tfZtddlZddlmZmZmZddlmcmZ ddl m Z deeddedddZ dZ dddddd ddd Zy) N)_xtol_rtol_iter) _RichResult)argsxatolxrtolfatolfrtolmaxitercallbackcxt|||||||| } | \}}}}}}}} tj|||f|} | \}} } }}}| \}}| \}}tj|tj t }d\}}|tn|}|tn|}|tj|jn|}|tjtj|tj|z}t||||ddd|||||||}gd}d}d}d }d }d }tj|| ||||||||||| S) aFind the root of an elementwise function using Chandrupatla's algorithm. For each element of the output of `func`, `chandrupatla` seeks the scalar root that makes the element 0. This function allows for `a`, `b`, and the output of `func` to be of any broadcastable shapes. Parameters ---------- func : callable The function whose root is desired. The signature must be:: func(x: ndarray, *args) -> ndarray where each element of ``x`` is a finite real and ``args`` is a tuple, which may contain an arbitrary number of components of any type(s). ``func`` must be an elementwise function: each element ``func(x)[i]`` must equal ``func(x[i])`` for all indices ``i``. `_chandrupatla` seeks an array ``x`` such that ``func(x)`` is an array of zeros. a, b : array_like The lower and upper bounds of the root of the function. Must be broadcastable with one another. args : tuple, optional Additional positional arguments to be passed to `func`. xatol, xrtol, fatol, frtol : float, optional Absolute and relative tolerances on the root and function value. See Notes for details. maxiter : int, optional The maximum number of iterations of the algorithm to perform. callback : callable, optional An optional user-supplied function to be called before the first iteration and after each iteration. Called as ``callback(res)``, where ``res`` is a ``_RichResult`` similar to that returned by `_chandrupatla` (but containing the current iterate's values of all variables). If `callback` raises a ``StopIteration``, the algorithm will terminate immediately and `_chandrupatla` will return a result. Returns ------- res : _RichResult An instance of `scipy._lib._util._RichResult` with the following attributes. The descriptions are written as though the values will be scalars; however, if `func` returns an array, the outputs will be arrays of the same shape. x : float The root of the function, if the algorithm terminated successfully. nfev : int The number of times the function was called to find the root. nit : int The number of iterations of Chandrupatla's algorithm performed. status : int An integer representing the exit status of the algorithm. ``0`` : The algorithm converged to the specified tolerances. ``-1`` : The algorithm encountered an invalid bracket. ``-2`` : The maximum number of iterations was reached. ``-3`` : A non-finite value was encountered. ``-4`` : Iteration was terminated by `callback`. ``1`` : The algorithm is proceeding normally (in `callback` only). success : bool ``True`` when the algorithm terminated successfully (status ``0``). fun : float The value of `func` evaluated at `x`. xl, xr : float The lower and upper ends of the bracket. fl, fr : float The function value at the lower and upper ends of the bracket. Notes ----- Implemented based on Chandrupatla's original paper [1]_. If ``xl`` and ``xr`` are the left and right ends of the bracket, ``xmin = xl if abs(func(xl)) <= abs(func(xr)) else xr``, and ``fmin0 = min(func(a), func(b))``, then the algorithm is considered to have converged when ``abs(xr - xl) < xatol + abs(xmin) * xrtol`` or ``fun(xmin) <= fatol + abs(fmin0) * frtol``. This is equivalent to the termination condition described in [1]_ with ``xrtol = 4e-10``, ``xatol = 1e-5``, and ``fatol = frtol = 0``. The default values are ``xatol = 2e-12``, ``xrtol = 4 * np.finfo(float).eps``, ``frtol = 0``, and ``fatol`` is the smallest normal number of the ``dtype`` returned by ``func``. References ---------- .. [1] Chandrupatla, Tirupathi