API reference · 11

Jacobian

Sparse rectangular matrices returned by differentiator.

Returned types

Type	Created by	Layout
`firstOrderJacobian`	`differentiator.diff1` with a vector-valued source	Source components form rows; target attributes form columns.
`secondOrderJacobian`	`differentiator.diff2` with different target lists	First target list forms rows; second target list forms columns.

Both types inherit the public sparse multiplication and storage API from matrix.

compute()

Generate any required kernels, assemble sparse coordinates, and update the numeric static and dynamic block values.

Example

previous_position_jacobian.compute()
young_jacobian.compute()

Returns: this jacobian.

spmv(x, transpose=False)

Apply the assembled jacobian or its transpose to a compatible YASPS vector.

Parameter	Type	Default	Description
`x`	compatible YASPS vector	required	Input vector matching the selected orientation.
`transpose`	`bool`	`False`	Apply the transpose when `True`.

Example

young_gradient = young_gradient - young_jacobian.spmv(auxiliary, transpose=True)

Returns: compatible YASPS vector.

left + right

Combine jacobian terms with identical row and column layouts. The result retains every static and dynamic symbolic contribution.

Example

combined_jacobian = inertia_jacobian + friction_jacobian

Returns: combined jacobian of the same type.

Raises: ValueError when the target layouts differ; TypeError when the jacobian types are incompatible.

Property	Type	Applies to	Description
`rows`	`int`	both	Numeric row count.
`cols`	`int`	both	Numeric column count.
`block_dimensions`	`list[int]`	both	Static sparse block dimensions.
`block_counts`	`list[int]`	both	Static block count per dimension category.
`block_dimensions_dynamic`	`list[int]`	both	Dynamic sparse block dimensions.
`block_counts_dynamic`	`list[int]`	both	Dynamic block count per dimension category.
`row_source`	attribute	first order	Vector-valued source whose components form the rows.
`wrt`	`list[attribute]`	first order	Ordered column targets.
`row_wrt`	`list[attribute]`	second order	Ordered row targets.
`column_wrt`	`list[attribute]`	second order	Ordered column targets.
`row_start_indices`	`list[int]`	second order	Cumulative row offsets for `row_wrt`.
`column_start_indices`	`list[int]`	second order	Cumulative column offsets for `column_wrt`.