7d2EddlZddlmZddlmZddlmZmZm Z ddgZ ddgZ ddl m Zd Zn#e$rd Zed ZYnwxYwGd d eZdS)N) interpolate) argrelextrema)TupleOptionalIterableconvexconcave increasing decreasingTFz\This function needs Matplotlib to be executed. Please run command `pip install kneed[plot]` c.eZdZdZ d'deed eed ed ed ed ededefdZ e deedeefdZ e d eed ed edefdZ dZ d(deeeefdedeedeefdZ d)deeeefdedeedeefdZedZed Zed!Zed"Zed#Zed$Zed%Zed&ZdS)* KneeLocatora0 Once instantiated, this class attempts to find the point of maximum curvature on a line. The knee is accessible via the `.knee` attribute. :param x: x values, must be the same length as y. :type x: 1D array of shape (`number_of_y_values`,) or list :param y: y values, must be the same length as x. :type y: 1D array of shape (`number_of_y_values`,) or list :param S: Sensitivity, the number of minimum number of data points below the local distance maximum before calling a knee. The original paper suggests default of 1.0 :type S: float :param curve: If 'concave', algorithm will detect knees. If 'convex', it will detect elbows. :type curve: str :param direction: one of {"increasing", "decreasing"} :type direction: str :param interp_method: one of {"interp1d", "polynomial"} :type interp_method: str :param online: kneed will correct old knee points if True, will return first knee if False :type online: bool :param polynomial_degree: The degree of the fitting polynomial. Only used when interp_method="polynomial". This argument is passed to numpy polyfit `deg` parameter. :type polynomial_degree: int :ivar x: x values. :vartype x: array-like :ivar y: y values. :vartype y: array-like :ivar S: Sensitivity, original paper suggests default of 1.0 :vartype S: integer :ivar curve: If 'concave', algorithm will detect knees. If 'convex', it will detect elbows. :vartype curve: str :ivar direction: one of {"increasing", "decreasing"} :vartype direction: str :ivar interp_method: one of {"interp1d", "polynomial"} :vartype interp_method: str :ivar online: kneed will correct old knee points if True, will return first knee if False :vartype online: str :ivar polynomial_degree: The degree of the fitting polynomial. Only used when interp_method="polynomial". This argument is passed to numpy polyfit `deg` parameter. :vartype polynomial_degree: int :ivar N: The number of `x` values in the :vartype N: integer :ivar all_knees: A set containing all the x values of the identified knee points. :vartype all_knees: set :ivar all_norm_knees: A set containing all the normalized x values of the identified knee points. :vartype all_norm_knees: set :ivar all_knees_y: A list containing all the y values of the identified knee points. :vartype all_knees_y: list :ivar all_norm_knees_y: A list containing all the normalized y values of the identified knee points. :vartype all_norm_knees_y: list :ivar Ds_y: The y values from the fitted spline. :vartype Ds_y: numpy array :ivar x_normalized: The normalized x values. :vartype x_normalized: numpy array :ivar y_normalized: The normalized y values. :vartype y_normalized: numpy array :ivar x_difference: The x values of the difference curve. :vartype x_difference: numpy array :ivar y_difference: The y values of the difference curve. :vartype y_difference: numpy array :ivar maxima_indices: The indices of each of the maxima on the difference curve. :vartype maxima_indices: numpy array :ivar maxima_indices: The indices of each of the maxima on the difference curve. :vartype maxima_indices: numpy array :ivar x_difference_maxima: The x values from the difference curve where the local maxima are located. :vartype x_difference_maxima: numpy array :ivar y_difference_maxima: The y values from the difference curve where the local maxima are located. :vartype y_difference_maxima: