A[:, :, chan].reshape(-1)  # reshape(-1) avoids a copy.
                  # Shifting the buffer start (`ac[offset:]`) avoids an array
                  # addition (`ac[idx_int + offset]`).
                  buf = f00 * ac[idx_int]
                  buf += f10 * ac[A.shape[1]:][idx_int]
                  buf += f01 * ac[1:][idx_int]
                  buf += f11 * ac[A.shape[1] + 1:][idx_int]
                  im[:, :, chan] = buf  # Implicitly casts to uint8.
          return im, l, b, IdentityTransform()
  
      def set_data(self, x, y, A):
          """
          Set the grid for the pixel centers, and the pixel values.
  
          Parameters
          ----------
          x, y : 1D array-like
              Monotonic arrays of shapes (N,) and (M,), respectively, specifying
              pixel centers.
          A : array-like
              (M, N) `~numpy.ndarray` or masked array of values to be
              colormapped, or (M, N, 3) RGB array, or (M, N, 4) RGBA array.
          """
          A = self._normalize_image_array(A)
          x = np.array(x, np.float32)
          y = np.array(y, np.float32)
          if not (x.ndim == y.ndim == 1 and A.shape[:2] == y.shape + x.shape):
              raise TypeError("Axes don't match array shape")
          self._A = A
          self._Ax = x
          self._Ay = y
          self._imcache = None
          self.stale = True
  
      def set_array(self, *args):
          raise NotImplementedError('Method not supported')
  
      def set_interpolation(self, s):
          """
          Parameters
          ----------
          s : {'nearest', 'bilinear'} or None
              If None, use :rc:`image.interpolation`.
          """
          if s is not None and s not in ('nearest', 'bilinear'):
              raise NotImplementedError('Only nearest neighbor and '
                                        'bilinear interpolations are supported')
          super().set_interpolation(s)
  
      def get_extent(self):
          if self._A is None:
              raise RuntimeError('Must set data first')
          return self._Ax[0], self._Ax[-1], self._Ay[0], self._Ay[-1]
  
      def set_filternorm(self, filternorm):
          pass
  
      def set_filterrad(self, filterrad):
          pass
  
      def set_norm(self, norm):
          if self._A is not None:
              raise RuntimeError('Cannot change colors after loading data')
          super().set_norm(norm)
  
      def set_cmap(self, cmap):
          if self._A is not None:
              raise RuntimeError('Cannot change colors after loading data')
          super().set_cmap(cmap)
  
      def get_cursor_data(self, event):
          # docstring inherited
          x, y = event.xdata, event.ydata
          if (x < self._Ax[0] or x > self._Ax[-1] or
                  y < self._Ay[0] or y > self._Ay[-1]):
              return None
          j = np.searchsorted(self._Ax, x) - 1
          i = np.searchsorted(self._Ay, y) - 1
          return self._A[i, j]
  
  
  class PcolorImage(AxesImage):
      """
      Make a pcolor-style plot with an irregular rectangular grid.
  
      This uses a variation of the original irregular image code,
      and it is used by pcolorfast for the corresponding grid type.
      """
  
      def __init__(self, ax,
                   x=None,
                   y=None,
                   A=None,
                   *,
                   cmap=None,
                   norm=None,
                   colorizer=None,
                   **kwargs
                   ):
          """
          Parameters
          ----------
          ax : `~matplotlib.axes.Axes`
              The Axes the image will belong to.
          x, y : 1D array-like, optional
              Monotonic arrays of length N+1 and M+1, respectively, specifying
              rectangle boundaries.  If not given, will default to
              ``range(N + 1)`` and ``range(M + 1)``, respectively.
          A : array-like
              The data to be color-coded. The interpretation depends on the
              shape:
  
