from __future__ import division
import torch
import sys
import math
from PIL import Image, ImageOps, ImageEnhance, PILLOW_VERSION
try:
    import accimage
except ImportError:
    accimage = None
import numpy as np
import numbers
import collections
import warnings

if sys.version_info < (3, 3):
    Sequence = collections.Sequence
    Iterable = collections.Iterable
else:
    Sequence = collections.abc.Sequence
    Iterable = collections.abc.Iterable


def _is_pil_image(img):
    if accimage is not None:
        return isinstance(img, (Image.Image, accimage.Image))
    else:
        return isinstance(img, Image.Image)


def _is_tensor_image(img):
    return torch.is_tensor(img) and img.ndimension() == 3


def _is_numpy_image(img):
    return isinstance(img, np.ndarray) and (img.ndim in {2, 3})


def to_tensor(pic):
    """Convert a ``PIL Image`` or ``numpy.ndarray`` to tensor.

    See ``ToTensor`` for more details.

    Args:
        pic (PIL Image or numpy.ndarray): Image to be converted to tensor.

    Returns:
        Tensor: Converted image.
    """
    if not(_is_pil_image(pic) or _is_numpy_image(pic)):
        raise TypeError('pic should be PIL Image or ndarray. Got {}'.format(type(pic)))

    if isinstance(pic, np.ndarray):
        # handle numpy array
        if pic.ndim == 2:
            pic = pic[:, :, None]

        img = torch.from_numpy(pic.transpose((2, 0, 1)))
        # backward compatibility
        if isinstance(img, torch.ByteTensor):
            return img.float().div(255)
        else:
            return img

    if accimage is not None and isinstance(pic, accimage.Image):
        nppic = np.zeros([pic.channels, pic.height, pic.width], dtype=np.float32)
        pic.copyto(nppic)
        return torch.from_numpy(nppic)

    # handle PIL Image
    if pic.mode == 'I':
        img = torch.from_numpy(np.array(pic, np.int32, copy=False))
    elif pic.mode == 'I;16':
        img = torch.from_numpy(np.array(pic, np.int16, copy=False))
    elif pic.mode == 'F':
        img = torch.from_numpy(np.array(pic, np.float32, copy=False))
    elif pic.mode == '1':
        img = 255 * torch.from_numpy(np.array(pic, np.uint8, copy=False))
    else:
        img = torch.ByteTensor(torch.ByteStorage.from_buffer(pic.tobytes()))
    # PIL image mode: L, LA, P, I, F, RGB, YCbCr, RGBA, CMYK
    if pic.mode == 'YCbCr':
        nchannel = 3
    elif pic.mode == 'I;16':
        nchannel = 1
    else:
        nchannel = len(pic.mode)
    img = img.view(pic.size[1], pic.size[0], nchannel)
    # put it from HWC to CHW format
    # yikes, this transpose takes 80% of the loading time/CPU
    img = img.transpose(0, 1).transpose(0, 2).contiguous()
    if isinstance(img, torch.ByteTensor):
        return img.float().div(255)
    else:
        return img


def to_pil_image(pic, mode=None):
    """Convert a tensor or an ndarray to PIL Image.

    See :class:`~torchvision.transforms.ToPILImage` for more details.

    Args:
        pic (Tensor or numpy.ndarray): Image to be converted to PIL Image.
        mode (`PIL.Image mode`_): color space and pixel depth of input data (optional).

    .. _PIL.Image mode: https://pillow.readthedocs.io/en/latest/handbook/concepts.html#concept-modes

    Returns:
        PIL Image: Image converted to PIL Image.
    """
    if not(isinstance(pic, torch.Tensor) or isinstance(pic, np.ndarray)):
        raise TypeError('pic should be Tensor or ndarray. Got {}.'.format(type(pic)))

    elif isinstance(pic, torch.Tensor):
        if pic.ndimension() not in {2, 3}:
            raise ValueError('pic should be 2/3 dimensional. Got {} dimensions.'.format(pic.ndimension()))

        elif pic.ndimension() == 2:
            # if 2D image, add channel dimension (CHW)
            pic = pic.unsqueeze(0)

    elif isinstance(pic, np.ndarray):
        if pic.ndim not in {2, 3}:
            raise ValueError('pic should be 2/3 dimensional. Got {} dimensions.'.format(pic.ndim))

