ftj dZddlmZddlmZdZdZdZdZd Z d Z d Z d Z d Z dZeee e e e e edZdZdZdZdZdZdS)aj 'Generic' Array API backend for RBF interpolation. The general logic is this: `_rbfinterp.py` implements the user API and calls into either `_rbfinterp_np` (the "numpy backend"), or `_rbfinterp_xp` (the "generic backend". The numpy backend offloads performance-critical computations to the pythran-compiled `_rbfinterp_pythran` extension. This way, the call chain is _rbfinterp.py <-- _rbfinterp_np.py <-- _rbfinterp_pythran.py The "generic" backend here is a drop-in replacement of the API of `_rbfinterp_np.py` for use in `_rbfinterp.py` with non-numpy arrays. The implementation closely follows `_rbfinterp_np + _rbfinterp_pythran`, with the following differences: - We used vectorized code not explicit loops in `_build_system` and `_build_evaluation_coefficients`; this is more torch/jax friendly; - RBF kernels are also "vectorized" and not scalar: they receive an array of norms not a single norm; - RBF kernels accept an extra xp= argument; In general, we would prefer less code duplication. The main blocker ATM is that pythran cannot compile functions with an xp= argument where xp is numpy. ) LinAlgError)_monomial_powers_implct||}||}|jddkr||d|f}|S)Nr)rasarrayshapereshape)ndimdegreexpouts ]/var/www/html/CA-Chatbot/venv/lib/python3.11/site-packages/scipy/interpolate/_rbfinterp_xp.py_monomial_powersr sM f - -C **S//C y|qjjq$i(( Jc `t|||||||\}}} } |j||} ns#t$rfd} |jd} | dkrAt || z | z ||}|j|}|| kr d|d| d} t| wxYw| | | fS)aBuild and solve the RBF interpolation system of equations. Parameters ---------- y : (P, N) float ndarray Data point coordinates. d : (P, S) float ndarray Data values at `y`. smoothing : (P,) float ndarray Smoothing parameter for each data point. kernel : str Name of the RBF. epsilon : float Shape parameter. powers : (R, N) int ndarray The exponents for each monomial in the polynomial. Returns ------- coeffs : (P + R, S) float ndarray Coefficients for each RBF and monomial. shift : (N,) float ndarray Domain shift used to create the polynomial matrix. scale : (N,) float ndarray Domain scaling used to create the polynomial matrix. zSingular matrixr)r zqSingular matrix. The matrix of monomials evaluated at the data point coordinates does not have full column rank (/z).) _build_systemlinalgsolve Exceptionrpolynomial_matrix matrix_rankr)yd smoothingkernelepsilonpowersr lhsrhsshiftscalecoeffsmsgnmonospmatranks r_build_and_solve_systemr((s8+ 1i&"  CeUc**   a A::$a%i%62FFFD9((..Df}}/!//$*/// #!$ % s 8A0B(c| SNrr s rlinearr.^s 2Ircj||dkd|dz||zS)Nr)wherelogr,s rthin_plate_spliner3bs/ 88AFAq!tbffQii/ 0 00rc |dzS)Nr+r,s rcubicr6gs a4Krc|dz S)Nr+r,s rquinticr9ks qD5Lrc:||dzdz S)Nr0rsqrtr,s r multiquadricr=os GGAqD1H   rc>d||dzdzz SN?r0r;r,s rinverse_multiquadricrAss! A$$ $$rcd|dzdzz Sr?r+r,s rinverse_quadraticrCws !Q$* rc4||dz S)Nr0)expr,s rgaussianrF{s 661a4%==r)r.r3r6r9r=rArCrFc ||j|dddddf|dddddfz d|S)z+Evaluate RBFs, with centers at `x`, at `x`.Naxis)r vector_norm)x kernel_funcr s r kernel_matrixrNsY ; aaaa ma4 m;"EEr  rcP||dddddf|zdS)z9Evaluate monomials, with exponents from `powers`, at `x`.NrHrI)prod)rLrr s rrrs/ 771QQQaaaZ=F*7 4 44rc |jd}|jd}t|} ||d} ||d} | | zdz } | | z dz } || dkd| } ||z}|| z | z }t || |}t |||}||||fd||j| ||ffdgd| ||| |gz}||| ||fgd}||| | fS)a=Build the system used to solve for the RBF interpolant coefficients. Parameters ---------- y : (P, N) float ndarray Data point coordinates. d : (P, S) float ndarray Data values at `y`. smoothing : (P,) float ndarray Smoothing parameter for each data point. kernel : str Name of the RBF. epsilon : float Shape parameter. powers : (R, N) int ndarray The exponents for each monomial in the polynomial. Returns ------- lhs : (P + R, P + R) float ndarray Left-hand side matrix. rhs : (P + R, S) float ndarray Right-hand side matrix. shift : (N,) float ndarray Domain shift used to create the polynomial matrix. scale : (N,) float ndarray Domain scaling used to create the polynomial matrix. rrrIr0gr@) r NAME_TO_FUNCminmaxr1rNrconcatTzerosdiag)rrrrrrr sr-rMminsmaxsr!r"yepsyhat out_kernelsout_polyrr s rrrs<  A QAv&K 66!!6  D 66!!6  D D[!OE D[!OE HHUc\3 . .E W9D Iu D {B77K vr22H )) K* 3 3 HJ!Q 0 01 : :      9bhhqkk":;;<<  =C ))Q!Q(()) 2 2C UE !!rc Bt|}||z} ||z} ||z |z } |||j| dddddf| dddddfz d||| dddddf|zdgd} | S)aConstruct the coefficients needed to evaluate the RBF. Parameters ---------- x : (Q, N) float ndarray Evaluation point coordinates. y : (P, N) float ndarray Data point coordinates. kernel : str Name of the RBF. epsilon : float Shape parameter. powers : (R, N) int ndarray The exponents for each monomial in the polynomial. shift : (N,) float ndarray Shifts the polynomial domain for numerical stability. scale : (N,) float ndarray Scales the polynomial domain for numerical stability. Returns ------- (Q, P + R) float ndarray NrHrI)rRrUrrKrP) rLrrrrr!r"r rMr\xepsxhatvecs r_build_evaluation_coefficientsrds8v&K W9D W9D Iu D )) K %%D!!!$tD!!!QQQJ'77b&   GGDD!!!$.RG 8 8     C Jrc 8t||||||||} | |zSr*)rd) rLrrrrr!r"r#r rcs rcompute_interpolationrfs. ( 1fgvueR  C <rN)__doc__ numpy.linalgr_rbfinterp_commonrrr(r.r3r6r9r=rArCrFrRrNrrrdrfr+rrrjsI6%$$$$$4444443 3 3 l111 %%% ) /)   555 ;";";"|...br