o EOf1@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 issubdtypecomplexfloatingZ complex128Zfloat64dtyper Ysz%NdBSpline.__init__..css|] }tj|tdVqdSr N)rascontiguousarrayfloatrZtir r rrZsTrrzSpline 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 ValueErrortuplektrasarraycboolrrangeshapendimZdiffanyuniqueZisfiniteallrr r) selfr!r#r rr'dZtdkdnZdtr r r__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=ZlongcSsg|]}t|qSr rrr r r sz&NdBSpline.__call__..css|]}|dVqdS)rNr )rr-r r rrz%NdBSpline.__call__..)r1csg|]}|jjqSr )r itemsize)rsZc1r rr3s)!rr!rr$rZzerosZintcr"r'r&rr(rreshaperr r emptymaxfillnanr%rZ unravel_indexZarangerZintpTr#ZravelstridesrZevaluate_ndbspline)r+Zxir0rr'xi_shapeZ_kZlen_tZ_tr,r&indicesZ _indices_k1dZc1rZ _strides_c1Znum_c_troutr r7r__call__sj      "  " zNdBSpline.__call__Tc Cstj|td}|jd}t||krtdt|d|dzt|Wnty3|f|}Ynwtj|tjd}t |||\}}} t ||| fS)a Construct the design matrix as a CSR format sparse array. Parameters ---------- xvals : ndarray, shape(npts, ndim) Data points. ``xvals[j, :]`` gives the ``j``-th data point as an ``ndim``-dimensional array. t : tuple of 1D ndarrays, length-ndim Knot vectors in directions 1, 2, ... ndim, k : int B-spline degree. extrapolate : bool, optional Whether to extrapolate out-of-bounds values of raise a `ValueError` Returns ------- design_matrix : a CSR array Each row of the design matrix corresponds to a value in `xvals` and contains values of b-spline basis elements which are non-zero at this value. r r1z*Data and knots are inconsistent: len(t) = z for ndim = r) rr"rr&rrrZint32rZ _colloc_ndr) clsxvalsr!r rr'Zkkdatar@Zindptrr r r design_matrixs      zNdBSpline.design_matrix)T)__name__ __module__ __qualname____doc__r/rB classmethodrFr r r rrs 29Xc Ks t|jtjr$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 r r _iter_solverealimagr'r&Z empty_liker%r) absolver solver_argsrMrNresjinfor r rrLs   .rLrQc 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|VqdSrr2)rxr r rr@r4zmake_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)rr,r pointsr rrOs$cSsg|]}|qSr r )rZxvr r rr3Qszmake_ndbspl..r NrWZatolgư>)rrr enumeraterZ atleast_1drr%r" itertoolsproductrrrFr&rr8sslZspsolve functoolspartialrL)rZvaluesr rQrRr'r?r,ZpointZnumptsr!rDZmatrZv_shapeZ vals_shapeZvalsZcoefr rYr make_ndbspl s>         rb)rV)r\r_rZnumpyrZmathrrZscipy.sparse.linalgZsparseZlinalgr^Z scipy.sparserZ _bsplinesr__all__rrZgcrotmkrLrbr r r rs    o