e,dZddlmZmZmZddlmZddlZddl m Z ddl m Z m Z ddlmZmZgd Zdd Zdd ZddZdZddZdS)zP 2D and nD Discrete Wavelet Transforms and Inverse Discrete Wavelet Transforms. )divisionprint_functionabsolute_import)productN)_have_c99_complex)dwt_axis idwt_axis)_wavelets_per_axis_modes_per_axis)dwt2idwt2dwtnidwtn symmetricc`t|}tj|}t|dkrt d|jttj|krt dt||||}|d|d|d|dffS)a 2D Discrete 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 containing a wavelet to apply along each axis in ``axes``. mode : str or 2-tuple of strings, optional Signal extension mode, see :ref:`Modes `. This can also be a tuple of modes specifying the mode to use on each axis in ``axes``. axes : 2-tuple of ints, optional Axes over which to compute the DWT. Repeated elements mean the DWT will be performed multiple times along these axes. Returns ------- (cA, (cH, cV, cD)) : tuple Approximation, horizontal detail, vertical detail and diagonal detail coefficients respectively. Horizontal refers to array axis 0 (or ``axes[0]`` for user-specified ``axes``). Examples -------- >>> import numpy as np >>> import pywt >>> data = np.ones((4,4), dtype=np.float64) >>> coeffs = pywt.dwt2(data, 'haar') >>> cA, (cH, cV, cD) = coeffs >>> cA array([[ 2., 2.], [ 2., 2.]]) >>> cV array([[ 0., 0.], [ 0., 0.]]) Expected 2 axesz8Input array has fewer dimensions than the specified axesaadaaddd)tuplenpasarraylen ValueErrorndimuniquer)datawaveletmodeaxescoefss .lib/python3.11/site-packages/pywt/_multidim.pyr r sR ;;D :d  D 4yyA~~*+++ y3ry'''' !! ! wd + +E ;teDk5;? ??c|\}\}}}t|}t|dkrtd||||d}t||||S)a 2-D Inverse Discrete Wavelet Transform. Reconstructs data from coefficient arrays. Parameters ---------- coeffs : tuple (cA, (cH, cV, cD)) A tuple with approximation coefficients and three details coefficients 2D arrays like from ``dwt2``. If any of these components are set to ``None``, it will be treated as zeros. 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``. mode : str or 2-tuple of strings, optional Signal extension mode, see :ref:`Modes `. This can also be a tuple of modes specifying the mode to use on each axis in ``axes``. axes : 2-tuple of ints, optional Axes over which to compute the IDWT. Repeated elements mean the IDWT will be performed multiple times along these axes. Examples -------- >>> import numpy as np >>> import pywt >>> data = np.array([[1,2], [3,4]], dtype=np.float64) >>> coeffs = pywt.dwt2(data, 'haar') >>> pywt.idwt2(coeffs, 'haar') array([[ 1., 2.], [ 3., 4.]]) rr)rrrr)rrr r)coeffsr$r%r&LLHLLHHHs r(rrMscFB R ;;D 4yyA~~*+++b" 5 5F $ - --r)ctjtsptjr\t j|||t j|||tfdDSj tj dkrtdj dkrtd|tj }fd|D}t||}t||}dfg}t!|||D]H\}}}g} |D];\} } t#| |||\} } | | d z| f| d z| fg<| }It|S) aO Single-level n-dimensional Discrete 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 containing a wavelet to apply along each axis in ``axes``. mode : str or tuple of string, optional Signal extension mode used in the decomposition, see :ref:`Modes `. This can also be a tuple of modes specifying the mode to use on each axis in ``axes``. axes : sequence of ints, optional Axes over which to compute the DWT. Repeated elements mean the DWT will be performed multiple times along these axes. A value of ``None`` (the default) selects all axes. Axes may be repeated, but information about the original size may be lost if it is not divisible by ``2 ** nrepeats``. The reconstruction will be larger, with additional values derived according to the ``mode`` parameter. ``pywt.wavedecn`` should be used for multilevel decomposition. Returns ------- coeffs : dict Results are arranged in a dictionary, where key specifies the transform type on each dimension and value is a n-dimensional coefficients array. For example, for a 2D case the result 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``. c3DK|]}||d|zzfVdS)?N).0kimagreals