o 0rzm;b;)rrcCs||||||Srr )r arcr r rmyquad4sr z$y = a x^2 + b x + c$cCrrr rr r rr9rza;b;c)rrrc@sNeZdZejddZejedZej dddddd Z d e fd d Z d dZ dS)FitFormz0Upload a CSV file with columns x,y,y_uncertainty) help_text)choicesrTFz+optional key-value pairs to format the plot) max_length min_lengthstriprequiredr"r cCs|d}|ddkrttd|ddd|d|d kr-ttd |dd dzt|}WnYd Sttd dd)z@ Screen the column heads for appropriate format rruImbalanced $ in “u”dollarscode{}uImbalanced braces in “bracesNz3The first row of the CSV file must hold axes labelslabels)countr_float)selfr dollar_signsvr r rdollarJs"   zFitForm.dollarc Cs|j}|d}||d<|jd}|jdd|vrdnd}z tj||d}Wn ttddd |j }t |D]\}}|t d t d fvrWttd |d d q=|j \} } | dkse| dkrqttdt| d d t|j|d<} | ddD]} || q| d|d<| d|d<|jdddf|d<|jdddf|d<z|jdddf|d<Wnd|d<Y|}||d<dS)Nrfilezutf-8r ,)sepz=Could not load data file; confirm that it is a valid CSV filer+float64int64z+Column %d has one or more nonnumeric valuescolumnsr)z+The CSV file must have 2 or 3 columns, not headerxlabelrylabelr yyunc) cleaned_datar8readdecodeseekpdread_csvrr2dtypes enumeratenpdtypeshapestrlistr>r7ilocto_numpy) r4cdr file_contentsr;dfrKndtrowscolsheadshr r rclean`sT        z FitForm.cleanN)__name__ __module__ __qualname__r FileFieldr ChoiceFieldfunction_choiceskind CharFieldoptionsrPr7r]r r r rr!=s  r!c Csd\}}}|jdkrt|j|j}|r|j}|d|d|d}}}|d|d} } |d} tdttt d } | | } | rG| j | j fngdf\}}t | |||||d }|d }i}| d D]2}zd d| dD\}}WnYqbzt|}Wnzt|}Wn|}YY|||<qbz@|jd| | |d|t}|dd}|dd}|jj|d||d|dtjt|}|d}|d}Wn+ty}zt|}|d|d| d|d}WYd}~n d}~wwnt}||||d}t!|d|S)N)NNNPOSTr rCrDrArBrd)rr r r )p0rDtexrfr:cSsg|]}|qSr r'rr r rrzfit..=)rArBridpi pad_inchesg?png)formatrmrorr@rHerer8)fitformfigurer@rzigor/fitform.htmlr )"methodr!rgFILESis_validrEdictrrr rhparamsFitsplitintr3plotioBytesIOgetfigsavefigrHurllibparsequotebase64 b64encoderF ExceptionrP add_errorindexr)requestrtrr@rsrTr rCrDrArBrdmapperfuncrhrifrfoptsfldkr6valbuffrmrooopserrargsr r rfitsp          1 r) curve_fitOptimizeWarning)*)chi2)rcParamsc@seZdZdZddZddZddZdd Zd d Zd d Z de j fddZ e d-ddZddZddZddZd.ddZe ddZe dd Zd!d"Zd#d$Zd%d&Zd/d(d)Zd*d+Zd,S)0rza Base class that performs (non)linear least-squares fits and can make carefully formatted plots of the results. The function to apply may either be specified by passing in appropriate keyword arguments or by subclassing this class and providing the requisite functions as methods of the subclass. By default, a Fit object immediately attempts to run the fit with the information passed to the constructor. If that fails, or if the information is insufficient, you can see what the data look like and the calculated curve with the passed values for p0 (or the values generated by the estimate_p0 function) by calling plot on the resulting object. If you want to start the process without attempting a fit, but just seeing the plot with the curve generated by values in p0, pass the key-value pair adjust=True to the constructor. You can These requisite functions/methods are - function(x:np.ndarray, *params, **kwargs): - tex_f: (optional) a string or callable that returns a string providing a representation of the function in LaTeX. - estimate_p0(**kwargs): (optional) a function that takes a dictionary of keyword arguments, including the instance of this Fit class with the name 