`iJ`dZddlZdZdZdZdZdd Zdd Zd ZddZ ddZ ddZ ddZ dS)z8 Routines for manipulating partial fraction expansions. Ncddl}tj|}tj||S)zEnp.roots replacement. XXX: calls into NumPy, then converts back. rN)numpycupyasarraygetroots)arrnps q/home/jaya/work/projects/VOICE-AGENT/VIET/agent-env/lib/python3.11/site-packages/cupyx/scipy/signal/_polyutils.pyrrsE ,s     ! !C < & &&c|j}t|dkr|d|dkr |ddkstdddl}|j|}|j}|d|}|D](}| ||j d| fd })t|jj tjr||t }|||||kr|j}tj|S) z7np.poly replacement for 2D A. Otherwise, use cupy.poly.rz*input must be a non-empty square 2d array.N)rdtypefull)mode)shapelen ValueErrorrlinalgeigvalsrronesconvolver_ issubclasstypercomplexfloatingrcomplexallsort conjugaterealcopy)Ashr seq_of_zerosdtazerors r polyr+sA B GGqLLRUbe^^1 EFFF9$$QUUWW--L  B BA99 KK25TE?K 8 8!', 455 $>> ? ?  A <??r c~tjtj|}tj||d|fS)z#Sort roots based on magnitude. r)rargsortabstake)pindxs r _cmplx_sortr2)s4 < $ $D 9Qa $ &&r ctj|dz}tj|dz}|d|dz}t|dz }t|dz }d|dz }tjt ||z dzdf|j}||j}td||z dzD]-}|||z} | ||<||||zdzxx| |zzcc<.tj|dddrI|j ddkr8|dd}tj|dddr|j ddk8||fS)Ngrrg?g+=)rtol) r atleast_1drzerosmaxrastyperangeallcloser) uvwmnscaleqrkds r _polydivrF1sl S A S A !qt A A A A A 1IE CA 1%%'11A A 1ac!e__   AaDL! !AEAI+!a% -!ae , , ,!'"+// abbE -!ae , , ,!'"+// a4Kr MbP?minc\|dvr tj}n1|dvr tj}n |dvr tj}nt dtj|jddf}tj||dddf<tj||dddf<tj |dddddf|dddddfz d }g}g}tj |jdt }t|D]t\} } || r| |k|z} | | } | jdkrD|||| || jdd || <utj|tj|fS) aDetermine unique roots and their multiplicities from a list of roots. Parameters ---------- p : array_like The list of roots. tol : float, optional The tolerance for two roots to be considered equal in terms of the distance between them. Default is 1e-3. Refer to Notes about the details on roots grouping. rtype : {'max', 'maximum', 'min', 'minimum', 'avg', 'mean'}, optional How to determine the returned root if multiple roots are within `tol` of each other. - 'max', 'maximum': pick the maximum of those roots - 'min', 'minimum': pick the minimum of those roots - 'avg', 'mean': take the average of those roots When finding minimum or maximum among complex roots they are compared first by the real part and then by the imaginary part. Returns ------- unique : ndarray The list of unique roots. multiplicity : ndarray The multiplicity of each root. See Also -------- scipy.signal.unique_roots Notes ----- If we have 3 roots ``a``, ``b`` and ``c``, such that ``a`` is close to ``b`` and ``b`` is close to ``c`` (distance is less than `tol`), then it doesn't necessarily mean that ``a`` is close to ``c``. It means that roots grouping is not unique. In this function we use "greedy" grouping going through the roots in the order they are given in the input `p`. This utility function is not specific to roots but can be used for any sequence of values for which uniqueness and multiplicity has to be determined. For a more general routine, see `numpy.unique`. )r8maximum)rHminimum)avgmeanzJ`rtype` must be one of {'max', 'maximum', 'min', 'minimum', 'avg', 'mean'}rrNrr5)axisrT)rr8rHrMremptyrr#imagrnormr7bool enumeratesizeappendr) r0tolrtypereducepointsdistp_uniquep_multiplicityusedidsmaskgroups r unique_rootsrbDs\ """ $ $ $ / ! !OPP PZQ ( (F9Q<> OOFF1T7OO , , ,  ! !%+a. 1 1 1T < ! !4<#?#? ??r Fctjdg}|g}t|ddd|dddD]c\}}tjd| f}t t |D]}tj||}||d|ddd}g} tjdg}t|||D]\}}} tjd| f}g} t t |D]G} | dks|r(| tj|| tj||}H| t| | |fS)z>Compute the total polynomial divided by factors for each root.rr5rN) rarrayziprr:intpolymulrUextendreversed) r multiplicityinclude_powerscurrentsuffixespolemultmonomial_factorssuffixblockr^s r _compute_factorsrus~j!ooGyH%1R.,r!Bw*?@@!! d71te8$s4yy!! 6 6Al7H55GG    "~HGj!ooG!%x@@((dF71te8$s4yy!! 6 6AAvvv T\'6::;;;l7H55GGx'''' G r ct||\}}||j}g}t|||D]\}}}|dkr?|t j||t j||z L|} t jd| f} t|| \}} g} tt|D]S}t| | \} } | d| dz }t j | ||z} | |T| t| t j|S)Nrr)rur9rrerUrpolyvalr$rrFr:rfpolysubrhrir)polesrj numeratordenominator_factorsrqresiduesrnrofactornumerrprErtr@rCs r _compute_residuesrsk-e\BB  --IH!