[;jG ddlZddlZddlZddlZddlmZddlmZddl m Z ddl m cm ZddlmZddlmZmZddlmZmZd gZd Zed d d gGdd ZdZej6fdZdej6ddZy)N)prod) GenericAlias)_dierckx) csr_array)array_namespacexp_capabilities) _not_a_knotBSpline NdBSplinectj|tjrtjStjS)z>Return np.complex128 for complex dtypes, np.float64 otherwise.)np issubdtypecomplexfloating complex128float64dtypes eG:\00. PROJECTS\API\Inventory\templateJSON\kerjaOCR\Lib\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_backendsceZdZdZeeZdddZedZ edZ edZ dddd Z ed d Z dd Zd Zy)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$t||\|_|_\|_|_t |g|j |_|d}t||_ tj ||_ |jjd}|jj|krtd|dt|D]}|j |}|j"|}|jd|z dz } |jj|| k7sStd|d|jj|dt%|d | d |d t'|jj(} tj*|j| |_ y) NTrzCoefficients must be at least z -dimensional.rz,Knots, coefficients and degree in dimension z are inconsistent: got z coefficients for z knots, need at least z for k=.r)_preprocess_inputs_k _indices_k1d_t_len_trasarray_asarrayboolrr_cshapendim ValueErrorrangetklenrrascontiguousarray) selfr-cr.rr*dtdkdndts r__init__zNdBSpline.__init__[sp=OPQST=U:"$:TWdk'.A.66  K ,**Q-ww}}Q 77<<$ =dV=QR RtABB b 1$Aww}}Q1$ $%%&C())-q)9(:;%%(WI-CA3G''(c ",--  &&&twwb9rc,t|jSN)tupler!r1s rr.z NdBSpline.kysTWW~rcltfdtjjdDS)Nc3|K|]3}jj|dj|f5ywr:)r&r#r$).0r3r1s r zNdBSpline.t..s9 @W1DMM$''!_dkk!n_"45 6@Ws9<r)r;r,r#r)r<s`rr-z NdBSpline.t}s2 @EdggmmTUFV@W   rc8|j|jSr:)r&r(r<s rr2z NdBSpline.cs}}TWW%%r)nurc |jjd}| |j}t|}|'t j |ftj }nt j|tj }|jdk7s|jd|k7r%td|dt|jdt|dkrtd|t j|t}|j}|jd |d }t j|}|d |k7rtd |d ||j j"j$d k(}|j }|r(|j j|k(r|j d }|j't}|j|jd|dz}|j)} t j|j*D cgc]} | |j"j,zc} tj } |jd } t/j0||j|j2|j4||| | | |j6 } | j'|j j"} | j|dd |j j|dz} |j9| Scc} w)aBEvaluate 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 = rz'derivatives must be positive, got nu = zShapes: xi.shape=z and ndim=r2).N)rF)r#r)rr'rzerosint64r%r*r+r/r-anyfloatreshaper0r(rkindviewravelstridesitemsizerevaluate_ndbspliner$r!r"r&)r1xirBrr*xi_shape was_complexccc1c1rs _strides_c1num_c_trouts r__call__zNdBSpline.__call__s*ww}}Q  **K;' :4'2BBbhh/Bww!|rxx{d2 @2'B!$&&k]!-..26{ #KbW!MNNZZ% (88 ZZHRL )  ! !" % B<4 0 *TFKL Lggmm((C/ WW 477<<4/#B WWU^ZZ$%/ 0hhjjj+-::"7+5a#$rxx'8'8"8+5"7>@hhH 88B<))"!%!%!%!#!,!$!)!,!%!2!2  hhtww}}%kk(3B-$''--*>>?}}S!!#"7s K9ctj|t}|jd}t ||k7rt dt |d|dt |\}\}tfdt|D}|ddd z} tj| dddtjdddj} tj|||| \} } } t| | | fS) 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. rrFz*Data and knots are inconsistent: len(t) = z for ndim = rc3:K|]}||z dz ywrN)r?r3r.len_ts rr@z*NdBSpline.design_matrix..s#A[a1Q4!+[srNr)rr%rJr)r/r+r r;r,cumprodrHcopyr _coloc_ndr)clsxvalsr-r.rr*r"r#c_shapecscstridesdataindicesindptrras ` @r design_matrixzNdBSpline.design_matrixs0 5.{{2 q6T>\\"%tt1SY-12++ArxxA /CQG}   bdd #(!,44 A  !N 24 E1d+e|rcdtj|tj}tj}|j dk7s|j d|k7r%td|dtjdt|dkrtd|tjj dDcgc]"}j|dj|f$}}tj}jj}t!