'self' and returns a vector of initial values for the fit parameters. The function may avail itself of data fields in the Fit object, including x, y. should be subclassed to implement a particular (nonlinear) fitting function. This base class provides all of the smarts, leaving to the subclass just the essentials particular to the chosen function. The subclass should implement the following fields and methods: - function(self, x:np.ndarray, *params), where self is an instance of a subclass of Fit - tex_f, a string or @property callable returning a string providing a representation of the function in LaTeX. If not defined, a crude approximation is generated by introspection of the function. - __str__(self), to produce a string representation of the fit - __init__(self, x:np.ndarray, y:np.ndarray, **kwargs), constructor that must call super().__init__(x, y, p0, tex, **kwargs), where p0 is an initial guess for the fitting parameters and tex is a list of strings with a LaTeX version of the names of the fit parameters If the fit is successful, the routine self.after_fit() is called; the default routine does nothing, but this would be an opportunity to adjust parameters, such as making sure that a parameter that enters quadratically has a positive value. In addition, the following fields are set: - self.valid is set to True - self.params is set to the list of optimized fitting parameters If yunc holds valid uncertainties, then - self.param_uncs is set to the list of parameter uncertainties - self.chisq is set - self.dof is set to the number of degrees of freedom of the fit - self.prob_greater indicates the probability that a greater value of chi-squared on repeating the experiment Optional keyword inputs: - yunc:np.ndarray, an array of uncertainties in the dependent variable - xunc:np.ndarray, an array of uncertainties in the independent variable - hold:str, a string of the form "01100", where "0" means the variable is optimized by the fitting routine and "1" means that it is held at the value given in p0 - tex:[str], a list of strings providing LaTeX code to represent the fit parametersc Ks||_t||_t||_t|jt|jksJd||_t|ds7t|jdr1|jj|_ n| d|_ d|_ d|_ d|_ d|_g|_g|_d|_| d|_t|t|j|_| d|_d|_d|_d|_d|_d|_d|_d|_d|_zvdD]C}z||}Wn t||dYq}t|tt frt!t||}nzt|}Wnd}Yt|||t|t|ksJq}t|j tj"rt|j tj"rdnd |_d |vs|jdkr|#WdS|$|j|%WdSt&y }z t'||_ WYd}~dSd}~ww) a kwargs may include hold="1011", where each 0 corresponds to a parameter allowed to vary and 1 to a value held fixed. If the function passed has a .tex attribute, it is assumed to be a string that can be passed to tex to describe the function in the fit annotation. Subclasses may define a string variable tex_f for this purpose. z,The x and y arrays must have the same length function_texriNhold)rDxuncxyrCadjust)(functionrMarrayr rClenrhhasattrrirrerrorrrDxerrorsry param_uncs weightingrdof tex_labelschisq prob_greateraxdata axyresidualsaxynorm axxresidualsaxxnormtop_axissetattr isinstancer3r|onesndarrayr}run_fit after_fitrrP) r4rr rCrhkwargsuncuncseepsr r r__init__)st             z Fit.