o iX@sddlZddlZejdkrddlmZnddlmZddlZddlmZddl m Z ddl m Z m Z mZmZddZd d d Zd d ZddZddZddZddZddZ d!ddZddZddZdS)"N2)normalize_axis_index)sparse)spsolve)_get_module_funcINTERVAL_MODULE D_BOOR_MODULEBSplinecCst|tjr tjStjS)z>Return np.complex128 for complex dtypes, np.float64 otherwise.)cupy issubdtypecomplexfloatingcomplex_float_dtyper^/home/ubuntu/veenaModal/venv/lib/python3.10/site-packages/cupyx/scipy/interpolate/_bspline2.py _get_dtypesrFcCsJt|}t|}t|j}|j|dd}|r#t|s#td|S)zConvert the input into a C contiguous float array. NB: Upcasts half- and single-precision floats to double precision. F)copyz$Array must not contain infs or nans.) r asarrayascontiguousarrayrrastypeisfiniteall ValueError)x check_finitedtyprrr_as_float_arrays   rcCsd}|D]}||9}q|S)z Product of a sequence of numbers. Faster than np.prod for short lists like array shapes, and does not overflow if using Python integers. r)iterableproductrrrrprod(s r"cCstt|}|ddkrtd||dd}||d| d}tj|df|d||df|df}|S)zSGiven data x, construct the knot vector w/ not-a-knot BC. cf de Boor, XIII(12).rz Odd degree for now only. Got %s.r)r rrr_)rkmtrrr _not_a_knot8s    ,r)cCs$tj|df|||df|fS)zBConstruct a knot vector appropriate for the order-k interpolation.rr$)r r%)rr&rrr_augkntEs$r*cCst|}t|}|ddkr$t|}|dd|ddd8<t|}t|d|}|||| <td|D]/}||||||d d|||d<|| |d|||d|| |<q>|S)z$Returns vector of nodes on a circle.r#rrr$N)r rlendiffzerosrange)rr&xcndxr(irrr_periodic_knotsJs     ..r3cCsRt|tr'|dkrdt|fg}|S|dkr!dt|fg}|Std||S)Nclampedrnaturalr#zUnknown boundary condition : %s) isinstancestrr r-r)deriv target_shaperrr_convert_string_aliases\s  r:c CsV|dur zt|\}}Wnty}zd}t||d}~wwgg}}t||S)Nz^Derivatives, `bc_type`, should be specified as a pair of iterables of pairs of (order, value).)zip TypeErrorrr atleast_1d)r8ordsvalsemsgrrr_process_deriv_specgs   rBTc#Cs~|dus |dks |dkrd\}}n%t|tr||}}nz|\}}Wnty5} ztd|| d} ~ wwt|}t||j}t||}t||}t ||d}|dkrftj |d|ddd sftd |j |j dkrxtd |j |j |d d|ddkrtd |jd ks|d d|ddkrtd|dkrtdd|||fDrtdtj||df}t|} tj| t| jd} tj|| ||dS|d kr|dur|dur|dustdtj|d||df}t|} tj| t| jd} tj|| ||dSt|}|dkr#|dur#td|durv|durq|durq|dkr=t||}n9|dkrk|d d|ddd}tj|df|d |d d|df|d f}n t||}nt||}t||}|dkrtd|jd ks|d d|ddkrtd|j |j |d krtd|j |j |d f|d||ks|d|| krtd||dkrt|||||St||j d d}t|\} } | j d} t||j d d}t|\}}|j d}|j }|j |d }||| |kr$td||| |f|j dkrBtj|f|j d dtd} tj|| ||dSt |||}| dksS|dkrtjd|d ftd}d }tj!||ftd}tj!d|jd}t"t#d|}tj!dtj$d}t"t%d}|d d!|tj|d|df|||d"df| dkrtj&|dg|jd}tj| |ftd}t'| D].\}}|d d |||t(||||||dd f |d}|d|d |||||d f<qt)*t)+||g}|dkrM|d|d<tj&|dg|jd}tj||ftd}t'|D].\}}|d d |||t(||||||dd f |d}|d|d |||||d f<qt)*|t)+|g}t,|j d d} tj!|| f|jd}!| dkro| -d| |!d| <|-d| |!| ||<|dkr|-d| |!||d<t.|!jtj/rt0||!j1t0||!j2d#}"nt0||!}"t|"-|f|j d d}"t||"|S)$aiCompute the (coefficients of) interpolating B-spline. Parameters ---------- x : array_like, shape (n,) Abscissas. y : array_like, shape (n, ...) Ordinates. k : int, optional B-spline degree. Default is cubic, ``k = 3``. t : array_like, shape (nt + k + 1,), optional. Knots. The number of knots needs to agree with the number of data points and the number of derivatives at the edges. Specifically, ``nt - n`` must equal ``len(deriv_l) + len(deriv_r)``. bc_type : 2-tuple or None Boundary conditions. Default is None, which means choosing the boundary conditions automatically. Otherwise, it must be a length-two tuple where the first element (``deriv_l``) sets the boundary conditions at ``x[0]`` and the second element (``deriv_r``) sets the boundary conditions at ``x[-1]``. Each of these must be an iterable of pairs ``(order, value)`` which gives the values of derivatives of specified orders at the given edge of the interpolation