^MhGdZddlZddlmZddlmZmZddlm Z gdZ GddZ Gd d e Z Gd d e Z Gd de ZdS)z@Hessian update strategies for quasi-Newton optimization methods.N)norm)get_blas_funcs issymmetric)warn)HessianUpdateStrategyBFGSSR1c0eZdZdZdZdZdZdZdZdS)raInterface for implementing Hessian update strategies. Many optimization methods make use of Hessian (or inverse Hessian) approximations, such as the quasi-Newton methods BFGS, SR1, L-BFGS. Some of these approximations, however, do not actually need to store the entire matrix or can compute the internal matrix product with a given vector in a very efficiently manner. This class serves as an abstract interface between the optimization algorithm and the quasi-Newton update strategies, giving freedom of implementation to store and update the internal matrix as efficiently as possible. Different choices of initialization and update procedure will result in different quasi-Newton strategies. Four methods should be implemented in derived classes: ``initialize``, ``update``, ``dot`` and ``get_matrix``. The matrix multiplication operator ``@`` is also defined to call the ``dot`` method. Notes ----- Any instance of a class that implements this interface, can be accepted by the method ``minimize`` and used by the compatible solvers to approximate the Hessian (or inverse Hessian) used by the optimization algorithms. c td)Initialize internal matrix. Allocate internal memory for storing and updating the Hessian or its inverse. Parameters ---------- n : int Problem dimension. approx_type : {'hess', 'inv_hess'} Selects either the Hessian or the inverse Hessian. When set to 'hess' the Hessian will be stored and updated. When set to 'inv_hess' its inverse will be used instead. z=The method ``initialize(n, approx_type)`` is not implemented.NotImplementedErrorselfn approx_types g/var/www/html/test/jupyter/venv/lib/python3.11/site-packages/scipy/optimize/_hessian_update_strategy.py initializez HessianUpdateStrategy.initialize%"#9:: :c td)Update internal matrix. Update Hessian matrix or its inverse (depending on how 'approx_type' is defined) using information about the last evaluated points. Parameters ---------- delta_x : ndarray The difference between two points the gradient function have been evaluated at: ``delta_x = x2 - x1``. delta_grad : ndarray The difference between the gradients: ``delta_grad = grad(x2) - grad(x1)``. z>The method ``update(delta_x, delta_grad)`` is not implemented.r rdelta_x delta_grads rupdatezHessianUpdateStrategy.update7rrc td)PCompute the product of the internal matrix with the given vector. Parameters ---------- p : array_like 1-D array representing a vector. Returns ------- Hp : array 1-D represents the result of multiplying the approximation matrix by vector p. z)The method ``dot(p)`` is not implemented.r rps rdotzHessianUpdateStrategy.dotIs"#9:: :rc td)zReturn current internal matrix. Returns ------- H : ndarray, shape (n, n) Dense matrix containing either the Hessian or its inverse (depending on how 'approx_type' is defined). z0The method ``get_matrix(p)`` is not implemented.r )rs r get_matrixz HessianUpdateStrategy.get_matrixZs"#9:: :rc,||SN)r!rs r __matmul__z HessianUpdateStrategy.__matmul__gsxx{{rN) __name__ __module__ __qualname____doc__rrr!r#r&rrrr si2:::$:::$:::" : : :rrceZdZdZeddZeddZeddZddZd Z d Z d Z d Z d Z dZdS)FullHessianUpdateStrategyzKHessian update strategy with full dimensional internal representation. syrddtypesyr2symvautocL||_d|_d|_d|_d|_dSr%) init_scalefirst_iterationrBH)rr6s r__init__z"FullHessianUpdateStrategy.