B †\J,@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 Modes (default: 'symmetric'). 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.]]) zExpected 2 axesz8Input array has fewer dimensions than the specified axesaadaaddd)tuplenpasarraylen ValueErrorndimuniquer)datawaveletmodeaxesZcoefsr$-lib/python3.7/site-packages/pywt/_multidim.pyr s)  cCsF|\}\}}}t|}t|dkr*td||||d}t||||S)a 2-D Inverse Discrete Wavelet Transform. Reconstructs data from coefficient arrays. Parameters ---------- coeffs : tuple (cA, (cH, cV, cD)) A tuple with approximation coefficients and three details coefficients 2D arrays like from `dwt2`. If any of these components are set to ``None``, it will be treated as zeros. wavelet : Wavelet object or name string, or 2-tuple of wavelets Wavelet to use. This can also be a tuple containing a wavelet to apply along each axis in ``axes``. mode : str or 2-tuple of strings, optional Signal extension mode, see Modes (default: 'symmetric'). This can also be a tuple of modes specifying the mode to use on each axis in ``axes``. axes : 2-tuple of ints, optional Axes over which to compute the IDWT. Repeated elements mean the IDWT will be performed multiple times along these axes. Examples -------- >>> import numpy as np >>> import pywt >>> data = np.array([[1,2], [3,4]], dtype=np.float64) >>> coeffs = pywt.dwt2(data, 'haar') >>> pywt.idwt2(coeffs, 'haar') array([[ 1., 2.], [ 3., 4.]]) rzExpected 2 axes)rrrr)rrrr)coeffsr!r"r#ZLLZHLZLHZHHr$r$r%r Ms # cs.ttsTtrTtj|||tj|||tfddDSj t dkrlt dj dkr~t d|dkrt j }fdd |D}t||}t||}d fg}xdt|||D]T\}}}g} x@|D]8\} } t| |||\} } | | d | f| d | fgqW| }qWt|S) aT Single-level n-dimensional Discrete Wavelet Transform. Parameters ---------- data : array_like n-dimensional array with input data. wavelet : Wavelet object or name string, or tuple of wavelets Wavelet to use. This can also be a tuple containing a wavelet to apply along each axis in ``axes``. mode : str or tuple of string, optional Signal extension mode used in the decomposition, see Modes (default: 'symmetric'). This can also be a tuple of modes specifying the mode to use on each axis in ``axes``. axes : sequence of ints, optional Axes over which to compute the DWT. Repeated elements mean the DWT will be performed multiple times along these axes. A value of ``None`` (the default) selects all axes. Axes may be repeated, but information about the original size may be lost if it is not divisible by ``2 ** nrepeats``. The reconstruction will be larger, with additional values derived according to the ``mode`` parameter. ``pywt.wavedecn`` should be used for multilevel decomposition. Returns ------- coeffs : dict Results are arranged in a dictionary, where key specifies the transform type on each dimension and value is a n-dimensional coefficients array. For example, for a 2D case the result will look something like this:: {'aa': # A(LL) - approx. on 1st dim, approx. on 2nd dim 'ad': # V(LH) - approx. on 1st dim, det. on 2nd dim 'da': # H(HL) - det. on 1st dim, approx. on 2nd dim 'dd': # D(HH) - det. on 1st dim, det. on 2nd dim } For user-specified ``axes``, the order of the characters in the dictionary keys map to the specified ``axes``. c3s&|]}||d|fVqdS)y?Nr$).0k)imagrealr$r% szdwtn..objectz"Input must be a numeric array-likerzInput data must be at least 1DNcs"g|]}|dkr|jn|qS)r)r)r'a)r r$r% szdwtn..r-d)rrr iscomplexobjrr*r)dictkeysdtype TypeErrorrrranger r ziprextend)r r!r"r#modeswaveletsr&axiswav new_coeffsZsubbandxZcAZcDr$)r r)r*r%rys.