#--------------------------------CUT HERE------------------------------------- #! /bin/sh # # This is a shell archive. Save this into a file, edit it # and delete all lines above this comment. Then give this # file to sh by executing the command 'sh file'. The files # will be extracted into the current directory owned by # you with default permissions. echo 'x - README' sed 's/^X//' << '________This_Is_The_END________' > README X XThis file describes a small package for fitting the autologistic Xregression models described in the papers of Huffer and Wu (1997, 1998). XThese programs have been written by Fred W. Huffer. If you have any Xquestions on using these programs, or if you discover any bugs in these Xprograms, please send them to huffer@stat.fsu.edu. If you wish to be Xplaced on a mailing list to be notified of future updates of these Xprograms, please send your e-mail address to huffer@stat.fsu.edu. X X------------------- XGENERAL INFORMATION X------------------- X XThis package consists of two parts: X Xcombo.f (a collection of Fortran subroutines) Xautolog.Splus (a collection of Splus functions) X XTo use this package, you must first compile the fortran programs combo.f Xand create an object file named combo.o. When compiling combo.f, you Xshould use the option to "compile, but do not link". (This is the -c Xoption on my compiler.) X XThe files combo.o and autolog.Splus must both be in the "current" Xdirectory, that is, the directory in which you are running the S-plus Xjob. X XIn order to use this package, when you start your S-plus job you must Xdo the following. X X1. Dynamically load the object file combo.o. The method of doing this X varies from machine to machine. You must read the Splus manuals to X find the method appropriate for your setup. X X2. Execute the command X source("autolog.Splus") X XThese two steps can be performed in either order. X XIn what follows, we shall use various S-plus functions. There will be Xlittle said about these functions. The necessary details are given in Xcomment statements embedded in the functions. In particular, the Xcomments given in the functions mcmc and newton.raphson are very Ximportant. (The comments in newton.raphson describe the estimation Xoutput supplied by mcmc.) The comments in the Fortran subroutine Xgibgen give a complete description of the arguments used in the S-plus Xfunctions gibgen() and gibgen.setup(). X X----------------------- XA Data Analysis Example X----------------------- X XThe file "sp38data" contains the data for species no. 38 that we Xused in our two papers. (The climate variables have been rounded Xto a smaller number of places, so do not expect to get exact Xagreement with our published results.) To illustrate the basic Xuse of our programs we will repeat the analysis from our papers. XThis particular data has a very high degree of spatial Xautocorrelation. This complicates the fitting process. If your Xdata has less spatial autocorrelation, the fitting process will Xproceed much more easily. In any case, the procedure you follow Xwill be similar to the one given below. X XDescription of the Data: XThere are 7 columns in the data set. XColumns 1 and 2 (named row and col) give the row and column X coordinates of the sites. XColumn 3 (named sp38) is a binary variable recording the presence X or absence of species number 38 at each site. XColumns 4--7 are the climate variables fzf, tav, prcp, mi. XThere are a total of 1845 sites, each corresponding to a row in X the data set. X XPut this data in a plain text (ascii) file called "sp38data" in Xyour working (current) directory. X XAn "attempt" to replicate the analysis in our Biometrics (1998) paper Xwould use the following commands. In this paper we modeled the species Xdistribution in terms of the variable fzf. X Xsource("autolog.Splus") Xdyn.load("combo.o") # or whatever method of dynamic loading is used X # on your computer. X Xdat<-read.table("sp38data",header=T,row.names=NULL) Xattach(dat) X Xcoords<-cbind(row,col) X Xfit1<-mcmc(sp38,fzf,coords,nrec=1000) Xfit2<-mcmc(sp38,fzf,coords,nrec=2000,psi=fit1$theta) Xfit3<-mcmc(sp38,fzf,coords,nrec=4000,psi=fit2$theta) X Xetc. X XContinue increasing the simulation sample size (nrec) until you Xare satisfied with the accuracy of the estimates. The first Xcommand (fit1) will compute estimates starting from the Xpseudo-likelihood estimates. The second command (fit2) takes the Xestimates from fit1 and starts from these, etc. The simulation Xsample size (nrec) is being progressively increased. X XThis procedure works well for most data sets. For data sets with a Xsmall amount of spatial correlation, the pseudo-likelihood estimates Xwill be fairly close to the MLE's and you may not even need fit2, fit3, Xetc. The answers from fit1 are often good enough. X XHowever, the data for species 38 has a very strong spatial correlation Xand the pseudo-likelihood estimates are very far from the MLE's. As a Xresult, the command for fit1 usually crashes with an error message about Xan "apparently singular matrix". (If you are lucky, or repeat the Xprocedure many times, you will get a Monte Carlo sample which produces Xreasonable values in fit1.) We need better starting values than the Xpseuod-likelihood estimates for this data. X XOne way to proceed is to pick a vector of initial parameter estimates X(call it start) in some ad hoc fashion, and then do: X Xstart<-c(9,-.05,3) Xfit1<-mcmc(sp38,fzf,coords,nrec=1000,psi=start) Xfit2<-mcmc(sp38,fzf,coords,nrec=2000,psi=fit1$theta) Xfit3<-mcmc(sp38,fzf,coords,nrec=4000,psi=fit2$theta) Xetc. X XAnother way is to use the function amcmc which is included with Xthe Splus code in the file "autolog.Splus". The name amcmc Xstands for "adaptive" MCMC method; the parameter estimates are Xmodified gradually until they are reasonably close to the MLE's. XUsing this function, you would do the following: X Xfit1<-amcmc(sp38,fzf,coords,nrec=1000) Xfit2<-mcmc(sp38,fzf,coords,nrec=4000,psi=fit1$theta) X XThe function amcmc will sometimes crash on this data. If it does, just Xtry it again. The function amcmc takes a long time to run, so do not be Xalarmed. If the output from fit1 is sufficiently accurate, there is no Xneed for fit2. X XIn our paper in "Environmental and Ecological Statistics" (1997) we used Xa three variable model with covariates tav, prcp, and mi. (In this Xpaper we scaled the variables to have mean zero and variance one, but Xneglected to mention this.) An "attempt" to replicate this analysis Xwould do the following: X Xsource("autolog.Splus") Xdyn.load("combo.o") X Xdat<-read.table("sp38data",header=T,row.names=NULL) Xattach(dat) X Xxcov<-scale(cbind(tav,prcp,mi)) Xcoords<-cbind(row,col) X Xfit1<-mcmc(sp38,xcov,coords,nrec=2000) Xfit2<-mcmc(sp38,xcov,coords,nrec=2000,psi=fit1$theta) Xfit3<-mcmc(sp38,xcov,coords,nrec=4000,psi=fit2$theta) Xetc. X XAgain, because of the extreme amount of spatial correlation and the big Xdifference between the pseudo-likelihood estimates and the MLE, the Xcommand for fit1 usually crashes (but works fine on most data sets). XYou proceed in the same way as before. Either put an option psi=start Xin the command for fit1 (where start is an appropriate vector of initial Xparameter values), or use the amcmc function as follows. X Xfit1<-amcmc(sp38,xcov,coords,nrec=1000) Xfit2<-mcmc(sp38,xcov,coords,nrec=4000,psi=fit1$theta) X XThe command for fit1 sometimes crashes. Just try it again. Take Xheart, all of this works much better on data with less spatial Xautocorrelation. X X----------------------------- XExamples Using Simulated Data X----------------------------- X XTo illustrate the use of the S-plus functions, we will simulate a data Xset and fit an autologistic regression model to this data. X XThe commands X X fake<-make.torus() X base<-fake$base X x<-fake$x.torus X Xcreate a map (described by the matrix "base") and a covariate x. The Xmatrix base lists the sites on the map; the i-th row of base contains Xthe row-column coordinates of the i-th site on the map. The vector x Xgives the values of a covariate at each site on the map. X XNow we simulate a data set from an autologistic model with the commands: X X y.init<-rep(1,length(x)) X L<-gibgen.setup(y=y.init,x= -1.5+0.5*x,b=0.8,base=base,g0=100) X L<-gibgen(L) X y<-gety(L) X XThe first command just creates an initial map which is 1 (species X"present") at all sites. The function gibgen.setup sets up a list of Xarguments L for the function gibgen which does the actual work. The Xarguments "x= -1.5+.5*x, b=0.8" specify that we are simulating from an Xautologistic model with the regression part -1.5+0.5*x and a spatial Xinteraction parameter of 0.8. The argument "y=y.init" says to start Xthe Gibbs sampler from the initial map y.init. The argument "g0=100" Xsays to run the Gibbs sampler for 100 sweeps. The command X"L<-gibgen(L)" runs the Gibbs sampler and passes the output back in L. XThen "y<-gety(L)" extracts the simulated data from the list L and puts Xit in the vector y. If you want to look at a map of the simulated Xbinary data, one quick (but crude) way is to use the following Xcommand: X X print.binary(y,base) X XThe above commands are not that important. If the user has real data Xset up as vectors y, x, and a matrix base, he/she can proceed directly Xto the model fitting stage, which is done next. X XTo fit the autologistic regression model (that is, compute the MCMC XMLE's), you execute the next command: X X mod<-mcmc(y,x,base,nrec=1000,g1=3) X XThis computes approximate MLE's based on an MCMC sample of 1000 sets Xof of sufficient statistics (set by the options "nrec = 1000") Xcollected after every third sweep performed by the Gibbs sampler (set Xby the option "g1 = 3"). The output of mcmc is a list. The Xcomponents of this list are explained in the comment statements of the XS-plus function newton.raphson. The complete sample of sufficient Xstatistics (and also some other information) produced by the most Xrecent mcmc run is always stored in the object tmp.mcmc. Examining Xthe sample of sufficient statistics can help to determine whether or Xnot the MCMC estimation procedure is producing reasonable answers. X XAfter fitting the model, one may wish to simulate from the fitted Xmodel and examine the resulting random presence/absence maps. One Xuseful thing is to find out the probability that the species will be Xpresent at each site on the map. This probability can be estimated by Xrunning the Gibbs sampler for a long time and computing the proportion Xof time the species is present at each site. We do this now. X X theta<-mod$theta X L<-gibgen.setup(x=theta[1]+theta[2]*x, b=theta[3], X y=y.init, base=base, X dotot=T, nrec=4000, g0=100, g1=2) X L<-gibgen(L) X prob<-L$tot/4000 X XThe above commands extract the parameter estimates (theta) from the Xfitted model (mod), and then set up the Gibbs sampler to simulate from Xthe fitted model. The parameters in theta are always ordered with the Xintercept first and the spatial interaction parameter last. The Xoptions "dotot=T, nrec=4000, g0=100, g1=2" instruct the program to Xcount the total number of times each site is occupied. This is done X4000 times (nrec=4000), with the counting beginning with the 100th Xsweep of the Gibbs sampler (g0=100), and taking place every second Xsweep thereafter (g1=2). The component L$tot contains the total count Xfor each site. Dividing by 4000 converts these to proportions. The XGibbs sampler is started from y.init, the map consisting entirely of X1's. X XA quick (but crude) plot of the fitted probabilities is produced by Xthis command: X X print.prob(prob,base,space=" ") X XThis displays only the first decimal place of the probabilities. X X----------------------------------- XModels With More Than One Covariate X----------------------------------- X XModels with many covariates are handled just like models with one Xcovariate. When the spatial correlation is high difficulties can Xarise in the MCMC estimation procedure, but the steps involved are the Xsame. X XWe give an example with two covariates. We shall use the row number Xfor each site as a second covariate z. This gives a covariate which Xincreases as one moves to the south. The covariate z is created by: X X z<-base[,1] X XWe now simulate from the autologistic model with the regression part Xgiven by "-3.2+0.9*x+0.2*z" and a spatial interaction parameter of 0.8. X X L<-gibgen.setup(y=y.init,x= -3.2+0.9*x+0.2*z,b=0.8,base=base,g0=100) X L<-gibgen(L) X y<-gety(L) X XTo fit a model with more than one covariate, just use the matrix of Xregression variables as the second argument of the function mcmc. For Xour simulated data, we use the command: X X mod<-mcmc(y,cbind(x,z),base,nrec=1000,g1=3) X XSimulating from the fitted model can now be carried out as before. X XThe mcmc default is to use the pseudo-likelihood estimates as the Xvector psi for generating the MCMC sample. If the pseudo-likelihood Xestimates do not work, and you cannot think up some other reasonable Xchoice for psi, I recommend using the function amcmc for the initial Xmodel fitting. The function amcmc is similar to mcmc, but implements Xa procedure for successively modifying psi. (The "a" in "amcmc" Xstands for "adaptive" or "automatic".) X X------------------------------------- XRemarks on Simulations Using gibgen() X------------------------------------- X XThe output of gibgen() is a list. The component y of this list is the Xlast random binary map produced by the Gibbs sampler. Since the input Xand output lists for gibgen have the same format, you can feed the Xoutput of gibgen back into gibgen, so that the last map produced by the Xprevious run becomes the initial map of the next run. Thus, the Gibbs Xsampler picks up right where it left off. This is often a useful Xfeature. X XExample: We generate 3 random maps y1, y2, y3, with each map Xserving as the initial map when generating the next map. X X L<-gibgen.setup(y=y.init,x= -1.5+0.5*x,b=0.8,base=base,g0=20) X L<-gibgen(L) X y1<-gety(L) X L<-gibgen(L) X y2<-gety(L) X L<-gibgen(L) X y3<-gety(L) X XTo view these maps, use print.binary. X X print.binary(y1,base) X print.binary(y2,base) X print.binary(y3,base) X XSince we have set g0=20 (so that the first 19 maps in each run are Xdiscarded), the maps y1, y2, y3 may be regarded as the 20th, 40th and X60th maps produced in a single run of the Gibbs sampler. X XNow we generate 3 random maps y1, y2, y3, but use the same map X(y.init) as the initial map for all of them. X X L.init<-gibgen.setup(y=y.init,x= -1.5+0.5*x,b=0.8,base=base,g0=20) X L<-gibgen(L.init) X y1<-gety(L) X L<-gibgen(L.init) X y2<-gety(L) X L<-gibgen(L.init) X y3<-gety(L) X XDepending on the circumstances, you may wish to use one mode of Xoperation or the other. ________This_Is_The_END________ if test `wc -l < README` -ne 351; then echo 'shar: README was damaged during transit (should have had 351 lines)' fi echo 'x - combo.f' sed 's/^X//' << '________This_Is_The_END________' > combo.f Xc This is a collection of Fortran subroutines which are intended Xc to be called from within S-plus. Xc The most important of these routines is gibgen. Xc Xc This program should be compiled with the "compile, but do not link" Xc option of the Fortran compiler. (This is the -c option on the Xc compiler I use.) This should create a single object file which Xc can be loaded using the dyn.load function in Splus. This object Xc file must be named combo.o. Xcccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc X X subroutine neibsum(y,base,sum,m,n,ns) Xc Xc This computes neighborhood sums for the map in the Xc matrix y with sites recorded in base. Xc The answer