        elif pic.ndim == 2:
            # if 2D image, add channel dimension (HWC)
            pic = np.expand_dims(pic, 2)

    npimg = pic
    if isinstance(pic, torch.FloatTensor):
        pic = pic.mul(255).byte()
    if isinstance(pic, torch.Tensor):
        npimg = np.transpose(pic.numpy(), (1, 2, 0))

    if not isinstance(npimg, np.ndarray):
        raise TypeError('Input pic must be a torch.Tensor or NumPy ndarray, ' +
                        'not {}'.format(type(npimg)))

    if npimg.shape[2] == 1:
        expected_mode = None
        npimg = npimg[:, :, 0]
        if npimg.dtype == np.uint8:
            expected_mode = 'L'
        elif npimg.dtype == np.int16:
            expected_mode = 'I;16'
        elif npimg.dtype == np.int32:
            expected_mode = 'I'
        elif npimg.dtype == np.float32:
            expected_mode = 'F'
        if mode is not None and mode != expected_mode:
            raise ValueError("Incorrect mode ({}) supplied for input type {}. Should be {}"
                             .format(mode, np.dtype, expected_mode))
        mode = expected_mode

    elif npimg.shape[2] == 2:
        permitted_2_channel_modes = ['LA']
        if mode is not None and mode not in permitted_2_channel_modes:
            raise ValueError("Only modes {} are supported for 2D inputs".format(permitted_2_channel_modes))

        if mode is None and npimg.dtype == np.uint8:
            mode = 'LA'

    elif npimg.shape[2] == 4:
        permitted_4_channel_modes = ['RGBA', 'CMYK', 'RGBX']
        if mode is not None and mode not in permitted_4_channel_modes:
            raise ValueError("Only modes {} are supported for 4D inputs".format(permitted_4_channel_modes))

        if mode is None and npimg.dtype == np.uint8:
            mode = 'RGBA'
    else:
        permitted_3_channel_modes = ['RGB', 'YCbCr', 'HSV']
        if mode is not None and mode not in permitted_3_channel_modes:
            raise ValueError("Only modes {} are supported for 3D inputs".format(permitted_3_channel_modes))
        if mode is None and npimg.dtype == np.uint8:
            mode = 'RGB'

    if mode is None:
        raise TypeError('Input type {} is not supported'.format(npimg.dtype))

    return Image.fromarray(npimg, mode=mode)


def normalize(tensor, mean, std, inplace=False):
    """Normalize a tensor image with mean and standard deviation.

    .. note::
        This transform acts out of place by default, i.e., it does not mutates the input tensor.

    See :class:`~torchvision.transforms.Normalize` for more details.

    Args:
        tensor (Tensor): Tensor image of size (C, H, W) to be normalized.
        mean (sequence): Sequence of means for each channel.
        std (sequence): Sequence of standard deviations for each channel.

    Returns:
        Tensor: Normalized Tensor image.
    """
    if not _is_tensor_image(tensor):
        raise TypeError('tensor is not a torch image.')

    if not inplace:
        tensor = tensor.clone()

    mean = torch.as_tensor(mean, dtype=torch.float32, device=tensor.device)
    std = torch.as_tensor(std, dtype=torch.float32, device=tensor.device)
    tensor.sub_(mean[:, None, None]).div_(std[:, None, None])
    return tensor


def resize(img, size, interpolation=Image.BILINEAR):
    r"""Resize the input PIL Image to the given size.

    Args:
        img (PIL Image): Image to be resized.
        size (sequence or int): Desired output size. If size is a sequence like
            (h, w), the output size will be matched to this. If size is an int,
            the smaller edge of the image will be matched to this number maintaing
            the aspect ratio. i.e, if height > width, then image will be rescaled to
            :math:`\left(\text{size} \times \frac{\text{height}}{\text{width}}, \text{size}\right)`
        interpolation (int, optional): Desired interpolation. Default is
            ``PIL.Image.BILINEAR``