%"577--dF 199 OODLD99 L667 8 8 8 8NN$$Ewq4%x(H 22IFAE3t99%%  #E844qaD1Q4K UAJ77 Q OOHUOO , , , , < ! !!r rLctj|}tj|}tjtj|d}t|||\}}t ||d\}}t |dkrd} ntj||} t||D]\} } tj| | | z} | |fS)aCompute b(s) and a(s) from partial fraction expansion. If `M` is the degree of numerator `b` and `N` the degree of denominator `a`:: b(s) b[0] s**(M) + b[1] s**(M-1) + ... + b[M] H(s) = ------ = ------------------------------------------ a(s) a[0] s**(N) + a[1] s**(N-1) + ... + a[N] then the partial-fraction expansion H(s) is defined as:: r[0] r[1] r[-1] = -------- + -------- + ... + --------- + k(s) (s-p[0]) (s-p[1]) (s-p[-1]) If there are any repeated roots (closer together than `tol`), then H(s) has terms like:: r[i] r[i+1] r[i+n-1] -------- + ----------- + ... + ----------- (s-p[i]) (s-p[i])**2 (s-p[i])**n This function is used for polynomials in positive powers of s or z, such as analog filters or digital filters in controls engineering. For negative powers of z (typical for digital filters in DSP), use `invresz`. Parameters ---------- r : array_like Residues corresponding to the poles. For repeated poles, the residues must be ordered to correspond to ascending by power fractions. p : array_like Poles. Equal poles must be adjacent. k : array_like Coefficients of the direct polynomial term. tol : float, optional The tolerance for two roots to be considered equal in terms of the distance between them. Default is 1e-3. See `unique_roots` for further details. rtype : {'avg', 'min', 'max'}, optional Method for computing a root to represent a group of identical roots. Default is 'avg'. See `unique_roots` for further details. Returns ------- b : ndarray Numerator polynomial coefficients. a : ndarray Denominator polynomial coefficients. See Also -------- scipy.signal.invres residue, invresz, unique_roots fTrkr rr6 trim_zerosrbrurrgrepolyadd rCr0rDrVrW unique_polesrjrr denominatorrzresiduer}s r invresrsr A A **C00A!-ae!>LGf,<== k !!r c tj|}tj|}tjtj|d}t|||\}}t ||d\}}t |dkrd} n'tj|ddd|ddd} t||D]&\} } tj| | | dddz} '| ddd|fS)aCompute b(z) and a(z) from partial fraction expansion. If `M` is the degree of numerator `b` and `N` the degree of denominator `a`:: b(z) b[0] + b[1] z**(-1) + ... + b[M] z**(-M) H(z) = ------ = ------------------------------------------ a(z) a[0] + a[1] z**(-1) + ... + a[N] z**(-N) then the partial-fraction expansion H(z) is defined as:: r[0] r[-1] = --------------- + ... + ---------------- + k[0] + k[1]z**(-1) ... (1-p[0]z**(-1)) (1-p[-1]z**(-1)) If there are any repeated roots (closer than `tol`), then the partial fraction expansion has terms like:: r[i] r[i+1] r[i+n-1] -------------- + ------------------ + ... + ------------------ (1-p[i]z**(-1)) (1-p[i]z**(-1))**2 (1-p[i]z**(-1))**n This function is used for polynomials in negative powers of z, such as digital filters in DSP. For positive powers, use `invres`. Parameters ---------- r : array_like Residues corresponding to the poles. For repeated poles, the residues must be ordered to correspond to ascending by power fractions. p : array_like Poles. Equal poles must be adjacent. k : array_like Coefficients of the direct polynomial term. tol : float, optional The tolerance for two roots to be considered equal in terms of the distance between them. Default is 1e-3. See `unique_roots` for further details. rtype : {'avg', 'min', 'max'}, optional Method for computing a root to represent a group of identical roots. Default is 'avg'. See `unique_roots` for further details. Returns ------- b : ndarray Numerator polynomial coefficients. a : ndarray Denominator polynomial coefficients. See Also -------- scipy.signal.invresz residuez, unique_roots, invres bTrrNr5rrs r invreszrs p A A **C00A!-ae!rs '''0'''&O@O@O@O@d2"""6I"I"I"I"XH(H(H(H(Vs%s%s%s%lj(j(j(j(j(j(r