m 寏Fc@sSdZdfdYZdkZdklZdeefdYZ[[defdYZd efd YZd efd YZd k l Z de efdYZ de eeefdYZ dZ dZdZde fdYZ[ [[dZee idddde_ee iddde_dS(sRepresentation of distributions. This is about giving a numeric semantics to dictionaries whose keys are the putative values of some quantity: to each, associate an interval (whose edges aren't specified but lie between the given key and its neighbours); the value for a key is the integral of the distribution across the interval associated with that key. In caricature at least, the value of a key is the probability that a random selection from the distribution would be closer to the given key than to any of the other keys in the same dictionary: and the keys are roughly the odd 2n-iles, where n is the number of keys, so have roughly equal weights. When combining two such `numeric' values, we want to combine each key of one with each key of the other, using the result as a key in the composite dictionary. This key gets a contribution to its value which is the product of the values of the two keys combined to produce it: if it is the result of several such combinations, its value will be a sum of such products. Then take the resulting big bok of weighted values, compute its odd 2n-iles for some chosen n, use these as the keys of a dictionary in which weight[key] is the sum of the big bok's values for keys which are closer to this key of weight than to any other. Various classes with Weighted in their names provide the underlying implementation for that; the class Sample packages this functionality up for external consumption. $Id: sample.py,v 1.38 2007/07/07 15:21:57 eddy Exp $ t _baseWeightedcBs tZdZdZdZRS(sBase class for weight dictionaries. A `weight dictionary' has `data points' as its keys and weights as the associated values. It is to be read as a `distribution': typically, as a probability distribution (when the sum of the weights is one). The presence of a given { key: value } within the dictionary indicates that there is some neighbourhood of the data point, key, in which there is a probability value of finding your random thing. I aim to coerce things into a form where, to the best of my knowledge, the neighbourhood of each key lies between the neighbouring keys above and below. The various kinds of functionality layered together to make this are split from one another in this file to allow the possibility of re-use of some of the toolset by alloying with some other implementation of other parts of the toolset. Each part's implementation assumes the exported functionality of the other parts, so only alloys analogous to Weighted are viable: instances of the component classes won't work. Sub-classes: statWeighted -- provides for statistical computations; joinWeighted -- provides for combining distributions (and transforming them); repWeighted -- integrating and rounding; _Weighted -- Object packaging a weights dictionary. These are all alloyed together to build the final class, Weighted, which is what Sample actually uses. cCst|iS(N(tmaxtselftkeys(R((t(/home/eddy/.sys/py/study/value/sample.pythigh=scCst|iS(N(tminRR(R((Rtlow>s(t__name__t __module__t__doc__RR(((RRs  N(sLazyt curveWeightedcBs}tZdZhddd<ddds(Rt_lazy_get_interpolator___cutstweigherRRttupletmaptsize(RRtignored((Rt__init__scCs d||S(Nf0.5(tatb(R$R%((RRscCs"t|djo+|pfSnd|d}||fSntdtd|d |d ptd|fd |d|d d |d|d}}|djo|ddjo d}n|djo|ddjo d}n|ftt||d |d|fS( Nif1.0icCs |djS(Ni(tx(R&((RRscCs||S(N(tyR&(R&R'((RRsiisexpected sorted dataf2.0i( R trowR&tfilterR tAssertionErrorttoptbotRtmean(RR(R-R,R&R+((Rt__cutss;-  cCs||S(N(R$R%(R$R%((RRscCst||idS(Ni(treduceRRR!(RR"R((Rt_lazy_get_total_scCs||S(N(R$R%(R$R%((RRsc Cs`td| p td|it||d}|i|i }}g|dd} }}xt|d|d D]}||} |||jo.| |d|||d|||} nx@|| jo2|| d||d|}}}||} qW|djo*||||d||||}n| i|q|Wt| S( sCuts the distribution into pieces in the proportions requested. Required argument, weights, is a list of non-negative values, having positive sum. A scaling is applied to all entries in the list to make its sum equal to self.total(). Returns a list, result, one entry shorter than weights, for which self.weigh(result) equals the re-scaled weights-list. cCs |djS(Ni(R&(R&((RRssweights cannot be negativef0.0icCs||S(N(R&ts(R&R1((RRsiiN(R)tweightsR*RRR/RtscaleRR!RtloadtanstpriortiR RtavailtappendR( RR2RR4R3R7R6RRR5R8((Rtsplits$ . $ *c Cs^dgdt||i|i} }}|ipt| Snt|idjo|id}tt |idd|}|t|jp(|||idjpt d|f|t|jo6|id||jo|d| |<| |dR7RAR1R=((RtweighsX +  ";+   6 :/>cCsh} x|iD]}d| |RtsigntrighttleftR*( RRRrRuR>RsR+RtRqRvR(((Rt __embraceRsL "              cCs|o |}nd}d}x'|djo|d|d}}q Wx'|djo|d|d}}qJWtd|d|}t||djo d|Sn|S(s2Returns a suitable power of 10 for examining what.iii f10.0N(thattwhattdecadeReR5tint(RRxRyR5Rz((Rt__units    cCs|djo<y|i}WqIttfj o|i}qIXnt|djo | Sn|o|d|jo | Snd|i}|djpt d||i f|i ||\}} |djod\}}n d\}}d\} } }|itt|| }| djo.d t|i} |td | d }nd}|djo d} nTt|} | d d jo(d| jod| idd} nd|d} x|| jp ||jobt||||}||||| | }} t!