`ik;ddlZddlmZdZd dZGddeZGddeZd d ZGd d eZdS)N)PPolyc`tj|pt|do |jdkS)z-Check whether x is if a scalar type, or 0-dimshape)cupyisscalarhasattrr)xs r/home/jaya/work/projects/VOICE-AGENT/VIET/agent-env/lib/python3.11/site-packages/cupyx/scipy/interpolate/_cubic.py _isscalarr s, =   Dwq'22Dqw"}Dcttj||f\}}tj|jtjrt d|t}tj|jtjrt}nt}|utj|}|j |j krt dtj|jtjrt}||d}||d}||j z}|j dkrt d|j dd krt d |j d|j |kr"t d |tj tj|st d tj tj|st d |5tj tj|st dtj|}tj|dkrt dtj||d}|tj||d}|||||fS)aPrepare input for cubic spline interpolators. All data are converted to numpy arrays and checked for correctness. Axes equal to `axis` of arrays `y` and `dydx` are moved to be the 0th axis. The value of `axis` is converted to lie in [0, number of dimensions of `y`). z`x` must contain real values.Nz/The shapes of `y` and `dydx` must be identical.F)copyz`x` must be 1-dimensional.rz%`x` must contain at least 2 elements.zBThe length of `y` along `axis`={0} doesn't match the length of `x`z$`x` must contain only finite values.z$`y` must contain only finite values.z'`dydx` must contain only finite values.z)`x` must be strictly increasing sequence.)maprasarray issubdtypedtypecomplexfloating ValueErrorastypefloatcomplexrndimformatallisfinitediffanymoveaxis)r yaxisdydxrdxs r prepare_inputr& sk t|aV $ $DAq qw 455:8999 A qw 455 |D!! 7dj NOO O ?4:t'; < < E{{5u{-- U##A !&=Dv{{5666wqzA~~@AAAwqzQWT]""3396$<<AA A 8DM!$$ % %A?@@@ 8DM!$$ % %A?@@@ t)<)< = =BCCC 1B xaFDEEE aq!!A }T4++ b!T4 r c$eZdZdZdfd ZxZS)CubicHermiteSplinea2 Piecewise-cubic interpolator matching values and first derivatives. The result is represented as a `PPoly` instance. [1]_ Parameters ---------- x : array_like, shape (n,) 1-D array containing values of the independent variable. Values must be real, finite and in strictly increasing order. y : array_like Array containing values of the dependent variable. It can have arbitrary number of dimensions, but the length along ``axis`` (see below) must match the length of ``x``. Values must be finite. dydx : array_like Array containing derivatives of the dependent variable. It can have arbitrary number of dimensions, but the length along ``axis`` (see below) must match the length of ``x``. Values must be finite. axis : int, optional Axis along which `y` is assumed to be varying. Meaning that for ``x[i]`` the corresponding values are ``cupy.take(y, i, axis=axis)``. Default is 0. extrapolate : {bool, 'periodic', None}, optional If bool, determines whether to extrapolate to out-of-bounds points based on first and last intervals, or to return NaNs. If 'periodic', periodic extrapolation is used. If None (default), it is set to True. Attributes ---------- x : ndarray, shape (n,) Breakpoints. The same ``x`` which was passed to the constructor. c : ndarray, shape (4, n-1, ...) Coefficients of the polynomials on each segment. The trailing dimensions match the dimensions of `y`, excluding ``axis``. For example, if `y` is 1-D, then ``c[k, i]`` is a coefficient for ``(x-x[i])**(3-k)`` on the segment between ``x[i]`` and ``x[i+1]``. axis : int Interpolation axis. The same axis which was passed to the constructor. See Also -------- Akima1DInterpolator : Akima 1D interpolator. PchipInterpolator : PCHIP 1-D monotonic cubic interpolator. PPoly : Piecewise polynomial in terms of coefficients and breakpoints Notes ----- If you want to create a higher-order spline matching higher-order derivatives, use `BPoly.from_derivatives`. References ---------- .. [1] `Cubic Hermite spline `_ on Wikipedia. rNcN|d}t||||\}}}}}||jdgdg|jdz zz}t j|d|z }|dd|ddzd|zz |z } t jdt|dz f|jddz| j} | |z | d<||ddz |z | z | d<|dd| d<|dd| d <t | || ||_ dS) NTrrr#r)r) extrapolate) r&reshaperrrremptylenrsuper__init__r#) selfr r"r$r#r.r%dxrslopetc __class__s r r3zCubicHermiteSpline.