S_fq\ddlZddlmZddlmZmZddlm Z ddl m Z ddl m Z mZdZGdd ZGd d ZGd d ZGddeZy)N)approx_derivative group_columns)HessianUpdateStrategy)LinearOperator) atleast_ndarray_namespace)z2-pointz3-pointcscDeZdZdZ d dZdZdZdZdZdZ d Z d Z y) ScalarFunctionaScalar function and its derivatives. This class defines a scalar function F: R^n->R and methods for computing or approximating its first and second derivatives. Parameters ---------- fun : callable evaluates the scalar function. Must be of the form ``fun(x, *args)``, where ``x`` is the argument in the form of a 1-D array and ``args`` is a tuple of any additional fixed parameters needed to completely specify the function. Should return a scalar. x0 : array-like Provides an initial set of variables for evaluating fun. Array of real elements of size (n,), where 'n' is the number of independent variables. args : tuple, optional Any additional fixed parameters needed to completely specify the scalar function. grad : {callable, '2-point', '3-point', 'cs'} Method for computing the gradient vector. If it is a callable, it should be a function that returns the gradient vector: ``grad(x, *args) -> array_like, shape (n,)`` where ``x`` is an array with shape (n,) and ``args`` is a tuple with the fixed parameters. Alternatively, the keywords {'2-point', '3-point', 'cs'} can be used to select a finite difference scheme for numerical estimation of the gradient with a relative step size. These finite difference schemes obey any specified `bounds`. hess : {callable, '2-point', '3-point', 'cs', HessianUpdateStrategy} Method for computing the Hessian matrix. If it is callable, it should return the Hessian matrix: ``hess(x, *args) -> {LinearOperator, spmatrix, array}, (n, n)`` where x is a (n,) ndarray and `args` is a tuple with the fixed parameters. Alternatively, the keywords {'2-point', '3-point', 'cs'} select a finite difference scheme for numerical estimation. Or, objects implementing `HessianUpdateStrategy` interface can be used to approximate the Hessian. Whenever the gradient is estimated via finite-differences, the Hessian cannot be estimated with options {'2-point', '3-point', 'cs'} and needs to be estimated using one of the quasi-Newton strategies. finite_diff_rel_step : None or array_like Relative step size to use. The absolute step size is computed as ``h = finite_diff_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 then finite_diff_rel_step is selected automatically, finite_diff_bounds : tuple of array_like Lower and upper bounds on independent variables. Defaults to no bounds, (-np.inf, np.inf). Each bound must match the size of `x0` or be a scalar, in the latter case the bound will be the same for all variables. Use it to limit the range of function evaluation. epsilon : None or array_like, optional Absolute step size to use, possibly adjusted to fit into the bounds. For ``method='3-point'`` the sign of `epsilon` is ignored. By default relative steps are used, only if ``epsilon is not None`` are absolute steps used. Notes ----- This class implements a memoization logic. There are methods `fun`, `grad`, hess` and corresponding attributes `f`, `g` and `H`. The following things should be considered: 1. Use only public methods `fun`, `grad` and `hess`. 