U ?h,@sdZddlmZmZmZddlmZddlZddl m Z ddl m Z m Z ddlmZmZd d d d gZddd Zddd Zddd ZddZddd ZdS)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_axisdwt2idwt2dwtnidwtn symmetriccCsnt|}t|}t|dkr&td|jtt|krBtdt||||}|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)datawaveletmodeaxesZcoefsr%@/var/www/html/venv/lib/python3.8/site-packages/pywt/_multidim.pyr s)  cCsF|\}\}}}t|}t|dkr*td||||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$ZLLZHLZLHZHHr%r%r&r Ms # cs&ttsTtrTtj|||tj|||tfddDSj t dkrlt dj dkr~t d|dkrt j }fdd |D}t||}t||}d fg}t|||D]P\}}}g} |D]8\} } t| |||\} } | | d | f| d | fgq| }qt|S) aO Single-level n-dimensional Discrete Wavelet Transform. Parameters ---------- data : array_like n-dimensional array with input data. wavelet : Wavelet object or name string, or tuple of wavelets Wavelet to use. This can also be a tuple containing a wavelet to apply along each axis in ``axes``. mode : str or tuple of string, optional Signal extension mode used in the decomposition, see :ref:`Modes `. This can also be a tuple of modes specifying the mode to use on each axis in ``axes``. axes : sequence of ints, optional Axes over which to compute the DWT. Repeated elements mean the DWT will be performed multiple times along these axes. A value of ``None`` (the default) selects all axes. Axes may be repeated, but information about the original size may be lost if it is not divisible by ``2 ** nrepeats``. The reconstruction will be larger, with additional values derived according to the ``mode`` parameter. ``pywt.wavedecn`` should be used for multilevel decomposition. Returns ------- coeffs : dict Results are arranged in a dictionary, where key specifies the transform type on each dimension and value is a n-dimensional coefficients array. For example, for a 2D case the result will look something like this:: {'aa': # A(LL) - approx. on 1st dim, approx. on 2nd dim 'ad': # V(LH) - approx. on 1st dim, det. on 2nd dim 'da': # H(HL) - det. on 1st dim, approx. on 2nd dim 'dd': # D(HH) - det. on 1st dim, det. on 2nd dim } For user-specified ``axes``, the order of the characters in the dictionary keys map to the specified ``axes``. c3s&|]}||d|fVqdS)?Nr%.0k)imagrealr%r& szdwtn..objectz"Input must be a numeric array-likerzInput data must be at least 1DNcs"g|]}|dkr|jn|qSrrr*a)r!r%r& szdwtn..r3d)rrr iscomplexobjrr-r,dictkeysdtype TypeErrorrrranger r ziprextend)r!r"r#r$modeswaveletsr'axiswav new_coeffsZsubbandxZcAZcDr%)r!r,r-r&rys0-        cCsdd|D}|r$td|dd|D}|rHtd|dd|D}tt|dkrttdtd d |DS) NcSsg|]\}}|dkr|qSNr%r*r+vr%r%r&r4sz_fix_coeffs..zThe following detail coefficients were set to None: {0} For multilevel transforms, rather than setting coeffs[key] = None use coeffs[key] = np.zeros_like(coeffs[key]) cSs$g|]\}}t|tdks|qS)r)setrFr%r%r&r4szOThe following invalid keys were found in the detail coefficient dictionary: {}.cSsg|] }t|qSr%rr)r%r%r&r4srz4All detail coefficient names must have equal length.css |]\}}|t|fVqdSrE)rrrFr%r%r&r.sz_fix_coeffs..)itemsrformatr9rrr r8)r'Z missing_keysZ invalid_keysZ key_lengthsr%r%r& _fix_coeffss( rLcsltdd|D}tdd|D}t|}tstdd|Drtdd|D}tdd|D}t||||dt||||Stdd|Dz"fd d|D}t |Wnt k rt d YnXtfd d|Drt d |d kr(t }nt fdd|D}t||}t||}tttt|||D]\} \} } }| dks| krtdi} ddtd| dD} | D]}||dd }||dd }|d k rD|d k rD|j|jkrD|jjdks|jjdkr"tj}ntj}tj||d}tj||d}t||| || | |<q| }qn|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. css"|]\}}|dk r||fVqdSrEr%rFr%r%r&r.szidwtn..css"|]\}}|dk r||fVqdSrEr%rFr%r%r&r.scss|]}t|VqdSrE)rr7)r*rGr%r%r&r.scss|]\}}||jfVqdSrE)r-rFr%r%r&r.scss|]\}}||jfVqdSrE)r,rFr%r%r&r. sr(css|]}t|VqdSrErI)r*keyr%r%r&r.sc3s,|]$\}}|dk rt|kr|jVqdSrE)rshaperF)ndim_transformr%r&r.s z8`coeffs` must contain at least one non-null wavelet bandc3s|]}|kVqdSrEr%)r*s) coeff_shaper%r&r.sz,`coeffs` must all be of equal size (or None)Ncs g|]}|dkr|n|qSr0r%r2r1r%r&r4szidwtn..rz!Axis greater than data dimensionscSsg|]}d|qS)r5)join)r*Zcoefr%r%r&r4)sr)repeatr3r6c)r:r5)r8rJrLranyvaluesrmaxr9next StopIterationrr<rr r reversedlist enumerater=rZ AxisErrorrgetr:kindZ complex128Zfloat64rr )r'r"r#r$Z real_coeffsZ imag_coeffsZ coeff_shapesr?r@Z key_lengthrArBrCZnew_keysrMLHr:r%)rQrrOr&rs\       )rr)rr)rN)rN)__doc__ __future__rrr itertoolsrnumpyrZ _c99_configrZ_extensions._dwtrr Z_utilsr r __all__r r rrLrr%r%r%r&s    5 , J