(ph=SSKJr SSKJr SSKrSSKJrJr \R"\ 5Rr Sr SrSrSrS rS r"S S 5r\ S -r\ S-r\ S-rS\ -rSrSrSSjrSrSrg))groupby)warnN)find coo_matrixcvUS::a [S5eU[R"X!- 5:a [S5eU$)z.Assert that first_step is valid and return it.rz`first_step` must be positive.z`first_step` exceeds bounds.) ValueErrornpabs) first_stept0t_bounds N/var/www/html/venv/lib/python3.13/site-packages/scipy/integrate/_ivp/common.pyvalidate_first_stepr s:Q9::BFF7<((788 c(US::a [S5eU$)z,Assert that max_Step is valid and return it.rz`max_step` must be positive.)r)max_steps rvalidate_max_steprs1}788 Orc\U(a%[SSRSU55S3SS9 gg)aEDisplay a warning for extraneous keyword arguments. The initializer of each solver class is expected to collect keyword arguments that it doesn't understand and warn about them. This function prints a warning for each key in the supplied dictionary. Parameters ---------- extraneous : dict Extraneous keyword arguments z"warn_extraneous..(s7JqAaS(Js. stacklevelN)rjoin) extraneouss rwarn_extraneousr"s6 K 7J778; rc[R"US[-:5(a3[SS[-S3SS9 [R"US[-5n[R "U5nUR S:aURU4:wa [S5e[R"US:5(a [S5eX4$) zValidate tolerance values.dzNAt least one element of `rtol` is too small. Setting `rtol = np.maximum(rtol, z)`.rrrz`atol` has wrong shape.z`atol` must be positive.) r anyEPSrmaximumasarrayndimshaper)rtolatolns r validate_tolr.,s vvdS3Y 114s 3@ zz$c * ::d D yy1}t+233 vvdQh344 :rc`[RRU5URS-- $)zCompute RMS norm.?)r linalgnormsize)rs rr2r2?s" 99>>! qvv} ,,rc URS:Xa[R$[X1- 5n U S:XagU [R"U5U--n [ X+- 5n [ X[- 5n U S:dU S:aSnOSU -U - n[ X5nX.U-U--nU"XU--U5n[ UU- U - 5U- nU S::aUS::a[ SUS-5nOS[ U U5- SUS-- -n[ S U-UX5$) a4Empirically select a good initial step. The algorithm is described in [1]_. Parameters ---------- fun : callable Right-hand side of the system. t0 : float Initial value of the independent variable. y0 : ndarray, shape (n,) Initial value of the dependent variable. t_bound : float End-point of integration interval; used to ensure that t0+step<=tbound and that fun is only evaluated in the interval [t0,tbound] max_step : float Maximum allowable step size. f0 : ndarray, shape (n,) Initial value of the derivative, i.e., ``fun(t0, y0)``. direction : float Integration direction. order : float Error estimator order. It means that the error controlled by the algorithm is proportional to ``step_size ** (order + 1)`. rtol : float Desired relative tolerance. atol : float Desired absolute tolerance. Returns ------- h_abs : float Absolute value of the suggested initial step. References ---------- .. [1] E. Hairer, S. P. Norsett G. Wanner, "Solving Ordinary Differential Equations I: Nonstiff Problems", Sec. II.4. rggh㈵>gư>g{Gz?gV瞯28??4>>8))LA !"A37??Q3FDOOa//0~~*X5H  %h/NG#c$u+&66I!!'*8 +JKA IIaL#K 0 YYr] 7 ^ r)rXrUrSrYrWrVrTrZN)F) __name__ __module__ __qualname____firstlineno____doc__r^rfrw__static_attributes__rrrrIrIs#H&8 -+rrIg?g?g?g@@ g?c [R"U5nURSnUS:Xa[R"S5U4$Uc[R"U[ S-5nOUR 5nS[R"U5S:R[5-S- nU[R"U[R"U55-n X%U --U- n [R"U S:H5SH8n XS:XdM X[==S-ss'X+X[X--X+- X'XS:XaM+M: Uc[XX#XU 5$Uup[XX#XU X5 $)aFinite differences Jacobian approximation tailored for ODE solvers. This function computes finite difference approximation to the Jacobian matrix of `fun` with respect to `y` using forward differences. The Jacobian matrix has shape (n, n) and its element (i, j) is equal to ``d f_i / d y_j``. A special feature of this function is the ability to correct the step size from iteration to iteration. The main idea is to keep the finite difference significantly separated from its round-off error which approximately equals ``EPS * np.abs(f)``. It reduces a possibility of a huge error and assures that the estimated derivative are reasonably close to the true values (i.e., the finite difference approximation is at least qualitatively reflects the structure of the true Jacobian). Parameters ---------- fun : callable Right-hand side of the system implemented in a vectorized fashion. t : float Current time. y : ndarray, shape (n,) Current state. f : ndarray, shape (n,) Value of the right hand side at (t, y). threshold : float Threshold for `y` value used for computing the step size as ``factor * np.maximum(np.abs(y), threshold)``. Typically, the value of absolute tolerance (atol) for a solver should be passed as `threshold`. factor : ndarray with shape (n,) or None Factor to use for computing the step size. Pass None for the very evaluation, then use the value returned from this function. sparsity : tuple (structure, groups) or None Sparsity structure of the Jacobian, `structure` must be csc_matrix. 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