# dot function

(Shortest import: `from brian2 import dot)`

brian2.units.unitsafefunctions.dot(a, b, out=None)

  Dot product of two arrays. Specifically,

  - If both `a` and `b` are 1-D arrays, it is inner product of vectors (without complex conjugation).

  - If both `a` and `b` are 2-D arrays, it is matrix multiplication, but using `matmul()` or `a @ b` is preferred.

  - If either `a` or `b` is 0-D (scalar), it is equivalent to `multiply()` and using `numpy.multiply(a, b)` or `a * b` is preferred.

  - If `a` is an N-D array and `b` is a 1-D array, it is a sum product over the last axis of `a` and `b`.

  - If `a` is an N-D array and `b` is an M-D array (where `M>=2`), it is a sum product over the last axis of `a` and the second-to-last axis of `b`:

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

  It uses an optimized BLAS library when possible (see `numpy.linalg`).

  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.

  `vecdot`

    Vector dot product of two arrays.

  `tensordot`

    Sum products over arbitrary axes.

  `einsum`

    Einstein summation convention.

  `matmul`

    ‘@’ operator as method with out parameter.

  `linalg.multi_dot`

    Chained dot product.

  Examples

      >>> import numpy as np
      >>> np.dot(3, 4)
      12

  Neither argument is complex-conjugated:

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

  For 2-D arrays it is 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