__init__ss-$ $rcd|_||_||_|dvrtd|jdkr"t j|t |_dSt j|t |_dS)r T)hessinv_hessz+`approx_type` must be 'hess' or 'inv_hess'.r<r0N) r7rr ValueErrornpeyefloatr8r9rs rrz$FullHessianUpdateStrategy.initialize|sx $& 2 2 2JKK K  v % %VAU+++DFFFVAU+++DFFFrctj||}tj||}tjtj||}|dks |dks|dkrdS|jdkr||z S||z S)Nrr<)r?r!absr)rrrs_norm2y_norm2yss r _auto_scalez%FullHessianUpdateStrategy._auto_scales&'**&Z00 VBF:w// 0 0 991 1 1  v % %R< < rc td)Nz9The method ``_update_implementation`` is not implemented.r rs r_update_implementationz0FullHessianUpdateStrategy._update_implementations!#9:: :rctj|dkrdStj|dkrtdtddS|jrt |jtr"|jdkr|||}n|j}d}tj |dkrt|}ntj |rtd d }|j d kr&tj|j}|jj}n%tj|j}|jj}tj||d }|tj|x}krt'd |d|dt)|st'd|j d kr|r||_n+|xj|zc_n|r||_n|xj|zc_d|_|||dS)rrCNzdelta_grad == 0.0. Check if the approximated function is linear. If the function is linear better results can be obtained by defining the Hessian as zero instead of using quasi-Newton approximations.) stacklevelr4FrDz3init_scale contains complex elements, must be real.Tr<)r1copyzMIf init_scale is an array, it must have the dimensions of the hess/inv_hess: z. Got .z}If init_scale is an array, it must be symmetric (passing scipy.linalg.issymmetric) to be an approximation of a hess/inv_hess.)r?allr UserWarningr7 isinstancer6strrIsizerA iscomplexobj TypeErrorrshaper8r1r9arrayr>rrK)rrrscalereplacerXr1 init_shapes rrz FullHessianUpdateStrategy.updatesO 6'S. ! !  F 6*# $ $  #   , , , , F  4 )$/3// (DOv4M4M((*== Gwu~~""e '' T!0111#v--HTV,,E FLEEHTV,,E FLEe$???28E??:Z;;$&;IN&;&;-7&;&;&;<<<#5))T$&STTT6))$"DFFFFeOFFF$"DFFFFeOFF#(D  ##GZ88888rc|jdkr|d|j|S|d|j|S)rr<rD)r_symvr8r9rs rr!zFullHessianUpdateStrategy.dotsB  v % %::a++ +::a++ +rc|jdkrtj|j}ntj|j}tj|d}|j|||<|S)zReturn the current internal matrix. Returns ------- M : ndarray, shape (n, n) Dense matrix containing either the Hessian or its inverse (depending on how `approx_type` was defined). r<)k)rr?rOr8r9tril_indices_fromT)rMlis rr#z$FullHessianUpdateStrategy.get_matrix s[  v % %AAA  !!r * * *B"rN)r4)r'r(r)r*r_syr_syr2r^r:rrIrKrr!r#r+rrr-r-ks >%s + + +D N6 - - -E N6 - - -E,,,4    :::N9N9N9`,,,&rr-c:eZdZdZ d fd ZdZdZdZxZS) raBroyden-Fletcher-Goldfarb-Shanno (BFGS) Hessian update strategy. Parameters ---------- exception_strategy : {'skip_update', 'damp_update'}, optional Define how to proceed when the curvature condition is violated. Set it to 'skip_update' to just skip the update. Or, alternatively, set it to 'damp_update' to interpolate between the actual BFGS result and the unmodified matrix. Both exceptions strategies are explained in [1]_, p.536-537. min_curvature : float This number, scaled by a normalization factor, defines the minimum curvature ``dot(delta_grad, delta_x)`` allowed to go unaffected by the exception strategy. By default is equal to 1e-8 when ``exception_strategy = 'skip_update'`` and equal to 0.2 when ``exception_strategy = 'damp_update'``. init_scale : {float, np.array, 'auto'} This parameter can be used to initialize the Hessian or its inverse. When a float is given, the relevant array is initialized to ``np.eye(n) * init_scale``, where ``n`` is the problem dimension. Alternatively, if a precisely ``(n, n)`` shaped, symmetric array is given, this array will be used. Otherwise an error is generated. Set it to 'auto' in