__all__ = ["FFT2D"]

import logging
import warnings
from typing import Dict, Optional, Sequence, Union

import numpy as np
import scipy.fft

from pylops import LinearOperator
from pylops.signalprocessing._baseffts import _BaseFFTND, _FFTNorms
from pylops.utils.decorators import reshaped
from pylops.utils.typing import DTypeLike, InputDimsLike

logging.basicConfig(format="%(levelname)s: %(message)s", level=logging.WARNING)


class _FFT2D_numpy(_BaseFFTND):
    """Two dimensional Fast-Fourier Transform using NumPy"""

    def __init__(
        self,
        dims: InputDimsLike,
        axes: InputDimsLike = (-2, -1),
        nffts: Optional[Union[int, InputDimsLike]] = None,
        sampling: Union[float, Sequence[float]] = 1.0,
        norm: str = "ortho",
        real: bool = False,
        ifftshift_before: bool = False,
        fftshift_after: bool = False,
        dtype: DTypeLike = "complex128",
    ) -> None:
        super().__init__(
            dims=dims,
            axes=axes,
            nffts=nffts,
            sampling=sampling,
            norm=norm,
            real=real,
            ifftshift_before=ifftshift_before,
            fftshift_after=fftshift_after,
            dtype=dtype,
        )
        if self.cdtype != np.complex128:
            warnings.warn(
                f"numpy backend always returns complex128 dtype. To respect the passed dtype, data will be casted to {self.cdtype}."
            )

        # checks
        if self.ndim < 2:
            raise ValueError("FFT2D requires at least two input dimensions")
        if self.naxes != 2:
            raise ValueError("FFT2D must be applied along exactly two dimensions")

        self.f1, self.f2 = self.fs
        del self.fs

        self._norm_kwargs: Dict[str, Union[None, str]] = {
            "norm": None
        }  # equivalent to "backward" in Numpy/Scipy
        if self.norm is _FFTNorms.ORTHO:
            self._norm_kwargs["norm"] = "ortho"
        elif self.norm is _FFTNorms.NONE:
            self._scale = np.prod(self.nffts)
        elif self.norm is _FFTNorms.ONE_OVER_N:
            self._scale = 1.0 / np.prod(self.nffts)

    @reshaped
    def _matvec(self, x):
        if self.ifftshift_before.any():
            x = np.fft.ifftshift(x, axes=self.axes[self.ifftshift_before])
        if not self.clinear:
            x = np.real(x)
        if self.real:
            y = np.fft.rfft2(x, s=self.nffts, axes=self.axes, **self._norm_kwargs)
            # Apply scaling to obtain a correct adjoint for this operator
            y = np.swapaxes(y, -1, self.axes[-1])
            y[..., 1 : 1 + (self.nffts[-1] - 1) // 2] *= np.sqrt(2)
            y = np.swapaxes(y, self.axes[-1], -1)
        else:
            y = np.fft.fft2(x, s=self.nffts, axes=self.axes, **self._norm_kwargs)
        if self.norm is _FFTNorms.ONE_OVER_N:
            y *= self._scale
        y = y.astype(self.cdtype)
        if self.fftshift_after.any():
            y = np.fft.fftshift(y, axes=self.axes[self.fftshift_after])
        return y

    @reshaped
    def _rmatvec(self, x):
        if self.fftshift_after.any():
            x = np.fft.ifftshift(x, axes=self.axes[self.fftshift_after])
        if self.real:
            # Apply scaling to obtain a correct adjoint for this operator
            x = x.copy()
            x = np.swapaxes(x, -1, self.axes[-1])
            x[..., 1 : 1 + (self.nffts[-1] - 1) // 2] /= np.sqrt(2)
            x = np.swapaxes(x, self.axes[-1], -1)
            y = np.fft.irfft2(x, s=self.nffts, axes=self.axes, **self._norm_kwargs)
        else:
            y = np.fft.ifft2(x, s=self.nffts, axes=self.axes, **self._norm_kwargs)
        if self.norm is _FFTNorms.NONE:
            y *= self._scale
        if self.nffts[0] > self.dims[self.axes[0]]:
            y = np.take(y, range(self.dims[self.axes[0]]), axis=self.axes[0])
        if self.nffts[1] > self.dims[self.axes[1]]:
            y = np.take(y, range(self.dims[self.axes[1]]), axis=self.axes[1])
        if self.doifftpad:
            y = np.pad(y, self.ifftpad)
        if not self.clinear:
            y = np.real(y)
        y = y.astype(self.rdtype)
        if self.ifftshift_before.any():
            y = np.fft.fftshift(y, axes=self.axes[self.ifftshift_before])
        return y

