doiE SSKrSSKrSSKrSSKrSSKJr SSKJr SSK J r SSK J s J r SSKJr SSKJrJr SSKJrJr S /rS r\"S S S /S9"SS 55rSr\R64SjrS\R6S.Sjjrg)N)prod) GenericAlias)_dierckx) csr_array)array_namespacexp_capabilities) _not_a_knotBSpline NdBSplinec[R"U[R5(a[R$[R$)z>Return np.complex128 for complex dtypes, np.float64 otherwise.)np issubdtypecomplexfloating complex128float64dtypes X/var/www/html/land-ocr/venv/lib/python3.13/site-packages/scipy/interpolate/_ndbspline.py _get_dtypers- }}UB..//}}zzTF)z dask.arrayz7https://github.com/data-apis/array-api-extra/issues/488)cpu_onlyjax_jit skip_backendsc\rSrSrSr\"\5rSS.Sjr\ S5r \ S5r \ S5r SSS .S jr \SS j5rSS jrS rSrg)r aTensor product spline object. The value at point ``xp = (x1, x2, ..., xN)`` is evaluated as a linear combination of products of one-dimensional b-splines in each of the ``N`` dimensions:: c[i1, i2, ..., iN] * B(x1; i1, t1) * B(x2; i2, t2) * ... * B(xN; iN, tN) Here ``B(x; i, t)`` is the ``i``-th b-spline defined by the knot vector ``t`` evaluated at ``x``. Parameters ---------- t : tuple of 1D ndarrays knot vectors in directions 1, 2, ... N, ``len(t[i]) == n[i] + k + 1`` c : ndarray, shape (n1, n2, ..., nN, ...) b-spline coefficients k : int or length-d tuple of integers spline degrees. A single integer is interpreted as having this degree for all dimensions. extrapolate : bool, optional Whether to extrapolate out-of-bounds inputs, or return `nan`. Default is to extrapolate. Attributes ---------- t : tuple of ndarrays Knots vectors. c : ndarray Coefficients of the tensor-product spline. k : tuple of integers Degrees for each dimension. extrapolate : bool, optional Whether to extrapolate or return nans for out-of-bounds inputs. Defaults to true. Methods ------- __call__ derivative design_matrix See Also -------- BSpline : a one-dimensional B-spline object NdPPoly : an N-dimensional piecewise tensor product polynomial N extrapolatec*[X15uUlUluUlUl[ U/UQ76R UlUcSn[U5Ul [R "U5Ul URRSnURRU:a[SUS35e[U5HnUR UnUR"UnURSU- S- n URRUU :wdMU[SUSURRUS[%U5S U S US 3 5e ['URR(5n [R*"URU S 9Ul g) NTrzCoefficients must be at least z -dimensional.rz,Knots, coefficients and degree in dimension z are inconsistent: got z coefficients for z knots, need at least z for k=.r)_preprocess_inputs_k _indices_k1d_t_len_trasarray_asarrayboolrr_cshapendim ValueErrorrangetklenrrascontiguousarray) selfr.cr/rr+dtdkdndts r__init__NdBSpline.__init__[sm=OPQ=U:"$:TWdk'.A.66  K ,**Q-ww}}Q 77<<$ =dV=QR RtABB b 1$Aww}}Q1$ $%%&C())-q)9(:;%%(WI-CA3G''(c ",--  &&&twwb9rc,[UR5$N)tupler"r2s rr/ NdBSpline.kysTWW~rcn^[U4Sj[TRRS555$)Nc3># UH4nTRTRUSTRU245v M6 g7fr<)r'r$r%).0r4r2s r NdBSpline.t..s; @W1DMM$''!