bMh|ddlZddlmZddlZddlmZddlmZddl m Z m Z m Z ddl mZddl mZdd l mZdd lmZmZdd lmZmZmZgd Zd Z ddZddZ ddZddZ ddZddZ dS)N)product)_have_c99_complex) idwt_single)ModesWavelet _check_dtype)swt)swt_axis) swt_max_level)idwt2idwtn) AxisError _as_wavelet_wavelets_per_axis)r r iswtswt2iswt2swtniswtnct|jdzfd|jD}|j|_|j|_|S)Nrc>g|]}tj|zS)npasarray).0fsfs I/var/www/html/test/jupyter/venv/lib/python3.11/site-packages/pywt/_swt.py z/_rescale_wavelet_filterbank..s&CCC!2:a==2%CCC)rname filter_bank orthogonal biorthogonal)waveletrwavs ` r _rescale_wavelet_filterbankr)sS ',$CCCCw/BCCC E EC'CN+C Jr"Fcntstj|rtj|}||||||d}t |jfi|}t |jfi|} |sBg} t|| D].\\} } \} }| | d| zz| d|zzf/ndt|| D} | St|}tj ||}t|}|r@|j stjdt|dtjdz }|dkr ||jz}d|cxkr |jksnt%d |t'|j|}|jdkrt+|||||}nt-||||||}|S) ah Multilevel 1D stationary wavelet transform. Parameters ---------- data : Input signal wavelet : Wavelet to use (Wavelet object or name) level : int, optional The number of decomposition steps to perform. start_level : int, optional The level at which the decomposition will begin (it allows one to skip a given number of transform steps and compute coefficients starting from start_level) (default: 0) axis: int, optional Axis over which to compute the SWT. If not given, the last axis is used. trim_approx : bool, optional If True, approximation coefficients at the final level are retained. norm : bool, optional If True, transform is normalized so that the energy of the coefficients will be equal to the energy of ``data``. In other words, ``np.linalg.norm(data.ravel())`` will equal the norm of the concatenated transform coefficients when ``trim_approx`` is True. Returns ------- coeffs : list List of approximation and details coefficients pairs in order similar to wavedec function:: [(cAn, cDn), ..., (cA2, cD2), (cA1, cD1)] where n equals input parameter ``level``. If ``start_level = m`` is given, then the beginning m steps are skipped:: [(cAm+n, cDm+n), ..., (cAm+1, cDm+1), (cAm, cDm)] If ``trim_approx`` is ``True``, then the output list is exactly as in ``pywt.wavedec``, where the first coefficient in the list is the approximation coefficient at the final level and the rest are the detail coefficients:: [cAn, cDn, ..., cD2, cD1] Notes ----- The implementation here follows the "algorithm a-trous" and requires that the signal length along the transformed axis be a multiple of ``2**level``. If this is not the case, the user should pad up to an appropriate size using a function such as ``numpy.pad``. A primary benefit of this transform in comparison to its decimated counterpart (``pywt.wavedecn``), is that it is shift-invariant. This comes at cost of redundancy in the transform (the size of the output coefficients is larger than the input). When the following three conditions are true: 1. The wavelet is orthogonal 2. ``swt`` is called with ``norm=True`` 3. ``swt`` is called with ``trim_approx=True`` the transform has the following additional properties that may be desirable in applications: 1. energy is conserved 2. variance is partitioned across scales When