o iwh"@sndZddlZddgZdddZdddZdd d Zdd d Zdd dZeeeeeedZ dddZ ddZ dS)z[ The thresholding helper module implements the most popular signal thresholding functions. N thresholdthreshold_firmcCst|}t|}tjddd||}|jdd|d||}Wdn1s-wY|dkr8|St||}t|||S)Nignoredividerminmaxoutnpasarrayabsoluteerrstatecliplesswheredatavalue substitute magnitude thresholdedcondrT/var/www/html/ecg_monitoring/venv/lib/python3.10/site-packages/pywt/_thresholding.pysofts     rcCst|}t|}tjddd|d|d}|jdd|d||}Wdn1s1wY|dkr<|St||}t|||S)zNon-negative Garrote.rrrrNrr rrrr nn_garrote!s    rcCs*t|}tt||}t|||S)N)r rrrr)rrrrrrrhard3s r cC2t|}t|rtdtt||||S)Nz,greater thresholding only supports real data)r r iscomplexobj ValueErrorrrrrrrrrgreater9  r%cCr!)Nz)less thresholding only supports real data)r rr"r#rr%r$rrrr@r&r)rr r%rgarrotegarottec CsLz t||||WSty%ddttD}tdd|w)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|dVqdS)'Nr).0keyrrr szthreshold..z.The mode parameter only takes values from: {}.z, )thresholding_optionsKeyErrorsortedkeysr#formatjoin)rrmoderr0rrrrQsR   cCs|dkrtd||krtdt|}t|}tjdd"||}|d|||}|jdd|d||}Wdn1sEwYt||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.rrrNr)r#r rrrrrany)r value_low value_highrvdiffr large_valsrrrrs$8    )r)rr) __doc__numpyr __all__rrr r%rr-rrrrrrs"      \