              - (M, N) `~numpy.ndarray` or masked array: values to be colormapped
              - (M, N, 3): RGB array
              - (M, N, 4): RGBA array
  
          cmap : str or `~matplotlib.colors.Colormap`, default: :rc:`image.cmap`
              The Colormap instance or registered colormap name used to map
              scalar data to colors.
          norm : str or `~matplotlib.colors.Normalize`
              Maps luminance to 0-1.
          **kwargs : `~matplotlib.artist.Artist` properties
          """
          super().__init__(ax, norm=norm, cmap=cmap, colorizer=colorizer)
          self._internal_update(kwargs)
          if A is not None:
              self.set_data(x, y, A)
  
      def make_image(self, renderer, magnification=1.0, unsampled=False):
          # docstring inherited
          if self._A is None:
              raise RuntimeError('You must first set the image array')
          if unsampled:
              raise ValueError('unsampled not supported on PColorImage')
  
          if self._imcache is None:
              A = self.to_rgba(self._A, bytes=True)
              self._imcache = np.pad(A, [(1, 1), (1, 1), (0, 0)], "constant")
          padded_A = self._imcache
          bg = mcolors.to_rgba(self.axes.patch.get_facecolor(), 0)
          bg = (np.array(bg) * 255).astype(np.uint8)
          if (padded_A[0, 0] != bg).all():
              padded_A[[0, -1], :] = padded_A[:, [0, -1]] = bg
  
          # Round to the nearest output pixels after magnification
          l, b, r, t = (self.axes.bbox.extents * magnification + 0.5).astype(int)
          width = r - l
          height = t - b
  
          vl = self.axes.viewLim
  
          x_pix_edges = np.linspace(vl.x0, vl.x1, width + 1)
          y_pix_edges = np.linspace(vl.y0, vl.y1, height + 1)
          x_pix_centers = (x_pix_edges[:-1] + x_pix_edges[1:]) / 2
          y_pix_centers = (y_pix_edges[:-1] + y_pix_edges[1:]) / 2
          x_int = self._Ax.searchsorted(x_pix_centers)
          y_int = self._Ay.searchsorted(y_pix_centers)
          im = (  # See comment in NonUniformImage.make_image re: performance.
              padded_A.view(np.uint32).ravel()[
                  np.add.outer(y_int * padded_A.shape[1], x_int)]
              .view(np.uint8).reshape((height, width, 4)))
          return im, l / magnification, b / magnification, IdentityTransform()
  
      def _check_unsampled_image(self):
          return False
  
      def set_data(self, x, y, A):
          """
          Set the grid for the rectangle boundaries, and the data values.
  
          Parameters
          ----------
          x, y : 1D array-like, optional
              Monotonic arrays of length N+1 and M+1, respectively, specifying
              rectangle boundaries.  If not given, will default to
              ``range(N + 1)`` and ``range(M + 1)``, respectively.
          A : array-like
              The data to be color-coded. The interpretation depends on the
              shape:
  
              - (M, N) `~numpy.ndarray` or masked array: values to be colormapped
              - (M, N, 3): RGB array
              - (M, N, 4): RGBA array
          """
          A = self._normalize_image_array(A)
          x = np.arange(0., A.shape[1] + 1) if x is None else np.array(x, float).ravel()
          y = np.arange(0., A.shape[0] + 1) if y is None else np.array(y, float).ravel()
          if A.shape[:2] != (y.size - 1, x.size - 1):
              raise ValueError(
                  "Axes don't match array shape. Got %s, expected %s." %
                  (A.shape[:2], (y.size - 1, x.size - 1)))
          # For efficient cursor readout, ensure x and y are increasing.
          if x[-1] < x[0]:
              x = x[::-1]
              A = A[:, ::-1]
          if y[-1] < y[0]:
              y = y[::-1]
              A = A[::-1]
          self._A = A
          self._Ax = x
          self._Ay = y
          self._imcache = None
          self.stale = True
  
      def set_array(self, *args):
          raise NotImplementedError('Method not supported')
  
      def get_cursor_data(self, event):
          # docstring inherited
          x, y = event.xdata, event.ydata
          if (x < self._Ax[0] or x > self._Ax[-1] or
                  y < self._Ay[0] or y > self._Ay[-1]):
              return None
          j = np.searchsorted(self._Ax, x) - 1
          i = np.searchsorted(self._Ay, y) - 1
          return self._A[i, j]
  
  
  class FigureImage(_ImageBase):
      """An image attached to a figure."""
  