used with ``norm=True``, this transform is closely related to the multiple-overlap DWT (MODWT) as popularized for time-series analysis, although the underlying implementation is slightly different from the one published in [1]_. Specifically, the implementation used here requires a signal that is a multiple of ``2**level`` in length. References ---------- .. [1] DB Percival and AT Walden. Wavelet Methods for Time Series Analysis. Cambridge University Press, 2000. )r'level start_level trim_approxaxisnorm?c$g|] \}}|d|zzSr1r)rcrcis r r!zswt..}s:JJJ'B2:JJJr"dtypezinorm=True, but the wavelet is not orthogonal: The conditions for energy preservation are not satisfied.rr!Axis greater than data dimensions)rr iscomplexobjrr realimagzipappendr arrayrr%warningswarnr)sqrtndimrr shape_swt _swt_axis)datar'r,r-r/r.r0kwargs coeffs_real coeffs_imag coeffs_cplxcA_rcD_rcA_icD_idtrets r r r s-l  !6!6 z$$u[%0$NN$)..v.. $)..v..  JK.1+{.K.K E E* tltT""D2d7ND2d7N#CDDDD EJJ+.{K+H+HJJJK d  B 8D # # #D'""G E! O MN O O O.gq|DD axxdi  ty ;<<< }dj.// yA~~4%kBBguk4MM Jr"ct|dttf }|r|dn |dd}|jdkr;|r|gd|ddDz}n d|D}t |||f|S|dkr|dkrt dt sltj|rX|rd |D}d |D}nd |D}d |D}||d } t|fi| } | dt|fi| zzS|r |dd}|jdkrtdt|} tj || d} t|} t|}|r"t|tjd}t#jd}t'| ddD]|}t)t+d|dz }|}|r || }n || \}}tj|t|}|j| jkre| jjdks|jjdkr tj}n tj}tj| |} tj||}t'|D]}tj|t||}|ddd}|ddd}t9| |||||}t9| |||||}tj|d}||zdz | |<~| S)aq Multilevel 1D inverse discrete stationary wavelet transform. Parameters ---------- coeffs : array_like Coefficients list of tuples:: [(cAn, cDn), ..., (cA2, cD2), (cA1, cD1)] where cA is approximation, cD is details. Index 1 corresponds to ``start_level`` from ``pywt.swt``. wavelet : Wavelet object or name string Wavelet to use norm : bool, optional Controls the normalization used by the inverse transform. This must be set equal to the value that was used by ``pywt.swt`` to preserve the energy of a round-trip transform. Returns ------- 1D array of reconstructed data. Examples -------- >>> import pywt >>> coeffs = pywt.swt([1,2,3,4,5,6,7,8], 'db2', level=2) >>> pywt.iswt(coeffs, 'db2') array([ 1., 2., 3., 4., 5., 6., 7., 8.]) rrcg|]}d|iS)dr)rrTs r r!ziswt..s===Qa===r"Ncg|] \}}||d S))arTr)rrVrTs r r!ziswt..s$===daqq))===r"axesr0r*r9cg|] }|j Srr;rcs r r!ziswt..222a16222r"cg|] }|j Srr<r[s r r!ziswt..r]r"c0g|]\}}|j|jfSrrZrcacds r r!ziswt..%CCC&"bBGRW-CCCr"c0g|]\}}|j|jfSrr_ras r r!ziswt..rdr"r'r0r1ziswt only supports 1D dataTr7copyr8 periodizationr6r\g@) isinstancetuplelistrCrrrrr:r ValueErrorr r?lenrr)rBr from_objectrangeintpowrr7kind complex128float64arangerroll)coeffsr'r0r/r.cA coeffs_ndrIrJrHyrPoutput num_levelsmodej step_size last_indexcD_r7firstindices even_indices odd_indicesx1x2s r rrsB!UDM:::K! 3vay|B w{{  >==&*====II==f===IYtgDAAAA trzz;<<<  4!4!4 4  D226222K226222KKCCFCCCKCCFCCCK$d33  ' ' ' '2[33F33333 w!||5666 b  B Xb . . .FVJ'""G C-grwqzzBB  _ - -D :q" % %)+)+Aqs $$   BBA2JEAr Z,r"2"2 3 3 3 8v| # #| C''28=C+?+?  Ze444FBe,,,B:&& + +Eis2ww ::G#14a4=L!!