linear#

ivy.linear(x, weight, /, *, bias=None, out=None)[source]#

Apply a linear transformation to the incoming data: y = x * t(weight) + bias. The operation also supports batching of the weight matrices. This is useful if a batch of different network parameters are to be represented.

Parameters:

  • x (Union[Array, NativeArray]) – The input x to compute linear transformation on. [outer_batch_shape,inner_batch_shape,in_features]

  • weight (Union[Array, NativeArray]) – The weight matrix. [outer_batch_shape,out_features,in_features]

  • bias (Optional[Union[Array, NativeArray]]) – The bias vector, default is None. [outer_batch_shape,out_features] (default: None)

  • 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 – Result array of the linear transformation. [outer_batch_shape,inner_batch_shape,out_features]

  • 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([1., 2., 3.])
>>> w = ivy.array([[1., 0., 0.]])
>>> y = ivy.linear(x, w)
>>> print(y)
ivy.array([1])

>>> x = ivy.array([[0.666, -0.4269, 1.911]])
>>> w = ivy.array([[1., 0., 0.], [0., 0., 1.]])
>>> y = ivy.zeros(2)
>>> ivy.linear(x, w, out=y)
>>> print(y)
ivy.array([[0.666, 1.91 ]])

>>> x = ivy.array([[1.546, 5.234, 6.487],                        [0.157, 5.753, 4.52],                        [5.165, 3.159, 7.101]])
>>> w = ivy.array([[1.545, 2.547, 3.124],                        [5.852, 8.753, 6.963]])
>>> b = ivy.array([-1., 1.])
>>> ivy.linear(x, w, bias=b, out=x)
>>> print(x)
ivy.array([[ 35. , 101. ],
           [ 28. ,  83.7],
           [ 37.2, 108. ]])

With ivy.Container input:

>>> x = ivy.Container(a=ivy.array([[1., 2., 3.],                                        [4., 5., 6.]]),                           b=ivy.array([1.1, 2.2, 3.3]))
>>> w = ivy.Container(a=ivy.array([[1., 2., 3.],                                        [-1., 1., 2.]]),                           b=ivy.array([[0., -1., 1.],                                        [0., 1., 1.]]))
>>> b = ivy.Container(a=ivy.array([1., -1.]), b=ivy.array([1., 1.]))
>>> y = ivy.linear(x, w, bias=b)
>>> print(y)
{
    a: ivy.array([[15., 6.],
                  [33., 12.]]),
    b: ivy.array([2.1, 6.5])
}

With a mix of ivy.Array and ivy.Container inputs:

>>> x = ivy.Container(a=ivy.array([[1.1, 2.2, 3.3],                                        [11., 22., 33.]]),                           b=ivy.array([[1.245, 0.278, 4.105],                                        [7., 13., 17.]]))
>>> w = ivy.array([[1., 2., 3.],                        [4., 5., 6.],                        [7., 8., 9.]])
>>> b = ivy.Container(a=ivy.array([1., 0., -1.]),                           b=ivy.array([1., 1., 0.]))
>>> ivy.linear(x, w, bias=b, out=x)
>>> print(x)
{
    a: ivy.array([[16.4, 35.2, 54.],
                  [155., 352., 549.]]),
    b: ivy.array([[15.1, 32., 47.9],
                  [85., 196., 306.]])
}
Array.linear(self, weight, /, *, bias=None, out=None)#

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

Parameters:

  • self (Array) – The input array to compute linear transformation on. [outer_batch_shape,inner_batch_shape,in_features]

  • weight (Union[Array, NativeArray]) – The weight matrix. [outer_batch_shape,out_features,in_features]

  • bias (Optional[Union[Array, NativeArray]]) – The bias vector, default is None. [outer_batch_shape,out_features] (default: None)

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

Return type:

Array

Returns:

ret – Result array of the linear transformation. [outer_batch_shape,inner_batch_shape,out_features]

Examples

>>> x = ivy.array([[1.1, 2.2, 3.3],                            [4.4, 5.5, 6.6],                            [7.7, 8.8, 9.9]])
>>> w = ivy.array([[1., 2., 3.],                            [4., 5., 6.],                            [7., 8., 9.]])
>>> b = ivy.array([1., 0., -1.])
>>> y = x.linear(w, bias=b)
>>> print(y)
ivy.array([[ 16.4,  35.2,  54. ],
           [ 36.2,  84.7, 133. ],
           [ 56. , 134. , 212. ]])
Container.linear(self, weight, /, *, bias=None, key_chains=None, to_apply=True, prune_unapplied=False, map_sequences=False, out=None)#

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

Parameters:

  • self (Container) – The input container to compute linear transformation on. [outer_batch_shape,inner_batch_shape,in_features]

  • weight (Union[Array, NativeArray]) – The weight matrix. [outer_batch_shape,out_features,in_features]

  • bias (Optional[Union[Array, NativeArray]]) – The bias vector, default is None. [outer_batch_shape,out_features] (default: None)

  • 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 (default: None) that the inputs broadcast to.

Return type:

Container

Returns:

ret – Result array of the linear transformation. [outer_batch_shape,inner_batch_shape,out_features]

Examples

>>> x = ivy.Container(a=ivy.array([[1.1, 2.2, 3.3],                                            [11., 22., 33.]]),                               b=ivy.array([[1.245, 0.278, 4.105],                                            [7., 13., 17.]]))
>>> w = ivy.array([[1., 2., 3.],                            [4., 5., 6.],                            [7., 8., 9.]])
>>> b = ivy.array([1, 0, -1])
>>> y = x.linear(w, bias=b)
>>> print(y)
{
    a: ivy.array([[16.4, 35.2, 54.],                           [155., 352., 549.]]),             b: ivy.array([[15.1, 31., 46.9],                           [85., 195., 305.]])
}