ó Uķ\c@`sÂdZddlmZmZmZddlZddgZdd„Zdd„Z dd„Z dd „Z dd „Z ied 6e d 6e d 6e d6e d6e d6Z d dd„Zd„ZdS(s[ The thresholding helper module implements the most popular signal thresholding functions. i(tdivisiontprint_functiontabsolute_importNt thresholdtthreshold_firmc C`sĪtj|ƒ}tj|ƒ}tjddƒ9d||}|jddddd|ƒ||}WdQX|dkr{|Stj||ƒ}tj|||ƒSdS(Ntdividetignoreitminitmaxtout(tnptasarraytabsoluteterrstatetcliptNonetlesstwhere(tdatatvaluet substitutet magnitudet thresholdedtcond((s1lib/python2.7/site-packages/pywt/_thresholding.pytsofts c C`sŽtj|ƒ}tj|ƒ}tjddƒAd|d|d}|jdddd d|ƒ||}Wd QX|dkrƒ|Stj||ƒ}tj|||ƒSd S( sNon-negative Garrote.RRiiRiRR N(R R R R RRRR(RRRRRR((s1lib/python2.7/site-packages/pywt/_thresholding.pyt nn_garrote"s cC`s=tj|ƒ}tjtj|ƒ|ƒ}tj|||ƒS(N(R R RR R(RRRR((s1lib/python2.7/site-packages/pywt/_thresholding.pythard4scC`sLtj|ƒ}tj|ƒr-tdƒ‚ntjtj||ƒ||ƒS(Ns,greater thresholding only supports real data(R R t iscomplexobjt ValueErrorRR(RRR((s1lib/python2.7/site-packages/pywt/_thresholding.pytgreater:scC`sLtj|ƒ}tj|ƒr-tdƒ‚ntjtj||ƒ||ƒS(Ns)less thresholding only supports real data(R R RRRR(RRR((s1lib/python2.7/site-packages/pywt/_thresholding.pyRAsRRRRtgarrotetgarottecC`sjyt||||ƒSWnKtk red„ttjƒƒDƒ}tdjdj|ƒƒƒ‚nXdS(sĸ Thresholds the input data depending on the mode argument. In ``soft`` thresholding [1]_, data values with absolute value less than `param` are replaced with `substitute`. Data values with absolute value greater or equal to the thresholding value are shrunk toward zero by `value`. In other words, the new value is ``data/np.abs(data) * np.maximum(np.abs(data) - value, 0)``. In ``hard`` thresholding, the data values where their absolute value is less than the value param are replaced with `substitute`. Data values with absolute value greater or equal to the thresholding value stay untouched. ``garrote`` corresponds to the Non-negative garrote threshold [2]_, [3]_. It is intermediate between ``hard`` and ``soft`` thresholding. It behaves like soft thresholding for small data values and approaches hard thresholding for large data values. In ``greater`` thresholding, the data is replaced with `substitute` where data is below the thresholding value. Greater data values pass untouched. In ``less`` thresholding, the data is replaced with `substitute` where data is above the thresholding value. Lesser data values pass untouched. Both ``hard`` and ``soft`` thresholding also support complex-valued data. Parameters ---------- data : array_like Numeric data. value : scalar Thresholding value. mode : {'soft', 'hard', 'garrote', 'greater', 'less'} Decides the type of thresholding to be applied on input data. Default is 'soft'. substitute : float, optional Substitute value (default: 0). Returns ------- output : array Thresholded array. See Also -------- threshold_firm References ---------- .. [1] D.L. Donoho and I.M. Johnstone. Ideal Spatial Adaptation via Wavelet Shrinkage. Biometrika. Vol. 81, No. 3, pp.425-455, 1994. DOI:10.1093/biomet/81.3.425 .. [2] L. Breiman. Better Subset Regression Using the Nonnegative Garrote. Technometrics, Vol. 37, pp. 373-384, 1995. DOI:10.2307/1269730 .. [3] H-Y. Gao. Wavelet Shrinkage Denoising Using the Non-Negative Garrote. Journal of Computational and Graphical Statistics Vol. 7, No. 4, pp.469-488. 1998. DOI:10.1080/10618600.1998.10474789 Examples -------- >>> import numpy as np >>> import pywt >>> data = np.linspace(1, 4, 7) >>> data array([ 1. , 1.5, 2. , 2.5, 3. , 3.5, 4. ]) >>> pywt.threshold(data, 2, 'soft') array([ 0. , 0. , 0. , 0.5, 1. , 1.5, 2. ]) >>> pywt.threshold(data, 2, 'hard') array([ 0. , 0. , 2. , 2.5, 3. , 3.5, 4. ]) >>> pywt.threshold(data, 2, 'garrote') array([ 0. , 0. , 0. , 0.9 , 1.66666667, 2.35714286, 3. ]) >>> pywt.threshold(data, 2, 'greater') array([ 0. , 0. , 2. , 2.5, 3. , 3.5, 4. ]) >>> pywt.threshold(data, 2, 'less') array([ 1. , 1.5, 2. , 0. , 0. , 0. , 0. ]) cs`s|]}dj|ƒVqdS(s'{0}'N(tformat(t.0tkey((s1lib/python2.7/site-packages/pywt/_thresholding.pys Ļss/The mode parameter only takes values from: {0}.s, N(tthresholding_optionstKeyErrortsortedtkeysRR tjoin(RRtmodeRR&((s1lib/python2.7/site-packages/pywt/_thresholding.pyRRsR  c C`sð|dkrtdƒ‚n||kr6tdƒ‚ntj|ƒ}tj|ƒ}tjddƒK||}|d|||}|jdddd d |ƒ||}Wd QXtj||kƒ}tj|dƒrė|||| value_high: return x elif value_low < np.abs(x) and np.abs(x) <= value_high: return x * value_high * (1 - value_low/x)/(value_high - value_low) ``firm`` is a continuous function (like soft thresholding), but is unbiased for large values (like hard thresholding). If ``value_high == value_low`` this function becomes hard-thresholding. If ``value_high`` is infinity, this function becomes soft-thresholding. Returns ------- val_new : array-like The values after firm thresholding at the specified thresholds. See Also -------- threshold References ---------- .. [1] H.-Y. Gao and A.G. Bruce. Waveshrink with firm shrinkage. Statistica Sinica, Vol. 7, pp. 855-874, 1997. .. [2] A. Bruce and H-Y. Gao. WaveShrink: Shrinkage Functions and Thresholds. Proc. SPIE 2569, Wavelet Applications in Signal and Image Processing III, 1995. DOI:10.1117/12.217582 isvalue_low must be non-negative.s6value_high must be greater than or equal to value_low.RRiRRR N( RR R R R RRRtany(Rt value_lowt value_highRtvdiffRt large_vals((s1lib/python2.7/site-packages/pywt/_thresholding.pyRŪs 8    (t__doc__t __future__RRRtnumpyR t__all__RRRRRR#RR(((s1lib/python2.7/site-packages/pywt/_thresholding.pyt s          \