U hY"@sdZddlmZmZmZddlZddgZdddZddd Z dd d Z dd d Z dddZ ee e e e e dZ dddZddZdS)z[ The thresholding helper module implements the most popular signal thresholding functions. )divisionprint_functionabsolute_importN thresholdthreshold_firmc Cszt|}t|}tjdd*d||}|jdd|d||}W5QRX|dkr\|St||}t|||SdS)Nignoredividerminmaxoutnpasarrayabsoluteerrstatecliplesswheredatavalue substitute magnitude thresholdedcondr6/tmp/pip-unpacked-wheel-mu97bu1x/pywt/_thresholding.pysofts    r c Cst|}t|}tjdd2d|d|d}|jdd|d||}W5QRX|dkrd|St||}t|||SdS)zNon-negative Garrote.rrr rNr rrrrr nn_garrote"s   r"cCs*t|}tt||}t|||S)N)rrrrr)rrrrrrrhard4s r#cCs2t|}t|rtdtt||||S)Nz,greater thresholding only supports real data)rr iscomplexobj ValueErrorrrrrrrrrgreater:s  r'cCs2t|}t|rtdtt||||S)Nz)less thresholding only supports real data)rrr$r%rr'r&rrrrAs  r)r r#r'rZgarroteZgarottec CsVzt||||WStk rPddttD}tdd|YnXdS)a 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. ]) css|]}d|VqdS)z'{0}'N)format).0keyrrr szthreshold..z/The mode parameter only takes values from: {0}.z, N)thresholding_optionsKeyErrorsortedkeysr%r(join)rrmoderr/rrrrRsR c Cs|dkrtd||kr tdt|}t|}tjdd:||}|d|||}|jdd|d||}W5QRXt||k}t|dr||||<|S) a_Firm threshold. The approach is intermediate between soft and hard thresholding [1]_. It behaves the same as soft-thresholding for values below `value_low` and the same as hard-thresholding for values above `thresh_high`. For intermediate values, the thresholded value is in between that corresponding to soft or hard thresholding. Parameters ---------- data : array-like The data to threshold. This can be either real or complex-valued. value_low : float Any values smaller then `value_low` will be set to zero. value_high : float Any values larger than `value_high` will not be modified. Notes ----- This thresholding technique is also known as semi-soft thresholding [2]_. For each value, `x`, in `data`. This function computes:: if np.abs(x) <= value_low: return 0 elif np.abs(x) > 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 rzvalue_low must be non-negative.z6value_high must be greater than or equal to value_low.rrr Nr )r%rrrrrrany)rZ value_lowZ value_highrZvdiffrZ large_valsrrrrs"8   )r)r)r)r)r)r r)__doc__ __future__rrrZnumpyr__all__r r"r#r'rr,rrrrrrs"      \