_dkk!n_"45 6 6@Wss`rr. NdBSpline.t}s2 @EdggmmTUFV@W   rc8URUR5$r<)r'r)r>s rr3 NdBSpline.cs}}TWW%%r)nurc URRSnUc URn[U5nUc%[R "U4[R S9nO[R"U[R S9nURS:wdURSU:wa&[SU<S[UR5S35e[US:5(a[SU<35e[R"U[S9nURnURS US 5n[R"U5nUS U:wa[S US U35eUR R"R$S :HnUR nU(a)UR RU:XaUR S nUR'[5nURURSUS-5nUR)5n [R"UR*V s/sHn XR"R,-PM sn [R S9n URS n [.R0"UURUR2UR4UUU U U UR65 n U R'UR R"5n U RUSS UR RUS-5n UR9U 5$s sn f)aEvaluate the tensor product b-spline at ``xi``. Parameters ---------- xi : array_like, shape(..., ndim) The coordinates to evaluate the interpolator at. This can be a list or tuple of ndim-dimensional points or an array with the shape (num_points, ndim). nu : sequence of length ``ndim``, optional Orders of derivatives to evaluate. Each must be non-negative. Defaults to the zeroth derivivative. extrapolate : bool, optional Whether to exrapolate based on first and last intervals in each dimension, or return `nan`. Default is to ``self.extrapolate``. Returns ------- values : ndarray, shape ``xi.shape[:-1] + self.c.shape[ndim:]`` Interpolated values at ``xi`` rNrr)invalid number of derivative orders nu = for ndim = r z'derivatives must be positive, got nu = zShapes: xi.shape=z and ndim=r3).N)rL)r$r*rr(rzerosint64r&r+r,r0r.anyfloatreshaper1r)rkindviewravelstridesitemsizerevaluate_ndbspliner%r"r#r')r2xirHrr+xi_shape was_complexccc1c1rs _strides_c1num_c_trouts r__call__NdBSpline.__call__s*ww}}Q  **K;' :4'2BBbhh/Bww!|rxx{d2 @2'B!$&&k]!-..26{{ #KbW!MNNZZ% (88 ZZHRL )  ! !" % B<4 0 *TFKL Lggmm((C/ WW 477<<4/#B WWU^ZZ$%/ 0hhjjj+-::"7+5a#$xx'8'8"8+5"7>@hhH 88B<))"!%!%!%!#!,!$!)!,!%!2!2  hhtww}}%kk(3B-$''--*>>?}}S!!#"7s"Lc^^[R"U[S9nURSn[ U5U:wa[ S[ U5SU<S35e[ TU5umnunm[UU4Sj[U555nUSSS -n [R"U SSS2[RS9SSS2R5n [R"UUTTXj5upn [XU 45$) a|Construct the design matrix as a CSR format sparse array. Parameters ---------- xvals : ndarray, shape(npts, ndim) Data points. ``xvals[j, :]`` gives the ``j``-th data point as an ``ndim``-dimensional array. t : tuple of 1D ndarrays, length-ndim Knot vectors in directions 1, 2, ... ndim, k : int B-spline degree. extrapolate : bool, optional Whether to extrapolate out-of-bounds values of raise a `ValueError` Returns ------- design_matrix : a CSR array Each row of the design matrix corresponds to a value in `xvals` and contains values of b-spline basis elements which are non-zero at this value. rrLz*Data and knots are inconsistent: len(t) = z for ndim = r c3@># UHnTUTU- S- v M g7frN)rBr4r/len_ts rrC*NdBSpline.design_matrix..s"A[a1Q4!+[srNr)rr&rPr*r0r,r!r=r-cumprodrNcopyr _coloc_ndr)clsxvalsr.r/rr+r#r$c_shapecscstridesdataindicesindptrrhs ` @r design_matrixNdBSpline.design_matrixs0 5.{{2 q6T>\\"%tt1SY-12++ArxxA /CQG}   bdd #(!,44 A  !N 24 E1d+|rc h^[R"U[RS9n[TR5nUR S:wdUR SU:wa&[SU<S[TR5S35e[US:5(a[SU<35e[TRR S5Vs/sH#nTRUSTRU24PM% nn[TR5nTRR5n[!U5H;upU S:XaM TR#XuUXhXS 9uouU'[%XhU - S5Xh'M= ['[)U4S jU55TR+U5[)U5TR,S 9$s snf) a+ Construct a new NdBSpline representing the partial derivative. Parameters ---------- nu : array_like of shape (ndim,) Orders of the partial derivatives to compute along each dimension. Returns ------- NdBSpline A new NdBSpline representing the partial derivative of the original spline. rrrrJrKr z-derivative orders must be positive, got nu = N)rHc3F># UHnTRU5v M g7fr<)r')rBr.r2s rrC'NdBSpline.derivative..Qs?At}}Q//s!r)rr&rNr0r.r+r*r,rOr-r$r%listr/r)rl enumeratermaxr r=r'r) r2rHnu_arrr+r4t_newk_newc_newryr7s ` rr|NdBSpline.derivative)sBbhh/466{ ;;! v||A$6dff+a)* * vz??MwOP P7.s%1Rq&1sN) isinstancer=r,r0 TypeErrorrr&operatorindexrNr-r*r+diffrOuniqueisfiniteall unravel_indexarangerTrlemptyrrPfillnan)r/t_tplr+kir4r5r6r7r*rtr#r.tirhr$s rr!r!WsH eU # # %wi1  u:D A 32HNN2&3288DA 1v~9SZLSVKqABB u:D 4[ ZZ ! T HHQK" q  6:1#>*+, , 77a<8<123 3 Av:~adQhZ8!!