is passed back in the array sum. Xc y is any matrix of real values; it is usually a binary matrix Xc with presence=1, absence= 0. Xc The entries of y should (usually) be set to zero for non-sites. Xc base is a matrix with two columns listing the sites Xc on the map. Column 1 gives the row, column 2 gives the column. Xc The i-th row of base gives the coordinates of the i-th Xc site on the map. Xc sum is an array of ns integers to contain the final answer. Xc m,n are the dimensions of the matrix y. Xc ns is the number of sites = number of rows in base. Xc X integer m,n,ns,base(ns,2),i,j,k X double precision y(m,n),sum(ns) X do 40 k=1,ns X i=base(k,1) X j=base(k,2) X sum(k)=y(i,j-1)+y(i,j+1)+y(i-1,j)+y(i+1,j) X 40 continue X return X end X X X subroutine sumprod(y,base,ans,m,n,ns) Xc Xc This computes the sum of all the neighborhood products for the Xc map in the matrix y with sites recorded in base. Xc The answer is passed back in the argument ans. Xc y is an m by n matrix of real values. Xc The entries of y should (usually) be set to zero for non-sites. Xc base is a matrix with two columns listing the sites Xc on the map. Column 1 gives the row, column 2 gives the column. Xc The i-th row of base gives the coordinates of the i-th Xc site on the map. Xc ans is a double precision value containing the final answer. Xc m,n are the dimensions of the matrix y. Xc ns is the number of sites = number of rows in base. Xc X integer m,n,ns,base(ns,2),i,j,k X double precision y(m,n),ans X ans=0.0d0 X do 40 k=1,ns X i=base(k,1) X j=base(k,2) X ans=ans+y(i,j)*(y(i,j-1)+y(i,j+1)+y(i-1,j)+y(i+1,j)) X 40 continue X ans=0.5d0*ans X return X end X X X subroutine nbprod(w,s,base,map,w1,w2,m1,m2) Xc Xc This computes the sum t(w(i))w(j) over all pairs of neighboring Xc sites i and j. Here w(j) is the j-th row of w. Xc t(w(i)) is the transpose of the i-th row of w. Xc w is a matrix. The i-th row of w are values associated with Xc the i-th site on the map which is located at coordinates Xc given in the i-th row of base. The number of rows in w and Xc base should be the same. Xc s is the matrix in which the final answer is returned. Xc The entries should all be zero initially. Xc base is a matrix with two columns listing the sites Xc on the map. Column 1 gives the row, column 2 gives the column. Xc The i-th row of base gives the coordinates of the i-th Xc site on the map. Xc map is an integer matrix initially filled with zeros. Xc The sites on the map are numbered according to their Xc corresponding row in base in the course of the subroutine. Xc w1, w2 are the dimensions of w. Xc m1, m2 are the dimensions of map. Xc X integer w1,w2,m1,m2 X integer base(w1,2),map(m1,m2) X double precision w(w1,w2),s(w2,w2) X integer pos(4,2),site,i,j,ni,nj,nsit,nbr,r,c X pos(1,1)= 1 X pos(1,2)= 0 X pos(2,1)= -1 X pos(2,2)= 0 X pos(3,1)= 0 X pos(3,2)= 1 X pos(4,1)= 0 X pos(4,2)= -1 X do 200 site =1,w1 X i=base(site,1) X j=base(site,2) X map(i,j)=site X do 100 nbr=1,4 X ni=i+pos(nbr,1) X nj=j+pos(nbr,2) X nsit=map(ni,nj) X if (nsit.ne.0) then X do 50 r=1,w2 X do 50 c=1,w2 X s(r,c)=s(r,c)+w(site,r)*w(nsit,c) X 50 continue X endif X 100 continue X 200 continue Xc Now symmetrize the answer matrix s. X do 300 r=1,w2 X do 300 c=1,r X s(r,c)=s(r,c)+s(c,r) X s(c,r)=s(r,c) X 300 continue X return X end X Xcccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc X X X subroutine gibgen(y,x,b,g0,g1,base,nrow,ncol,nsite,nrec, X $ dosuff,cov,suff,ncov, X $ nzbd,sittyp, X $ dotot,tot) Xc Xc This is a gibbs sampler which collects Xc sufficient statistics every g1 generations. Xc It handles the non-rectangular lattice specified in "base". Xc y is a map stored as a matrix (lattice), Xc but x, cov are indexed by base. Xc Xc y(nrow,ncol) is the presence/absence map, presence=1, absence= 0, Xc neutral = 0.5 (sometimes used for boundary cells). Xc x(nsite) is the offset. Xc It contains the combined covariate information. (see below) Xc b is the spatial correlation parameter in the auto-logistic model. Xc Together, x and b specify the autologistic model. Xc The conditional probability p of a response at a site Xc with lattice coordinates (i,j) is given by Xc Xc p = eta/(1+eta) where Xc eta=exp(x(site)+b*(y(i,j-1)+y(i,j+1)+y(i-1,j)+y(i+1,j))). Xc Xc g0 is the number of generations to run the gibbs sampler Xc before collecting any sufficient statistics Xc (the warm up period). Xc g1 is the spacing, the interval (in generations) between Xc collecting suff. stats. Xc base(nsite,2) lists the sites on the map. Xc The k-th row of base gives the coordinates (i,j) of Xc the k-th site on the map Xc nrow,ncol are dimensions of the matrix y. Xc nsite is the number of sites on the map. Xc nsite = number of rows in base, x, cov. Xc nrec is number of vectors of suff. stats. to record. Xc dosuff is a logical value indicating whether suff stats should Xc be collected. Xc cov(nsite,ncov) contains the covariates. Xc suff(nrec,ncov+2) will contain the suff. stats. Xc All entries in suff must be initialized to zero. Xc ncov is the number of covariates (excluding intercept and Xc nearest neighbor terms). Xc nzbd is a logical value indicating whether nonzero boundary Xc values are used. This is needed only when suff. stats are Xc being collected (dosuff = .TRUE.). Xc sittyp(nrow,ncol) is an integer array indicating site type. Xc 0 = outside region (or map). Xc 1 = interior of region. Xc 2 = boundary of region. Xc The interior (sittyp=1) consists of the sites listed in base. Xc sittyp is needed ONLY when suff stats are being collected Xc (dosuff = .TRUE.) AND nonzero boundary values are being Xc used (nzbd = .TRUE). Xc dotot is a logical value indicating whether totals should kept Xc for each site. These totals are stored in tot (see below). Xc tot is indexed by base and will contain the total number of times Xc (out of nrec) that the site was 1 (= present). Xc tot must be initialized to zero. Xc X integer g0, g1, nrec, base(nsite,2), nrow, ncol, nsite, ncov, X $ sittyp(nrow,ncol), tot(nsite), i, j, k, site, X $ g, count, nsuff, nloop X double precision y(nrow,ncol), x(nsite), b, cov(nsite,ncov), X $ suff(nrec,ncov+2), p, yy, pmax, pmin X real ranf X logical dosuff, dotot, nzbd, first X parameter(pmax=2.0d0**24-1,pmin=1.0d0/pmax) Xc X nsuff=ncov+2 X g=g0 X first=.TRUE. X nloop=nrec X if(nrec .le. 0) then X dosuff=.FALSE. X dotot=.FALSE. X nloop=1 X endif X do 200 count=1,nloop X do 50 k=1,g X do 40 site=1,nsite X i=base(site,1) X j=base(site,2) X p=exp(x(site)+b*(y(i,j-1)+y(i,j+1)+y(i-1,j)+y(i+1,j))) X if(p .gt. pmax) then X y(i,j)=1 X else if(p .lt. pmin) then X y(i,j)=0 X else X p=p/(1.0+p) X if(ranf() .lt. p) then X y(i,j)=1 X else X y(i,j)=0 X endif X endif X 40 continue X 50 continue X if (first) then X g=g1 X first=.FALSE. X endif X if (dosuff) then X do 90 site=1,nsite X i=base(site,1) X j=base(site,2) X yy=y(i,j) X suff(count,1)=suff(count,1)+yy X do 80 k=1,ncov X suff(count,k+1)=suff(count,k+1)+yy*cov(site,k) X 80 continue X if(yy .eq. 1.0) then X if (nzbd) then X suff(count,nsuff)=suff(count,nsuff)+ X $ sittyp(i,j-1)*y(i,j-1)+ X $ sittyp(i,j+1)*y(i,j+1)+ X $ sittyp(i-1,j)*y(i-1,j)+ X $ sittyp(i+1,j)*y(i+1,j) X else X suff(count,nsuff)=suff(count,nsuff)+ X $ y(i,j-1)+y(i,j+1)+y(i-1,j)+y(i+1,j) X endif X endif X 90 continue X suff(count,nsuff)=0.5d0*suff(count,nsuff) X endif X if (dotot) then X do 120 site=1,nsite X tot(site)=tot(site)+y(base(site,1),base(site,2)) X 120 continue X endif X 200 continue X return X end X Xcccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc X X X X REAL FUNCTION ranf() XC********************************************************************** XC XC REAL FUNCTION RANF() XC RANDom number generator as a Function XC XC Returns a random floating point number from a uniform distribution XC over 0 - 1 (endpoints of this interval are not returned) using the XC current generator XC XC This is a transcription from Pascal to Fortran of routine XC Uniform_01 from the paper XC XC L'Ecuyer, P. and Cote, S. "Implementing a Random Number Package XC with Splitting Facilities." ACM Transactions on Mathematical XC Software, 17:98-111 (1991) XC XC********************************************************************** XC The functions ranf() and ignlgi() have been combined into ranf(). XC********************************************************************** XC XC INTEGER FUNCTION IGNLGI() XC GeNerate LarGe Integer XC XC Returns a random integer following a uniform distribution over XC (1, 2147483562) using the current generator. XC XC This is a transcription from Pascal to Fortran of routine XC Random from the paper XC XC L'Ecuyer, P. and Cote, S. "Implementing a Random Number Package XC with Splitting Facilities." ACM Transactions on Mathematical XC Software, 17:98-111 (1991) XC XC********************************************************************** XC .. Parameters .. X INTEGER numg X PARAMETER (numg=32) XC .. XC .. Scalars in Common .. X INTEGER sss1,sss2,a1,a1vw,a1w,a2,a2vw,a2w,m1,m2 XC .. XC .. Arrays in Common .. X INTEGER cg1(numg),cg2(numg),ig1(numg),ig2(numg),lg1(numg), X + lg2(numg) X LOGICAL qanti(numg) XC .. XC .. Local Scalars .. X INTEGER k,z XC .. XC .. XC .. Common blocks .. X COMMON /globe/m1,m2,sss1,sss2,a1,a2,a1w,a2w,a1vw,a2vw, X + ig1,ig2,lg1,lg2,cg1, X + cg2,qanti XC .. XC .. Save statement .. X SAVE /globe/ XC .. XC .. Executable Statements .. XC X k = sss1/53668 X sss1 = a1* (sss1-k*53668) - k*12211 X IF (sss1.LT.0) sss1 = sss1 + m1 X k = sss2/52774 X sss2 = a2* (sss2-k*52774) - k*3791 X IF (sss2.LT.0) sss2 = sss2 + m2 X z = sss1 - sss2 X IF (z.LT.1) z = z + m1 - 1 XC XC 4.656613057E-10 is 1/M1 M1 is set in a data statement in IGNLGI XC and is currently 2147483563. If M1 changes, change this also. XC X ranf = z*4.656613057E-10 X RETURN X X END X X X LOGICAL FUNCTION qrgnin() XC********************************************************************** XC XC LOGICAL FUNCTION QRGNIN() XC Q Random GeNerators INitialized? XC XC A trivial routine to determine whether or not the random XC number generator has been initialized. Returns .TRUE. if XC it has, else .FALSE. XC XC********************************************************************** XC .. Scalar Arguments .. X LOGICAL qvalue XC .. XC .. Local Scalars .. X LOGICAL qinit XC .. XC .. Entry Points .. X LOGICAL qrgnsn XC .. XC .. Save statement .. X SAVE qinit XC .. XC .. Data statements .. X DATA qinit/.FALSE./ XC .. XC .. Executable Statements .. X qrgnin = qinit X RETURN X X ENTRY qrgnsn(qvalue) XC********************************************************************** XC XC LOGICAL FUNCTION QRGNSN( QVALUE ) XC Q Random GeNerators Set whether iNitialized XC XC Sets state of whether random number generator is initialized XC to QVALUE. XC XC This routine is actually an entry in QRGNIN, hence it is a XC logical function. It returns the (meaningless) value .TRUE. XC XC********************************************************************** X qinit = qvalue X qrgnsn = .TRUE. X RETURN X X END X X X SUBROUTINE getcgn(g) X INTEGER g XC********************************************************************** XC XC SUBROUTINE GETCGN(G) XC Get GeNerator XC XC Returns in G the number of the current random number generator XC XC XC Arguments XC XC XC G <-- Number of the current random number generator (1..32) XC INTEGER G XC XC********************************************************************** XC X INTEGER curntg,numg X SAVE curntg X PARAMETER (numg=32) X DATA curntg/1/ XC XC .. XC .. Scalars in Common .. X INTEGER sss1,sss2,a1,a1vw,a1w,a2,a2vw,a2w,m1,m2 XC .. XC .. Arrays in Common .. X INTEGER cg1(numg),cg2(numg),ig1(numg),ig2(numg),lg1(numg), X + lg2(numg) X LOGICAL qanti(numg) XC .. XC .. Common blocks .. X COMMON /globe/m1,m2,sss1,sss2,a1,a2,a1w,a2w,a1vw,a2vw, X + ig1,ig2,lg1,lg2,cg1, X + cg2,qanti XC .. XC .. Save statement .. X SAVE /globe/ XC .. XC .. Executable Statments X g = curntg X RETURN X X ENTRY setcgn(g) XC********************************************************************** XC XC SUBROUTINE SETCGN( G ) XC Set GeNerator XC XC Sets the current generator to G. All references to a generat XC are to the current generator. XC XC XC Arguments XC XC XC G --> Number of the current random number generator (1..32) XC INTEGER G XC XC********************************************************************** XC XC Abort if generator number out of range XC X X X 10 continue X if((sss1.eq.-999).and.(sss2.eq.-999))then X curntg = g X else X cg1(curntg)=sss1 X cg2(curntg)=sss2 X curntg = g X sss1=cg1(curntg) X sss2=cg2(curntg) X endif X RETURN X X END X X X SUBROUTINE inrgcm() XC********************************************************************** XC XC SUBROUTINE INRGCM() XC INitialize Random number Generator CoMmon XC XC XC Function XC XC XC Initializes common area for random number generator. This saves XC the nuisance of a BLOCK DATA routine and the difficulty of XC assuring that the routine is loaded with the other routines. XC XC********************************************************************** XC .. Parameters .. X INTEGER numg X PARAMETER (numg=32) XC .. XC .. Scalars in Common .. X INTEGER sss1,sss2,a1,a1vw,a1w,a2,a2vw,a2w,m1,m2 XC .. XC .. Arrays in Common .. X INTEGER cg1(numg),cg2(numg),ig1(numg),ig2(numg),lg1(numg), X + lg2(numg) X LOGICAL qanti(numg) XC .. XC .. Local Scalars .. X INTEGER i X LOGICAL qdum XC .. XC .. External Functions .. X LOGICAL qrgnsn X EXTERNAL qrgnsn XC .. XC .. Common blocks .. X COMMON /globe/m1,m2,sss1,sss2,a1,a2,a1w,a2w,a1vw,a2vw, X + ig1,ig2,lg1,lg2,cg1, X + cg2,qanti XC .. XC .. Save statement .. X SAVE /globe/ XC .. XC .. Executable Statements .. XC V=20; W=30; XC XC A1W = MOD(A1**(2**W),M1) A2W = MOD(A2**(2**W),M2) XC A1VW = MOD(A1**(2**(V+W)),M1) A2VW = MOD(A2**(2**(V+W)),M2) XC XC If V or W is changed A1W, A2W, A1VW, and A2VW need to be recomputed. XC An efficient way to precompute a**(2*j) MOD m is to start with XC a and square it j times modulo m using the function MLTMOD. XC X m1 = 2147483563 X m2 = 2147483399 X a1 = 40014 X a2 = 40692 X a1w = 1033780774 X a2w = 1494757890 X a1vw = 2082007225 X a2vw = 784306273 X DO 10,i = 1,numg X qanti(i) = .FALSE. X 10 CONTINUE XC XC Tell the world that common has been initialized XC X qdum = qrgnsn(.TRUE.) X RETURN X X END X X X SUBROUTINE setall(iseed1,iseed2) XC********************************************************************** XC XC SUBROUTINE SETALL(ISEED1,ISEED2) XC SET ALL random number generators XC XC Sets the initial seed of generator 1 to ISEED1 and ISEED2. The XC initial seeds of the other generators are set accordingly, and XC all generators states are set to these seeds. XC XC This is a transcription from Pascal to Fortran of routine XC Set_Initial_Seed from the paper XC XC L'Ecuyer, P. and Cote, S. "Implementing a Random Number Package XC with Splitting Facilities." ACM Transactions on Mathematical XC Software, 17:98-111 (1991) XC XC XC Arguments XC XC XC ISEED1 -> First of two integer seeds XC INTEGER ISEED1 XC XC ISEED2 -> Second of two integer seeds XC INTEGER ISEED1 XC XC********************************************************************** XC .. Parameters .. X INTEGER numg X PARAMETER (numg=32) XC .. XC .. Scalar Arguments .. X INTEGER iseed1,iseed2 X LOGICAL qssd XC .. XC .. Scalars in Common .. X INTEGER sss1,sss2,a1,a1vw,a1w,a2,a2vw,a2w,m1,m2 XC .. XC .. Arrays in Common .. X INTEGER cg1(numg),cg2(numg),ig1(numg),ig2(numg),lg1(numg), X + lg2(numg) X LOGICAL qanti(numg) XC .. XC .. Local Scalars .. X INTEGER g,ocgn X LOGICAL qqssd XC .. XC .. External Functions .. X INTEGER mltmod X LOGICAL qrgnin X EXTERNAL mltmod,qrgnin XC .. XC .. External Subroutines .. X EXTERNAL getcgn,initgn,inrgcm,setcgn