anabel

Transient

General transformations and utilities for transient modeling.

Functions

def linear_hot(f, df)

Add a linear higher order term to a function

Examples

First define some matrices

>>A = jnp.array([[1.0, 0.0, 0.0],
                 [0.0, 4.0, 2.0],
                 [0.0, 2.0, 4.0]])
>>B = jnp.array([[-0.23939017,  0.58743526, -0.77305379],
                 [ 0.81921268, -0.30515101, -0.48556508],
                 [-0.52113619, -0.74953498, -0.40818426]])
>>C = A@B

Next define a linear function, f: x -> Ax:

>>f = anon.dual.wrap(
    lambda x,*args,**kwds: x, A@x, {},
    dim=3
)

Create a new function with a linear higher order term (ff: x,dx -> f(x) + Bdx)

>>ff = linear_hot(f, B)

>>x = dx = jnp.ones((3,1))

>>f(x)
(DeviceArray([[1.],
            [1.],
            [1.]], dtype=float32),
DeviceArray([[1.],
            [6.],
            [6.]], dtype=float32),
{})

>>ff((x, dx))
((DeviceArray([[1.],
            [1.],
            [1.]], dtype=float32),
DeviceArray([[1.],
            [1.],
            [1.]], dtype=float32)),
DeviceArray([[0.57499135],
            [6.0284967 ],
            [4.3211446 ]], dtype=float32),
{})

Studies

elle-0008