#N1#Q89 9 GGBK!O " "21#6678 8 ryyq1u& '! + ++,#Q01 1{{2""$$21#6./0 0)2 %1% %Eryye5u=G::gRXX688==?L%* *EqRZZ]EE * u:D$ %uSWuE % 4U$E 2BGGBFFO 4[ %ns58}n  JJuBHH -E RK ''m  DI4R + %s# M( M? N?N (M<;M<c F[R"UR[R5(a6[ XR U40UD6n[ XR U40UD6nUSU--$URS:XaURSS:wan[R"U5n[URS5H:nU"XSS2U440UD6uUSS2U4'nUS:wdM%[SU<SU<SUS35e U$U"X40UD6uphUS:wa[SU<S U<S35eU$) Ny?rrrz solver = z returns info =z for column r z returns info = ) rrrr _iter_solverealimagr+r* empty_liker-r,) arsolver solver_argsrrresjinfos rrrs  }}QWWb00111fff< <1fff< <bg~vv{qwwqzA~mmAqwwqz"A$Q!Q$?;?OC1Itqy IF;.>x|A3a!PQQ# 1/;/  19 {*;D9A>? ? rrc ^^[T5n[ST55n[T5 [T5HNupx[[R "U55n U TU::dM/[ SU SUSTUSTUS-S3 5e [UU4Sj[U555n [R"[R"T6V s/sHoPM sn [S 9n [RXT5n TS S :aU R5 URn[!US U5[!XS 54nUR#U5nU[$R&:wa$[(R*"[,US 9nSU;aSUS'U"U U40UD6nUR#XnUS -5n[U UT5$![a T4U-mGNf=fs sn f)a+Construct an interpolating NdBspline. Parameters ---------- points : tuple of ndarrays of float, with shapes (m1,), ... (mN,) The points defining the regular grid in N dimensions. The points in each dimension (i.e. every element of the `points` tuple) must be strictly ascending or descending. values : ndarray of float, shape (m1, ..., mN, ...) The data on the regular grid in n dimensions. k : int, optional The spline degree. Must be odd. Default is cubic, k=3 solver : a `scipy.sparse.linalg` solver (iterative or direct), optional. An iterative solver from `scipy.sparse.linalg` or a direct one, `sparse.sparse.linalg.spsolve`. Used to solve the sparse linear system ``design_matrix @ coefficients = rhs`` for the coefficients. Default is `scipy.sparse.linalg.gcrotmk` solver_args : dict, optional Additional arguments for the solver. The call signature is ``solver(csr_array, rhs_vector, **solver_args)`` Returns ------- spl : NdBSpline object Notes ----- Boundary conditions are not-a-knot in all dimensions. c38# UHn[U5v M g7fr<)r0)rBxs rrCmake_ndbspl..s,VSVVVsz There are z points in dimension z , but order z requires at least rz points per dimension.c3v># UH.n[[R"TU[S9TU5v M0 g7f)rN)r rr&rP)rBr4r/pointss rrCrs5$"!"**VAYe)r0r=rrr atleast_1dr,r-r& itertoolsproductrPr rveliminate_zerosr*rrQsslspsolve functoolspartialr)rvaluesr/rrr+rYr4pointnumptsr.xvromatrv_shape vals_shapevalscoefs` ` r make_ndbsplrs> v;D,V,,H A f%R]]5)* QqT>z&1FqcJ++,Q4&1!!"1a(>@A A& $T{$ $A JJY%6%6%?@%?r%?@ NE  " "5Q /D tqy  llGwu~&WU^(<=J >>* %D "";v>  $"&K  $ , ,D <<45>1 2D Qa  M  DIAs F. G.GG)r)rrrnumpyrmathrtypesrrscipy.sparse.linalgsparselinalgr scipy.sparserscipy._lib._array_apirr _bsplinesr r __all__rr r!gcrotmkrrrgrrrs!!"B+ - 5 Dr r r h J(Z![[0J!s{{J!r