image.py

"""
The image module supports basic image loading, rescaling and display
operations.
"""

from io import BytesIO
import math
import os
import logging
from numbers import Number
from pathlib import Path
import urllib.parse

import numpy as np

from matplotlib import rcParams
import matplotlib.artist as martist
from matplotlib.backend_bases import FigureCanvasBase
import matplotlib.colors as mcolors
import matplotlib.cm as cm
import matplotlib.cbook as cbook

# For clarity, names from _image are given explicitly in this module:
import matplotlib._image as _image

# For user convenience, the names from _image are also imported into
# the image namespace:
from matplotlib._image import *

from matplotlib.transforms import (Affine2D, BboxBase, Bbox, BboxTransform,
                                   IdentityTransform, TransformedBbox)

_log = logging.getLogger(__name__)

# map interpolation strings to module constants
_interpd_ = {
    'antialiased': _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,
}

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 instance

    magnification : float
        The additional magnification to apply for the renderer in use.

    Returns
    -------
    tuple : image, offset_x, offset_y
        Returns the tuple:

        - image: A numpy array of the same type as the input images.

        - offset_x, offset_y: The offset of the image (left, bottom)
          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():
                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*.
    """

    # 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 == 'antialiased':
        # 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()
    _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(martist.Artist, cm.ScalarMappable):
    """
    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 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.

    Additional kwargs are matplotlib.artist properties
    """
    zorder = 0

    def __init__(self, ax,
                 cmap=None,
                 norm=None,
                 interpolation=None,
                 origin=None,
                 filternorm=True,
                 filterrad=4.0,
                 resample=False,
                 **kwargs
                 ):
        martist.Artist.__init__(self)
        cm.ScalarMappable.__init__(self, norm, cmap)
        self._mouseover = True
        if origin is None:
            origin = rcParams['image.origin']
        self.origin = origin
        self.set_filternorm(filternorm)
        self.set_filterrad(filterrad)
        self.set_interpolation(interpolation)
        self.set_resample(resample)
        self.axes = ax

        self._imcache = None

        self.update(kwargs)

    def __getstate__(self):
        state = super().__getstate__()
        # We can't pickle the C Image cached object.
        state['_imcache'] = None
        return state

    def get_size(self):
        """Return the size of the image as tuple (numrows, numcols)."""
        if self._A is None:
            raise RuntimeError('You must first set the image array')

        return self._A.shape[:2]

    def set_alpha(self, alpha):
        """
        Set the alpha value used for blending - not supported on all backends.

        Parameters
        ----------
        alpha : float
        """
        if alpha is not None and not isinstance(alpha, Number):
            alpha = np.asarray(alpha)
            if alpha.ndim != 2:
                raise TypeError('alpha must be a float, two-dimensional '
                                'array, or None')
        self._alpha = alpha
        self.pchanged()
        self.stale = True
        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 state
        """
        self._imcache = None
        self._rgbacache = None
        cm.ScalarMappable.changed(self)

    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.

        *A* may be a greyscale image (M, N) with a dtype of float32, float64,
        float128, uint16 or uint8, or an (M, N, 4) RGBA image with a dtype of
        float32, float64, float128, or uint8.

        If *unsampled* is True, the image will not be scaled, but an
        appropriate affine transformation will be returned instead.

        If *round_to_pixel_border* is 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) 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 : 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

        out_width_base = clipped_bbox.width * magnification
        out_height_base = clipped_bbox.height * magnification

        if out_width_base == 0 or out_height_base == 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()
                .translate(-clipped_bbox.x0, -clipped_bbox.y0)
                .scale(magnification)))

        # So that the image is aligned with the edge of the axes, we want to
        # round up the output width to the next integer.  This also means
        # scaling the transform slightly to account for the extra subpixel.
        if (t.is_affine and round_to_pixel_border and
                (out_width_base % 1.0 != 0.0 or out_height_base % 1.0 != 0.0)):
            out_width = math.ceil(out_width_base)
            out_height = math.ceil(out_height_base)
            extra_width = (out_width - out_width_base) / out_width_base
            extra_height = (out_height - out_height_base) / out_height_base
            t += Affine2D().scale(1.0 + extra_width, 1.0 + extra_height)
        else:
            out_width = int(out_width_base)
            out_height = int(out_height_base)
        out_shape = (out_height, out_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")

            if A.ndim == 2:
                # 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