__init__cGs||}|j|g|RS) ) parametersr)r4r rypr r rfhold{s z Fit.fholdc spt|_d}|d7}|dD]}t|dqjrZtjts$dtjtjkr0dfddtt|D_ tj tj _ fd d }fd dj D}nfd d }z tj t jrn|nt|j j|jd d\__Wn tydwt jjvst jjvrd_dSj_jjj gjR_djvr jj_t jd_djvrj j _!j"}t #t $jdt $|j d}j|_%t j%d_jj _&dt'(jj _)t #t *j}jr3t +jj,_-t.j D] \}}||j-|<q$dS|_-dS)z`Run or re-run the fitting procedure, starting from the passed parameter values. zFerror;xerrors;yerrors;chisq;prob_greater;norm_yresiduals;reduced_chisqz;params;param_uncsrNz6hold must be a string with 1 for fixed, 0 for variablez@The number of digits in hold must match the number of parameterscsg|] }j|dkr|qS)0)rrr4r rrszFit.run_fit..cj|g|RSr)rr rrr rzFit.run_fit..csg|]}j|qSr )rh)rrWrr rrcrr)rrrr rrrT)rhsigmaabsolute_sigmazFailed to convergerCr)r r)/rQrhr{rrrrPrrangevariabler rrrMrrun_odrrrCrDrycovarsrinfnanrrr yresidualsrnorm_yresidualssumr xresidualsnorm_xresiduals_slopesqrtpowernorm_residuals reduced_chisqrcdfrdiagzerossizerrL) r4rhfieldsrrrerrsrWpnumr rrrsp             z Fit.run_fitcCsdS)z9Override to perform any post-fit alteration of parametersNr rr r rrsz Fit.after_fitc st|j|jdt|jddt|jdd}fdd}t|}t|||j }| ||_ |j }|j dkrJ|j|_|j|_|j|_|j|_dSdS)z>Run an orthogonal distance regression to handle errors along x?r))wdwecs|g|RSrr )betar rr rf_odrszFit.run_odr..f_odrrN)Datar rCrMrrrDModelODRrhrunodroutputinforrycov_betarepsrdeltar)r4rrrmodelrrr rrrs$   z Fit.run_odrcCs:|jr|j}t|jD] \}}||||<q t|S|S)z?Handle the subset of parameters that are being allowed to vary.)rrhrLrrMr)r4parrrWrr r rrs  zFit.parameterstcCs<|jdkrgS|jr|j|g|jRS|j|g|jRS)z=Evaluate the fitting function using current parameter values.N)rvalidryrh)r4rr r r__call__s z Fit.__call__ư>cCs(||j|||j|}|d|S)z>Return a numerical approximation to the slope at each data ptr))r )r4dxdyr r rr s z Fit._slopec CsH|jj}t|j}|jdd}|g}t|jtj}|j rt t |j D]D}| ||dd|j |d|ri|dd|j|d7<|j|dkri|dd t|j||j |d dd 7<q%|r| d |jd |jd|dd |jdd7<|ddd |jdd7<n| |jd|S)Nr>16sz = z^8.4gu ± .2grz (dz%)zN_dof = z , chisq = .3g)z, P> = % )rr^inspectgetfullargspecrrrDrMrrrrryappenderrorsrabsrrrrrjoin)r4namerargnameslineshas_uncrWr r r__str__s2 "$   z Fit.__str__cCsnd|vr|Std|}|r/|dd}|ddkr |d7}|tt|dd7}|Std ||S) zI Render a string representation of a value in TeX format ez#([-+0-9.]*)\s?e\s?([+-])\s?([0-9]*)rz \times 10^{r)-r?r.z Ack! for )researchgrouprPr|print)r4r rsr r rtexval)s  z Fit.texvalc Cs,|dkr t|ddfSzp|dkr|dksJttt|}tt|}d||}| |}t||}t||}|t|} dt|d} || |} ||d} | dkra| d} n| d krnd | d d } n td | d} | | fWSty}z|d|dfWYd}~Sd}~ww)zQ Produce a LaTeX representation of the value and its uncertainty grr)z{:0.zf}rrz.2fgMbP?r.1fz\%g.Az \;\rm ppmrN) rPr|rMlog10rroundrrqr)r4r rxdigitsdxdigitsdigits round_spotxrounddxroundratiofmtmainrrelrr r r tex_val_unc9s0       zFit.tex_val_uncTc Cs t|dr |jr |jn|jj}|jr|j}n t|j}|jdd}|g}t|j t j }|rL|j rLd| |jdd|jdd|jd d g}|j r|ra|d d |d |dtt|jD]Z}|r|d||d|ddd||j||j|Dqh|||dd||j||j|\} } } | dkr| d} nd| | | } |d| 7<qh|r|r|d||d d|dd|dn||d ||dn|r|dn||jd|} | S)z\Generate an annotation showing the fit function and the fitting parameters. rrNz$\chi_\nu^2 = rz\;\; \mathrm{for}\;\; \nu = %d$z$P_> = rrz\%$rz'\begin{tabular}{lcc}\multicolumn{3}{c}{z }\\[0.05in]z/\textbf{Param} & \textbf{Value} & \textbf{Unc.