    Returns:
        PIL Image: Resized image.
    """
    if not _is_pil_image(img):
        raise TypeError('img should be PIL Image. Got {}'.format(type(img)))
    if not (isinstance(size, int) or (isinstance(size, Iterable) and len(size) == 2)):
        raise TypeError('Got inappropriate size arg: {}'.format(size))

    if isinstance(size, int):
        w, h = img.size
        if (w <= h and w == size) or (h <= w and h == size):
            return img
        if w < h:
            ow = size
            oh = int(size * h / w)
            return img.resize((ow, oh), interpolation)
        else:
            oh = size
            ow = int(size * w / h)
            return img.resize((ow, oh), interpolation)
    else:
        return img.resize(size[::-1], interpolation)


def scale(*args, **kwargs):
    warnings.warn("The use of the transforms.Scale transform is deprecated, " +
                  "please use transforms.Resize instead.")
    return resize(*args, **kwargs)


def pad(img, padding, fill=0, padding_mode='constant'):
    r"""Pad the given PIL Image on all sides with specified padding mode and fill value.

    Args:
        img (PIL Image): Image to be padded.
        padding (int or tuple): Padding on each border. If a single int is provided this
            is used to pad all borders. If tuple of length 2 is provided this is the padding
            on left/right and top/bottom respectively. If a tuple of length 4 is provided
            this is the padding for the left, top, right and bottom borders
            respectively.
        fill: Pixel fill value for constant fill. Default is 0. If a tuple of
            length 3, it is used to fill R, G, B channels respectively.
            This value is only used when the padding_mode is constant
        padding_mode: Type of padding. Should be: constant, edge, reflect or symmetric. Default is constant.

            - constant: pads with a constant value, this value is specified with fill

            - edge: pads with the last value on the edge of the image

            - reflect: pads with reflection of image (without repeating the last value on the edge)

                       padding [1, 2, 3, 4] with 2 elements on both sides in reflect mode
                       will result in [3, 2, 1, 2, 3, 4, 3, 2]

            - symmetric: pads with reflection of image (repeating the last value on the edge)

                         padding [1, 2, 3, 4] with 2 elements on both sides in symmetric mode
                         will result in [2, 1, 1, 2, 3, 4, 4, 3]

    Returns:
        PIL Image: Padded image.
    """
    if not _is_pil_image(img):
        raise TypeError('img should be PIL Image. Got {}'.format(type(img)))

    if not isinstance(padding, (numbers.Number, tuple)):
        raise TypeError('Got inappropriate padding arg')
    if not isinstance(fill, (numbers.Number, str, tuple)):
        raise TypeError('Got inappropriate fill arg')
    if not isinstance(padding_mode, str):
        raise TypeError('Got inappropriate padding_mode arg')

    if isinstance(padding, Sequence) and len(padding) not in [2, 4]:
        raise ValueError("Padding must be an int or a 2, or 4 element tuple, not a " +
                         "{} element tuple".format(len(padding)))

    assert padding_mode in ['constant', 'edge', 'reflect', 'symmetric'], \
        'Padding mode should be either constant, edge, reflect or symmetric'

    if padding_mode == 'constant':
        if img.mode == 'P':
            palette = img.getpalette()
            image = ImageOps.expand(img, border=padding, fill=fill)
            image.putpalette(palette)
            return image

        return ImageOps.expand(img, border=padding, fill=fill)
    else:
        if isinstance(padding, int):
            pad_left = pad_right = pad_top = pad_bottom = padding
        if isinstance(padding, Sequence) and len(padding) == 2:
            pad_left = pad_right = padding[0]
            pad_top = pad_bottom = padding[1]
        if isinstance(padding, Sequence) and len(padding) == 4:
            pad_left = padding[0]
            pad_top = padding[1]
            pad_right = padding[2]
            pad_bottom = padding[3]

        if img.mode == 'P':
            palette = img.getpalette()
            img = np.asarray(img)
            img = np.pad(img, ((pad_top, pad_bottom), (pad_left, pad_right)), padding_mode)
            img = Image.fromarray(img)
            img.putpalette(palette)
            return img

        img = np.asarray(img)
        # RGB image
        if len(img.shape) == 3:
            img = np.pad(img, ((pad_top, pad_bottom), (pad_left, pad_right), (0, 0)), padding_mode)
        # Grayscale image
        if len(img.shape) == 2:
            img = np.pad(img, ((pad_top, pad_bottom), (pad_left, pad_right)), padding_mode)

        return Image.fromarray(img)


def crop(img, i, j, h, w):
    """Crop the given PIL Image.

