bMh,|dZddlmZddlZddlmZddlmZm Z ddl m Z m Z m Z gdZdd Zdd Zdd ZdZddZdS)zP 2D and nD Discrete Wavelet Transforms and Inverse Discrete Wavelet Transforms. )productN)_have_c99_complex)dwt_axis idwt_axis) AxisError_modes_per_axis_wavelets_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 N/var/www/html/test/jupyter/venv/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)rrrr)coeffsr"r#r$LLHLLHHHs r&r r KscFB R ;;D 4yyA~~*+++b" 5 5F $ - --r'ctjtsQtjr=t j|||t j|||fdDSjtjdkrtdj 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``. c:i|]}||d|zzS)?).0kimagreals r& zdwtn..s,888a47R$q'\)888r'objectz"Input must be a numeric array-likerzInput data must be at least 1DNc4g|]}|dkr |jzn|Sr)r)r2ar!s r& zdwtn..s+ 8 8 8aQUUA MM 8 8 8r'r:d)rrr iscomplexobjr r5r4dtype TypeErrorrrranger r ziprextenddict)r!r"r#r$modeswaveletsr)axiswav new_coeffssubbandxcAcDr4r5s` @@r&r r wsZ :d  D 9!6!69DIwd33DIwd338888848888 zRXh''''<=== y1}}9::: |TY 8 8 8 84 8 8 8D D$ ' 'E!'400H4j\FtXu55c4   5 5JGQadD11FB   # r2 '# r24 5 5 5 5 <<r'cd|D}|rtd|dd|D}|rtd|dd|D}ttj|dkrtd d |DS) Ncg|] \}}|| SNr1r2r3vs r&r;z_fix_coeffs..s>>>$!QAIAIIIr'z4The following detail coefficients were set to None: zr For multilevel transforms, rather than setting coeffs[key] = None use coeffs[key] = np.zeros_like(coeffs[key]) cXg|]'\}}t|tdk%|(S)r)setrQs r&r;z_fix_coeffs..s<---$!QA#d))+++++r'zLThe following invalid keys were found in the detail coefficient dictionary: .c,g|]}t|Sr1r)r2r3s r&r;z_fix_coeffs..s***a3q66***r'rz4All detail coefficient names must have equal length.c>i|]\}}|tj|Sr1)rrrQs r&r6z_fix_coeffs..s& 8 8 8AArz!}} 8 8 8r')itemsrrrr )r) missing_keys invalid_keys key_lengthss r& _fix_coeffsr]s >>&,,..>>>L< ; ; ; ;<< <--&,,..---L8 7'3 7 7 788 8+*6***K 29[ ! !""Q&& BDD D 9 8 8 8 88r'c &d|D}d|D}t|}tstd|Drdd|D}d|D}t ||||dt ||||zzSt d|D fd|D}t|n#t$rtd wxYwtfd |Drtd |t}ntfd |D}t||}t||}ttt!t#|||D] \} \} } }| dks| krt%di} dt'd| D} | D]}||dzd }||dzd }|w|u|j|jkre|jjdks|jjdkr t.j}n t.j}t/j||}t/j||}t7||| || | |<| } |dS)aV Single-level n-dimensional Inverse Discrete Wavelet Transform. Parameters ---------- coeffs: dict Dictionary as in output of ``dwtn``. Missing or ``None`` items will be treated as zeros. wavelet : Wavelet object or name string, or tuple of wavelets Wavelet to use. This can also be a tuple containing a wavelet to apply along each axis in ``axes``. mode : str or list of string, optional Signal extension mode used in the decomposition, see :ref:`Modes `. This can also be a tuple of modes specifying the mode to use on each axis in ``axes``. axes : sequence of ints, optional Axes over which to compute the IDWT. Repeated elements mean the IDWT will be performed multiple times along these axes. A value of ``None`` (the default) selects all axes. For the most accurate reconstruction, the axes should be provided in the same order as they were provided to ``dwtn``. Returns ------- data: ndarray Original signal reconstructed from input data. ci|] \}}||| SrPr1rQs r&r6zidwtn.. ? ? ?tq!ar'ci|] \}}||| SrPr1rQs r&r6zidwtn..r`r'c3>K|]}tj|VdSrP)rr>)r2rRs r& zidwtn..s,<. <<.rer'r0c34K|]}t|VdSrPrW)r2keys r&rczidwtn.. s(44cS444444r'c3VK|]#\}}|t|k|jV$dSrP)rshape)r2r3rRndim_transforms r&rczidwtn..sMGGDAq=SVV~-E-E-E-E-E-EGGr'z8`coeffs` must contain at least one non-null wavelet bandc3$K|] }|kV dSrPr1)r2s coeff_shapes r&rczidwtn..s( 2 21  2 2 2 2 2 2r'z,`coeffs` must all be of equal size (or None)Nc*g|]}|dkr|zn|Sr9r1)r2r:rs r&r;zidwtn..s) 3 3 3AAHH1 3 3 3r'rz!Axis greater than data dimensionsc8g|]}d|S)r<)join)r2coefs r&r;zidwtn..&s"OOOdBGGDMMOOOr'r)repeatr:r=c)r?r<)rYr]ranyvaluesrmaxnext StopIterationrrArr r reversedlist enumeraterBrrgetr?kindr complex128float64rr)r)r"r#r$ real_coeffs imag_coeffs coeff_shapesrErF key_lengthrGrHrInew_keysrhLHr?rnrrks @@@r&rrst@@ ?v||~~ ? ? ?F@ ?v||~~ ? ? ?F F > <<44V44444N!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||?@@ @ OOgd:.N.N.NOOO ? ?C 39d++A 39d++A}7ag%%w|s**aglc.A.A "  "  1E222A 1E222A'1c4>>JsOO ":s ?/D//E )rr)rN)__doc__ itertoolsrnumpyr _c99_configr_extensions._dwtrr_utilsrr r __all__r r r r]rr1r'r&rs  ******11111111BBBBBBBBBB , , ,2@2@2@2@j).).).).XGGGGT9994\\\\\\r'