$Q$-K VL1 -$d,,BVK0 _$d,,B QB "BwlF7OO3 +6 Mr"r*c t|}tj|}t|dkrt dt|tt |krt d|jttj|krt dt|||||||}g}|r%| |d|dd}|D]a} |r+| | d| d | d f/| | d | d| d | d ffb|S) a Multilevel 2D stationary wavelet transform. Parameters ---------- data : array_like 2D array with input data wavelet : Wavelet object or name string, or 2-tuple of wavelets Wavelet to use. This can also be a tuple of wavelets to apply per axis in ``axes``. level : int The number of decomposition steps to perform. start_level : int, optional The level at which the decomposition will start (default: 0) axes : 2-tuple of ints, optional Axes over which to compute the SWT. Repeated elements are not allowed. trim_approx : bool, optional If True, approximation coefficients at the final level are retained. norm : bool, optional If True, transform is normalized so that the energy of the coefficients will be equal to the energy of ``data``. In other words, ``np.linalg.norm(data.ravel())`` will equal the norm of the concatenated transform coefficients when ``trim_approx`` is True. Returns ------- coeffs : list Approximation and details coefficients (for ``start_level = m``). If ``trim_approx`` is ``False``, approximation coefficients are retained for all levels:: [ (cA_m+level, (cH_m+level, cV_m+level, cD_m+level) ), ..., (cA_m+1, (cH_m+1, cV_m+1, cD_m+1) ), (cA_m, (cH_m, cV_m, cD_m) ) ] where cA is approximation, cH is horizontal details, cV is vertical details, cD is diagonal details and m is ``start_level``. If ``trim_approx`` is ``True``, approximation coefficients are only retained at the final level of decomposition. This matches the format used by ``pywt.wavedec2``:: [ cA_m+level, (cH_m+level, cV_m+level, cD_m+level), ..., (cH_m+1, cV_m+1, cD_m+1), (cH_m, cV_m, cD_m), ] Notes ----- The implementation here follows the "algorithm a-trous" and requires that the signal length along the transformed axes be a multiple of ``2**level``. If this is not the case, the user should pad up to an appropriate size using a function such as ``numpy.pad``. A primary benefit of this transform in comparison to its decimated counterpart (``pywt.wavedecn``), is that it is shift-invariant. This comes at cost of redundancy in the transform (the size of the output coefficients is larger than the input). When the following three conditions are true: 1. The wavelet is orthogonal 2. ``swt2`` is called with ``norm=True`` 3. ``swt2`` is called with ``trim_approx=True`` the transform has the following additional properties that may be desirable in applications: 1. energy is conserved 2. variance is partitioned across scales r8zExpected 2 axesz'The axes passed to swt2 must be unique.z8Input array has fewer dimensions than the specified axesrrNdaadddaa) rkrrrnrmsetrCuniquerr>) rGr'r,r-rXr.r0coefsrQr\s r rrs]l ;;D :d  D 4yyA~~*+++ 4yyCD NN""BCCC y3ry'''' !! ! w{D+t L LE C 58abb  ??  ? JJ$4!D'2 3 3 3 3 JJ$!D'1T7AdG!<= > > > > Jr"c  t|dttf }|r|dn |dd}|jdks|dkr:|r|gd|ddDz}n d|D}t ||||St st j|r~|r?|jg}|d |ddDz }|j g}|d |ddDz }nd |D}d |D}||d } t|fi| } | dt|fi| zzS|r |dd}t|} t j || d} | jdkrtdt|} t|d}|r d|D}t!| D]}t#t%d| |z dz }|}|r ||\}}}n||\}\}}}|j|jks|j|jkrt)dt j| gd|||fDz}| j|kr| |} t!