                # TODO slice input array first
                inp_dtype = A.dtype
                a_min = A.min()
                a_max = A.max()
                # figure out the type we should scale to.  For floats,
                # leave as is.  For integers cast to an appropriate-sized
                # float.  Small integers get smaller floats in an attempt
                # to keep the memory footprint reasonable.
                if a_min is np.ma.masked:
                    # all masked, so values don't matter
                    a_min, a_max = np.int32(0), np.int32(1)
                if inp_dtype.kind == 'f':
                    scaled_dtype = A.dtype
                    # Cast to float64
                    if A.dtype not in (np.float32, np.float16):
                        if A.dtype != np.float64:
                            cbook._warn_external(
                                f"Casting input data from '{A.dtype}' to "
                                f"'float64' for imshow")
                        scaled_dtype = np.float64
                else:
                    # probably an integer of some type.
                    da = a_max.astype(np.float64) - a_min.astype(np.float64)
                    # give more breathing room if a big dynamic range
                    scaled_dtype = np.float64 if da > 1e8 else np.float32

                # scale the input data to [.1, .9].  The Agg
                # interpolators clip to [0, 1] internally, use a
                # smaller input scale to identify which of the
                # interpolated points need to be should be flagged as
                # over / under.
                # This may introduce numeric instabilities in very broadly
                # scaled data
                # Always copy, and don't allow array subtypes.
                A_scaled = np.array(A, dtype=scaled_dtype)
                # clip scaled data around norm if necessary.
                # This is necessary for big numbers at the edge of
                # float64's ability to represent changes.  Applying
                # a norm first would be good, but ruins the interpolation
                # of over numbers.
                self.norm.autoscale_None(A)
                dv = np.float64(self.norm.vmax) - np.float64(self.norm.vmin)
                vmid = self.norm.vmin + dv / 2
                fact = 1e7 if scaled_dtype == np.float64 else 1e4
                newmin = vmid - dv * fact
                if newmin < a_min:
                    newmin = None
                else:
                    a_min = np.float64(newmin)
                newmax = vmid + dv * fact
                if newmax > a_max:
                    newmax = None
                else:
                    a_max = np.float64(newmax)
                if newmax is not None or newmin is not None:
                    np.clip(A_scaled, newmin, newmax, out=A_scaled)

                A_scaled -= a_min
                # a_min and a_max might be ndarray subclasses so use
                # item to avoid errors
                a_min = a_min.astype(scaled_dtype).item()
                a_max = a_max.astype(scaled_dtype).item()

                if a_min != a_max:
                    A_scaled /= ((a_max - a_min) / 0.8)
                A_scaled += 0.1
                # resample the input data to the correct resolution and shape
                A_resampled = _resample(self, A_scaled, out_shape, t)
                # done with A_scaled now, remove from namespace to be sure!
                del A_scaled
                # un-scale the resampled data to approximately the
                # original range things that interpolated to above /
                # below the original min/max will still be above /
                # below, but possibly clipped in the case of higher order
                # interpolation + drastically changing data.
                A_resampled -= 0.1
                if a_min != a_max:
                    A_resampled *= ((a_max - a_min) / 0.8)
                A_resampled += a_min
                # if using NoNorm, cast back to the original datatype
                if isinstance(self.norm, mcolors.NoNorm):
                    A_resampled = A_resampled.astype(A.dtype)

