+ [j)xRt^RIHt^RIt^RIHtHt^RIH t H t H t .R Ot R Rlt R RltR RltRtR R ltR#) zP 2D and nD Discrete Wavelet Transforms and Inverse Discrete Wavelet Transforms. )productN)dwt_axis idwt_axis) AxisError_modes_per_axis_wavelets_per_axiscJ\V4p\P!V4p\V4^8wd \ R4hVP \\P !V448d \ R4h\WW#4pVR,VR,VR,VR,33#)ae 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 ValueErrorndimuniquedwtn)datawaveletmodeaxescoefss&&&& O/home/luca/screen-checking/.venv/lib/python3.14/site-packages/pywt/_multidim.pydwt2rsR ;D ::d D 4yA~*++ yy3ryy'' ! !  +E ;teDk5;? ??cVwpwrVp\V4p\V4^8wd \R4hRVRVRVRV/p\WW#4#)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.]]) r r r r r )rrridwtn)coeffsrrrLLHLLHHHs&&&& ridwt2r%JsVFB  ;D 4yA~*++Bb$D" 5F $ --rcP\P!V4pVP\P!R48Xd \R4hVP^8d \ R4hVf\ VP4pVUu.uFqD^8dW@P,MTNK pp\W#4p\W4pRV3.p\W6V4FHwrp.p VF8wr\WW(4wrV PV R,V 3V R,V3.4K: T pKJ \V4#uupi)a 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``. objectz"Input must be a numeric array-likezInput data must be at least 1Dad) rrdtype TypeErrorrrrangerrziprextenddict)rrrrr)modeswaveletsr axiswav new_coeffssubbandxcAcDs&&&& rrrvsZ ::d D zzRXXh''<== yy1}9:: |TYY37 84aUA M )4D 8 D 'E!'0H4j\Ftu54  JGad1FB   # r2 '# r24 5! 6 < 9s#D#c^VP4UUu.uF wrVeK VNK pppV'd\RV R24hVP4UUu.uF"wr\V4\R48:dK VNK$ pppV'd\RV R24hVUu.uFp\V4NK pp\\P !V44^8d \R4hVP4UUu/uFwrV\P !V4bK upp#uuppiuuppiuupiuuppi)Nz4The 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]) r zLThe following invalid keys were found in the detail coefficient dictionary: .z4All detail coefficient names must have equal length.)itemsrsetrrrr)r kv missing_keys invalid_keys key_lengthss& r _fix_coeffsrCs"(,,.>.$!AAA.L> Cn; ;< <#),,.-.$!A#d)+A.L- ''3nA 78 8$**6a3q66K* 299[ !"Q& BD D*0 8Arzz!}  88-?-+ 9s"DDD6DD$2"D)c aaVP4UUu/uF wrEVfK WEbK pppVP4UUu/uF wrEVfK WEbK ppp\V4p\RV44oV3RlVP44p\V4o\ ;QJdT3RlT4F 'gK RM RM!T3RlT44'd \ R4hTf\S4pSpM \S4pTUu.uFq^8d Y,MTNK pp\Y#4p \Y4p \\\\Y:T 4444EFGwp wrpT ^8gY8d \R 4h/p\!R T R 7Uu.uFpR P#T4NK ppTFpTP%TR ,R4pTP%TR,R4pTeTeTP&TP&8wdTP&P(R8XgTP&P(R8Xd\*P,pM\*P.p\*P0!TTR7p\*P0!TTR7p\3TTYT 4TT&K TpEKJ TR ,#uuppiuuppi \d \ R4hi;iuupiuupi)a Single-level n-dimensional Inverse Discrete Wavelet Transform. Parameters ---------- coeffs: dict Dictionary as in output of ``dwtn``. Missing or ``None`` items will be treated as zeros. wavelet : Wavelet object or name string, or tuple of wavelets Wavelet to use. This can also be a tuple containing a wavelet to apply along each axis in ``axes``. mode : str or list of string, optional Signal extension mode used in the decomposition, see :ref:`Modes `. This can also be a tuple of modes specifying the mode to use on each axis in ``axes``. axes : sequence of ints, optional Axes over which to compute the IDWT. Repeated elements mean the IDWT will be performed multiple times along these axes. A value of ``None`` (the default) selects all axes. For the most accurate reconstruction, the axes should be provided in the same order as they were provided to ``dwtn``. Returns ------- data: ndarray Original signal reconstructed from input data. Nc38"TFp\V4xK R#5iN)r).0keys& r idwtn..s4VcSVsc3p<"TF+wrVfK \V4S8XgKVPxK- R#5irF)rshape)rGr>r?ndim_transforms& rrIrJs3GNDA -0V~-E Ns 6 66z8`coeffs` must contain at least one non-null wavelet bandc3,<"TF qS8gxK R#5irF)rGs coeff_shapes& rrIrJ s 2\ \sTFz,`coeffs` must all be of equal size (or None)z!Axis greater than data dimensionsr )repeatr(r)r*c)r+)r<rCmaxnext StopIterationranyr-rrrreversedlist enumerater.rrjoingetr+kindr complex128float64rr)r rrrr>r? coeff_shapesrr)r1r2 key_lengthr3r4r5coefnew_keysrHLHr+rQrMs&&&& @@rrrsz@ &||~ ?~tqdad~F ? &||~ ?~tqdad~F ? F4V44N!GFLLNG <(  s 2\ 2sss 2\ 222GHH |^$;.2 3dAAH1 $dD 3 D 'E!'0H)1 3tu56 7*9% %T !8t|?@ @ .5d:.NO.NdBGGDM.NOC 39d+A 39d+A}77agg%ww||s*aggllc.A "  "  1E2A 1E2A'1c>JsO+*9. ":m@@ ! ! !! 4Ps-J1J1J7 J73%J=KK=K)rr%rr) symmetric))rfN)__doc__ itertoolsrnumpyr_extensions._dwtrr_utilsrrr__all__rr%rrCrrOrrros?  1BB ,2@j).XCL94Vr