+ LV-jLx^RIt^RIHtHt^RIHtHtHt^RI H t ^RI H t ^RI HtHtHtHtHtHtHtHt^RIHtHtRt]P4!^], ^ , ^],^ , ^.4t]P4!R^],, R^],,R.4^, tRtRt]P4!.RO.RO.RO.4t]P4!.RO.RO.RO.4t ] ^,t!] ^,R] ^,,,t"]P4!R^],^, ,R^],^, , R^],,.R^],^, , R^],^, ,R^],, ..RO.4t#^t$R t%^ t&R t'R t(!R R ]4t)!RR]4t*R#)N) lu_factorlu_solve) csc_matrixissparseeye)splu) group_columns)validate_max_step validate_tolselect_initial_stepnormnum_jacEPSwarn_extraneousvalidate_first_step) OdeSolver DenseOutput?g?c VP^,p \V, p \V, p \P V4p Tp\ P !^V 34pV\,pRp\ P!V 4pRpRp\\4EFp\^4F*pV!VVV,,W.V,,4VV&K, \ P!\ P!V44'gEMZVPP \4W^,,, pVPP \4W^,RV ^,,,,, pV !VV4pV !VV4pVV^&VP V^&VP"V^&\%VV, 4pVe VV, pVe8V^8g/V\V, ,^V, , V,V8dMPV V, p \P V 4pV^8Xg!Ve!V^V, , V,V8dRpMTpEK VX^,VV3#)aSolve the collocation system. Parameters ---------- fun : callable Right-hand side of the system. t : float Current time. y : ndarray, shape (n,) Current state. h : float Step to try. Z0 : ndarray, shape (3, n) Initial guess for the solution. It determines new values of `y` at ``t + h * C`` as ``y + Z0``, where ``C`` is the Radau method constants. scale : ndarray, shape (n) Problem tolerance scale, i.e. ``rtol * abs(y) + atol``. tol : float Tolerance to which solve the system. This value is compared with the normalized by `scale` error. LU_real, LU_complex LU decompositions of the system Jacobians. solve_lu : callable Callable which solves a linear system given a LU decomposition. The signature is ``solve_lu(LU, b)``. Returns ------- converged : bool Whether iterations converged. n_iter : int Number of completed iterations. Z : ndarray, shape (3, n) Found solution. rate : float The rate of convergence. NFrT)shapeMU_REAL MU_COMPLEXTIdotnpemptyC empty_likerangeNEWTON_MAXITERallisfiniteTTI_REAL TI_COMPLEXrealimagr )funtyhZ0scaletolLU_real LU_complexsolve_lunM_real M_complexWZFch dW_norm_olddW convergedratekif_real f_complexdW_real dW_complexdW_norms&&&&&&&&&& k/Volumes/fast/ai/experiments/ui-tars-smoke/.venv/lib/python3.14/site-packages/scipy/integrate/_ivp/radau.pysolve_collocation_systemrE0sN  A q[FQI r A A !QA QBK q BI D > "qAq2a5y!d(+AaDvvbkk!n%% !FqTM1CCGGJ')tb1Q4i7G*HH 7F+j)4 111rEz"  "[(D  $!)!+,D9GCcI  R EE!H qL TQX%6%@3%FI  C#F a!eQ $$cVe VeV^8Xd^pMW, W2, R,,p\P!RR7;_uu_4\^V4VR,,pRRR4V# +'giX#;i)aPredict by which factor to increase/decrease the step size. The algorithm is described in [1]_. Parameters ---------- h_abs, h_abs_old : float Current and previous values of the step size, `h_abs_old` can be None (see Notes). error_norm, error_norm_old : float Current and previous values of the error norm, `error_norm_old` can be None (see Notes). Returns ------- factor : float Predicted factor. Notes ----- If `h_abs_old` and `error_norm_old` are both not None then a two-step algorithm is used, otherwise a one-step algorithm is used. References ---------- .. [1] E. Hairer, S. P. Norsett G. Wanner, "Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems", Sec. IV.8. Ng?ignore)dividegп)rerrstatemin)h_abs h_abs_old error_normerror_norm_old multiplierfactors&&&& rDpredict_factorrRsp:!2jAo &.