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# numpy.trace

`numpy.``trace`(a, offset=0, axis1=0, axis2=1, dtype=None, out=None)

  Return the sum along diagonals of the array.

  If a is 2-D, the sum along its diagonal with the given offset is returned, i.e., the sum of elements `a[i,i+offset]` for all i.

  If a has more than two dimensions, then the axes specified by axis1 and axis2 are used to determine the 2-D sub-arrays whose traces are returned. The shape of the resulting array is the same as that of a with axis1 and axis2 removed.

  Parameters : | a : array_like Input array, from which the diagonals are taken. offset : int, optional Offset of the diagonal from the main diagonal. Can be both positive and negative. Defaults to 0. axis1, axis2 : int, optional Axes to be used as the first and second axis of the 2-D sub-arrays from which the diagonals should be taken. Defaults are the first two axes of a. dtype : dtype, optional Determines the data-type of the returned array and of the accumulator where the elements are summed. If dtype has the value None and a is of integer type of precision less than the default integer precision, then the default integer precision is used. Otherwise, the precision is the same as that of a. out : ndarray, optional Array into which the output is placed. Its type is preserved and it must be of the right shape to hold the output.
  Returns : | sum_along_diagonals : ndarray If a is 2-D, the sum along the diagonal is returned. If a has larger dimensions, then an array of sums along diagonals is returned.

  See also

  `diag`, `diagonal`, `diagflat`

  Examples

      >>> np.trace(np.eye(3))
      3.0
      >>> a = np.arange(8).reshape((2,2,2))
      >>> np.trace(a)
      array([6, 8])

      >>> a = np.arange(24).reshape((2,2,2,3))
      >>> np.trace(a).shape
      (2, 3)

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