o wThOj@sdZddlmZddlmZddlZgdZGdddeZ d d Z    d-ddZ  d.ddZ e Z   d/ddZ    d0ddZddZddZddZd1d d!Zd1d"d#Zd2d$d%Z 'd3d(d)Z ' *d4d+d,ZdS)5z Functions --------- .. autosummary:: :toctree: generated/ line_search_armijo line_search_wolfe1 line_search_wolfe2 scalar_search_wolfe1 scalar_search_wolfe2 )warn)DCSRCHN)LineSearchWarningline_search_wolfe1line_search_wolfe2scalar_search_wolfe1scalar_search_wolfe2line_search_armijoc@s eZdZdS)rN)__name__ __module__ __qualname__rr[/home/air/segue/gemini/back/venv/lib/python3.10/site-packages/scipy/optimize/_linesearch.pyrsrcCs2d|kr|krdkstdtddS)Nrrz.'c1' and 'c2' do not satisfy'0 < c1 < c2 < 1'.) ValueError)c1c2rrr _check_c1_c2s rr-C6??2:0yE>+=c  s|dur gR}|gdgdgfdd} fdd}t|}t| |||||| | | | d \}}}|dd||dfS)a1 As `scalar_search_wolfe1` but do a line search to direction `pk` Parameters ---------- f : callable Function `f(x)` fprime : callable Gradient of `f` xk : array_like Current point pk : array_like Search direction gfk : array_like, optional Gradient of `f` at point `xk` old_fval : float, optional Value of `f` at point `xk` old_old_fval : float, optional Value of `f` at point preceding `xk` The rest of the parameters are the same as for `scalar_search_wolfe1`. Returns ------- stp, f_count, g_count, fval, old_fval As in `line_search_wolfe1` gval : array Gradient of `f` at the final point Notes ----- Parameters `c1` and `c2` must satisfy ``0 < c1 < c2 < 1``. Nrc(dd7<|gRSNrrrsargsffcpkxkrrphiRzline_search_wolfe1..phics<|gRd<dd7<tdSrnpdotr)rfprimegcgvalr!r"rrderphiVsz"line_search_wolfe1..derphi)rramaxaminxtol)r&r'r)rr(r"r!gfkold_fval old_old_fvalrrrr,r-r.r#r+derphi0stpfvalr)rrr r(r)r*r!r"rr%s&    rc Cst|||dur |d}|dur|d}|dur/|dkr/tdd|||} | dkr.d} nd} d} t||||| ||} | | ||| d\} }}}| ||fS)a Scalar function search for alpha that satisfies strong Wolfe conditions alpha > 0 is assumed to be a descent direction. Parameters ---------- phi : callable phi(alpha) Function at point `alpha` derphi : callable phi'(alpha) Objective function derivative. Returns a scalar. phi0 : float, optional Value of phi at 0 old_phi0 : float, optional Value of phi at previous point derphi0 : float, optional Value derphi at 0 c1 : float, optional Parameter for Armijo condition rule. c2 : float, optional Parameter for curvature condition rule. amax, amin : float, optional Maximum and minimum step size xtol : float, optional Relative tolerance for an acceptable step. Returns ------- alpha : float Step size, or None if no suitable step was found phi : float Value of `phi` at the new point `alpha` phi0 : float Value of `phi` at `alpha=0` Notes ----- Uses routine DCSRCH from MINPACK. Parameters `c1` and `c2` must satisfy ``0 < c1 < c2 < 1`` as described in [1]_. References ---------- .. [1] Nocedal, J., & Wright, S. J. (2006). Numerical optimization. In Springer Series in Operations Research and Financial Engineering. (Springer Series in Operations Research and Financial Engineering). Springer Nature. Nr?)