³ò A¶GJc@sidZddkZddkZdefd„ƒYZd„Zd„Zd„Zdefd „ƒYZdS( sf aver.py Classes: 'Mean' represents an average of a set of numbers or a random number 'LinearFit' represents a result of a straight line fit. Functions: 'average', 'combine', 'stdcorrection' To get an array of mean values from an 'array' of 'Mean' objects you can try '[x.mean for x in array]' or 'numpy.array([x.mean for x in array])'. Lev, 17 Dec 2008 iÿÿÿÿNtMeancBs>eZdZeieiei eidd„Zd„Zd„Zd„Z e d„ƒZ d„Z d„Z d „Zd „Zd „Zd „Zd „Zd„Zd„Zd„Zd„Zd„Zd„ZeZd„ZeZeZd„Zd„ZeZd„Z d„Z!d„Z"de$d„Z%ddd„Z&RS(sú Represent a result of averaging numbers together or a random number: mean - (the best estimate of) the mean std - standard deviation. Note that for correct combination of uncertainties, this is should be calculated using std = \sqrt{ rac{\sum x^2 - (\sum x)^2}/(N-1)}, with N-1 in the denominator, rather N (and 1 for N < 2). This accounts for the fact that the average, from which individual points deviate is not known precisely. min, max - extrema of the data N - amount of data. 0 means unknown/undefined, such as in case of combining random quantities. derived properties (calculated on creation): error = std/sqrt(N) - error of the mean (equal to 'std' for N < 2) median = (max + min)/2 halfspan = (max - min)/2 - to be used for errorbars that encompass all data points rmsdev - root of mean square of deviation of individual values from the best estimate of the mean rmsdev = \sqrt{ rac{N-1}{N}}std for N > 1, 0 for N = 1 and just std for N < 1. stderror - error of the standard deviation (equal to 0 for N < 2) Arithmetic operations +,-,*,/,** are supported between Mean objects as well as between Mean objects and numbers. The arguments are considered uncorrelated. When combining uncertainties all information about number of points is lost (because it can be different for the two arguments). Standard deviation, rather than error of the mean is retained, such that the result represents scatter of the hypothetic combination of the numbers averaged together. Use 'be()' before combining uncertainties to get best estimates of the means with its errors. DISCLAIMER: When dividing by or deriving a power of a 'Mean' object the standard deviation of the result is only valid under the assumption that for the argument it is much smaller than the mean. Only a real number can be used as a right hand side argument for **. A number is equal ('==' returns True) to the Mean object if it is within one 'std' from the mean. Two Mean objects are equal if their difference is equal to 0 in the above sense. 'fromtuple()'/'totuple()' methods are primarily for spreadsheet I/O. icCs¬||_t|ƒ|_ti||gƒ|_ti||gƒ|_ti|iƒoti |_nti|iƒoti|_nt|ƒ|_ |i ƒdS(s2 Construct a Mean from its statistical properties. 