`iIndZddlZddlZddlmZddlmZmZddl m Z ddl Z dZ dZdZejd Zejd Zejd Zd Zd ZdZdZd#dZd#dZd$dZd$dZd%dZd%dZd&dZejdddddd !Z d"Z!dS)'a Signal processing B-Splines Some of the functions defined here were ported directly from CuSignal under terms of the MIT license, under the following notice: Copyright (c) 2019-2023 NVIDIA CORPORATION & AFFILIATES. All rights reserved. Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions: The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software. THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. N) apply_iir_sos)_symiirorder1_nd_symiirorder2_nd)BSplinectd||fDrtd|j}|jdkr)|tjkr tjn tj}n4|tjks |jdkr tj}n tj }| |d}| |d}| |d}|ddd |ddd ftj jj|d fd dd d S) a}Convolve with a 2-D separable FIR filter. Convolve the rank-2 input array with the separable filter defined by the rank-1 arrays hrow, and hcol. Mirror symmetric boundary conditions are assumed. This function can be used to find an image given its B-spline representation. The arguments `hrow` and `hcol` must be 1-dimensional and of off length. Args: input (cupy.ndarray): The input signal hrow (cupy.ndarray): Row direction filter hcol (cupy.ndarray): Column direction filter Returns: cupy.ndarray: The filtered signal .. seealso:: :func:`scipy.signal.sepfir2d` c3HK|]}|jdkp |jdzdkVdS)rN)ndimsize).0xs p/home/jaya/work/projects/VOICE-AGENT/VIET/agent-env/lib/python3.11/site-packages/cupyx/scipy/signal/_bsplines.py zsepfir2d..;s7 @ @a16Q; )!&1*/ @ @ @ @ @ @z2hrow and hcol must be 1 dimensional and odd lengthcr F)copyN)rr c|S)N)ifilterss rzsepfir2d..Is rreflectr)any ValueErrordtypekindcupy complex64 complex128float32itemsizefloat64astypeconjcupyxscipyndimage_filters_run_1d_correlates)inputhrowhcolrrs @rsepfir2dr/'s;( @ @D$< @ @ @@@OMNNN KE zS"'4>"9"9t $,  %.A"5"5   LLUL + +E ;;u5; ) )D ;;u5; ) )DDDbDz  $ttt*//"3"34G ;  ' : : v++++T9a A AArcttj|t}t jtjgdd}||}d||dk|dkz<|S)Nr)gg??F extrapolaterr2r3)absrasarrayfloatr basis_elementrbouts r _quadraticr=Lsw DL% ( ( ())A +++,,% A A AA !A$$C"#CTa#g Jrctj|t}tjtjgdd}||}d||dk|dkz<|S)Nr1)rrr r Fr4rr?r )rr7r8rr9r:s r_cubicr@Usl Qe$$$A &&&''U < <  utx ';';;; ==rc t|\}}dd|ztj|zz ||zz}t|}tj|f|jj}tj|}td||||dztj t|dz||||zz}td||||dztd||||dzztj t|dz||||zz} tj dd|| f} tj | } tj |dddd|ztj|z||zf} tj | } t|dd| | |j\}} tj || |f}tj t||||t|dz|||z|dddz}tj t|dz |||t|dz|||z|dddz} tj dd|| f} tj | } t|ddd| | |j\} } tj | ddd| |f} | S)Nr r rr?zirr)rMrrWlenzerosrchararangerTsumr_ atleast_2drr\)signallambrLrSrRKyprQstate_0state_1r_coef_ys r_cubic_smooth_coeffrqxst$$JC QWtx & &s 2B F A QD&,+ , ,B AA1b#u%%q 1xAE2sE22V;<<=G1b#u%%q 11b#u%%q 12xAE2sE22V;<<=G Aw' (B   B 72q!QS48E?? :C#IE FD ?4 D &*dr F F FEB '2% &BhAr3..AE2sE2236> !FAvvq B&6/!:!:::rAv&v&&& GAq!TXfvo666 7E OE " "E 71aAsA% &D ?4 D VTeu#)<111HE1R!V}uQU|+H GAq!X% &E OE " "E 7B31a"a' (D ?4 D  bf"f tV\;;;IFA WVDDbD\8+ ,F C<rcddtjdzz}t|}|tj|z}|dkrB|d|tj||zzz}||dz z |z}tj|Stjdddtj||zf}tj|}tjdddd| df}tj|}t|||d|j \}}||dz z ||dz z} tjddd| f}tj|}tj| ddd| df}tj|}t|ddd |||j \}}tj|ddd | f}|d zS) Nr`r @r rFrsr?rr^ @rvrxs r_quadratic_coeffrs a$)C.. B F A 4;q>> !FAvvq B&6/!:!:::rAv&v&&& GAq!TXfvo666 7E OE " "E 71aAsA% &D ?4 D VTeu#)<111HE1R!V}uQU|+H GAq!X% &E OE " "E 7B31a"a' (D ?4 D  bf"f tV\;;;IFA WVDDbD\8+ ,F C<rcPtjdd|zz}dd|zz d|z|zz}tjtjd|zdz |z }tj|}d|zdz |z d|zz tjd|zd|z|zzz|z }||fS)NrDrEr rBrC?rF)nprGarctan)ritmprJrStmp2rs rcompute_root_from_lambdars '!cDj. ! !C R$YdS (B IbgsTzC/2566 7 7E 72;;D t)a-$ 29 - "T'BIO+ - - .04 5A e8OrcL|dkrt||St|S)a Compute cubic spline coefficients for