a Sic @sdZddlZddlmZddlZddlmZmZm Z ddZ ddZ d5d d Z d6d d Z d7d dZddZedd8ddZd9ddZd:ddZd;ddZejjddddejdd,d-Z"ejd.d/ee ddd0dfd1d2Z#Gd3d4d4Z$dS)?a Numerical Python functions written for compatibility with MATLAB commands with the same names. Most numerical Python functions can be found in the `NumPy`_ and `SciPy`_ libraries. What remains here is code for performing spectral computations and kernel density estimations. .. _NumPy: https://numpy.org .. _SciPy: https://www.scipy.org Spectral functions ------------------ `cohere` Coherence (normalized cross spectral density) `csd` Cross spectral density using Welch's average periodogram `detrend` Remove the mean or best fit line from an array `psd` Power spectral density using Welch's average periodogram `specgram` Spectrogram (spectrum over segments of time) `complex_spectrum` Return the complex-valued frequency spectrum of a signal `magnitude_spectrum` Return the magnitude of the frequency spectrum of a signal `angle_spectrum` Return the angle (wrapped phase) of the frequency spectrum of a signal `phase_spectrum` Return the phase (unwrapped angle) of the frequency spectrum of a signal `detrend_mean` Remove the mean from a line. `detrend_linear` Remove the best fit line from a line. `detrend_none` Return the original line. `stride_windows` Get all windows in an array in a memory-efficient manner N)Number)_api _docstringcbookcCstt||S)z Return *x* times the Hanning (or Hann) window of len(*x*). See Also -------- window_none : Another window algorithm. )nphanninglenxr K/var/www/html/django/DPS/env/lib/python3.9/site-packages/matplotlib/mlab.pywindow_hanning=sr cCs|S)zz No window function; simply return *x*. See Also -------- window_hanning : Another window algorithm. r r r r r window_noneHsrcCs|dus|dvrt|t|dS|dkr4t|t|dS|dkrJt|t|dSt|rt|}|dur|d|jkrtd|d|dur|jd ks|s|jdkr||Sz|||d WSt ytj |||d YS0ntd |d dS)al Return *x* with its trend removed. Parameters ---------- x : array or sequence Array or sequence containing the data. key : {'default', 'constant', 'mean', 'linear', 'none'} or function The detrending algorithm to use. 'default', 'mean', and 'constant' are the same as `detrend_mean`. 'linear' is the same as `detrend_linear`. 'none' is the same as `detrend_none`. The default is 'mean'. See the corresponding functions for more details regarding the algorithms. Can also be a function that carries out the detrend operation. axis : int The axis along which to do the detrending. See Also -------- detrend_mean : Implementation of the 'mean' algorithm. detrend_linear : Implementation of the 'linear' algorithm. detrend_none : Implementation of the 'none' algorithm. N)constantmeandefault)keyaxislinearnonezaxis(=z) out of boundsrr)rarrzUnknown value for key: zH, must be one of: 'default', 'constant', 'mean', 'linear', or a function) detrend detrend_meandetrend_linear detrend_nonecallablerasarrayndim ValueError TypeErrorapply_along_axis)r rrr r r rSs&    rcCs>t|}|dur,|d|jkr,td|||j|ddS)a Return *x* minus the mean(*x*). Parameters ---------- x : array or sequence Array or sequence containing the data Can have any dimensionality axis : int The axis along which to take the mean. See `numpy.mean` for a description of this argument. See Also -------- detrend_linear : Another detrend algorithm. detrend_none : Another detrend algorithm. detrend : A wrapper around all the detrend algorithms. Nrzaxis(=%s) out of boundsT)keepdims)rrrr rr rr r r rs  rcCs|S)a Return *x*: no detrending. Parameters ---------- x : any object An object containing the data axis : int This parameter is ignored. It is included for compatibility with detrend_mean See Also -------- detrend_mean : Another detrend algorithm. detrend_linear : Another detrend algorithm. detrend : A wrapper around all the detrend algorithms. r r$r r r rsrcCst|}|jdkrtd|js2tjd|jdStj|jtd}tj ||dd}|d|d}| || }||||S)ab Return *x* minus best fit line; 'linear' detrending. Parameters ---------- y : 0-D or 1-D array or sequence Array or sequence containing the data See Also -------- detrend_mean : Another detrend algorithm. detrend_none : Another detrend algorithm. detrend : A wrapper around all the detrend algorithms. rzy cannot have ndim > 1g)dtype)bias)rr)rr) rrrr arrayr%arangesizefloatcovr)yr Cbar r r rs  rz3.6cCs0|dur d}t|dkr"tdt||||S)al Get all windows of *x* with length *n* as a single array, using strides to avoid data duplication. .. warning:: It is not safe to write to the output array. Multiple elements may point to the same piece of memory, so modifying one value may change others. Parameters ---------- x : 1D array or sequence Array or sequence containing the data. n : int The number of data points in each window. noverlap : int, default: 0 (no overlap) The overlap between adjacent windows. axis : int The axis along which the windows will run. References ---------- `stackoverflow: Rolling window for 1D arrays in Numpy? `_ `stackoverflow: Using strides for an efficient moving average filter `_ Nrrz%only 1-dimensional arrays can be used)rrr _stride_windows)r nnoverlaprr r r stride_windowss r3cCsHttjjdrJ|dkrJ||kr&tdtjjj||dddd||jS||krZtd|dkrjtdt|}|dkr|dkr|dkr|tjS|tjjS||j krtdt |}t |}||}|dkr||j d||f}|j d||j df}n.