interval. Alternatively, the following string aliases are recognized: * ``"clamped"``: The first derivatives at the ends are zero. This is equivalent to ``bc_type=([(1, 0.0)], [(1, 0.0)])``. * ``"natural"``: The second derivatives at ends are zero. This is equivalent to ``bc_type=([(2, 0.0)], [(2, 0.0)])``. * ``"not-a-knot"`` (default): The first and second segments are the same polynomial. This is equivalent to having ``bc_type=None``. * ``"periodic"``: The values and the first ``k-1`` derivatives at the ends are equivalent. axis : int, optional Interpolation axis. Default is 0. check_finite : bool, optional Whether to check that the input arrays contain only finite numbers. Disabling may give a performance gain, but may result in problems (crashes, non-termination) if the inputs do contain infinities or NaNs. Default is True. Returns ------- b : a BSpline object of the degree ``k`` and with knots ``t``. N not-a-knotperiodicNNUnknown boundary condition: %srr$gV瞯<)atolzAFirst and last points does not match while periodic case expectedz(Shapes of x {} and y {} are incompatiblerzExpect x to not have duplicatesz1Expect x to be a 1D strictly increasing sequence.css|]}|duVqdS)Nr).0_rrr sz%make_interp_spline..z6Too much info for k=0: t and bc_type can only be None.r)axisz0Too much info for k=1: bc_type can only be None.zOFor periodic case t is constructed automatically and can not be passed manuallyr#g@zExpect non-negative k.z'Expect t to be a 1-D sorted array_like.zGot %d knots, need at least %d.zOut of bounds w/ x = %s.zPThe number of derivatives at boundaries does not match: expected %s, got %s + %s)rrd_boor find_intervalrr#Fy?)3r6r7r<rr rrndimrmoveaxisallclosesizeshapeformatanyr%rrrr construct_fastoperatorindexNotImplementedErrorr3r)r*_make_periodic_spliner:rBr-float design_matrixemptyrrint64rarray enumerateintrvstack csr_matrixr"reshaper r rrealimag)#ryr&r(bc_typerLrderiv_lderiv_rr@c deriv_l_ords deriv_l_valsnleft deriv_r_ords deriv_r_valsnrightr0ntmatrtempnum_cdummy_cout d_boor_kernel intervals_bcinterval_kernelx0rowsjr'leftextradimrhscoefrrrmake_interp_splinets*3          &            *&            (   (      rc#Cs|dus|dkr d\}}n%t|tr||}}nz|\}}Wnty1}ztd||d}~wwt||jdd}t|\}} |jd} t||jdd}t|\} } | jd} |j}|j|d}t||jdd}t|\}} |jd} t||jdd}t|\} } | jd} |j}|j|d}||| | ksJtj |tj d}t t d}||jdd dd fd |||||d |jdftj |dftd}tj t|t|jddf|jd}t|jdd}t |jdd |d}t td |}||jdd dd fd |||d|||||d|jdf tj||ftd}| }tt|D])}||}||d |d|d |d|d||||||df<q3tj dtj d}| dkr|d|d<tj|dg|jd}t|D].\}}|dd|||t||||||ddf |d}|d|d|||||df<q| dkr|d|d<tj|dg|jd}t| D]6\}}|dd|||t||||||ddf |d}| t||}|d|d|||||df<qt|jdd}tj ||f|jd} | dkr!| d|| d| <|d|| | || <| dkr>| d|| || d<ddlm}!|!|| }"t|"|f|jdd}"t||"|S)z Construct the interpolating spline spl(x) = y with *full* linalg. Only useful for testing, do not call directly! This version is O(N**2) in memory and O(N**3) in flop count. NrDrFrGrrrrN)rFr#rMrOr$)solve)r6r7r<rr:rUrBrTr empty_liker`rrr_r]r+r"rrr-r.rarbrcrf cupy.linalgrrr )#rrir&r(rjrkrlr@rnrorprqrrrsr0rt intervalsr|rxryrwrvrzAoffsetrrr{r}r'rowrrrrrrr_make_interp_spline_full_matrix}s               H  (  (      rcCs*|j}t|||}tjdd|dtd}d}tj|j|d|ftd} tjd| jd} tt d| } tj |d|df} tj |||dgtj d} tj|d||dftd}t |dD]F}| dd || ||d| | | ||ddf |d|d||d|df<||| df|d|dd|d|ddd8<qctt||g}t|jdd}tj||d|ftd}d|d|dddf<|jdkr||dn|d|f||ddddf<t||}t|||df|jdd}tj|||d |d S) Nr#rr)r#rrMrr$rOrPrE) extrapolaterL)rTr r^r r-r]r_rrrr%rar`r.rrdrer"rUrfrrrX)rrir(r&rLr0rurvrwrxryrzr}r{r~r'matr_csrrrrrrrr\sH   D   ( r\)F)rCNNrT)rYnumpy __version__numpy.core.multiarrayrnumpy.lib.array_utilsr cupyx.scipyrcupyx.scipy.sparse.linalgr cupyx.scipy.interpolate._bsplinerrrr rrr"r)r*r3r:rBrrr\rrrrs2