      zorder = 0
  
      _interpolation = 'nearest'
  
      def __init__(self, fig,
                   *,
                   cmap=None,
                   norm=None,
                   colorizer=None,
                   offsetx=0,
                   offsety=0,
                   origin=None,
                   **kwargs
                   ):
          """
          cmap is a colors.Colormap instance
          norm is a colors.Normalize instance to map luminance to 0-1
  
          kwargs are an optional list of Artist keyword args
          """
          super().__init__(
              None,
              norm=norm,
              cmap=cmap,
              colorizer=colorizer,
              origin=origin
          )
          self.set_figure(fig)
          self.ox = offsetx
          self.oy = offsety
          self._internal_update(kwargs)
          self.magnification = 1.0
  
      def get_extent(self):
          """Return the image extent as tuple (left, right, bottom, top)."""
          numrows, numcols = self.get_size()
          return (-0.5 + self.ox, numcols-0.5 + self.ox,
                  -0.5 + self.oy, numrows-0.5 + self.oy)
  
      def make_image(self, renderer, magnification=1.0, unsampled=False):
          # docstring inherited
          fig = self.get_figure(root=True)
          fac = renderer.dpi/fig.dpi
          # fac here is to account for pdf, eps, svg backends where
          # figure.dpi is set to 72.  This means we need to scale the
          # image (using magnification) and offset it appropriately.
          bbox = Bbox([[self.ox/fac, self.oy/fac],
                       [(self.ox/fac + self._A.shape[1]),
                       (self.oy/fac + self._A.shape[0])]])
          width, height = fig.get_size_inches()
          width *= renderer.dpi
          height *= renderer.dpi
          clip = Bbox([[0, 0], [width, height]])
          return self._make_image(
              self._A, bbox, bbox, clip, magnification=magnification / fac,
              unsampled=unsampled, round_to_pixel_border=False)
  
      def set_data(self, A):
          """Set the image array."""
          super().set_data(A)
          self.stale = True
  
  
  class BboxImage(_ImageBase):
      """
      The Image class whose size is determined by the given bbox.
  
      Parameters
      ----------
      bbox : BboxBase or Callable[RendererBase, BboxBase]
          The bbox or a function to generate the bbox
  
          .. warning ::
  
              If using `matplotlib.artist.Artist.get_window_extent` as the
              callable ensure that the other artist is drawn first (lower zorder)
              or you may need to renderer the figure twice to ensure that the
              computed bbox is accurate.
  
      cmap : str or `~matplotlib.colors.Colormap`, default: :rc:`image.cmap`
          The Colormap instance or registered colormap name used to map scalar
          data to colors. This parameter is ignored if X is RGB(A).
      norm : str or `~matplotlib.colors.Normalize`
          Maps luminance to 0-1. This parameter is ignored if X is RGB(A).
      interpolation : str, default: :rc:`image.interpolation`
          Supported values are 'none', 'auto', 'nearest', 'bilinear',
          'bicubic', 'spline16', 'spline36', 'hanning', 'hamming', 'hermite',
          'kaiser', 'quadric', 'catrom', 'gaussian', 'bessel', 'mitchell',
          'sinc', 'lanczos', 'blackman'.
      origin : {'upper', 'lower'}, default: :rc:`image.origin`
          Place the [0, 0] index of the array in the upper left or lower left
          corner of the Axes. The convention 'upper' is typically used for
          matrices and images.
      filternorm : bool, default: True
          A parameter for the antigrain image resize filter
          (see the antigrain documentation).
          If filternorm is set, the filter normalizes integer values and corrects
          the rounding errors. It doesn't do anything with the source floating
          point values, it corrects only integers according to the rule of 1.0
          which means that any sum of pixel weights must be equal to 1.0. So,
          the filter function must produce a graph of the proper shape.
      filterrad : float > 0, default: 4
          The filter radius for filters that have a radius parameter, i.e. when
          interpolation is one of: 'sinc', 'lanczos' or 'blackman'.
      resample : bool, default: False
          When True, use a full resampling method. When False, only resample when
          the output image is larger than the input image.
      **kwargs : `~matplotlib.artist.Artist` properties
  
