+ /iRt^RIHt^RIHtRtRtRtRtRt Rt R t R t R t R tR ]R]R] R] R] R] R] R]/tRtRtRtRtRtR#)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_implc\W4pVPV4pVP^,^8XdVPV^V34pV#)rasarrayshapereshape)ndimdegreexpouts&&& ]/var/www/html/photoedit/myenv/lib/python3.14/site-packages/scipy/interpolate/_rbfinterp_xp.py_monomial_powersr sB  -C **S/C yy|qjjq$i( Jc X\WW#WEV4wrxrVPPWx4p YT 3# \dmRp TP^,p T ^8dE\ Y , T , YVR7pTPP T4pY8d RT RT R2p \T 4hi;i)aBuild and solve the RBF interpolation system of equations. Parameters ---------- y : (P, N) float ndarray Data point coordinates. d : (P, S) float ndarray Data values at `y`. smoothing : (P,) float ndarray Smoothing parameter for each data point. kernel : str Name of the RBF. epsilon : float Shape parameter. powers : (R, N) int ndarray The exponents for each monomial in the polynomial. Returns ------- coeffs : (P + R, S) float ndarray Coefficients for each RBF and monomial. shift : (N,) float ndarray Domain shift used to create the polynomial matrix. scale : (N,) float ndarray Domain scaling used to create the polynomial matrix. zSingular matrix)r zqSingular matrix. The matrix of monomials evaluated at the data point coordinates does not have full column rank (/z).) _build_systemlinalgsolve Exceptionrpolynomial_matrix matrix_rankr)yd smoothingkernelepsilonpowersr lhsrhsshiftscalecoeffsmsgnmonospmatranks&&&&&&& r_build_and_solve_systemr((s8+ i" Ce*&  %   a A:$ai%6FD99((.D}!F!F82/ #!s 2A7B)cV)#Nrr s&&rlinearr.^s 2IrchVPV^8H^V^,VPV4,4#r)wherelogr,s&&rthin_plate_spliner2bs* 88AFAq!tbffQi/ 00rcV^,#)r+r,s&&rcubicr5gs a4KrcV^,)#)r+r,s&&rquinticr8ks qD5LrcBVPV^,^,4)#sqrtr,s&&r multiquadricr>os GGAqD1H  rcNRVPV^,R,4, #?r<r,s&&rinverse_multiquadricrBss A$ $$rc0RV^,R,, #r@r+r,s&&rinverse_quadraticrDws !Q$* rc4VPV^,)4#r:)expr,s&&rgaussianrG{s 661a4%=rr.r2r5r8r>rBrDrGctV!VPPVR,VR,, RR7V4#)z+Evaluate RBFs, with centers at `x`, at `x`.axisNNNNrLrLNrL)r vector_norm)x kernel_funcr s&&&r kernel_matrixrRs5  a ma m;"Er rcDVPVR,V,RR7#)z9Evaluate monomials, with exponents from `powers`, at `x`.rIrMrN)prod)rPrr s&&&rrrs 771Z=F*7 44rc VP^,pVP^,p\V,p VPV^R7p VPV^R7p W,^, p W, ^, p VP V R8HRV 4p W,pW , V , p\ WV4p\ WV4pVPVPVV3^R7VPVPVPW343^R7.^R7VPVPW&PV4.44,pVPWPW34.^R7pVVW3#)aBuild 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. rIgrA) r NAME_TO_FUNCminmaxr0rRrconcatTzerosdiag)rrrrrrr sr-rQminsmaxsr!r"yepsyhat out_kernelsout_polyrr s&&&&&&& rrrsS<  A QAv&K 66!!6 D 66!!6 D [!OE [!OE HHUc\3 .E 9D Iu D B7K r2H )) K* 3 HJJ! 01 :     9hhqk":;<  =C ))Q!()) 2C U !!rc 4\V,pW,p W,p W, V, p VPV!VPPV R,V R,, RR7V4VP V R,V,RR7.RR7p V #)a-Construct 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 rIrMrKrN)rVrYrrOrT) rPrrrrr!r"r rQr`xepsxhatvecs &&&&&&&& r_build_evaluation_coefficientsrhs8v&K 9D 9D Iu D ))  %%$tJ'77b&  GGD$.RG 8    C Jrc .\WW#WEWh4p W,#r*)rh) rPrrrrr!r"r#r rgs &&&&&&&&& rcompute_interpolationrjs ( fve C <rN)__doc__ numpy.linalgr_rbfinterp_commonrrr(r.r2r5r8r>rBrDrGrVrRrrrhrjr+rrrns6%43 l1 %  V) E g</) x  5 ;"|.br