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.'
                             'However, got tensor1.shape={} and tensor2.shape={}'.format(tensor1.shape, 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('Incorrect shapes for inner product along {} common modes.'
                         'tensor_1.shape={}, tensor_2.shape={}'.format(n_modes, shape_t1, shape_t2))
    inner_product = T.dot(T.reshape(tensor1, (-1, common_size)),
                          T.reshape(tensor2, (common_size, -1)))
    return T.reshape(inner_product, output_shape)