      """
      def __init__(self, bbox,
                   *,
                   cmap=None,
                   norm=None,
                   colorizer=None,
                   interpolation=None,
                   origin=None,
                   filternorm=True,
                   filterrad=4.0,
                   resample=False,
                   **kwargs
                   ):
  
          super().__init__(
              None,
              cmap=cmap,
              norm=norm,
              colorizer=colorizer,
              interpolation=interpolation,
              origin=origin,
              filternorm=filternorm,
              filterrad=filterrad,
              resample=resample,
              **kwargs
          )
          self.bbox = bbox
  
      def get_window_extent(self, renderer=None):
          if isinstance(self.bbox, BboxBase):
              return self.bbox
          elif callable(self.bbox):
              if renderer is None:
                  renderer = self.get_figure()._get_renderer()
              return self.bbox(renderer)
          else:
              raise ValueError("Unknown type of bbox")
  
      def contains(self, mouseevent):
          """Test whether the mouse event occurred within the image."""
          if self._different_canvas(mouseevent) or not self.get_visible():
              return False, {}
          x, y = mouseevent.x, mouseevent.y
          inside = self.get_window_extent().contains(x, y)
          return inside, {}
  
      def make_image(self, renderer, magnification=1.0, unsampled=False):
          # docstring inherited
          width, height = renderer.get_canvas_width_height()
          bbox_in = self.get_window_extent(renderer).frozen()
          bbox_in._points /= [width, height]
          bbox_out = self.get_window_extent(renderer)
          clip = Bbox([[0, 0], [width, height]])
          self._transform = BboxTransformTo(clip)
          return self._make_image(
              self._A,
              bbox_in, bbox_out, clip, magnification, unsampled=unsampled)
  
  
  def imread(fname, format=None):
      """
      Read an image from a file into an array.
  
      .. note::
  
          This function exists for historical reasons.  It is recommended to
          use `PIL.Image.open` instead for loading images.
  
      Parameters
      ----------
      fname : str or file-like
          The image file to read: a filename, a URL or a file-like object opened
          in read-binary mode.
  
          Passing a URL is deprecated.  Please open the URL
          for reading and pass the result to Pillow, e.g. with
          ``np.array(PIL.Image.open(urllib.request.urlopen(url)))``.
      format : str, optional
          The image file format assumed for reading the data.  The image is
          loaded as a PNG file if *format* is set to "png", if *fname* is a path
          or opened file with a ".png" extension, or if it is a URL.  In all
          other cases, *format* is ignored and the format is auto-detected by
          `PIL.Image.open`.
  
      Returns
      -------
      `numpy.array`
          The image data. The returned array has shape
  
          - (M, N) for grayscale images.
          - (M, N, 3) for RGB images.
          - (M, N, 4) for RGBA images.
  
          PNG images are returned as float arrays (0-1).  All other formats are
          returned as int arrays, with a bit depth determined by the file's
          contents.
      """
      # hide imports to speed initial import on systems with slow linkers
      from urllib import parse
  
      if format is None:
          if isinstance(fname, str):
              parsed = parse.urlparse(fname)
              # If the string is a URL (Windows paths appear as if they have a
              # length-1 scheme), assume png.
              if len(parsed.scheme) > 1:
                  ext = 'png'
              else:
                  ext = Path(fname).suffix.lower()[1:]
          elif hasattr(fname, 'geturl'):  # Returned by urlopen().
              # We could try to parse the url's path and use the extension, but
              # returning png is consistent with the block above.  Note that this
              # if clause has to come before checking for fname.name as
              # urlopen("file:///...") also has a name attribute (with the fixed
              # value "<urllib response>").
              ext = 'png'
          elif hasattr(fname, 'name'):
              ext = Path(fname.name).suffix.lower()[1:]
          else:
              ext = 'png'
      else:
          ext = format
      img_open = (
          PIL.PngImagePlugin.PngImageFile if ext == 'png' else PIL.Image.open)
      if isinstance(fname, str) and len(parse.urlparse(fname).scheme) > 1:
          # Pillow doesn't handle URLs directly.
          raise ValueError(
              "Please open the URL for reading and pass the "
              "result to Pillow, e.g. with "
              "``np.array(PIL.Image.open(urllib.request.urlopen(url)))``."
              )
      with img_open(fname) as image:
          return (_pil_png_to_float_array(image)
                  if isinstance(image, PIL.PngImagePlugin.PngImageFile) else
                  pil_to_array(image))
  
