p:i9SSKrSSKrSSKrSSKrSSKJr SSKJr SSK J s J r SSK Jr SSKJr S/rSr"S S5rS r\ R*4S jrS\ R*S .S jjrg)N)prod)_dierckx) csr_array) _not_a_knot NdBSplinec[R"U[R5(a[R$[R$)z>Return np.complex128 for complex dtypes, np.float64 otherwise.)np issubdtypecomplexfloating complex128float64dtypes _/srv/projetos/modelo_ml_acdoc/venv/lib/python3.13/site-packages/scipy/interpolate/_ndbspline.py _get_dtypers- }}UB..//}}zzcj\rSrSrSrSS.Sjr\S5r\S5rSSS.S jr \ S S j5r S r g) ra Tensor 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__ design_matrix See Also -------- BSpline : a one-dimensional B-spline object NdPPoly : an N-dimensional piecewise tensor product polynomial N) extrapolatec[X15uUlUluUlUlUcSn[ U5Ul[R"U5Ul URRSnURRU:a[SUS35e[U5HnURUnURUnURSU- S- n URRUU :wdMU[SUSURRUS[!U5S U S US 3 5e [#URR$5n [R&"URU S 9Ul g) NTrzCoefficients must be at least z -dimensional.rz,Knots, coefficients and degree in dimension z are inconsistent: got z coefficients for z knots, need at least z for k=.r)_preprocess_inputs_k _indices_k1d_t_len_tboolrr asarraycshapendim ValueErrorrangetklenrrascontiguousarray) selfr%r r&rr"dtdkdndts r__init__NdBSpline.__init__MsT=OPQ=U:"$:TWdk  K ,Aww}}Q 66;; =dV=QR RtABB b 1$Avv||A!# $%%&C())-a(9:%%(WI-CA3G''(c ",--  %%%dffB7rc,[UR5$N)tuplerr)s rr& NdBSpline.kisTWW~rcn^[U4Sj[TRRS555$)Nc3d># UH%nTRUSTRU24v M' g7fr2)rr).0r*r)s r NdBSpline.t..ps-R:QQTWWQQ/0:Qs-0r)r3r$rr!r4s`rr% NdBSpline.tms(R% a@P:QRRRr)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$S :HnUR nU(a)UR RU:XaUR S nUR'[5nURURSUS-5nUR)5n [R"UR*V s/sHn XR"R,-PM sn [R S9n URS n [.R0"UURUR2UR4UUU U U UR65 n U R'UR R"5n U RUSS UR RUS-5$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 : array_like, optional, shape (ndim,) 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`` rNrrz)invalid number of derivative orders nu = z for ndim = rz'derivatives must be positive, got nu = zShapes: xi.shape=z and ndim=r ).N)r>)rr!rrr zerosint64rr"r#r'r%anyfloatreshaper(r rkindviewravelstridesitemsizerevaluate_ndbsplinerrr)r)xir<rr"xi_shape was_complexccc1c1rs _strides_c1num_c_trouts r__call__NdBSpline.__call__rs*ww}}Q  **K;' :4'2BBbhh/Bww!|rxx{d2 @2'B!$&&k]!-..26{{ #KbW!MNNZZ% (88 ZZHRL )  ! !" % B<4 0 *TFKL Lffll''3. VV 466;;$. "B WWU^ZZ$%/ 0hhjjj+-::"7+5a#$xx'8'8"8+5"7>@hhH 88B<))"!%!%!%!#!,!$!)!,!%!2!2  hhtvv||${{8CR=466<<+>>??!"7s"K6c^^[R"U[S9nURSn[ U5U:wa[ S[ U5SU<S35e[ TU5umnunm[UU4Sj[U555nUSSS -n [R"U SSS2[RS9SSS2R5n [R"UUTTXj5upn [XU 45$) a|Construct the design matrix as a CSR format sparse array. Parameters ---------- xvals : ndarray, shape(npts, ndim) Data points. ``xvals[j, :]`` gives the ``j``-th data point as an ``ndim``-dimensional array. t : tuple of 1D ndarrays, length-ndim Knot vectors in directions 1, 2, ... ndim, k : int B-spline degree. extrapolate : bool, optional Whether to extrapolate out-of-bounds values of raise a `ValueError` Returns ------- design_matrix : a CSR array Each row of the design matrix corresponds to a value in `xvals` and contains values of b-spline basis elements which are non-zero at this value. rr>z*Data and knots are inconsistent: len(t) = z for ndim = rc3@># UHnTUTU- S- v M g7frN)r8r*r&len_ts rr9*NdBSpline.design_matrix..s"A[a1Q4!+[srN)r)r rrBr!r'r#rr3r$cumprodr@copyr _coloc_ndr)clsxvalsr%r&rr"rrc_shapecscstridesdataindicesindptrrZs ` @r design_matrixNdBSpline.design_matrixs0 5.{{2 q6T>.-s%1Rq&1sN) isinstancer3r#r' TypeErrorr roperatorindexr@r$r!r"diffrAuniqueisfiniteall unravel_indexarangerTr]emptymaxrBfillnan)r&t_tplr"kir*r+r,r-r!rertirZrs rrrs) 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 u:D$ %uSWuE % 4U$E 2BGGBFFO 4[ %ns58}n  JJuBHH -E RK ''k  DI4T &s M MMMMc F[R"UR[R5(a6[ XR U40UD6n[ XR U40UD6nUSU--$URS:XaURSS:wan[R"U5n[URS5H:nU"XSS2U440UD6uUSS2U4'nUS:wdM%[SU<SU<SUS35e U$U"X40UD6uphUS:wa[SU<S U<S35eU$) Ny?rrrrz solver = z returns info =z for column rz returns info = ) r r rr _iter_solverealimagr"r! empty_liker$r#) absolver solver_argsrrresjinfos rrrAs  }}QWWb00111fff< <1fff< <bg~vv{qwwqzA~mmAqwwqz"A$Q!Q$?;?OC1Itqy IF;.>x|A3a!PQQ# 1/;/  19 {*;D9A>? ? rrc b^^[T5n[ST55n[T5 [T5HNupx[[R "U55n U TU::dM/[ SU SUSTUSTUS-S3 5e [UU4Sj[U555n [R"[R"T6V s/sHoPM sn [S 9n [RXT5n URn[US U5[XS 54nUR!U5nU["R$:wa$[&R("[*US 9nS U;aS US 'U"U U40UD6nUR!XnUS -5n[U UT5$![a T4U-mGN|f=fs sn f)a1Construct 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 g7fr2)r')r8xs rr9make_ndbspl..ys,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)rr rrB)r8r*r&pointss rr9rs5$"!"**VAYe)r'r3rv enumerater atleast_1dr#r$r itertoolsproductrBrrgr!rrCsslspsolve functoolspartialr)rvaluesr&rrr"rKr*pointnumptsr%xvr`matrv_shape vals_shapevalscoefs` ` r make_ndbsplrYs> 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 llGwu~&WU^(<=J >>* %D "";v>  $"&K  $ , ,D <<45>1 2D Qa  C  DIAs F F,F)(F)))rrrwnumpyr mathrrscipy.sparse.linalgsparselinalgr scipy.sparser _bsplinesr__all__rrrgcrotmkrrrYrrrsc!!"" -X2X2vI(X![[0E!s{{E!r