XC .. XC .. Common blocks .. X COMMON /globe/m1,m2,sss1,sss2,a1,a2,a1w,a2w,a1vw,a2vw, X $ ig1,ig2,lg1,lg2,cg1, X + cg2,qanti XC .. XC .. Save statement .. X SAVE /globe/,qqssd XC .. XC .. Data statements .. X DATA qqssd/.FALSE./ XC .. XC .. Executable Statements .. X sss1=-999 X sss2=-999 XC XC TELL IGNLGI, THE ACTUAL NUMBER GENERATOR, THAT THIS ROUTINE XC HAS BEEN CALLED. XC X qqssd = .TRUE. X CALL getcgn(ocgn) XC XC Initialize Common Block if Necessary XC X IF (.NOT. (qrgnin())) CALL inrgcm() X ig1(1) = iseed1 X ig2(1) = iseed2 X CALL initgn(-1) X DO 10,g = 2,numg X ig1(g) = mltmod(a1vw,ig1(g-1),m1) X ig2(g) = mltmod(a2vw,ig2(g-1),m2) X CALL setcgn(g) X CALL initgn(-1) X 10 CONTINUE X CALL setcgn(ocgn) X sss1=cg1(ocgn) X sss2=cg2(ocgn) X RETURN X X ENTRY rgnqsd(qssd) XC********************************************************************** XC XC SUBROUTINE RGNQSD XC Random Number Generator Query SeeD set? XC XC Returns (LOGICAL) QSSD as .TRUE. if SETALL has been invoked, XC otherwise returns .FALSE. XC XC********************************************************************** X qssd = qqssd X RETURN X X END X X X X INTEGER FUNCTION mltmod(a,s,m) XC********************************************************************** XC XC INTEGER FUNCTION MLTMOD(A,S,M) XC XC Returns (A*S) MOD M XC XC This is a transcription from Pascal to Fortran of routine XC MULtMod_Decompos from the paper XC XC L'Ecuyer, P. and Cote, S. "Implementing a Random Number Package XC with Splitting Facilities." ACM Transactions on Mathematical XC Software, 17:98-111 (1991) XC XC XC Arguments XC XC XC A, S, M --> XC INTEGER A,S,M XC XC********************************************************************** XC .. Parameters .. X INTEGER h X PARAMETER (h=32768) XC .. XC .. Scalar Arguments .. X INTEGER a,m,s XC .. XC .. Local Scalars .. X INTEGER a0,a1,k,p,q,qh,rh XC .. XC .. Executable Statements .. XC XC H = 2**((b-2)/2) where b = 32 because we are using a 32 bit XC machine. On a different machine recompute H XC X X 10 IF (.NOT. (a.LT.h)) GO TO 20 X a0 = a X p = 0 X GO TO 120 X X 20 a1 = a/h X a0 = a - h*a1 X qh = m/h X rh = m - h*qh X IF (.NOT. (a1.GE.h)) GO TO 50 X a1 = a1 - h X k = s/qh X p = h* (s-k*qh) - k*rh X 30 IF (.NOT. (p.LT.0)) GO TO 40 X p = p + m X GO TO 30 X X 40 GO TO 60 X X 50 p = 0 XC XC P = (A2*S*H)MOD M XC X 60 IF (.NOT. (a1.NE.0)) GO TO 90 X q = m/a1 X k = s/q X p = p - k* (m-a1*q) X IF (p.GT.0) p = p - m X p = p + a1* (s-k*q) X 70 IF (.NOT. (p.LT.0)) GO TO 80 X p = p + m X GO TO 70 X X 80 CONTINUE X 90 k = p/qh XC XC P = ((A2*H + A1)*S)MOD M XC X p = h* (p-k*qh) - k*rh X 100 IF (.NOT. (p.LT.0)) GO TO 110 X p = p + m X GO TO 100 X X 110 CONTINUE X 120 IF (.NOT. (a0.NE.0)) GO TO 150 XC XC P = ((A2*H + A1)*H*S)MOD M XC X q = m/a0 X k = s/q X p = p - k* (m-a0*q) X IF (p.GT.0) p = p - m X p = p + a0* (s-k*q) X 130 IF (.NOT. (p.LT.0)) GO TO 140 X p = p + m X GO TO 130 X X 140 CONTINUE X 150 mltmod = p XC X RETURN X X END X X X X SUBROUTINE initgn(isdtyp) XC********************************************************************** XC XC SUBROUTINE INITGN(ISDTYP) XC INIT-ialize current G-e-N-erator XC XC Reinitializes the state of the current generator XC XC This is a transcription from Pascal to Fortran of routine XC Init_Generator from the paper XC XC L'Ecuyer, P. and Cote, S. "Implementing a Random Number Package XC with Splitting Facilities." ACM Transactions on Mathematical XC Software, 17:98-111 (1991) XC XC XC Arguments XC XC XC ISDTYP -> The state to which the generator is to be set XC XC ISDTYP = -1 => sets the seeds to their initial value XC ISDTYP = 0 => sets the seeds to the first value of XC the current block XC ISDTYP = 1 => sets the seeds to the first value of XC the next block XC XC INTEGER ISDTYP XC XC********************************************************************** XC .. Parameters .. X INTEGER numg X PARAMETER (numg=32) XC .. XC .. Scalar Arguments .. X INTEGER isdtyp XC .. XC .. Scalars in Common .. X INTEGER sss1,sss2,a1,a1vw,a1w,a2,a2vw,a2w,m1,m2 XC .. XC .. Arrays in Common .. X INTEGER cg1(numg),cg2(numg),ig1(numg),ig2(numg),lg1(numg), X + lg2(numg) X LOGICAL qanti(numg) XC .. XC .. Local Scalars .. X INTEGER g XC .. XC .. External Functions .. X LOGICAL qrgnin X INTEGER mltmod X EXTERNAL qrgnin,mltmod XC .. XC .. External Subroutines .. X EXTERNAL getcgn XC .. XC .. Common blocks .. X COMMON /globe/m1,m2,sss1,sss2,a1,a2,a1w,a2w,a1vw,a2vw, X $ ig1,ig2,lg1,lg2,cg1, X + cg2,qanti XC .. XC .. Save statement .. X SAVE /globe/ XC .. XC .. Executable Statements .. XC Abort unless random number generator initialized X IF (qrgnin()) GO TO 10 X X 10 CALL getcgn(g) X IF ((-1).NE. (isdtyp)) GO TO 20 X lg1(g) = ig1(g) X lg2(g) = ig2(g) X GO TO 50 X X 20 IF ((0).NE. (isdtyp)) GO TO 30 X CONTINUE X GO TO 50 XC do nothing X 30 continue Xc 30 IF ((1).NE. (isdtyp)) GO TO 40 X lg1(g) = mltmod(a1w,lg1(g),m1) X lg2(g) = mltmod(a2w,lg2(g),m2) X GO TO 50 X X 50 cg1(g) = lg1(g) X cg2(g) = lg2(g) X RETURN X X END ________This_Is_The_END________ if test `wc -l < combo.f` -ne 852; then echo 'shar: combo.f was damaged during transit (should have had 852 lines)' fi echo 'x - autolog.Splus' sed 's/^X//' << '________This_Is_The_END________' > autolog.Splus X"amcmc"<- Xfunction(y, xcov, base, bdval = 0, maxit = 20, c1 = 8, c2 = c1/2, g0 = 100, g1 X = 5, nrec = 200, psi = NA, init = if(is.na(psi[1])) 1 else 0, b = 0, X look = F, draw = look, verbose = F, dotot = F, max.smp = 2000) X{ X# COMMENTS: X# Sometimes the pseudo-likelihood estimates do not work well as the X# vector psi needed in the MCMC MLE procedure. This function is X# an experimental procedure for coming up with a reasonable choice X# for psi. The pseudo-likelihood estimates (or user-supplied values) X# serve as the initial psi, which is then progressively modified by X# generating MCMC samples and modifying psi in the direction suggested X# by the sample. If look = T and draw = T, the program becomes interactive X# and allows the user to inspect the MCMC samples and change various control X# parameters while the program is running. The arguments are mostly the X# same as in mcmc(). The arguments c1 and c2 control the process of X# modifying psi. c1 should always be rather larger than c2. As the X# values of c1 and c2 are increased, the program becomes more "cautious", X# using larger MCMC samples, and making smaller successive changes to psi. X# The default is to use the pseudo-likelihood estimates as the psi to X# generate the first MCMC sample. If that does not work, I recommend X# setting init = 2 which uses the logistic regression estimates (with the X# spatial interaction parameter equal to zero) to generate the first sample. X# X L <- gibgen.setup(y = y, base = base, bdval = bdval) X map <- L$y X base <- L$base # X# Compute observed sufficient statistics. X L <- gibgen.setup(y = map, base = base, g0 = 0, nrec = 1, dosuff = T, X cov = xcov, dotot = dotot) X tobs <- as.vector(gibgen(L)$suff) X last <- 2 + if(is.null(dim(xcov))) 1 else ncol(xcov) X cloud <- 0 X past.psi <- c() X attn <- paste(paste(rep("=", 50), collapse = ""), "\n", sep = "") X repeat { X cloud <- cloud + 1 X done <- F X abort <- F X OK <- T X suff <- c() # X# Set initial control values for Gibbs sampler. X# These can be changed later using the browser() below. X L$y <- map X L$g0 <- g0 X L$g1 <- g1 X L$nrec <- nrec X L$suff <- matrix(0, nrec, last) X if(dotot) X L$tot <- rep(0, nrow(base)) X if(init == 1) { X nbsum <- neibsum(map, base) X ple <- glm(y ~ xcov + nbsum, family = binomial, maxit X = maxit) X psi <- ple$coef X } X else if(init == 2) { X nbsum <- neibsum(map, base) X ple <- glm(y ~ xcov + offset(b * nbsum), family = X binomial, maxit = maxit) X psi <- c(ple$coef, b) X } X init <- 0 X L$x <- cbind(1, xcov) %*% psi[ - last] X L$b <- b <- psi[last] X batch <- 0 X repeat { X batch <- batch + 1 X if(batch == 2) X L$g0 <- g1 X L <- gibgen(L) X suff <- rbind(suff, L$suff) X tdiff <- tobs - apply(suff, 2, mean) X crit <- (nrow(suff) * (mahad2 <- (tdiff) %*% solve(var( X suff), tdiff)))^0.5 X if(batch <= 1 && look) { X OK <- T X if(draw) { X tmp <- par(mfrow = c(2, 1)) X plot(suff[, 1]) X acf(suff[, 1]) X par(tmp) X } X cat(attn, "Inspect batch 1 of cloud", cloud, X ".\n", "If not satisfactory, modify\n", X " g0, g1, nrec, init, b, psi\n", X "as desired and set OK<-F .\n") X browser() X } X if(!look) X done <- (nrow(suff) >= max.smp) & (crit <= c1) X if(!OK || (crit > c1) || done) X break X } X if(!OK) X next X repeat { X OK <- T X past.psi <- rbind(past.psi, psi) X if(!done) { X# X# Sometimes the newton.raphson routine crashes (due to a nearly singular X# Hessian matrix). So, just in case, we save the Gibbs sampler output X# in advance, so that we can look at it to see what is happening. X assign("tmp.amcmc", list(tobs = tobs, suff = X suff, psi = psi, k1 = c2, past.psi = past.psi, X cloud = cloud, smp.size = nrow(suff)), where X = 1, immediate = T) X newton <- newton.penalty(tobs, suff, psi, k1 = X c2, verbose = verbose) X if(look || newton$error) { X cat(attn) X cat("Estimation results from cloud", cloud, X ".\n") X print(newton) X cat("Options:\n", X " modify c2 etc. and set OK<-F to re-estimate parameters.\n", X " Set abort<-T to discard these estimates and generate a", X "new cloud using the old parameter estimates.\n", X " Set done<-T to compute final estimates using this cloud.\n" X ) X browser() X } X } X if(OK || abort || done) X break X } X if(abort) X next X else if(done) { X assign("tmp.amcmc", list(tobs = tobs, suff = suff, psi X = psi, past.psi = past.psi, cloud = cloud, X smp.size = nrow(suff), L = L, map = map, call X = sys.call()), where = 1, immediate = T) X newton <- newton.raphson(tobs, suff, psi) X return(c(newton, list(tobs = tobs, mahad2 = mahad2, X smp.size = nrow(suff), call = sys.call()))) X } X else { X psi.old <- psi X psi <- newton$theta X } X } X} X"edge"<- Xfunction(base, d) X{ X# base is a list of occupied sites. X# d is the dimension of the rectangular lattice X# indexed by base. X# ans is a list of unoccupied sites which are adjacent X# to occupied sites. X y <- array(0, dim = d + 2) X y[base + 1] <- 1 X outside <- cbind(as.vector(row(y)), as.vector(col(y)))[y == 0, ] X outside[neibsum(zpad(y), outside + 1) > 0, ] - 1 X} X"gety"<- Xfunction(L) X{ X# This function extracts the simulated data from X# the gibgen list L. X L$y[L$base] X} X"gibgen"<- Xfunction(L,seed = NULL) X{ X# This function calls the Fortran subroutine gibgen which is a X# Gibbs sampler for generating from the autologistic model. X# The components of the list L are described in the comment X# statements of the Fortran subroutine gibgen. X# X# The function start.ranf initializes the random number generators X# if this is needed. See the comments in start.ranf(). X# X start.ranf(seed=seed) X L$suff[] <- 0 X L$tot[] <- 0 X storage.mode(L$y) <- "double" X storage.mode(L$x) <- "double" X storage.mode(L$b) <- "double" X storage.mode(L$g0) <- "integer" X storage.mode(L$g1) <- "integer" X storage.mode(L$base) <- "integer" X storage.mode(L$nrow) <- "integer" X storage.mode(L$ncol) <- "integer" X storage.mode(L$nsite) <- "integer" X storage.mode(L$nrec) <- "integer" X storage.mode(L$dosuff) <- "logical" X storage.mode(L$cov) <- "double" X storage.mode(L$suff) <- "double" X storage.mode(L$ncov) <- "integer" X storage.mode(L$nzbd) <- "logical" X storage.mode(L$sittyp) <- "integer" X storage.mode(L$dotot) <- "logical" X storage.mode(L$tot) <- "integer" X .Fortran("gibgen", X y = L$y, X x = L$x, X b = L$b, X g0 = L$g0, X g1 = L$g1, X base = L$base, X nrow = L$nrow, X ncol = L$ncol, X nsite = L$nsite, X nrec = L$nrec, X dosuff = L$dosuff, X cov = L$cov, X suff = L$suff, X ncov = L$ncov, X nzbd = L$nzbd, X sittyp = L$sittyp, X dotot = L$dotot, X tot = L$tot) X} X"gibgen.setup"<- Xfunction(y = stop("no y arg"), base = stop("no base arg"), x = log(0.5), b = 0, X g0 = 1, g1 = 0, dosuff = F, nrec = 0, cov = NULL, nzbd = NULL, dotot = X F, bdval = 0, d = NULL, bdsit = NULL) X{ X############################################### X# Comments: X# This function sets up the list (usually called L) which is used to pass X# input and output to and from the Gibbs sampler program gibgen(). X# It is easily customizable, so if your most common values for variables X# differs from mine, go ahead and change it. The current version has X# grown by accretion, and has become excessively complicated. X# The use of this function is optional. The list L can easily be created X# directly. The required components of L are described in the comment X# statements in the Fortran subroutine gibgen. See also the comments X# in the S-plus function mcmc(). X################################################# X# X# If the map y is given as a vector (indexed by base) it will be converted X# into a matrix with dimensions determined by the program or specified X# by the user using the optional argument d. X# If the map y is given as a matrix, it is assumed to be correct and is X# not checked in any way. X# X if(is.null(dim(y))) { X if(is.null(d)) { X# X# The matrix containing the map must be empty in the first and last rows X# and columns. (If not, the Gibbs sampler will try to read outside the X# matrix when computing neighborhood sums for sites located in the first X# or last row or column.) The next few lines of code ensure this. X# X if(min(base[, 1]) == 1) base[, 1] <- base[, 1] + 1 X if(min(base[, 2]) == 1) X base[, 2] <- base[, 2] + 1 X d <- 1 + c(max(base[, 1]), max(base[, 2])) X } X tmp <- array(bdval, dim = d) X tmp[base] <- y X y <- tmp X nzbd <- if(bdval == 0) F else T X } X else if(is.null(nzbd)) X nzbd <- T X nsite <- nrow(base) X if(length(x) == 1) { X alleq <- T X x <- rep(x, nsite) X } X else alleq <- F X if(nrec <= 0) { X dosuff <- F X dotot <- F X g1 <- 0 X } X if(dosuff) { X if(!is.null(cov)) { X cov <- cbind(cov) X ncov <- ncol(cov) X } X else if(alleq) { X cov <- 0 X ncov <- 0 X } X else { X cov <- cbind(x) X ncov <- 1 X } X suff <- matrix(0, nrec, ncov + 2) X if(nzbd && is.null(bdsit)) { X bdsit <- edge(base, d = dim(y)) X nzbd <- any(y[bdsit] != 0) X } X if(nzbd) { X sittyp <- array(0, dim = dim(y)) X sittyp[base] <- 1 X sittyp[bdsit] <- 2 X } X else sittyp <- 0 X } X else { X cov <- 0 X suff <- 0 X ncov <- 0 X nzbd <- F X sittyp <- 0 X } X if(dotot) X tot <- rep(0, nsite) X else tot <- 0 X list(y = y, x = x, b = b, g0 = g0, g1 = g1, base = base, nrow = nrow(y), X ncol = ncol(y), nsite = nsite, nrec = nrec, dosuff = dosuff, X cov = cov, suff = suff, ncov = ncov, nzbd = nzbd, sittyp = X sittyp, dotot = dotot, tot = tot) X} X"make.torus"<- Xfunction(d = 30, q1 = 0.325, q2 = 0.65) X{ X# COMMENTS: X# This function creates a "map" of a circular island. X# Along with the map are created two covariates. X# This is useful for experimenting with simulating and X# fitting autologistic models. X# ARGUMENTS: X# d is "size" of the square lattice which contains the map. X# The circular island is contained in a d by d square lattice. X# The circular island consists of two parts: the inner and outer parts. X# The outer part forms a torus (doughnut). X# q1 is the proportion of the d by d square within the "inner" part. X# q2 is the proportion of the d by d square within the entire circle, X# including both the inner and outer part. (q1 <= q2 is required.) X# VALUE: X# This function returns a list with the following components. X# x.torus is a "covariate" (indexed by base) which is -1 in the X# inner part and +1 in the outer part of the circular island. X# x.d2 is a covariate (indexed by base) which is the squared distance X# from the center of the island. X# base determines the circular island. It lists all the sites X# (in the d by d