e8ddlmZmZddlZddlmZmZmZm Z m Z m Z m Z ddl mZmZmZmZmZmZmZddlmZmZgdZ dd Zd Z ddZdZ ddZdZdS))partialreduceN)_prep_axes_wavedecnwavedecwavedec2wavedecnwaverecwaverec2waverecn)iswtiswt2iswtnswtswt2 swt_max_levelswtn)_modes_per_axis_wavelets_per_axis)mramra2mranimraimra2imranr periodizationc<|dkrQ|dkrtdt||d}ttf|dd|}ttfi|}d} nc|dkr;t|||}tt fd |i|}tt fi|}d } n"td |||} g} t| } | r!tj | d } | g| z}n d | D}t| D]}| |||<||}|j |j kr$|td|j D}| || r| ||<itj ||||<| S)aForward 1D multiresolution analysis. It is a projection onto the wavelet subspaces. Parameters ---------- data: array_like Input data wavelet : Wavelet object or name string Wavelet to use level : int, optional Decomposition level (must be >= 0). If level is None (default) then it will be calculated using the `dwt_max_level` function. axis: int, optional Axis over which to compute the DWT. If not given, the last axis is used. Currently only available when ``transform='dwt'``. transform : {'dwt', 'swt'} Whether to use the DWT or SWT for the transforms. mode : str, optional Signal extension mode, see `Modes` (default: 'symmetric'). This option is only used when transform='dwt'. Returns ------- [cAn, {details_level_n}, ... {details_level_1}] : list For more information, see the detailed description in `wavedec` See Also -------- imra, swt Notes ----- This is sometimes referred to as an additive decomposition because the inverse transform (``imra``) is just the sum of the coefficient arrays [1]_. The decomposition using ``transform='dwt'`` corresponds to section 2.2 while that using an undecimated transform (``transform='swt'``) is described in section 3.2 and appendix A. This transform does not share the variance partition property of ``swt`` with `norm=True`. It does however, result in coefficients that are temporally aligned regardless of the symmetry of the wavelet used. The redundancy of this transform is ``(level + 1)``. References ---------- .. [1] Donald B. Percival and Harold O. Mofjeld. Analysis of Subtidal Coastal Sea Level Fluctuations Using Wavelets. Journal of the American Statistical Association Vol. 92, No. 439 (Sep., 1997), pp. 868-880. https://doi.org/10.2307/2965551 rr0transform swt only supports mode='periodization'T)waveletaxisnormlevel trim_approxdwt)r moder!r$Funrecognized transform: {}rc6g|]}tj|Snp zeros_like.0cs )lib/python3.11/site-packages/pywt/_mra.py zmra.._s"444Ar}Q444c,g|]}t|Sr*slicer/szs r1r2zmra..is<<<2U2YY<<C#  +CFF]3q6**CFF r3c$td|S)aWInverse 1D multiresolution analysis via summation. Parameters ---------- mra_coeffs : list of ndarray Multiresolution analysis coefficients as returned by `mra`. Returns ------- rec : ndarray The reconstructed signal. See Also -------- mra References ---------- .. [1] Donald B. Percival and Harold O. Mofjeld. Analysis of Subtidal Coastal Sea Level Fluctuations Using Wavelets. Journal of the American Statistical Association Vol. 92, No. 439 (Sep., 1997), pp. 868-880. https://doi.org/10.2307/2965551 c ||zSNr*)xys r1zimra..s q1ur3)r)rHs r1rrts0 $$j 1 11r3rrc|dkro|dkrtd|td|jD}t||d}t t f|dd|}t t fi|}na|d kr9t||| }t tfd |i|}t tfi|}n"td |||} g} t| } tj | d } | g} td| D]'}| d| |D(| d | d <|| }|j|jkr$|td|jD}| || | d <td| D]}g}tdD]}| ||} | ||| ||<|| }|j|jkr$|td|jD}||| | ||<| t|| S)aForward 2D multiresolution analysis. It is a projection onto wavelet subspaces. Parameters ---------- data: array_like Input data wavelet : Wavelet object or name string, or 2-tuple of wavelets Wavelet to use. This can also be a tuple containing a wavelet to apply along each axis in `axes`. level : int, optional Decomposition level (must be >= 0). If level is None (default) then it will be