*E$)NN H % %Q #jE&99 & M & % Ms A33 B ctaa]tRt^toRt]P RRRRRR3V3RlltRtRt R t R t R t Vt V;t#) RadauaImplicit Runge-Kutta method of Radau IIA family of order 5. The implementation follows [1]_. The error is controlled with a third-order accurate embedded formula. A cubic polynomial which satisfies the collocation conditions is used for the dense output. 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. 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)``. HHere `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, array_like, sparse_matrix, callable}, optional Jacobian matrix of the right-hand side of the system with respect to y, required by this method. The Jacobian matrix has shape (n, n) and its element (i, j) is equal to ``d f_i / d y_j``. There are three ways to define the Jacobian: * If array_like or sparse_matrix, the Jacobian is assumed to be constant. * If callable, the Jacobian is assumed to depend on both t and y; it will be called as ``jac(t, y)`` as necessary. For the 'Radau' and 'BDF' methods, the return value might be a sparse matrix. * 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. jac_sparsity : {None, array_like, sparse matrix}, optional Defines a sparsity structure of the Jacobian matrix for a finite-difference approximation. Its shape must be (n, n). This argument is ignored if `jac` is not `None`. If the Jacobian has only few non-zero elements in *each* row, providing the sparsity structure will greatly speed up the computations [2]_. A zero entry means that a corresponding element in the Jacobian is always zero. If None (default), the Jacobian is assumed to be dense. vectorized : bool, optional Whether `fun` can be called in a vectorized fashion. Default is False. 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 this method, but may result in slower execution overall in some circumstances (e.g. small ``len(y0)``). 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. step_size : float Size of the last successful step. 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. nlu : int Number of LU decompositions. References ---------- .. [1] E. Hairer, G. Wanner, "Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems", Sec. IV.8. .. [2] A. Curtis, M. J. D. Powell, and J. Reid, "On the estimation of sparse Jacobian matrices", Journal of the Institute of Mathematics and its Applications, 13, pp. 117-120, 1974. MbP?gư>NFc <a\V 4\SS` WW4V 4RSn\ V4Sn\ WgSP4wSnSn SPSPSP4Sn V f`\SPSPSPWESPSP^SPSP4 SnM\#WV4SnRSnRSn\)^ \*,V, \-RVR,44SnRSnRSnSP5W4wSnSn\;SP84'd"V3Rlp Rp\=SPRR7pM)V3Rlp Rp\>P@!SP4pV Sn!VSn"VSn#R Sn$RSn%RSn&RSn'R#) NgQ??cL<S;P^, un\V4#)nlurAselfs&rDluRadau.__init__..luAsA AwrFc$VPV4#N)solveLUbs&&rDr1 Radau.__init__..solve_luEsxx{"rFcsc)formatcP<S;P^, un\VRR7#)rZT) overwrite_a)r[rr\s&rDr_r`JsA  55rFc\WRR7#)T) overwrite_b)rrds&&rDr1rgNs488rFT)(rsuper__init__y_oldr max_stepr r2rtolatolr(r)r*fr directionrLrrMrOmaxrrK newton_tolsol jac_factor _validate_jacjacJrrridentityr_r1I current_jacr/r0r6)r^r(t0y0t_boundrqrrrsr{ jac_sparsity vectorized first_step extraneousr_r1r~ __class__sf&&&&&&&&&&&, rDroRadau.