import numpy as np
from scipy.linalg import lu

import xarray as xr

class InvalidDimException(Exception):
    "Raised when the program can not identify (index of images, x, y) axes."
    def __init__(self, dims):
        if len(dims)>3:
            self.message = 'The input data must have two or three axes: (index of images(alternative), x, y)'
        else:
            self.message = 'Can not identify (index of images(alternative), x, y) from ' + str(dims)
        super().__init__(self.message)


class DataSizeException(Exception):
    "Raised when the shape of the data is not correct."
    def __init__(self):
        self.message = 'The input data size does not match.'
        super().__init__(self.message)


class FringeRemoval():
    """A class for fringes removal
    """
    
    def __init__(self) -> None:
        """Initialize the class
        """
        self.nimgsR = 0 # The number of the reference images
        self.xdim = 0 # The shape of x axis
        self.ydim = 0 # The shape of y axis
        
        self._mask = None # The mask array to choose the region of interest for fringes removal
        
        self.reshape=True # If it is necessary to reshape the data from (index of images(alternative), x, y) to (y, x, index of images(alternative))
        
        self.P = None
        self.L = None
        self.U = None
        
    def reshape_data(self, data):
        """The function is to reshape the data to the correct shape.
        In order to minimize the calculation time, the data has to have a shape of (y, x, index of images(alternative)).
        However, usually the input data has a shape of (index of images(alternative), x, y).
        It can also convert the xarray DataArray and Dataset to numpy array.

        :param data: The input data.
        :type data: xarray, numpy array or list
        :raises InvalidDimException: Raised when the program can not identify (index of images, x, y) axes.
        :raises InvalidDimException: Raised when the shape of the data is not correct.
        :return: The data with correct shape
        :rtype: xarray, numpy array or list
        """
        
        if data is None:
            return data

        if isinstance(data, type(xr.DataArray())):
            
            dims = data.dims
            
            if len(dims)>3:
                raise InvalidDimException(dims)
            
            xAxis = None
            yAxis = None
            if len(dims) == 2:
                imageAxis = ''
            else:
                imageAxis = None
                
            for dim in dims:
                if (dim == 'x') or ('_x' in dim):
                    xAxis = dim
                elif (dim == 'y') or ('_y' in dim):
                    yAxis = dim
                else:
                    imageAxis = dim
                    
            if (xAxis is None) or (yAxis is None) or (imageAxis is None):
                raise InvalidDimException(dims)
            
            if len(dims) == 2:
                data = data.transpose(yAxis, xAxis)
            else:
                data = data.transpose(yAxis, xAxis, imageAxis)
                
            data = data.to_numpy()
            
        else:
            data = np.array(data)
            if len(data.shape) == 3:
                data = np.swapaxes(data, 0, 2)
                # data = np.swapaxes(data, 0, 1)
            elif len(data.shape) == 2:
                data = np.swapaxes(data, 0, 1)
        
        return data
    
    @property
    def referenceImages(self):
        res = self._referenceImages.reshape(self.ydim, self.xdim, self.nimgsR)
        res = np.swapaxes(res, 0, 2)
        return res
    
    @referenceImages.setter
    def referenceImages(self, value):
        if self.reshape:
            value = self.reshape_data(value)
        elif isinstance(value, type(xr.DataArray())):
            value = value.to_numpy()
            
        self.nimgsR = value.shape[2]
        self.xdim = value.shape[1]
        self.ydim = value.shape[0]
        
        self._referenceImages = (value.reshape(self.xdim * self.ydim, self.nimgsR).astype(np.float32))

    def add_reference_images(self, data):
        """Add a new reference images

        :param data: The new reference image.
        :type data: xarray, numpy array or list
        :raises DataSizeException: Raised when the shape of the data is not correct.
        """
        
        if self.reshape:
            data = self.reshape_data(data)
        elif isinstance(data, type(xr.DataArray())):
            data = data.to_numpy()
        
        if not ((data.shape[0]==self.ydim) and (data.shape[1]==self.xdim)):
            raise DataSizeException

        data = data.reshape(self.xdim * self.ydim)
        
        self._referenceImages = np.append(self._referenceImages, data, axis=1)
    
    def _remove_first_reference_images(self):
        """Remove the first reference images
        """
        self._referenceImages = np.delete(self._referenceImages, 0, axis=1)
    
    def update_reference_images(self, data):
        """Update the reference images set by removing the first one and adding a new one at the end.