'mean' is (the best estimate of) the mean 'std' is standard deviation 'min' and 'max' are value limits 'N' is number of points that contributed to the estimate of the mean/std or '0' if unavailable. N( tmeantabststdtnumpytmintmaxtisnantInftinttNt calculate(tselfRRRRR ((sc:\py\lib\aver.pyt__init__Ws cCsÃ|idjo |in|i|id|_d|i|i|_d|i|i|_|idjo|it|iƒnd|_|idjodn|it i dƒ|_ dS(sCalculate derived quantitiesigà?iiN( R RterrorRRtmedianthalfspant stdcorrectiontrmsdevRtsqrttstderror(R ((sc:\py\lib\aver.pyR is 10cCs"t|i|i|i|idƒS(sa Return the best estimate of the mean, an object with both 'std' and 'error' set to the 'error' of the processed Mean and zero as number of points. This is useful when combining uncertainties, because then the number of points is lost and the standard deviation, the scatter of points, is kept as both 'std' and 'error'. i(RRRRR(R ((sc:\py\lib\aver.pytbeqscCs"|i|i|i|i|ifS(s-Convert into a tuple (mean, std, min, max, N)(RRRRR (R ((sc:\py\lib\aver.pyttotupleyscCs t|ŒS(sFConvert a tuple/list/array (mean, std, min, max, N) into a Mean object(R(tarray((sc:\py\lib\aver.pyt fromtuplezscCsti|iƒƒS(N(RRR(R ((sc:\py\lib\aver.pytcopy}scCsAd|i|i|i|i|idjod|indfS(Nsx = %g +- %g (%g <= x <= %g)%sis , %d samplest(RRRRR (R ((sc:\py\lib\aver.pyt__repr__scCs|iS(N(R(R ((sc:\py\lib\aver.pyt__min__scCs|iS(N(R(R ((sc:\py\lib\aver.pyt__max__‚scCs(t|i |i|i |i |iƒS(N(RRRRRR (R ((sc:\py\lib\aver.pyt__neg__ƒscCs t|iƒS(N(RR(R ((sc:\py\lib\aver.pyt__abs__„scCs t|iƒS(N(tcomplexR(R ((sc:\py\lib\aver.pyt __complex__…scCs t|iƒS(N(R R(R ((sc:\py\lib\aver.pyt__int__†scCs t|iƒS(N(tfloatR(R ((sc:\py\lib\aver.pyt __float__‡scCs­t|tƒoNt|i|i|id|idd|i|i|i|idƒSnFti|ƒo5t|i||i|i||i||iƒSnt ‚dS(Nigà?i( t isinstanceRRRRRRtisscalarR tNotImplemented(R tother((sc:\py\lib\aver.pyt__add__‰s)%"cCs || S(N((R R(((sc:\py\lib\aver.pyt__sub__’scCs-t|tƒo¬|i|i|i|i|i|i|i|ig}t|i|i|id|id|id|id|id|iddt|ƒt|ƒdƒSnhti|ƒoW|i||i|g}t|i|t|i|ƒt|ƒt|ƒ|i ƒSnt ‚dS(Nigà?i( R%RRRRRRR&RR R'(R R(textrema((sc:\py\lib\aver.pyt__mul__”s:+ cCs ||dS(Niÿÿÿÿ((R R(((sc:\py\lib\aver.pyt __truediv__¡scCsti|ƒp t‚n|i|idjoT|djoGt|i|t||i|d|iƒti ti |i ƒSn|i||i|g}|i|idjo|i dƒnt|i|t||i|d|iƒt|ƒt|ƒ|i ƒS(Nii( RR&R'RRRRRRRR tappend(R R(R+((sc:\py\lib\aver.pyt__pow__¤s $G,cCs | |S(N((R R(((sc:\py\lib\aver.pyt__rsub__·scCs ||dS(Niÿÿÿÿ((R R(((sc:\py\lib\aver.pyt __rtruediv__¸scCs„t|tƒo4t|i|iƒd|id|idjSn7ti|ƒo&t|i|ƒd|idjSnt‚dS(Ni(R%RRRRRR&R'(R R(((sc:\py\lib\aver.pyt__eq__»s 4&cCs„t|tƒotti|i|iƒo[ti|i|iƒoBti|i|iƒo)ti|i|iƒo|i|ijS(sÀ Compares two Mean objects to be identical. Return True only if all 5 fields, the mean, standard deviation, value boundaries and number of points are the same. ( R%RtflibtfloatcmpRRRRR (R R(((sc:\py\lib\aver.pytsameÂs)2cCstti|iƒƒƒS(sGReturn True if a Mean object has all properties finite, otherwise False(tallRtisfiniteR(R ((sc:\py\lib\aver.pyR7ÌscCs§|djor|idjotiti|iƒƒ}nd}|djod| }q|djo d}qd}n||i|odnd||iS(s1Return a string representation without boundariesis%%.%dfs%gs%ds\pm s+-N(tNoneRRtfloortlog10R(R tfmtttext std_order((sc:\py\lib\aver.pytbriefÐs     txs%gcCs‚ti|iƒo||idnd}ti|iƒod||ind}did|ƒ||i|i|||fS(sReturn a neat TeX represenations \les -\infty RB(((sc:\py\lib\aver.pyR"s>3%                   cCs$|djo||ddndS(s Return sqrt(N/(N-1)) for N > 1, else 1 This factor can be included in standard deviation calculation to account for uncertainty of the mean igð?gà?