ó ˽÷Xc@`sûdZddlmZmZmZddlZddlmZddl m Z m Z ddl m Z ddd d gZdd d d „Zdd d d„Zdd d d„Zdd d d„Zd„Zddd dd„Zddddd dd„ZdS(s- Functions for identifying peaks in signals. i(tdivisiontprint_functiontabsolute_importN(txrange(tcwttricker(tscoreatpercentilet argrelmint argrelmaxt argrelextrematfind_peaks_cwtitclipc C`st|ƒ|ks|dkr-tdƒ‚n|j|}tjd|ƒ}tj|jdtƒ}|j|d|d|ƒ}xtd|dƒD]{} |j|| d|d|ƒ} |j|| d|d|ƒ} |||| ƒM}|||| ƒM}|j ƒr“|Sq“W|S(sÌ Calculate the relative extrema of `data`. Relative extrema are calculated by finding locations where ``comparator(data[n], data[n+1:n+order+1])`` is True. Parameters ---------- data : ndarray Array in which to find the relative extrema. comparator : callable Function to use to compare two data points. Should take two arrays as arguments. axis : int, optional Axis over which to select from `data`. Default is 0. order : int, optional How many points on each side to use for the comparison to consider ``comparator(n,n+x)`` to be True. mode : str, optional How the edges of the vector are treated. 'wrap' (wrap around) or 'clip' (treat overflow as the same as the last (or first) element). Default 'clip'. See numpy.take Returns ------- extrema : ndarray Boolean array of the same shape as `data` that is True at an extrema, False otherwise. See also -------- argrelmax, argrelmin Examples -------- >>> testdata = np.array([1,2,3,2,1]) >>> _boolrelextrema(testdata, np.greater, axis=0) array([False, False, True, False, False], dtype=bool) isOrder must be an int >= 1itdtypetaxistmode( tintt ValueErrortshapetnptarangetonestboolttakeRtany( tdatat comparatorR torderRtdatalentlocstresultstmaintshifttplustminus((s9/tmp/pip-build-7oUkmx/scipy/scipy/signal/_peak_finding.pyt_boolrelextremas)  cC`st|tj|||ƒS(s~ Calculate the relative minima of `data`. Parameters ---------- data : ndarray Array in which to find the relative minima. axis : int, optional Axis over which to select from `data`. Default is 0. order : int, optional How many points on each side to use for the comparison to consider ``comparator(n, n+x)`` to be True. mode : str, optional How the edges of the vector are treated. Available options are 'wrap' (wrap around) or 'clip' (treat overflow as the same as the last (or first) element). Default 'clip'. See numpy.take Returns ------- extrema : tuple of ndarrays Indices of the minima in arrays of integers. ``extrema[k]`` is the array of indices of axis `k` of `data`. Note that the return value is a tuple even when `data` is one-dimensional. See Also -------- argrelextrema, argrelmax Notes ----- This function uses `argrelextrema` with np.less as comparator. .. versionadded:: 0.11.0 Examples -------- >>> from scipy.signal import argrelmin >>> x = np.array([2, 1, 2, 3, 2, 0, 1, 0]) >>> argrelmin(x) (array([1, 5]),) >>> y = np.array([[1, 2, 1, 2], ... [2, 2, 0, 0], ... [5, 3, 4, 4]]) ... >>> argrelmin(y, axis=1) (array([0, 2]), array([2, 1])) (R Rtless(RR RR((s9/tmp/pip-build-7oUkmx/scipy/scipy/signal/_peak_finding.pyRKs2cC`st|tj|||ƒS(s~ Calculate the relative maxima of `data`. Parameters ---------- data : ndarray Array in which to find the relative maxima. axis : int, optional Axis over which to select from `data`. Default is 0. order : int, optional How many points on each side to use for the comparison to consider ``comparator(n, n+x)`` to be True. mode : str, optional How