trace¶
- trace(x: array, /, *, offset: int = 0, dtype: dtype | None = None) array ¶
Returns the sum along the specified diagonals of a matrix (or a stack of matrices)
x
.- Parameters:
x (array) – input array having shape
(..., M, N)
and whose innermost two dimensions formMxN
matrices. Should have a numeric data type.offset (int) –
offset specifying the off-diagonal relative to the main diagonal.
offset = 0
: the main diagonal.offset > 0
: off-diagonal above the main diagonal.offset < 0
: off-diagonal below the main diagonal.
Default:
0
.dtype (Optional[dtype]) –
data type of the returned array. If
None
, the returned array must have the same data type asx
, unlessx
has an integer data type supporting a smaller range of values than the default integer data type (e.g.,x
has anint16
oruint32
data type and the default integer data type isint64
). In those latter cases:if
x
has a signed integer data type (e.g.,int16
), the returned array must have the default integer data type.if
x
has an unsigned integer data type (e.g.,uint16
), the returned array must have an unsigned integer data type having the same number of bits as the default integer data type (e.g., if the default integer data type isint32
, the returned array must have auint32
data type).
If the data type (either specified or resolved) differs from the data type of
x
, the input array should be cast to the specified data type before computing the sum (rationale: thedtype
keyword argument is intended to help prevent overflows). Default:None
.
- Returns:
out (array) – 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 rankk
and shape(I, J, K, ..., L, M, N)
, then an output array has rankk-2
and shape(I, J, K, ..., L)
whereout[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.
Notes
Special Cases
Let
N
equal the number of elements over which to compute the sum.If
N
is0
, the sum is0
(i.e., the empty sum).
For both real-valued and complex floating-point operands, special cases must be handled as if the operation is implemented by successive application of
add()
.Changed in version 2022.12: Added complex data type support.
Changed in version 2023.12: Required the function to return a floating-point array having the same data type as the input array when provided a floating-point array.