2. After one of the methods is called, the corresponding attribute will be set. However, a subsequent call with a different argument of *any* of the methods may overwrite the attribute. Nc "tstvrtdtdts+tvs#ttstdtdtvrtvr tdt |x_} t|d| } | j} | j| jdr | j} | j| | _ | _ jj_d_d_d_d _d _d _d_t.j0_itvrd <|d <|d <|d <tvrd <|d <|d <dd<fdfd} | _j7trfdfd} ntvrfd}  _j;trt/j<|g_d_xj$dz c_tAjBj>r,fdtAjDj>_n`tj>tFrfdn>fdt/jHt/jJj>_fd}nutvrfd}|d_nWttrG_j>jMjdd_d_'d_(fd}_)ttr fd}|_*yfd}|_*y)Nz)`grad` must be either callable or one of .z@`hess` must be either callable, HessianUpdateStrategy or one of zWhenever the gradient is estimated via finite-differences, we require the Hessian to be estimated using one of the quasi-Newton strategies.rndimxp real floatingrFmethodrel_stepabs_stepboundsTas_linear_operatorc\xjdz c_tj|g}tj|s$ tj|j }|jkr|_ |_|S#t tf$r}td|d}~wwxYw)Nrz@The user-provided objective function must return a scalar value.) nfevnpcopyisscalarasarrayitem TypeError ValueError _lowest_f _lowest_x)xfxeargsfunselfs Hlib/python3.12/site-packages/scipy/optimize/_differentiable_functions.py fun_wrappedz,ScalarFunction.__init__..fun_wrappeds IINIRWWQZ'$'B;;r?B,,.BDNN"!"!#I":.$6s #B B+ B&&B+c4j_yNr#fr*r(sr) update_funz+ScalarFunction.__init__..update_fun (DFcxjdz c_tjtj|gSNr)ngevr atleast_1dr)r#r&gradr(s r) grad_wrappedz-ScalarFunction.__init__..grad_wrappeds1 Q }}T"''!*%.update_grad%dff-r2cjxjdz c_tjfdji_y)Nrf0) _update_funr5rr#r.r:finite_diff_optionsr*r(sr)r;z,ScalarFunction.__init__..update_gradsF  " Q *;B466B-@Br2cxjdz c_tjtj|gSr4)nhevsps csr_matrixrrr#r&hessr(s r) hess_wrappedz-ScalarFunction.__init__..hess_wrappeds1IINI>>$rwwqz*AD*ABBr2cfxjdz c_tj|gSr4)rCrrrFs r)rHz-ScalarFunction.__init__..hess_wrappeds(IINI 2T22r2c xjdz c_tjtjtj|gSr4)rCr atleast_2drrrFs r)rHz-ScalarFunction.__init__..hess_wrappeds:IINI==D4Kd4K)LMMr2c4j_yr,)r#HrHr(sr) update_hessz,ScalarFunction.__init__..update_hessr<r2cjtjfdji_jSNr>) _update_gradrr#r:rM)rAr8r(sr)rOz,ScalarFunction.__init__..update_hesssB!!#*<BDFFB-@Bvv r2rGcjjjjjz j j z yr,)rRrMupdater#x_prevr:g_prevr(sr)rOz,ScalarFunction.__init__..update_hesss;!!# dfft{{2DFFT[[4HIr2c:jj_j_t |dj }j j|j_d_ d_ d_ jyNrrF) rRr#rUr:rVrrastypex_dtype f_updated g_updated H_updated _update_hessr#_xr(s r)update_xz)ScalarFunction.__init__..update_xst!!#"ff "ff  dgg6DLL9!&!&!&!!#r2ct|dj}jj|j_d_d_d_yrY)rrrZr[r#r\r]r^r`s r)rbz)ScalarFunction.__init__..update_xsF dgg6DLL9!&!&!&r2)+callable FD_METHODSr isinstancerr rrfloat64isdtypedtyperZr#r[sizenrr5rCr\r]r^r"rinfr!_update_fun_implr?_update_grad_implrRrrMrDissparserErrKr initializerUrV_update_hess_impl_update_x_impl)r(r'x0r&r7rGfinite_diff_rel_stepfinite_diff_boundsepsilonrra_dtyper0r;rOrbrAr*r8rHs`` ``` @@@@r)__init__zScalarFunction.__init__Ws.~$j"8;J  ) : ,0  ).B  +.5  +8<  4 5 , )!+  D> > .Z  B "-  D>"''"+--DF!DN IINI||DFF#C/DFFN33 Nrzz$&&'9: .Z   M!DN 3 4DF FF  dfff -!DNDKDK J"- d1 2 $,' ''r2cL|js|jd|_yyNTr\rmrWs r)r?zScalarFunction._update_fun!~~  ! ! #!DNr2cL|js|jd|_yyrz)r]rnrWs r)rRzScalarFunction._update_grad !