R. "A new hybrid quadratic/bisection algorithm for finding the zero of a nonlinear function without using derivatives". Advances in Engineering Software, 28(3), 145-149. https://doi.org/10.1016/s0965-9978(96)00051-8 See Also -------- brentq, brenth, ridder, bisect, newton Examples -------- >>> from scipy import optimize >>> def f(x, c): ... return x**3 - 2*x - c >>> c = 5 >>> res = optimize._chandrupatla._chandrupatla(f, 0, 3, args=(c,)) >>> res.x 2.0945514818937463 >>> c = [3, 4, 5] >>> res = optimize._chandrupatla._chandrupatla(f, 0, 3, args=(c,)) >>> res.x array([1.8932892 , 2. , 2.09455148]) dtype)rN?)x1f1x2f2x3f3tr r r r nitnfevstatus) rr)xxmin)funfminrrrrxlrflr)xrr)frrcl|j|j|j|jz zz}|SN)rrr)workr s f/var/www/html/software/conda/envs/higlass/lib/python3.12/site-packages/scipy/optimize/_chandrupatla.py pre_func_evalz$_chandrupatla..pre_func_evals+ GGdff$'' 12 2c|jj|jjc|_|_t j |t j |jk(}|}|j||j|c|j|<|j|<|j||j|c|j|<|j|<||c|_|_yr-) rcopyrrrnpsignrr)r fr.jnjs r/post_func_evalz%_chandrupatla..post_func_evals 77<<>477<<> GGAJ"''$''* *R!%TWWQZ DGGAJ#'772;   TWWR[ar1c6tj|jtj|jk}tj||j |j f|_tj||j|jf|_tj|j t}t|j |j z |_ t|j|jz|jz|_|j|jk}|tj|j|j|j zkz}t"j$|j&|<d||<tj(|jtj(|jk(|z}tj*tj*t"j,c|j|<|j|<|j&|<d||<tj.|j tj.|j ztj.|jztj.|jz|z}tj*tj*t"j0c|j|<|j|<|j&|<d||<|S)NrT)r4absrrchooserrr!r# zeros_likebooldxr r tolr r eim _ECONVERGEDrr5nan _ESIGNERRisfinite _EVALUEERR)r.istops r/check_terminationz(_chandrupatla..check_terminations FF477ObffTWWo -IIa$''477!34 IIa$''477!34 }}TWWD1dgg'(tyy>DJJ.; GGdhh  RVVDII $**tzz"9 99 AQ WWTWW !1 1dU :57VVRVVS]]2 ! diilDKKNQ{{477#bkk$''&::TWW%&(* DGG(<=@DE F57VVRVVS^^2 ! diilDKKNQ r1c|j|jz |j|jz z }|j|jz |j |jz z }|j|jz |j|jz z }dt jd|z z |k|t j|kz}|j||j||j |||f\}}}}t j|d} |||z z |z||z z ||z||z z |z||z z z | |<d|jz|jz } t j| | d| z |_ y)Nrr) rrrrrrr4sqrt full_liker@r?clipr) r.xi1phi1alphar7f1jf2jf3jalphajrtls r/post_termination_checkz-_chandrupatla..post_termination_checksSww TWWtww%67$''!dgg&78477"tww'89"''!c'""d *tbggcl/B C $ DGGAJ E!H LS#v LL $sSy!C'3953,#),s2cCi@A! 488^dgg %BB'r1c"|d|d|d|df\}}}}|d|dk}tj|||f|d<tj|||f|d<tj|||f|d<tj|||f|d<|SNr'r*r)r+r4r<resshaper'r*r)r+rGs r/customize_resultz'_chandrupatla..customize_resultTCIs4y#d)CBB ID !IIa"b*D IIa"b*D IIa"b*D IIa"b*D  r1)_chandrupatla_ivrA _initializer4rL _EINPROGRESSintrrfinfotinyminimumr;r_loop)funcabr r r r r rrr[tempxsfsr\rrrrrrrrr.res_work_pairsr0r9rIrVr]s r/ _chandrupatlarnsdd 4ue %( 344 ;;t w :: 1uq % 1uq % 1uq % 1uq: ;D MM$**bii 0BFF4!84Dvvbhhtn%t);CDDg,K+1DEEHX$6788 ueUE7H DDr1dcTt||||||| | } | \}}}}}}} } |||f} tj|| |} | \}} }}}}| \}}}|\}}}|jd}t j |tj t}d\}}|t j|jn|}|t j|jn|}|t j|jn|}|2t jt j|jn|}t j|||ft j|||f}} t j| d}t j| |d\}}}t j||d\}}}|j}t!did|d|d|d |d |d |d |d |d|d|d|d|d|d|d|d|}gd}d}d}d}d}d} tj"|| || |||||||| | S)aFind the minimizer of an elementwise function. For each element of the output of `func`, `_chandrupatla_minimize` seeks the scalar minimizer that minimizes the element. This function allows for `x1`, `x2`, `x3`, and the elements of `args` to be arrays of any broadcastable shapes. Parameters ---------- func : callable The function whose minimizer is desired. The signature must be:: func(x: ndarray, *args) -> ndarray where each element of ``x`` is a finite real and ``args`` is a tuple, which may contain an arbitrary number of arrays that are broadcastable with `x`. ``func`` must be an elementwise function: each element ``func(x)[i]`` must equal ``func(x[i])`` for all indices ``i``. `_chandrupatla` seeks an array ``x`` such that ``func(x)`` is an array of minima. x1, x2, x3 : array_like The abscissae of a standard scalar minimization bracket. A bracket is valid if ``x1 < x2 < x3`` and ``func(x1) > func(x2) <= func(x3)``. Must be broadcastable with one another