lattice) which belong to the island. X# base is a matrix with two columns. base[i,] gives the X# row-column coordinates of the i-th site on the island. X# map.circle is a matrix showing the circular island. X# map.torus is a matrix showing the covariate x.torus. X# X map.circle <- matrix(0, d, d) X dimnames(map.circle) <- list(rep("", d), rep("", d)) X mu <- (1 + d)/2 X d2 <- (row(map.circle) - mu)^2 + (col(map.circle) - mu)^2 X q <- quantile(d2, c(q1, q2)) X base <- cbind(as.vector(row(map.circle)), as.vector(col(map.circle)))[ X d2 <= q[2], ] X map.circle[base] <- 1 X map.torus <- map.circle X map.torus[d2 <= q[1]] <- -1 X list(x.torus = map.torus[base], x.d2 = d2[base], base = base, X map.circle = map.circle, map.torus = map.torus) X} X"mcmc"<- Xfunction(y, xcov, base, bdval = 0, g0 = 100, g1 = 3, nrec = 100, psi = NA, init X = if(is.na(psi[1])) 1 else 0, dotot = T, maxit = 20, ...) X{ X# Comments: X# This function "fits" autologistic regression models. X# The parameter estimates obtained are MCMC approximations to the maximum X# likelihood estimates. X# This program was written by Fred Huffer and implements the methods X# described in the papers by Fred Huffer and Hulin Wu. X# Arguments: X# y is the vector of binary responses (recorded at each site of the map). X# xcov is the matrix (or vector) of covariates X# (recorded at each site of the map). X# base is a matrix with two columns which specifies the map and the X# the ordering of the sites. The i-th row of base base[i,] gives the X# row and column coordinates of the i-th site in the map which is a X# subset of a rectangular lattice. The values y[i] and xcov[i,] are X# the response and covariates at the i-th site. X# bdval gives a "response" value to be placed at sites outside the map for X# the purposes of computing neighborhood sums. The default is bdval = 0. X# This is probably the safest option, since I am not sure all the code X# is correctly written to handle nonzero boundary values. Setting X# bdval = .5 corresponds to a "neutral" boundary. X# g0 and g1 control the recording of the Gibbs sampler output. X# g0 is the "burn-in" or "warm-up", that is, the number of cycles of the X# Gibbs sampler that are discarded at the beginning. X# g1 is the "spacing". After the warm-up period, the sufficient statistics X# are recorded every g1 cycles of the Gibbs sampler. X# nrec is the simulation sample size; the sufficient statistics are recorded X# a total of nrec times. (In the course of this, the Gibbs sampler runs X# for a total of g0+g1*nrec cycles.) A small value of nrec (such as 100) X# is useful in checking whether the initial parameter values psi are X# reasonable. Larger values of nrec (say, 1000) are needed to obtain X# accurate final estimates. X# psi is the vector of initial parameter values. These values are used X# for running the Gibbs sampler. The parameters are ordered with the X# intercept first, then the covariate parameters, and last is the spatial X# interaction parameter. X# If no values psi or init (see below) are supplied, the pseudo-likelihood X# estimates are used for psi. X# init directly controls the choice of the initial parameter values psi. X# It is not needed if the user supplies values for psi or wishes to use the X# pseudo-likelihood estimates for psi. Setting X# init = 0 indicates the user has supplied values for psi, X# init = 1 says to use the pseudo-likelihood estimates for psi, X# init = 2 says to use the logistic regression estimates for psi. X# This option fits a standard logistic regression model to the X# data and uses the resulting parameter estimates for psi. X# This option sets the spatial interaction parameter to zero. X# (A Gibbs sampler is not really needed in this situation. X# Standard "independent" simulations would suffice.) X# dotot = T or F. If dotot = T, the program tabulates the number X# of times (out of nrec) each site is occupied during the runnning of X# the Gibbs sampler. X# maxit is the maximum number of iterations performed by glm in fitting X# the pseudo-likelihood or logistic regression estimates. X# ... Trailing arguments are sent to the function newton.raphson. X# X L <- gibgen.setup(y = y, base = base, g0 = 0, nrec = 1, dosuff = T, X bdval = bdval, cov = xcov, dotot = dotot) X tobs <- as.vector(gibgen(L)$suff) X dm <- dim(L$cov) X last <- 2 + if(is.null(dm)) 1 else dm[2] X L$g0 <- g0 X L$g1 <- g1 X L$nrec <- nrec X L$dosuff <- T X L$suff <- matrix(0, nrec, last) X if(init == 1) { X nbsum <- neibsum(L$y, L$base) X psi <- glm(L$y[L$base] ~ L$cov + nbsum, family = binomial, X maxit = maxit)$coef X } X else if(init == 2) { X psi <- glm(L$y[L$base] ~ L$cov, family = binomial, maxit = X maxit)$coef X psi <- c(psi, 0) X } X L$x <- cbind(1, L$cov) %*% psi[ - last] X L$b <- psi[last] X L <- gibgen(L) # X# Sometimes the newton.raphson routine crashes (due to a nearly singular X# Hessian matrix). So, just in case, we save the Gibbs sampler output X# in advance, so that we can look at it to see what is happening. X L$tobs <- tobs X L$psi <- psi X assign("tmp.mcmc", L, where = 1, immediate = T) X newton.raphson(tobs, L$suff, psi, ...) X} X"neibsum"<- Xfunction(y, base) X{ X storage.mode(y) <- "double" X storage.mode(base) <- "integer" X .Fortran("neibsum", X y, X base, X double(length = nrow(base)), X as.integer(nrow(y)), X as.integer(ncol(y)), X as.integer(nrow(base)))[[3]] X} X"newton.penalty"<- Xfunction(xobs, xsim, psi, k1 = 4, k2 = 1, start = NULL, maxiter = 30, eps1 = X 1e-15, eps2 = 1e-08, verbose = F) X{ X# GOAL: This function uses Newton-Raphson iteration to find the vector X# theta which maximizes the penalized log-likelihood: X# loglik - k1*P X# where P is an estimate of the standard error of the log-likelihood. X# ARGUMENTS: X# xobs is the vector of observed suff. stats. X# xsim is the matrix of simulated suff.stats obtained from the Gibbs X# sampler. The rows are cases, that is, ncol(xsim) = length(xobs). X# psi is the vector of parameters used by the Gibbs sampler to simulate X# the matrix xsim; length(psi) = length(xobs). X# k1 is the multiplier for the penalty. X# k2 determines the maximum size of the initial guess for theta. X# start is the vector of initial parameter values for the Newton-Raphson X# method; length(start) = length(xobs). X# If start is not given, the program supplies its own. X# maxiter = maximum number of iterations. X# eps1 and eps2 determine the convergence criterion for X# the algorithm. X# VALUE: X# theta is vector of parameter estimates. X# E is the vector of (estimated) expected values for the suff. stats. X# when the true parameter is theta. X# If the iterations have converged, then E = xobs. X# V is the (estimated) covariance matrix of the suff. stats. under X# theta. Also, V is the Fisher information matrix. X n <- nrow(xsim) X iter <- 0 X av <- apply(xsim, 2, mean) X xobs <- xobs - av X xsim <- sweep(xsim, 2, av) X S <- ((n - 1)/n) * var(xsim) X if(is.null(start)) { X nxt <- solve(S, xobs) X maha <- sum(xobs * nxt) X mult <- min(1 - k1/(n * maha)^0.5, (log(1 + k2 * n)/maha)^0.5) X if(mult <= 0) { X cat("k1 is too large or sample size nrow(xsim) is too small.\n" X ) X return(list(error = T)) X } X nxt <- mult * nxt X } X else nxt <- start - psi X Func <- 0 X cur <- 0 * psi X repeat { X iter <- iter + 1 X shrink <- 0 X if(verbose) X cat("newton.penalty: === starting iteration ", iter, X " ===\n") X repeat { X w <- as.vector(exp(xsim %*% nxt)) X LLnew <- sum(nxt * xobs) - log(mean(w)) X sc <- S %*% nxt X e <- exp(sum(nxt * sc)) X P <- ((e - 1)/n)^0.5 X Fnew <- LLnew - k1 * P X if(Fnew > Func) { X if(verbose) { X cat("Fnew = ", Fnew, "\n") X cat("Fnew - Func = ", Fnew - Func, "\n") X } X break X } X else { X if((shrink <- shrink + 1) >= 8) X return(list(error = T)) X if(verbose) X cat("shrinking\n") X nxt <- (cur + nxt)/2 X } X } X cur <- as.vector(nxt) X loglik <- LLnew X Func <- Fnew X w <- w/sum(w) X E <- apply(xsim * w, 2, sum) X d <- sweep(xsim, 2, E, "-") X V <- t(d) %*% (w * d) X v1 <- ((2 * e)/n) * sc X v2 <- (e/n) * (4 * sc %*% t(sc) + 2 * S) X G <- (xobs - E) - (k1/(2 * P)) * v1 X H <- - V + (k1/(4 * P^3)) * (v1 %*% t(v1)) - (k1/(2 * P)) * v2 X nxt <- cur + (delt <- - solve(H, G)) X Fdelt <- 0.5 * sum(G * delt) X if(verbose) { X cat("Fdelt = ", Fdelt, "\n") X cat("theta = ", cur + psi, "\n") X } X if((Fdelt < eps1) || max(abs(delt/cur)) < eps2 || (iter >= X maxiter)) X break X } X list(theta = cur + psi, E = E + av, V = V, loglik = loglik, P = P, psi X = psi, iter = iter, error = F) X} X"newton.raphson"<- Xfunction(xobs, xsim, psi, start = psi, maxiter = 30, eps1 = 1e-15, eps2 = 1e-08, X look = F, do.mc.se = T, lag.max = round(nrow(xsim)^0.5)) X{ X# Comments: This function computes parameter estimates for autologistic X# regression models by Newton-Raphson iteration. X# ARGUMENTS: X# xobs is the vector of observed suff. stats (computed from the data). X# xsim is the matrix of simulated suff. stats obtained from the Gibbs X# sampler. The rows are cases, that is, ncol(xsim) = length(xobs). X# psi is the vector of parameters used by the Gibbs sampler to simulate X# the matrix xsim; length(psi) = length(xobs). X# start is the vector of initial parameter values for the Newton-Raphson X# method; length(start) = length(xobs). X# maxiter = maximum number of iterations. X# eps1 is the convergence criterion for the log-likelihood. If the X# change in the log-likelihood from one iteration to the next is X# less than eps1, the iterations are stopped. X# eps2 is the convergence criterion for the parameter estimates. X# If the maximum relative change in all of the parameter estimates X# from one iteration to the next is less than eps2, the iterations X# are stopped. X# look = T or F. Setting look = T will cause the parameter estimates X# to be printed for each of the iterations. X# do.mc.se = T or F. If do.mc.se = T, the output will contain estimated X# standard errors of the Monte Carlo variability in the parameter X# estimates. These standard errors give some idea how far the X# parameter estimates might be from the "true" exact values of the X# maximum likelihood estimates. These standard errors can themselves X# be highly variable and should be used with caution. X# lag.max is the number of lags of the sample autocovariance function X# which are used in the estimation of the Monte Carlo standard errors. X# VALUE: X# theta is the vector of parameter estimates. X# se contains standard errors for the parameter estimates. X# mc.se contains standard errors for the Monte Carlo variability in X# the parameter estimates. (These standard errors are explaind in X# the Huffer and Wu, Biometrics 1998 article.) X# psi is the same as in the argument list above. X# iter is the number of Newton-Raphson iterations performed. X# loglik is an estimate of the increase in the log-likelihood function X# from psi to theta. It can be used to form a test of the hypothesis X# that the "true" theta equals psi. X# E is the vector of (estimated) expected values for the suff. stats. X# when the true parameter is theta. X# If the iterations have converged, then E = xobs. X# V is the Fisher information matrix (which is also the estimated X# covariance matrix of the suff. stats. under theta). X# cov.zbar is the estimated covariance matrix of zbar. This is an X# important piece in the computation of mc.se (see above). X########################################################################## X iter <- 0 X nxt <- start - psi X av <- apply(xsim, 2, mean) X xobs <- xobs - av X xsim <- sweep(xsim, 2, av) X ll <- 0 X repeat { X iter <- iter + 1 X cur <- nxt X prob <- exp(xsim %*% cur) X prob <- prob/sum(prob) X E <- apply(sweep(xsim, 1, prob, "*"), 2, sum) X vtmp <- sweep(sweep(xsim, 2, E, "-"), 1, prob^0.5, "*") X V <- t(vtmp) %*% vtmp X nxt <- cur + (delt <- solve(V, xobs - E)) X ll.old <- ll X repeat { X ll <- sum(xobs * nxt) - log(mean(exp(xsim %*% nxt))) X if(ll > ll.old - eps1) X break X else nxt <- cur + (delt <- delt/2) X } X if(look) X print(cur + psi) X if((abs(ll - ll.old) < eps1) || max(abs(delt/cur)) < eps2 || ( X iter >= maxiter)) X break X } X loglik <- ll.old X cur <- nxt X if(do.mc.se) { X prob <- as.vector(exp(xsim %*% cur)) X prob <- prob/sum(prob) X n <- length(prob) X z <- sweep(xsim, 2, xobs, "-") * prob * n X R <- acf(z, lag.max = lag.max, type = "covariance", plot = F)$ X acf X part <- apply(R[-1, , ], c(2, 3), sum) X cov.zbar <- (R[1, , ] + part + t(part))/n X mc.se <- diag(solve(V, t(solve(V, cov.zbar))))^0.5 X } X if(do.mc.se) X list(theta = cur + psi, se = diag(solve(V))^0.5, mc.se = mc.se, X psi = psi, iter = iter, loglik = loglik, E = E + av, V X = V, cov.zbar = cov.zbar) X else list(theta = cur + psi, se = diag(solve(V))^0.5, psi = psi, iter X = iter, loglik = loglik, E = E + av, V = V) X} X"start.ranf"<- Xfunction(seed = NULL) X{ X# seed is a vector of 3 positive integers. X# seed[1] must be less than or equal to 32. X# X# This function initializes the random number generator. X# If you want to be able to reproduce your simulation X# results exactly at a later time, then you must supply X# a vector of seeds as the argument to start.ranf(). (And X# you must record this vector of seeds for later use.) X# If you do not care about this, then you can use start.ranf() X# with a NULL argument or no arguments at all. X#------------------------------------------------------------ X# First check to see if ranf has already been initialized. X if(is.null(seed) && .Fortran("rgnqsd", X T)[[1]]) return(NULL) X if(is.null(seed)) { X i1 <- ceiling(32 * runif(1)) X i2 <- ceiling(9999 * runif(1)) X i3 <- ceiling(9999 * runif(1)) X } X else { X i1 <- seed[1] X if(i1 > 32) X i1 <- (i1 %% 32) + 1 X i2 <- seed[2] X i3 <- seed[3] X } X .Fortran("setall", X as.integer(i2), X as.integer(i3)) X .Fortran("setcgn", X as.integer(i1)) X NULL X} X"zpad"<- Xfunction(y) X{ X# Pads matrix y with a single layer of zeros on all sides. X rbind(0, cbind(0, y, 0), 0) X} X"print.binary"<- Xfunction(y,base=NULL,space="") X{ X# Comments: X# This function prints a binary matrix y, or a binary map X# described by the binary vector y and the matrix base X# (which lists the sites on the map). The printing is X# done compactly without spacing between the values. X# If you want to insert a single space between the digits, X# set space=" ". X#----------------------------------------------------- Xmrk<-c("0","1"," ") Xif(is.null(base)){ X# In this case, y must be a matrix. X if(is.null(dim(y)) || length(dim(y))!