a aH@sdZddlZddlmZmZmZmZddlmZddl m Z m Z m Z m Z ddlmZddlmZd d gZddd ZdddZGdd d eZdS)zR Functions --------- .. autosummary:: :toctree: generated/ fmin_l_bfgs_b N)arrayasarrayfloat64zeros)_lbfgsb) MemoizeJacOptimizeResult_check_unknown_options_prepare_scalar_function)old_bound_to_new)LinearOperator fmin_l_bfgs_bLbfgsInvHessProduct cAh㈵>:0yE>:c Cs|r|}d}n |dur&t|}|j}n|}|}| dur:| } | | ||ttj|| | | ||d }t||f|||d|}|d|d|d|d|dd }|d }|d }|||fS) a Minimize a function func using the L-BFGS-B algorithm. Parameters ---------- func : callable f(x,*args) Function to minimize. x0 : ndarray Initial guess. fprime : callable fprime(x,*args), optional The gradient of `func`. If None, then `func` returns the function value and the gradient (``f, g = func(x, *args)``), unless `approx_grad` is True in which case `func` returns only ``f``. args : sequence, optional Arguments to pass to `func` and `fprime`. approx_grad : bool, optional Whether to approximate the gradient numerically (in which case `func` returns only the function value). bounds : list, optional ``(min, max)`` pairs for each element in ``x``, defining the bounds on that parameter. Use None or +-inf for one of ``min`` or ``max`` when there is no bound in that direction. m : int, optional The maximum number of variable metric corrections used to define the limited memory matrix. (The limited memory BFGS method does not store the full hessian but uses this many terms in an approximation to it.) factr : float, optional The iteration stops when ``(f^k - f^{k+1})/max{|f^k|,|f^{k+1}|,1} <= factr * eps``, where ``eps`` is the machine precision, which is automatically generated by the code. Typical values for `factr` are: 1e12 for low accuracy; 1e7 for moderate accuracy; 10.0 for extremely high accuracy. See Notes for relationship to `ftol`, which is exposed (instead of `factr`) by the `scipy.optimize.minimize` interface to L-BFGS-B. pgtol : float, optional The iteration will stop when ``max{|proj g_i | i = 1, ..., n} <= pgtol`` where ``pg_i`` is the i-th component of the projected gradient. epsilon : float, optional Step size used when `approx_grad` is True, for numerically calculating the gradient iprint : int, optional Controls the frequency of output. ``iprint < 0`` means no output; ``iprint = 0`` print only one line at the last iteration; ``0 < iprint < 99`` print also f and ``|proj g|`` every iprint iterations; ``iprint = 99`` print details of every iteration except n-vectors; ``iprint = 100`` print also the changes of active set and final x; ``iprint > 100`` print details of every iteration including x and g. disp : int, optional If zero, then no output. If a positive number, then this over-rides `iprint` (i.e., `iprint` gets the value of `disp`). maxfun : int, optional Maximum number of function evaluations. maxiter : int, optional Maximum number of iterations. callback : callable, optional Called after each iteration, as ``callback(xk)``, where ``xk`` is the current parameter vector. maxls : int, optional Maximum number of line search steps (per iteration). Default is 20. Returns ------- x : array_like Estimated position of the minimum. f : float Value of `func` at the minimum. d : dict Information dictionary. * d['warnflag'] is - 0 if converged, - 1 if too many function evaluations or too many iterations, - 2 if stopped for another reason, given in d['task'] * d['grad'] is the gradient at the minimum (should be 0 ish) * d['funcalls'] is the number of function calls made. * d['nit'] is the number of iterations. See also -------- minimize: Interface to minimization algorithms for multivariate functions. See the 'L-BFGS-B' `method` in particular. Note that the `ftol` option is made