((R ((sc:\py\lib\aver.pyRæscOst|ƒdjo"ti|dƒo|d}nti|ƒ}d|jo"|do|ti|ƒ}nt|ƒdjo'ttititi tidƒSnQt|ƒ}tti|ƒti |ƒt |ƒti |ƒti |ƒ|ƒSdS(s$ Construct a Mean object from an array of numbers. If a single argument is supplied and it is iterable, it is used as an array of values, otherwise each argument is one of the values. Mean.fromarray([1,2,3]) is equivalent to Mean.fromarray(1,2,3) If a keyword argument 'finites' is specified and is 'True', then all Not-a-Number's are discarded from averaging. Other keyword arguments are discarded and not taken as numbers to average. A NaN-Mean object is returned if no finite arguments are encountered. iitfinitesN( tlenRtiterabletasarrayR7RRFRRRRRR(targstvargstvalueR ((sc:\py\lib\aver.pytaverageîs '' cOsãt|ƒdjo"ti|dƒo|d}nd|jo!|dotd„|ƒ}nd|jo|d}t|ƒdjo tƒSntit|ƒgƒ}tit|ƒgƒ}tit|ƒgƒ}tit|ƒgƒ}tit|ƒgƒ}tit|ƒgƒ}x¬tt|ƒƒD]˜} t|| tƒptd| dƒ‚n|| i || <|| i || <|| i || <|| i || <|| i || <|| i|| st weightonstds"Argument %d of an unsupported typeiþÿÿÿgà¿igà?(RNRROtfilterRtzerostrangeR%t ValueErrorR RRRRRtsumR(RQRRRVtNstmeanstrmsdevststdstminstmaxestitwtNtotalRtrmsdev2((sc:\py\lib\aver.pytcombinesB'  J  .t LinearFitcBsƒeZdZd„Zedd„ƒZd„Zd„Zd„Z d„Z d„Z d„Z d „Z d „Zed d d „ZRS(s¥ Straight line fit y(x) = A*x + B with errorbars Keeps the information necessary to reconstruct uncertainties of the intercepts of the fit with x=X. cCsC||_||_||_||_||_||_||_dS(s¯ Construct a linear fit object. The model is: y(x) = A*(x-x_mean) + B. A - slope of the fit B - intercept of the fit N(tAtBtA_errtB_errtx_meantx_std2tchi2(R RhRiRjRkRlRmRn((sc:\py\lib\aver.pyR Hs      c Csti|ƒ}t|dtƒo{|d j otdƒ‚ntig}|D]}||iqQ~ƒ}tig}|D]}||iq~~ƒ}nti|ƒ}t|ƒdjotdƒ‚nt|ƒt|ƒjotdƒ‚n|d j opti |ƒo|ti |i ƒ}nti|ƒ}t|ƒt|ƒjotdƒ‚n|d}nti |i ƒ}ti |ƒ}ti ||ƒ|}||}ti ||ƒ|} ti ||dƒ|} ti |||ƒ|} | | } | } |d jo|ti |i ƒt | || |d|ƒt|ƒdd}|d}ti |ƒ}|djo d }qÌd }n/t | || |d|ƒt|ƒd}|| d }|d }t | | |||| |ƒS( s Evaluate a straight line fit to a model y(x) = A*x + B. x are considered precise and y uncertain. A fit is unweighted unless y are 'Mean' objects or 'y_err' are supplied. Return a LinearFit object isG'y_err' should not be specified when 'y' have uncertainties themselves.is1it takes at least 2 points to fit a straight lines'x' and 'y' are different sizes"'y' and 'y_err' are different sizeiþÿÿÿgà?gð?ggà¿N(RRPR%RR8RZRRRNR&tonestshapeR[Rg(R?tyty_errt_[1]Rbt_[2]Rctsum_wtmean_xtmean_ytmean_x2tmean_xyRhRiRnRjRk((sc:\py\lib\aver.pytfitYsL  -1    B    . cCst|i|iƒS(s,slope of the linear fit with its uncertainty(RRhRj(R ((sc:\py\lib\aver.pytslope—scCsqti|ƒo#t|i|ƒ|i|ƒƒSn;g}|D](}|t|i|ƒ|i|ƒƒq>~SdS(s$intercept of the linear fit with x=XN(RR&Rty_meanRr(R tXRsR?((sc:\py\lib\aver.pyRq™s#cCsxti|ƒo<|i||i|i}t||i|ƒ|iƒSn)g}|D]}||i|ƒqW~SdS(s$intercept of the linear fit with y=YN(RR&RlRiRhRRrR?(R tYtx0RsRq((sc:\py\lib\aver.pyR? s!cCs|i||i|iS(N(RhRlRi(R R?((sc:\py\lib\aver.pyR|¨scCs%|id||id|idS(Niigà?(RkRlRm(R R?((sc:\py\lib\aver.pyRr«scOs+ddk}|i||i|ƒ||ŽS(Niÿÿÿÿ(tpylabtplotR|(R R?RQRRR€((sc:\py\lib\aver.pyt plot_line®s cOsQddk}|i||i|ƒ|i|ƒ|i|ƒ|i|ƒ||ŽS(Niÿÿÿÿ(R€t fill_betweenR|Rr(R R?RQRRR€((sc:\py\lib\aver.pyt plot_envelope²s cCs|idtddddƒS(NR<R?Rq(tstrRL(R ((sc:\py\lib\aver.pyR¶sR?Rqc CsŠ|iƒ}|idƒ}|idjo|id9_d}nd}d||id|ƒ|odnd|||id|ƒfS( Niiÿÿÿÿt-t+s%s = (%s)%s%s %s %sR<s\times t (R{RqRR>(R R<R?RqR{t intercepttisign((sc:\py\lib\aver.pyR…¸s  N(RCRDRER RGR8RzR{RqR?R|RrR‚R„RRLR…(((sc:\py\lib\aver.pyRgAs =        ( RERR3tobjectRRRTRfRg(((sc:\py\lib\aver.pys s Ä   :