  
  def imsave(fname, arr, vmin=None, vmax=None, cmap=None, format=None,
             origin=None, dpi=100, *, metadata=None, pil_kwargs=None):
      """
      Colormap and save an array as an image file.
  
      RGB(A) images are passed through.  Single channel images will be
      colormapped according to *cmap* and *norm*.
  
      .. note::
  
         If you want to save a single channel image as gray scale please use an
         image I/O library (such as pillow, tifffile, or imageio) directly.
  
      Parameters
      ----------
      fname : str or path-like or file-like
          A path or a file-like object to store the image in.
          If *format* is not set, then the output format is inferred from the
          extension of *fname*, if any, and from :rc:`savefig.format` otherwise.
          If *format* is set, it determines the output format.
      arr : array-like
          The image data. Accepts NumPy arrays or sequences
          (e.g., lists or tuples). The shape can be one of
          MxN (luminance), MxNx3 (RGB) or MxNx4 (RGBA).
      vmin, vmax : float, optional
          *vmin* and *vmax* set the color scaling for the image by fixing the
          values that map to the colormap color limits. If either *vmin*
          or *vmax* is None, that limit is determined from the *arr*
          min/max value.
      cmap : str or `~matplotlib.colors.Colormap`, default: :rc:`image.cmap`
          A Colormap instance or registered colormap name. The colormap
          maps scalar data to colors. It is ignored for RGB(A) data.
      format : str, optional
          The file format, e.g. 'png', 'pdf', 'svg', ...  The behavior when this
          is unset is documented under *fname*.
      origin : {'upper', 'lower'}, default: :rc:`image.origin`
          Indicates whether the ``(0, 0)`` index of the array is in the upper
          left or lower left corner of the Axes.
      dpi : float
          The DPI to store in the metadata of the file.  This does not affect the
          resolution of the output image.  Depending on file format, this may be
          rounded to the nearest integer.
      metadata : dict, optional
          Metadata in the image file.  The supported keys depend on the output
          format, see the documentation of the respective backends for more
          information.
          Currently only supported for "png", "pdf", "ps", "eps", and "svg".
      pil_kwargs : dict, optional
          Keyword arguments passed to `PIL.Image.Image.save`.  If the 'pnginfo'
          key is present, it completely overrides *metadata*, including the
          default 'Software' key.
      """
      from matplotlib.figure import Figure
  