r( zdwtn..s9EEAQQ"tAw,./EEEEEEr)objectz"Input must be a numeric array-likerzInput data must be at least 1DNc4g|]}|dkr |jzn|Sr)r!)r4ar#s r( zdwtn..s+ 8 8 8aQUUA MM 8 8 8r)r<d)rrr iscomplexobjrr7r6dictkeysdtype TypeErrorr!r ranger r zipr extend)r#r$r%r&modeswaveletsr+axiswav new_coeffssubbandxcAcDr6r7s` @@r(rrysZ :d  D F!6!6FDIwd33DIwd33EEEEEEEEEEE zRXh''''<=== y1}}9::: |TY 8 8 8 84 8 8 8D D$ ' 'E!'400H4j\FtXu55c4   5 5JGQadD11FB   # r2 '# r24 5 5 5 5 <<r)cd|D}|r"td|d|D}|r"td|d|D}t t j|dkrtdtd|DS) Ncg|] \}}|| SNr3r4r5vs r(r=z_fix_coeffs..s>>>$!QAIAIIIr)zThe following detail coefficients were set to None: {0} For multilevel transforms, rather than setting coeffs[key] = None use coeffs[key] = np.zeros_like(coeffs[key]) cXg|]'\}}t|tdk%|(S)r)setrTs r(r=z_fix_coeffs..s<---$!QA#d))+++++r)zOThe following invalid keys were found in the detail coefficient dictionary: {}.c,g|]}t|Sr3r)r4r5s r(r=z_fix_coeffs..s111a3q66111r)rz4All detail coefficient names must have equal length.c3HK|]\}}|tj|fVdSrS)rrrTs r(r8z_fix_coeffs..s3>>tq!BJqMM">>>>>>r))itemsr formatrBrrr"rA)r+ missing_keys invalid_keys key_lengthss r( _fix_coeffsr`s>>&,,..>>>L ; *>@@ @216;;==111K 29[ ! !""Q&& BDD D >>v||~~>>> > >>r)c td|D}td|D}t|}tst d|Dr~td|D}td|D}t ||||dt ||||zzStd|D fd|D}t|n#t$rtd wxYwt fd |Drtd |t}ntfd |D}t||}t||}t!t#t%t'|||D]\} \} } }| dks| krt)jdi} dt-d| D} | D]}||dzd }||dzd }|w|u|j|jkre|jjdks|jjdkr t(j}n t(j}t)j||}t)j||}t;||| || | |<| }|dS)aV Single-level n-dimensional Inverse Discrete Wavelet Transform. Parameters ---------- coeffs: dict Dictionary as in output of ``dwtn``. Missing or ``None`` items will be treated as zeros. wavelet : Wavelet object or name string, or tuple of wavelets Wavelet to use. This can also be a tuple containing a wavelet to apply along each axis in ``axes``. mode : str or list of string, optional Signal extension mode used in the decomposition, see :ref:`Modes `. This can also be a tuple of modes specifying the mode to use on each axis in ``axes``. axes : sequence of ints, optional Axes over which to compute the IDWT. Repeated elements mean the IDWT will be performed multiple times along these axes. A value of ``None`` (the default) selects all axes. For the most accurate reconstruction, the axes should be provided in the same order as they were provided to ``dwtn``. Returns ------- data: ndarray Original signal reconstructed from input data. c3(K|] \}}|||fVdSrSr3rTs r(r8zidwtn..*EETQq}1a&}}}}EEr)c3(K|] \}}|||fVdSrSr3rTs r(r8zidwtn..rcr)c3>K|]}tj|VdSrS)rr@)r4rUs r(r8zidwtn..s,<.,BB41aAqv;BBBBBBr)c3.K|]\}}||jfVdSrS)r6rTs r(r8zidwtn.. rgr)r2c34K|]}t|VdSrSrY)r4keys r(r8zidwtn..s(;;cS;;;;;;r)c3VK|]#\}}|t|k|jV$dSrS)rshape)r4r5rUndim_transforms r(r8zidwtn..sMGGDAq=SVV~-E-E-E-E-E-EGGr)z8`coeffs` must contain at least one non-null wavelet bandc3$K|] }|kV dSrSr3)r4s coeff_shapes r(r8zidwtn..s( 2 21  2 2 2 2 2 2r)z,`coeffs` must all be of equal size (or None)Nc*g|]}|dkr|zn|Sr;r3)r4r<r!s r(r=zidwtn..s) 3 3 3AAHH1 3 3 3r)rz!Axis greater than data dimensionsc8g|]}d|S)r>)join)r4coefs r(r=zidwtn..)s"OOOdBGGDMMOOOr)r)repeatr<r?c)rCr>)rAr[r`ranyvaluesrmaxrBnext StopIterationr rErr r reversedlist enumeraterFr AxisErrorrgetrCkind complex128float64rr )r+r$r%r& real_coeffs imag_coeffs coeff_shapesrHrI key_lengthrJrKrLnew_keysrjLHrCrpr!rms @@@r(rrs@EEV\\^^EEE E EFEEV\\^^EEE E EF F > <BB6<<>>BBBBB BB6<<>>BBBBB k7D$77U;t<<<= >;;V[[]];;;;;N!GGGGFLLNNGGG <(( !!! !! !! 2 2 2 2\ 2 2 222IGHHH |^$$; 3 3 3 3d 3 3 3D D$ ' 'E!'400H)1 3tXu5566 7 7*9*9% %T3 !88tt||,BCC C OOgd:.N.N.NOOO ? ?C 39d++A 39d++A}7ag%%w|s**aglc.A.A "  "  1E222A 1E222A'1c4>>JsOO ":s /E55F)rr)rN)__doc__ __future__rrr itertoolsrnumpyr _c99_configr_extensions._dwtr r _utilsr r __all__r rrr`rr3r)r(rs A@@@@@@@@@******1111111177777777 - , ,2@2@2@2@j).).).).XGGGGT???6\\\\\\r)