=2) X return("Without base, y must be a matrix.") X yy<-y X yy[y<1]<-0 X yy<-yy+1 X } Xelse{ X# In this case, y must be a vector. X if(!is.null(dim(y))) return("With base, y must be a vector.") X nr<-max(base[,1]) X nc<-max(base[,2]) X yy<-matrix(3,nr,nc) X yy[base]<-1+y X } Xfor(i in 1:nrow(yy)) X cat(paste(mrk[yy[i,]],sep="",collapse=space),"\n") Xcat("\n") X} X"print.prob"<- Xfunction(p,base,mult=10,scale=F,space=""){ X# Comments: X# This function prints a map of the probabilities given X# by the vector p and the matrix base (which lists the X# sites on the map). The probabilities are rounded to X# one decimal place and printed (without spacing). X# Probabilities which round to 1.0 are printed as an X# asterisk (*). If you want to insert a single space X# between the digits, set space=" ". X#----------------------------------------------------- X symb<-paste(c(" ",0:9,"*",LETTERS)) X if(scale)p<-(p-min(p))/(max(p)-min(p)) X dig1<-1+round(mult*p) X nr<-max(base[,1]) X nc<-max(base[,2]) X yy<-matrix(1,nr,nc) X yy[base]<-dig1 Xfor(i in 1:nrow(yy)) X cat(paste(symb[yy[i,]],sep="",collapse=space),"\n") Xcat("\n") X} ________This_Is_The_END________ if test `wc -l < autolog.Splus` -ne 752; then echo 'shar: autolog.Splus was damaged during transit (should have had 752 lines)' fi echo 'x - sp38data' sed 's/^X//' << '________This_Is_The_END________' > sp38data Xrow col sp38 fzf tav prcp mi X 1 16 0 365.0 25.11 1033 0.7003 X 1 17 0 365.0 25.26 1017 0.6857 X 1 18 0 365.0 25.40 1001 0.6700 X 2 14 0 365.0 25.01 1046 0.7116 X 2 15 0 365.0 25.20 1028 0.6926 X 2 16 0 365.0 25.11 1033 0.7003 X 2 17 0 365.0 25.12 1033 0.7014 X 3 9 0 365.0 24.89 1086 0.7391 X 3 10 0 365.0 24.91 1068 0.7266 X 3 11 0 365.0 25.10 1050 0.7076 X 3 12 0 365.0 25.01 1055 0.7153 X 3 13 0 365.0 24.91 1059 0.7229 X 3 14 0 365.0 24.82 1064 0.7306 X 3 15 0 365.0 24.72 1069 0.7383 X 3 16 0 365.0 24.84 1065 0.7327 X 4 7 0 365.0 25.02 1141 0.7756 X 4 8 0 365.0 24.80 1110 0.7597 X 4 9 0 365.0 24.89 1086 0.7391 X 5 6 0 365.0 24.94 1170 0.7989 X 5 7 0 365.0 25.02 1141 0.7756 X 6 5 0 365.0 24.86 1198 0.8223 X 6 6 0 365.0 24.86 1198 0.8223 X 7 4 0 365.0 24.48 1283 0.8944 X 7 5 0 365.0 24.48 1283 0.8944 X 7 7 0 365.0 24.14 1260 0.8891 X 7 8 0 365.0 23.83 1240 0.8857 X 7 9 0 365.0 23.51 1220 0.8823 X 7 10 0 365.0 23.36 1205 0.8769 X 7 11 0 365.0 23.54 1199 0.8675 X 7 12 0 365.0 23.71 1193 0.8581 X 8 3 0 365.0 24.51 1286 0.8963 X 8 4 0 365.0 24.51 1286 0.8963 X 8 5 0 365.0 24.51 1286 0.8963 X 8 6 0 365.0 24.05 1358 0.9627 X 8 7 0 365.0 23.74 1341 0.9593 X 8 8 0 365.0 23.42 1321 0.9559 X 8 9 0 365.0 23.35 1269 0.9239 X 8 10 0 365.0 23.36 1231 0.8947 X 8 11 0 365.0 23.43 1225 0.8895 X 8 12 0 365.0 23.61 1219 0.8801 X 9 3 0 365.0 24.33 1281 0.8964 X 9 4 0 365.0 24.20 1335 0.9411 X 9 5 0 365.0 24.10 1368 0.9706 X 9 6 0 365.0 23.65 1435 1.0330 X 9 7 0 365.0 23.33 1420 1.0300 X 9 8 0 365.0 23.35 1353 0.9872 X 9 9 0 365.0 23.51 1287 0.9292 X 9 10 0 365.0 23.48 1257 0.9085 X 9 11 0 365.0 23.33 1251 0.9114 X 10 2 0 365.0 24.45 1237 0.8592 X 10 3 0 365.0 24.45 1237 0.8592 X 10 4 0 365.0 24.29 1301 0.9115 X 10 5 0 365.0 23.69 1450 1.0450 X 10 6 0 365.0 23.24 1508 1.1030 X 10 7 0 365.0 23.35 1437 1.0500 X 10 8 0 365.0 23.51 1371 0.9925 X 10 9 0 365.0 23.66 1304 0.9345 X 10 10 0 365.0 23.59 1283 0.9222 X 10 11 0 365.0 23.44 1277 0.9252 X 10 12 0 365.0 23.40 1271 0.9240 X 11 2 0 365.0 24.61 1172 0.8070 X 11 4 0 365.0 23.83 1407 1.0040 X 11 5 0 365.0 23.32 1536 1.1200 X 11 6 0 365.0 23.36 1524 1.1100 X 11 7 0 365.0 23.51 1457 1.0560 X 11 8 0 365.0 23.66 1388 0.9977 X 11 9 0 365.0 23.82 1322 0.9398 X 11 10 0 365.0 23.70 1309 0.9360 X 11 11 0 365.0 23.55 1303 0.9389 X 11 12 0 365.0 23.41 1296 0.9419 X 11 13 0 365.0 23.48 1290 0.9366 X 12 2 0 365.0 24.27 1235 0.8619 X 12 3 0 365.0 24.11 1299 0.9141 X 12 4 0 365.0 23.57 1501 1.0810 X 12 5 0 365.0 23.48 1558 1.1270 X 12 6 0 365.0 23.58 1511 1.0890 X 12 7 0 365.0 23.69 1465 1.0510 X 12 8 0 365.0 23.82 1407 1.0030 X 12 9 0 365.0 23.96 1341 0.9467 X 12 10 0 365.0 23.81 1335 0.9497 X 12 11 0 365.0 23.67 1329 0.9527 X 12 12 0 365.0 23.52 1322 0.9556 X 12 13 0 365.0 23.37 1316 0.9586 X 12 14 0 365.0 23.55 1310 0.9492 X 13 2 0 365.0 24.43 1170 0.8096 X 13 3 0 365.0 24.09 1392 0.9823 X 13 4 0 365.0 23.59 1591 1.1430 X 13 5 0 365.0 23.69 1545 1.1050 X 13 6 0 365.0 23.80 1499 1.0670 X 13 7 0 365.0 23.91 1453 1.0290 X 13 8 0 365.0 24.01 1407 0.9915 X 13 9 0 365.0 24.08 1367 0.9605 X 13 10 0 365.0 23.93 1361 0.9634 X 13 11 0 365.0 23.78 1355 0.9664 X 13 12 0 365.0 23.63 1348 0.9694 X 13 13 0 365.0 23.48 1342 0.9723 X 13 14 0 365.0 23.44 1336 0.9712 X 13 15 0 365.0 23.59 1324 0.9577 X 14 2 0 365.0 24.28 1256 0.8766 X 14 3 0 365.0 23.84 1531 1.0880 X 14 4 0 365.0 23.78 1571 1.1190 X 14 5 0 365.0 23.86 1521 1.0790 X 14 6 0 365.0 23.95 1470 1.0400 X 14 7 0 365.0 24.04 1420 1.0010 X 14 8 0 365.0 23.96 1391 0.9828 X 14 9 0 365.0 24.00 1353 0.9536 X 14 10 0 365.0 23.89 1354 0.9604 X 14 11 0 365.0 23.78 1355 0.9672 X 14 12 0 365.0 23.66 1357 0.9741 X 14 13 0 365.0 23.55 1358 0.9809 X 14 14 0 365.0 23.44 1360 0.9877 X 14 15 0 365.0 23.47 1345 0.9767 X 14 16 0 365.0 23.57 1323 0.9566 X 14 17 0 365.0 23.67 1300 0.9366 X 14 18 0 365.0 23.77 1278 0.9166 X 15 2 0 365.0 24.19 1333 0.9362 X 15 3 0 365.0 23.79 1581 1.1270 X 15 4 0 365.0 23.88 1531 1.0880 X 15 5 0 365.0 23.97 1480 1.0480 X 15 6 0 365.0 23.92 1447 1.0260 X 15 7 0 365.0 23.84 1418 1.0090 X 15 8 0 365.0 23.76 1390 0.9910 X 15 9 0 365.0 23.92 1337 0.9460 X 15 10 0 365.0 23.81 1338 0.9528 X 15 11 0 361.0 23.69 1340 0.9597 X 15 12 0 363.4 23.58 1341 0.9665 X 15 13 0 363.4 23.47 1343 0.9733 X 15 14 0 363.4 23.34 1348 0.9841 X 15 15 0 364.2 23.37 1355 0.9842 X 15 16 0 365.0 23.44 1344 0.9756 X 15 17 0 365.0 23.54 1322 0.9556 X 15 18 0 365.0 23.64 1299 0.9356 X 16 2 0 365.0 24.09 1413 0.9975 X 16 3 0 365.0 23.89 1540 1.0960 X 16 4 0 365.0 23.88 1503 1.0700 X 16 5 0 365.0 23.80 1474 1.0520 X 16 6 0 365.0 23.72 1446 1.0340 X 16 7 0 365.0 23.64 1417 1.0170 X 16 8 0 365.0 23.56 1389 0.9991 X 16 9 0 365.0 23.80 1327 0.9443 X 16 10 0 364.0 23.73 1323 0.9453 X 16 11 0 357.4 23.61 1324 0.9521 X 16 12 0 361.1 23.50 1326 0.9589 X 16 13 0 361.8 23.39 1327 0.9658 X 16 14 0 361.8 23.27 1343 0.9796 X 16 15 0 362.4 23.32 1352 0.9788 X 16 16 0 363.8 23.36 1349 0.9780 X 16 17 0 365.0 23.41 1343 0.9746 X 16 18 0 365.0 23.51 1321 0.9545 X 17 2 0 365.0 23.98 1493 1.0590 X 17 3 0 365.0 23.76 1530 1.0950 X 17 4 0 365.0 23.68 1502 1.0780 X 17 5 0 365.0 23.60 1473 1.0600 X 17 6 0 365.0 23.52 1445 1.0420 X 17 7 0 365.0 23.44 1416 1.0250 X 17 8 0 365.0 23.37 1386 1.0060 X 17 9 0 365.0 23.69 1317 0.9425 X 17 10 0 360.8 23.65 1307 0.9377 X 17 11 0 354.1 23.53 1309 0.9445 X 17 12 0 356.3 23.42 1310 0.9514 X 17 13 0 360.1 23.28 1316 0.9629 X 17 14 0 360.1 23.21 1339 0.9743 X 17 15 0 360.7 23.26 1349 0.9735 X 17 16 0 362.1 23.30 1346 0.9727 X 17 17 0 363.5 23.35 1343 0.9719 X 17 18 0 364.8 23.39 1340 0.9711 X 17 19 0 364.5 23.46 1319 0.9538 X 18 2 0 365.0 23.88 1558 1.1100 X 18 3 0 365.0 23.65 1530 1.0990 X 18 4 0 365.0 23.47 1501 1.0860 X 18 5 0 365.0 23.39 1472 1.0680 X 18 6 0 365.0 23.31 1444 1.0510 X 18 7 0 365.0 23.23 1415 1.0330 X 18 8 0 365.0 23.25 1376 1.0040 X 18 9 0 364.2 23.57 1308 0.9408 X 18 10 0 357.5 23.57 1292 0.9301 X 18 11 0 350.9 23.45 1293 0.9370 X 18 12 0 351.6 23.34 1294 0.9438 X 18 13 0 356.4 23.14 1312 0.9665 X 18 14 0 358.5 23.16 1334 0.9690 X 18 15 0 359.0 23.20 1346 0.9682 X 18 16 0 360.4 23.25 1343 0.9674 X 18 17 0 361.7 23.29 1340 0.9666 X 18 18 0 363.8 23.35 1338 0.9703 X 18 19 0 364.5 23.34 1340 0.9728 X 19 1 0 365.0 23.78 1552 1.1100 X 19 2 0 365.0 23.78 1552 1.1100 X 19 3 0 365.0 23.53 1533 1.1060 X 19 4 0 365.0 23.33 1500 1.0910 X 19 5 0 365.0 23.19 1471 1.0760 X 19 6 0 365.0 23.11 1443 1.0590 X 19 7 0 365.0 23.03 1414 1.0410 X 19 8 0 365.0 23.14 1367 1.0020 X 19 9 0 360.9 23.45 1298 0.9390 X 19 10 0 354.3 23.48 1276 0.9226 X 19 11 0 347.6 23.37 1277 0.9294 X 19 12 0 346.8 23.23 1284 0.9418 X 19 13 0 351.6 23.05 1307 0.9644 X 19 14 0 356.5 23.10 1330 0.9636 X 19 15 0 357.3 23.14 1343 0.9629 X 19 16 0 358.6 23.19 1340 0.9621 X 19 17 0 360.9 23.25 1337 0.9662 X 19 18 0 363.3 23.31 1342 0.9736 X 19 19 0 364.6 23.29 1353 0.9822 X 19 20 0 363.8 23.27 1339 0.9722 X 20 1 0 365.0 23.67 1546 1.1100 X 20 2 0 365.0 23.67 1546 1.1100 X 20 3 0 365.0 23.32 1544 1.1240 X 20 4 0 365.0 23.20 1504 1.1000 X 20 5 0 365.0 23.01 1470 1.0830 X 20 6 0 365.0 22.91 1442 1.0670 X 20 7 0 365.0 22.83 1413 1.0490 X 20 8 0 364.3 23.02 1357 1.0000 X 20 9 0 357.7 23.34 1288 0.9373 X 20 10 0 351.0 23.40 1260 0.9150 X 20 11 0 344.4 23.29 1262 0.9218 X 20 12 0 342.0 23.09 1280 0.9453 X 20 13 0 346.9 23.00 1303 0.9591 X 20 14 0 351.7 23.04 1325 0.9583 X 20 15 0 355.5 23.09 1340 0.9575 X 20 16 0 357.9 23.14 1337 0.9620 X 20 17 0 360.4 23.21 1338 0.9695 X 20 18 0 362.8 23.27 1346 0.9769 X 20 19 0 364.9 23.31 1356 0.9847 X 20 20 0 363.8 23.14 1360 0.9912 X 20 21 0 363.0 23.20 1337 0.9717 X 20 22 0 362.3 23.26 1314 0.9522 X 21 1 0 365.0 23.57 1539 1.1110 X 21 2 0 365.0 23.57 1539 1.1110 X 21 3 0 365.0 23.10 1555 1.1410 X 21 4 0 365.0 22.99 1516 1.1170 X 21 5 0 365.0 22.87 1476 1.0930 X 21 6 0 365.0 22.70 1441 1.0750 X 21 7 0 365.0 22.62 1412 1.0580 X 21 8 0 361.1 22.91 1347 0.9985 X 21 9 0 354.4 23.22 1278 0.9355 X 21 10 0 347.8 23.32 1245 0.9074 X 21 11 0 341.2 23.18 1252 0.9206 X 21 12 0 337.2 22.95 1275 0.9488 X 21 13 0 342.2 22.94 1298 0.9538 X 21 14 0 348.8 22.98 1321 0.9530 X 21 15 0 354.8 23.04 1337 0.9579 X 21 16 0 357.3 23.11 1334 0.9653 X 21 17 0 359.8 23.17 1342 0.9728 X 21 18 0 362.3 23.24 1351 0.9802 X 21 19 0 364.8 23.30 1359 0.9877 X 21 20 0 363.9 23.12 1372 0.9986 X 21 21 0 363.0 23.08 1359 0.9907 X 21 22 0 362.3 23.14 1336 0.9711 X 21 23 0 361.4 23.19 1285 0.9521 X 22 1 0 365.0 23.46 1533 1.1110 X 22 2 0 365.0 23.46 1533 1.1110 X 22 3 0 365.0 22.92 1561 1.1530 X 22 4 0 365.0 22.77 1527 1.1340 X 22 5 0 365.0 22.65 1487 1.1110 X 22 6 0 365.0 22.53 1447 1.0870 X 22 7 0 364.4 22.47 1406 1.0600 X 22 8 0 357.8 22.79 1337 0.9968 X 22 9 0 353.3 23.11 1269 0.9338 X 22 10 0 349.1 23.24 1229 0.8998 X 22 11 0 344.8 23.04 1248 0.9241 X 22 12 0 340.6 22.84 1271 0.9492 X 22 13 0 341.4 22.88 1294 0.9485 X 22 14 0 348.1 22.94 1316 0.9538 X 22 15 0 354.1 23.01 1334 0.9612 X 22 16 0 356.6 23.07 1337 0.9686 X 22 17 0 359.1 23.13 1346 0.9761 X 22 18 0 361.6 23.18 1348 0.9848 X 22 19 0 364.1 23.24 1345 0.9836 X 22 20 0 364.2 23.14 1375 1.0010 X 22 21 0 363.0 22.95 1380 1.0100 X 22 22 0 362.3 23.01 1357 0.9901 X 22 23 0 361.5 23.07 1312 0.9706 X 23 1 0 365.0 23.48 1510 1.0940 X 23 2 0 365.0 23.48 1510 1.0940 X 23 3 0 365.0 22.94 1539 1.1360 X 23 4 0 365.0 22.77 1507 1.1200 X 23 5 0 365.0 22.67 1465 1.0950 X 23 6 0 365.0 22.56 1423 1.0690 X 23 7 0 365.0 22.45 1378 1.0390 X 23 8 0 365.0 22.71 1317 0.9847 X 23 9 0 365.0 23.01 1255 0.9279 X 23 10 0 363.0 23.12 1221 0.8994 X 23 11 0 357.0 22.89 1243 0.9276 X 23 12 0 353.8 22.78 1266 0.9439 X 23 13 0 353.5 22.84 1289 0.9496 X 23 14 0 353.2 22.90 1312 0.9572 X 23 15 0 353.4 22.95 1331 0.9660 X 23 16 0 355.9 23.00 1328 0.9748 X 23 17 0 358.4 23.04 1325 0.9836 X 23 18 0 360.9 23.10 1322 0.9858 X 23 19 0 363.3 23.17 1319 0.9701 X 23 20 0 364.5 23.15 1350 0.9836 X 23 21 0 363.2 22.95 1392 1.0150 X 23 23 0 361.5 22.95 1341 0.9896 X 24 1 0 365.0 23.56 1479 1.0690 X 24 2 0 365.0 23.56 1479 1.0690 X 24 3 0 365.0 23.02 1508 1.1110 X 24 4 0 365.0 22.86 1474 1.0930 X 24 5 0 365.0 22.76 1432 1.0680 X 24 6 0 365.0 22.65 1388 1.0400 X 24 7 0 365.0 22.54 1342 1.0090 X 24 10 0 364.7 22.97 1216 0.8992 X 24 11 0 364.4 22.75 1248 0.9297 X 24 12 0 360.2 22.72 1274 0.9471 X 24 13 0 354.9 22.76 1294 0.9559 X 24 14 0 349.7 22.81 1315 0.9647 X 24 15 0 345.9 22.86 1330 0.9735 X 24 16 0 347.6 22.90 1326 0.9823 X 24 17 0 355.6 22.95 1305 0.9880 X 24 18 0 360.1 23.02 1295 0.9723 X 24 19 0 362.6 23.09 1293 0.9566 X 24 20 0 365.0 23.16 1292 0.9429 X 24 21 0 363.5 22.96 1394 1.0170 X 24 23 0 361.6 22.82 1371 1.0090 X 25 1 0 365.0 23.33 1478 1.0780 X 25 2 0 365.0 23.33 1478 1.0780 X 25 3 0 365.0 23.10 1477 1.0860 X 25 4 0 365.0 22.95 1441 1.0660 X 25 5 0 365.0 22.85 1398 1.0400 X 25 6 0 365.0 22.74 1352 1.0090 X 25 11 0 359.9 22.68 1241 0.9259 X 25 12 0 352.9 22.64 1273 0.9511 X 25 13 0 347.2 22.67 1296 0.9635 X 25 14 0 342.0 22.72 1316 0.9723 X 25 15 0 339.0 22.76 1328 0.9811 X 25 16 0 337.9 22.81 1332 0.9899 X 25 17 0 340.8 22.88 1325 0.9745 X 25 18 0 348.8 22.95 1304 0.9588 X 25 19 0 356.8 23.02 1283 0.9431 X 25 20 0 364.3 23.09 1263 0.9275 X 25 21 0 363.9 22.97 1336 0.9760 X 25 22 0 362.5 22.77 1412 1.0310 X 25 23 0 361.6 22.70 1398 1.0270 X 25 24 0 360.7 22.75 1342 1.0090 X 26 2 0 365.0 23.17 1446 1.0620 X 26 3 0 365.0 23.17 1446 1.0620 X 26 4 0 365.0 23.04 1407 1.0390 X 26 5 0 365.0 22.94 1362 1.0090 X 26 6 0 364.2 22.83 1316 0.9783 X 26 7 0 358.6 22.72 1270 0.9474 X 26 10 0 356.5 22.69 1201 0.8959 X 26 11 0 353.6 22.65 1233 0.9210 X 26 12 0 346.6 22.61 1265 0.9462 X 26 13 0 339.5 22.58 1297 0.9711 X 26 14 0 334.3 22.62 1317 0.9799 X 26 15 0 332.1 22.67 1326 0.9887 X 26 16 0 331.0 22.74 1330 0.9767 X 26 17 0 329.9 22.81 1334 0.9610 X 26 18 0 334.1 22.87 1323 0.9471 X 26 19 0 342.0 22.86 1302 0.9493 X 26 20 0 350.4 22.86 1285 0.9510 X 26 21 0 362.2 22.93 1307 0.9481 X 26 22 0 362.9 22.78 1380 1.0090 X 26 23 0 361.6 22.58 1419 1.0450 X 26 24 0 360.8 22.63 1368 1.0270 X 26 25 0 358.6 22.66 1343 1.0140 X 27 2 0 365.0 23.25 1415 1.0370 X 27 3 0 365.0 23.25 1415 1.0370 X 27 4 0 365.0 23.13 1372 1.0100 X 27 5 0 365.0 23.02 1326 0.9786 X 27 6 0 361.7 22.91 1280 0.9477 X 27 7 0 356.1 22.81 1234 0.9168 X 27 8 0 353.0 22.70 1188 0.8859 X 27 9 0 352.7 22.70 1162 0.8658 X 27 10 0 352.4 22.66 1194 0.8910 X 27 11 0 347.2 22.62 1226 0.9162 X 27 12 0 340.2 22.59 1258 0.9413 X 27 13 0 333.2 22.55 1290 0.9665 X 27 14 0 326.6 22.53 1319 0.9875 X 27 15 0 325.2 22.59 1324 0.9793 X 27 16 0 324.1 22.58 1328 0.9814 X 27 17 0 323.0 22.57 1332 0.9836 X 27 18 0 321.9 22.56 1336 0.9857 X 27 19 0 327.3 22.55 1322 0.9879 X 27 20 0 337.5 22.59 1326 0.9870 X 27 21 0 349.3 22.67 1349 0.9841 X 27 22 0 361.1 22.75 1371 0.9812 X 27 23 0 361.9 22.60 1423 1.0420 X 27 24 0 360.8 22.51 1398 1.0460 X 27 25 0 359.1 22.54 1361 1.0310 X 28 3 0 365.0 23.19 1380 1.0140 X 28 4 0 365.0 23.13 1346 0.9905 X 28 5 0 364.8 23.02 1300 0.9596 X 28 6 0 359.2 22.91 1254 0.9287 X 28 7 0 353.6 22.80 1208 0.8978 X 28 8 0 348.9 22.69 1163 0.8673 X 28 9 0 348.6 22.70 1157 0.8622 X 28 10 0 347.9 22.68 1188 0.8864 X 28 11 0 340.9 22.65 1220 0.9116 X 28 12 0 333.9 22.62 1252 0.9368 X 28 13 0 326.8 22.59 1284 0.9620 X 28 14 0 326.5 22.56 1317 0.9872 X 28 15 0 325.0 22.51 1327 0.9976 X 28 16 0 322.7 22.46 1330 1.0030 X 28 17 0 320.4 22.41 1333 1.0090 X 28 18 0 318.1 22.36 1336 1.0150 X 28 19 0 315.4 22.30 1339 1.0200 X 28 20 0 324.7 22.33 1361 1.0230 X 28 21 0 336.5 22.41 1384 1.0200 X 28 22 0 348.3 22.48 1406 1.0170 X 28 23 0 360.1 22.56 1429 1.0140 X 28 24 0 360.9 22.41 1427 1.0620 X 28 25 0 359.5 22.43 1380 1.0480 X 28 26 0 357.0 22.45 1363 1.0370 X 29 3 0 365.0 22.93 1341 0.9949 X 29 4 0 365.0 22.93 1341 0.9949 X 29 5 0 362.3 22.82 1295 0.9640 X 29 6 0 356.7 22.71 1249 0.9331 X 29 7 0 351.1 22.63 1209 0.9052 X 29 8 0 345.5 22.63 1164 0.8708 X 29 9 0 344.5 22.67 1171 0.8750 X 29 10 0 341.6 22.70 1194 0.8909 X 29 11 0 334.6 22.73 1216 0.9073 X 29 12 0 328.7 22.70 1249 0.9325 X 29 13 0 329.5 22.67 1281 0.9577 X 29 14 0 330.3 22.64 1313 0.9829 X 29 15 0 329.9 22.60 1333 1.0000 X 29 16 0 327.6 22.55 1337 1.0060 X 29 17 0 325.3 22.50 1340 1.0120 X 29 18 0 322.5 22.44 1342 1.0170 X 29 19 0 317.5 22.33 1344 1.0210 X 29 20 0 324.1 22.31 1367 1.0300 X 29 21 0 330.6 22.28 1389 1.0400 X 29 22 0 337.1 22.25 1410 1.0490 X 29 23 0 347.3 22.30 1417 1.0500 X 29 24 0 359.1 22.37 1424 1.0470 X 29 25 0 360.0 22.31 1398 1.0650 X 29 26 0 357.5 22.33 1381 1.0540 X 29 27 0 355.0 22.35 1364 1.0430 X 30 4 0 365.0 22.73 1336 0.9993 X 30 5 0 359.8 22.65 1294 0.9708 X 30 6 0 354.2 22.57 1255 0.9432 X 30 7 0 348.6 22.55 1211 0.9106 X 30 8 0 343.0 22.59 1164 0.8720 X 30 9 0 340.4 22.63 1186 0.8878 X 30 10 0 335.2 22.66 1208 0.9037 X 30 11 0 331.7 22.70 1230 0.9195 X 30 12 0 332.5 22.73 1253 0.9353 X 30 13 0 333.3 22.75 1277 0.9534 X 30 14 0 334.1 22.72 1309 0.9786 X 30 15 0 334.8 22.69 1340 1.0030 X 30 16 0 332.5 22.64 1343 1.0090 X 30 17 0 329.9 22.59 1346 1.0140 X 30 18 0 323.4 22.46 1345 1.0180 X 30 19 0 319.7 22.36 1349 1.0220 X 30 20 0 326.2 22.33 1372 1.0310 X 30 21 0 332.7 22.31 1385 1.0410 X 30 22 0 339.3 22.28 1392 1.0500 X 30 23 0 345.8 22.26 1399 1.0600 X 30 24 0 352.4 22.23 1406 1.0690 X 30 25 0 358.9 22.20 1413 1.0780 X 30 26 0 357.9 22.22 1400 1.0710 X 30 27 0 355.4 22.24 1383 1.0600 X 30 28 0 352.9 22.26 1365 1.0480 X 31 4 0 358.7 22.93 1378 1.0250 X 31 5 0 361.4 22.51 1301 0.9813 X 31 6 0 354.1 22.47 1259 0.9504 X 31 7 0 346.9 22.51 1211 0.9116 X 31 8 0 340.5 22.55 1178 0.8848 X 31 9 0 335.9 22.59 1201 0.9007 X 31 10 0 334.7 22.62 1223 0.9165 X 31 11 0 335.5 22.66 1245 0.9323 X 31 12 