      # Normalizing input (e.g., list or tuples) to NumPy array if needed
      arr = np.asanyarray(arr)
  
      if isinstance(fname, os.PathLike):
          fname = os.fspath(fname)
      if format is None:
          format = (Path(fname).suffix[1:] if isinstance(fname, str)
                    else mpl.rcParams["savefig.format"]).lower()
      if format in ["pdf", "ps", "eps", "svg"]:
          # Vector formats that are not handled by PIL.
          if pil_kwargs is not None:
              raise ValueError(
                  f"Cannot use 'pil_kwargs' when saving to {format}")
          fig = Figure(dpi=dpi, frameon=False)
          fig.figimage(arr, cmap=cmap, vmin=vmin, vmax=vmax, origin=origin,
                       resize=True)
          fig.savefig(fname, dpi=dpi, format=format, transparent=True,
                      metadata=metadata)
      else:
          # Don't bother creating an image; this avoids rounding errors on the
          # size when dividing and then multiplying by dpi.
          origin = mpl._val_or_rc(origin, "image.origin")
          _api.check_in_list(('upper', 'lower'), origin=origin)
          if origin == "lower":
              arr = arr[::-1]
          if (isinstance(arr, memoryview) and arr.format == "B"
                  and arr.ndim == 3 and arr.shape[-1] == 4):
              # Such an ``arr`` would also be handled fine by sm.to_rgba below
              # (after casting with asarray), but it is useful to special-case it
              # because that's what backend_agg passes, and can be in fact used
              # as is, saving a few operations.
              rgba = arr
          else:
              sm = mcolorizer.Colorizer(cmap=cmap)
              sm.set_clim(vmin, vmax)
              rgba = sm.to_rgba(arr, bytes=True)
          if pil_kwargs is None:
              pil_kwargs = {}
          else:
              # we modify this below, so make a copy (don't modify caller's dict)
              pil_kwargs = pil_kwargs.copy()
          pil_shape = (rgba.shape[1], rgba.shape[0])
          rgba = np.require(rgba, requirements='C')
          image = PIL.Image.frombuffer(
              "RGBA", pil_shape, rgba, "raw", "RGBA", 0, 1)
          if format == "png":
              # Only use the metadata kwarg if pnginfo is not set, because the
              # semantics of duplicate keys in pnginfo is unclear.
              if "pnginfo" in pil_kwargs:
                  if metadata:
                      _api.warn_external("'metadata' is overridden by the "
                                         "'pnginfo' entry in 'pil_kwargs'.")
              else:
                  metadata = {
                      "Software": (f"Matplotlib version{mpl.__version__}, "
                                   f"https://matplotlib.org/"),
                      **(metadata if metadata is not None else {}),
                  }
                  pil_kwargs["pnginfo"] = pnginfo = PIL.PngImagePlugin.PngInfo()
                  for k, v in metadata.items():
                      if v is not None:
                          pnginfo.add_text(k, v)
          elif metadata is not None:
              raise ValueError(f"metadata not supported for format {format!r}")
          if format in ["jpg", "jpeg"]:
              format = "jpeg"  # Pillow doesn't recognize "jpg".
              facecolor = mpl.rcParams["savefig.facecolor"]
              if cbook._str_equal(facecolor, "auto"):
                  facecolor = mpl.rcParams["figure.facecolor"]
              color = tuple(int(x * 255) for x in mcolors.to_rgb(facecolor))
              background = PIL.Image.new("RGB", pil_shape, color)
              background.paste(image, image)
              image = background
          pil_kwargs.setdefault("format", format)
          pil_kwargs.setdefault("dpi", (dpi, dpi))
          image.save(fname, **pil_kwargs)
  
  
  def pil_to_array(pilImage):
      """
      Load a `PIL image`_ and return it as a numpy int array.
  
      .. _PIL image: https://pillow.readthedocs.io/en/latest/reference/Image.html
  
      Returns
      -------
      numpy.array
  
          The array shape depends on the image type:
  
          - (M, N) for grayscale images.
          - (M, N, 3) for RGB images.
          - (M, N, 4) for RGBA images.
      """
      if pilImage.mode in ['RGBA', 'RGBX', 'RGB', 'L']:
          # return MxNx4 RGBA, MxNx3 RBA, or MxN luminance array
          return np.asarray(pilImage)
      elif pilImage.mode.startswith('I;16'):
          # return MxN luminance array of uint16
          raw = pilImage.tobytes('raw', pilImage.mode)
          if pilImage.mode.endswith('B'):
              x = np.frombuffer(raw, '>u2')
          else:
              x = np.frombuffer(raw, '<u2')
          return x.reshape(pilImage.size[::-1]).astype('=u2')
      else:  # try to convert to an rgba image
          try:
              pilImage = pilImage.convert('RGBA')
          except ValueError as err:
              raise RuntimeError('Unknown image mode') from err
          return np.asarray(pilImage)  # return MxNx4 RGBA array
  