-      cCsdd|D}|r$td|dd|D}|rHtd|dd|D}tt|dkrttdtd d |DS) NcSsg|]\}}|dkr|qS)Nr$)r'r(vr$r$r%r.sz_fix_coeffs..zThe following detail coefficients were set to None: {0} For multilevel transforms, rather than setting coeffs[key] = None use coeffs[key] = np.zeros_like(coeffs[key]) cSs$g|]\}}t|tdks|qS)r)set)r'r(r?r$r$r%r.szOThe following invalid keys were found in the detail coefficient dictionary: {}.cSsg|] }t|qSr$)r)r'r(r$r$r%r.srz4All detail coefficient names must have equal length.css |]\}}|t|fVqdS)N)rr)r'r(r?r$r$r%r+sz_fix_coeffs..)itemsrformatr3rrrr2)r&Z missing_keysZ invalid_keysZ key_lengthsr$r$r% _fix_coeffssrCcs\tdd|D}t|}tstdd|Drtdd|D}tdd|D}t||||dt||||Stdd|Dy"fdd|D}t |Wnt k rt d YnXtfd d|Drt d |d krt }nt fd d|D}t||}t||}xtttt|||D]\} \} } }| dks|| krt di} ddtd| dD} x| D]}||dd }||dd }|d k r0|d k r0|j|jkr0|jjdks|jjdkrtj}ntj}tj||d}tj||d}t||| || | |<qW| }qZW|dS)a[ Single-level n-dimensional Inverse Discrete Wavelet Transform. Parameters ---------- coeffs: dict Dictionary as in output of ``dwtn``. Missing or ``None`` items will be treated as zeros. wavelet : Wavelet object or name string, or tuple of wavelets Wavelet to use. This can also be a tuple containing a wavelet to apply along each axis in ``axes``. mode : str or list of string, optional Signal extension mode used in the decomposition, see Modes (default: 'symmetric'). This can also be a tuple of modes specifying the mode to use on each axis in ``axes``. axes : sequence of ints, optional Axes over which to compute the IDWT. Repeated elements mean the IDWT will be performed multiple times along these axes. A value of ``None`` (the default) selects all axes. For the most accurate reconstruction, the axes should be provided in the same order as they were provided to ``dwtn``. Returns ------- data: ndarray Original signal reconstructed from input data. css"|]\}}|dk r||fVqdS)Nr$)r'r(r?r$r$r%r+szidwtn..css|]}t|VqdS)N)rr1)r'r?r$r$r%r+scss|]\}}||jfVqdS)N)r*)r'r(r?r$r$r%r+scss|]\}}||jfVqdS)N)r))r'r(r?r$r$r%r+sy?css|]}t|VqdS)N)r)r'keyr$r$r%r+ sc3s,|]$\}}|dk rt|kr|jVqdS)N)rshape)r'r(r?)ndim_transformr$r%r+sz8`coeffs` must contain at least one non-null wavelet bandc3s|]}|kVqdS)Nr$)r's) coeff_shaper$r%r+sz,`coeffs` must all be of equal size (or None)Ncs g|]}|dkr|n|qS)rr$)r'r-)rr$r%r.szidwtn..rz!Axis greater than data dimensionscSsg|]}d|qS)r/)join)r'Zcoefr$r$r%r.&sr)repeatr-r0c)r4r/)r2rArCranyvaluesrmaxr3next StopIterationrr6rr r reversedlist enumerater7rgetr4ZkindrZ complex128Zfloat64rr )r&r!r"r#Z real_coeffsZ imag_coeffsZ coeff_shapesr9r:Z key_lengthr;r<r=Znew_keysrDLHr4r$)rHrrFr%rsT      $  )rr)rr)rN)rN)__doc__Z __future__rrr itertoolsrZnumpyrZ _c99_configrZ_extensions._dwtrr Z_utilsr r __all__r r rrCrr$r$r$r%s    5 , J