the edges of the vector are treated. Available options are 'wrap' (wrap around) or 'clip' (treat overflow as the same as the last (or first) element). Default 'clip'. See `numpy.take`. Returns ------- extrema : tuple of ndarrays Indices of the maxima in arrays of integers. ``extrema[k]`` is the array of indices of axis `k` of `data`. Note that the return value is a tuple even when `data` is one-dimensional. See Also -------- argrelextrema, argrelmin Notes ----- This function uses `argrelextrema` with np.greater as comparator. .. versionadded:: 0.11.0 Examples -------- >>> from scipy.signal import argrelmax >>> x = np.array([2, 1, 2, 3, 2, 0, 1, 0]) >>> argrelmax(x) (array([3, 6]),) >>> y = np.array([[1, 2, 1, 2], ... [2, 2, 0, 0], ... [5, 3, 4, 4]]) ... >>> argrelmax(y, axis=1) (array([0]), array([1])) (R Rtgreater(RR RR((s9/tmp/pip-build-7oUkmx/scipy/scipy/signal/_peak_finding.pyR€s1cC`s%t|||||ƒ}tj|ƒS(s¿ Calculate the relative extrema of `data`. Parameters ---------- data : ndarray Array in which to find the relative extrema. comparator : callable Function to use to compare two data points. Should take two arrays as arguments. axis : int, optional Axis over which to select from `data`. Default is 0. order : int, optional How many points on each side to use for the comparison to consider ``comparator(n, n+x)`` to be True. mode : str, optional How the edges of the vector are treated. 'wrap' (wrap around) or 'clip' (treat overflow as the same as the last (or first) element). Default is 'clip'. See `numpy.take`. Returns ------- extrema : tuple of ndarrays Indices of the maxima in arrays of integers. ``extrema[k]`` is the array of indices of axis `k` of `data`. Note that the return value is a tuple even when `data` is one-dimensional. See Also -------- argrelmin, argrelmax Notes ----- .. versionadded:: 0.11.0 Examples -------- >>> from scipy.signal import argrelextrema >>> x = np.array([2, 1, 2, 3, 2, 0, 1, 0]) >>> argrelextrema(x, np.greater) (array([3, 6]),) >>> y = np.array([[1, 2, 1, 2], ... [2, 2, 0, 0], ... [5, 3, 4, 4]]) ... >>> argrelextrema(y, np.less, axis=1) (array([0, 2]), array([2, 1])) (R"Rtwhere(RRR RRR((s9/tmp/pip-build-7oUkmx/scipy/scipy/signal/_peak_finding.pyR ´s3 cC`st|ƒ|jdkr(tdƒ‚nt|tjddddƒ}tj|jddƒƒd}t|ƒdkr{gS|d}gtj||ƒdD]}|g|gdg^q}g}tj|dddƒ} tjd|jdƒ} x—| D]} | || } x|D]} | dcd7>> data = np.random.rand(5,5) >>> ridge_lines = _identify_ridge_lines(data, 1, 1) Notes ----- This function is intended to be used in conjunction with `cwt` as part of `find_peaks_cwt`. is5Max_distances must have at least as many rows as matrR iRiÿÿÿÿiN(tlenRRR"RR$R%RRtarrayt enumeratetNonetabstargmintappendRtargsortt zeros_like(tmatrt max_distancest gap_thresht all_max_colst has_relmaxt start_rowtcolt ridge_linest final_linestrowstcolstrowt this_max_colstlinetprev_ridge_colstindtdiffstclosesttnew_linet out_linestsortargs((s9/tmp/pip-build-7oUkmx/scipy/scipy/signal/_peak_finding.pyt_identify_ridge_linesìsZ. 