    def __truediv__(self, y):
        if self.norm is not _FFTNorms.ORTHO:
            return self._rmatvec(y) / self._scale
        return self._rmatvec(y)


class _FFT2D_scipy(_BaseFFTND):
    """Two dimensional Fast-Fourier Transform using SciPy"""

    def __init__(
        self,
        dims: InputDimsLike,
        axes: InputDimsLike = (-2, -1),
        nffts: Optional[Union[int, InputDimsLike]] = None,
        sampling: Union[float, Sequence[float]] = 1.0,
        norm: str = "ortho",
        real: bool = False,
        ifftshift_before: bool = False,
        fftshift_after: bool = False,
        dtype: DTypeLike = "complex128",
    ) -> None:
        super().__init__(
            dims=dims,
            axes=axes,
            nffts=nffts,
            sampling=sampling,
            norm=norm,
            real=real,
            ifftshift_before=ifftshift_before,
            fftshift_after=fftshift_after,
            dtype=dtype,
        )

        # checks
        if self.ndim < 2:
            raise ValueError("FFT2D requires at least two input dimensions")
        if self.naxes != 2:
            raise ValueError("FFT2D must be applied along exactly two dimensions")

        self.f1, self.f2 = self.fs
        del self.fs

        self._norm_kwargs: Dict[str, Union[None, str]] = {
            "norm": None
        }  # equivalent to "backward" in Numpy/Scipy
        if self.norm is _FFTNorms.ORTHO:
            self._norm_kwargs["norm"] = "ortho"
        elif self.norm is _FFTNorms.NONE:
            self._scale = np.sqrt(np.prod(self.nffts))
        elif self.norm is _FFTNorms.ONE_OVER_N:
            self._scale = np.sqrt(1.0 / np.prod(self.nffts))

    @reshaped
    def _matvec(self, x):
        if self.ifftshift_before.any():
            x = scipy.fft.ifftshift(x, axes=self.axes[self.ifftshift_before])
        if not self.clinear:
            x = np.real(x)
        if self.real:
            y = scipy.fft.rfft2(x, s=self.nffts, axes=self.axes, **self._norm_kwargs)
            # Apply scaling to obtain a correct adjoint for this operator
            y = np.swapaxes(y, -1, self.axes[-1])
            y[..., 1 : 1 + (self.nffts[-1] - 1) // 2] *= np.sqrt(2)
            y = np.swapaxes(y, self.axes[-1], -1)
        else:
            y = scipy.fft.fft2(x, s=self.nffts, axes=self.axes, **self._norm_kwargs)
        if self.norm is _FFTNorms.ONE_OVER_N:
            y *= self._scale
        if self.fftshift_after.any():
            y = scipy.fft.fftshift(y, axes=self.axes[self.fftshift_after])
        return y

    @reshaped
    def _rmatvec(self, x):
        if self.fftshift_after.any():
            x = scipy.fft.ifftshift(x, axes=self.axes[self.fftshift_after])
        if self.real:
            # Apply scaling to obtain a correct adjoint for this operator
            x = x.copy()
            x = np.swapaxes(x, -1, self.axes[-1])
            x[..., 1 : 1 + (self.nffts[-1] - 1) // 2] /= np.sqrt(2)
            x = np.swapaxes(x, self.axes[-1], -1)
            y = scipy.fft.irfft2(x, s=self.nffts, axes=self.axes, **self._norm_kwargs)
        else:
            y = scipy.fft.ifft2(x, s=self.nffts, axes=self.axes, **self._norm_kwargs)
        if self.norm is _FFTNorms.NONE:
            y *= self._scale
        y = np.take(y, range(self.dims[self.axes[0]]), axis=self.axes[0])
        y = np.take(y, range(self.dims[self.axes[1]]), axis=self.axes[1])
        if not self.clinear:
            y = np.real(y)
        if self.ifftshift_before.any():
            y = scipy.fft.fftshift(y, axes=self.axes[self.ifftshift_before])
        return y

    def __truediv__(self, y):
        if self.norm is not _FFTNorms.ORTHO:
            return self._rmatvec(y) / self._scale / self._scale
        return self._rmatvec(y)


def FFT2D(
    dims: InputDimsLike,
    axes: InputDimsLike = (-2, -1),
    nffts: Optional[Union[int, InputDimsLike]] = None,
    sampling: Union[float, Sequence[float]] = 1.0,
    norm: str = "ortho",
    real: bool = False,
    ifftshift_before: bool = False,
    fftshift_after: bool = False,
    engine: str = "numpy",
    dtype: DTypeLike = "complex128",
    name: str = "F",
) -> LinearOperator:
    r"""Two dimensional Fast-Fourier Transform.

