o 5ήc @sddlZddZddZddZdd Zd d Zd d ZddZddZ eeeeeeee dZ ddZ ddZ ddZ ddZddZddZdd Zd!d"ZdS)#NcCs| S)NrrrK/tmp/pip-target-vg8gfxp4/lib/python/scipy/interpolate/_rbfinterp_pythran.pylinearsrcCs|dkrdS|dt|S)Nr)nplogrrrrthin_plate_splinesr cCs|dS)Nrrrrrcubicsr cCs |d S)Nrrrrrquintics rcCst|dd S)Nrr sqrtrrrr multiquadricsrcCsdt|ddSNrrrrrrrinverse_multiquadricsrcCsd|ddSrrrrrrinverse_quadraticrcCst|d S)Nr)r exprrrrgaussian#rr)rr r rrrrrcCs4t|jdD]}|tj|||||<qdS)z5Evaluate RBFs, with centers at `y`, at the point `x`.rNrangeshaper linalgnorm)xy kernel_funcoutirrr kernel_vector3sr$cCs.t|jdD] }t|||||<qdS)zCEvaluate monomials, with exponents from `powers`, at the point `x`.rNrrr prod)rpowersr"r#rrrpolynomial_vector9sr(cCsbt|jdD]'}t|dD]}|tj|||||||f<|||f|||f<qqdS)z+Evaluate RBFs, with centers at `x`, at `x`.rrNr)rr!r"r#jrrr kernel_matrix?s $r*cCsJt|jdD]}t|jdD]}t|||||||f<qqdS)z9Evaluate monomials, with exponents from `powers`, at `x`.rNr%)rr'r"r#r)rrrpolynomial_matrixGs  r+cCs6tj|jd|jdftd}t|}t||||S)z3Return RBFs, with centers at `x`, evaluated at `x`.rdtype)r emptyrfloat NAME_TO_FUNCr*)rkernelr"r!rrr_kernel_matrixOs r2cCs.tj|jd|jdftd}t||||S)zAReturn monomials, with exponents from `powers`, evaluated at `x`.rr,)r r.rr/r+)rr'r"rrr_polynomial_matrixXs r3cCsj|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)axisrg?rr,N) rr0r minmaxr.r/Tr*r+r)r d smoothingr1epsilonr'psrr!minsmaxsshiftscaleyepsyhatlhsr#rhsrrr _build_systemes,       &    rEc Cs|jd}|jd}|jd} t|} ||} ||} |||} tj||| ftd}t|D]}t| || | ||d|ft| |||||dfq0|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 rr,N)rr0r r.r/rr$r()rr r1r:r'r?r@qr;rr!rAxepsxhatvecr#rrr_build_evaluation_coefficientss     rJ)numpyr rr r rrrrrr0r$r(r*r+r2r3rErJrrrrs4   I