scipy.integrate.OdeSolver#
- class scipy.integrate.OdeSolver(fun, t0, y0, t_bound, vectorized, support_complex=False)[source]#
Base class for ODE solvers.
In order to implement a new solver you need to follow the guidelines:
A constructor must accept parameters presented in the base class (listed below) along with any other parameters specific to a solver.
A constructor must accept arbitrary extraneous arguments
**extraneous
, but warn that these arguments are irrelevant using common.warn_extraneous function. Do not pass these arguments to the base class.A solver must implement a private method _step_impl(self) which propagates a solver one step further. It must return tuple
(success, message)
, wheresuccess
is a boolean indicating whether a step was successful, andmessage
is a string containing description of a failure if a step failed or None otherwise.A solver must implement a private method _dense_output_impl(self), which returns a
DenseOutput
object covering the last successful step.A solver must have attributes listed below in Attributes section. Note that
t_old
andstep_size
are updated automatically.Use fun(self, t, y) method for the system rhs evaluation, this way the number of function evaluations (nfev) will be tracked automatically.
For convenience, a base class provides fun_single(self, t, y) and fun_vectorized(self, t, y) for evaluating the rhs in non-vectorized and vectorized fashions respectively (regardless of how fun from the constructor is implemented). These calls don’t increment nfev.
If a solver uses a Jacobian matrix and LU decompositions, it should track the number of Jacobian evaluations (njev) and the number of LU decompositions (nlu).
By convention, the function evaluations used to compute a finite difference approximation of the Jacobian should not be counted in nfev, thus use fun_single(self, t, y) or fun_vectorized(self, t, y) when computing a finite difference approximation of the Jacobian.
- Parameters:
- funcallable
Right-hand side of the system: the time derivative of the state
y
at timet
. The calling signature isfun(t, y)
, wheret
is a scalar andy
is an ndarray withlen(y) = len(y0)
.fun
must return an array of the same shape asy
. See vectorized for more information.- t0float
Initial time.
- y0array_like, shape (n,)
Initial state.
- t_boundfloat
Boundary time — the integration won’t continue beyond it. It also determines the direction of the integration.
- vectorizedbool
Whether fun can be called in a vectorized fashion. Default is False.
If
vectorized
is False, fun will always be called withy
of shape(n,)
, wheren = len(y0)
.If
vectorized
is True, fun may be called withy
of shape(n, k)
, wherek
is an integer. In this case, fun must behave such thatfun(t, y)[:, i] == fun(t, y[:, i])
(i.e. each column of the returned array is the time derivative of the state corresponding with a column ofy
).Setting
vectorized=True
allows for faster finite difference approximation of the Jacobian by methods ‘Radau’ and ‘BDF’, but will result in slower execution for other methods. It can also result in slower overall execution for ‘Radau’ and ‘BDF’ in some circumstances (e.g. smalllen(y0)
).- support_complexbool, optional
Whether integration in a complex domain should be supported. Generally determined by a derived solver class capabilities. Default is False.
- Attributes:
- nint
Number of equations.
- statusstring
Current status of the solver: ‘running’, ‘finished’ or ‘failed’.
- t_boundfloat
Boundary time.
- directionfloat
Integration direction: +1 or -1.
- tfloat
Current time.
- yndarray
Current state.
- t_oldfloat
Previous time. None if no steps were made yet.
- step_sizefloat
Size of the last successful step. None if no steps were made yet.
- nfevint
Number of the system’s rhs evaluations.
- njevint
Number of the Jacobian evaluations.
- nluint
Number of LU decompositions.
Methods
Compute a local interpolant over the last successful step.
step
()Perform one integration step.