\(@d)phi0r2maxiter)rminr)r#r+r9old_phi0r2rrr,r-r.alpha1r:dcsrchr3phi1taskrrrrds" 5 r c  sdgdgdgdg fdd} | fdd|dur0 gR}t| }durF fdd}nd}t| ||||| | || d \}}}}|durftd td d nd}|dd|||fS) a Find alpha that satisfies strong Wolfe conditions. Parameters ---------- f : callable f(x,*args) Objective function. myfprime : callable f'(x,*args) Objective function gradient. xk : ndarray Starting point. pk : ndarray Search direction. The search direction must be a descent direction for the algorithm to converge. gfk : ndarray, optional Gradient value for x=xk (xk being the current parameter estimate). Will be recomputed if omitted. old_fval : float, optional Function value for x=xk. Will be recomputed if omitted. old_old_fval : float, optional Function value for the point preceding x=xk. args : tuple, optional Additional arguments passed to objective function. c1 : float, optional Parameter for Armijo condition rule. c2 : float, optional Parameter for curvature condition rule. amax : float, optional Maximum step size extra_condition : callable, optional A callable of the form ``extra_condition(alpha, x, f, g)`` returning a boolean. Arguments are the proposed step ``alpha`` and the corresponding ``x``, ``f`` and ``g`` values. The line search accepts the value of ``alpha`` only if this callable returns ``True``. If the callable returns ``False`` for the step length, the algorithm will continue with new iterates. The callable is only called for iterates satisfying the strong Wolfe conditions. maxiter : int, optional Maximum number of iterations to perform. Returns ------- alpha : float or None Alpha for which ``x_new = x0 + alpha * pk``, or None if the line search algorithm did not converge. fc : int Number of function evaluations made. gc : int Number of gradient evaluations made. new_fval : float or None New function value ``f(x_new)=f(x0+alpha*pk)``, or None if the line search algorithm did not converge. old_fval : float Old function value ``f(x0)``. new_slope : float or None The local slope along the search direction at the new value ````, or None if the line search algorithm did not converge. Notes ----- Uses the line search algorithm to enforce strong Wolfe conditions. See Wright and Nocedal, 'Numerical Optimization', 1999, pp. 59-61. The search direction `pk` must be a descent direction (e.g. ``-myfprime(xk)``) to find a step length that satisfies the strong Wolfe conditions. If the search direction is not a descent direction (e.g. ``myfprime(xk)``), then `alpha`, `new_fval`, and `new_slope` will be None. Examples -------- >>> import numpy as np >>> from scipy.optimize import line_search A objective function and its gradient are defined. >>> def obj_func(x): ... return (x[0])**2+(x[1])**2 >>> def obj_grad(x): ... return [2*x[0], 2*x[1]] We can find alpha that satisfies strong Wolfe conditions. >>> start_point = np.array([1.8, 1.7]) >>> search_gradient = np.array([-1.0, -1.0]) >>> line_search(obj_func, obj_grad, start_point, search_gradient) (1.0, 2, 1, 1.1300000000000001, 6.13, [1.6, 1.4]) rNcrrralpharrrr#r$zline_search_wolfe2..phicsDdd7<|gRd<|d<tdSrr%rB)rr(r)r* gval_alphar!r"rrr+#sz"line_search_wolfe2..derphics2d|kr ||}|||dS)Nrr)rCr#x)r+extra_conditionr*rDr!r"rrextra_condition20s  z,line_search_wolfe2..extra_condition2)r:*The line search algorithm did not converge stacklevel)r&r'r rr)rmyfprimer"r!r/r0r1rrrr,rFr:r#r2rG alpha_starphi_star derphi_starr) rr+rFrr r(r)r*rDr!r"rrs.