o 4Bi1@sddlZddlZddlZddlZddlmZddlmZddl m m Z ddl mZddlmZdgZdd ZGd ddZe jfd d Zde jdddZdS)N)prod)_bspl) csr_array) _not_a_knot NdBSplinecCst|tjr tjStjS)z>Return np.complex128 for complex dtypes, np.float64 otherwise.)np issubdtypecomplexfloating complex128float64dtyper\/var/www/html/Trade-python/venv/lib/python3.10/site-packages/scipy/interpolate/_ndbspline.py _get_dtypesrc@s<eZdZdZddddZdddddZed d d ZdS) raTensor 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-produce 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 Cs:t|}zt|Wnty|f|}Ynwt||kr.tdt|dt|dtdd|D|_tdd|D|_t||_|durNd}t ||_ t||_t |D]}|j|}|j|}|j d|d } |dkr~td |d |j d krtd |d | |d krtdd|dd|d|dt|dkrtd|dtt||| d dkrtd|dt|std|d|jj |krtd|d|jj || kr td|d|jj |dt|d| d|d q]t|jj} tj|j| d|_dS)Nz len(t) = z != len(k) = .css|]}t|VqdSN)operatorindex).0kirrr Ysz%NdBSpline.__init__..css|] }tj|tdVqdSr N)rascontiguousarrayfloatrtirrrrZsTrrzSpline degree in dimension z cannot be negative.zKnot vector in dimension z must be one-dimensional.zNeed at least z knots for degree z in dimension zKnots in dimension z# must be in a non-decreasing order.z.Need at least two internal knots in dimension z should not have nans or infs.zCoefficients 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 )len TypeError ValueErrortuplektrasarraycboolrrangeshapendimdiffanyuniqueisfiniteallrrr) selfr%r'r$rr+dtdkdndtrrr__init__Msp                  zNdBSpline.__init__)nurc s\t|j}|dur |j}t|}|durtj|ftjd}n/tj|tjd}|jdks2|j d|kr@t d|dt|jdt |dkrMt d|tj|t d}|j }| d |d }t|}|d |krtt d |d |tj|jtd d}d d|jD}tj|t|ft d}|tjt|D]} |j| || dt|j| f<qtj|td d}tdd|jD} ttt| | } tj| tjdj} |j |jj d|d} tjfddjDtjd}j d }tj|j dd |fjd}t ||||||| ||| | | |dd |jj |dS)a@Evaluate the tensor product b-spline at ``xi``. Parameters ---------- xi : array_like, shape(..., ndim) The coordinates to evaluate the interpolator at. This can be a list or tuple of ndim-dimensional points or an array with the shape (num_points, ndim). nu : array_like, optional, shape (ndim,) Orders of derivatives to evaluate. Each must be non-negative. Defaults to the zeroth derivivative. extrapolate : bool, optional Whether to exrapolate based on first and last intervals in each dimension, or return `nan`. Default is to ``self.extrapolate``. Returns ------- values : ndarray, shape ``xi.shape[:-1] + self.c.shape[ndim:]`` Interpolated values at ``xi`` Nr rrz)invalid number of derivative orders nu = z for ndim = rz'derivatives must be positive, got nu = zShapes: xi.shape=z and ndim=longcSsg|]}t|qSrr rrrr sz&NdBSpline.__call__..css|]}|dVqdS)rNr)rr4rrrrz%NdBSpline.__call__..)r9csg|]}|jjqSr)ritemsize)rsc1rrr<s)!r r%rr(rzerosintcr&r+r*r"r-rreshaperr$remptymaxfillnanr)r# unravel_indexarangerintpTr'ravelstridesrevaluate_ndbspline)r1xir8rr+xi_shape_klen_t_tr2r*indices _indices_k1dc1r _strides_c1num_c_troutrr@r__call__sj      "  " zNdBSpline.__call__Tc Cstj|td}|jd}t||krtdt|d|dzt|Wnty3|f|}Ynwtj|tjd}t |||\}}} 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. r r9z*Data and knots are inconsistent: len(t) = z for ndim = r) rr&rr*r r"r!int32r _colloc_ndr) clsxvalsr%r$rr+kkdatarUindptrrrr design_matrixs      zNdBSpline.design_matrix)T)__name__ __module__ __qualname____doc__r7r[ classmethodrcrrrrrs 29Xc Ks t|jtjr$t||j|fi|}t||j|fi|}|d|S|jdkrj|jddkrjt |}t |jdD]+}|||dd|ffi|\|dd|f<}|dkrgt d|d|d|dq<|S|||fi|\}}|dkrt d|d |d|S) Ny?rrrz solver = z returns info =z for column rz returns info = ) rr rr _iter_solverealimagr+r* empty_liker)r") absolver solver_argsrjrkresjinforrrris   .riroc srt}tddD}ztWnty!f|YnwtD](\}}tt|} | |krNtd| d|d|d|dd q&tfd dt|D} tjd d t j Dt d } t | | } |j} t| d |t| |d f}||}|tjkrtjt|d}d|vrd|d<|| |fi|}||| |d }t | |S)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. css|]}t|VqdSrr;)rxrrrr@r=zmake_ndbspl..z There are z points in dimension z , but order z requires at least rz points per dimension.c3s,|]}ttj|td|VqdSr)rrr&r)rr2r$pointsrrrOs$cSsg|]}|qSrr)rxvrrrr<Qszmake_ndbspl..r Nruatolgư>)r r#r! enumerater atleast_1dr"r)r& itertoolsproductrrrcr*rrDsslspsolve functoolspartialri)rxvaluesr$rorpr+rQr2pointnumptsr%r_matrv_shape vals_shapevalscoefrrwr make_ndbspl s>         r)rt)r}rrnumpyrmathrrscipy.sparse.linalgsparselinalgr scipy.sparser _bsplinesr__all__rrgcrotmkrirrrrrs    o