                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)
                # done with the mask now, delete from namespace to be sure!
                del mask
                # Agg updates out_alpha in place.  If the pixel has no image
                # data it will not be updated (and still be 0 as we initialized
                # it), if input data that would go into that output pixel than
                # it will be `nan`, if all the input data for a pixel is good
                # it will be 1, and if there is _some_ good data in that output
                # pixel it will be between [0, 1] (such as a rotated image).
                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
                output = self.norm(np.ma.masked_array(A_resampled, out_mask))
            else:
                if A.shape[2] == 3:
                    A = _rgb_to_rgba(A)
                alpha = self._get_scalar_alpha()
                output_alpha = _resample(  # resample alpha channel
                    self, A[..., 3], out_shape, t, alpha=alpha)
                output = _resample(  # resample rgb channels
                    self, _rgb_to_rgba(A[..., :3]), out_shape, t, alpha=alpha)
                output[..., 3] = output_alpha  # recombine rgb and alpha

            # at this point output is either a 2D array of normed data
            # (of int or float)
            # or an RGBA array of re-sampled input
            output = self.to_rgba(output, 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[:] = np.asarray(
                    np.asarray(alpha_channel, np.float32) * out_alpha * alpha,
                    np.uint8)

        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, clipped_bbox.x0, clipped_bbox.y0, 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) 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 : Affine2D
            The affine transformation from image to pixel space.
        """
        raise NotImplementedError('The make_image method must be overridden')

    def _draw_unsampled_image(self, renderer, gc):
        """
        Draw unsampled image. The renderer should support a draw_image method
        with scale parameter.
        """
        im, l, b, trans = self.make_image(renderer, unsampled=True)

        if im is None:
            return

        trans = Affine2D().scale(im.shape[1], im.shape[0]) + trans

        renderer.draw_image(gc, l, b, im, trans)

    def _check_unsampled_image(self, renderer):
        """
        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, *args, **kwargs):
        # 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 (self._check_unsampled_image(renderer) and
                self.get_transform().is_affine):
            self._draw_unsampled_image(renderer, gc)
        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.
        """
        inside, info = self._default_contains(mouseevent)
        if inside is not None:
            return inside, info
        # 1) This doesn't work for figimage; but figimage also needs a fix
        #    below (as the check cannot use x/ydata and extents).
        # 2) As long as the check below uses x/ydata, we need to test axes
        #    identity instead of `self.axes.contains(event)` because even if
        #    axes overlap, x/ydata is only valid for event.inaxes anyways.
        if self.axes is not mouseevent.inaxes:
            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
        x, y = mouseevent.xdata, mouseevent.ydata
        xmin, xmax, ymin, ymax = self.get_extent()
        if xmin > xmax:
            xmin, xmax = xmax, xmin
        if ymin > ymax:
            ymin, ymax = ymax, ymin

        if x is not None and y is not None:
            inside = (xmin <= x <= xmax) and (ymin <= y <= ymax)
        else:
            inside = False

        return inside, {}

    def write_png(self, fname):
        """Write the image to png file with fname"""
        from matplotlib import _png
        im = self.to_rgba(self._A[::-1] if self.origin == 'lower' else self._A,
                          bytes=True, norm=True)
        with cbook.open_file_cm(fname, "wb") as file:
            _png.write_png(im, file)

    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`
        """
        try:
            from PIL import Image
        except ImportError:
            pass
        else:
            if isinstance(A, Image.Image):
                A = pil_to_array(A)  # Needed e.g. to apply png palette.
        self._A = cbook.safe_masked_invalid(A, copy=True)

        if (self._A.dtype != np.uint8 and
                not np.can_cast(self._A.dtype, float, "same_kind")):
            raise TypeError("Image data of dtype {} cannot be converted to "
                            "float".format(self._A.dtype))

        if not (self._A.ndim == 2
                or self._A.ndim == 3 and self._A.shape[-1] in [3, 4]):
            raise TypeError("Invalid shape {} for image data"
                            .format(self._A.shape))

        if self._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(self._A.dtype, np.integer) else 1
            if self._A.min() < 0 or high < self._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).'
                )
                self._A = np.clip(self._A, 0, high)
            # Cast unsupported integer types to uint8
            if self._A.dtype != np.uint8 and np.issubdtype(self._A.dtype,
                                                           np.integer):
                self._A = self._A.astype(np.uint8)

        self._imcache = None
        self._rgbacache = 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 '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 a value from rc setting. 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 : {'antialiased', 'nearest', 'bilinear', 'bicubic', 'spline16',
'spline36', 'hanning', 'hamming', 'hermite', 'kaiser', 'quadric', 'catrom', \
'gaussian', 'bessel', 'mitchell', 'sinc', 'lanczos', 'none'}