numpy array :ivar minima_indices: The indices of each of the minima on the difference curve. :vartype minima_indices: numpy array :ivar minima_indices: The indices of each of the minima on the difference curve. :vartype maxima_indices: numpy array :ivar x_difference_minima: The x values from the difference curve where the local minima are located. :vartype x_difference_minima: numpy array :ivar y_difference_minima: The y values from the difference curve where the local minima are located. :vartype y_difference_minima: numpy array :ivar Tmx: The y values that correspond to the thresholds on the difference curve for determining the knee point. :vartype Tmx: numpy array :ivar knee: The x value of the knee point. None if no knee/elbow was detected. :vartype knee: float :ivar knee_y: The y value of the knee point. None if no knee/elbow was detected :vartype knee_y: float :ivar norm_knee: The normalized x value of the knee point. None if no knee/elbow was detected :vartype norm_knee: float :ivar norm_knee_y: The normalized y value of the knee point. None if no knee/elbow was detected :vartype norm_knee_y: float :ivar all_knees: The x values of all the identified knee points. :vartype all_knees: set :ivar all_knees_y: The y values of all the identified knee points. :vartype all_knees: set :ivar all_norm_knees: The normalized x values of all the identified knee points. :vartype all_norm_knees: set :ivar all_norm_knees_y: The normalized y values of all the identified knee points. :vartype all_norm_knees: set :ivar elbow: The x value of the elbow point (elbow and knee are interchangeable). None if no knee/elbow was detected :vartype elbow: float :ivar elbow_y: The y value of the knee point (elbow and knee are interchangeable). None if no knee/elbow was detected :vartype elbow_y: float :ivar norm_elbow: The normalized x value of the knee point (elbow and knee are interchangeable). None if no knee/elbow was detected :vartype norm_knee: float :ivar norm_elbow_y: The normalized y value of the knee point (elbow and knee are interchangeable). None if no knee/elbow was detected :vartype norm_elbow_y: float :ivar all_elbows: The x values of all the identified knee points (elbow and knee are interchangeable). :vartype all_elbows: set :ivar all_elbows_y: The y values of all the identified knee points (elbow and knee are interchangeable). :vartype all_elbows: set :ivar all_norm_elbows: The normalized x values of all the identified knee points (elbow and knee are interchangeable). :vartype all_norm_elbows: set :ivar all_norm_elbows_y: The normalized y values of all the identified knee points (elbow and knee are interchangeable). :vartype all_norm_elbows: set ?r r interp1dFxyScurve direction interp_methodonlinepolynomial_degreec Ftj||_tj||_||_||_t |j|_||_t|_ t|_ g|_ g|_ ||_||_|jt v} |jt"v} t%| | fst'd|dkr5t)j|j|j} | |j|_nf|dkr>tjtj|||j} | ||_n"t'd|||j|_||j|_||j|j|j|_|j|jz |_|j|_ tC|jtj"d|_#|j |j#|_$|j|j#|_%tC|jtj&d|_'|j |j'|_(|j|j'|_)|j%|jtj*tj+|j,zz |_-|.\|_/|_0dx|_1|_2|j/rN|j|j|j/kd|_1|j|j|j0kd|_2dSdS)Nz>Please check that the curve and direction arguments are valid.r polynomialzO{} is an invalid interp_method parameter, use either 'interp1d' or 'polynomial'r)3nparrayrrrrlenNrset all_kneesall_norm_knees all_knees_yall_norm_knees_yrr VALID_CURVEVALID_DIRECTIONall ValueErrorrrDs_ypoly1dpolyfitformat_KneeLocator__normalize x_normalized y_normalized transform_y y_differencecopy x_differencer greater_equalmaxima_indicesx_difference_maximay_difference_maxima less_equalminima_indicesx_difference_minimay_difference_minimaabsdiffmeanTmx find_kneeknee norm_kneeknee_y norm_knee_y) selfrrrrrrrr valid_curvevalid_directionusplineps 2lib/python3.11/site-packages/kneed/knee_locator.py__init__zKneeLocator.