}z\\ z & cSrrr rr r rrs z"Fit.legend_tex..rz = $rz $ (fixed)z{0} \pm {1}\; ({2})$rz\\[0.05in]\multicolumn{3}{c}{z \qquad r.z \end{tabular}r)rrrr^rrrrrrDrMrrrrrrinsertrrrryr r$rrqr)r4 use_tabler r rr r statsrWr6urvalsresr r r legend_tex[sz            zFit.legend_texcCs|jduo t|dS)zDid the fit exit successfully?Nr)rrrr r rrsz Fit.validcCs*|jr t|jtjs dSt|j|jS)zK By what factor errors need to grow to yield chisq/DoF = 1 N)rrrrMrrrrrr r r error_scaleszFit.error_scalec Ksd\}}|dd}d}g}|jr0|dd|jvo|}|r#|d|dd }|r0|d |d ||_|jd9i||j||d d}|d d}|dt |j } |dt |j } |dt |j } |dt |j } |d|d} }|dd}|r|j jdddt| tjstdtt| t| |} n t| tjst| | |} |s|| }|r|j jdddt| t|kr|j | ||dt|j dkrdnd}|jr|j j|j |j |j|jdd |d!n |j j|j |j d |d"d#|vr|j |d#d$|vr$|j |d$|r|r2|jjddd|jj| | gd%d%gd&d d'|jd(kr[|d(}|jj|j |j |dd)d*d+}nd,}|jj|j |j |jd-d|d.|jd/d0|jvr|r|j!jddd|j!jd%d%g| | gd&d d'|j!j|j"|j |d)dd1|j!j|j"|j |jdd-|d2|j!d/|r|r|j#jddd|j#j| | gd%d%gd&d d'|d}|j#j|j |j$d)d|d3|j#d4d0|jvr|j%}|jd%d%g| | gd&d d'|d0}|j|j&|j d)d|d3|d4 |j(}|)|j*z|j+}|,||j-d5d6d7WnY|d|df}|d%d8ksK|d+d8krQ|j j.||d|df}|d%d8ksi|d+d8krq|j j/|d8Sd8S):ap Generate a plot showing the data, fit, residuals, and normalized residuals. Optional kwargs: - residuals (boolean) - normalized_residuals (boolean) - title (str) - xlabel (str) - ylabel (str) - figsize (width, height) - msize (marker size, in pts) - logx (boolean) - logy (boolean) - xmin (float) - xmax (float) - ymin (float) - ymax (float) - xfit (array of positions at which to compute the fitted curve) - yfit (array of precomputed fit values). If yfit is not supplied, the fitted curve will be evaluated at xfit values. - npoints (int) defaults to 200 and specifies the number of points to use in computing the fitted curve - legend (xfrac, yfrac) specifies the anchor position of the annotation, expressed as a fraction of the width and height of the plot area. Defaults to (0.1, 0.1). Alternatively, can be a suitable combination of north, east, south, and west for position outside the plot area. )FFtitlerFnormalized_residualsrCr residualsTrrlogxlogyxminxmaxyminymaxxfityfitnpointslogclip)nonposx )nonposymsizeo?)yerrxerrr!alpha markersize)rHrrArBrzk-)rHr)rmarkerrrr?None)rFlsrKmszRes.r )rrrK)rGrKrMrN)rrKrzN.R.gQ?g{Gz?)hspacewspaceNr )0rrrr axes_order make_gspecr set_titlerMminr maxrCr set_xscalerrrlinspacerr set_yscalerr}errorbarrDrscatter set_xlabel set_ylabelrnorm_res_colorsrrrrrrr fit_resultsr align_ylabelsaxesgs tight_layoutupdateset_xlimset_ylim)r4rrnormalized_yresidualsr.NORMrQr1r2r3r4r5r6r7r8r9r@colorsrNaxrraxlimylimr r rr}s                           zFit.plotc KsZ|dd}|dtd}td}|dd}dtd <d td<dtd <dtd <d td<dtd<d td<dtd<|j}|\}}tdgdgddddd} |js^tj| d\|_|_|j|_ dS| |} dt |j } | |dd} d| vr|| dd} t| | | |ddd d!ddd" |_|j} td#d$d d d%}d&}t|tr||d'<t |d(krgd)| d*<n t |d+krdd,g| d*<tjt |d|| d-\|_|_d.D]}||vrt|||j||q|jd/|_ |jj| fi|t|trd0d1|d2D}|d/| d3<t |dkrdn|d| d4<| d3d5vrdtj||| d6fd7|_d}| d3d8kr=|d/d9| |7} n |d9|| } t |d(krgdd,| d|g| d*<d:|jvrfd+}d,dg| d;<n,t |d,krddd,| d<|g| d*<d:|jvrd(}gd=| d;<n d,| d>|g| d*<| d3d8krt| d*d| d*<|jjdP|t |d?| }||_|j d@dA|dB}|j!||d/f|_t"|D]7\}}|dCvrڐq|jj!||d/f|jdD}tj#|$dEdFtj%d/d/dGt||||d/kr||_ q|dkrEt&dd+gdHdIgD]/\}}||kr n%|jj!|||f|jdJ}tj#|'dEdFtj%d/d/dGt|||q|j!||d9d/f|_(|j()dK|j(j| fi|ntj|d/dL|dfd7|_dM}| d3dNkr||gn||g| d;<t |d+krdd,g| d*<n t |d(krgd)| d*<|jjdPd+t |d?| }| d3dOkrd/nd}|j!|dd|f|_(|j(j| fi||j(*|dB}|j!||d|f|_t"|D]2\}}|dCvrq|jj!||d|f|jdD}t|||tj#|$dEdF|d/kr||_ q|d/}t+||}||_ dS)Qz Figure out how to layout the axes of the plot. 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