~~  " " $!DNr2cL|js|jd|_yyrzr^rqrWs r)r_zScalarFunction._update_hessr~r2ctj||js|j||j |j Sr,)r array_equalr#rrr?r.r(r#s r)r'zScalarFunction.funs7~~a(    " vv r2ctj||js|j||j |j Sr,)rrr#rrrRr:rs r)r7zScalarFunction.grad7~~a(    " vv r2ctj||js|j||j |j Sr,)rrr#rrr_rMrs r)rGzScalarFunction.hessrr2ctj||js|j||j |j |j |jfSr,)rrr#rrr?rRr.r:rs r) fun_and_gradzScalarFunction.fun_and_grad%sL~~a(    "  vvtvv~r2r,) __name__ __module__ __qualname____doc__rxr?rRr_r'r7rGrr2r)r r s8IV.2k'Z" " "    r2r cFeZdZdZdZdZdZdZdZdZ dZ d Z d Z y ) VectorFunctionaVector function and its derivatives. This class defines a vector function F: R^n->R^m and methods for computing or approximating its first and second derivatives. Notes ----- This class implements a memoization logic. There are methods `fun`, `jac`, hess` and corresponding attributes `f`, `J` and `H`. The following things should be considered: 1. Use only public methods `fun`, `jac` and `hess`. 2. After one of the methods is called, the corresponding attribute will be set. However, a subsequent call with a different argument of *any* of the methods may overwrite the attribute. c  tstvrtdtdts+tvs#ttstdtdtvrtvr tdt |x_} t|d| } | j} | j| jdr | j} | j| | _ | _ jj_d_d_d_d _d _d _itvrGd <|d <|t-|} || fd <|d <t/j0j_tvr3d <|d <dd<t/j0j_tvrtvr tdfdfd} | _| t/j6j8_j:j_tr j_d_xj"dz c_|s!|QtAjBj>r2fdtAjDj>_d_#n}tAjBj>r-fdj>jI_d _#n1fdt/jJj>_d _#fd}n tvrtMjfdj8i_d_|s!|RtAjBj>r3fd}tAjDj>_d_#ntAjBj>r.fd}j>jI_d _#n2fd}t/jJj>_d _#_'trjj:_(d_xj$dz c_tAjBjPr+fdtAjDjP_(n^tjPtRrfdn=fdt/jJt/jTjP_(fd}nztvrfdfd}|d_nWttrG_(jPjWjd d_d_,d_-fd!}_.ttr fd"}|_/yfd#}|_/y)$Nz(`jac` must be either callable or one of rz?`hess` must be either callable,HessianUpdateStrategy or one of zWhenever the Jacobian is estimated via finite-differences, we require the Hessian to be estimated using one of the quasi-Newton strategies.rrrrFrrsparsityrTrcdxjdz c_tj|Sr4)rrr6)r#r'r(s r)r*z,VectorFunction.__init__..fun_wrappedws# IINI==Q( (r2c4j_yr,r-r/sr)r0z+VectorFunction.__init__..update_fun{r1r2cdxjdz c_tj|Sr4)njevrDrEr#jacr(s r) jac_wrappedz,VectorFunction.__init__..jac_wrappeds#IINI>>#a&11r2cZxjdz c_|jSr4)rtoarrayrs r)rz,VectorFunction.__init__..jac_wrappeds!IINIq6>>++r2cdxjdz c_tj|Sr4)rrrKrs r)rz,VectorFunction.__init__..jac_wrappeds#IINI==Q00r2c4j_yr,)r#J)rr(sr) update_jacz+VectorFunction.__init__..update_jacs$TVV,r2r>cjtjtjfdj i_yrQ)r?rDrErr#r.rr@sr)rz+VectorFunction.__init__..update_jacsF$$& ^^)+tvvA$&&A,?ABDFr2cjtjfdjij _yrQ)r?rr#r.rrr@sr)rz+VectorFunction.__init__..update_jacsC$$&.{DFFFtvvF1DFFMgiFr2cjtjtjfdj i_yrQ)r?rrKrr#r.rr@sr)rz+VectorFunction.__init__..update_jacsF$$&]])+tvvA$&&A,?ABDFr2cfxjdz c_tj||Sr4)rCrDrEr#vrGr(s r)rHz-VectorFunction.__init__..hess_wrappeds%IINI>>$q!*55r2c@xjdz c_||Sr4)rCrs r)rHz-VectorFunction.__init__..hess_wrappedsIINI1:%r2cxjdz c_tjtj||Sr4)rCrrKrrs r)rHz-VectorFunction.__init__..hess_wrappeds.IINI==DAJ)?@@r2cJjj_yr,)r#rrMrNsr)rOz,VectorFunction.__init__..update_hesss%dffdff5r2cF|jj|Sr,)Tdot)r#rrs r) jac_dot_vz*VectorFunction.__init__..jac_dot_vs"1~''++A..r2cjtjfjjj j j fd_y)N)r>r&) _update_jacrr#rrrrrM)rArr(sr)rOz,VectorFunction.