        """
        if s is None:
            s = rcParams['image.interpolation']
        s = s.lower()
        cbook._check_in_list(_interpd_, interpolation=s)
        self._interpolation = 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 or None
            If None, use :rc:`image.resample` = True.
        """
        if v is None:
            v = rcParams['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 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):
    """
    Parameters
    ----------
    ax : `~.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 : `~matplotlib.colors.Normalize`
        Maps luminance to 0-1.
    interpolation : str, default: :rc:`image.interpolation`
        Supported values are 'none', 'antialiased', 'nearest', 'bilinear',
        'bicubic', 'spline16', 'spline36', 'hanning', 'hamming', 'hermite',
        'kaiser', 'quadric', 'catrom', 'gaussian', 'bessel', 'mitchell',
        'sinc', 'lanczos'.
    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 : `.Artist` properties

    """
    def __str__(self):
        return "AxesImage(%g,%g;%gx%g)" % tuple(self.axes.bbox.bounds)

    def __init__(self, ax,
                 cmap=None,
                 norm=None,
                 interpolation=None,
                 origin=None,
                 extent=None,
                 filternorm=1,
                 filterrad=4.0,
                 resample=False,
                 **kwargs
                 ):

        self._extent = extent

        super().__init__(
            ax,
            cmap=cmap,
            norm=norm,
            interpolation=interpolation,
            origin=origin,
            filternorm=filternorm,
            filterrad=filterrad,
            resample=resample,
            **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.axes.transData)

    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)
        return self._make_image(
            self._A, bbox, transformed_bbox,
            self.get_clip_box() or self.axes.bbox,
            magnification, unsampled=unsampled)

    def _check_unsampled_image(self, renderer):
        """
        Return whether the image would be better drawn unsampled.
        """
        return (self.get_interpolation() == "none"
                and renderer.option_scale_image())

    def set_extent(self, extent):
        """
        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.

        Notes
        -----
        This updates ``ax.dataLim``, and, if autoscaling, sets ``ax.viewLim``
        to tightly fit the image, regardless of ``dataLim``.  Autoscaling
        state is not changed, so following this with ``ax.autoscale_view()``
        will redo the autoscaling in accord with ``dataLim``.
        """
        self._extent = xmin, xmax, ymin, ymax = 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._autoscaleXon:
            self.axes.set_xlim((xmin, xmax), auto=None)
        if self.axes._autoscaleYon:
            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([[ymin, xmin], [ymax, xmax]])
        array_extent = Bbox([[0, 0], arr.shape[:2]])
        trans = BboxTransform(boxin=data_extent, boxout=array_extent)
        point = trans.transform([event.ydata, event.xdata])
        if any(np.isnan(point)):
            return None
        i, j = 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]

    def format_cursor_data(self, data):
        if np.ndim(data) == 0 and self.colorbar:
            return (
                "["
                + cbook.strip_math(
                    self.colorbar.formatter.format_data_short(data)).strip()
                + "]")
        else:
            return super().format_cursor_data(data)


class NonUniformImage(AxesImage):
    def __init__(self, ax, *, interpolation='nearest', **kwargs):
        """
        Parameters
        ----------
        interpolation : {'nearest', 'bilinear'}

        **kwargs
            All other keyword arguments are identical to those of `.AxesImage`.
        """
        super().__init__(ax, **kwargs)
        self.set_interpolation(interpolation)