|D]}t!|D]}t1||jd|}t1||jd|}t1||jdd|z}t1||jdd|z}t1||z|jdd|z}t1||z|jdd|z}t3| ||f|||f|||f|||fff|d}t3| ||f|||f|||f|||fff|d} t3| ||f|||f|||f|||fff|d}!t3| ||f|||f|||f|||fff|d}"t j| dd} t j|!dd}!t j|"dd}"t j|"dd}"|| z|!z|"zdz | ||f<| S)a Multilevel 2D inverse discrete stationary wavelet transform. Parameters ---------- coeffs : list Approximation and details coefficients:: [ (cA_n, (cH_n, cV_n, cD_n) ), ..., (cA_2, (cH_2, cV_2, cD_2) ), (cA_1, (cH_1, cV_1, cD_1) ) ] where cA is approximation, cH is horizontal details, cV is vertical details, cD is diagonal details and n is the number of levels. Index 1 corresponds to ``start_level`` from ``pywt.swt2``. wavelet : Wavelet object or name string, or 2-tuple of wavelets Wavelet to use. This can also be a 2-tuple of wavelets to apply per axis. norm : bool, optional Controls the normalization used by the inverse transform. This must be set equal to the value that was used by ``pywt.swt2`` to preserve the energy of a round-trip transform. Returns ------- 2D array of reconstructed data. Examples -------- >>> import pywt >>> coeffs = pywt.swt2([[1,2,3,4],[5,6,7,8], ... [9,10,11,12],[13,14,15,16]], ... 'db1', level=2) >>> pywt.iswt2(coeffs, 'db1') array([[ 1., 2., 3., 4.], [ 5., 6., 7., 8.], [ 9., 10., 11., 12.], [ 13., 14., 15., 16.]]) rr8rc"g|] \}}}|||d S))rrrrrhvrTs r r!ziswt2..s8 ; ; ;$+Aq!() ; ; ; ; ;r"rNc*g|]\}\}}}||||dS))rrrrrrrVrrrTs r r!ziswt2..s>555)Q Aq!"!1==555r"rWc>g|]\}}}|j|j|jfSrrZrs r r!ziswt2..+OOOAqQVQVQV4OOOr"c>g|]\}}}|j|j|jfSrr_rs r r!ziswt2..rr"cRg|]$\}\}}}|j|j|j|jff%SrrZrs r r!ziswt2..F888 ,9Aq!FQVQVQV$<=888r"cRg|]$\}\}}}|j|j|j|jff%Srr_rs r r!ziswt2..rr"rfr1TrgzKiswt2 only supports 2D arrays. see iswtn for a general n-dimensionsal ISWTrrrXcRg|]$}t|tjd%Sr8r)rrBrr(s r r!ziswt2..:)))0RWQZZ@@)))r"4Mismatch in shape of intermediate coefficient arraysc,g|]}t|Sr)r r[s r r!ziswt2..s<<>>>  5!4!4 5  87)K OOF122JOOO OK7)K OOF122JOOO OKK8806888K8806888K$d33 + ( ( ( (2k44V44444 b  B Xb . . .F {a "## #VJ!'777H )))'))):  :G:GAz!|A~..//   (!!9LRRR$QiOA|B H bh"(&:&:FHH H ~ F<<B|<<< <? << ' ']]<00FZ((' G' GG ,,& G& G!'28A; BB !'28A; BB "7BHQK9EE "7BHQK9EE !'I"5rx{AiKPP !'I"5rx{AiKPP F:z#9:z:56z:56z:5689$_ 66 F:y#89z945z945z94578$_ 66 F9j#89y*45y*45y*4578$_ 66 F9i#78y)34y)34y)3467$_ 66WR+++WR+++WR+++WR+++02R" r0AQ/Fy)+,,M& G' GR Mr"c tjtstjr||||||d}t jfi|}t jfi|} |r|dd| dzzg} d} ng} d} t|| d| | dD]'\| fdD(| Sj tj dkrtdj dkrtd |tj }fd |D}tfd |Drtd t!|t!t#|krtd t!|} t%||} |r>tjd| Dst)jdd| D} g}t|||zD]}dfg}t|| D]O\}}g}|D]C\}}t-||d||d\}}||dz|f|dz|fgD|}Pt1|}|||d| z|r|d| z|r|||S)aI n-dimensional stationary wavelet transform. Parameters ---------- data : array_like n-dimensional array with input data. wavelet : Wavelet object or name string, or tuple of wavelets Wavelet to use. This can also be a tuple of wavelets to apply per axis in ``axes``. level : int The number of decomposition steps to perform. start_level : int, optional The level at which the decomposition will start (default: 0) axes : sequence of ints, optional Axes over which to compute the SWT. A value of ``None`` (the default) selects all axes. Axes may not be repeated. trim_approx : bool, optional If True, approximation coefficients at the final level are retained. norm : bool, optional If True, transform is normalized so that the energy of the coefficients will be equal to the energy of ``data``. In other words, ``np.linalg.norm(data.ravel())`` will equal the norm of the concatenated transform coefficients when ``trim_approx`` is True. Returns ------- [{coeffs_level_n}, ..., {coeffs_level_1}]: list of dict Results for each level are arranged in a dictionary, where the key specifies the transform type on each dimension and value is a n-dimensional coefficients array. For example, for a 2D case the result at a given level will look something like this:: {'aa': # A(LL) - approx. on 1st dim, approx. on 2nd dim 'ad': # V(LH) - approx. on 1st dim, det. on 2nd dim 'da': # H(HL) - det. on 1st dim, approx. on 2nd dim 'dd': # D(HH) - det. on 1st dim, det. on 2nd dim } For user-specified ``axes``, the order of the characters in the dictionary keys map to the specified ``axes``. If ``trim_approx`` is ``True``, the first element of the list contains the array of approximation coefficients from the final level of decomposition, while the remaining coefficient dictionaries contain only detail coefficients. This matches the behavior of `pywt.wavedecn`. Notes ----- The implementation here follows the "algorithm a-trous" and requires that the signal length along the transformed axes be a multiple of ``2**level``. If this is not the case, the user should pad up to an appropriate size using a function such as ``numpy.pad``. A primary benefit of this transform in comparison to its decimated counterpart (``pywt.wavedecn``), is that it is shift-invariant. This comes at cost of redundancy in the transform (the size of the output coefficients is larger than the input). When the following three conditions are true: 1. The wavelet is orthogonal 2. ``swtn`` is called with ``norm=True`` 3. ``swtn`` is called with ``trim_approx=True`` the transform has the following additional properties that may be desirable in applications: 1. energy is conserved 2. variance is partitioned across scales )r'r,r-r.rXr0rr1rNc:i|]}||d|zzSr3r)rkidictrdicts r zswtn..vs,<<<E!HrE!H},<<.s+ 8 8 8aQUUA MM 8 8 8r"c3:K|]}|dkp |jkVdS)rNrrs r zswtn..s2 1 1q1q5 "AN 1 1 1 1 1 1r"r9'The axes passed to swtn must be unique.cg|] }|j Sr)r%rs r r!zswtn..s:::#s~:::r"zpnorm=True, but the wavelets used are not orthogonal: The conditions for energy preservation are not satisfied.c Xg|]'}t|dtjdz (S)rr8rrs r r!zswtn..s>)))0Qrwqzz\BB)))r")r,r-r/rVrT)rrrr:rr;r<r=r>r7 TypeErrorrCrmrpanyrrnrrallr@rArFextenddictpopreverse)rGr'r,r-rXr.r0rHr;r<cplxoffsetnum_axesrrQirxr/ new_coeffssubbandxryrrrs` @@r rrsX :d  D !6!6$u[%0$NNDI((((DI((((  Gb47l*+DFFDFVWW tFGG}== > >LE5 KK<<<< > > >  zRXh''''<=== y1}}9::: |TY 8 8 8 84 8 8 8D 1 1 1 1D 1 1 111=;<<< 4yyCD NN""BCCC4yyH!'400H )v:::::;; O MN O O O))'))) C ; e 3 4 4''t* x00  MD'J$ 9 9 "1gQA(,..../1B!!GcM2#6$+cM2#6#89999FFf 6cHn%  ' JJsX~ & & & 4KKMMM Jr"c  &'td|dD}t|dt }|r|dn|dd|z}tst j|rq|r'|djg}|djg}|dd}ng}g}|d|Dz }|d|Dz }|||d } t|fi| } | d t|fi| zzS|r |dd}t|} t j || d } | j &|t| j }&fd |D}t|tt|krtd|t|krtdt|} t!