available via that interface, while `factr` is provided via this interface, where `factr` is the factor multiplying the default machine floating-point precision to arrive at `ftol`: ``ftol = factr * numpy.finfo(float).eps``. Notes ----- License of L-BFGS-B (FORTRAN code): The version included here (in fortran code) is 3.0 (released April 25, 2011). It was written by Ciyou Zhu, Richard Byrd, and Jorge Nocedal . It carries the following condition for use: This software is freely available, but we expect that all publications describing work using this software, or all commercial products using it, quote at least one of the references given below. This software is released under the BSD License. References ---------- * R. H. Byrd, P. Lu and J. Nocedal. A Limited Memory Algorithm for Bound Constrained Optimization, (1995), SIAM Journal on Scientific and Statistical Computing, 16, 5, pp. 1190-1208. * C. Zhu, R. H. Byrd and J. Nocedal. L-BFGS-B: Algorithm 778: L-BFGS-B, FORTRAN routines for large scale bound constrained optimization (1997), ACM Transactions on Mathematical Software, 23, 4, pp. 550 - 560. * J.L. Morales and J. Nocedal. L-BFGS-B: Remark on Algorithm 778: L-BFGS-B, FORTRAN routines for large scale bound constrained optimization (2011), ACM Transactions on Mathematical Software, 38, 1. N) dispiprintmaxcorftolgtolepsmaxfunmaxitercallbackmaxls)argsjacboundsr#messagenfevnitstatus)ZgradtaskZfuncallsr'warnflagfunx)rZ derivativenpfinfofloatr_minimize_lbfgsb)funcx0Zfprimer"Z approx_gradr$mfactrpgtolepsilonrrrrr r!r+r#optsresdfr,rre/Users/vegardjervell/Documents/master/model/venv/lib/python3.9/site-packages/scipy/optimize/lbfgsb.pyr0sB} #>c2Kst||}|}|ttj}t|}|j\}|durFdg|}t||krZt ddd|D}t |}|d|dk rt dt ||d|d}|dur|dkrd } n|} t ||||| ||d }|j}tjjj}t||}t|t}t|t}ddd d d }td|D]N}||\}}|dur>|||<d}|durT|||<d}|||f||<q|dkszt dt|t} tdt}!t|ft}"td ||d|d||d|t}#td ||}$tdd}%tdd}&td|}'td|}(tdt})d|%dd<d}*t|| ||||!|"|||#|$|%| |&|'|(|)||%}+|+drf|| \}!}"nb|+dr|*d7}*| dur| t| |*| krd|%dd<n|j| krd|%dd<nq̐q|%d}+|+drd},n |j| ks|*| kr d},nd },|#d||||}-|#||d ||||}.|(d}/t|/|}0t|-d|0|.d|0}1|+ }+t!|!|"|j|j"|*|,|+| |,dk|1d S) a Minimize a scalar function of one or more variables using the L-BFGS-B algorithm. Options ------- disp : None or int If `disp is None` (the default), then the supplied version of `iprint` is used. If `disp is not None`, then it overrides the supplied version of `iprint` with the behaviour you outlined. maxcor : int The maximum number of variable metric corrections used to define the limited memory matrix. (The limited memory BFGS method does not store the full hessian but uses this many terms in an approximation to it.) ftol : float The iteration stops when ``(f^k - f^{k+1})/max{|f^k|,|f^{k+1}|,1} <= ftol``. gtol : float The iteration will stop when ``max{|proj g_i | i = 1, ..., n} <= gtol`` where ``pg_i`` is the i-th component of the projected gradient. eps : float or ndarray If `jac is None` the absolute step size used for numerical approximation of the jacobian via forward differences. maxfun : int Maximum number of function evaluations. maxiter : int Maximum number of iterations. iprint : int, optional Controls the frequency of output. ``iprint < 0`` means no output; ``iprint = 0`` print only one line at the last iteration; ``0 < iprint < 99`` print also f and ``|proj g|`` every iprint iterations; ``iprint = 99`` print details of every iteration except n-vectors; ``iprint = 100`` print also the changes of active set and final x; ``iprint > 100`` print details of every iteration including x and g. callback : callable, optional Called after each iteration, as ``callback(xk)``, where ``xk`` is the current parameter vector. maxls : int, optional