ó ÚÆ÷Xc@`s=dZddlmZmZmZddlZddlmZmZm Z m Z m Z ddl m Z ddlmZmZmZmZmZmZddlmZd d gZdd'ddd d d dddddddd„Zd(dddd dd ddddddd„ Zd efd„ƒYZedkr9d„Zd„Zd„Zde fd„ƒYZ!d Z"d Z#dZ$d Z%d)ge$Z&x$e'de$dƒD]Z(d*e&e(g:Œ0âŽyE>iÿÿÿÿi˜:ic C`s8|r|}d}n0|dkr9t|ƒ}|j}n |}|}| dkrZ| } ni | d6| d6|d6|tjtƒjd6|d6| d6| d6| d6|d 6|d 6}t||d |d |d ||}i|d d6|dd6|dd6|dd6|dd6}|d}|d}|||fS(sÝ Minimize a function func using the L-BFGS-B algorithm. Parameters ---------- func : callable f(x,*args) Function to minimise. 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. 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. 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. 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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 Rhtcopyiiiÿÿÿÿ(RlRmRgRoR+RRhtTrueRiRGRPRRKtdot( RpR(RdReRgRotqtalphaR[trtbeta((s4/tmp/pip-build-X4mzal/scipy/scipy/optimize/lbfgsb.pyt_matvec™s*""c C`sJ|j|j|j|jf\}}}}tjd|j|jŒ}|}xøt|ƒD]ê}|||dd…tj f||tj dd…f||}|||dd…tj f||tj dd…f||} tj |tj || ƒƒ||||dd…tj f||tj dd…f}qXW|S(süReturn 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`. 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