0 336.3 22.69 1267 0.9482 X 31 13 0 337.1 22.73 1289 0.9640 X 31 14 0 337.9 22.77 1311 0.9798 X 31 15 0 338.7 22.77 1338 0.9995 X 31 16 0 337.3 22.73 1350 1.0110 X 31 17 0 330.8 22.60 1349 1.0150 X 31 18 0 324.2 22.48 1348 1.0180 X 31 19 0 321.8 22.39 1353 1.0230 X 31 20 0 327.8 22.36 1361 1.0320 X 31 21 0 332.9 22.33 1371 1.0410 X 31 22 0 338.0 22.31 1380 1.0490 X 31 23 0 343.1 22.28 1389 1.0580 X 31 24 0 348.2 22.25 1399 1.0660 X 31 25 0 353.9 22.21 1384 1.0570 X 31 26 0 359.6 22.29 1402 1.0680 X 31 27 0 355.9 22.12 1401 1.0760 X 31 28 0 353.4 22.14 1384 1.0650 X 32 4 0 361.9 22.69 1340 1.0050 X 32 5 0 365.0 22.44 1302 0.9854 X 32 6 0 358.0 22.43 1258 0.9514 X 32 7 0 350.6 22.47 1210 0.9127 X 32 8 0 343.1 22.51 1193 0.8977 X 32 9 0 337.2 22.55 1215 0.9135 X 32 10 0 333.0 22.58 1237 0.9293 X 32 11 0 332.5 22.62 1259 0.9452 X 32 12 0 333.6 22.65 1282 0.9610 X 32 13 0 334.7 22.69 1304 0.9768 X 32 14 0 335.8 22.73 1326 0.9927 X 32 15 0 336.8 22.74 1343 1.0040 X 32 16 0 335.1 22.69 1344 1.0080 X 32 17 0 327.9 22.56 1341 1.0100 X 32 18 0 320.8 22.42 1338 1.0130 X 32 19 0 319.7 22.41 1351 1.0220 X 32 20 0 322.0 22.38 1357 1.0280 X 32 21 0 327.1 22.35 1366 1.0370 X 32 22 0 332.2 22.32 1376 1.0450 X 32 23 0 337.3 22.30 1385 1.0540 X 32 24 0 342.4 22.27 1394 1.0620 X 32 25 0 348.8 22.22 1346 1.0280 X 32 26 0 359.9 22.61 1360 1.0210 X 32 28 0 353.8 22.03 1402 1.0820 X 33 5 0 361.4 22.48 1330 0.9906 X 33 6 0 360.9 22.40 1258 0.9525 X 33 7 0 353.4 22.44 1210 0.9137 X 33 8 0 346.0 22.47 1208 0.9105 X 33 9 0 341.5 22.51 1230 0.9263 X 33 10 0 337.3 22.54 1252 0.9422 X 33 11 0 333.1 22.58 1274 0.9580 X 33 12 0 328.9 22.62 1296 0.9738 X 33 13 0 327.5 22.64 1314 0.9860 X 33 14 0 328.5 22.63 1325 0.9911 X 33 15 0 329.6 22.63 1333 0.9962 X 33 16 0 330.3 22.61 1330 1.0010 X 33 17 0 323.2 22.48 1328 1.0040 X 33 18 0 320.2 22.42 1336 1.0120 X 33 19 0 321.8 22.45 1356 1.0250 X 33 20 0 316.1 22.40 1353 1.0240 X 33 21 0 321.3 22.37 1362 1.0330 X 33 22 0 326.4 22.34 1372 1.0420 X 33 23 0 331.5 22.32 1381 1.0500 X 33 24 0 337.3 22.28 1356 1.0330 X 33 25 0 343.7 22.23 1309 0.9999 X 33 27 0 363.1 22.89 1350 1.0090 X 33 28 0 356.5 22.26 1390 1.0640 X 33 29 0 351.8 21.93 1404 1.0880 X 34 5 0 354.9 22.48 1346 1.0200 X 34 6 0 363.8 22.36 1257 0.9535 X 34 7 0 356.3 22.40 1209 0.9148 X 34 8 0 350.0 22.43 1222 0.9233 X 34 9 0 345.8 22.47 1244 0.9392 X 34 10 0 341.6 22.50 1266 0.9550 X 34 11 0 337.5 22.53 1286 0.9683 X 34 12 0 333.3 22.52 1296 0.9734 X 34 13 0 329.1 22.52 1306 0.9785 X 34 14 0 324.9 22.51 1317 0.9836 X 34 15 0 322.4 22.51 1320 0.9886 X 34 16 0 323.5 22.50 1317 0.9937 X 34 17 0 318.5 22.40 1314 0.9969 X 34 18 0 321.4 22.44 1338 1.0130 X 34 19 0 323.9 22.48 1361 1.0280 X 34 20 0 317.8 22.43 1358 1.0270 X 34 21 0 315.4 22.39 1358 1.0290 X 34 22 0 320.5 22.36 1368 1.0380 X 34 23 0 325.9 22.33 1366 1.0380 X 34 24 0 332.3 22.28 1319 1.0050 X 34 26 0 347.6 22.43 1257 0.9520 X 34 27 0 363.5 22.82 1309 0.9914 X 34 28 0 361.5 22.88 1345 1.0060 X 34 29 0 354.9 22.25 1384 1.0610 X 35 6 0 363.0 22.36 1311 0.9571 X 35 7 0 359.2 22.36 1214 0.9203 X 35 8 0 354.4 22.39 1237 0.9361 X 35 9 0 350.2 22.42 1257 0.9506 X 35 10 0 346.0 22.42 1268 0.9557 X 35 11 0 341.8 22.41 1278 0.9608 X 35 12 0 337.6 22.41 1288 0.9659 X 35 13 0 333.4 22.40 1298 0.9710 X 35 14 0 329.2 22.39 1309 0.9760 X 35 15 0 325.0 22.39 1307 0.9811 X 35 16 0 320.1 22.40 1303 0.9858 X 35 17 0 324.3 22.41 1300 0.9858 X 35 18 0 329.9 22.44 1315 0.9948 X 35 19 0 329.3 22.50 1318 0.9940 X 35 20 0 320.5 22.48 1349 1.0190 X 35 21 0 313.7 22.42 1359 1.0290 X 35 22 0 314.7 22.38 1363 1.0340 X 35 23 0 320.8 22.34 1329 1.0100 X 35 24 0 327.2 22.29 1281 0.9763 X 35 25 0 333.5 22.24 1233 0.9427 X 35 26 0 341.6 22.29 1204 0.9216 X 35 28 0 363.0 22.63 1300 1.0060 X 35 29 0 359.7 22.81 1339 1.0080 X 36 6 0 356.9 22.25 1325 0.9859 X 36 7 0 362.9 22.32 1229 0.9329 X 36 8 0 358.6 22.31 1239 0.9380 X 36 9 0 353.4 22.32 1249 0.9425 X 36 10 0 348.1 22.34 1260 0.9470 X 36 11 0 342.9 22.35 1270 0.9516 X 36 12 0 337.7 22.36 1280 0.9561 X 36 13 0 332.5 22.37 1290 0.9606 X 36 14 0 327.3 22.38 1296 0.9652 X 36 15 0 322.1 22.39 1293 0.9697 X 36 16 0 321.4 22.38 1284 0.9756 X 36 17 0 320.4 22.18 1292 0.9919 X 36 18 0 333.6 22.26 1275 0.9729 X 36 19 0 324.7 22.39 1253 0.9497 X 36 20 0 315.9 22.58 1233 0.9238 X 36 21 0 313.3 22.49 1295 0.9753 X 36 22 0 312.1 22.38 1364 1.0310 X 36 23 0 319.4 22.32 1337 1.0040 X 36 24 0 326.7 22.27 1302 0.9759 X 36 25 0 334.1 22.21 1246 0.9481 X 36 26 0 342.8 22.13 1237 0.9506 X 36 27 0 353.3 22.09 1254 0.9708 X 36 28 0 364.0 22.27 1301 1.0130 X 36 29 0 360.7 22.44 1299 1.0150 X 37 6 0 350.7 22.13 1327 1.0150 X 37 7 0 360.6 22.27 1257 0.9572 X 37 8 0 355.4 22.31 1236 0.9344 X 37 9 0 350.1 22.33 1241 0.9309 X 37 10 0 344.9 22.34 1252 0.9355 X 37 11 0 339.7 22.35 1262 0.9400 X 37 12 0 334.5 22.36 1272 0.9445 X 37 13 0 329.3 22.37 1282 0.9490 X 37 14 0 324.1 22.39 1283 0.9536 X 37 15 0 324.0 22.40 1272 0.9581 X 37 16 0 323.8 22.27 1271 0.9703 X 37 17 0 322.9 22.08 1279 0.9865 X 37 18 0 323.9 22.09 1286 0.9905 X 37 19 0 322.7 22.35 1262 0.9571 X 37 20 0 321.4 22.48 1257 0.9466 X 37 21 0 320.0 22.45 1279 0.9660 X 37 22 0 318.3 22.36 1341 1.0150 X 37 23 0 322.0 22.28 1391 1.0220 X 37 24 0 329.3 22.23 1316 0.9939 X 37 25 0 337.6 22.16 1284 0.9857 X 37 26 0 346.7 22.07 1294 0.9971 X 37 27 0 355.9 21.99 1305 1.0090 X 37 28 0 365.0 21.90 1315 1.0200 X 37 29 0 361.7 22.08 1288 1.0220 X 38 6 0 343.6 22.30 1365 1.0440 X 38 7 0 358.4 22.13 1318 0.9525 X 38 8 0 352.1 22.26 1285 0.9761 X 38 9 0 346.9 22.30 1263 0.9534 X 38 10 0 341.7 22.34 1244 0.9307 X 38 11 0 336.5 22.36 1254 0.9284 X 38 12 0 331.3 22.37 1264 0.9329 X 38 13 0 326.4 22.38 1273 0.9375 X 38 14 0 326.7 22.39 1263 0.9420 X 38 15 0 327.1 22.36 1249 0.9487 X 38 16 0 326.3 22.18 1259 0.9649 X 38 17 0 327.2 22.13 1293 0.9811 X 38 18 0 330.7 22.10 1293 0.9937 X 38 19 0 329.4 22.36 1269 0.9603 X 38 20 0 328.1 22.38 1281 0.9693 X 38 21 0 326.4 22.35 1303 0.9888 X 38 22 0 324.7 22.32 1325 1.0080 X 38 23 0 324.6 22.24 1384 1.0400 X 38 24 0 332.4 22.18 1331 1.0210 X 38 25 0 341.5 22.09 1341 1.0320 X 38 26 0 346.4 22.01 1339 1.0340 X 38 27 0 348.9 21.92 1329 1.0290 X 38 28 0 354.5 21.87 1310 1.0170 X 38 29 0 359.7 21.81 1276 1.0230 X 39 6 0 347.9 22.16 1343 1.0130 X 39 7 0 352.3 22.01 1320 0.9813 X 39 8 0 348.9 22.21 1332 1.0180 X 39 9 0 343.7 22.25 1311 0.9951 X 39 10 0 338.5 22.29 1290 0.9724 X 39 11 0 333.3 22.33 1269 0.9496 X 39 12 0 329.0 22.37 1256 0.9269 X 39 13 0 329.4 22.39 1254 0.9259 X 39 14 0 329.8 22.40 1235 0.9304 X 39 15 0 329.8 22.29 1241 0.9434 X 39 16 0 329.1 22.24 1277 0.9595 X 39 17 0 333.0 22.19 1295 0.9757 X 39 18 0 336.9 22.14 1297 0.9918 X 39 19 0 336.1 22.31 1283 0.9726 X 39 20 0 334.6 22.28 1305 0.9921 X 39 21 0 332.8 22.25 1327 1.0120 X 39 22 0 331.1 22.22 1349 1.0310 X 39 23 0 326.2 22.17 1366 1.0480 X 39 24 0 327.8 22.11 1362 1.0470 X 39 25 0 330.3 22.02 1352 1.0430 X 39 26 0 332.8 21.93 1342 1.0390 X 39 27 0 335.3 21.88 1325 1.0280 X 39 28 0 344.1 21.84 1304 1.0140 X 40 6 0 346.2 21.90 1323 1.0100 X 40 7 0 346.2 21.90 1323 1.0100 X 40 8 0 347.9 22.10 1362 1.0230 X 40 9 0 340.5 22.19 1358 1.0370 X 40 10 0 335.3 22.23 1337 1.0140 X 40 11 0 331.7 22.28 1316 0.9913 X 40 12 1 332.1 22.32 1281 0.9686 X 40 13 1 332.4 22.36 1245 0.9459 X 40 14 0 332.8 22.37 1226 0.9267 X 40 15 0 332.2 22.34 1260 0.9392 X 40 16 0 334.9 22.30 1296 0.9541 X 40 17 0 338.8 22.25 1298 0.9703 X 40 18 0 342.7 22.20 1300 0.9864 X 40 19 0 342.7 22.21 1307 0.9954 X 40 20 0 335.9 22.15 1322 1.0120 X 40 21 0 325.7 22.06 1332 1.0250 X 40 22 0 315.5 21.97 1342 1.0390 X 40 23 0 315.0 21.99 1358 1.0500 X 40 24 0 320.0 22.04 1366 1.0520 X 40 25 0 317.6 21.95 1356 1.0480 X 40 26 0 319.2 21.88 1341 1.0390 X 40 27 0 324.2 21.85 1320 1.0250 X 41 6 0 339.8 21.84 1332 1.0390 X 41 7 0 339.8 21.84 1332 1.0390 X 41 8 0 349.7 21.92 1316 0.9838 X 41 9 0 337.3 22.14 1405 1.0780 X 41 10 0 334.4 22.18 1381 1.0560 X 41 11 0 334.8 22.21 1339 1.0300 X 41 12 1 335.1 22.22 1297 0.9975 X 41 13 1 335.5 22.24 1259 0.9652 X 41 14 0 335.7 22.23 1258 0.9547 X 41 15 0 336.9 22.20 1290 0.9671 X 41 16 0 340.8 22.17 1308 0.9796 X 41 17 0 344.7 22.14 1310 0.9920 X 41 18 0 336.3 22.06 1310 1.0040 X 41 19 0 325.5 21.95 1305 1.0070 X 41 20 0 315.0 21.86 1309 1.0160 X 41 21 0 304.8 21.77 1319 1.0300 X 41 22 0 295.1 21.68 1329 1.0440 X 41 23 0 305.4 21.83 1350 1.0510 X 41 24 0 314.8 21.96 1369 1.0570 X 41 25 0 312.5 21.89 1356 1.0500 X 41 26 0 311.4 21.85 1335 1.0360 X 41 27 0 313.8 21.82 1315 1.0220 X 42 7 0 343.8 21.81 1324 1.0080 X 42 8 0 347.7 21.78 1316 0.9766 X 42 9 0 335.6 22.05 1427 1.1020 X 42 10 0 337.4 22.07 1396 1.0780 X 42 11 0 337.8 22.08 1354 1.0450 X 42 12 0 338.1 22.09 1312 1.0130 X 42 13 0 338.5 22.10 1273 0.9810 X 42 14 0 338.8 22.08 1290 0.9826 X 42 15 0 342.7 22.05 1321 0.9951 X 42 16 0 338.2 21.99 1326 1.0100 X 42 17 0 327.2 21.90 1327 1.0250 X 42 18 0 316.4 21.79 1321 1.0270 X 42 19 0 305.6 21.69 1316 1.0300 X 42 20 0 294.7 21.58 1311 1.0330 X 42 21 0 283.9 21.48 1306 1.0350 X 42 22 0 285.5 21.53 1321 1.0450 X 42 23 0 297.5 21.69 1345 1.0530 X 42 24 0 310.3 21.86 1370 1.0620 X 42 25 0 312.8 21.86 1351 1.0470 X 42 26 0 309.7 21.82 1330 1.0340 X 42 27 0 303.6 21.79 1309 1.0200 X 43 8 0 341.6 21.66 1318 1.0050 X 43 9 0 335.3 21.93 1410 1.0880 X 43 10 0 335.8 21.92 1377 1.0680 X 43 11 0 338.8 21.94 1355 1.0510 X 43 12 0 341.2 21.96 1327 1.0290 X 43 13 0 341.5 21.97 1289 0.9981 X 43 14 0 340.2 21.92 1321 1.0120 X 43 15 0 329.1 21.83 1342 1.0290 X 43 16 0 318.1 21.74 1343 1.0450 X 43 17 0 307.3 21.64 1338 1.0480 X 43 18 0 296.5 21.53 1333 1.0500 X 43 19 0 285.6 21.43 1327 1.0530 X 43 20 0 280.3 21.40 1323 1.0520 X 43 21 0 279.8 21.43 1318 1.0470 X 43 22 0 288.1 21.52 1332 1.0520 X 43 23 0 301.8 21.67 1358 1.0640 X 43 24 0 314.1 21.84 1381 1.0720 X 43 25 0 312.2 21.82 1353 1.0510 X 43 26 0 307.5 21.79 1325 1.0310 X 43 27 0 302.4 21.76 1304 1.0170 X 44 9 0 337.1 21.75 1364 1.0490 X 44 10 0 332.9 21.77 1349 1.0530 X 44 11 0 336.0 21.79 1327 1.0350 X 44 12 0 339.0 21.81 1305 1.0170 X 44 13 0 331.1 21.76 1320 1.0310 X 44 14 0 320.0 21.67 1351 1.0480 X 44 15 0 309.0 21.58 1359 1.0650 X 44 16 1 298.2 21.48 1354 1.0680 X 44 17 1 287.3 21.37 1349 1.0710 X 44 18 1 284.5 21.38 1344 1.0680 X 44 19 0 284.0 21.41 1340 1.0630 X 44 20 0 283.4 21.45 1335 1.0580 X 44 21 0 282.9 21.49 1330 1.0530 X 44 22 0 289.8 21.57 1341 1.0570 X 44 23 0 304.2 21.70 1368 1.0700 X 44 24 0 314.8 21.79 1383 1.0760 X 44 25 0 310.0 21.77 1357 1.0570 X 44 26 0 305.3 21.75 1329 1.0360 X 44 27 0 300.5 21.72 1301 1.0160 X 45 10 0 330.1 21.67 1350 1.0580 X 45 11 0 333.1 21.64 1299 1.0190 X 45 12 0 336.2 21.66 1277 1.0010 X 45 13 0 315.4 21.53 1337 1.0530 X 45 14 0 299.9 21.42 1375 1.0840 X 45 15 1 289.1 21.32 1371 1.0890 X 45 16 1 288.6 21.36 1366 1.0840 X 45 17 1 288.1 21.39 1361 1.0790 X 45 18 1 287.6 21.43 1357 1.0740 X 45 19 1 287.1 21.47 1352 1.0690 X 45 20 0 286.6 21.50 1347 1.0640 X 45 21 0 286.1 21.54 1343 1.0590 X 45 22 0 291.5 21.62 1351 1.0620 X 45 23 0 305.9 21.75 1378 1.0750 X 45 24 0 308.6 21.75 1366 1.0650 X 45 25 0 307.8 21.72 1347 1.0520 X 45 26 0 303.1 21.70 1328 1.0380 X 45 27 0 298.3 21.68 1305 1.0220 X 46 10 0 327.4 21.62 1380 1.0850 X 46 11 0 330.3 21.50 1272 1.0040 X 46 12 0 325.9 21.47 1275 1.0070 X 46 13 0 299.9 21.31 1352 1.0740 X 46 14 0 292.6 21.33 1384 1.0950 X 46 15 1 292.3 21.37 1383 1.0940 X 46 16 1 291.8 21.41 1379 1.0900 X 46 17 1 291.3 21.45 1374 1.0850 X 46 18 1 290.8 21.49 1369 1.0800 X 46 19 1 290.2 21.52 1365 1.0750 X 46 20 1 289.7 21.56 1360 1.0710 X 46 21 1 289.2 21.60 1355 1.0660 X 46 22 1 293.1 21.66 1360 1.0660 X 46 23 0 301.9 21.73 1368 1.0680 X 46 24 0 302.2 21.70 1349 1.0550 X 46 25 0 302.4 21.68 1330 1.0410 X 46 26 0 300.8 21.66 1311 1.0270 X 46 27 0 296.1 21.63 1292 1.0140 X 46 28 0 290.2 21.61 1273 0.9999 X 47 10 0 324.7 21.57 1409 1.1110 X 47 11 0 327.4 21.35 1248 0.9912 X 47 12 0 316.4 21.31 1279 1.0150 X 47 13 0 306.7 21.34 1324 1.0460 X 47 14 0 297.0 21.38 1370 1.0760 X 47 15 0 294.5 21.41 1377 1.0820 X 47 16 1 294.2 21.45 1376 1.0810 X 47 17 1 293.8 21.49 1375 1.0800 X 47 18 1 293.5 21.53 1374 1.0790 X 47 19 1 293.2 21.57 1373 1.0770 X 47 20 1 292.9 21.61 1372 1.0760 X 47 21 1 292.4 21.65 1368 1.0720 X 47 22 1 294.8 21.71 1369 1.0710 X 47 23 1 295.5 21.69 1351 1.0580 X 47 24 1 295.8 21.66 1332 1.0440 X 47 25 1 296.0 21.64 1313 1.0300 X 47 26 1 296.3 21.61 1294 1.0170 X 47 27 1 293.9 21.59 1275 1.0030 X 47 28 1 289.0 21.57 1256 0.9893 X 47 29 1 280.3 21.54 1238 0.9767 X 47 30 1 279.0 21.51 1220 0.9640 X 47 31 1 287.1 21.46 1207 0.9575 X 48 11 0 324.7 21.30 1277 1.0180 X 48 12 0 323.9 21.36 1258 0.9857 X 48 13 0 314.2 21.39 1295 1.0160 X 48 14 0 304.5 21.42 1341 1.0470 X 48 15 0 296.7 21.46 1371 1.0700 X 48 16 1 296.4 21.50 1370 1.0690 X 48 17 1 296.1 21.54 1369 1.0680 X 48 18 1 295.7 21.58 1368 1.0670 X 48 19 1 295.4 21.61 1367 1.0650 X 48 20 1 295.1 21.65 1366 1.0640 X 48 21 1 294.8 21.69 1360 1.0630 X 48 22 1 290.1 21.61 1363 1.0700 X 48 23 1 289.3 21.57 1349 1.0610 X 48 24 1 289.3 21.54 1331 1.0480 X 48 25 1 289.6 21.51 1313 1.0360 X 48 26 1 289.9 21.48 1295 1.0230 X 48 27 1 290.2 21.45 1277 1.0100 X 48 28 1 286.9 21.42 1259 0.9976 X 48 29 1 279.1 21.39 1241 0.9850 X 48 30 1 270.5 21.37 1225 0.9741 X 48 31 1 277.9 21.20 1246 1.0020 X 49 11 0 322.0 21.25 1307 1.0440 X 49 12 0 322.6 21.21 1267 1.0080 X 49 13 0 319.8 21.40 1292 0.9969 X 49 14 0 311.9 21.47 1317 1.0170 X 49 15 0 302.2 21.50 1358 1.0470 X 49 16 1 298.6 21.54 1364 1.0570 X 49 17 1 298.3 21.58 1363 1.0560 X 49 18 1 298.0 21.62 1359 1.0550 X 49 19 1 297.6 21.66 1353 1.0530 X 49 20 1 297.3 21.70 1348 1.0520 X 49 21 1 292.5 21.61 1351 1.0600 X 49 22 1 287.1 21.51 1355 1.0680 X 49 23 1 283.7 21.43 1352 1.0690 X 49 24 1 283.7 21.40 1334 1.0560 X 49 25 1 283.7 21.37 1316 1.0440 X 49 26 1 283.7 21.34 1298 1.0310 X 49 27 1 283.8 21.31 1280 1.0190 X 49 28 1 284.1 21.28 1262 1.0060 X 49 29 1 277.9 21.26 1247 0.9962 X 49 30 1 269.3 21.16 1251 1.0060 X 49 31 1 267.5 20.94 1285 1.0470 X 49 32 1 273.0 20.91 1290 1.0540 X 50 12 0 321.0 21.08 1271 1.0230 X 50 13 0 318.6 21.25 1301 1.0190 X 50 14 0 315.8 21.43 1326 1.0080 X 50 15 0 309.6 21.54 1351 1.0180 X 50 16 1 300.9 21.58 1352 1.0450 X 50 17 1 300.5 21.62 1346 1.0440 X 50 18 1 300.2 21.66 1340 1.0430 X 50 19 1 299.9 21.70 1335 1.0420 X 50 20 1 294.9 21.60 1338 1.0490 X 50 21 1 289.5 21.50 1343 1.0580 X 50 22 1 284.2 21.40 1348 1.0660 X 50 23 1 278.8 21.30 1352 1.0750 X 50 24 1 278.2 21.26 1337 1.0650 X 50 25 1 278.2 21.23 1319 1.0520 X 50 26 1 278.2 21.20 1301 1.0390 X 50 27 1 278.2 21.18 1284 1.0280 X 50 28 1 278.2 21.16 1269 1.0180 X 50 29 1 276.1 21.13 1256 1.0100 X 50 30 1 268.1 20.91 1290 1.0510 X 50 31 1 259.5 20.68 1324 1.0920 X 50 32 1 264.1 20.56 1341 1.1140 X 50 33 1 267.7 20.71 1319 1.0880 X 50 34 1 271.2 20.86 1297 1.0620 X 51 12 0 318.7 20.99 1262 1.0200 X 51 13 0 317.3 21.10 1310 1.0410 X 51 14 0 314.5 21.29 1335 1.0300 X 51 15 0 311.8 21.47 1360 1.0190 X 51 16 0 307.3 21.62 1342 1.0190 X 51 17 1 302.8 21.66 1328 1.0320 X 51 18 1 302.4 21.70 1322 1.0310 X 51 19 1 297.3 21.60 1326 1.0390 X 51 20 1 291.9 21.50 1331 1.0470 X 51 21 1 286.6 21.40 1335 1.0560 X 51 22 1 281.2 21.29 1340 1.0650 X 51 23 1 275.8 21.19 1344 1.0730 X 51 24 1 272.6 21.12 1340 1.0730 X 51 25 1 272.6 21.09 1322 1.0600 X 51 26 1 272.8 21.07 1306 1.0500 X 51 27 1 273.7 21.05 1292 1.0400 X 51 28 1 274.4 21.03 1277 1.0310 X 51 29 1 269.4 20.87 1295 1.0550 X 51 30 1 264.5 20.65 1329 1.0960 X 51 31 1 258.3 20.42 1362 1.1370 X 51 32 1 255.3 20.22 1392 1.1740 X 51 33 1 258.8 20.37 1370 1.1480 X 51 34 1 262.4 20.52 1348 1.1220 X 52 13 0 316.0 20.95 1319 1.0620 X 52 14 0 313.3 21.14 1344 1.0520 X 52 15 0 310.5 21.32 1355 1.0410 X 52 16 0 307.8 21.51 1338 1.0310 X 52 17 1 