|D]B\}} | dk(r j#||||||| \}||<t%||| z d||<Dt't)fd |Dj+|t)|j, Scc}w) a{ Construct a new NdBSpline representing the partial derivative. Parameters ---------- nu : array_like of shape (ndim,) Orders of the partial derivatives to compute along each dimension. Returns ------- NdBSpline A new NdBSpline representing the partial derivative of the original spline. rrrrDrErz-derivative orders must be positive, got nu = N)rBc3@K|]}j|ywr:)r&)r?r-r1s rr@z'NdBSpline.derivative..Qs?At}}Q/sr)rr%rHr/r-r*r)r+rIr,r#r$listr.r(rd enumerater~maxr r;r&r) r1rBnu_arrr*r3t_newk_newc_newrpr6s ` rrszNdBSpline.derivative)sBbhh/466{ ;;! v||A$6dff+a)* * vz?MwOP P7.s%1R"q&1sN) isinstancer;r+r/ TypeErrorrr%operatorindexrHr,r)r*diffrIuniqueisfiniteall unravel_indexarangerTrdemptyrrJfillnan)r.t_tplr*kir3r4r5r6r)rlr"r-tirar#s rr r WsQ eU # %wi1  u:D A 32HNN2&3288DA 1v~9SZLSVKqABB u:D 4[ ZZa ! qT HHQK" q  6:1#>*+, , 77a<8<123 3 rAv:~adQhZ8!!#N1#Q89 9 GGBK!O "21#6678 8 ryyBq1u& '! + ++,#Q01 1{{2""$21#6./0 0)2 %1% %Eryye5u=G::gRXX688==?L%* *EqRZZ]EE * u:D$ %uSWuE % 4U$E 2BGGBFFO 4[ %a1ns58}n  JJuBHH -E lRK ''m  DI4R + %s# M M%5M*"M/M"!M"c .tj|jtjr8t ||j |fi|}t ||j |fi|}|d|zzS|jdk(r{|jddk7ritj|}t|jdD]7}|||dd|ffi|\|dd|f<}|dk7s$td|d|d|d|S|||fi|\}}|dk7rtd|d |d|S) Ny?rrrz solver = z returns info =z for column rz returns info = ) rrrr _iter_solverealimagr*r) empty_liker,r+) ar{solver solver_argsrrresjinfos rrrs&  }}QWWb0011afff< <1afff< <bg~vv{qwwqzA~mmAqwwqz"A$Q!Q$?;?OC1Itqy IF;.>x|A3a!PQQ# 1a/;/ T 19 {*;D9A>? ? rrc t}tdD} ttD]L\}}tt j |} | |ks-t d| d|d|d|dzd tfdt|D} t jtjD cgc]} | c} t } tj| | } d d k\r| j|j}t!|d |t!||d f}|j#|}|t$j&k7r$t)j*t,| }d|vrd|d<|| |fi|}|j#|||d z}t| |S#t$r f|zYwxYwcc} w)aConstruct an interpolating NdBspline. Parameters ---------- points : tuple of ndarrays of float, with shapes (m1,), ... (mN,) The points defining the regular grid in N dimensions. The points in each dimension (i.e. every element of the `points` tuple) must be strictly ascending or descending. values : ndarray of float, shape (m1, ..., mN, ...) The data on the regular grid in n dimensions. k : int, optional The spline degree. Must be odd. Default is cubic, k=3 solver : a `scipy.sparse.linalg` solver (iterative or direct), optional. An iterative solver from `scipy.sparse.linalg` or a direct one, `sparse.sparse.linalg.spsolve`. Used to solve the sparse linear system ``design_matrix @ coefficients = rhs`` for the coefficients. Default is `scipy.sparse.linalg.gcrotmk` solver_args : dict, optional Additional arguments for the solver. The call signature is ``solver(csr_array, rhs_vector, **solver_args)`` Returns ------- spl : NdBSpline object Notes ----- Boundary conditions are not-a-knot in all dimensions. c32K|]}t|ywr:)r/)r?xs rr@zmake_ndbspl..s,VSVVsz There are z points in dimension z , but order z requires at least rz points per dimension.c3tK|]/}ttj|t|1yw)rN)r rr%rJ)r?r3r.pointss rr@zmake_ndbspl..s3$"!"**VAYe)r/r;rrr atleast_1dr+r,r% itertoolsproductrJr rneliminate_zerosr)rrKsslspsolve functoolspartialr)rvaluesr.rrr*rSr3pointnumptsr-xvrgmatrv_shape vals_shapevalscoefs` ` r make_ndbsplrs> v;D,V,,H A f%5R]]5)* QqT>z&1FqcJ++,Q4&1!!"1a(>@A A& $T{$ $A JJY%6%6%?@%?r%?@ NE  " "5!Q /D tqy  llGwu~&WTU^(<=J >>* %D "";v>  $"&K  $ , ,D <<745>1 2D Qa  M  DIAs F* G*F=<F=)r)rrrnumpyrmathrtypesrrscipy.sparse.linalgsparselinalgr scipy.sparserscipy._lib._array_apirr _bsplinesr r __all__rr r gcrotmkrrr`rrrs!!"B+ - 5 Dr r r h J(Z![[0J!s{{J!r