    def _check_unsampled_image(self, renderer):
        """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)
                self.is_grayscale = self.cmap.is_gray()
            else:
                A = np.repeat(A[:, :, np.newaxis], 4, 2)
                A[:, :, 3] = 255
                self.is_grayscale = True
        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
            self.is_grayscale = False
        x0, y0, v_width, v_height = self.axes.viewLim.bounds
        l, b, r, t = self.axes.bbox.extents
        width = (round(r) + 0.5) - (round(l) - 0.5)
        height = (round(t) + 0.5) - (round(b) - 0.5)
        width *= magnification
        height *= magnification
        im = _image.pcolor(self._Ax, self._Ay, A,
                           int(height), int(width),
                           (x0, x0+v_width, y0, y0+v_height),
                           _interpd_[self._interpolation])
        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-likes
            Monotonic arrays of shapes (N,) and (M,), respectively, specifying
            pixel centers.
        A : array-like
            (M, N) ndarray or masked array of values to be colormapped, or
            (M, N, 3) RGB array, or (M, N, 4) RGBA array.
        """
        x = np.array(x, np.float32)
        y = np.array(y, np.float32)
        A = cbook.safe_masked_invalid(A, copy=True)
        if not (x.ndim == y.ndim == 1 and A.shape[0:2] == y.shape + x.shape):
            raise TypeError("Axes don't match array shape")
        if A.ndim not in [2, 3]:
            raise TypeError("Can only plot 2D or 3D data")
        if A.ndim == 3 and A.shape[2] not in [1, 3, 4]:
            raise TypeError("3D arrays must have three (RGB) "
                            "or four (RGBA) color components")
        if A.ndim == 3 and A.shape[2] == 1:
            A.shape = A.shape[0:2]
        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 : str, None
            Either 'nearest', 'bilinear', or ``None``.
        """
        if s is not None and s not in ('nearest', 'bilinear'):
            raise NotImplementedError('Only nearest neighbor and '
                                      'bilinear interpolations are supported')
        AxesImage.set_interpolation(self, 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, s):
        pass

    def set_filterrad(self, s):
        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)


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,
                 **kwargs
                 ):
        """
        cmap defaults to its rc setting

        cmap is a colors.Colormap instance
        norm is a colors.Normalize instance to map luminance to 0-1

        Additional kwargs are matplotlib.artist properties
        """
        super().__init__(ax, norm=norm, cmap=cmap)
        self.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')
        fc = self.axes.patch.get_facecolor()
        bg = mcolors.to_rgba(fc, 0)
        bg = (np.array(bg)*255).astype(np.uint8)
        l, b, r, t = self.axes.bbox.extents
        width = (round(r) + 0.5) - (round(l) - 0.5)
        height = (round(t) + 0.5) - (round(b) - 0.5)
        # The extra cast-to-int is only needed for python2
        width = int(round(width * magnification))
        height = int(round(height * magnification))
        if self._rgbacache is None:
            A = self.to_rgba(self._A, bytes=True)
            self._rgbacache = A
            if self._A.ndim == 2:
                self.is_grayscale = self.cmap.is_gray()
        else:
            A = self._rgbacache
        vl = self.axes.viewLim
        im = _image.pcolor2(self._Ax, self._Ay, A,
                            height,
                            width,
                            (vl.x0, vl.x1, vl.y0, vl.y1),
                            bg)
        return im, l, b, IdentityTransform()

    def _check_unsampled_image(self, renderer):
        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-likes or None
            Monotonic arrays of shapes (N + 1,) and (M + 1,), respectively,
            specifying rectangle boundaries.  If None, will default to
            ``range(N + 1)`` and ``range(M + 1)``, respectively.
        A : array-like
            (M, N) ndarray or masked array of values to be colormapped, or
            (M, N, 3) RGB array, or (M, N, 4) RGBA array.
        """
        A = cbook.safe_masked_invalid(A, copy=True)
        if x is None:
            x = np.arange(0, A.shape[1]+1, dtype=np.float64)
        else:
            x = np.array(x, np.float64).ravel()
        if y is None:
            y = np.arange(0, A.shape[0]+1, dtype=np.float64)
        else:
            y = np.array(y, np.float64).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)))
        if A.ndim not in [2, 3]:
            raise ValueError("A must be 2D or 3D")
        if A.ndim == 3 and A.shape[2] == 1:
            A.shape = A.shape[:2]
        self.is_grayscale = False
        if A.ndim == 3:
            if A.shape[2] in [3, 4]:
                if ((A[:, :, 0] == A[:, :, 1]).all() and
                        (A[:, :, 0] == A[:, :, 2]).all()):
                    self.is_grayscale = True
            else:
                raise ValueError("3D arrays must have RGB or RGBA as last dim")