calculated using the `dwt_max_level` function. axes : 2-tuple of ints, optional Axes over which to compute the DWT. Repeated elements are not allowed. Currently only available when ``transform='dwt2'``. transform : {'dwt2', 'swt2'} Whether to use the DWT or SWT for the transforms. mode : str or 2-tuple of str, optional Signal extension mode, see `Modes` (default: 'symmetric'). This option is only used when transform='dwt2'. Returns ------- coeffs : list For more information, see the detailed description in `wavedec2` Notes ----- This is sometimes referred to as an additive decomposition because the inverse transform (``imra2``) is just the sum of the coefficient arrays [1]_. The decomposition using ``transform='dwt'`` corresponds to section 2.2 while that using an undecimated transform (``transform='swt'``) is described in section 3.2 and appendix A. This transform does not share the variance partition property of ``swt2`` with `norm=True`. It does however, result in coefficients that are temporally aligned regardless of the symmetry of the wavelet used. The redundancy of this transform is ``3 * level + 1``. See Also -------- imra2, swt2 References ---------- .. [1] Donald B. Percival and Harold O. Mofjeld. Analysis of Subtidal Coastal Sea Level Fluctuations Using Wavelets. Journal of the American Statistical Association Vol. 92, No. 439 (Sep., 1997), pp. 868-880. https://doi.org/10.2307/2965551 rrrNc34K|]}t|VdSrPrr/ss r1 zmra2..*==Q a((======r3Tr axesr"r#dwt2r r'r^r$r(rrc6g|]}tj|Sr*r+r.s r1r2zmra2..s"<<<BM!$$<<.888rr888r3c,g|]}t|Sr*r5r7s r1r2zmra2.. @ @ @rr @ @ @r3)r9minr>r:rrrrr r;r<r,r-r=r@r?)rAr r$r^rBr'rCrDrErGrHrIrJrKrLrMdcoeffsns r1rrsnF ? " "BDD D ===$*=====EgDt<<<$HeHHHH%**6** f  gDt<<<(::%:6::(--f--5<> <= 0). If level is None (default) then it will be calculated using the `dwt_max_level` function. axes : tuple of ints, optional Axes over which to compute the DWT. Repeated elements are not allowed. transform : {'dwtn', 'swtn'} Whether to use the DWT or SWT for the transforms. mode : str or tuple of str, optional Signal extension mode, see `Modes` (default: 'symmetric'). This option is only used when transform='dwtn'. Returns ------- coeffs : list For more information, see the detailed description in `wavedecn`. See Also -------- imran, swtn Notes ----- This is sometimes referred to as an additive decomposition because the inverse transform (``imran``) is just the sum of the coefficient arrays [1]_. The decomposition using ``transform='dwt'`` corresponds to section 2.2 while that using an undecimated transform (``transform='swt'``) is described in section 3.2 and appendix A. This transform does not share the variance partition property of ``swtn`` with `norm=True`. It does however, result in coefficients that are temporally aligned regardless of the symmetry of the wavelet used. The redundancy of this transform is ``(2**n - 1) * level + 1`` where ``n`` corresponds to the number of axes transformed. References ---------- .. [1] Donald B. Percival and Harold O. Mofjeld. Analysis of Subtidal Coastal Sea Level Fluctuations Using Wavelets. Journal of the American Statistical Association Vol. 92, No. 439 (Sep., 1997), pp. 868-880. https://doi.org/10.2307/2965551 rrrNc34K|]}t|VdSrPrXrYs r1r[zmran..Zr\r3Tr]r#dwtnr`r$r(rrc>i|]\}}|tj|Sr*r+)r/kvs r1 zmran..ms(JJJDAqAr}Q''JJJr3c,g|]}t|Sr*r5r7s r1r2zmran..urcr3c,g|]}t|Sr*r5r7s r1r2zmran..rfr3)rr>rr9rgr:rrrrr r r;r<r,r-r=r@itemsr?listkeys)rAr r$r^rBr' axes_shapesndim_transformwaveletsrCrDrEmodesrGrHrIrJrKrLrMrhdkeysros r1rrsn)>>(::%:6::(--f--5<rsx%%%%%%%%777777777777777777DDDDDDDDDDDDDDDDDD77777777 ; ; ;7< ddddN2226>DjjjjZ>:@qqqqhr3