+ LV-jE^RIt^RIt^RIt^RIt^RIHt^RIHt^RI H t ^RI H uH t^RIHt^RIHtHt^RIHtHtR.tR t]!R R R.R 7!R R44tRt]P63RltRR]P6/RlltR#)N)prod) GenericAlias)_dierckx) csr_array)array_namespacexp_capabilities) _not_a_knotBSpline NdBSplinec\P!V\P4'd\P#\P#)z>Return np.complex128 for complex dtypes, np.float64 otherwise.)np issubdtypecomplexfloating complex128float64dtypes&m/Volumes/fast/ai/experiments/ui-tars-smoke/.venv/lib/python3.14/site-packages/scipy/interpolate/_ndbspline.py _get_dtypers- }}UB..//}}zzTF)cpu_onlyjax_jit skip_backendsca]tRt^toRt]!]4tRR/Rlt] R4t ] R4t ] R4t RRRR/R lt ]RR l4tRR ltR tR tVtR#)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 extrapolateNcz\W14wVnVnwVnVn\ V.VO5!P VnVfRp\V4Vn \P !V4Vn VPP^,pVPPV8d\RV R24h\V4FpVP V,pVP"V,pVP^,V, ^, p VPPV,V 8wgKn\RV RVPPV, R\%V4 RV RV R 2 4h \'VPP(4p \P*!VPV R 7Vn R#) NTzCoefficients must be at least z -dimensional.z,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$Aww}}Q1$ $%%&C())-q)9(:;%%(WI-CA3G''(c ",--  &&&twwb9rc,\VP4#N)tuplerr/s&rr, NdBSpline.kysTWW~rca\;QJd;.V3Rl\SPP^,44FNK 5#!V3Rl\SPP^,444#)c3<"TF<pSPSPVRSPV,13,4xK> R#5ir9)r$r!r").0r1r/s& r NdBSpline.t..s; @W1DMM$''!_dkk!n_"45 6 6@WsAA)r:r*r!r'r;sfrr+ NdBSpline.t}s]u @EdggmmTUFV@W u u @EdggmmTUFV@W   rc8VPVP4#r9)r$r&r;s&rr0 NdBSpline.cs}}TWW%%rnuc  VPP^,pVf VPp\V4pVf)\P !V3\P R7pM\P!V\P R7pVP^8wgVP^,V8wd'\RV: R\VP4 R24h\V^84'd\RV: 24h\P!V\R7pVPpVPR VR ,4p\P!V4pVR ,V8wd\RV RV 24hVP P"P$R 8HpVP pV'd/VP PV8XdVP R ,pVP'\4pVPVPRVR ,4pVP)4p \P!VP*U u.uFp WP"P,,NK! up \P R7p VPR ,p \.P0!VVPVP2VP4VVV V V VP64 p V P'VP P"4p V PVRR VP PVR,4p VP9V 4#uup i) aEvaluate the tensor product b-spline at ``xi``. Parameters ---------- xi : array_like, shape(..., ndim) The coordinates to evaluate the interpolator at. This can be a list or tuple of ndim-dimensional points or an array with the shape (num_points, ndim). nu : sequence of length ``ndim``, optional Orders of derivatives to evaluate. Each must be non-negative. Defaults to the zeroth derivivative. extrapolate : bool, optional Whether to exrapolate based on first and last intervals in each dimension, or return `nan`. Default is to ``self.extrapolate``. Returns ------- values : ndarray, shape ``xi.shape[:-1] + self.c.shape[ndim:]`` Interpolated values at ``xi`` Nr)invalid number of derivative orders nu = for ndim = rz'derivatives must be positive, got nu = zShapes: xi.shape=z and ndim=r0).N)rI)r!r'rr%r zerosint64r#r(r)r-r+anyfloatreshaper.r&rkindviewravelstridesitemsizerevaluate_ndbspliner"rr r$)r/xirErr(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#$xx'8'8"8"8+5"7>@hhH 88B<))"!%!%!%!#!,!$!)!,!%!2!2  hhtww}}%kk(3B-$''--*>>?}}S!!#"7s%L>c raa\P!V\R7pVPR,p\ V4V8wd\ R\ V4 RV: R24h\ SV4wopwpo\;QJd!.VV3Rl\V44FNK 5M!VV3Rl\V444pVR,R ,p \P!V RRR1,\PR7RRR1,P4p \P!VVSSWj4wrp \WV 34#) 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. rz*Data and knots are inconsistent: len(t) = z for ndim = rc3`<"TF#pSV,SV,, ^, xK% R#5iN)r?r1r,len_ts& rr@*NdBSpline.design_matrix..s%A[a1Q4!