    Args:
        img (PIL Image): Image to be cropped.
        i (int): i in (i,j) i.e coordinates of the upper left corner.
        j (int): j in (i,j) i.e coordinates of the upper left corner.
        h (int): Height of the cropped image.
        w (int): Width of the cropped image.

    Returns:
        PIL Image: Cropped image.
    """
    if not _is_pil_image(img):
        raise TypeError('img should be PIL Image. Got {}'.format(type(img)))

    return img.crop((j, i, j + w, i + h))


def center_crop(img, output_size):
    if isinstance(output_size, numbers.Number):
        output_size = (int(output_size), int(output_size))
    w, h = img.size
    th, tw = output_size
    i = int(round((h - th) / 2.))
    j = int(round((w - tw) / 2.))
    return crop(img, i, j, th, tw)


def resized_crop(img, i, j, h, w, size, interpolation=Image.BILINEAR):
    """Crop the given PIL Image and resize it to desired size.

    Notably used in :class:`~torchvision.transforms.RandomResizedCrop`.

    Args:
        img (PIL Image): Image to be cropped.
        i (int): i in (i,j) i.e coordinates of the upper left corner
        j (int): j in (i,j) i.e coordinates of the upper left corner
        h (int): Height of the cropped image.
        w (int): Width of the cropped image.
        size (sequence or int): Desired output size. Same semantics as ``resize``.
        interpolation (int, optional): Desired interpolation. Default is
            ``PIL.Image.BILINEAR``.
    Returns:
        PIL Image: Cropped image.
    """
    assert _is_pil_image(img), 'img should be PIL Image'
    img = crop(img, i, j, h, w)
    img = resize(img, size, interpolation)
    return img


def hflip(img):
    """Horizontally flip the given PIL Image.

    Args:
        img (PIL Image): Image to be flipped.

    Returns:
        PIL Image:  Horizontall flipped image.
    """
    if not _is_pil_image(img):
        raise TypeError('img should be PIL Image. Got {}'.format(type(img)))

    return img.transpose(Image.FLIP_LEFT_RIGHT)


def _get_perspective_coeffs(startpoints, endpoints):
    """Helper function to get the coefficients (a, b, c, d, e, f, g, h) for the perspective transforms.

    In Perspective Transform each pixel (x, y) in the orignal image gets transformed as,
     (x, y) -> ( (ax + by + c) / (gx + hy + 1), (dx + ey + f) / (gx + hy + 1) )

    Args:
        List containing [top-left, top-right, bottom-right, bottom-left] of the orignal image,
        List containing [top-left, top-right, bottom-right, bottom-left] of the transformed
                   image
    Returns:
        octuple (a, b, c, d, e, f, g, h) for transforming each pixel.
    """
    matrix = []

    for p1, p2 in zip(endpoints, startpoints):
        matrix.append([p1[0], p1[1], 1, 0, 0, 0, -p2[0] * p1[0], -p2[0] * p1[1]])
        matrix.append([0, 0, 0, p1[0], p1[1], 1, -p2[1] * p1[0], -p2[1] * p1[1]])

    A = torch.tensor(matrix, dtype=torch.float)
    B = torch.tensor(startpoints, dtype=torch.float).view(8)
    res = torch.gels(B, A)[0]
    return res.squeeze_(1).tolist()


def perspective(img, startpoints, endpoints, interpolation=Image.BICUBIC):
    """Perform perspective transform of the given PIL Image.

    Args:
        img (PIL Image): Image to be transformed.
        coeffs (tuple) : 8-tuple (a, b, c, d, e, f, g, h) which contains the coefficients.
                            for a perspective transform.
        interpolation: Default- Image.BICUBIC
    Returns:
        PIL Image:  Perspectively transformed Image.
    """
    if not _is_pil_image(img):
        raise TypeError('img should be PIL Image. Got {}'.format(type(img)))

    coeffs = _get_perspective_coeffs(startpoints, endpoints)
    return img.transform(img.size, Image.PERSPECTIVE, coeffs, interpolation)


def vflip(img):
    """Vertically flip the given PIL Image.

    Args:
        img (PIL Image): Image to be flipped.

