B †\Q@sddlZddlmZddlZddlmZddlmZddl m Z m Z m ZddlmZmZddlmZmZdd lmZmZd d d d dddgZddd Z dd Zddd ZddZdddZdddZdS)N)product)_have_c99_complex) idwt_single) swt_max_levelswtswt_axis)Modes _check_dtype)idwt2idwtn) _as_wavelet_wavelets_per_axisrriswtswt2iswt2swtniswtncCsts~t|r~t|}t|j|||}t|j|||}g}xVszswt..)rr iscomplexobjrrrealimagzipappendr arrayr ndim ValueErrorrshape_swt _swt_axis)datawaveletlevel start_levelaxis coeffs_real coeffs_imagZ coeffs_cplxZcA_rZcD_rZcA_iZcD_idtretrrrrs** "  cCst|dd}tj|dd|dd}tsjt|rjdd|D}dd|D}t||dt||St|}t|}t d}x*t |dd D]}t t d |d } | } |||\} } tj | t| d } | j|jkr$|jjd ks| jjd krtj} ntj} tj || d }tj | | d } xt | D]|}t|t| | }|ddd }|d dd }t||| |||}t||| |||}t|d }||d||<q.WqW|S)a 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 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.]) rT)rcopycSsg|]\}}|j|jfqSr)r)rrrrrrrzsziswt..cSsg|]\}}|j|jfqSr)r )rrrrrrr{sy? periodizationrr)rcNg@)r rr#rrrlenr r Z from_objectrangeintpowrrZkindZ complex128Zfloat64Zarangerroll)coeffsr*r0outputr.r/ num_levelsmodej step_size last_index_rrfirstindices even_indices odd_indicesx1x2rrrrYsB  rcCst|}t|}t|dkr&tdt|tt|krBtd|jtt|kr^tdt|||||}g}x0|D](}| |d|d|d|dffqxW|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. Returns ------- coeffs : list Approximation and details coefficients (for ``start_level = m``):: [ (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``. 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``. r4zExpected 2 axesz'The axes passed to swt2 must be unique.z8Input array has fewer dimensions than the specified axesZaaZdaZadZdd) tuplerrr6r%setr$uniquerr")r)r*r+r,axesZcoefsr1r5rrrrs.   (c Cst|dd}tj|dd|dd}|jdkr:tdt|}t|dd}xvt|D]h}tt d||d}|}||\} \} } } | j | j ks| j | j krt d tj |gd d | | | gD} |j | kr|| }xt|D]}xt|D]}t|| j d|}t|| j d|}t|| j dd|}t|| j dd|}t||| j dd|}t||| j dd|}t|||f| ||f| ||f| ||fff|d }t|||f| ||f| ||f| ||fff|d }t|||f| ||f| ||f| ||fff|d }t|||f| ||f| ||f| ||fff|d }tj|ddd }tj|ddd }tj|ddd }tj|ddd }||||d|||f<qWqWqZW|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. 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.]]) rT)rr2r4zKiswt2 only supports 2D arrays. see iswtn for a general n-dimensionsal ISWT)rr)rNrz4Mismatch in shape of intermediate coefficient arrayscSsg|] }t|qSr)r )rr5rrrr4sziswt2..r3)r-)r rr#r$r%r6rr7r8r9r& RuntimeError result_typerastypeslicer r:)r;r*r0r<r=waveletsr?r@rArBZcHZcVr common_dtypeZfirst_hZfirst_wZ indices_hZ indices_wZ even_idx_hZ even_idx_wZ odd_idx_hZ odd_idx_wrGrHZx3Zx4rrrrsh0                (c stts~tr~tj||||}tj||||}g}x8t||D]*\|t fdd DqLW|Sj t dkrt dj dkrtd|dkrtj }fdd |D}t|tt|krtd t|}t||} g} xt|||D]} d fg} xlt|| D]^\} }g}xJ| D]B\}}t||d| | d d \}}||d|f|d|fgq:W|} q(Wt | } | | | d|qW| | S)a 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. 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``. 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``. c3s&|]}||d|fVqdS)y?Nr)rk)idictrdictrr szswtn..objectz"Input must be a numeric array-likerzInput data must be at least 1DNcs"g|]}|dkr|jn|qS)r)r$)ra)r)rrrszswtn..z'The axes passed to swtn must be unique.)r+r,r-rr[d)rrrrrrr r!r"dictkeysr TypeErrorr$r%r7r6rLrr(extendreverse)r)r*r+r,rNrr ZcplxZnum_axesrTr1ir;r-Z new_coeffsZsubbandxrrr)r)rWrXrrdsH- "       c sZtdd|dD}t|dd|}tj|dd||dd}|j|dkrbt|j}fdd |D}t|tt|krt d |t|krt d t|}t ||}t dg}t dg} t dg} t dg} xdt|D]V} t t d || d } | }|| d|}|| }tj|gdd |D}|j|krh||}dd |Dttd krtdtfdd |D}xtt|g|D]|}xXt|||D]H\}}}t ||| ||<t ||d | | |<t || |d | | |<qW|}d|t|<d}xtdg|D]}x8t||D]*\}}|rt| || |<n | || |<qXWi}x&|D]\}}|t| ||<qW|t| |d|<t||d|d}x.t||D] \}}|rtj|d |d}qW|t||7<|d 7}qHW|t||<qW||| d|<qW|S)a Multilevel nD inverse discrete stationary wavelet transform. Parameters ---------- coeffs : list [{coeffs_level_n}, ..., {coeffs_level_1}]: list of dict wavelet : Wavelet object or name string, or tuple of wavelets Wavelet to use. This can also be a tuple of wavelets to apply per axis in ``axes``. axes : sequence of ints, optional Axes over which to compute the inverse SWT. Axes may not be repeated. The default is ``None``, which means transform all axes (``axes = range(data.ndim)``). Returns ------- nD array of reconstructed data. Examples -------- >>> import pywt >>> coeffs = pywt.swtn([[1,2,3,4],[5,6,7,8], ... [9,10,11,12],[13,14,15,16]], ... 'db1', level=2) >>> pywt.iswtn(coeffs, 'db1') array([[ 1., 2., 3., 4.], [ 5., 6., 7., 8.], [ 9., 10., 11., 12.], [ 13., 14., 15., 16.]]) css|]}t|VqdS)N)r6)rkeyrrrrYsziswtn..rr[T)rr2Ncs g|]}|dkr|n|qS)rr)rr[)r$rrrsziswtn..z'The axes passed to swtn must be unique.zYThe number of axes used in iswtn must match the number of dimensions transformed in swtn.r4rcSsg|] }|jqSr)r)rvrrrrscSsg|]\}}|jqSr)r&)rrVrfrrrr sz4Mismatch in shape of intermediate coefficient arrayscsg|]}d|qS)rr)rax)shapesrrrs)rrr3)rN)r-)maxr_r rr#r$r7r6rLr%rrSr8r9poprQvaluesrrRitemsrPrKrr!r2r r:)r;r*rNZndim_transformr0r<r=rTrDrErFZodd_even_slicesr?r@rAr[ZdetailsrUZcoeff_trans_shapeZfirstsrCZshrgZapproxZ ntransformsZoddsoZ details_slicerevaluerdr)r$rhrrst#      )Nrr)rrI)rN)N)warnings itertoolsrZnumpyrZ _c99_configrZ_extensions._dwtrZ_extensions._swtrrr'rr(Z_extensions._pywtr r Z _multidimr r Z_utilsr r__all__rrrrrrrrrs    HT @w [