__init__..update_hesssW  "*9dffB.2ffhhll466.B15 B.ABr2rGcjjjjjz }jj j jjj j jz }jj||yyyr,) rrUJ_prevr#rrrrrMrT)delta_xdelta_gr(s r)rOz,VectorFunction.__init__..update_hesss  ";;*t{{/F"fft{{2G"ffhhll4662T[[]]5F5Ftvv5NNGFFMM'730G*r2c:jj_j_t |dj }j j|j_d_ d_ d_ jyrY) rr#rUrrrrrZr[r\ J_updatedr^r_r`s r)rbz)VectorFunction.__init__..update_xsr  ""ff "ff dgg6DLL9!&!&!&!!#r2ct|dj}jj|j_d_d_d_yrY)rrrZr[r#r\rr^r`s r)rbz)VectorFunction.__init__..update_xsDdgg6DLL9!&!&!&r2)0rdrer rfrr rrrgrhrirZr#r[rjrkrrrCr\rr^rrrx_diffrm zeros_liker.rmrrDrorEsparse_jacobianrrKr_update_jac_implrMrrrprUrrqrr)r(r'rsrrGrtfinite_diff_jac_sparsityrurrrarwsparsity_groupsr0rrOrbrAr*rHrrs`` `` @@@@@r)rxzVectorFunction.__init__>s}J!6G |STUV V$*"4d$9:@@J|1NO O * !3+, , 'r**" r * ::bhh 0XXF2v&      * ,/  ).B  +'3"/0H"I3K3B3D#J/,>  )''$&&/DK : ,0  ).B  +8<  4 5''$&&/DK * !3+, ,  ) )!+ tvv& C=[DF!DN IINI#+ TVV0D2/'+$dff%,)',$1tvv.',$ -J &{DFF>tvv>)<>DF!DN#+ TVV0DB /'+$dff%P)',$B tvv.',$ * D>$&&$&&)DF!DN IINI||DFF#6/DFFN3& Arzz$&&'9: 6 Z  / B M!DN 3 4DF FF  dfff -!DNDKDK 4"- d1 2 $$' ''r2cbtj||js||_d|_yy)NF)rrrr^)r(rs r) _update_vzVectorFunction._update_vs'~~a(DF"DN)r2chtj||js|j|yyr,)rrr#rrrs r) _update_xzVectorFunction._update_xs'~~a(    ")r2cL|js|jd|_yyrzr{rWs r)r?zVectorFunction._update_funr|r2cL|js|jd|_yyrz)rrrWs r)rzVectorFunction._update_jacr|r2cL|js|jd|_yyrzrrWs r)r_zVectorFunction._update_hess$r~r2c\|j||j|jSr,)rr?r.rs r)r'zVectorFunction.fun)# q vv r2c\|j||j|jSr,)rrrrs r)rzVectorFunction.jac.rr2c~|j||j||j|jSr,)rrr_rMr(r#rs r)rGzVectorFunction.hess3s/ q q vv r2N) rrrrrxrrr?rr_r'rrGrr2r)rr-s6 Q'f# #" " "   r2rc.eZdZdZdZdZdZdZdZy)LinearVectorFunctionzLinear vector function and its derivatives. Defines a linear function F = A x, where x is N-D vector and A is m-by-n matrix. The Jacobian is constant and equals to A. The Hessian is identically zero and it is returned as a csr matrix. c|s|7tj|r"tj||_d|_nftj|r|j |_d|_n4t jt j||_d|_|jj\|_ |_ t|x|_ }t|d|}|j}|j!|j"dr |j"}|j%|||_||_|jj+|j&|_d|_t j0|jt2|_tj|j|jf|_y)NTFrrr)ri)rDrorErrrrrKrshaperrkr rrrgrhrirZr#r[rr.r\zerosfloatrrM)r(Arsrrrarws r)rxzLinearVectorFunction.__init__Bs3 o5#,,q/^^A&DF#'D \\!_YY[DF#(D ]]2::a=1DF#(D &r**" r * ::bhh 0XXF2v& DFF#$&&. 01r2ctj||jsKt|d|j}|jj ||j |_d|_yyrY)rrr#rrrZr[r\)r(r#ras r)rzLinearVectorFunction._update_x`sL~~a(AA$''2BWW^^B 5DF"DN)r2c|j||js'|jj||_d|_|jSrz)rr\rrr.rs r)r'zLinearVectorFunction.funfs8 q~~VVZZ]DF!DNvv r2c<|j||jSr,)rrrs r)rzLinearVectorFunction.jacms qvv r2cJ|j|||_|jSr,)rrrMrs r)rGzLinearVectorFunction.hessqs qvv r2N) rrrrrxrr'rrGrr2r)rr;s  2<# r2rc"eZdZdZfdZxZS)IdentityVectorFunctionzIdentity vector function and its derivatives. The Jacobian is the identity matrix, returned as a dense array when `sparse_jacobian=False` and as a csr matrix otherwise. The Hessian is identically zero and it is returned as a csr matrix. ct|}|s|tj|d}d}ntj|}d}t||||y)Ncsr)formatTF)lenrDeyersuperrx)r(rsrrkr __class__s r)rxzIdentityVectorFunction.__init__~sL G o5%(A"Oq A#O B0r2)rrrrrx __classcell__)rs@r)rrws 11r2r)numpyr scipy.sparsesparserD_numdiffrr_hessian_update_strategyrscipy.sparse.linalgrscipy._lib._array_apirr rer rrrrr2r)rsP6;.=* ^^B KK\99x111r2