6  *   #  i c`s-ˆjd}ˆdkr6tjˆjddƒ‰n|dkrXtj|dƒ}nt|ƒ}t|dƒ\}}ˆddd…f} tj| ƒ‰xat| ƒD]S\} } t| |dƒ} t | |||ƒ} t | | | !d|ƒˆ| tvalt window_startt window_endRL((RRIRJRKs9/tmp/pip-build-7oUkmx/scipy/scipy/signal/_peak_finding.pyt_filter_ridge_linesds #    c C`sÜtj|ƒ}|dkr1tj|dƒ}n|dkrJ|d}n|dkr_t}nt|||ƒ}t|||ƒ} t|| d|d|d|ƒ} tjg| D]} | dd^q±ƒ} | jƒ| S(sw Attempt to find the peaks in a 1-D array. The general approach is to smooth `vector` by convolving it with `wavelet(width)` for each width in `widths`. Relative maxima which appear at enough length scales, and with sufficiently high SNR, are accepted. Parameters ---------- vector : ndarray 1-D array in which to find the peaks. widths : sequence 1-D array of widths to use for calculating the CWT matrix. In general, this range should cover the expected width of peaks of interest. wavelet : callable, optional Should take two parameters and return a 1-D array to convolve with `vector`. The first parameter determines the number of points of the returned wavelet array, the second parameter is the scale (`width`) of the wavelet. Should be normalized and symmetric. Default is the ricker wavelet. max_distances : ndarray, optional At each row, a ridge line is only connected if the relative max at row[n] is within ``max_distances[n]`` from the relative max at ``row[n+1]``. Default value is ``widths/4``. gap_thresh : float, optional If a relative maximum is not found within `max_distances`, there will be a gap. A ridge line is discontinued if there are more than `gap_thresh` points without connecting a new relative maximum. Default is 2. min_length : int, optional Minimum length a ridge line needs to be acceptable. Default is ``cwt.shape[0] / 4``, ie 1/4-th the number of widths. min_snr : float, optional Minimum SNR ratio. Default 1. The signal is the value of the cwt matrix at the shortest length scale (``cwt[0, loc]``), the noise is the `noise_perc`th percentile of datapoints contained within a window of `window_size` around ``cwt[0, loc]``. noise_perc : float, optional When calculating the noise floor, percentile of data points examined below which to consider noise. Calculated using `stats.scoreatpercentile`. Default is 10. Returns ------- peaks_indices : ndarray Indices of the locations in the `vector` where peaks were found. The list is sorted. See Also -------- cwt Notes ----- This approach was designed for finding sharp peaks among noisy data, however with proper parameter selection it should function well for different peak shapes. The algorithm is as follows: 1. Perform a continuous wavelet transform on `vector`, for the supplied `widths`. This is a convolution of `vector` with `wavelet(width)` for each width in `widths`. See `cwt` 2. Identify "ridge lines" in the cwt matrix. These are relative maxima at each row, connected across adjacent rows. See identify_ridge_lines 3. Filter the ridge_lines using filter_ridge_lines. .. versionadded:: 0.11.0 References ---------- .. [1] Bioinformatics (2006) 22 (17): 2059-2065. :doi:`10.1093/bioinformatics/btl355` http://bioinformatics.oxfordjournals.org/content/22/17/2059.long Examples -------- >>> from scipy import signal >>> xs = np.arange(0, np.pi, 0.05) >>> data = np.sin(xs) >>> peakind = signal.find_peaks_cwt(data, np.arange(1,10)) >>> peakind, xs[peakind], data[peakind] ([32], array([ 1.6]), array([ 0.9995736])) ig@RIRJRTiN( RtasarrayR)RMRRRDR\tsort( tvectortwidthstwaveletR0R1RIRJRTtcwt_datR6tfilteredtxtmax_locs((s9/tmp/pip-build-7oUkmx/scipy/scipy/signal/_peak_finding.pyR ¤sW     * (t__doc__t __future__RRRtnumpyRtscipy._lib.sixRtscipy.signal.waveletsRRt scipy.statsRt__all__R"RRR RDR)R\R (((s9/tmp/pip-build-7oUkmx/scipy/scipy/signal/_peak_finding.pyts ;548 x?