|||d|} | djo$hdd<dd<|d } n| djo |}n|||}|ot|||joK| o-| ddjp t | d| d} nt| dj}Pnt| | jo d}Pq$n|i$|d||d|}d |}qWt| djp| djp ||j}yx| djo| d}| d } ychdd<dd<dd<dd<dd<dd<dd<dd<dd<|| } Wnt&j od| } qXd} qWWnt'j o|d}nX| | } | o!|o| d d| d} n|| S( s?Returns a rounding-string for estim. Argument, estim, is optional: if omitted, the distribution's median (if available) or mean (likewise) will be used. Result is a string representing this value to some accuracy, in %e-style format. This implicity represents an interval, given by `plus or minus a half in the last digit'. This interval will contain estim. Normally, the interval denoted by the result string will contain less than half the weight of self's distribution and is the shortest such representation. E.g. if self.between(3.05, 3.15) >= .5 > self.between(3.135, 3.145) then self.round(pi) will return '3.14'. That's impossible if half (or more) of self's weight sits at estim, i.e. self's half-width about estim is zero. In this case, the result string will only give estim to as many significant digits as eight more than the number of sample-points of self; and if the next five digits would all have been 0, any trailing zeros will be elided from the ones given [for various sanity reasons]. Sugar: in this `exact' case, any exponent used will employ E rather than e (thus 1.2E1 for 12); and if no digits appear after the '.' in an exact representation, the '.' is omitted. if10.0f0.5is2Weights need to be positive for rounding algorithmt-itif0.10000000000000001iis1.tes%.0etEt0t1t2t3t4t5t6t7t8t9t.N(R}i(R~i(R~ii((testimR RtmedianRRnR-R Rt thresholdR*Rdt_repWeighted__embraceR>twidththeadRttbodyttweaktaimt_repWeighted__unitRtabstunitRRARettinyttailtstrR:R{tdigtcmpRotadddotRjR?tKeyErrorR@(RRR>RRtRRRoRRRRRRAR?RRR((Rtrounds   &       $  ",   c ( RR R R2R RjRmRpRRR(((RRi s     4 t joinWeightedcBsttZdZdZdeddZdZddZedd Zd Z ed Z d Z RS( sInterface-class defining how to stick distributions together. Provides apparatus for adding data to a distribution, re-sampling a distribution, obtaining a canonical distribution (i.e. one whose weights' neighbourhoods don't overlap) and for performing `cartesion product' operations (i.e. taking two distributions and obtaining the joint distribution for some combination of their parameters), including comparison. cCs ||_dS(N(tdetailRt_joinWeighted__detail(RR((RR#<sicCs |dfS(Ni(R&(R&((RR?scCs#y|i}WnRtj oFyt||}Wqettfj o|dfg}qeXnXx|D]\}}||}|djot d|||fnt |t o |i }nt |to|i|||ql|dj o||}n|||||d<Z?d=Z@d>ZAd?ZBd@dAZCedBZDRS(Ds(Models numeric values by distributions. t_strt_reprtbestcCs|djoy |WnEtj o9yt|i}Wqjtj o d}qjXnXt|}|djo d}nd}||djo |}qx+||djo||d}}qWn|||S(Niif-1.0f1.0f0.5( R3R R2RRRdttotRR R'tklaz(RR2R3RRR'((RR<s$     cOs,y|d}Wn tj o|i|d|i|io d}n|i|io d}qn[t |to|i|o d}qn-|d|df|i|o d}ny |iWn6tj o*|pt|i|i|_nX|o.y |`Wntj onX|indS(sCImplements the .observe() functionality of quantity.Quantity (q.v.)iif2.2999999999999998f1.7N(R RR RRRRRR9RRRRCRt_Sample__updateRRR RR*Rtsimplify(RRCRRR((RRsL        cCs#|ii||_|idS(sSimplifies the distribution describing self. Argument, count, is optional (default: None). If count is omitted or None, the distribution's view of how many sample points it should be using is used as count. Otherwise, it specifies the number of sample points to retain in the simplification; if it exceeds the number of sample points in use, nothing changes. N(RRRRt _lazy_reset_(RR((RR scCs|ii|_dS(N(RRR(R((RRscCs|ii|_dS(N(RRRf(R((RRfscCs|ii}x@|iD]2}|ddjp|i|o ||=qqW|o||i|d>> gr = (1 + Sample({5.**.5: 1, -(5.**.5): 1}))/2 >>> gr 0. >>> gr+1 2. >>> gr**2 0. >>> gr**2 > gr+1 1 in which gr's weighs are the roots to x*x=x+1 (and its .best is .5). Notice that gr.copy(lambda x: x**2-x-1) and gr**2-gr-1 will have quite different weight dictionaries ! RiR s$Unit width zero-centred error bar. Also known as 0 +/- .5, which can readily be used as a simple way to implement a+/-b as a + 2*b*tophat. For asymmetric error bars, use Sample.upward, which has best estimate zero, like tophat, but is uniformly distributed on the interval from zero to one.f-0.5f0.5(R RR_tstudy.snake.lazyRhR RiRRtobjectRRRRRRRt _surpriseRgtupward(RhRRRRRRRRRRRiRER_R ((Rt?s."  ( t