    Returns:
        PIL Image:  Vertically flipped image.
    """
    if not _is_pil_image(img):
        raise TypeError('img should be PIL Image. Got {}'.format(type(img)))

    return img.transpose(Image.FLIP_TOP_BOTTOM)


def five_crop(img, size):
    """Crop the given PIL Image into four corners and the central crop.

    .. Note::
        This transform returns a tuple of images and there may be a
        mismatch in the number of inputs and targets your ``Dataset`` returns.

    Args:
       size (sequence or int): Desired output size of the crop. If size is an
           int instead of sequence like (h, w), a square crop (size, size) is
           made.

    Returns:
       tuple: tuple (tl, tr, bl, br, center)
                Corresponding top left, top right, bottom left, bottom right and center crop.
    """
    if isinstance(size, numbers.Number):
        size = (int(size), int(size))
    else:
        assert len(size) == 2, "Please provide only two dimensions (h, w) for size."

    w, h = img.size
    crop_h, crop_w = size
    if crop_w > w or crop_h > h:
        raise ValueError("Requested crop size {} is bigger than input size {}".format(size,
                                                                                      (h, w)))
    tl = img.crop((0, 0, crop_w, crop_h))
    tr = img.crop((w - crop_w, 0, w, crop_h))
    bl = img.crop((0, h - crop_h, crop_w, h))
    br = img.crop((w - crop_w, h - crop_h, w, h))
    center = center_crop(img, (crop_h, crop_w))
    return (tl, tr, bl, br, center)


def ten_crop(img, size, vertical_flip=False):
    r"""Crop the given PIL Image into four corners and the central crop plus the
        flipped version of these (horizontal flipping is used by default).

    .. Note::
        This transform returns a tuple of images and there may be a
        mismatch in the number of inputs and targets your ``Dataset`` returns.

    Args:
       size (sequence or int): Desired output size of the crop. If size is an
            int instead of sequence like (h, w), a square crop (size, size) is
            made.
       vertical_flip (bool): Use vertical flipping instead of horizontal

    Returns:
       tuple: tuple (tl, tr, bl, br, center, tl_flip, tr_flip, bl_flip, br_flip, center_flip)
                Corresponding top left, top right, bottom left, bottom right and center crop
                and same for the flipped image.
    """
    if isinstance(size, numbers.Number):
        size = (int(size), int(size))
    else:
        assert len(size) == 2, "Please provide only two dimensions (h, w) for size."

    first_five = five_crop(img, size)

    if vertical_flip:
        img = vflip(img)
    else:
        img = hflip(img)

    second_five = five_crop(img, size)
    return first_five + second_five


def adjust_brightness(img, brightness_factor):
    """Adjust brightness of an Image.

    Args:
        img (PIL Image): PIL Image to be adjusted.
        brightness_factor (float):  How much to adjust the brightness. Can be
            any non negative number. 0 gives a black image, 1 gives the
            original image while 2 increases the brightness by a factor of 2.

    Returns:
        PIL Image: Brightness adjusted image.
    """
    if not _is_pil_image(img):
        raise TypeError('img should be PIL Image. Got {}'.format(type(img)))

    enhancer = ImageEnhance.Brightness(img)
    img = enhancer.enhance(brightness_factor)
    return img


def adjust_contrast(img, contrast_factor):
    """Adjust contrast of an Image.

    Args:
        img (PIL Image): PIL Image to be adjusted.
        contrast_factor (float): How much to adjust the contrast. Can be any
            non negative number. 0 gives a solid gray image, 1 gives the
            original image while 2 increases the contrast by a factor of 2.

    Returns:
        PIL Image: Contrast adjusted image.
    """
    if not _is_pil_image(img):
        raise TypeError('img should be PIL Image. Got {}'.format(type(img)))

    enhancer = ImageEnhance.Contrast(img)
    img = enhancer.enhance(contrast_factor)
    return img


def adjust_saturation(img, saturation_factor):
    """Adjust color saturation of an image.

    Args:
        img (PIL Image): PIL Image to be adjusted.
        saturation_factor (float):  How much to adjust the saturation. 0 will
            give a black and white image, 1 will give the original image while
            2 will enhance the saturation by a factor of 2.