__init__|sD  K,Q4>>2q$jj"(1+! );;<< !!$$$s* #2#Yabb !AI - 4 J3q66A:4AG D D D3w!SbS !S(1,!CRCy!"v! A;777 r rN)__name__ __module__ __qualname____doc__r3 __classcell__r9s@r r(r(BsH77rr r(cPeZdZdZdfd ZedZedZxZS)PchipInterpolatora PCHIP 1-D monotonic cubic interpolation. ``x`` and ``y`` are arrays of values used to approximate some function f, with ``y = f(x)``. The interpolant uses monotonic cubic splines to find the value of new points. (PCHIP stands for Piecewise Cubic Hermite Interpolating Polynomial). Parameters ---------- x : ndarray A 1-D array of monotonically increasing real values. ``x`` cannot include duplicate values (otherwise f is overspecified) y : ndarray A 1-D array of real values. ``y``'s length along the interpolation axis must be equal to the length of ``x``. If N-D array, use ``axis`` parameter to select correct axis. axis : int, optional Axis in the y array corresponding to the x-coordinate values. extrapolate : bool, optional Whether to extrapolate to out-of-bounds points based on first and last intervals, or to return NaNs. See Also -------- CubicHermiteSpline : Piecewise-cubic interpolator. Akima1DInterpolator : Akima 1D interpolator. PPoly : Piecewise polynomial in terms of coefficients and breakpoints. Notes ----- The interpolator preserves monotonicity in the interpolation data and does not overshoot if the data is not smooth. The first derivatives are guaranteed to be continuous, but the second derivatives may jump at :math:`x_k`. Determines the derivatives at the points :math:`x_k`, :math:`f'_k`, by using PCHIP algorithm [1]_. Let :math:`h_k = x_{k+1} - x_k`, and :math:`d_k = (y_{k+1} - y_k) / h_k` are the slopes at internal points :math:`x_k`. If the signs of :math:`d_k` and :math:`d_{k-1}` are different or either of them equals zero, then :math:`f'_k = 0`. Otherwise, it is given by the weighted harmonic mean .. math:: \frac{w_1 + w_2}{f'_k} = \frac{w_1}{d_{k-1}} + \frac{w_2}{d_k} where :math:`w_1 = 2 h_k + h_{k-1}` and :math:`w_2 = h_k + 2 h_{k-1}`. The end slopes are set using a one-sided scheme [2]_. References ---------- .. [1] F. N. Fritsch and J. Butland, A method for constructing local monotone piecewise cubic interpolants, SIAM J. Sci. Comput., 5(2), 300-304 (1984). `10.1137/0905021 `_. .. [2] see, e.g., C. Moler, Numerical Computing with Matlab, 2004. `10.1137/1.9780898717952 `_ rNct|||\}}}}}||jdfd|jdz zz}|||}t |||d|||_dS)Nr)rrr#r.)r&r/rr_find_derivativesr2r3r#) r4r r"r#r._xpdkr9s r r3zPchipInterpolator.__init__s(At441aq YY }tQVAX6 7 7  # #B * * Ar{CCC r cjd|z|z|z||zz ||zz }tj|tj|k}tj|tj|ktj|dtj|zkz}||z}d||<d||z||<|S)Nrg@)rsignabs)h0h1m0m1dmaskmask2mmms r _edge_casezPchipInterpolator._edge_cases"frkR "r' )b2g 6y||ty}},2$)B--/ HQKK"TXb\\/ )+uo$BsG#r c|j}|jdkr|dddf}|dddf}|dd|ddz }|dd|ddz |z }|jddkr3tj|}||d<||d<||Stj|}|dd|ddk|dddkz|dddkz}d|ddz|ddz}|ddd|ddzz} ||ddz | |ddz z|| zz } tj|}tj|dd| z |dd<t|d|d|d|d|d<t|d|d|d|d|d<||S)Nrr+rrrJg?) rrr zeros_liker/rKwhererBrU) r r"y_shapehkmkrHsmk conditionw1w2whmeans r rEz#PchipInterpolator._find_derivativess' 6Q;;!!!T' A!!!T' A qrrUQssV^eafn " 71:??