numpy.linalg.trace

linalg.trace(x, /, *, offset=0, dtype=None)[source]

Returns the sum along the specified diagonals of a matrix (or a stack of matrices) x.

This function is Array API compatible, contrary to numpy.trace.

Parameters:

x(…,M,N) array_like

Input array having shape (…, M, N) and whose innermost two dimensions form MxN matrices.

offsetint, optional

Offset specifying the off-diagonal relative to the main diagonal, where:

* offset = 0: the main diagonal.
* offset > 0: off-diagonal above the main diagonal.
* offset < 0: off-diagonal below the main diagonal.

dtypedtype, optional

Data type of the returned array.

Returns:

outndarray

An array containing the traces and whose shape is determined by removing the last two dimensions and storing the traces in the last array dimension. For example, if x has rank k and shape: (I, J, K, …, L, M, N), then an output array has rank k-2 and shape: (I, J, K, …, L) where:

out[i, j, k, ..., l] = trace(a[i, j, k, ..., l, :, :])

The returned array must have a data type as described by the dtype parameter above.

See also

numpy.trace

Examples

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>>> np.linalg.trace(np.eye(3))
3.0
>>> a = np.arange(8).reshape((2, 2, 2))
>>> np.linalg.trace(a)
array([3, 11])

Trace is computed with the last two axes as the 2-d sub-arrays. This behavior differs from numpy.trace which uses the first two axes by default.

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

Traces adjacent to the main diagonal can be obtained by using the offset argument:

>>> a = np.arange(9).reshape((3, 3)); a
array([[0, 1, 2],
       [3, 4, 5],
       [6, 7, 8]])
>>> np.linalg.trace(a, offset=1)  # First superdiagonal
6
>>> np.linalg.trace(a, offset=2)  # Second superdiagonal
2
>>> np.linalg.trace(a, offset=-1)  # First subdiagonal
10
>>> np.linalg.trace(a, offset=-2)  # Second subdiagonal
6

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