ftj'vddlZddlmZddlmZmZmZddlm Z m Z Gdde Z Gdd e Z dS) N)ode) validate_tolvalidate_first_stepwarn_extraneous) OdeSolver DenseOutputc LeZdZdZddejddddddf fd ZdZd ZxZ S) LSODAaAdams/BDF method with automatic stiffness detection and switching. This is a wrapper to the Fortran solver from ODEPACK [1]_. It switches automatically between the nonstiff Adams method and the stiff BDF method. The method was originally detailed in [2]_. Parameters ---------- fun : callable Right-hand side of the system: the time derivative of the state ``y`` at time ``t``. The calling signature is ``fun(t, y)``, where ``t`` is a scalar and ``y`` is an ndarray with ``len(y) = len(y0)``. ``fun`` must return an array of the same shape as ``y``. See `vectorized` for more information. 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 `rtol` controls a relative accuracy (number of correct digits), while `atol` controls absolute accuracy (number of correct decimal places). To achieve the desired `rtol`, set `atol` to be smaller than the smallest value that can be expected from ``rtol * abs(y)`` so that `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 `rtol` such that ``rtol * abs(y)`` is always smaller 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 `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 `fun` may be called in a vectorized fashion. False (default) is recommended for this solver. If ``vectorized`` is False, `fun` will always be called with ``y`` of shape ``(n,)``, where ``n = len(y0)``. If ``vectorized`` is True, `fun` may be called with ``y`` of shape ``(n, k)``, where ``k`` is an integer. In this case, `fun` must behave such that ``fun(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 of ``y``). Setting ``vectorized=True`` allows for faster finite difference approximation of the Jacobian by methods 'Radau' and 'BDF', but will result in slower execution for this solver. 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. References ---------- .. [1] A. C. Hindmarsh, "ODEPACK, A Systematized Collection of ODE Solvers," IMACS Transactions on Scientific Computation, Vol 1., pp. 55-64, 1983. .. [2] L. Petzold, "Automatic selection of methods for solving stiff and nonstiff systems of ordinary differential equations", SIAM Journal on Scientific and Statistical Computing, Vol. 4, No. 1, pp. 136-148, 1983. NggMbP?gư>Fc Tt|t||||| |d}nt|||}||jz}|t jkrd}n|dkrtd|dkrtdt|| |j \}} t|j | }| d|| |||| | | |||j|jjd<|jj|jjd<||_dS)Nrz`max_step` must be positive.z`min_step` must be nonnegative.lsoda)rtolatolmax_stepmin_step first_steplbanduband)rsuper__init__r directionnpinf ValueErrorrnrfunset_integratorset_initial_valuet_bound _integratorrwork call_args _lsoda_solver)selfrt0y0r rrrrrjacrr vectorized extraneoussolver __class__s X/var/www/html/CA-Chatbot/venv/lib/python3.11/site-packages/scipy/integrate/_ivp/lsoda.pyrzLSODA.__init__vsH  ### b"gz:::  JJ,ZWEEJdn$ rv  HH ]];<< < a<<>?? ?!$df55 dTXs##gDth'/J$)  8 8 8   R((('+l #*0*<*B$Q'#c |j}|j}|jd}d|jd<||j|jpd|j|j|j|j |j \|_|_||jd<| rP|j|_|j |_ |jd|_|jd|_dSdS)NcdS)Nr3r.r-z"LSODA._step_impl..sTr. )TN)FzUnexpected istate in LSODA.)r$r!r#runfr(_ytr f_params jac_params successfulcopyyiworknjevnlu)r%r+ integratoritasks r- _step_implzLSODA._step_impls#' $Q'"# Q(nn Hfj2\\FIvx L&/6+<>> 68#( Q      8XDFY^^%%DF"(,DI!'+DH:77r.c|jjj}|jjj}|d}|d}t j|dd|dz|jzz|j|dzfd}|d|kr |dddfxx||d z |zzcc<t|j |j |||S) N rF)order ) r$r!r?r"rreshaperr=LsodaDenseOutputt_oldr9)r%r?r"rJhyhs r-_dense_output_implzLSODA._dense_output_impls".4".4b  "I ZbuqyDF&:!::;+38888< 9u   qqq"uIII!eBi-E1 1III DFAubAAAr.) __name__ __module__ __qualname____doc__rrrrDrS __classcell__r,s@r-r r smm\9=s&t$D!$!$!$!$!$!$F8884 B B B B B B Br.r c$eZdZfdZdZxZS)rOct||||_||_t j|dz|_dS)Nr)rrrQrRrarangep)r%rPr9rQrJrRr,s r-rzLsodaDenseOutput.__init__sD """519%%r.c|jdkr||jz |jz |jz}n$||jz |jz |jdddfz}t j|j|S)Nr)ndimr9rQr]rdotrR)r%r9xs r- _call_implzLsodaDenseOutput._call_implsa 6Q;;df*&461AAdf*&46!!!T'?:Avdgq!!!r.)rTrUrVrrbrXrYs@r-rOrOsG&&&&& """""""r.rO) numpyrscipy.integratercommonrrrbaserr r rOr3r.r-rgsFFFFFFFFFF((((((((LBLBLBLBLBILBLBLB^ " " " " "{ " " " " "r.