##BBqEBqE::g&& &immWCRC(RVq[9RW\J r!""vX3B3  Va3B3i r#2#w,bf,b9 _Q  :icFl;;1R4",,RUBqE2a5"Q%HH1"--bfbfbfbfMM2zz'"""r r:) r;r<r=r>r3 staticmethodrUrEr?r@s@r rBrBs~??B  \ ,#,#\,#,#,#,#,#r rBct||||dkr St|r|Sfd|DS)a^ Convenience function for pchip interpolation. xi and yi are arrays of values used to approximate some function f, with ``yi = f(xi)``. The interpolant uses monotonic cubic splines to find the value of new points x and the derivatives there. See `scipy.interpolate.PchipInterpolator` for details. Parameters ---------- xi : array_like A sorted list of x-coordinates, of length N. yi : array_like A 1-D array of real values. `yi`'s length along the interpolation axis must be equal to the length of `xi`. If N-D array, use axis parameter to select correct axis. x : scalar or array_like Of length M. der : int or list, optional Derivatives to extract. The 0th derivative can be included to return the function value. axis : int, optional Axis in the yi array corresponding to the x-coordinate values. See Also -------- PchipInterpolator : PCHIP 1-D monotonic cubic interpolator. Returns ------- y : scalar or array_like The result, of length R or length M or M by R. r*rcLg|] }|!Sr) derivative).0nuPr s r z%pchip_interpolate..Bs0222  R  ##222r )rBr re)xiyir derr#rhs ` @r pchip_interpolatermsxD "bt,,,A axxqtt 33 q||C  ###22222c2222r c\eZdZdZd fd Zd dZed dZed dZxZ S) Akima1DInterpolatoral Akima interpolator Fit piecewise cubic polynomials, given vectors x and y. The interpolation method by Akima uses a continuously differentiable sub-spline built from piecewise cubic polynomials. The resultant curve passes through the given data points and will appear smooth and natural [1]_. Parameters ---------- x : ndarray, shape (m, ) 1-D array of monotonically increasing real values. y : ndarray, shape (m, ...) N-D array of real values. The length of ``y`` along the first axis must be equal to the length of ``x``. axis : int, optional Specifies the axis of ``y`` along which to interpolate. Interpolation defaults to the first axis of ``y``. See Also -------- CubicHermiteSpline : Piecewise-cubic interpolator. PchipInterpolator : PCHIP 1-D monotonic cubic interpolator. PPoly : Piecewise polynomial in terms of coefficients and breakpoints Notes ----- Use only for precise data, as the fitted curve passes through the given points exactly. This routine is useful for plotting a pleasingly smooth curve through a few given points for purposes of plotting. References ---------- .. [1] A new method of interpolation and smooth curve fitting based on local procedures. Hiroshi Akima, J. ACM, October 1970, 17(4), 589-602. rct|||\}}}}}tj|jdzf|jddz}|t dfd|jdz zz}tj|d|z |dd<d|dz|dz |d<d|dz|dz |d<d|d z|d z |d<d|dz|d z |d <d |dd|dd zz}tjtj|d}|dd} |dd} | | z} |jdkr tj ntj | } tj | d | zk} | d| dd}}| | ||dzf|zz| | ||dzf|zzz| | z || <t |||dd||_dS)Nr-rNrr*rrWg@r+g?g& .>FrD)r&rr0sizerslicerrrLinfmaxnonzeror2r3r#)r4r r"r#r%rFmr7dmf1f2f12 max_valueindx_indy_indr9s r r3zAkima1DInterpolator.__init__ls$*!Q552q$ J ~ 3 4 4 t(afqj"99 :)AA&&&+!B$AaDy1Q4!AaDy1Q4!QrU QrU""QrU QrU"" !ABB%!CRC&. ! Xdi*** + + V W2g!"1TXII$(3-- l3 !11221vs122wuS'AuqylU233S'AuqylU23347:3x@# Aqqe<<< r Tc td)Nz9Extending a 1-D Akima interpolator is not yet implementedNotImplementedError)r4r8r rights r extendzAkima1DInterpolator.extends!#455 5r Nc tdNz:This method does not make sense for an Akima interpolator.r)clstckr.s r from_splinezAkima1DInterpolator.from_spline!#;<< r3r classmethodrrr?r@s@r roroEs$$L""""""H5555 <<<[<<<<[<<<<rs 666666EEE 4 4 4 4 nKKKKKKKK\F#F#F#F#F#*F#F#F#R)3)3)3)3XY<Y<Y<Y<Y<,Y<Y<Y<Y<Y