__init__'s  # "z: )(3 +D? 49$&&$&&)  ,$&&$&&'TVVT^^499dii)DJ-ZWEDJ"b3hos4/EF--c@$& DFF    #DFF5)A 6 9 DFF#A   rFcaaaSPpSPpSfMSe,\S4'd \S4o\ S4pSV3oVV3RlpV!W4SP 4pWg3#\ S4'dS!W44p^Sn\V4'd\V4pRVV3RllpM%\P!V\R7pRVV3RllpVPSPSP38wd3\RSPSP3 RVP R24hWg3#\S4'd \S4pM\P!S\R7pVPSPSP38wd3\RSPSP3 RVP R24hRpWg3#) Nc <S;P^, un\SPWVSPSPS4wpSnV#rY)njevrfun_vectorizedrsry)r)r*rtr|r^sparsitys&&& rD jac_wrapped(Radau._validate_jac..jac_wrappedgsD Q %,T-@-@!-1YY-5&7"4?rFcd<S;P^, un\S!W4\R7#rZdtype)rrfloatr)r*_r{r^s&&&rDrrts!IINI%c!iu==rFrcz<S;P^, un\P!S!W4\R7#r)rrasarrayrrs&&&rDrr{s%IINI::c!iu==rFz `jac` is expected to have shape z, but actually has .rb)r)r*rrr rtcallablerrrrrr2 ValueError)r^r{rrrgroupsrr|sfff rDrzRadau._validate_jac\s VV VV ;#H%%)(3H&x0$f-  BDFF+A@~?c]]B ADI{{qM>> JJq.>>ww466466** #CTVVTVVDTCUV667ggYa"ABB+~}}sOJJs%0ww466466** #CTVVTVVDTCUV667ggYa"ABBK~rFc t VPpVPpVPpVPpVPpVP p^ \ P!\ P!WP\ P,4V, 4,pVPV8dTpRp Rp MWVVVVP@WVPB4 wppppV'dKV'dMVP%WV4p RpRp Rp KV'gVR,pRp Rp EKVXR,,pVP2PE\F4V, pVPCWV,4pV\ PH!\ P!V4\ P!V44V,,p\KVV, 4pR^\L,^,,^\L,X,, pV'dHV^8dAVPCWP?WV,4V,4p\KVV, 4pV^8d5\OWVV 4p V\Q\RVV ,4,pRp Rp RpEK{RpEKVRJ;'dX^8;'dXR8p!\OWXV 4p \U\VXV ,4p V!'g V R8d^p MRp Rp VP?XX4p"V!'dV!VVV"4p RpMVeRpVPVn VVn VV ,Vn W n,VVnVVnV"VnXVn-WnWnWnWnWn.VP_4VnVV3#) NFTrWg?rUg333333?)0r)r*rtrqrsrrrabs nextafterruinfrLrMrOr|r/r0rr{TOO_SMALL_STEPrrxzerosrrr#r_rr~rrEr(rwr1rEmaximumr r rRrv MIN_FACTORrK MAX_FACTORrpr6t_old_compute_dense_output)#r^r)r*rtrqrsrrmin_steprLrMrOr|r/r0rr{rejected step_acceptedmessager+t_newr,r-r;n_iterr6r<y_newZEerrorrNsafetyrQ recompute_jacf_news#& rD _step_implRadau._step_impls FF FF FF==yyyyr||A~~/FG!KLL :: EI!N ZZ( "EI!NJJEI!00N FF,,__ && hh -d1111&AEE~~!56:  AFF1IExxXXq!''!*o.XXa!a%i(**Q.266!9t++EI?j&8"gggkDFF&:Q&>?G!%a$&&)@1)D!EJ-EHHaAr5$//.8* 61d!y"q)A"&K"G!%J ! "IEaBMM'r62E2::bffQi?$FFEeem,JA.23q>7I9?8@AFJN gxxu9/E/JK!%%-0 A~'(2NDZ&99!  $ 4FFFQJFF4$; *nMZ&1#FGJ& E5%(AK _K(V^   $& --/g%%rFc\P!VPP\4p\ VP VPVPV4#rb) rrr6r#PRadauDenseOutputrr)rp)r^Qs& rDrRadau._compute_dense_outputs7 FF46688Q  DFFDJJBBrFcVP#rb)rx)r^s&rD_dense_output_implRadau._dense_output_impl!s xxrF)r~r|r0r/r6rsrrOrtrLrMr{ryr_rqrwrrrrxr1r)rr*rp)__name__ __module__ __qualname____firstlineno____doc__rrrorzrrr__static_attributes____classdictcell__ __classcell__r __classdict__s@@rDrTrTsFrf79ff4d!d3j1fL&\CrFrTc8aa]tRtRtoV3RltRtRtVtV;t#)ri%c<\SV`W4W!, VnW@nVP^,^, VnW0nR#)rZN)rnror+rrorderrp)r^rr)rprrs&&&&&rDroRadauDenseOutput.__init__&s6 "WWQZ!^  rFc*WP, VP, pVP^8Xd?\P!W P ^,4p\P !V4pMA\P!W P ^,^34p\P !V^R7p\P!VPV4pVP^8XdW@PR,, pV#W@P, pV#)r)axis):NNNN) rr+ndimrtilercumprodrrrp)r^r)xpr*s&& rD _call_implRadauDenseOutput._call_impl-s ^tvv % 66Q;::>*A 1 AJJNA./A 11%A FF4661  66Q; G$ $A OArF)rr+rrp) rrrrrorrrrrs@@rDrr%srFrg.! @irgs>H @yrr@Gg)g{g]#-?g;@L¿ghm?)g }?gQ  ?gmؿ)rZrZr)gF@gN]?gV?)gFgN]Կg!R?)g$Z?goNg{?gUUUUUU@g竪 @)gUUUUUU?gUUUUUUr)+numpyr scipy.linalgrr scipy.sparserrrscipy.sparse.linalgrscipy.optimize._numdiffr commonr r r r rrrrbaserrS6arrayrrrrr#rr$r%rr rrrErRrTrrFrDrs,22$1***) HHq2vma"f]A ./HHcAFlC!b&L" -.2 *5 HHDD XXCEDFG Q% UR"Q%Z  HH AbDF]EBrE!GOTAF]3 AbDF]EBrE!GOTAF]3    X%v%PoIod {rF