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AttributesParameters

Attributes

n : int

Number of equations.

status : string

Current status of the solver: 'running', 'finished' or 'failed'.

t_bound : float

Boundary time.

direction : float

Integration direction: +1 or -1.

t : float

Current time.

y : ndarray

Current state.

t_old : float

Previous time. None if no steps were made yet.

nfev : int

Number of evaluations of the right-hand side.

njev : int

Number of evaluations of the Jacobian.

This is a wrapper to the Fortran solver from ODEPACK . It switches automatically between the nonstiff Adams method and the stiff BDF method. The method was originally detailed in .

Parameters

fun : callable

Right-hand side of the system. The calling signature is fun(t, y) . Here t is a scalar, and there are two options for the ndarray y : It can either have shape (n,); then fun must return array_like with shape (n,). Alternatively it can have shape (n, k); then fun must return an array_like with shape (n, k), i.e. each column corresponds to a single column in y . The choice between the two options is determined by :None:None:`vectorized` argument (see below). The vectorized implementation allows a faster approximation of the Jacobian by finite differences (required for this solver).

t0 : float

Initial time.

y0 : array_like, shape (n,)

Initial state.

t_bound : float

Boundary time - the integration won't continue beyond it. It also determines the direction of the integration.

first_step : float or None, optional

Initial step size. Default is None which means that the algorithm should choose.

min_step : float, optional

Minimum allowed step size. Default is 0.0, i.e., the step size is not bounded and determined solely by the solver.

max_step : float, optional

Maximum allowed step size. Default is np.inf, i.e., the step size is not bounded and determined solely by the solver.

rtol, atol : float and array_like, optional

Relative and absolute tolerances. The solver keeps the local error estimates less than atol + rtol * abs(y) . Here :None:None:`rtol` controls a relative accuracy (number of correct digits), while atol controls absolute accuracy (number of correct decimal places). To achieve the desired :None:None:`rtol`, set atol to be lower than the lowest value that can be expected from rtol * abs(y) so that :None:None:`rtol` dominates the allowable error. If atol is larger than rtol * abs(y) the number of correct digits is not guaranteed. Conversely, to achieve the desired atol set :None:None:`rtol` such that rtol * abs(y) is always lower than atol . If components of y have different scales, it might be beneficial to set different atol values for different components by passing array_like with shape (n,) for atol . Default values are 1e-3 for :None:None:`rtol` and 1e-6 for atol .

jac : None or callable, optional

Jacobian matrix of the right-hand side of the system with respect to y . The Jacobian matrix has shape (n, n) and its element (i, j) is equal to d f_i / d y_j . The function will be called as jac(t, y) . If None (default), the Jacobian will be approximated by finite differences. It is generally recommended to provide the Jacobian rather than relying on a finite-difference approximation.

lband, uband : int or None

Parameters defining the bandwidth of the Jacobian, i.e., jac[i, j] != 0 only for i - lband <= j <= i + uband . Setting these requires your jac routine to return the Jacobian in the packed format: the returned array must have n columns and uband + lband + 1 rows in which Jacobian diagonals are written. Specifically jac_packed[uband + i - j , j] = jac[i, j] . The same format is used in scipy.linalg.solve_banded (check for an illustration). These parameters can be also used with jac=None to reduce the number of Jacobian elements estimated by finite differences.

vectorized : bool, optional

Whether :None:None:`fun` is implemented in a vectorized fashion. A vectorized implementation offers no advantages for this solver. Default is False.

Adams/BDF method with automatic stiffness detection and switching.

Examples

See :

Local connectivity graph

Hover to see nodes names; edges to Self not shown, Caped at 50 nodes.

Using a canvas is more power efficient and can get hundred of nodes ; but does not allow hyperlinks; , arrows or text (beyond on hover)

SVG is more flexible but power hungry; and does not scale well to 50 + nodes.

All aboves nodes referred to, (or are referred from) current nodes; Edges from Self to other have been omitted (or all nodes would be connected to the central node "self" which is not useful). Nodes are colored by the library they belong to, and scaled with the number of references pointing them


GitHub : /scipy/integrate/_ivp/lsoda.py#7
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