tKg1ddlZddlZddlZddlZddlmZddlmZddl m cm Z ddl mZddlmZdgZdZGd dZe j(fd Zd e j(d d Zy)N)prod)_bspl) csr_array) _not_a_knot NdBSplinectj|tjrtjStjS)z>Return np.complex128 for complex dtypes, np.float64 otherwise.)np issubdtypecomplexfloating complex128float64dtypes `/home/alanp/www/video.onchill/myenv/lib/python3.12/site-packages/scipy/interpolate/_ndbspline.py _get_dtypers* }}UB../}}zzc<eZdZdZdddZddddZeddZy) 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) extrapolatect|} t|t||k7r$tdt|dt|dtd|D|_td|D|_t j||_|d}t||_ t j||_t|D]}|j |}|j|}|jd|z dz } |dkrtd |d |jdk7rtd |d | |dzkrtd d|zdzd|d|dt j|dkjrtd|dtt j ||| dzdkrtd|dt j"|j%std|d|jj|krtd|d|jj|| k7sotd|d|jj|dt|d| d|d t'|jj(} t j*|j| |_y#t$r |f|z}YwxYw)Nz len(t) = z != len(k) = .c3FK|]}tj|ywN)operatorindex).0kis r z%NdBSpline.__init__..Ys6Abx~~b)As!c3RK|]}tj|t!ywrN)r ascontiguousarrayfloat)rtis rrz%NdBSpline.__init__..Zs!Iqr++Be< A{.s1vk;< <6A66IqIIA  K ,AtABB b 1$AAv #>qcB."/00ww!| #!B$(<%%'Dqc"<== a$$& #6qc::";<<299R1q5\*+a/ $//0c"455;;r?&&( #6qc:2"344vv{{T! $%%&C}"677vv||A!# $%%&C())-a(9:%%(WI-CA3G''(c ",--5@ %%%dffB7e T A s J<<KK)nurc t|j}| |j}t|}|'t j |ftj }nt j|tj }|jdk7s|jd|k7r%td|dt|jdt|dkrtd|t j|t}|j}|jd |d }t j|}|d |k7rtd |d |t j|jt j d }|jDcgc] }t|}}t j"|t%|ft} | j'tj(t+|D].} |j| | | dt|j| f<0t j|t j d }t-d |jD} t j.t j0t3| | } t j| tj4j6} |j8j|j8jd|dz}|j;}t j|j<Dcgc]}||j j>zc}tj4}|jd }t j"|jdd |fz|j }tAjB|| |||||||| | |j|dd |j8j|dzScc}wcc}w)a@Evaluate the tensor product b-spline at ``xi``. Parameters ---------- xi : array_like, shape(..., ndim) The coordinates to evaluate the interpolator at. This can be a list or tuple of ndim-dimensional points or an array with the shape (num_points, ndim). nu : array_like, optional, shape (ndim,) Orders of derivatives to evaluate. Each must be non-negative. Defaults to the zeroth derivivative. extrapolate : bool, optional Whether to exrapolate based on first and last intervals in each dimension, or return `nan`. Default is to ``self.extrapolate``. Returns ------- values : ndarray, shape ``xi.shape[:-1] + self.c.shape[ndim:]`` Interpolated values at ``xi`` Nrrrz)invalid number of derivative orders nu = z for ndim = rz'derivatives must be positive, got nu = zShapes: xi.shape=z and ndim=longc3&K|] }|dz yw)rN)rr9s rrz%NdBSpline.__call__..s.vb1fvs)r?)"r%r*rr-r zerosintcr+r0r/r'r2r"reshaper!r)remptymaxfillnanr.r( unravel_indexarangerintpTr,ravelstridesitemsizerevaluate_ndbspline)r6xir=rr0xi_shape_kr#len_t_tr7r/indices _indices_k1dc1c1rs _strides_c1num_c_trouts r__call__zNdBSpline.__call__s:*466{  **K;' :4'1BBbgg.Bww!|rxx{d2 @2'B!$&&k]!-..26{ #KbW!MNNZZ% (88 ZZHRL )  ! !" % B<4 0 *TFKL LZZbhhv&6 7$(66*6RR6* XXtSZ( 6 tA%)VVAYBq/3tvvay>/! " 5(89.tvv..""299T%[#95Azz'9;; VV^^DFFLL$/%7 8hhjjj+-::"7+5a#$rxx'8'8"8+5"7>@ggG 88B<hhrxx}{2"((C   !#!&!#!#!,!$!)!,!-!$ '{{8CR=466<<+>>??G+""7s O.) O3ctj|t}|jd}t ||k7rt dt |d|d t |tj|tj}tj|||\}}} t||| fS#t $r |f|z}Y_wxYw)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 = r) r r+r"r/r%r'r&int32r _colloc_ndr) clsxvalsr*r)rr0kkdatarWindptrs r design_matrixzNdBSpline.design_matrixs0 5.{{2 q6T>gv$011  T A s B..C?C)T)__name__ __module__ __qualname____doc__r<r_ classmethodrhrBrrrrs61d0478r"&4V@p&2&2rc .tj|jtjr8t ||j |fi|}t ||j |fi|}|d|zzS|jdk(r{|jddk7ritj|}t|jdD]7}|||dd|ffi|\|dd|f<}|dk7s$td|d|d|d|S|||fi|\}}|dk7rtd|d |d|S) Ny?r$rrz solver = z returns info =z for column rz returns info = ) r r rr _iter_solverealimagr0r/ empty_liker.r') absolver solver_argsrprqresjinfos rroros&  }}QWWb0011afff< <1afff< <bg~vv{qwwqzA~mmAqwwqz"A$Q!Q$?;?OC1Itqy IF;.>x|A3a!PQQ# 1a/;/ T 19 {*;D9A>? ? rruc Zt}tdD} ttD]L\}}tt j |} | |ks-t d| d|d|d|dzd tfdt|D} t jtjD cgc]} | c} t } tj| | } |j}t|d |t||d f}|j!|}|t"j$k7r$t'j(t*| }d |vrd |d <|| |fi|}|j!|||d z}t| |S#t$r f|zYxwxYwcc} 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%)rxs rrzmake_ndbspl..@s,VSVVsz There are z points in dimension z , but order z requires at least rz points per dimension.c3tK|]/}ttj|t|1ywr )rr r+r")rr7r)pointss rrzmake_ndbspl..Os3$"!"**VAYe)r%r(r& enumerater atleast_1dr'r.r+ itertoolsproductr"rrhr/rrEsslspsolve functoolspartialro)rvaluesr)rurvr0rSr7pointnumptsr*xvrdmatrv_shape vals_shapevalscoefs` ` r make_ndbsplr s> 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 llGwu~&WTU^(<=J >>* %D "";v>  $"&K  $ , ,D <<745>1 2D Qa  C  DIAs F F(F%$F%))rrrnumpyr mathrrscipy.sparse.linalgsparselinalgr scipy.sparser _bsplinesr__all__rrgcrotmkrorrBrrrs\!!"" -k2k2\![[0E!s{{E!r