__init__s,!! "TV!ee " !2jK/ .O;K122 P  J & &!*4646::GDII l * * "*Q4+ABBCCA!DIIahh! !,,TV44 ,,TY77!,,  t~tz  !-0AA -2244,D,=r?OPPQRS#'#4T5H#I #'#4T5H#I ,D,=r}MMaP#'#4T5H#I #'#4T5H#I + FRVBGD$566;;==>> >  %)NN$4$4! 4>*.- d& 9 Y&49!45a8DK#01Bdn1TUVWXD    Y Yareturncf|t|z t|t|z z S)zDnormalize an array :param a: The array to normalize )minmax)rLs rI __normalizezKneeLocator.__normalizes) CFF s1vvA//rKc|dkr9|dkrtj|}nS|dkr||z }n5|dkr/|dkr)tj||z }|S)zEtransform y to concave, increasing based on given direction and curver r rr )rfliprP)rrrs rIr/zKneeLocator.transform_ys{  $ $ !!GAJJ(""EEGGaK , & &5H+<+<! $$ArKc|jjsdSd}d}d}t|jD]\}}||jdkr|dz}|t |jdz krn|j|kr|j|}|}|dz }|j|krd}|dz }|j||krW|j dkrE|j dkr|j |} |j |} nn|j |dz } |j |} nO|j dkrD|j dkr|j |dz } |j |} n|j |} |j |} |j |j | kd} |j|j | kd} | |jvr4|j| |j| |j| |j| |jdur| | fcS|jt-krdS| | fS) zxThis function is called when KneeLocator is instantiated. It identifies the knee value and sets the instance attributes.)NNrFgrr r )r4size enumerater2ranyr>r8r0rrrr-rr.r r"appendr#addr!rr) rDmaxima_threshold_indexminima_threshold_indextraversed_maximairj thresholdthreshold_indexr@rA y_at_kneey_norm_at_knees rIr?zKneeLocator.find_knees"'  :!"!" d/003 +3 +DAq4&q)))AAS*++a/00#q(--// , H%;< "#&!+&#q(--// , &!+& #i//:))~55#vo6$($5o$F #v!(;&<=$($5o$F Z9,,~55#v!(;&<=$($5o$F #vo6$($5o$F !F46T>215 !%!243D 3Q!RST!Ut~--$++I666)00@@@""4(((#'' 222;%''?*** >SUU " ":YrKNNormalized Knee Pointfigsizetitlexlabelylabelctst|d}tj|tj||rtj||rtj|tj|j|j ddtj|j |j ddtj tj|j|jd zd tjtj|j |j d zd tj|jtjd tjd d d tjddS)aPlot the normalized curve, the difference curve (x_difference, y_normalized) and the knee, if it exists. :param figsize: Optional[Tuple[int, int] The figure size of the plot. Example (12, 8) :param title: str Title of the visualization, defaults to "Normalized Knee Point" :param xlabel: Optional[str] X-axis label :param ylabel: Optional[str] y-axis label :return: NoReturn Nrkrebznormalized curvelabelrzdifference curveg?rrU-- knee/elbow linestylesrobestloc)_has_matplotlib_matplotlib_not_found_errpltfigurerfrgrhplotr-r.r2r0xticksrarangerOrPyticksvlinesrAylimlegendrDrerfrgrhs rIplot_knee_normalizedz KneeLocator.plot_knee_normalized;s& ,+ + ?G 7#### %   Jv      Jv    "D$5sBTUUUU "D$5sBTUUUU Id'++--t/@/D/D/F/F/Lc R R    Id'++--t/@/D/D/F/F/Lc R R    N HJJqM HJJqM      vrK Knee Pointctst|d}tj|tj||rtj||rtj|tj|j|j ddtj |j tj dtj dd d tj d dS)a Plot the curve and the knee, if it exists :param figsize: Optional[Tuple[int, int] The figure size of the plot. Example (12, 8) :param title: str Title of the visualization, defaults to "Knee Point" :param xlabel: Optional[str] X-axis label :param ylabel: Optional[str] y-axis label :return: NoReturn NrjrlrmdatarnrrUrqrrrsrurv)rxryrzr{rfrgrhr|rrrr@rrrs rI plot_kneezKneeLocator.plot_kneels( ,+ + ?G 7#### %   Jv      Jv    F3333 Isxzz!}chjjmL     vrKc|jSN)r@rDs rIelbowzKneeLocator.elbows yrKc|jSr)rArs rI norm_elbowzKneeLocator.norm_elbow ~rKc|jSr)rBrs rIelbow_yzKneeLocator.elbow_ys {rKc|jSr)rCrs rI norm_elbow_yzKneeLocator.norm_elbow_y rKc|jSr)r rs rI all_elbowszKneeLocator.all_elbowsrrKc|jSr)r!rs rIall_norm_elbowszKneeLocator.all_norm_elbowss ""rKc|jSr)r"rs rI all_elbows_yzKneeLocator.all_elbows_yrrKc|jSr)r#rs rIall_norm_elbows_yzKneeLocator.all_norm_elbows_ys $$rK)rr r rFr)NrdNN)NrNN)__name__ __module__ __qualname____doc__rfloatstrboolintrJ staticmethodr,r/r?rrrrpropertyrrrrrrrrrKrIr r slld%'!"WYWY E?WY E?WY  WY  WY  WYWYWYWYWYWYWYr0x08E?000\0  x 3 s u   \ HHHX.2, $ $ //%S/*// /  ////f.2! $ $ $$%S/*$$ $  $$$$NXXX  X X##X#  X %%X%%%rKr )numpyrscipyr scipy.signalrtypingrrrr$r%matplotlib.pyplotpyplotrzrx ImportErrorModuleNotFoundErrorryobjectr rrKrIrs&&&&&&,,,,,,,,,,# .######OO O 3 3f!!]%]%]%]%]%&]%]%]%]%]%s-AA