API reference · 12

Hessian

A symmetric block-sparse second derivative together with the symbolic terms needed to assemble its numeric values and gradient.

Hessians are normally returned by differentiator.diff2 when its two target lists match.

hessian

hessian(wrt, local_targets=[], dynamic_instances=False)

Create an empty hessian layout for a set of static target attributes. The differentiator fills the symbolic assembly data.

Parameter	Type	Default	Description
`wrt`	`list[attribute]`	required	Ordered, static differentiation targets.
`local_targets`	`list[attribute]`	`[]`	Local targets associated with the first symbolic term.
`dynamic_instances`	`bool`	`False`	Whether the initial symbolic term uses dynamic instances.

Returns: new hessian.

Raises: ValueError for dynamic targets or an empty total target layout.

compute(local_gradient=None)

Assemble the numeric sparse blocks, diagonal data, and gradient using current attribute and connectivity values.

Parameter	Type	Default	Description
`local_gradient`	gradient or `None`	`None`	Optional existing gradient buffer with the same target layout.

Example

adjoint_hessian.compute()
right_hand_side = adjoint_hessian.gradient

Returns: this hessian.

left + right

Combine hessian terms with the same ordered wrt layout. Static and dynamic contributions remain separate until numeric assembly.

Example

adjoint_hessian = elastic_hessian + inertia_hessian

Returns: combined hessian.

Raises: ValueError when target layouts differ; TypeError when the other operand is not a hessian.

Property	Type	Description
`rows`	`int`	Hessian row count.
`cols`	`int`	Hessian column count; equal to `rows`.
`wrt`	`list[attribute]`	Ordered differentiation targets.
`wrt_start_indices`	`list[int]`	Cumulative offsets for the target segments.
`local_targets`	`list[list[attribute]]`	Local targets for each combined symbolic term.
`dynamic_instances`	`bool`	Whether the original term was marked dynamic.
`gradient`	gradient or `None`	Assembled gradient associated with this hessian.
`diagonal`	`pycuda.gpuarray.GPUArray`	Flat numeric hessian diagonal.
`diagonal_blocks`	`pycuda.gpuarray.GPUArray`	Flattened diagonal blocks used by the solver preconditioner.
`diagonal_blocks_inverse`	`pycuda.gpuarray.GPUArray`	Storage for inverted diagonal blocks.
`gradient_segments_start_cpu`	`list[int]`	CPU offsets delimiting gradient segments.
`block_dimensions`	`list[int]`	Static sparse block dimensions.
`block_counts`	`list[int]`	Static block count per dimension category.
`block_dimensions_dynamic`	`list[int]`	Dynamic sparse block dimensions.
`block_counts_dynamic`	`list[int]`	Dynamic block count per dimension category.
`hash`	`int`	Hash derived from the ordered `wrt` attributes.