        :param data: The new reference image.
        :type data: xarray, numpy array or list
        """
        self._remove_first_reference_images()
        self.add_reference_images(data)
        
        if self._mask is None:
            self.mask = np.ones((self.ydim, self.xdim), dtype=np.uint8)

        self.decompose_referenceImages()
        
    @property
    def mask(self):
        return self._mask
    
    @mask.setter
    def mask(self, value):
        if self.reshape:
            value = self.reshape_data(value)
        elif isinstance(value, type(xr.DataArray())):
            value = value.to_numpy()
            
        if not ((value.shape[0]==self.ydim) and (value.shape[1]==self.xdim)):
            raise DataSizeException
        
        self._mask = value
        self.k = np.where(self._mask.flatten() == 1)[0]
    
    def decompose_referenceImages(self):
        self.P, self.L, self.U = lu(self._referenceImages[self.k, :].T @ self._referenceImages[self.k, :], permute_l = False, p_indices = True)
    
    def solve_coefficient(self):
        pass
    
    def _fringe_removal(self, absorptionImages, referenceImages=None, mask=None, reshape=None, dask='forbidden'):
        if not reshape is None:
            self.reshape = reshape
        if not referenceImages is None:
            self.referenceImages = referenceImages
        if not mask is None:
            self.mask = mask
        if self.P is None:
            self.decompose_referenceImages()
        
        absorptionImages = np.atleast_3d(absorptionImages)
            
        if self.reshape:
            absorptionImages = self.reshape_data(absorptionImages)
        
        self.nimgs = absorptionImages.shape[2]
        absorptionImages = (absorptionImages.reshape(self.xdim * self.ydim, self.nimgs).astype(np.float32))
        
        optrefimages = np.zeros_like(absorptionImages, dtype=np.float32)
        
        if dask=='forbidden':
            for j in range(self.nimgs):
                b = self._referenceImages[self.k, :].T @ absorptionImages[self.k, j]
        
                # Obtain coefficients c which minimize least-square residuals
                c = np.linalg.solve(self.U, np.linalg.solve(self.L[self.P], b))
                # Compute optimized reference image
                optrefimages[:, j] = (self._referenceImages @ c)
        else:
            pass

        return optrefimages
    
    def fringe_removal(self, absorptionImages, referenceImages=None, mask=None, reshape=None, dask='forbidden'):
        """
        This function will generate a 'fake' background images, which can help to remove the fringes.
        
        Important: Please substract the drak images from the both of images with atoms and without atoms before using this function!!!

        :param absorptionImages: A set of images with atoms in absorption imaging
        :type absorptionImages: xarray, numpy array or list
        :param referenceImages: A set of images without atoms in absorption imaging, defaults to None
        :type referenceImages: xarray, numpy array or list, optional
        :param mask: An array to choose the region of interest for fringes removal, defaults to None, defaults to None
        :type mask: numpy array, optional
        :param reshape: If it needs to reshape the data, defaults to None
        :type reshape: bool, optional
        :param dask: Please refer to xarray.apply_ufunc()
        :type dask: {"forbidden", "allowed", "parallelized"}, optional
        :return: The 'fake' background to help removing the fringes
        :rtype: numpy array
        """
        
        res = self._fringe_removal(absorptionImages, referenceImages, mask, reshape, dask)
        res = res.reshape(self.ydim, self.xdim, self.nimgs)
        if self.reshape:
            return np.swapaxes(res, 0, 2)
        else:
            return res