    Returns:
        PIL Image: Saturation adjusted image.
    """
    if not _is_pil_image(img):
        raise TypeError('img should be PIL Image. Got {}'.format(type(img)))

    enhancer = ImageEnhance.Color(img)
    img = enhancer.enhance(saturation_factor)
    return img


def adjust_hue(img, hue_factor):
    """Adjust hue of an image.

    The image hue is adjusted by converting the image to HSV and
    cyclically shifting the intensities in the hue channel (H).
    The image is then converted back to original image mode.

    `hue_factor` is the amount of shift in H channel and must be in the
    interval `[-0.5, 0.5]`.

    See `Hue`_ for more details.

    .. _Hue: https://en.wikipedia.org/wiki/Hue

    Args:
        img (PIL Image): PIL Image to be adjusted.
        hue_factor (float):  How much to shift the hue channel. Should be in
            [-0.5, 0.5]. 0.5 and -0.5 give complete reversal of hue channel in
            HSV space in positive and negative direction respectively.
            0 means no shift. Therefore, both -0.5 and 0.5 will give an image
            with complementary colors while 0 gives the original image.

    Returns:
        PIL Image: Hue adjusted image.
    """
    if not(-0.5 <= hue_factor <= 0.5):
        raise ValueError('hue_factor is not in [-0.5, 0.5].'.format(hue_factor))

    if not _is_pil_image(img):
        raise TypeError('img should be PIL Image. Got {}'.format(type(img)))

    input_mode = img.mode
    if input_mode in {'L', '1', 'I', 'F'}:
        return img

    h, s, v = img.convert('HSV').split()

    np_h = np.array(h, dtype=np.uint8)
    # uint8 addition take cares of rotation across boundaries
    with np.errstate(over='ignore'):
        np_h += np.uint8(hue_factor * 255)
    h = Image.fromarray(np_h, 'L')

    img = Image.merge('HSV', (h, s, v)).convert(input_mode)
    return img


def adjust_gamma(img, gamma, gain=1):
    r"""Perform gamma correction on an image.

    Also known as Power Law Transform. Intensities in RGB mode are adjusted
    based on the following equation:

    .. math::
        I_{\text{out}} = 255 \times \text{gain} \times \left(\frac{I_{\text{in}}}{255}\right)^{\gamma}

    See `Gamma Correction`_ for more details.

    .. _Gamma Correction: https://en.wikipedia.org/wiki/Gamma_correction

    Args:
        img (PIL Image): PIL Image to be adjusted.
        gamma (float): Non negative real number, same as :math:`\gamma` in the equation.
            gamma larger than 1 make the shadows darker,
            while gamma smaller than 1 make dark regions lighter.
        gain (float): The constant multiplier.
    """
    if not _is_pil_image(img):
        raise TypeError('img should be PIL Image. Got {}'.format(type(img)))

    if gamma < 0:
        raise ValueError('Gamma should be a non-negative real number')

    input_mode = img.mode
    img = img.convert('RGB')

    gamma_map = [255 * gain * pow(ele / 255., gamma) for ele in range(256)] * 3
    img = img.point(gamma_map)  # use PIL's point-function to accelerate this part

    img = img.convert(input_mode)
    return img


def rotate(img, angle, resample=False, expand=False, center=None):
    """Rotate the image by angle.


    Args:
        img (PIL Image): PIL Image to be rotated.
        angle (float or int): In degrees degrees counter clockwise order.
        resample (``PIL.Image.NEAREST`` or ``PIL.Image.BILINEAR`` or ``PIL.Image.BICUBIC``, optional):
            An optional resampling filter. See `filters`_ for more information.
            If omitted, or if the image has mode "1" or "P", it is set to ``PIL.Image.NEAREST``.
        expand (bool, optional): Optional expansion flag.
            If true, expands the output image to make it large enough to hold the entire rotated image.
            If false or omitted, make the output image the same size as the input image.
            Note that the expand flag assumes rotation around the center and no translation.
        center (2-tuple, optional): Optional center of rotation.
            Origin is the upper left corner.
            Default is the center of the image.

