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# numpy.dot

`numpy.``dot`(a, b, out=None)

  Dot product of two arrays.

  For 2-D arrays it is equivalent to matrix multiplication, and for 1-D arrays to inner product of vectors (without complex conjugation). For N dimensions it is a sum product over the last axis of a and the second-to-last of b:

      dot(a, b)[i,j,k,m] = sum(a[i,j,:] * b[k,:,m])

  Parameters : | a : array_like First argument. b : array_like Second argument. out : ndarray, optional Output argument. This must have the exact kind that would be returned if it was not used. In particular, it must have the right type, must be C-contiguous, and its dtype must be the dtype that would be returned for dot(a,b). This is a performance feature. Therefore, if these conditions are not met, an exception is raised, instead of attempting to be flexible.
  Returns : | output : ndarray Returns the dot product of a and b. If a and b are both scalars or both 1-D arrays then a scalar is returned; otherwise an array is returned. If out is given, then it is returned.
  Raises : | ValueError : If the last dimension of a is not the same size as the second-to-last dimension of b.

  See also

  `vdot`
    Complex-conjugating dot product.
  `tensordot`
    Sum products over arbitrary axes.
  `einsum`
    Einstein summation convention.

  Examples

      >>> np.dot(3, 4)
      12

  Neither argument is complex-conjugated:

      >>> np.dot([2j, 3j], [2j, 3j])
      (-13+0j)

  For 2-D arrays it’s the matrix product:

      >>> a = [[1, 0], [0, 1]]
      >>> b = [[4, 1], [2, 2]]
      >>> np.dot(a, b)
      array([[4, 1],
             [2, 2]])

      >>> a = np.arange(3*4*5*6).reshape((3,4,5,6))
      >>> b = np.arange(3*4*5*6)[::-1].reshape((5,4,6,3))
      >>> np.dot(a, b)[2,3,2,1,2,2]
      499128
      >>> sum(a[2,3,2,:] * b[1,2,:,2])
      499128

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