rank-1 array. Find the cubic spline coefficients for a 1-D signal assuming mirror-symmetric boundary conditions. To obtain the signal back from the spline representation mirror-symmetric-convolve these coefficients with a length 3 FIR window [1.0, 4.0, 1.0]/ 6.0 . Parameters ---------- signal : ndarray A rank-1 array representing samples of a signal. lamb : float, optional Smoothing coefficient, default is 0.0. Returns ------- c : ndarray Cubic spline coefficients. See Also -------- cspline1d_eval : Evaluate a cubic spline at the new set of points. r)rqr~rhris r cspline1drs+4 s{{"64000F###rcJ|dkrtdt|S)aCompute quadratic spline coefficients for rank-1 array. Parameters ---------- signal : ndarray A rank-1 array representing samples of a signal. lamb : float, optional Smoothing coefficient (must be zero for now). Returns ------- c : ndarray Quadratic spline coefficients. See Also -------- qspline1d_eval : Evaluate a quadratic spline at the new set of points. Notes ----- Find the quadratic spline coefficients for a 1-D signal assuming mirror-symmetric boundary conditions. To obtain the signal back from the spline representation mirror-symmetric-convolve these coefficients with a length 3 FIR window [1.0, 6.0, 1.0]/ 8.0 . rz.Smoothing quadratic splines not supported yet.)rrrs r qspline1dr$s*6 s{{IJJJ'''rrctj||z t|z }tj||j}|jdkr|St |}|dk}||dz k}||z}t||| ||<t|d|dz z||z ||<||}|jdkr|Stj||j} tj|dz  tdz} tdD]>} | | z} | d|dz } | || t|| z zz } ?| ||<|S)aDEvaluate a cubic spline at the new set of points. `dx` is the old sample-spacing while `x0` was the old origin. In other-words the old-sample points (knot-points) for which the `cj` represent spline coefficients were at equally-spaced points of: oldx = x0 + j*dx j=0...N-1, with N=len(cj) Edges are handled using mirror-symmetric boundary conditions. Parameters ---------- cj : ndarray cublic spline coefficients newx : ndarray New set of points. dx : float, optional Old sample-spacing, the default value is 1.0. x0 : int, optional Old origin, the default value is 0. Returns ------- res : ndarray Evaluated a cubic spline points. See Also -------- cspline1d : Compute cubic spline coefficients for rank-1 array. r1rr r rV)rr7r8 zeros_likerr racspline1d_evalfloorr%intrangeclipr@cjnewxdxx0resNcond1cond2cond3resultjlowerrthisjindjs rrrEsm@ L   #uRyy 0D /$bh / / /C x1}}  BA 1HE AENEem ET%[L11CJAQK$u+$=>>CJ ;D yA~~ _T 2 2 2F Zq ! ! ( ( - - 1F 1XX22 zz!QU##"T(VD5L1111CJ Jrctj||z |z }tj|}|jdkr|St |}|dk}||dz k}||z}t ||| ||<t |d|dz z||z ||<||}|jdkr|Stj|} tj|dz tdz} tdD]>} | | z} | d|dz } | || t|| z zz } ?| ||<|S)ahEvaluate a quadratic spline at the new set of points. Parameters ---------- cj : ndarray Quadratic spline coefficients newx : ndarray New set of points. dx : float, optional Old sample-spacing, the default value is 1.0. x0 : int, optional Old origin, the default value is 0. Returns ------- res : ndarray Evaluated a quadratic spline points. See Also -------- qspline1d : Compute quadratic spline coefficients for rank-1 array. Notes ----- `dx` is the old sample-spacing while `x0` was the old origin. In other-words the old-sample points (knot-points) for which the `cj` represent spline coefficients were at equally-spaced points of:: oldx = x0 + j*dx j=0...N-1, with N=len(cj) Edges are handled using mirror-symmetric boundary conditions. rr r r3rD) rr7rr raqspline1d_evalrr%rrrr=rs rrr}sYD L   #r )D /$  C x1}}  BA 1HE AENEem ET%[L11CJAQK$u+$=>>CJ ;D yA~~ _T " "F Zs # # * *3 / /! 