    .. _filters: https://pillow.readthedocs.io/en/latest/handbook/concepts.html#filters

    """

    if not _is_pil_image(img):
        raise TypeError('img should be PIL Image. Got {}'.format(type(img)))

    return img.rotate(angle, resample, expand, center)


def _get_inverse_affine_matrix(center, angle, translate, scale, shear):
    # Helper method to compute inverse matrix for affine transformation

    # As it is explained in PIL.Image.rotate
    # We need compute INVERSE of affine transformation matrix: M = T * C * RSS * C^-1
    # where T is translation matrix: [1, 0, tx | 0, 1, ty | 0, 0, 1]
    #       C is translation matrix to keep center: [1, 0, cx | 0, 1, cy | 0, 0, 1]
    #       RSS is rotation with scale and shear matrix
    #       RSS(a, scale, shear) = [ cos(a)*scale    -sin(a + shear)*scale     0]
    #                              [ sin(a)*scale    cos(a + shear)*scale     0]
    #                              [     0                  0          1]
    # Thus, the inverse is M^-1 = C * RSS^-1 * C^-1 * T^-1

    angle = math.radians(angle)
    shear = math.radians(shear)
    scale = 1.0 / scale

    # Inverted rotation matrix with scale and shear
    d = math.cos(angle + shear) * math.cos(angle) + math.sin(angle + shear) * math.sin(angle)
    matrix = [
        math.cos(angle + shear), math.sin(angle + shear), 0,
        -math.sin(angle), math.cos(angle), 0
    ]
    matrix = [scale / d * m for m in matrix]

    # Apply inverse of translation and of center translation: RSS^-1 * C^-1 * T^-1
    matrix[2] += matrix[0] * (-center[0] - translate[0]) + matrix[1] * (-center[1] - translate[1])
    matrix[5] += matrix[3] * (-center[0] - translate[0]) + matrix[4] * (-center[1] - translate[1])

    # Apply center translation: C * RSS^-1 * C^-1 * T^-1
    matrix[2] += center[0]
    matrix[5] += center[1]
    return matrix


def affine(img, angle, translate, scale, shear, resample=0, fillcolor=None):
    """Apply affine transformation on the image keeping image center invariant

    Args:
        img (PIL Image): PIL Image to be rotated.
        angle (float or int): rotation angle in degrees between -180 and 180, clockwise direction.
        translate (list or tuple of integers): horizontal and vertical translations (post-rotation translation)
        scale (float): overall scale
        shear (float): shear angle value in degrees between -180 to 180, clockwise direction.
        resample (``PIL.Image.NEAREST`` or ``PIL.Image.BILINEAR`` or ``PIL.Image.BICUBIC``, optional):
            An optional resampling filter.
            See `filters`_ for more information.
            If omitted, or if the image has mode "1" or "P", it is set to ``PIL.Image.NEAREST``.
        fillcolor (int): Optional fill color for the area outside the transform in the output image. (Pillow>=5.0.0)
    """
    if not _is_pil_image(img):
        raise TypeError('img should be PIL Image. Got {}'.format(type(img)))

    assert isinstance(translate, (tuple, list)) and len(translate) == 2, \
        "Argument translate should be a list or tuple of length 2"

    assert scale > 0.0, "Argument scale should be positive"

    output_size = img.size
    center = (img.size[0] * 0.5 + 0.5, img.size[1] * 0.5 + 0.5)
    matrix = _get_inverse_affine_matrix(center, angle, translate, scale, shear)
    kwargs = {"fillcolor": fillcolor} if PILLOW_VERSION[0] == '5' else {}
    return img.transform(output_size, Image.AFFINE, matrix, resample, **kwargs)


def to_grayscale(img, num_output_channels=1):
    """Convert image to grayscale version of image.

    Args:
        img (PIL Image): Image to be converted to grayscale.

    Returns:
        PIL Image: Grayscale version of the image.
            if num_output_channels = 1 : returned image is single channel

            if num_output_channels = 3 : returned image is 3 channel with r = g = b
    """
    if not _is_pil_image(img):
        raise TypeError('img should be PIL Image. Got {}'.format(type(img)))

    if num_output_channels == 1:
        img = img.convert('L')
    elif num_output_channels == 3:
        img = img.convert('L')
        np_img = np.array(img, dtype=np.uint8)
        np_img = np.dstack([np_img, np_img, np_img])
        img = Image.fromarray(np_img, 'RGB')
    else:
        raise ValueError('num_output_channels should be either 1 or 3')

    return img
