a j,3@sddlZddlZddlZddlZddlmZddlmZddl m m Z ddl mZddlmZdgZdd ZGd ddZe jfd d Zde jdddZdS)N)prod)_bspl) csr_array) _not_a_knot NdBSplinecCst|tjrtjStjSdS)z>Return np.complex128 for complex dtypes, np.float64 otherwise.N)np issubdtypecomplexfloatingZ complex128Zfloat64dtyper BE:\soccer\ml_env\Lib\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 CsFt|}z t|Wnty0|f|}Yn0t||kr\tdt|dt|dtdd|D|_tdd|D|_t||_|durd}t ||_ t||_t |D]f}|j|}|j|}|j d|d } |dkrtd |d |j d krtd |d | |d krLtdd|dd|d|dt|dkrptd|dtt||| d dkrtd|dt|std|d|jj |krtd|d|jj || krtd|d|jj |dt|d| d|d qt|jj} tj|j| d|_dS)Nz len(t) = z != len(k) = .css|]}t|VqdSN)operatorindex).0Zkir r r Yz%NdBSpline.__init__..css|]}tj|tdVqdSr N)rascontiguousarrayfloatrtir r rrZrTrrzSpline 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 ValueErrortuplektrasarraycboolrrangeshapendimdiffanyuniqueisfiniteallrr r) selfr#r%r"rr)dtdkdndtr r r__init__Msl                zNdBSpline.__init__)nurc s^t|j}|dur|j}t|}|durrz&NdBSpline.__call__..css|]}|dVqdS)rNr )rr2r r rrrz%NdBSpline.__call__..)r7csg|]}|jjqSr )r itemsize)rsc1r rr:s)!rr#rr&rZzerosZintcr$r)r(r r+rreshaperr"r emptymaxfillnanr'r!Z unravel_indexZarangerZintpTr%ZravelstridesrZevaluate_ndbspline)r/xir6rr)xi_shapeZ_kZlen_tZ_tr0r(indicesZ _indices_k1dZc1rZ _strides_c1Znum_c_troutr r=r__call__sj      $   zNdBSpline.__call__Tc Cstj|td}|jd}t||kr>tdt|d|dz t|Wntyf|f|}Yn0tj|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 r7z*Data and knots are inconsistent: len(t) = z for ndim = r) rr$rr(rr rZint32rZ _colloc_ndr) clsxvalsr#r"rr)kkdatarHZindptrr r r design_matrixs     zNdBSpline.design_matrix)T)__name__ __module__ __qualname____doc__r5rJ classmethodrOr r r rrs 29Xc Kst|jtjrHt||j|fi|}t||j|fi|}|d|S|jdkr|jddkrt |}t |jdD]V}|||dd|ffi|\|dd|f<}|dkrxt d|d|d|dqx|S|||fi|\}}|dkr t d|d |d|SdS) Ny?rrrz solver = z returns info =z for column rz returns info = ) rr r r _iter_solverealimagr)r(Z empty_liker'r ) absolver solver_argsrVrWresjinfor r rrUs  . rUrZc svt}tddD}z tWntyBf|Yn0tD]P\}}tt|} | |krLtd| d|d|d|dd qLtfd dt|D} tjd d t j Dt d } t | | } |j} t| d |t| |d f}||}|tjkrBtjt|d}d|vrBd|d<|| |fi|}||| |d }t | |S)aConstruct an interpolating NdBspline. Parameters ---------- points : tuple of ndarrays of float, with shapes (m1,), ... (mN,) The points defining the regular grid in N dimensions. The points in each dimension (i.e. every element of the `points` tuple) must be strictly ascending or descending. values : ndarray of float, shape (m1, ..., mN, ...) The data on the regular grid in n dimensions. k : int, optional The spline degree. Must be odd. Default is cubic, k=3 solver : a `scipy.sparse.linalg` solver (iterative or direct), optional. An iterative solver from `scipy.sparse.linalg` or a direct one, `sparse.sparse.linalg.spsolve`. Used to solve the sparse linear system ``design_matrix @ coefficients = rhs`` for the coefficients. Default is `scipy.sparse.linalg.gcrotmk` solver_args : dict, optional Additional arguments for the solver. The call signature is ``solver(csr_array, rhs_vector, **solver_args)`` Returns ------- spl : NdBSpline object Notes ----- Boundary conditions are not-a-knot in all dimensions. css|]}t|VqdSrr9)rxr r rr@rzmake_ndbspl..z There are z points in dimension z , but order z requires at least rz points per dimension.c3s*|]"}ttj|td|VqdSr)rrr$r)rr0r"pointsr rrOscSsg|]}|qSr r )rZxvr r rr:Qrzmake_ndbspl..r Nr`Zatolgư>)rr!r enumeraterZ atleast_1dr r'r$ itertoolsproductrrrOr(rr?sslZspsolve functoolspartialrU)rcvaluesr"rZr[r)rGr0pointZnumptsr#rLZmatrZv_shapeZ vals_shapevalsZcoefr rbr make_ndbspl s:        rm)r_)rerhrnumpyrmathrrZscipy.sparse.linalgsparseZlinalgrgZ scipy.sparserZ _bsplinesr__all__rrZgcrotmkrUrmr r r rs    o