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)