^ rc Cst|||dur |d}|dur|d}d} |dur+|dkr+tdd|||} nd} | dkr3d} |dur 0 is assumed to be a descent direction. Parameters ---------- phi : callable phi(alpha) Objective scalar function. derphi : callable phi'(alpha) Objective function derivative. Returns a scalar. phi0 : float, optional Value of phi at 0. old_phi0 : float, optional Value of phi at previous point. derphi0 : float, optional Value of derphi at 0 c1 : float, optional Parameter for Armijo condition rule. c2 : float, optional Parameter for curvature condition rule. amax : float, optional Maximum step size. extra_condition : callable, optional A callable of the form ``extra_condition(alpha, phi_value)`` returning a boolean. The line search accepts the value of ``alpha`` only if this callable returns ``True``. If the callable returns ``False`` for the step length, the algorithm will continue with new iterates. The callable is only called for iterates satisfying the strong Wolfe conditions. maxiter : int, optional Maximum number of iterations to perform. Returns ------- alpha_star : float or None Best alpha, or None if the line search algorithm did not converge. phi_star : float phi at alpha_star. phi0 : float phi at 0. derphi_star : float or None derphi at alpha_star, or None if the line search algorithm did not converge. Notes ----- Uses the line search algorithm to enforce strong Wolfe conditions. See Wright and Nocedal, 'Numerical Optimization', 1999, pp. 59-61. Nr5rr6r7cSsdS)NTr)rCr#rrrrFsz-scalar_search_wolfe2..extra_conditionz7Rounding errors prevent the line search from convergingz4The line search algorithm could not find a solution zless than or equal to amax: rIrJrH)rr;rangerr_zoomabs)r#r+r9r<r2rrr,rFr:alpha0r=phi_a1phi_a0 derphi_a0irMrNrOmsgnot_first_iteration derphi_a1alpha2rrrr Is 8        r c CsDtjddddzp|}||}||} || d|| } td} | d| d<|d | d<| d | d<|d| d <t| t|||||||| g\} } | | } | | } | | d| |}|| t|d| }WntyYWd d SwWd n1swYt|sd S|S) z Finds the minimizer for a cubic polynomial that goes through the points (a,fa), (b,fb), and (c,fc) with derivative at a of fpa. If no minimizer can be found, return None. raisedivideoverinvalidrI)rIrI)rr)rr)rr)rrN) r&errstateemptyr'asarrayflattensqrtArithmeticErrorisfinite)afafpabfbcr Cdbdcdenomd1ABradicalxminrrr _cubicmins:       rxc Cstjdddd9z |}|}||d}||||||}||d|} Wnty9YWddSwWdn1sDwYt| sPdS| S)z Finds the minimizer for a quadratic polynomial that goes through the points (a,fa), (b,fb) with derivative at a of fpa. r\r]r6@N)r&rbrgrh) rirjrkrlrmDrorprurwrrr_quadmins    r{c Csd} d} d}d}|}d} ||}|dkr||}}n||}}| dkr2||}t|||||||}| dksF|dusF|||ksF|||krh||}t|||||}|dusb|||ksb|||krh|d|}||}||| ||ksz||kr|}|}|}|}n4||}t|| |kr| ||r|}|}|}n+|||dkr|}|}|}|}n|}|}|}|}|}| d7} | | krd}d}d}nq |||fS) a Zoom stage of approximate linesearch satisfying strong Wolfe conditions. Part of the optimization algorithm in `scalar_search_wolfe2`. Notes ----- Implements Algorithm 3.6 (zoom) in Wright and Nocedal, 'Numerical Optimization', 1999, pp. 61. rArg?皙?TN?r)rxr{rR)a_loa_hiphi_lophi_hi derphi_lor#r+r9r2rrrFr:rWdelta1delta2phi_reca_recdalpharirlcchka_jqchkphi_aj derphi_aja_starval_star valprime_starrrrrQsf     (   ArQc sjtdgfdd}|dur|d} n|} t|} t|| | ||d\} } | d| fS)aMinimize over alpha, the function ``f(xk+alpha pk)``. Parameters ---------- f : callable Function to be minimized. xk : array_like Current point. pk : array_like Search direction. gfk : array_like Gradient of `f` at point `xk`. old_fval : float Value of `f` at point `xk`. args : tuple, optional Optional arguments. c1 : float, optional Value to control stopping criterion. alpha0 : scalar, optional Value of `alpha` at start of the optimization. Returns ------- alpha f_count f_val_at_alpha Notes ----- Uses the interpolation