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 form MxN 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,

    • if the default data type corresponding to the data type “kind” (integer, real-valued floating-point, or complex floating-point) of x has a smaller range of values than the data type of x (e.g., x has data type int64 and the default data type is int32, or x has data type uint64 and the default data type is int64), the returned array must have the same data type as x.

    • if x has a real-valued floating-point data type, the returned array must have the default real-valued floating-point data type.

    • if x has a complex floating-point data type, the returned array must have the default complex floating-point data type.

    • 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 is int32, the returned array must have a uint32 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. Default: None.

    Note

    keyword argument is intended to help prevent data type overflows.

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 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.

Notes

Special Cases

Let N equal the number of elements over which to compute the sum.

  • If N is 0, the sum is 0 (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.