    Apply two dimensional Fast-Fourier Transform (FFT) to any pair of ``axes`` of a
    multi-dimensional array.

    Using the default NumPy engine, the FFT operator is an overload to either the NumPy
    :py:func:`numpy.fft.fft2` (or :py:func:`numpy.fft.rfft2` for real models) in
    forward mode, and to :py:func:`numpy.fft.ifft2` (or :py:func:`numpy.fft.irfft2`
    for real models) in adjoint mode, or their CuPy equivalents.
    Alternatively, when the SciPy engine is chosen, the overloads are of
    :py:func:`scipy.fft.fft2` (or :py:func:`scipy.fft.rfft2` for real models) in
    forward mode, and to :py:func:`scipy.fft.ifft2` (or :py:func:`scipy.fft.irfft2`
    for real models) in adjoint mode.

    When using ``real=True``, the result of the forward is also multiplied by
    :math:`\sqrt{2}` for all frequency bins except zero and Nyquist, and the input of
    the adjoint is multiplied by :math:`1 / \sqrt{2}` for the same frequencies.

    For a real valued input signal, it is advised to use the flag ``real=True``
    as it stores the values of the Fourier transform of the last axis in ``axes`` at positive
    frequencies only as values at negative frequencies are simply their complex conjugates.

    Parameters
    ----------
    dims : :obj:`tuple`
        Number of samples for each dimension
    axes : :obj:`tuple`, optional
        .. versionadded:: 2.0.0

        Pair of axes along which FFT2D is applied
    nffts : :obj:`tuple` or :obj:`int`, optional
        Number of samples in Fourier Transform for each axis in ``axes``. In case only one
        dimension needs to be specified, use ``None`` for the other dimension in the
        tuple. An axis with ``None`` will use ``dims[axis]`` as ``nfft``.
        When supplying a tuple, the length must be 2.
        When a single value is passed, it will be used for both
        axes. As such the default is equivalent to ``nffts=(None, None)``.
    sampling : :obj:`tuple` or :obj:`float`, optional
        Sampling steps for each axis in ``axes``. When supplied a single value, it is used
        for both axes. Unlike ``nffts``, any ``None`` will not be converted to the
        default value.
    norm : `{"ortho", "none", "1/n"}`, optional
        .. versionadded:: 1.17.0

        - "ortho": Scales forward and adjoint FFT transforms with :math:`1/\sqrt{N_F}`,
          where :math:`N_F` is the number of samples in the Fourier domain given by
          product of all elements of ``nffts``.

        - "none": Does not scale the forward or the adjoint FFT transforms.

        - "1/n": Scales both the forward and adjoint FFT transforms by
          :math:`1/N_F`.

        .. note:: For "none" and "1/n", the operator is not unitary, that is, the
          adjoint is not the inverse. To invert the operator, simply use ``Op \ y``.

    real : :obj:`bool`, optional
        Model to which fft is applied has real numbers (``True``) or not
        (``False``). Used to enforce that the output of adjoint of a real
        model is real. Note that the real FFT is applied only to the first
        dimension to which the FFT2D operator is applied (last element of
        ``axes``)
    ifftshift_before : :obj:`tuple` or :obj:`bool`, optional
        Apply ifftshift (``True``) or not (``False``) to model vector (before FFT).
        Consider using this option when the model vector's respective axis is symmetric
        with respect to the zero value sample. This will shift the zero value sample to
        coincide with the zero index sample. With such an arrangement, FFT will not
        introduce a sample-dependent phase-shift when compared to the continuous Fourier
        Transform.
        When passing a single value, the shift will the same for every axis in ``axes``. Pass
        a tuple to specify which dimensions are shifted.
    fftshift_after : :obj:`tuple` or :obj:`bool`, optional
        Apply fftshift (``True``) or not (``False``) to data vector (after FFT).
        Consider using this option when you require frequencies to be arranged
        naturally, from negative to positive. When not applying fftshift after FFT,
        frequencies are arranged from zero to largest positive, and then from negative
        Nyquist to the frequency bin before zero.
        When passing a single value, the shift will the same for every axis in ``axes``. Pass
        a tuple to specify which dimensions are shifted.
    engine : :obj:`str`, optional
        .. versionadded:: 1.17.0