Maximum number of line search steps (per iteration). Default is 20. finite_diff_rel_step : None or array_like, optional If `jac in ['2-point', '3-point', 'cs']` the relative step size to use for numerical approximation of the jacobian. The absolute step size is computed as ``h = rel_step * sign(x0) * max(1, abs(x0))``, possibly adjusted to fit into the bounds. For ``method='3-point'`` the sign of `h` is ignored. If None (default) then step is selected automatically. Notes ----- The option `ftol` is exposed via the `scipy.optimize.minimize` interface, but calling `scipy.optimize.fmin_l_bfgs_b` directly exposes `factr`. The relationship between the two is ``ftol = factr * numpy.finfo(float).eps``. I.e., `factr` multiplies the default machine floating-point precision to arrive at `ftol`. NNNz length of x0 != length of boundscSs6g|].\}}|tj krdn||tjkr,dn|fqS)N)r-inf).0lurrr; z$_minimize_lbfgsb..rrz@LBFGSB - one of the lower bounds is greater than an upper bound.r)r#r"r6r$finite_diff_rel_step)r=)rN)rr)Nrzmaxls must be positive.g ZS60,STARTsFGsNEW_Xz+STOP: TOTAL NO. of ITERATIONS REACHED LIMITz4STOP: TOTAL NO. of f AND g EVALUATIONS EXCEEDS LIMITsCONV) r+r#r&Znjevr'r(r%r,successhess_inv)#r r-r.r/rrZravelshapelen ValueErrorr anyZclipr Z fun_and_gradrtypesZintvardtyperrrangerZsetulbtobytes startswithcopyr&stripreshapeminrdecoder Zngev)2r+r2r"r#r$rrrrrrrrr r!rDZunknown_optionsr3r5r4nZ new_boundsZsfZ func_and_gradZ fortran_intZnbdZlow_bndZ upper_bndZ bounds_mapir@rAr,r:gwaZiwar)ZcsaveZlsaveZisaveZdsaveZ n_iterationsZtask_strr*syZn_bfgs_updatesn_corrsrQrrr;r0s?               .                r0cs0eZdZdZfddZddZddZZS)raMLinear operator for the L-BFGS approximate inverse Hessian. This operator computes the product of a vector with the approximate inverse of the Hessian of the objective function, using the L-BFGS limited memory approximation to the inverse Hessian, accumulated during the optimization. Objects of this class implement the ``scipy.sparse.linalg.LinearOperator`` interface. Parameters ---------- sk : array_like, shape=(n_corr, n) Array of `n_corr` most recent updates to the solution vector. (See [1]). yk : array_like, shape=(n_corr, n) Array of `n_corr` most recent updates to the gradient. (See [1]). References ---------- .. [1] Nocedal, Jorge. "Updating quasi-Newton matrices with limited storage." Mathematics of computation 35.151 (1980): 773-782. csh|j|jks|jdkrtd|j\}}tjtj||fd||_||_||_ dt d|||_ dS)zConstruct the operator.rEz0sk and yk must have matching shape, (n_corrs, n))rWrRrzij,ij->iN) rRndimrTsuper__init__r-rskykrfZeinsumrho)selfrjrkrfr` __class__rr;ris zLbfgsInvHessProduct.__init__c Cs|j|j|j|jf\}}}}tj||jdd}|jdkrP|jddkrP| d}t |}t |dddD]4}||t |||||<|||||}qj|} t |D]4}||t ||| } | ||||| } q| S)aEEfficient matrix-vector multiply with the BFGS matrices. This calculation is described in Section (4) of [1]. Parameters ---------- x : ndarray An array with shape (n,) or (n,1). Returns ------- y : ndarray The matrix-vector product T)rWr[rErr) rjrkrfrlr-rrWrgrRr]emptyrXdot) rmr,rdrerfrlqalphararbetarrr;_matvecs   zLbfgsInvHessProduct._matvecc Cs|j|j|j|jf\}}}}tj|jd|ji}|}t|D]}|||ddtj f||tj ddf||}|||ddtj f||tj ddf||} t |t || ||||ddtj f||tj ddf}q<|S)zReturn a dense array representation of this operator. Returns ------- arr : ndarray, shape=(n, n) An array with the same shape and containing the same data represented by this `LinearOperator`. rWN) rjrkrfrlr-ZeyerRrWrXZnewaxisrq) rmrdrerfrlIZHkraA1A2rrr;todenses  88.zLbfgsInvHessProduct.todense)__name__ __module__ __qualname____doc__rirvrz __classcell__rrrnr;rs ")NrrNrrrrrrrNNr)rNNNrr<rrrrrNrN)r~Znumpyr-rrrrroptimizerr r r _constraintsr Zscipy.sparse.linalgr __all__rr0rrrrr;s.#    # A