svdvals

ivy.svdvals(x, /, *, out=None)

Return the singular values 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.

• 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 – array with shape (..., K) that contains the vector(s) of singular values of length K, where K = min(M, N). The values are sorted in descending order by magnitude.

This function conforms to the Array API Standard. This docstring is an extension of the docstring # noqa 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.

Functional Examples

With ivy.Array input:

>>> x = ivy.array([[5.0, 7.0], [4.0, 3.0]])
>>> S = ivy.svdvals(x)
>>> print(S.shape)
(2,)

With comparison of the singular value S ivy.svdvals() by the result ivy.svd().

>>> _, SS, _ = ivy.svd(x)
>>> print(SS.shape)
(2,)

>>> error = (SS - S).abs()
>>> print(error)
ivy.array([0.,0.])

With ivy.NativeArray input:

>>> x = ivy.native_array([[1.0, 2.0, 3.0], [2.0, 3.0, 4.0],
...                       [2.0, 1.0, 3.0], [3.0, 4.0, 5.0]])
>>> print(x.shape)
(4, 3)

>>> S = ivy.svdvals(x)
>>> print(S)
ivy.array([10.3, 1.16, 0.615])

>>> _, SS, _ = ivy.svd(x)
>>> print(SS)
ivy.array([10.3, 1.16, 0.615])

with comparison of singular value S ivy.svdvals() by the result ivy.svd().

>>> error = (SS - S).abs()
>>> print(error)
ivy.array([0., 0., 0.])

With ivy.Container input:

>>> x = ivy.Container(a=ivy.array([[2.0, 3.0], [3.0, 4.0],
...                                [1.0, 3.0], [3.0, 5.0]]),
...                   b=ivy.array([[7.0, 1.0, 2.0, 3.0],
...                                [2.0, 5.0, 3.0, 4.0],
...                                [2.0, 6.0, 1.0, 3.0],
...                                [3.0, 4.0, 5.0, 9.0]]))
>>> y = ivy.svdvals(x)
>>> print(y)
{
    a: ivy.array([9.01, 0.866]),
    b: ivy.array([15.8, 5.56, 4.17, 0.864])
}

Instance Method Examples

Using ivy.Array instance method:

>>> x = ivy.array([[8.0, 3.0], [2.0, 3.0],
...                [2.0, 1.0], [3.0, 4.0],
...                [4.0, 1.0], [5.0, 6.0]])
>>> y = x.svdvals()
>>> print(y)
ivy.array([13.4, 3.88])

Using ivy.Container instance method:

>>> x = ivy.Container(a=ivy.array([[2.0, 3.0, 6.0], [5.0, 3.0, 4.0],
...                                [1.0, 7.0, 3.0], [3.0, 2.0, 5.0]]),
...                   b=ivy.array([[7.0, 1.0, 2.0, 3.0, 9.0],
...                                [2.0, 5.0, 3.0, 4.0, 10.0],
...                                [2.0, 11.0, 6.0, 1.0, 3.0],
...                                [8.0, 3.0, 4.0, 5.0, 9.0]]))
>>> y = x.svdvals()
>>> print(y)
{
    a: ivy.array([13., 4.64, 2.55]),
    b: ivy.array([23.2, 10.4, 4.31, 1.36])
}

Array.svdvals(self, /, *, out=None)

Return type:

Array

Container.svdvals(self, /, *, key_chains=None, to_apply=True, prune_unapplied=False, map_sequences=False, out=None)

Return type:

Container