from ... import backend as T
import numpy as np

# Author: Jean Kossaifi
# License: BSD 3 clause


def inner(tensor1, tensor2, n_modes=None):
    """Generalised inner products between tensors

        Takes the inner product between the last (respectively first)
        `n_modes` of `tensor1` (respectively `tensor2`)

    Parameters
    ----------
    tensor1, tensor2 : tensor
    n_modes : int, default is None
        * if None, the traditional inner product is returned (i.e. a float)
        * otherwise, the product between the `n_modes` last modes of `tensor1`
            and the `n_modes` first modes of `tensor2` is returned.
            The resulting tensor's order is `ndim(tensor1) - n_modes`.

    Returns
    -------
    inner_product : float if n_modes is None, tensor otherwise
    """
    # Traditional inner product
    if n_modes is None:
        if tensor1.shape != tensor2.shape:
            raise ValueError(
                "Taking a generalised product between two tensors without specifying common modes"
                " is equivalent to taking inner product."
                "This requires tensor1.shape == tensor2.shape."
                f"However, got shapes {tensor1.shape} and {tensor2.shape}"
            )
        return T.sum(tensor1 * tensor2)

    # Inner product along `n_modes` common modes
    shape_t1 = list(T.shape(tensor1))
    shape_t2 = list(T.shape(tensor2))
    common_modes = shape_t1[len(shape_t1) - n_modes :]
    common_size = int(np.prod(common_modes))
    output_shape = shape_t1[:-n_modes] + shape_t2[n_modes:]

    if common_modes != shape_t2[:n_modes]:
        raise ValueError(
            f"Incorrect shapes for inner product along {n_modes} common modes."
            f"Shapes {tensor1.shape} and {tensor2.shape}"
        )
    inner_product = T.dot(
        T.reshape(tensor1, (-1, common_size)), T.reshape(tensor2, (common_size, -1))
    )
    return T.reshape(inner_product, output_shape)