trace#

ivy.trace(x, /, *, offset=0, axis1=0, axis2=1, out=None)[source]#

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

Parameters:

  • x (Union[Array, NativeArray]) – 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. (default: 0) - offset = 0: the main diagonal. - offset > 0: off-diagonal above the main diagonal. - offset < 0: off-diagonal below the main diagonal.

    Default: 0.

  • out (Optional[Array]) – optional output array, for writing the result to. It must have a shape that the (default: None) inputs broadcast to.

Return type:

Array

Returns:

ret – 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 the same data type as x.

Examples

With ivy.Array inputs:

>>> x = ivy.array([[2., 0., 3.],
...                [3., 5., 6.]])
>>> y = ivy.trace(x, offset=0)
>>> print(y)
ivy.array(7.)

>>> x = ivy.array([[[1., 2.],
...                 [3., 4.]],
...                [[5., 6.],
...                 [7., 8.]]])
>>> y = ivy.trace(x, offset=1)
>>> print(y)
ivy.array([3., 4.])

With ivy.NativeArray inputs:

>>> x = ivy.native_array([[2., 0., 3.],[3., 5., 6.]])
>>> y = ivy.trace(x, offset=0)
>>> print(y)
ivy.array(7.)

>>> x = ivy.native_array([[0, 1, 2],
...                       [3, 4, 5],
...                       [6, 7, 8]])
>>> y = ivy.trace(x, offset=0)
>>> print(y)
ivy.array(12)

With ivy.Container inputs:

>>> x = ivy.Container(
...        a = ivy.array([[7, 1, 2],
...                       [1, 3, 5],
...                       [0, 7, 4]]),
...        b = ivy.array([[4, 3, 2],
...                       [1, 9, 5],
...                       [7, 0, 6]])
...    )
>>> y = ivy.trace(x, offset=0)
>>> print(y)
{
    a: ivy.array(14),
    b: ivy.array(19)
}

>>> x = ivy.Container(
...        a = ivy.array([[7, 1, 2],
...                       [1, 3, 5],
...                       [0, 7, 4]]),
...        b = ivy.array([[4, 3, 2],
...                       [1, 9, 5],
...                       [7, 0, 6]])
...    )
>>> y = ivy.trace(x, offset=1)
>>> print(y)
{
    a: ivy.array(6),
    b: ivy.array(8)
}
Array.trace(self, /, *, offset=0, axis1=0, axis2=1, out=None)#

ivy.Array instance method variant of ivy.trace. This method Returns the sum along the specified diagonals of a matrix (or a stack of matrices).

Parameters:

  • self (Array) – input array having shape (..., M, N) and whose innermost two dimensions form MxN matrices. Should have a floating-point data type.

  • offset (int) – Offset of the diagonal from the main diagonal. Can be both positive and (default: 0) negative. Defaults to 0.

  • out (Optional[Array]) – optional output array, for writing the result to. It must have a shape that (default: None) the inputs broadcast to.

Return type:

Array

Returns:

ret – 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 the same data type as x.

Examples

>>> x = ivy.array([[1., 2.], [3., 4.]])
>>> y = x.trace()
>>> print(y)
ivy.array(5.)

>>> x = ivy.array([[1., 2., 4.], [6., 5., 3.]])
>>> y = ivy.Array.trace(x)
>>> print(y)
ivy.array(6.)
Container.trace(self, /, *, offset=0, axis1=0, axis2=1, key_chains=None, to_apply=True, prune_unapplied=False, map_sequences=False, out=None)#

ivy.Container instance method variant of ivy.trace. This method Returns the sum along the specified diagonals of a matrix (or a stack of matrices).

Parameters:

  • self (Container) – input container having shape (..., M, N) and whose innermost two dimensions form MxN matrices. Should have a floating-point data type.

  • offset (int) – Offset of the diagonal from the main diagonal. Can be both positive and (default: 0) negative. Defaults to 0.

  • key_chains (Optional[Union[List[str], Dict[str, str]]]) – The key-chains to apply or not apply the method to. Default is None. (default: None)

  • to_apply (bool) – If True, the method will be applied to key_chains, otherwise key_chains (default: True) will be skipped. Default is True.

  • prune_unapplied (bool) – Whether to prune key_chains for which the function was not applied. (default: False) Default is False.

  • map_sequences (bool) – Whether to also map method to sequences (lists, tuples). (default: False) Default is False.

  • out (Optional[Container]) – optional output array, for writing the result to. It must have a shape that (default: None) the inputs broadcast to.

Return type:

Container

Returns:

ret – a container 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 the same data type as x.

Examples

With ivy.Container input: >>> x = ivy.Container( … a = ivy.array([[7, 1, 2], … [1, 3, 5], … [0, 7, 4]]), … b = ivy.array([[4, 3, 2], … [1, 9, 5], … [7, 0, 6]])) >>> y = x.trace() >>> print(y) {

a: ivy.array(14), b: ivy.array(19)

}