|j d|||f}||j d|j df}tjjj |||d S) Nsliding_window_viewrznoverlap must be less than nrrzn cannot be less than 1z(n cannot be greater than the length of x)shapestrides)hasattrrlib stride_tricksr r4Trnewaxisr)intr6r7 as_strided)r r1r2rstepr6r7r r r r0s8      r0c CsT|durd} n||u} |dur"d}|dur.d}|dur:t}|durFt}|durRd}| dusb| dkrfd} tjgd| d | s| dkrtd t|}| st|}|dus|dkrt|rd }nd }tjgd |dt||krt|} t ||}d|| d<| s= signal length (=z).rfrC)rr warn_externalrerg) r r[r\rr^r2r_rKr`rHrhrbrdr r r specgrams(>    rrrAr@rc  Cst|d|krtdt||||||||| \} } t||||||||| \} } t|||||||||| \} } t| d| | }|| fS)a The coherence between *x* and *y*. Coherence is the normalized cross spectral density: .. math:: C_{xy} = \frac{|P_{xy}|^2}{P_{xx}P_{yy}} Parameters ---------- x, y Array or sequence containing the data %(Spectral)s %(PSD)s noverlap : int, default: 0 (no overlap) The number of points of overlap between segments. Returns ------- Cxy : 1-D array The coherence vector. freqs : 1-D array The frequencies for the elements in *Cxy*. See Also -------- :func:`psd`, :func:`csd` : For information about the methods used to compute :math:`P_{xy}`, :math:`P_{xx}` and :math:`P_{yy}`. r@zvCoherence is calculated by averaging over *NFFT* length segments. Your signal is too short for your choice of *NFFT*.)rr rBrlrrV)r r,r[r\rr^r2r_rKr`rmfZPyyrnZCxyr r r coheres$rtc@s:eZdZdZd ddZddZddZeZd d ZeZ dS) GaussianKDEap Representation of a kernel-density estimate using Gaussian kernels. Parameters ---------- dataset : array-like Datapoints to estimate from. In case of univariate data this is a 1-D array, otherwise a 2D array with shape (# of dims, # of data). bw_method : str, scalar or callable, optional The method used to calculate the estimator bandwidth. This can be 'scott', 'silverman', a scalar constant or a callable. If a scalar, this will be used directly as `kde.factor`. If a callable, it should take a `GaussianKDE` instance as only parameter and return a scalar. If None (default), 'scott' is used. Attributes ---------- dataset : ndarray The dataset passed to the constructor. dim : int Number of dimensions. num_dp : int Number of datapoints. factor : float The bandwidth factor, obtained from `kde.covariance_factor`, with which the covariance matrix is multiplied. covariance : ndarray The covariance matrix of *dataset*, scaled by the calculated bandwidth (`kde.factor`). inv_cov : ndarray The inverse of *covariance*. Methods ------- kde.evaluate(points) : ndarray Evaluate the estimated pdf on a provided set of points. kde(points) : ndarray Same as kde.evaluate(points) NcsDt|_tjjdks&tdtjj\__durFnrt dr\j _ n\t drrj _ nFttrd_fdd_ n&tr_fdd_ ntd  _td sttjjdd d _tjj_jjd _jjd _ttjd tjjj_dS)Nrz.`dataset` input should have multiple elements.scottZ silvermanz use constantcsSNr r ) bw_methodr r z&GaussianKDE.__init__..cs Srw) _bw_methodr selfr r ryrzzB`bw_method` should be 'scott', 'silverman', a scalar or a callableZ _data_inv_covF)rowvarr&r@)r atleast_2ddatasetr'r)r r6dimnum_dpr _str_equal scotts_factorcovariance_factorsilverman_factor isinstancerr{rfactorr8r+Zdata_covariancelinalginvZ data_inv_cov covarianceinv_covsqrtdetpi norm_factor)r}rrxr )rxr}r __init__ws@        zGaussianKDE.__init__cCst|jd|jdS)Nrpowerrrr|r r r rszGaussianKDE.scotts_factorcCs&t|j|jddd|jdS)NrLg@rrrr|r r r rszGaussianKDE.silverman_factorc Cst|}t|j\}}||jkr6td||jt|}||jkrt |jD]R}|j dd|tj f|}t |j |}tj||ddd}|t| }qTnft |D]\}|j |dd|tj f}t |j |}tj||ddd}tjt| dd||<q||j}|S)a Evaluate the estimated pdf on a set of points. Parameters ---------- points : (# of dimensions, # of points)-array Alternatively, a (# of dimensions,) vector can be passed in and treated as a single point. Returns ------- (# of points,)-array The values at each point. Raises ------ ValueError : if the dimensionality of the input points is different than the dimensionality of the KDE. z2points have dimension {}, dataset has dimension {}NrrrL)rrr'r6rr formatzerosrrangerr<dotrrWexpr) r}pointsrZnum_mraidiffZtdiffenergyr r r evaluates(      zGaussianKDE.evaluate)N) __name__ __module__ __qualname____doc__rrrrr__call__r r r r ruKs+ )1ru)NN)N)N)Nr)rr) NNNNNNNNNN)NNNN)NNNNNNNN)NNNNNNNN) NNNNNNNNN)%r functoolsnumbersrnumpyr matplotlibrrrr rrrrr deprecatedr3r0rerjinterpdupdatededent_interpdrBrlZ_single_spectrum_docspartialZcomplex_spectrumrparamsmagnitude_spectrumangle_spectrumphase_spectrumrrrtrur r r r s4   1  " $ &   : 7 ?&     R 1