305.0 21.70 1309 1.0200 X 52 18 1 299.6 21.59 1314 1.0290 X 52 19 1 294.2 21.49 1319 1.0380 X 52 20 1 288.8 21.38 1324 1.0480 X 52 21 1 283.4 21.28 1329 1.0570 X 52 22 1 278.0 21.17 1335 1.0660 X 52 23 1 272.5 21.07 1340 1.0750 X 52 24 1 267.4 20.97 1344 1.0830 X 52 25 1 268.3 20.96 1329 1.0720 X 52 26 1 269.2 20.94 1314 1.0620 X 52 27 1 270.1 20.92 1299 1.0530 X 52 28 1 267.8 20.84 1300 1.0590 X 52 29 1 262.8 20.61 1334 1.1000 X 52 30 1 257.8 20.39 1367 1.1410 X 52 31 1 252.8 20.16 1401 1.1820 X 52 32 1 247.8 19.94 1434 1.2230 X 52 33 1 250.0 20.02 1421 1.2080 X 52 34 1 253.5 20.17 1399 1.1820 X 52 49 1 306.9 20.24 1381 1.1620 X 52 50 1 307.7 20.18 1395 1.1750 X 52 51 1 306.2 20.21 1394 1.1750 X 52 52 1 305.2 20.25 1400 1.1790 X 52 53 1 304.2 20.29 1406 1.1830 X 53 13 0 314.3 20.82 1321 1.0740 X 53 14 0 312.0 20.99 1353 1.0740 X 53 15 0 309.2 21.17 1349 1.0630 X 53 16 0 306.4 21.37 1338 1.0450 X 53 17 1 301.1 21.50 1334 1.0320 X 53 18 1 294.4 21.38 1331 1.0550 X 53 19 1 289.0 21.27 1336 1.0640 X 53 20 1 283.6 21.17 1341 1.0740 X 53 21 1 278.1 21.06 1346 1.0830 X 53 22 1 272.7 20.96 1351 1.0920 X 53 23 1 267.3 20.85 1356 1.1010 X 53 24 1 263.8 20.79 1355 1.1030 X 53 25 1 264.7 20.81 1338 1.0870 X 53 26 1 265.6 20.81 1322 1.0750 X 53 27 1 266.1 20.80 1307 1.0650 X 53 28 1 261.1 20.58 1339 1.1040 X 53 29 1 256.1 20.35 1373 1.1450 X 53 30 1 253.3 20.21 1394 1.1720 X 53 31 1 250.8 20.08 1415 1.1980 X 53 32 1 248.2 19.95 1436 1.2230 X 53 33 1 248.9 19.92 1440 1.2280 X 53 34 1 250.3 19.91 1440 1.2290 X 53 35 1 252.7 19.98 1428 1.2160 X 53 36 1 256.0 20.13 1406 1.1900 X 53 48 1 295.9 20.07 1390 1.1780 X 53 49 1 299.3 20.06 1394 1.1800 X 53 51 1 304.7 20.10 1397 1.1810 X 53 52 1 304.7 20.12 1404 1.1860 X 53 53 1 303.7 20.16 1410 1.1900 X 53 54 1 302.6 20.20 1415 1.1940 X 53 55 1 301.6 20.24 1421 1.1980 X 54 13 0 312.0 20.73 1312 1.0720 X 54 14 0 310.7 20.84 1357 1.0960 X 54 15 0 307.9 21.04 1339 1.0710 X 54 16 0 305.0 21.25 1335 1.0390 X 54 17 1 297.2 21.30 1356 1.0430 X 54 18 1 289.8 21.20 1354 1.0660 X 54 19 1 283.8 21.06 1353 1.0910 X 54 20 1 278.3 20.95 1358 1.1000 X 54 21 1 272.9 20.85 1363 1.1090 X 54 22 1 267.5 20.74 1368 1.1180 X 54 23 1 262.1 20.63 1373 1.1270 X 54 24 1 260.3 20.60 1365 1.1220 X 54 25 1 261.1 20.63 1348 1.1070 X 54 26 1 262.0 20.66 1331 1.0910 X 54 27 1 261.8 20.64 1331 1.0920 X 54 28 1 259.3 20.50 1352 1.1180 X 54 29 1 256.7 20.37 1373 1.1440 X 54 30 1 254.1 20.24 1394 1.1690 X 54 31 1 251.5 20.11 1414 1.1950 X 54 32 1 248.9 19.97 1435 1.2210 X 54 33 1 249.6 19.94 1439 1.2260 X 54 34 1 251.0 19.93 1439 1.2270 X 54 35 1 252.4 19.92 1439 1.2280 X 54 36 1 253.8 19.91 1440 1.2290 X 54 37 1 255.6 19.93 1435 1.2240 X 54 46 1 285.5 19.89 1405 1.1990 X 54 47 1 288.9 19.84 1409 1.2050 X 54 48 1 292.1 19.86 1411 1.2050 X 54 49 1 294.0 19.91 1410 1.2020 X 54 50 1 297.5 19.96 1409 1.1990 X 54 51 1 298.1 20.01 1408 1.1950 X 54 52 1 297.2 20.08 1404 1.1880 X 54 53 1 297.8 20.12 1406 1.1870 X 54 54 1 301.0 20.09 1418 1.1990 X 54 55 1 301.1 20.11 1425 1.2050 X 55 14 0 309.3 20.71 1343 1.0960 X 55 15 0 306.4 20.91 1323 1.0650 X 55 16 0 302.4 21.09 1329 1.0410 X 55 17 1 293.4 21.09 1348 1.0550 X 55 18 1 285.4 21.03 1370 1.0750 X 55 19 1 279.1 20.87 1375 1.1040 X 55 20 1 273.1 20.73 1374 1.1260 X 55 21 1 267.7 20.63 1379 1.1350 X 55 22 1 262.3 20.52 1385 1.1440 X 55 23 1 256.9 20.42 1390 1.1530 X 55 24 1 256.7 20.42 1376 1.1420 X 55 25 1 257.6 20.45 1359 1.1260 X 55 26 1 259.4 20.48 1346 1.1130 X 55 27 1 259.9 20.47 1336 1.1150 X 55 28 1 258.4 20.41 1346 1.1310 X 55 29 1 256.8 20.36 1370 1.1470 X 55 30 1 254.8 20.26 1393 1.1670 X 55 31 1 252.3 20.13 1414 1.1930 X 55 32 1 249.7 20.00 1434 1.2180 X 55 33 1 250.4 19.97 1438 1.2230 X 55 34 1 251.8 19.96 1438 1.2240 X 55 35 1 253.1 19.94 1439 1.2260 X 55 36 1 254.5 19.93 1439 1.2270 X 55 37 1 255.9 19.92 1439 1.2280 X 55 38 1 257.3 19.91 1440 1.2290 X 55 44 1 275.1 19.92 1419 1.2100 X 55 45 1 278.4 19.85 1422 1.2160 X 55 46 1 281.0 19.80 1437 1.2310 X 55 47 1 282.9 19.76 1421 1.2190 X 55 48 1 284.8 19.77 1421 1.2190 X 55 49 1 288.4 19.82 1420 1.2160 X 55 50 1 292.4 19.87 1420 1.2130 X 55 51 1 291.5 19.93 1419 1.2090 X 55 52 1 290.5 20.00 1415 1.2020 X 55 53 1 289.6 20.07 1411 1.1940 X 55 54 1 288.7 20.14 1407 1.1860 X 55 55 1 291.2 20.13 1416 1.1950 X 55 56 1 294.4 20.10 1428 1.2070 X 56 14 0 307.8 20.58 1327 1.0900 X 56 15 0 305.0 20.79 1307 1.0590 X 56 16 0 298.5 20.88 1322 1.0530 X 56 17 1 289.5 20.89 1340 1.0660 X 56 18 1 281.0 20.87 1362 1.0830 X 56 19 1 274.7 20.70 1384 1.1130 X 56 20 1 268.3 20.54 1395 1.1430 X 56 21 1 262.5 20.41 1396 1.1610 X 56 22 1 257.1 20.31 1401 1.1700 X 56 23 1 252.3 20.21 1404 1.1770 X 56 24 1 253.1 20.24 1387 1.1620 X 56 25 1 254.9 20.27 1373 1.1480 X 56 26 1 257.4 20.31 1362 1.1360 X 56 27 1 257.9 20.30 1352 1.1380 X 56 28 1 256.4 20.24 1344 1.1530 X 56 29 1 254.8 20.18 1360 1.1690 X 56 30 1 253.3 20.13 1384 1.1850 X 56 31 1 251.8 20.07 1409 1.2010 X 56 32 1 250.3 20.01 1433 1.2170 X 56 33 1 251.1 19.99 1437 1.2210 X 56 34 1 252.5 19.98 1438 1.2220 X 56 35 1 253.9 19.97 1438 1.2230 X 56 36 1 255.3 19.96 1438 1.2240 X 56 37 1 256.6 19.95 1439 1.2250 X 56 38 1 258.0 19.94 1439 1.2260 X 56 39 1 259.4 19.93 1439 1.2270 X 56 40 1 260.8 19.92 1440 1.2280 X 56 44 1 269.9 19.83 1455 1.2460 X 56 45 1 271.8 19.78 1474 1.2640 X 56 46 1 273.7 19.73 1492 1.2830 X 56 47 1 275.7 19.72 1414 1.2160 X 56 48 1 279.4 19.71 1427 1.2280 X 56 49 1 285.7 19.74 1431 1.2300 X 56 50 1 285.8 19.79 1430 1.2270 X 56 51 1 284.9 19.84 1429 1.2230 X 56 52 1 283.9 19.91 1425 1.2160 X 56 53 1 283.0 19.98 1421 1.2080 X 56 54 1 282.0 20.05 1417 1.2000 X 56 55 1 281.1 20.12 1413 1.1930 X 56 56 1 281.4 20.17 1414 1.1910 X 57 14 0 305.5 20.49 1327 1.0950 X 57 15 0 303.5 20.67 1297 1.0520 X 57 16 0 294.6 20.68 1315 1.0640 X 57 17 1 285.6 20.69 1333 1.0780 X 57 18 1 276.6 20.70 1354 1.0910 X 57 19 1 270.3 20.54 1376 1.1210 X 57 20 1 263.9 20.37 1398 1.1510 X 57 21 1 257.6 20.21 1416 1.1810 X 57 22 1 251.9 20.09 1418 1.1960 X 57 23 1 248.7 20.03 1415 1.1970 X 57 24 1 250.5 20.06 1401 1.1830 X 57 25 1 252.9 20.10 1390 1.1710 X 57 26 1 255.4 20.14 1378 1.1580 X 57 27 1 255.9 20.13 1368 1.1600 X 57 28 1 254.4 20.07 1360 1.1760 X 57 29 1 252.7 20.03 1352 1.1870 X 57 30 1 251.0 19.99 1374 1.1990 X 57 31 1 249.3 19.94 1398 1.2100 X 57 32 1 249.6 19.95 1408 1.2120 X 57 33 1 253.9 20.05 1412 1.1960 X 57 34 1 255.2 20.03 1413 1.1980 X 57 35 1 256.5 20.02 1414 1.2000 X 57 36 1 257.8 20.01 1415 1.2020 X 57 37 1 259.1 20.00 1417 1.2040 X 57 38 1 260.4 19.99 1418 1.2060 X 57 39 1 261.7 19.97 1419 1.2070 X 57 40 1 263.0 19.96 1420 1.2090 X 57 41 1 263.9 19.93 1423 1.2140 X 57 42 1 261.7 19.81 1449 1.2430 X 57 43 1 260.7 19.81 1492 1.2790 X 57 44 1 262.7 19.77 1510 1.2970 X 57 45 1 264.6 19.72 1528 1.3160 X 57 46 1 266.5 19.69 1495 1.2880 X 57 47 1 270.3 19.67 1416 1.2200 X 57 48 1 276.6 19.66 1429 1.2320 X 57 49 1 280.1 19.65 1441 1.2440 X 57 50 1 279.2 19.70 1441 1.2410 X 57 51 1 278.2 19.76 1440 1.2380 X 57 52 1 277.3 19.83 1436 1.2300 X 57 53 1 276.4 19.90 1432 1.2220 X 57 54 1 275.4 19.97 1428 1.2150 X 57 55 1 274.5 20.04 1424 1.2070 X 57 56 1 273.5 20.11 1420 1.1990 X 57 57 1 272.6 20.18 1416 1.1910 X 57 58 1 274.8 20.18 1424 1.1990 X 57 59 1 278.0 20.15 1436 1.2100 X 58 14 0 303.1 20.40 1327 1.1000 X 58 15 0 299.8 20.47 1290 1.0630 X 58 16 0 290.8 20.48 1308 1.0760 X 58 17 1 281.7 20.49 1327 1.0890 X 58 18 1 272.7 20.50 1346 1.1020 X 58 19 1 265.9 20.37 1368 1.1290 X 58 20 1 259.5 20.21 1389 1.1590 X 58 21 1 253.2 20.04 1411 1.1890 X 58 22 1 246.8 19.88 1433 1.2190 X 58 23 1 246.0 19.85 1429 1.2180 X 58 24 1 249.3 19.92 1410 1.1980 X 58 25 1 252.8 20.00 1390 1.1760 X 58 26 1 255.8 20.07 1371 1.1560 X 58 27 1 253.5 20.01 1379 1.1680 X 58 28 1 251.6 19.97 1375 1.1790 X 58 29 1 249.9 19.92 1368 1.1900 X 58 30 1 248.2 19.88 1363 1.2020 X 58 31 1 246.5 19.84 1377 1.2130 X 58 32 1 250.1 19.92 1381 1.2000 X 58 33 1 255.3 20.05 1385 1.1800 X 58 34 1 258.0 20.09 1387 1.1730 X 58 35 1 259.3 20.08 1388 1.1750 X 58 36 1 260.6 20.06 1389 1.1770 X 58 37 1 261.9 20.05 1390 1.1790 X 58 38 1 263.3 20.04 1392 1.1810 X 58 39 1 264.2 20.01 1394 1.1840 X 58 40 1 262.1 19.85 1411 1.2080 X 58 41 1 260.1 19.68 1428 1.2320 X 58 42 1 257.5 19.68 1477 1.2740 X 58 43 1 254.8 19.72 1535 1.3220 X 58 44 1 255.4 19.70 1565 1.3490 X 58 45 1 257.3 19.65 1577 1.3610 X 58 46 1 261.2 19.64 1487 1.2830 X 58 47 1 267.5 19.63 1418 1.2240 X 58 48 1 273.8 19.62 1430 1.2360 X 58 49 1 273.5 19.61 1443 1.2480 X 58 50 1 272.6 19.62 1452 1.2550 X 58 51 1 271.6 19.67 1451 1.2520 X 58 52 1 270.7 19.74 1447 1.2440 X 58 53 1 269.7 19.81 1443 1.2360 X 58 54 1 268.8 19.88 1439 1.2290 X 58 55 1 267.8 19.95 1435 1.2210 X 58 56 1 268.0 20.02 1428 1.2110 X 58 57 1 268.4 20.08 1416 1.1970 X 58 58 1 266.7 20.08 1447 1.2240 X 58 59 1 264.3 19.93 1460 1.2460 X 58 60 1 266.0 19.94 1461 1.2470 X 58 77 1 276.2 19.95 1599 1.3660 X 58 78 1 275.4 19.90 1604 1.3720 X 58 79 1 274.2 19.84 1610 1.3800 X 58 80 1 273.9 19.81 1614 1.3840 X 59 15 0 296.4 20.37 1289 1.0710 X 59 16 1 286.9 20.28 1302 1.0870 X 59 17 1 277.9 20.29 1320 1.1010 X 59 18 1 268.8 20.30 1338 1.1140 X 59 19 1 261.5 20.20 1359 1.1380 X 59 20 1 255.1 20.04 1381 1.1670 X 59 21 1 248.8 19.88 1403 1.1970 X 59 22 1 246.6 19.83 1415 1.2080 X 59 23 1 248.8 19.88 1402 1.1940 X 59 24 1 252.2 19.95 1382 1.1720 X 59 25 1 255.7 20.03 1362 1.1500 X 59 26 1 253.8 19.98 1367 1.1590 X 59 27 1 251.5 19.92 1375 1.1700 X 59 28 1 249.1 19.86 1383 1.1820 X 59 29 1 247.2 19.82 1380 1.1930 X 59 30 1 245.5 19.78 1373 1.2050 X 59 31 1 245.4 19.77 1362 1.2090 X 59 32 1 250.6 19.90 1353 1.1880 X 59 33 1 255.8 20.02 1357 1.1680 X 59 34 1 260.8 20.14 1361 1.1480 X 59 35 1 262.1 20.13 1362 1.1500 X 59 36 1 263.5 20.12 1363 1.1520 X 59 37 1 264.6 20.10 1365 1.1550 X 59 38 1 262.5 19.93 1382 1.1780 X 59 39 1 260.4 19.77 1399 1.2020 X 59 40 1 258.3 19.60 1415 1.2260 X 59 41 1 256.0 19.50 1445 1.2570 X 59 42 1 253.3 19.54 1504 1.3050 X 59 43 1 250.6 19.59 1563 1.3530 X 59 44 1 248.1 19.63 1620 1.4000 X 59 45 1 252.2 19.61 1569 1.3570 X 59 46 1 258.4 19.60 1478 1.2780 X 59 47 1 264.7 19.58 1420 1.2280 X 59 48 1 267.8 19.57 1432 1.2400 X 59 49 1 266.9 19.56 1445 1.2520 X 59 50 1 265.9 19.55 1458 1.2640 X 59 51 1 265.0 19.59 1461 1.2660 X 59 52 1 264.1 19.66 1457 1.2580 X 59 53 1 264.1 19.73 1453 1.2500 X 59 54 1 264.4 19.79 1444 1.2380 X 59 55 1 264.7 19.85 1432 1.2250 X 59 56 1 265.1 19.91 1420 1.2110 X 59 57 1 265.0 19.96 1416 1.2040 X 59 58 1 262.8 19.95 1458 1.2420 X 59 59 1 260.6 19.92 1495 1.2770 X 59 60 1 258.2 19.75 1505 1.2970 X 59 61 1 255.9 19.58 1515 1.3180 X 59 62 1 255.6 19.50 1520 1.3280 X 59 63 1 260.1 19.63 1516 1.3150 X 59 69 1 284.0 20.02 1527 1.2970 X 59 70 1 283.2 20.05 1534 1.3020 X 59 71 1 282.1 20.09 1540 1.3050 X 59 72 1 281.0 20.09 1548 1.3140 X 59 73 1 279.9 20.05 1560 1.3260 X 59 74 1 278.8 20.01 1571 1.3370 X 59 75 1 277.7 19.97 1582 1.3490 X 59 76 1 276.5 19.94 1593 1.3610 X 59 77 1 275.4 19.90 1604 1.3720 X 59 78 1 274.7 19.85 1609 1.3780 X 59 79 1 273.0 19.78 1617 1.3890 X 60 15 0 293.8 20.41 1296 1.0740 X 60 16 1 284.1 20.29 1307 1.0910 X 60 17 1 274.4 20.18 1318 1.1090 X 60 18 1 265.0 20.09 1331 1.1250 X 60 19 1 257.1 20.03 1351 1.1460 X 60 20 1 253.1 19.93 1367 1.1650 X 60 21 1 251.0 19.89 1379 1.1750 X 60 22 1 249.0 19.85 1390 1.1850 X 60 23 1 251.7 19.91 1374 1.1680 X 60 24 1 255.2 19.98 1354 1.1460 X 60 25 1 254.2 19.96 1355 1.1500 X 60 26 1 251.8 19.90 1363 1.1610 X 60 27 1 249.5 19.84 1371 1.1730 X 60 28 1 247.1 19.78 1379 1.1850 X 60 29 1 244.7 19.72 1388 1.1960 X 60 30 1 242.8 19.67 1385 1.2080 X 60 31 1 245.9 19.74 1373 1.1970 X 60 32 1 251.1 19.87 1361 1.1770 X 60 33 1 256.3 20.00 1349 1.1560 X 60 34 1 261.5 20.12 1337 1.1360 X 60 35 1 264.9 20.19 1336 1.1250 X 60 36 1 262.9 20.02 1353 1.1490 X 60 37 1 260.8 19.85 1369 1.1720 X 60 38 1 258.7 19.69 1386 1.1960 X 60 39 1 256.6 19.52 1403 1.2200 X 60 40 1 254.5 19.35 1420 1.2430 X 60 41 1 251.8 19.37 1473 1.2880 X 60 42 1 249.1 19.41 1532 1.3360 X 60 43 1 249.0 19.52 1573 1.3660 X 60 44 1 249.5 19.57 1576 1.3650 X 60 45 1 250.0 19.56 1554 1.3460 X 60 46 1 255.7 19.55 1470 1.2740 X 60 47 1 261.9 19.54 1421 1.2320 X 60 48 1 261.2 19.53 1434 1.2440 X 60 49 1 260.3 19.52 1447 1.2560 X 60 50 1 260.1 19.51 1459 1.2680 X 60 51 1 260.5 19.50 1472 1.2800 X 60 52 1 260.8 19.56 1460 1.2660 X 60 53 1 261.1 19.62 1448 1.2520 X 60 54 1 261.4 19.68 1436 1.2380 X 60 55 1 261.8 19.74 1424 1.2250 X 60 56 1 262.1 19.80 1412 1.2110 X 60 57 1 261.2 19.83 1427 1.2220 X 60 58 1 259.0 19.82 1469 1.2600 X 60 59 1 256.8 19.81 1512 1.2980 X 60 60 1 254.5 19.73 1541 1.3280 X 60 61 1 252.1 19.56 1550 1.3490 X 60 62 1 249.8 19.40 1560 1.3690 X 60 63 1 247.4 19.23 1569 1.3890 X 60 64 1 245.2 19.07 1579 1.4080 X 60 65 1 249.7 19.19 1574 1.3960 X 60 66 1 254.1 19.32 1570 1.3830 X 60 67 1 258.6 19.44 1566 1.3710 X 60 68 1 263.1 19.56 1561 1.3580 X 60 69 1 267.6 19.68 1557 1.3460 X 60 70 1 272.0 19.81 1553 1.3340 X 60 71 1 276.5 19.93 1548 1.3210 X 60 72 1 280.6 20.00 1549 1.3170 X 60 73 1 279.5 19.99 1559 1.3260 X 60 74 1 278.4 19.95 1570 1.3370 X 60 75 1 277.3 19.92 1581 1.3490 X 60 76 1 276.1 19.88 1592 1.3610 X 60 77 1 275.0 19.84 1603 1.3730 X 60 78 1 273.9 19.81 1614 1.3840 X 60 79 1 271.8 19.72 1624 1.3980 X 61 15 0 291.2 20.45 1302 1.0770 X 61 16 1 281.5 20.33 1313 1.0940 X 61 17 1 271.8 20.22 1325 1.1120 X 61 18 1 262.2 20.09 1331 1.1290 X 61 19 1 257.7 20.00 1331 1.1360 X 61 20 1 255.4 19.95 1343 1.1420 X 61 21 1 253.4 19.91 1354 1.1530 X 61 22 1 251.3 19.86 1365 1.1630 X 61 23 1 254.7 19.94 1346 1.1420 X 61 24 1 254.6 19.93 1343 1.1410 X 61 25 1 252.2 19.87 1351 1.1520 X 61 26 1 249.8 19.81 1359 1.1640 X 61 27 1 247.4 19.75 1367 1.1760 X 61 28 1 245.1 19.69 1375 1.1870 X 61 29 1 243.1 19.63 1383 1.1990 X 61 30 1 242.1 19.58 1386 1.2060 X 61 31 1 244.5 19.64 1382 1.1950 X 61 32 1 249.2 19.75 1369 1.1770 X 61 33 1 253.9 19.86 1356 1.1590 X 61 34 1 258.7 19.97 1343 1.1410 X 61 35 1 263.4 20.07 1330 1.1220 X 61 36 1 261.3 19.97 1347 1.1310 X 61 37 1 258.7 19.77 1366 1.1620 X 61 38 1 256.2 19.56 1385 1.1930 X 61 39 1 253.6 19.35 1404 1.2240 X 61 40 1 252.0 19.25 1424 1.2530 X 61 41 1 252.6 19.37 1462 1.2780 X 61 42 1 253.2 19.49 1499 1.3040 X 61 43 1 253.8 19.52 1495 1.2980 X 61 44 1 254.5 19.51 1473 1.2790 X 61 45 1 255.1 19.51 1450 1.2590 X 61 46 1 255.7 19.50 1428 1.2400 X 61 47 1 256.2 19.49 1421 1.2350 X 61 48 1 256.5 19.47 1428 1.2460 X 61 49 1 256.8 19.46 1435 1.2560 X 61 50 1 257.2 19.44 1442 1.2660 X 61 51 1 257.5 19.43 1447 1.2750 X 61 52 1 257.8 19.46 1448 1.2650 X 61 53 1 258.1 19.51 1440 1.2520 X 61 54 1 258.5 19.57 1428 1.2380 X 61 55 1 258.8 19.63 1416 1.2250 X 61 56 1 259.1 19.69 1404 1.2110 X 61 57 1 257.3 19.69 1438 1.2410 X 61 58 1 255.1 19.68 1481 1.2780 X 61 59 1 252.9 19.67 1523 1.3160 X 61 60 1 250.7 19.66 1566 1.3540 X 61 61 1 248.4 19.55 1586 1.3800 X 61 62 1 246.0 19.38 1595 1.4000 X 61 63 1 243.7 19.21 1605 1.4200 X 61 64 1 241.3 19.04 1614 1.4400 X 61 65 1 239.1 18.87 1621 1.4580 X 61 66 1 238.5 18.82 1618 1.4590 X 61 67 1 244.2 18.99 1618 1.4460 X 61 68 1 249.5 19.15 1611 1.4290 X 61 69 1 254.8 19.31 1604 1.4120 X 61 70 1 260.1 19.47 1598 1.3940 X 61 71 1 265.4 19.63 1591 1.3770 X 61 72 1 270.7 19.79 1584 1.3600 X 61 73 1 270.1 19.76 1595 1.3710 X 61 74 1 266.8 19.64 1614 1.3970 X 61 75 1 263.5 19.52 1634 1.4220 X 61 76 1 260.2 19.40 1653 1.4480 X 61 77 1 257.8 19.31 1668 1.4690 X 61 78 1 263.2 19.45 1653 1.4430 X 61 79 1 269.8 19.64 1634 1.4110 X 62 15 0 288.6 20.49 1309 1.0800 X 62 16 1 278.9 20.36 1313 1.0960 X 62 17 1 269.2 20.21 1313 1.1120 X 62 18 1 263.6 20.07 1313 1.1270 X 62 19 1 260.9 20.02 1313 1.1270 X 62 20 1 258.2 19.97 1316 1.1270 X 62 21 1 255.7 19.92 1329 1.1300 X 62 22 1 254.1 19.89 1338 1.1380 