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scipy.linalg.

# khatri_rao

scipy.linalg.khatri_rao(a, b)

  Khatri-Rao product of two matrices.

  A column-wise Kronecker product of two matrices

  The documentation is written assuming array arguments are of specified “core” shapes. However, array argument(s) of this function may have additional “batch” dimensions prepended to the core shape. In this case, the array is treated as a batch of lower-dimensional slices; see Batched Linear Operations for details. Note that calls with zero-size batches are unsupported and will raise a `ValueError`.

  Parameters:
    a(n, k) array_like

      Input array

    b(m, k) array_like

      Input array

  Returns:
    c: (n*m, k) ndarray

      Khatri-rao product of a and b.

  Notes

  The mathematical definition of the Khatri-Rao product is:

  \[(A_{ij} \bigotimes B_{ij})_{ij}\]

  which is the Kronecker product of every column of A and B, e.g.:

      c = np.vstack([np.kron(a[:, k], b[:, k]) for k in range(b.shape[1])]).T

  Examples

      >>> import numpy as np
      >>> from scipy import linalg
      >>> a = np.array([[1, 2, 3], [4, 5, 6]])
      >>> b = np.array([[3, 4, 5], [6, 7, 8], [2, 3, 9]])
      >>> linalg.khatri_rao(a, b)
      array([[ 3,  8, 15],
             [ 6, 14, 24],
             [ 2,  6, 27],
             [12, 20, 30],
             [24, 35, 48],
             [ 8, 15, 54]])