        # 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._rgbacache = 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
        try:
            return self._A[i, j]
        except IndexError:
            return None


class FigureImage(_ImageBase):
    zorder = 0

    _interpolation = 'nearest'

    def __init__(self, fig,
                 cmap=None,
                 norm=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,
            origin=origin
        )
        self.figure = fig
        self.ox = offsetx
        self.oy = offsety
        self.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
        fac = renderer.dpi/self.figure.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 = self.figure.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."""
        cm.ScalarMappable.set_array(self,
                                    cbook.safe_masked_invalid(A, copy=True))
        self.stale = True


class BboxImage(_ImageBase):
    """The Image class whose size is determined by the given bbox."""

    @cbook._delete_parameter("3.1", "interp_at_native")
    def __init__(self, bbox,
                 cmap=None,
                 norm=None,
                 interpolation=None,
                 origin=None,
                 filternorm=1,
                 filterrad=4.0,
                 resample=False,
                 interp_at_native=True,
                 **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,
            cmap=cmap,
            norm=norm,
            interpolation=interpolation,
            origin=origin,
            filternorm=filternorm,
            filterrad=filterrad,
            resample=resample,
            **kwargs
        )

        self.bbox = bbox
        self._interp_at_native = interp_at_native
        self._transform = IdentityTransform()

    @cbook.deprecated("3.1")
    @property
    def interp_at_native(self):
        return self._interp_at_native

    def get_transform(self):
        return self._transform

    def get_window_extent(self, renderer=None):
        if renderer is None:
            renderer = self.get_figure()._cachedRenderer

        if isinstance(self.bbox, BboxBase):
            return self.bbox
        elif callable(self.bbox):
            return self.bbox(renderer)
        else:
            raise ValueError("unknown type of bbox")

    def contains(self, mouseevent):
        """Test whether the mouse event occurred within the image."""
        inside, info = self._default_contains(mouseevent)
        if inside is not None:
            return inside, info

        if not self.get_visible():  # or self.get_figure()._renderer is None:
            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 = BboxTransform(Bbox([[0, 0], [1, 1]]), 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.

    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.
    format : str, optional
        The image file format assumed for reading the data. If not
        given, the format is deduced from the filename.  If nothing can
        be deduced, PNG is tried.

    Returns
    -------
    imagedata : :class:`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.

    Notes
    -----
    Matplotlib can only read PNGs natively. Further image formats are
    supported via the optional dependency on Pillow. Note, URL strings
    are not compatible with Pillow. Check the `Pillow documentation`_
    for more information.

    .. _Pillow documentation: http://pillow.readthedocs.io/en/latest/
    """
    if format is None:
        if isinstance(fname, str):
            parsed = urllib.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:
                basename, ext = os.path.splitext(fname)
                ext = ext.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'):
            basename, ext = os.path.splitext(fname.name)
            ext = ext.lower()[1:]
        else:
            ext = 'png'
    else:
        ext = format
    if ext != 'png':
        try:  # Try to load the image with PIL.
            from PIL import Image
        except ImportError:
            raise ValueError('Only know how to handle PNG; with Pillow '
                             'installed, Matplotlib can handle more images')
        with Image.open(fname) as image:
            return pil_to_array(image)
    from matplotlib import _png
    if isinstance(fname, str):
        parsed = urllib.parse.urlparse(fname)
        # If fname is a URL, download the data
        if len(parsed.scheme) > 1:
            from urllib import request
            fd = BytesIO(request.urlopen(fname).read())
            return _png.read_png(fd)
    with cbook.open_file_cm(fname, "rb") as file:
        return _png.read_png(file)


def imsave(fname, arr, vmin=None, vmax=None, cmap=None, format=None,
           origin=None, dpi=100, *, metadata=None, pil_kwargs=None):
    """
    Save an array as an image file.