X 62 23 1 254.9 19.90 1331 1.1310 X 62 24 1 252.5 19.84 1339 1.1430 X 62 25 1 250.2 19.78 1347 1.1550 X 62 26 1 249.2 19.71 1353 1.1650 X 62 27 1 248.2 19.63 1359 1.1760 X 62 28 1 247.3 19.56 1365 1.1870 X 62 29 1 246.3 19.49 1370 1.1950 X 62 30 1 245.3 19.50 1367 1.1950 X 62 31 1 244.3 19.51 1364 1.1940 X 62 32 1 245.4 19.56 1362 1.1870 X 62 33 1 250.1 19.66 1359 1.1690 X 62 34 1 254.8 19.77 1347 1.1510 X 62 35 1 259.6 19.88 1334 1.1320 X 62 36 1 260.9 19.89 1336 1.1260 X 62 37 1 258.4 19.79 1355 1.1340 X 62 38 1 255.8 19.62 1374 1.1570 X 62 39 1 253.3 19.41 1374 1.1880 X 62 40 1 251.2 19.33 1388 1.2170 X 62 41 1 251.3 19.45 1426 1.2430 X 62 42 1 252.0 19.47 1414 1.2310 X 62 43 1 252.6 19.46 1392 1.2120 X 62 44 1 253.2 19.47 1380 1.2000 X 62 45 1 253.8 19.49 1391 1.2080 X 62 46 1 254.5 19.51 1401 1.2160 X 62 47 1 255.5 19.41 1398 1.2320 X 62 48 1 255.1 19.40 1404 1.2420 X 62 49 1 254.8 19.38 1412 1.2530 X 62 50 1 254.4 19.36 1419 1.2630 X 62 51 1 254.5 19.36 1422 1.2690 X 62 52 1 254.9 19.39 1423 1.2600 X 62 53 1 255.2 19.42 1425 1.2500 X 62 54 1 255.5 19.46 1420 1.2380 X 62 55 1 255.8 19.52 1408 1.2250 X 62 56 1 255.7 19.57 1407 1.2210 X 62 57 1 253.5 19.56 1450 1.2590 X 62 58 1 251.3 19.55 1492 1.2960 X 62 59 1 249.1 19.54 1534 1.3340 X 62 60 1 246.9 19.53 1577 1.3720 X 62 61 1 244.7 19.52 1619 1.4100 X 62 62 1 242.3 19.36 1631 1.4310 X 62 63 1 239.9 19.19 1640 1.4510 X 62 64 1 238.7 18.99 1625 1.4520 X 62 65 1 237.6 18.79 1607 1.4510 X 62 66 1 235.2 18.72 1602 1.4520 X 62 67 1 233.4 18.81 1612 1.4550 X 62 68 1 240.3 18.98 1629 1.4550 X 62 69 1 246.8 19.15 1638 1.4490 X 62 70 1 252.0 19.31 1631 1.4320 X 62 71 1 257.3 19.47 1624 1.4150 X 62 72 1 262.6 19.63 1617 1.3970 X 62 73 1 260.3 19.55 1634 1.4180 X 62 74 1 257.0 19.43 1653 1.4430 X 62 75 1 255.1 19.35 1666 1.4610 X 62 76 1 256.4 19.34 1664 1.4600 X 62 77 1 257.6 19.34 1662 1.4600 X 62 78 1 261.3 19.42 1653 1.4460 X 62 79 1 267.9 19.60 1634 1.4130 X 62 80 1 267.9 19.60 1634 1.4130 X 63 15 1 286.0 20.42 1307 1.0830 X 63 16 1 276.3 20.33 1303 1.0940 X 63 17 1 266.6 20.18 1300 1.1100 X 63 18 1 266.8 20.09 1297 1.1180 X 63 19 1 264.2 20.04 1294 1.1180 X 63 20 1 261.5 19.99 1294 1.1180 X 63 21 1 258.8 19.94 1302 1.1180 X 63 22 1 256.6 19.86 1317 1.1210 X 63 23 1 255.4 19.79 1323 1.1320 X 63 24 1 254.4 19.71 1329 1.1430 X 63 25 1 253.4 19.64 1335 1.1530 X 63 26 1 252.4 19.56 1341 1.1640 X 63 27 1 251.4 19.48 1347 1.1740 X 63 28 1 250.5 19.41 1353 1.1850 X 63 29 1 249.5 19.42 1350 1.1840 X 63 30 1 248.5 19.43 1347 1.1830 X 63 31 1 247.5 19.44 1345 1.1830 X 63 32 1 246.5 19.45 1342 1.1820 X 63 33 1 246.3 19.47 1340 1.1790 X 63 34 1 251.0 19.58 1337 1.1610 X 63 35 1 255.7 19.69 1335 1.1430 X 63 36 1 260.5 19.79 1326 1.1240 X 63 37 1 258.0 19.70 1337 1.1320 X 63 38 1 255.5 19.60 1336 1.1390 X 63 39 1 252.9 19.47 1335 1.1520 X 63 40 1 251.0 19.42 1352 1.1810 X 63 41 1 250.1 19.42 1337 1.1670 X 63 42 1 250.7 19.45 1348 1.1750 X 63 43 1 251.3 19.47 1359 1.1820 X 63 44 1 251.9 19.50 1370 1.1900 X 63 45 1 252.5 19.52 1381 1.1980 X 63 46 1 253.5 19.47 1384 1.2110 X 63 47 1 254.6 19.37 1381 1.2270 X 63 48 1 254.8 19.32 1381 1.2390 X 63 49 1 254.4 19.30 1388 1.2500 X 63 50 1 254.1 19.29 1395 1.2600 X 63 51 1 253.7 19.29 1397 1.2640 X 63 52 1 253.3 19.32 1398 1.2540 X 63 53 1 253.0 19.35 1400 1.2450 X 63 54 1 252.6 19.38 1401 1.2350 X 63 55 1 252.9 19.42 1401 1.2250 X 63 56 1 251.8 19.44 1419 1.2390 X 63 57 1 249.6 19.43 1461 1.2770 X 63 58 1 247.4 19.42 1503 1.3150 X 63 59 1 245.2 19.41 1546 1.3520 X 63 60 1 243.1 19.39 1586 1.3900 X 63 61 1 241.2 19.38 1624 1.4280 X 63 62 1 239.4 19.32 1648 1.4480 X 63 63 1 238.3 19.11 1629 1.4470 X 63 64 1 237.2 18.90 1611 1.4450 X 63 65 1 236.1 18.70 1592 1.4430 X 63 66 1 233.7 18.63 1587 1.4440 X 63 67 1 230.1 18.70 1596 1.4480 X 63 68 1 228.3 18.79 1606 1.4520 X 63 69 1 235.3 18.96 1623 1.4510 X 63 70 1 242.2 19.14 1640 1.4510 X 63 71 1 249.2 19.32 1657 1.4510 X 63 72 1 253.7 19.45 1653 1.4390 X 63 73 1 252.5 19.38 1663 1.4530 X 63 74 1 253.8 19.38 1661 1.4520 X 63 75 1 255.0 19.38 1659 1.4520 X 63 76 1 256.3 19.37 1658 1.4520 X 63 77 1 257.5 19.37 1656 1.4520 X 63 78 1 259.4 19.38 1652 1.4480 X 63 79 1 263.6 19.49 1643 1.4300 X 63 80 1 263.6 19.49 1643 1.4300 X 64 15 1 283.4 20.31 1304 1.0860 X 64 16 1 273.7 20.31 1299 1.0930 X 64 17 1 272.7 20.16 1296 1.1080 X 64 18 1 270.1 20.11 1292 1.1090 X 64 19 1 267.4 20.06 1289 1.1090 X 64 20 1 264.7 20.01 1286 1.1090 X 64 21 1 263.1 19.88 1283 1.1150 X 64 22 1 261.6 19.73 1301 1.1210 X 64 23 1 260.1 19.64 1311 1.1300 X 64 24 1 258.7 19.56 1317 1.1410 X 64 25 1 257.2 19.49 1323 1.1510 X 64 26 1 255.7 19.41 1329 1.1620 X 64 27 1 254.7 19.34 1335 1.1720 X 64 28 1 253.7 19.34 1333 1.1730 X 64 29 1 252.7 19.35 1330 1.1720 X 64 30 1 251.7 19.36 1328 1.1720 X 64 31 1 250.7 19.36 1325 1.1710 X 64 32 1 249.7 19.37 1323 1.1700 X 64 33 1 248.8 19.38 1320 1.1700 X 64 34 1 247.8 19.39 1318 1.1690 X 64 35 1 251.9 19.49 1317 1.1530 X 64 36 1 256.6 19.60 1317 1.1340 X 64 37 1 257.7 19.60 1316 1.1290 X 64 38 1 255.1 19.50 1313 1.1370 X 64 39 1 252.7 19.40 1311 1.1450 X 64 40 1 250.8 19.43 1316 1.1490 X 64 41 1 248.9 19.45 1327 1.1560 X 64 42 1 249.4 19.48 1338 1.1640 X 64 43 1 250.1 19.50 1349 1.1720 X 64 44 1 250.7 19.52 1360 1.1800 X 64 45 1 251.4 19.53 1369 1.1890 X 64 46 1 252.5 19.42 1366 1.2050 X 64 47 1 253.7 19.32 1364 1.2210 X 64 48 1 254.5 19.24 1361 1.2360 X 64 49 1 254.1 19.23 1365 1.2470 X 64 50 1 253.7 19.21 1371 1.2570 X 64 51 1 253.4 19.21 1372 1.2590 X 64 52 1 253.0 19.25 1374 1.2490 X 64 53 1 252.6 19.28 1375 1.2390 X 64 54 1 252.3 19.31 1380 1.2290 X 64 55 1 251.9 19.32 1391 1.2250 X 64 56 1 250.1 19.30 1393 1.2580 X 64 57 1 248.1 19.28 1428 1.2960 X 64 58 1 246.2 19.27 1466 1.3330 X 64 59 1 244.2 19.26 1505 1.3710 X 64 60 1 242.3 19.25 1543 1.4090 X 64 61 1 240.3 19.21 1581 1.4250 X 64 62 1 238.3 19.16 1612 1.4350 X 64 63 1 236.8 19.02 1615 1.4390 X 64 64 1 235.7 18.82 1596 1.4370 X 64 65 1 234.6 18.61 1577 1.4360 X 64 66 1 232.2 18.54 1572 1.4370 X 64 67 1 228.6 18.61 1581 1.4410 X 64 68 1 225.0 18.68 1590 1.4450 X 64 69 1 223.2 18.77 1600 1.4480 X 64 70 1 230.2 18.95 1617 1.4480 X 64 71 1 237.1 19.12 1634 1.4480 X 64 72 1 242.8 19.25 1636 1.4470 X 64 73 1 246.0 19.28 1640 1.4460 X 64 74 1 249.3 19.32 1643 1.4450 X 64 75 1 252.5 19.36 1647 1.4440 X 64 76 1 255.8 19.39 1650 1.4430 X 64 77 1 257.4 19.40 1649 1.4430 X 64 78 1 258.6 19.39 1648 1.4430 X 64 79 1 258.6 19.39 1648 1.4430 X 64 80 1 258.6 19.39 1648 1.4430 X 65 15 1 280.8 20.21 1300 1.0900 X 65 16 1 275.4 20.28 1295 1.0910 X 65 17 1 276.0 20.18 1292 1.1000 X 65 18 1 273.3 20.13 1288 1.1000 X 65 19 1 271.0 20.05 1285 1.1020 X 65 20 1 269.5 19.90 1283 1.1080 X 65 21 1 268.1 19.76 1281 1.1140 X 65 22 1 266.6 19.61 1283 1.1200 X 65 23 1 265.1 19.49 1299 1.1280 X 65 24 1 263.7 19.42 1305 1.1390 X 65 25 1 262.2 19.34 1310 1.1490 X 65 26 1 260.7 19.26 1316 1.1600 X 65 27 1 259.3 19.25 1316 1.1620 X 65 28 1 257.8 19.26 1313 1.1620 X 65 29 1 256.3 19.27 1311 1.1610 X 65 30 1 254.9 19.28 1308 1.1600 X 65 31 1 253.9 19.29 1306 1.1600 X 65 32 1 252.9 19.30 1304 1.1590 X 65 33 1 252.0 19.31 1304 1.1580 X 65 34 1 251.0 19.32 1305 1.1580 X 65 35 1 250.0 19.33 1305 1.1570 X 65 36 1 252.8 19.41 1305 1.1450 X 65 37 1 257.3 19.51 1305 1.1270 X 65 38 1 254.8 19.41 1303 1.1350 X 65 39 1 252.5 19.33 1301 1.1420 X 65 40 1 250.6 19.42 1309 1.1430 X 65 41 1 248.7 19.48 1317 1.1460 X 65 42 1 248.2 19.50 1329 1.1540 X 65 43 1 248.8 19.53 1340 1.1620 X 65 44 1 249.4 19.55 1351 1.1690 X 65 45 1 250.4 19.48 1352 1.1830 X 65 46 1 251.6 19.38 1349 1.2000 X 65 47 1 252.7 19.28 1347 1.2160 X 65 48 1 253.9 19.18 1344 1.2320 X 65 49 1 253.8 19.15 1342 1.2430 X 65 50 1 253.4 19.13 1346 1.2540 X 65 51 1 253.0 19.14 1348 1.2530 X 65 52 1 252.7 19.17 1359 1.2440 X 65 53 1 252.3 19.21 1370 1.2340 X 65 54 1 251.9 19.22 1382 1.2270 X 65 55 1 251.2 19.16 1392 1.2390 X 65 56 1 249.2 19.15 1389 1.2770 X 65 57 1 247.3 19.14 1392 1.3140 X 65 58 1 245.3 19.13 1423 1.3520 X 65 59 1 243.3 19.11 1461 1.3880 X 65 60 1 241.3 19.07 1499 1.3980 X 65 61 1 239.3 19.02 1535 1.4090 X 65 62 1 237.3 18.97 1565 1.4200 X 65 63 1 235.4 18.92 1595 1.4300 X 65 64 1 234.2 18.73 1581 1.4300 X 65 65 1 233.1 18.52 1562 1.4280 X 65 66 1 230.7 18.46 1557 1.4290 X 65 67 1 227.1 18.52 1566 1.4330 X 65 68 1 223.5 18.59 1575 1.4370 X 65 69 1 219.9 18.66 1584 1.4410 X 65 70 1 218.1 18.75 1594 1.4440 X 65 71 1 225.1 18.93 1611 1.4440 X 65 72 1 229.6 19.01 1598 1.4430 X 65 73 1 232.9 19.05 1599 1.4430 X 65 74 1 236.1 19.08 1602 1.4420 X 65 75 1 239.4 19.12 1606 1.4410 X 65 76 1 247.6 19.17 1609 1.4370 X 65 77 1 252.5 19.28 1613 1.4400 X 65 78 1 258.6 19.39 1630 1.4430 X 65 79 1 258.6 19.39 1630 1.4430 X 65 80 1 259.0 19.39 1638 1.4450 X 66 15 1 278.2 20.11 1297 1.0930 X 66 16 1 281.6 20.26 1291 1.0900 X 66 17 1 279.2 20.20 1288 1.0910 X 66 18 1 277.5 20.08 1285 1.0960 X 66 19 1 276.0 19.93 1283 1.1020 X 66 20 1 274.6 19.78 1280 1.1080 X 66 21 1 273.1 19.64 1278 1.1140 X 66 22 1 271.6 19.49 1275 1.1200 X 66 23 1 270.2 19.35 1286 1.1270 X 66 24 1 268.7 19.27 1292 1.1370 X 66 25 1 267.2 19.19 1298 1.1480 X 66 26 1 265.8 19.17 1299 1.1510 X 66 27 1 264.3 19.18 1296 1.1510 X 66 28 1 262.8 19.19 1294 1.1500 X 66 29 1 261.4 19.20 1291 1.1490 X 66 30 1 259.9 19.21 1292 1.1490 X 66 31 1 258.4 19.22 1292 1.1480 X 66 32 1 257.0 19.23 1292 1.1470 X 66 33 1 255.5 19.24 1292 1.1470 X 66 34 1 254.2 19.25 1293 1.1460 X 66 35 1 253.2 19.26 1293 1.1450 X 66 36 1 252.2 19.27 1293 1.1450 X 66 37 1 253.7 19.32 1294 1.1360 X 66 38 1 254.4 19.31 1292 1.1330 X 66 39 1 252.3 19.31 1295 1.1370 X 66 40 1 250.4 19.40 1302 1.1370 X 66 41 1 248.5 19.49 1309 1.1380 X 66 42 1 246.9 19.53 1319 1.1440 X 66 43 1 247.5 19.56 1330 1.1510 X 66 44 1 248.3 19.54 1337 1.1620 X 66 45 1 249.5 19.44 1335 1.1780 X 66 46 1 250.6 19.34 1332 1.1940 X 66 47 1 251.8 19.24 1329 1.2100 X 66 48 1 252.9 19.14 1327 1.2260 X 66 49 1 253.5 19.07 1330 1.2400 X 66 50 1 253.1 19.06 1337 1.2510 X 66 51 1 252.7 19.07 1349 1.2480 X 66 52 1 252.4 19.10 1361 1.2380 X 66 53 1 252.0 19.13 1372 1.2290 X 66 54 1 251.4 19.06 1384 1.2380 X 66 55 1 250.3 19.02 1389 1.2580 X 66 56 1 248.4 19.01 1385 1.2950 X 66 57 1 246.4 19.00 1388 1.3330 X 66 58 1 244.4 18.97 1391 1.3610 X 66 59 1 242.4 18.92 1417 1.3720 X 66 60 1 240.4 18.88 1455 1.3830 X 66 61 1 238.4 18.83 1488 1.3930 X 66 62 1 236.4 18.78 1518 1.4040 X 66 63 1 234.4 18.73 1548 1.4150 X 66 64 1 232.7 18.64 1566 1.4220 X 66 65 1 231.6 18.44 1547 1.4210 X 66 66 1 229.2 18.37 1542 1.4220 X 66 67 1 225.6 18.44 1551 1.4260 X 66 68 1 222.0 18.51 1560 1.4300 X 66 69 1 218.4 18.58 1569 1.4340 X 66 70 1 214.8 18.65 1578 1.4370 X 66 71 1 213.0 18.73 1588 1.4410 X 66 72 1 221.4 18.79 1562 1.4370 X 66 73 1 239.5 18.87 1557 1.4280 X 66 74 1 237.8 18.98 1561 1.4350 X 66 75 1 239.4 19.12 1565 1.4410 X 66 76 1 247.6 19.17 1587 1.4370 X 66 77 1 252.5 19.28 1613 1.4400 X 66 78 1 258.6 19.39 1630 1.4430 X 66 79 1 258.0 19.39 1637 1.4430 X 66 80 1 258.6 19.39 1648 1.4430 X 67 14 1 284.3 20.01 1293 1.0970 X 67 15 1 284.3 20.01 1293 1.0970 X 67 16 1 285.4 20.25 1287 1.0830 X 67 17 1 284.0 20.10 1285 1.0890 X 67 18 1 282.5 19.95 1282 1.0950 X 67 19 1 281.0 19.81 1280 1.1020 X 67 20 1 279.6 19.66 1278 1.1080 X 67 21 1 278.1 19.51 1275 1.1140 X 67 22 1 276.6 19.37 1273 1.1200 X 67 23 1 275.2 19.22 1270 1.1260 X 67 24 1 273.7 19.12 1280 1.1350 X 67 25 1 272.2 19.09 1282 1.1410 X 67 26 1 270.8 19.10 1280 1.1400 X 67 27 1 269.3 19.11 1279 1.1390 X 67 28 1 267.8 19.12 1279 1.1390 X 67 29 1 266.4 19.13 1279 1.1380 X 67 30 1 264.9 19.13 1280 1.1370 X 67 31 1 263.4 19.14 1280 1.1370 X 67 32 1 262.0 19.15 1280 1.1360 X 67 33 1 260.5 19.16 1281 1.1350 X 67 34 1 259.0 19.17 1281 1.1350 X 67 35 1 257.6 19.18 1281 1.1340 X 67 36 1 256.1 19.19 1281 1.1330 X 67 37 1 254.6 19.20 1282 1.1330 X 67 38 1 254.1 19.22 1282 1.1300 X 67 39 1 252.1 19.29 1288 1.1320 X 67 40 1 250.2 19.38 1295 1.1320 X 67 41 1 248.3 19.47 1303 1.1330 X 67 42 1 246.4 19.56 1310 1.1340 X 67 43 1 246.3 19.58 1321 1.1410 X 67 44 1 247.3 19.50 1320 1.1560 X 67 45 1 248.5 19.40 1317 1.1720 X 67 46 1 249.6 19.30 1322 1.1880 X 67 47 1 250.8 19.20 1328 1.2050 X 67 48 1 251.9 19.10 1335 1.2210 X 67 49 1 253.1 19.00 1341 1.2370 X 67 50 1 252.8 18.98 1347 1.2470 X 67 51 1 252.4 19.00 1352 1.2430 X 67 52 1 252.0 19.03 1363 1.2330 X 67 53 1 251.5 18.97 1374 1.2400 X 67 54 1 250.9 18.91 1386 1.2490 X 67 55 1 249.5 18.88 1387 1.2760 X 67 56 1 247.5 18.86 1381 1.3140 X 67 57 1 245.5 18.83 1383 1.3350 X 67 58 1 243.5 18.78 1387 1.3460 X 67 59 1 241.5 18.73 1390 1.3560 X 67 60 1 239.5 18.68 1412 1.3670 X 67 61 1 237.5 18.64 1442 1.3780 X 67 62 1 235.5 18.59 1471 1.3890 X 67 63 1 233.5 18.54 1501 1.3990 X 67 64 1 231.5 18.49 1531 1.4100 X 67 65 1 230.1 18.35 1532 1.4130 X 67 66 1 227.7 18.28 1527 1.4140 X 67 67 1 224.1 18.35 1536 1.4180 X 67 68 1 220.5 18.42 1545 1.4220 X 67 69 1 216.9 18.49 1554 1.4260 X 67 70 1 231.4 18.57 1547 1.4190 X 67 71 1 222.2 18.65 1538 1.4300 X 67 72 1 221.4 18.79 1525 1.4370 X 67 73 1 239.5 18.87 1516 1.4280 X 67 74 1 237.8 18.98 1539 1.4350 X 67 75 1 239.4 19.12 1565 1.4410 X 67 76 1 247.6 19.17 1587 1.4370 X 67 77 1 248.1 19.23 1613 1.4400 X 67 78 1 253.1 19.28 1623 1.4400 X 67 79 1 254.5 19.32 1613 1.4410 X 67 80 1 258.6 19.39 1630 1.4430 X 68 13 1 281.2 20.06 1295 1.0950 X 68 14 1 284.3 20.01 1293 1.0970 X 68 15 1 284.3 20.01 1293 1.0970 X 68 16 1 285.4 20.25 1287 1.0830 X 68 17 1 284.0 20.10 1285 1.0890 X 68 18 1 282.5 19.95 1282 1.0950 X 68 19 1 281.0 19.81 1280 1.1020 X 68 20 1 279.6 19.66 1278 1.1080 X 68 21 1 278.1 19.51 1275 1.1140 X 68 22 1 276.6 19.37 1273 1.1200 X 68 23 1 275.2 19.11 1269 1.1280 X 68 24 1 273.7 19.01 1267 1.1300 X 68 25 1 272.2 19.03 1269 1.1310 X 68 26 1 270.8 19.06 1272 1.1310 X 68 27 1 269.3 19.09 1274 1.1320 X 68 28 1 270.5 19.11 1277 1.1330 X 68 29 1 273.1 19.14 1279 1.1330 X 68 30 1 271.2 19.16 1282 1.1340 X 68 31 1 269.3 19.19 1285 1.1350 X 68 32 1 267.4 19.21 1287 1.1350 X 68 33 1 265.6 19.24 1290 1.1360 X 68 34 1 263.7 19.27 1292 1.1360 X 68 35 1 261.8 19.29 1295 1.1370 X 68 36 1 259.9 19.32 1297 1.1380 X 68 37 1 258.0 19.34 1300 1.1380 X 68 38 1 256.1 19.37 1302 1.1390 X 68 39 1 254.2 19.40 1305 1.1390 X 68 40 1 252.3 19.42 1307 1.1400 X 68 41 1 250.5 19.45 1310 1.1410 X 68 42 1 248.6 19.47 1312 1.1410 X 68 43 1 246.7 19.50 1315 1.1420 X 68 44 1 246.4 19.46 1319 1.1510 X 68 45 1 247.5 19.36 1326 1.1670 X 68 46 1 248.7 19.26 1332 1.1830 X 68 47 1 249.8 19.16 1339 1.1990 X 68 48 1 251.0 19.06 1345 1.2150 X 68 49 1 252.1 18.96 1351 1.2310 X 68 50 1 252.4 18.90 1358 1.2440 X 68 51 1 252.1 18.93 1363 1.2370 X 68 52 1 251.5 18.88 1368 1.2430 X 68 53 1 251.0 18.81 1376 1.2520 X 68 54 1 250.4 18.75 1388 1.2600 X 68 55 1 248.6 18.73 1384 1.2950 X 68 56 1 246.6 18.69 1379 1.3090 X 68 57 1 244.6 18.64 1379 1.3190 X 68 58 1 242.6 18.59 1382 1.3300 X 68 59 1 240.6 18.54 1393 1.3410 X 68 60 1 238.6 18.49 1407 1.3520 X 68 61 1 236.6 18.44 1421 1.3620 X 68 62 1 234.6 18.40 1435 1.3730 X 68 63 1 232.6 18.35 1454 1.3840 X 68 64 1 230.6 18.30 1484 1.3940 X 68 65 1 228.6 18.25 1514 1.4050 X 68 66 1 226.2 18.19 1512 1.4070 X 68 67 1 223.3 18.26 1521 1.4100 X 68 68 1 221.9 18.34 1511 1.4160 X 68 69 1 216.9 18.49 1502 1.4260 X 68 70 1 231.4 18.57 1492 1.4190 X 68 71 1 222.2 18.65 1515 1.4300 X 68 72 1 221.4 18.79 1525 1.4370 X 68 73 1 239.5 18.87 1516 1.4280 X 68 74 1 232.3 18.91 1539 1.4360 X 68 75 1 239.4 18.99 1565 1.4340 X 68 76 1 247.6 19.17 1578 1.4370 X 68 77 1 248.1 19.23 1589 1.4400 X 68 78 1 253.1 19.28 1609 1.4400 X 68 79 1 251.7 19.29 1613 1.4410 X 68 80 1 254.5 19.32 1630 1.4410 ________This_Is_The_END________ if test `wc -l < sp38data` -ne 1846; then echo 'shar: sp38data was damaged during transit (should have had 1846 lines)' fi