o Ebb @sddlZddZddZddZdd Zd d Zd d ZddZddZ eeeeeeee dZ ddZ ddZ ddZ ddZddZddZdd Zd!d"ZdS)#NcCs| S)NrrrF/usr/lib/python3/dist-packages/scipy/interpolate/_rbfinterp_pythran.pylinearsrcCs|dkrdS|dt|S)Nr)nplogrrrrthin_plate_splinesr cCs|dS)Nrrrrrcubicsr cCs |d S)Nrrrrrquintics rcCst|dd S)Nrr Zsqrtrrrr multiquadricsrcCsdt|ddSNrrrrrrrinverse_multiquadricsrcCsd|ddSrrrrrrinverse_quadraticrcCst|d S)Nr)r Zexprrrrgaussian#rr)rr r rrrrrcCs4t|jdD]}|tj|||||<qdS)z5Evaluate RBFs, with centers at `y`, at the point `x`.rNrangeshaper ZlinalgZnorm)xy kernel_funcoutirrr kernel_vector3sr cCs.t|jdD] }t|||||<qdS)zCEvaluate monomials, with exponents from `powers`, at the point `x`.rNrrr Zprod)rpowersrrrrrpolynomial_vector9sr#cCsbt|jdD]'}t|dD]}|tj|||||||f<|||f|||f<qqdS)z+Evaluate RBFs, with centers at `x`, at `x`.rrNr)rrrrjrrr kernel_matrix?s $r%cCsJt|jdD]}t|jdD]}t|||||||f<qqdS)z9Evaluate monomials, with exponents from `powers`, at `x`.rNr!)rr"rrr$rrrpolynomial_matrixGs  r&cCs6tj|jd|jdftd}t|}t||||S)z3Return RBFs, with centers at `x`, evaluated at `x`.rZdtype)r emptyrfloat NAME_TO_FUNCr%)rkernelrrrrr_kernel_matrixOs r,cCs.tj|jd|jdftd}t||||S)zAReturn monomials, with exponents from `powers`, evaluated at `x`.rr')r r(rr)r&)rr"rrrr_polynomial_matrixXs r-cCsj|jd}|jd}|jd}t|} tj|dd} tj|dd} | | d} | | d} d| | dk<||}|| | }tj||||ftdj}t|| |d|d|ft |||d||df|d||dfj||dd|f<d||d|df<t |D]}|||f||7<qtj|||ftdj}||d|<d||d<||| | 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. rr)Zaxisrg?rr'N) rr*r minmaxr(r)Tr%r&r)rdZ smoothingr+epsilonr"psrrZminsZmaxsshiftscaleyepsZyhatZlhsrZrhsrrr _build_systemes,       &    r8c Cs|jd}|jd} |jd} |jd} t|} ||} ||}|||}tj|| ftd}tj| | ftd}t|D]=}t||| | |d| t||||| dt| D]}t| | D]}|||f|||f||7<qdq\q=|S)aEvaluate the RBF interpolant at `x`. 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. coeffs : (P + R, S) float ndarray Coefficients for each RBF and monomial. Returns ------- (Q, S) float ndarray rrr'N) rr*r Zzerosr)r(rr r#)rrr+r2r"r5r6Zcoeffsqr3rr4rr7ZxepsZxhatrZvecrr$krrr _evaluates&       &r;)Znumpyr rr r rrrrrr*r r#r%r&r,r-r8r;rrrrs4   J