||}|r d|D}t#dg&z}t#dg&z}t#dg&z}t#dg&z}t| D]}t%t'd| |z dz }|}|s||d|z}||}t j| gd|Dz}| j|kr| |} d|D'tt'dkrt5dt7'fd|D}t9t|g|zD]}t;|||D]K\}}}t#|||||<t#||d|z||<t#||z|d|z||<L| }d| t7|<d}t9dg|zD]} t;| |D]\}!}|!r ||||<||||<i}"|D]\}#}$|$t7||"|#<|t7||"d|z<t?|"|d|}%t;| |D]\}!}|!rt j |%d|}%| t7|xx|%z cc<|dz }| t7|xx|zcc<|s|||d|z<| S)a Multilevel nD inverse discrete stationary wavelet transform. Parameters ---------- coeffs : list [{coeffs_level_n}, ..., {coeffs_level_1}]: list of dict wavelet : Wavelet object or name string, or tuple of wavelets Wavelet to use. This can also be a tuple of wavelets to apply per axis in ``axes``. axes : sequence of ints, optional Axes over which to compute the inverse SWT. Axes may not be repeated. The default is ``None``, which means transform all axes (``axes = range(data.ndim)``). norm : bool, optional Controls the normalization used by the inverse transform. This must be set equal to the value that was used by ``pywt.swtn`` to preserve the energy of a round-trip transform. Returns ------- nD array of reconstructed data. Examples -------- >>> import pywt >>> coeffs = pywt.swtn([[1,2,3,4],[5,6,7,8], ... [9,10,11,12],[13,14,15,16]], ... 'db1', level=2) >>> pywt.iswtn(coeffs, 'db1') array([[ 1., 2., 3., 4.], [ 5., 6., 7., 8.], [ 9., 10., 11., 12.], [ 13., 14., 15., 16.]]) c34K|]}t|VdS)N)rn)rkeys r rziswtn..s(88cS888888r"r*rrVrNcJg|] }d|D!S)c$i|] \}}||jSrrZrrrs r rz$iswtn... 999tq!AF999r"itemsr[s r r!ziswtn../JJJa99qwwyy999JJJr"cJg|] }d|D!S)c$i|] \}}||jSrr_rs r rz$iswtn...rr"rr[s r r!ziswtn..rr")r'rXr0r1Trgc*g|]}|dkr|zn|Srr)rrVrCs r r!ziswtn..s) 3 3 3AAHH1 3 3 3r"rzYThe number of axes used in iswtn must match the number of dimensions transformed in swtn.cRg|]$}t|tjd%Srrrs r r!ziswtn..rr"r8cg|] }|j Srr6)rrs r r!ziswtn..s888!ag888r"c"g|] \}}|j Sr)rDrs r r!ziswtn.. s666da!'666r"rc,g|]}d|Srr)raxshapess r r!ziswtn..s!"@"@"@R6!9R="@"@"@r"rrirr)!maxrjrrrr:r;r<rr r?rCrprnrrmrrrqrrrrvaluesr7rrrrkrr=rhrrw)(rxr'rXr0ndim_transformr.ryrIrJrHr{rPr|r}rrrrodd_even_slicesrrrrVdetailsrcoeff_trans_shapefirstsrshrapprox ntransformsoddso details_slicervaluerrCrs( @@r rrsN88VBZ88888N D111K! Dvay^1C'DB  5!4!4 5  !!9>*K!!9>*KABBZFFKKJJ6JJJJ JJ6JJJJ $dDAA + ( ( ( (2k44V44444 b  B Xb . . .F ;D |V[!! 3 3 3 3d 3 3 3D 4yyCD NN""BCCCT""EFF FVJ!'400H )))'))) T{{od"G$KK?4'L;;/$&KT{{od*O :  8.8.Az!|A~..//   2q c.011A)~ F88w~~'7'7888 8; << ' ']]<00F76gmmoo666 s6{{  q FHH H""@"@"@"@4"@"@"@AAz!2!2 5n DF 2 2F!$V->!E!E J J r2#E2y99 #(AiK#@#@ R "'iQy["I"I B[[]]F%&F5>> "K6*^";= ! ! t__??EAr?.9"o++.:2.>++ " ")--//GGJC).u_/E/E)FM#&&4:/**5, c.01 -?NNN t__33EAr3GAqr222uW~~&&&!+&&&q 5>> " " "k 1 " " " " .,-F1Ic.( ) Mr")Nrr*FF)Fr*)rrFF)Fr)rNFF)NF)!r@ itertoolsrnumpyr _c99_configr_extensions._dwtr_extensions._pywtrrr _extensions._swtr rEr rFr _multidimr r_utilsrrr__all__r)rrrrrrr"r rs******))))));;;;;;;;;;))))))333333++++++########>>>>>>>>>> L L L8: %}}}}@qqqqh4