        Engine used for fft computation (``numpy`` or ``scipy``).
    dtype : :obj:`str`, optional
        Type of elements in input array. Note that the ``dtype`` of the operator
        is the corresponding complex type even when a real type is provided.
        In addition, note that the NumPy backend does not support returning ``dtype``
        different than ``complex128``. As such, when using the NumPy backend, arrays will
        be force-casted to types corresponding to the supplied ``dtype``.
        The SciPy backend supports all precisions natively.
        Under both backends, when a real ``dtype`` is supplied, a real result will be
        enforced on the result of the ``rmatvec`` and the input of the ``matvec``.
    name : :obj:`str`, optional
        .. versionadded:: 2.0.0

        Name of operator (to be used by :func:`pylops.utils.describe.describe`)

    Attributes
    ----------
    dimsd : :obj:`tuple`
        Shape of the array after the forward, but before linearization.

        For example, ``y_reshaped = (Op * x.ravel()).reshape(Op.dimsd)``.
    f1 : :obj:`numpy.ndarray`
        Discrete Fourier Transform sample frequencies along ``axes[0]``
    f2 : :obj:`numpy.ndarray`
        Discrete Fourier Transform sample frequencies along ``axes[1]``
    real : :obj:`bool`
        When ``True``, uses ``rfft2``/``irfft2``
    rdtype : :obj:`bool`
        Expected input type to the forward
    cdtype : :obj:`bool`
        Output type of the forward. Complex equivalent to ``rdtype``.
    shape : :obj:`tuple`
        Operator shape
    clinear : :obj:`bool`
        .. versionadded:: 1.17.0

        Operator is complex-linear. Is false when either ``real=True`` or when
        ``dtype`` is not a complex type.
    explicit : :obj:`bool`
        Operator contains a matrix that can be solved explicitly
        (``True``) or not (``False``)

    Raises
    ------
    ValueError
        - If ``dims`` has less than two elements.
        - If ``axes`` does not have exactly two elements.
        - If ``nffts`` or ``sampling`` are not either a single value or a tuple with
          two elements.
        - If ``norm`` is not one of "ortho", "none", or "1/n".
    NotImplementedError
        If ``engine`` is neither ``numpy``, nor ``scipy``.

    See Also
    --------
    FFT: One-dimensional FFT
    FFTND: N-dimensional FFT

    Notes
    -----
    The FFT2D operator (using ``norm="ortho"``) applies the two-dimensional forward
    Fourier transform to a signal :math:`d(y, x)` in forward mode:

    .. math::
        D(k_y, k_x) = \mathscr{F} (d) = \frac{1}{\sqrt{N_F}} \iint\limits_{-\infty}^\infty d(y, x) e^{-j2\pi k_yy}
        e^{-j2\pi k_xx} \,\mathrm{d}y \,\mathrm{d}x

    Similarly, the  two-dimensional inverse Fourier transform is applied to
    the Fourier spectrum :math:`D(k_y, k_x)` in adjoint mode:

    .. math::
        d(y,x) = \mathscr{F}^{-1} (D) = \frac{1}{\sqrt{N_F}} \iint\limits_{-\infty}^\infty D(k_y, k_x) e^{j2\pi k_yy}
        e^{j2\pi k_xx} \,\mathrm{d}k_y  \,\mathrm{d}k_x

    where :math:`N_F` is the number of samples in the Fourier domain given by the
    product of the element of ``nffts``.
    Both operators are effectively discretized and solved by a fast iterative
    algorithm known as Fast Fourier Transform. Note that the FFT2D operator
    (using ``norm="ortho"``) is a special operator in that the adjoint is also
    the inverse of the forward mode. For other norms, this does not hold (see ``norm``
    help). However, for any norm, the 2D Fourier transform is Hermitian for real input
    signals.

    """
    if engine == "numpy":
        f = _FFT2D_numpy(
            dims=dims,
            axes=axes,
            nffts=nffts,
            sampling=sampling,
            norm=norm,
            real=real,
            ifftshift_before=ifftshift_before,
            fftshift_after=fftshift_after,
            dtype=dtype,
        )
    elif engine == "scipy":
        f = _FFT2D_scipy(
            dims=dims,
            axes=axes,
            nffts=nffts,
            sampling=sampling,
            norm=norm,
            real=real,
            ifftshift_before=ifftshift_before,
            fftshift_after=fftshift_after,
            dtype=dtype,
        )
    else:
        raise NotImplementedError("engine must be numpy or scipy")
    f.name = name
    return f
