trace(a, offset=0, axis1=0, axis2=1, dtype=None, out=None)[source]¶
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.
- 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.
- 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.
>>> 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)