algorithm (Armijo backtracking) as suggested by Wright and Nocedal in 'Numerical Optimization', 1999, pp. 56-57 rcrrr)r=rrrr#r$zline_search_armijo..phiNr5)rrS)r& atleast_1dr'scalar_search_armijo) rr"r!r/r0rrrSr#r9r2rCr?rrrr os "    r c Cs0t||||||||d}|d|dd|dfS)z8 Compatibility wrapper for `line_search_armijo` )rrrSrrrI)r ) rr"r!r/r0rrrSrrrrline_search_BFGSsrcCs||}|||||kr||fS| |dd||||}||}|||||kr5||fS||kr|d|d||} |d|||||d||||} | | } |d |||||d||||} | | } | tt| dd| |d| } || } | ||| |kr| | fS|| |dksd| |dkr|d} |}| }|}| }||ks9d|fS)a(Minimize over alpha, the function ``phi(alpha)``. Uses the interpolation algorithm (Armijo backtracking) as suggested by Wright and Nocedal in 'Numerical Optimization', 1999, pp. 56-57 alpha > 0 is assumed to be a descent direction. Returns ------- alpha phi1 rIryrag@rgQ?N)r&rfrR)r#r9r2rrSr-rUr=rTfactorrirlr[phi_a2rrrrs:", rr|r}cCs|d}t|} d} d} d} || |} || \}}|| ||| d|kr,| } nU| d||d| d|}|| |} || \}}|| ||| d|krZ| } n'| d||d| d|}t||| || } t||| || } q| | ||fS)a@ Nonmonotone backtracking line search as described in [1]_ Parameters ---------- f : callable Function returning a tuple ``(f, F)`` where ``f`` is the value of a merit function and ``F`` the residual. x_k : ndarray Initial position. d : ndarray Search direction. prev_fs : float List of previous merit function values. Should have ``len(prev_fs) <= M`` where ``M`` is the nonmonotonicity window parameter. eta : float Allowed merit function increase, see [1]_ gamma, tau_min, tau_max : float, optional Search parameters, see [1]_ Returns ------- alpha : float Step length xp : ndarray Next position fp : float Merit function value at next position Fp : ndarray Residual at next position References ---------- [1] "Spectral residual method without gradient information for solving large-scale nonlinear systems of equations." W. La Cruz, J.M. Martinez, M. Raydan. Math. Comp. **75**, 1429 (2006). rTrI)maxr&clip)rx_kdprev_fsetagammatau_mintau_maxf_kf_baralpha_palpha_mrCxpfpFpalpha_tpalpha_tmrrr_nonmonotone_line_search_cruzs,(       r333333?c Cs*d} d} d} || |}||\}}||||| d|kr$| } nU| d||d| d|}|| |}||\}}||||| d|krR| } n'| d||d| d|}t||| | | } t||| | | } q| |d}| |||||}|}| |||||fS)a Nonmonotone line search from [1] Parameters ---------- f : callable Function returning a tuple ``(f, F)`` where ``f`` is the value of a merit function and ``F`` the residual. x_k : ndarray Initial position. d : ndarray Search direction. f_k : float Initial merit function value. C, Q : float Control parameters. On the first iteration, give values Q=1.0, C=f_k eta : float Allowed merit function increase, see [1]_ nu, gamma, tau_min, tau_max : float, optional Search parameters, see [1]_ Returns ------- alpha : float Step length xp : ndarray Next position fp : float Merit function value at next position Fp : ndarray Residual at next position C : float New value for the control parameter C Q : float New value for the control parameter Q References ---------- .. [1] W. Cheng & D.-H. Li, ''A derivative-free nonmonotone line search and its application to the spectral residual method'', IMA J. Numer. Anal. 29, 814 (2009). rTrI)r&r)rrrrroQrrrrnurrrCrrrrrQ_nextrrr_nonmonotone_line_search_cheng2s./       r) NNNrrrrrr)NNNrrrrr) NNNrrrNNrA)NNNrrNNrA)rrr)rrr)rr|r})rr|r}r)__doc__warningsr_dcsrchrnumpyr&__all__RuntimeWarningrrrr line_searchrr rxr{rQr rrrrrrrrsN   ? M   " [ 4 ? I