    Parameters
    ----------
    fname : str or PathLike 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. The shape can be one of
        MxN (luminance), MxNx3 (RGB) or MxNx4 (RGBA).
    vmin, vmax : scalar, 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`, optional
        A Colormap instance or registered colormap name. The colormap
        maps scalar data to colors. It is ignored for RGB(A) data.
        Defaults to :rc:`image.cmap` ('viridis').
    format : str, optional
        The file format, e.g. 'png', 'pdf', 'svg', ...  The behavior when this
        is unset is documented under *fname*.
    origin : {'upper', 'lower'}, optional
        Indicates whether the ``(0, 0)`` index of the array is in the upper
        left or lower left corner of the axes.  Defaults to :rc:`image.origin`
        ('upper').
    dpi : int
        The DPI to store in the metadata of the file.  This does not affect the
        resolution of the output image.
    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.
    pil_kwargs : dict, optional
        If set to a non-None value, always use Pillow to save the figure
        (regardless of the output format), and pass these keyword arguments to
        `PIL.Image.save`.

        If the 'pnginfo' key is present, it completely overrides
        *metadata*, including the default 'Software' key.
    """
    from matplotlib.figure import Figure
    from matplotlib import _png
    if isinstance(fname, os.PathLike):
        fname = os.fspath(fname)
    if format is None:
        format = (Path(fname).suffix[1:] if isinstance(fname, str)
                  else 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.
        sm = cm.ScalarMappable(cmap=cmap)
        sm.set_clim(vmin, vmax)
        if origin is None:
            origin = rcParams["image.origin"]
        if origin == "lower":
            arr = arr[::-1]
        rgba = sm.to_rgba(arr, bytes=True)
        if format == "png" and pil_kwargs is None:
            with cbook.open_file_cm(fname, "wb") as file:
                _png.write_png(rgba, file, dpi=dpi, metadata=metadata)
        else:
            try:
                from PIL import Image
                from PIL.PngImagePlugin import PngInfo
            except ImportError as exc:
                if pil_kwargs is not None:
                    raise ImportError("Setting 'pil_kwargs' requires Pillow")
                else:
                    raise ImportError(f"Saving to {format} requires Pillow")
            if pil_kwargs is None:
                pil_kwargs = {}
            pil_shape = (rgba.shape[1], rgba.shape[0])
            image = Image.frombuffer(
                "RGBA", pil_shape, rgba, "raw", "RGBA", 0, 1)
            if format == "png" and metadata:
                # cf. backend_agg's print_png.
                if "pnginfo" in pil_kwargs:
                    cbook._warn_external("'metadata' is overridden by the "
                                         "'pnginfo' entry in 'pil_kwargs'.")
                else:
                    pnginfo = PngInfo()
                    for k, v in metadata.items():
                        pnginfo.add_text(k, v)
                    pil_kwargs["pnginfo"] = pnginfo
            if format in ["jpg", "jpeg"]:
                format = "jpeg"  # Pillow doesn't recognize "jpg".
                color = tuple(
                    int(x * 255)
                    for x in mcolors.to_rgb(rcParams["savefig.facecolor"]))
                background = 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 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:
            raise RuntimeError('Unknown image mode')
        return np.asarray(pilImage)  # return MxNx4 RGBA array


def thumbnail(infile, thumbfile, scale=0.1, interpolation='bilinear',
              preview=False):
    """
    Make a thumbnail of image in *infile* with output filename *thumbfile*.

    See :doc:`/gallery/misc/image_thumbnail_sgskip`.

    Parameters
    ----------
    infile : str or file-like
        The image file -- must be PNG, or Pillow-readable if you have Pillow_
        installed.

        .. _Pillow: http://python-pillow.org/

    thumbfile : str or file-like
        The thumbnail filename.

    scale : float, optional
        The scale factor for the thumbnail.

    interpolation : str, optional
        The interpolation scheme used in the resampling. See the
        *interpolation* parameter of `~.Axes.imshow` for possible values.

    preview : bool, optional
        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 `~matplotlib.figure.savefig` would normally do.

    Returns
    -------
    figure : `~.figure.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