  
  def _pil_png_to_float_array(pil_png):
      """Convert a PIL `PNGImageFile` to a 0-1 float array."""
      # Unlike pil_to_array this converts to 0-1 float32s for backcompat with the
      # old libpng-based loader.
      # The supported rawmodes are from PIL.PngImagePlugin._MODES.  When
      # mode == "RGB(A)", the 16-bit raw data has already been coarsened to 8-bit
      # by Pillow.
      mode = pil_png.mode
      rawmode = pil_png.png.im_rawmode
      if rawmode == "1":  # Grayscale.
          return np.asarray(pil_png, np.float32)
      if rawmode == "L;2":  # Grayscale.
          return np.divide(pil_png, 2**2 - 1, dtype=np.float32)
      if rawmode == "L;4":  # Grayscale.
          return np.divide(pil_png, 2**4 - 1, dtype=np.float32)
      if rawmode == "L":  # Grayscale.
          return np.divide(pil_png, 2**8 - 1, dtype=np.float32)
      if rawmode == "I;16B":  # Grayscale.
          return np.divide(pil_png, 2**16 - 1, dtype=np.float32)
      if mode == "RGB":  # RGB.
          return np.divide(pil_png, 2**8 - 1, dtype=np.float32)
      if mode == "P":  # Palette.
          return np.divide(pil_png.convert("RGBA"), 2**8 - 1, dtype=np.float32)
      if mode == "LA":  # Grayscale + alpha.
          return np.divide(pil_png.convert("RGBA"), 2**8 - 1, dtype=np.float32)
      if mode == "RGBA":  # RGBA.
          return np.divide(pil_png, 2**8 - 1, dtype=np.float32)
      raise ValueError(f"Unknown PIL rawmode: {rawmode}")
  
  
  @_api.deprecated('3.11', alternative="Pillow's `PIL.Image.Image.thumbnail`")
  def thumbnail(infile, thumbfile, scale=0.1, interpolation='bilinear',
                preview=False):
      """
      Make a thumbnail of image in *infile* with output filename *thumbfile*.
  
      See `Pillow for a replacement
      <https://pillow.readthedocs.io/en/stable/handbook/tutorial.html#create-jpeg-thumbnails>`_.
  
      Parameters
      ----------
      infile : str or file-like
          The image file. Matplotlib relies on Pillow_ for image reading, and
          thus supports a wide range of file formats, including PNG, JPG, TIFF
          and others.
  
          .. _Pillow: https://python-pillow.github.io
  
      thumbfile : str or file-like
          The thumbnail filename.
  
      scale : float, default: 0.1
          The scale factor for the thumbnail.
  
      interpolation : str, default: 'bilinear'
          The interpolation scheme used in the resampling. See the
          *interpolation* parameter of `~.Axes.imshow` for possible values.
  
      preview : bool, default: False
          If True, the default backend (presumably a user interface
          backend) will be used which will cause a figure to be raised if
          `~matplotlib.pyplot.show` is called.  If it is False, the figure is
          created using `.FigureCanvasBase` and the drawing backend is selected
          as `.Figure.savefig` would normally do.
  
      Returns
      -------
      `.Figure`
          The figure instance containing the thumbnail.
      """
  
      im = imread(infile)
      rows, cols, depth = im.shape
  
      # This doesn't really matter (it cancels in the end) but the API needs it.
      dpi = 100
  
      height = rows / dpi * scale
      width = cols / dpi * scale
  
      if preview:
          # Let the UI backend do everything.
          import matplotlib.pyplot as plt
          fig = plt.figure(figsize=(width, height), dpi=dpi)
      else:
          from matplotlib.figure import Figure
          fig = Figure(figsize=(width, height), dpi=dpi)
          FigureCanvasBase(fig)
  
      ax = fig.add_axes((0, 0, 1, 1), aspect='auto',
                        frameon=False, xticks=[], yticks=[])
      ax.imshow(im, aspect='auto', resample=True, interpolation=interpolation)
      fig.savefig(thumbfile, dpi=dpi)
      return fig
  