and `args`. args : tuple, optional Additional positional arguments to be passed to `func`. Must be arrays broadcastable with `x1`, `x2`, and `x3`. If the callable to be differentiated requires arguments that are not broadcastable with `x`, wrap that callable with `func` such that `func` accepts only `x` and broadcastable arrays. xatol, xrtol, fatol, frtol : float, optional Absolute and relative tolerances on the minimizer and function value. See Notes for details. maxiter : int, optional The maximum number of iterations of the algorithm to perform. callback : callable, optional An optional user-supplied function to be called before the first iteration and after each iteration. Called as ``callback(res)``, where ``res`` is a ``_RichResult`` similar to that returned by `_chandrupatla_minimize` (but containing the current iterate's values of all variables). If `callback` raises a ``StopIteration``, the algorithm will terminate immediately and `_chandrupatla_minimize` will return a result. Returns ------- res : _RichResult An instance of `scipy._lib._util._RichResult` with the following attributes. (The descriptions are written as though the values will be scalars; however, if `func` returns an array, the outputs will be arrays of the same shape.) success : bool ``True`` when the algorithm terminated successfully (status ``0``). status : int An integer representing the exit status of the algorithm. ``0`` : The algorithm converged to the specified tolerances. ``-1`` : The algorithm encountered an invalid bracket. ``-2`` : The maximum number of iterations was reached. ``-3`` : A non-finite value was encountered. ``-4`` : Iteration was terminated by `callback`. ``1`` : The algorithm is proceeding normally (in `callback` only). x : float The minimizer of the function, if the algorithm terminated successfully. fun : float The value of `func` evaluated at `x`. nfev : int The number of points at which `func` was evaluated. nit : int The number of iterations of the algorithm that were performed. xl, xm, xr : float The final three-point bracket. fl, fm, fr : float The function value at the bracket points. Notes ----- Implemented based on Chandrupatla's original paper [1]_. If ``x1 < x2 < x3`` are the points of the bracket and ``f1 > f2 <= f3`` are the values of ``func`` at those points, then the algorithm is considered to have converged when ``x3 - x1 <= abs(x2)*xrtol + xatol`` or ``(f1 - 2*f2 + f3)/2 <= abs(f2)*frtol + fatol``. Note that first of these differs from the termination conditions described in [1]_. The default values of `xrtol` is the square root of the precision of the appropriate dtype, and ``xatol=fatol = frtol`` is the smallest normal number of the appropriate dtype. References ---------- .. [1] Chandrupatla, Tirupathi R. (1998). "An efficient quadratic fit-sectioning algorithm for minimization without derivatives". Computer Methods in Applied Mechanics and Engineering, 152 (1-2), 211-217. https://doi.org/10.1016/S0045-7825(97)00190-4 See Also -------- golden, brent, bounded Examples -------- >>> from scipy.optimize._chandrupatla import _chandrupatla_minimize >>> def f(x, args=1): ... return (x - args)**2 >>> res = _chandrupatla_minimize(f, -5, 0, 5) >>> res.x 1.0 >>> c = [1, 1.5, 2] >>> res = _chandrupatla_minimize(f, -5, 0, 5, args=(c,)) >>> res.x array([1. , 1.5, 2. ]) gw?r)rr)axisrrrrrrphir r r r rrrq0r ) r)r r)r"rr$r%r&)xmr)r*rr()fmr)r+rc|j|jz }|j|jz }||j|jz z}||j |jz z}|||zz }d||j|jz z|jz|jzz}t ||jz dt |zk}||}t |||j|z |j|k} |j|| tj||| |j|| zz|| <|jd|jz |zz} || |<||_| S)Nrr) rrrrrrr;rxtolr4r5r) r.x21x32ABCq1rGxir7r s r/r0z-_chandrupatla_minimize..pre_func_evalsWgggg 477TWW$ % 477TWW$ % QK Atww()DGG3dgg= > TWW c#h . 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