3F 1XX66 zz!QU##"T(Zu 5555CJ Jrc|dkrIdtjdz}t|| dz||d}t|| dz||d}|St|\}}t ||||d}t ||||d}|S)a8 Coefficients for 2-D cubic (3rd order) B-spline. Return the third-order B-spline coefficients over a regularly spaced input grid for the two-dimensional input image. Parameters ---------- input : ndarray The input signal. lamb : float Specifies the amount of smoothing in the transfer function. precision : float Specifies the precision for computing the infinite sum needed to apply mirror-symmetric boundary conditions. Returns ------- output : ndarray The filtered signal. gqq|?r?g@rur precisionaxisr)rrGrrr)rhrirrr<rSs r cspline2drs, y  vrCxi$&(((sQBHa9$%''' '--HAu 61eyr J J JC 35IA F F FC Jrc|dkrtdddtjdzz}t|| dz||d}t|| dz||d}|S) a= Coefficients for 2-D quadratic (2nd order) B-spline. Return the second-order B-spline coefficients over a regularly spaced input grid for the two-dimensional input image. Parameters ---------- input : ndarray The input signal. lamb : float Specifies the amount of smoothing in the transfer function. precision : float Specifies the precision for computing the infinite sum needed to apply mirror-symmetric boundary conditions. Returns ------- output : ndarray The filtered signal. rzlambda must be negative or zeror`r rrrr)rrrGr)rhrirrr<s r qspline2drsv. axx:;;; Q A 6A28Q)" M M MC 3S!yq I I IC Jr@c|jj}tjgdddz }|dvr}|d}t |j|}t |j|}t|||}t|||}|d|zz|}nJ|dvr7t ||}t|||}||}ntd|S) aSmoothing spline (cubic) filtering of a rank-2 array. Filter an input data set, `Iin`, using a (cubic) smoothing spline of fall-off `lmbda`. Parameters ---------- Iin : array_like input data set lmbda : float, optional spline smooghing fall-off value, default is `5.0`. Returns ------- res : ndarray filtered input data )rg@rfru)FDry?)rdzInvalid data type for Iin) rrcrr7r%rrealimagr/ TypeError) Iinlmbdaintyper.ckrckioutroutir<s r spline_filterrs&Y^F < - - 3D jjoo%((%((T4((T4((b4i''// :  U##sD$''jj  3444 Jrz T x, int32 nzT outputzR output = 1 / sqrt( 2.0 * M_PI * signsq ) * exp( -( x * x ) * r_signsq ); _gauss_spline_kernel)z -std=c++11z`const double signsq { ( n + 1 ) / 12.0 }; const double r_signsq { 0.5 / signsq };)options loop_prepcJtj|}t||S)axGaussian approximation to B-spline basis function of order n. Parameters ---------- x : array_like a knot vector n : int The order of the spline. Must be nonnegative, i.e. n >= 0 Returns ------- res : ndarray B-spline basis function values approximated by a zero-mean Gaussian function. Notes ----- The B-spline basis function can be approximated well by a zero-mean Gaussian function with standard-deviation equal to :math:`\sigma=(n+1)/12` for large `n` : .. math:: \frac{1}{\sqrt {2\pi\sigma^2}}exp(-\frac{x^2}{2\sigma}) See [1]_, [2]_ for more information. References ---------- .. [1] Bouma H., Vilanova A., Bescos J.O., ter Haar Romeny B.M., Gerritsen F.A. (2007) Fast and Accurate Gaussian Derivatives Based on B-Splines. In: Sgallari F., Murli A., Paragios N. (eds) Scale Space and Variational Methods in Computer Vision. SSVM 2007. Lecture Notes in Computer Science, vol 4485. Springer, Berlin, Heidelberg .. [2] http://folk.uio.no/inf3330/scripting/doc/python/SciPy/tutorial/old/node24.html )rr7r)rns r gauss_spliner0s"F QA 1 % %%r)r)rr)rr)r)"__doc__rcupyx.scipy.ndimager'cupyx.scipy.signal._iir_utilsrcupyx.scipy.signal._splinesrr cupyx.scipy.interpolate._bsplinernumpyrr/r=r@fuserMrTr\rqr~rrrrrrrrrElementwiseKernelrrrrrrs'6 777777JJJJJJJJ444444"A"A"AJ   !! !  == =5 5 5 p"""J"""J$$$$@((((B5555p7777t""""JD""""J.t- 8   $&$&$&$&$&r