++[s+.rdNNNrIrd)r r#rMr'r-r)rr:r*cumprodrKcopyr _coloc_ndr)clsxvalsr+r,rr(r r!c_shapecscstridesdataindicesindptrrfs&&&f& @r design_matrixNdBSpline.design_matrixs 0 5.{{2 q6T>\\"%tt1SY-12++ArxxA /CQG}   bdd #(!,44 A  !N 24 E1d+|rc  a\P!V\PR7p\SP4pVP ^8wgVP ^,V8wd'\RV: R\SP4 R24h\V^84'd\RV: 24h\SPP ^,4Uu.uF+pSPVRSPV,13,NK- pp\SP4pSPP4p\!V4FOwrV ^8XdKSP#WuV,Wh,WR7wquV&\%Wh,V , ^4Wh&KQ \'\(;QJd.V3RlV4FNK 5M!V3RlV44SP+V4\)V4SP,R 7#uupi) 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. rrGrHrz-derivative orders must be positive, got nu = N)rEc3F<"TFpSPV4xK R#5ir9)r$)r?r+r/s& rr@'NdBSpline.derivative..Qs?At}}Q//s!)r)r r#rKr-r+r(r'r)rLr*r!r"listr,r&rk enumeratermaxr r:r$r) r/rEnu_arrr(r1t_newk_newc_newryr4s f& rr|NdBSpline.derivative)sBbhh/466{ ;;! v||A$6dff+a)* * vz??MwOP P7.s%1Rq&&1sN) isinstancer:r)r- TypeErrorr r#operatorindexrKr*r'r(diffrLuniqueisfiniteall unravel_indexarangerTrkemptyrrMfillnan)r,t_tplr(kir1r2r3r4r'rsr r+tirfr!s&& rrrWsV 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 E%1%EE%1% %Eryye5u=G::gRXX688==?L%* *EqRZZ]EE * u:D$ %uSWuE % 4U$E 2BGGBFFO 4[ %ns58}n  JJuBHH -E RK ''m  DI4R + %s# N?OO  O%?OOc p\P!VP\P4'd?\ WP V3/VBp\ WP V3/VBpVRV,,#VP^8XdVP^,^8wdt\P!V4p\VP^,4F;pV!WRV3,3/VBwVRV3&pV^8wgK&\RV: RV: RV R24h V#V!W3/VBwrhV^8wd\RV: RV: R24hV#)y?rxz solver = z returns info =z for column rz returns info = ) r rrr _iter_solverealimagr(r' empty_liker*r)) arsolver solver_argsrrresjinfos &&&, rrrs  }}QWWb00111fff< <1fff< <bg~vv{qwwqzA~mmAqwwqz"A$Q!Q$?;?OC1Itqy IF;.>x|A3a!PQQ# 1/;/  19 {*;D9A>? ? rrc daa\S4p\;QJd.RS4FNK 5M !RS44p\S4\S4F_wrx\\P !V44p V SV,8:gK4\ RV RV RSV, RSV,^, R2 4h \;QJd!.VV3Rl\V44FNK 5M!VV3Rl\V444p \P!\P!S!U u.uFqNK up \R7p \PWS4p S^,^8dV P4VPp\!VR V4\!WR 43pVP#V4pV\$P&8wd)\(P*!\,VR 7pR V9dR VR &V!V V3/VBpVP#WnVR ,4p\V VS4# \dS3T,oELi;iuup i) 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"TFp\V4xK R#5ir9)r-)r?xs& rr@make_ndbspl..s,VSVVVsz There are z points in dimension z , but order z requires at least z points per dimension.c3<"TF9p\\P!SV,\R7SV,4xK; R#5i)rN)r r r#rM)r?r1r,pointss& rr@rs5$"!"**VAYe)r-r:rrr atleast_1dr)r*r# itertoolsproductrMr rueliminate_zerosr'rrNsslspsolve functoolspartialr)rvaluesr,rrr(rVr1pointnumptsr+xvrnmatrv_shape vals_shapevalscoefsf&f$, r make_ndbsplrs> v;Du,V,uu,V,,H A f%R]]5)* QqT>z&1FqcJ++,Q4&1!!"1a(>@A A& $T{$$T{$ $A JJY%6%6%?@%?r%?@ NE  " "5Q /D tqy  llGwu~&WU^(<=J >>* %D "";v>  $"&K  $ , ,D <<45>1 2D Qa  M  DIAs H H-H*)H*)z dask.arrayz7https://github.com/data-apis/array-api-extra/issues/488))rrrnumpyr mathrtypesrrscipy.sparse.linalgsparselinalgr scipy.sparserscipy._lib._array_apirr _bsplinesr r __all__rr rgcrotmkrrrerrrs!!"B+ - 5 Dr r r h J(Z![[0J!s{{J!r