order to use an automatic heuristic for choosing the initial scale. The heuristic is described in [1]_, p.143. The default is 'auto'. Notes ----- The update is based on the description in [1]_, p.140. References ---------- .. [1] Nocedal, Jorge, and Stephen J. Wright. "Numerical optimization" Second Edition (2006). skip_updateNr4c|dkr|||_n/d|_n'|dkr|||_nd|_ntdt|||_dS)Nri:0yE> damp_updateg?z<`exception_strategy` must be 'skip_update' or 'damp_update'.) min_curvaturer>superr:exception_strategy)rrormr6 __class__s rr:z BFGS.__init__Bs  . .(%2""%)"" = 0 0(%2""%(""122 2 $$$"4rc|d|z |||j|_|||z|dzz ||j|_dS)aUpdate the inverse Hessian matrix. BFGS update using the formula: ``H <- H + ((H*y).T*y + s.T*y)/(s.T*y)^2 * (s*s.T) - 1/(s.T*y) * ((H*y)*s.T + s*(H*y).T)`` where ``s = delta_x`` and ``y = delta_grad``. This formula is equivalent to (6.17) in [1]_ written in a more efficient way for implementation. References ---------- .. [1] Nocedal, Jorge, and Stephen J. Wright. "Numerical optimization" Second Edition (2006). arMN)rgr9rf)rrHHyyHyss r_update_inverse_hessianzBFGS._update_inverse_hessianUsQ"D2Iq"77BHa/df==rc|d|z ||j|_|d|z ||j|_dS)aUpdate the Hessian matrix. BFGS update using the formula: ``B <- B - (B*s)*(B*s).T/s.T*(B*s) + y*y^T/s.T*y`` where ``s`` is short for ``delta_x`` and ``y`` is short for ``delta_grad``. Formula (6.19) in [1]_. References ---------- .. [1] Nocedal, Jorge, and Stephen J. Wright. "Numerical optimization" Second Edition (2006). g?rsrrN)rfr8)rrHBssBsys r_update_hessianzBFGS._update_hessianisF38Q$&114#:rTV44rc|jdkr|}|}n|}|}tj||}||z}||}|dkr|||}|jdkr)|tj|jt z|_n(|tj|jt z|_||z}||}||j |zkrN|j dkrdS|j dkr6d|j z d||z z z } | |zd| z |zz}tj||}|jdkr| ||||dS| ||||dS)Nr<rCr0rirlrD) rr?r!rIr@rrAr8r9rmror}rx) rrrwzwzMwwMwrZ update_factors rrKzBFGS._update_implementation{s  v % %AAAAA VAq\\ AXffQii #::$$Wj99E6))e!>>(555$+9+9+9+9+9+9+9rrc*eZdZdZdfd ZdZxZS)r a}Symmetric-rank-1 Hessian update strategy. Parameters ---------- min_denominator : float This number, scaled by a normalization factor, defines the minimum denominator magnitude allowed in the update. When the condition is violated we skip the update. By default uses ``1e-8``. init_scale : {float, np.array, 'auto'}, optional This parameter can be used to initialize the Hessian or its inverse. When a float is given, the relevant array is initialized to ``np.eye(n) * init_scale``, where ``n`` is the problem dimension. Alternatively, if a precisely ``(n, n)`` shaped, symmetric array is given, this array will be used. Otherwise an error is generated. Set it to 'auto' in order to use an automatic heuristic for choosing the initial scale. The heuristic is described in [1]_, p.143. The default is 'auto'. Notes ----- The update is based on the description in [1]_, p.144-146. References ---------- .. [1] Nocedal, Jorge, and Stephen J. Wright. "Numerical optimization" Second Edition (2006). rkr4cX||_t|dSr%)min_denominatorrnr:)rrr6rps rr:z SR1.__init__s). $$$$$rc|jdkr|}|}n|}|}||z}||z }tj||}tj||jt |zt |zkrdS|jdkr'|d|z ||j|_dS|d|z ||j|_dS)Nr<rDrs) rr?r!rErrrfr8r9)rrrrrr z_minus_Mw denominators rrKzSR1._update_implementations  v % %AAAAA AXV fQ ++  6+  $"6tAww">tJ?O?O"O O O F  v % %YYq}jDFYCCDFFFYYq}jDFYCCDFFFr)rkr4)r'r(r)r*r:rKrrs@rr r s]:%%%%%%DDDDDDDrr )r*numpyr? numpy.linalgr scipy.linalgrrwarningsr__all__rr-rr r+rrrs8FF44444444 3 2 2]]]]]]]]@ooooo 5ooodI9I9I9I9I9 $I9I9I9X6D6D6D6D6D #6D6D6D6D6Dr