heyoka.var_ode_sys

heyoka.var_ode_sys#

class heyoka.var_ode_sys#

Class to represent variational ODE systems.

Added in version 5.0.0.

Note

A tutorial explaining the use of this class is available.

Methods

__init__(self, sys, args[, order])

Constructor.

Attributes

n_orig_sv

The number of original state variables.

order

The differentitation order.

sys

The full system of equations (including partials).

vargs

The list of variational arguments.
__init__(self, sys: list[tuple[expression, expression]], args: var_args | list[expression], order: int = 1)#

Constructor.

A variational ODE system is constructed from two mandatory arguments: the original ODE system sys and an args parameter representing the quantities with respect to which the variational equations will be formulated.

If args is of type var_args, then the variational equations will be constructed with respect to arguments deduced from sys. E.g., if sys contains the two state variables x and y and args is the vars enumerator of var_args, then the variational equations will be formulated with respect to the initial conditions of x and y. Similarly, if sys contains two parameters par[0] and par[1] and args is the params enumerator of var_args, then the variational equations will be formulated with respect to the two parameters.

If args is a list of expression, then the variational equations will be formulated with respect to the quantities contained in the list. Specifically:

  • variable expression are used to request derivatives with respect to the intial conditions for that state variable;

  • parameter expressions are used to request derivatives with respect to those parameters;

  • heyoka.time is used to request the derivative with respect to the initial integration time.

Several checks are run on the input arguments. Specifically:

  • sys must be a valid ODE system;

  • if args is of type var_args, it must be either one of the valid enumerators or a combination of the valid enumerators;

  • if args is a list of expressions:

    • it must not be empty,

    • it must consists only of variables, parameters or the heyoka.time expression,

    • it must not contain duplicates,

    • any variable expression must refer to a state variable in sys.

Additionally, the differentiation order order must be at least 1.

Parameters:

  • sys – the input ODE system.

  • args – the variational arguments.

  • order – the differentiation order.

Raises:

ValueError – if one or more input arguments are malformed, as explained above.

property n_orig_sv#

The number of original state variables.

Return type:

int

property order#

The differentitation order.

Return type:

int

property sys#

The full system of equations (including partials).

Return type:

list[tuple[expression, expression]]

property vargs#

The list of variational arguments.

Return type:

list[expression]

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