slogdet#

ivy.slogdet(x, /)[source]#

Return the sign and the natural logarithm of the absolute value of the determinant of a square matrix (or a stack of square matrices) x. .. note:

The purpose of this function is to calculate the determinant more accurately
when the determinant is either very small or very large, as calling ``det`` may
overflow or underflow.

Special cases

For real-valued floating-point operands,

If the determinant is zero, the sign should be 0``and ``logabsdet

should be infinity.

For complex floating-point operands,

If the detereminant is 0 + 0j, the sign should be 0 + 0j

and logabsdet should be infinity + 0j.

Parameters:

x (Union[Array, NativeArray]) – input array having shape (..., M, M) and whose innermost two dimensions form square matrices. Should have a real-valued floating-point data type.

Return type:

Tuple[Union[Array, NativeArray], Union[Array, NativeArray]]

Returns:

ret – a namedtuple (sign, logabsdet) whose - first element must have the field name sign and must be an array containing a number representing the sign of the determinant for each square matrix. - second element must have the field name logabsdet and must be an array containing the determinant for each square matrix. For a real matrix, the sign of the determinant must be either 1, 0, or -1. Each returned array must have shape shape(x)[:-2] and a real-valued floating-point data type determined by type-promotion. If x is complex, the returned array must have a real-valued floating-point data type having the same precision as x (1.g., if x is complex64, logabsdet must have a float32 data type) .. note:
```
If a determinant is zero, then the corresponding ``sign`` should be ``0``
and ``logabsdet`` should be ``-infinity``; however, depending on the
underlying algorithm, the returned result may differ. In all cases,
the determinant should be equal to ``sign * exp(logsabsdet)``
(although, again, the result may be subject to numerical precision errors).
```
This function conforms to the `Array API Standard
<https (//data-apis.org/array-api/latest/>`_. This docstring is an extension of the)
`docstring <https (//data-apis.org/array-api/latest/)
extensions/generated/array_api.linalg.slogdet.html>`_
in the standard.
Both the description and the type hints above assumes an array input for simplicity,
but this function is nestable, and therefore also accepts ivy.Container
instances in place of any of the arguments.

Examples

With ivy.Array input:

>>> x = ivy.array([[2.0, 1.0],
...                [3.0, 4.0]])
>>> y = ivy.slogdet(x)
>>> print(y)
slogdet(sign=ivy.array(1.), logabsdet=ivy.array(1.60943794))

>>> ivy.set_backend('numpy') # As the precision of results depends on backend.
>>> x = ivy.array([[1.2, 2.0, 3.1],
...                [6.0, 5.2, 4.0],
...                [9.0, 8.0, 7.0]])
>>> y = ivy.slogdet(x)
>>> print(y)
slogdet(sign=ivy.array(-1.), logabsdet=ivy.array(1.098611))

With ivy.Container input:

>>> ivy.unset_backend() # unset backend again.
>>> x = ivy.Container(a=ivy.array([[1.0, 2.0],
...                                [3.0, 4.0]]),
...                   b=ivy.array([[1.0, 2.0],
...                                [2.0, 1.0]]))
>>> y = ivy.slogdet(x)
>>> print(y)
[{
    a: ivy.array(-1.),
    b: ivy.array(-1.)
}, {
    a: ivy.array(0.69314718),
    b: ivy.array(1.09861231)
}]

Array.slogdet(self)[source]#

ivy.Array instance method variant of ivy.slogdet. This method simply wraps the function, and so the docstring for ivy.slogdet also applies to this method with minimal changes.

Parameters:

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

Return type:

Tuple[Array, Array]

Returns:

ret –

This function returns NamedTuple with two values -

sign: An array containing a number representing the sign of the determinant for each square matrix.

logabsdet: An array containing natural log of the absolute determinant of each square matrix.

Examples

>>> x = ivy.array([[1.0, 2.0],
...                [3.0, 4.0]])
>>> y = x.slogdet()
>>> print(y)
slogdet(sign=ivy.array(-1.), logabsdet=ivy.array(0.69314718))

>>> x = ivy.array([[1.2, 2.0, 3.1],
...                [6.0, 5.2, 4.0],
...                [9.0, 8.0, 7.0]])
>>> y = x.slogdet()
>>> print(y)
slogdet(sign=ivy.array(-1.), logabsdet=ivy.array(1.098611))

Container.slogdet(self, /, *, key_chains=None, to_apply=True, prune_unapplied=False, map_sequences=False)[source]#

ivy.Container instance method variant of ivy.slogdet. This method simply wraps the function, and so the docstring for ivy.slogdet also applies to this method with minimal changes.

Parameters:

self (Container) – input container having shape (…, M, M) and whose innermost two dimensions form square matrices. Should have a floating-point data type.
key_chains (Optional[Union[List[str], Dict[str, str], Container]], default: None) – The key-chains to apply or not apply the method to. Default is None.
to_apply (Union[bool, Container], default: True) – If True, the method will be applied to key_chains, otherwise key_chains will be skipped. Default is True.
prune_unapplied (Union[bool, Container], default: False) – Whether to prune key_chains for which the function was not applied. Default is False.
map_sequences (Union[bool, Container], default: False) – Whether to also map method to sequences (lists, tuples). Default is False.

Return type:

Container

Returns:

ret – This function returns container containing NamedTuples. Each NamedTuple of output will have -

sign: An array of a number representing the sign of the determinant of each square.

logabsdet: An array of the natural log of the absolute value of the determinant of each square.

Examples

>>> x = ivy.Container(a=ivy.array([[1.0, 2.0],
...                                [3.0, 4.0]]),
...                   b=ivy.array([[1.0, 2.0],
...                                [2.0, 1.0]]))
>>> y = x.slogdet()
>>> print(y)
[{
    a: ivy.array(-1.),
    b: ivy.array(-1.)
}, {
    a: ivy.array(0.69314718),
    b: ivy.array(1.09861231)
}]