### This is R code for defining functions, constants and loading data ### This file should be sourced by another file controling the mcmc algorithm library(msm) library(mvtnorm) library(MCMCpack) ## constants required as model inputs n <- 4330 # number of locations n.block <- 8 n.family <- 139 M.H <- 3 # number of time points for heights t <- c(3,6,10) #observation times for heights ##number of lattice points for kernel convolution J <- 170 ## sigma and nu are assigned unif(a,b) priors ## here we set the hyperparameters for these uniform priors a.sigma <- 0 b.sigma <- 100 a.nu <- .005 b.nu <- 30 ####################### ## load required data## ####################### ## response variables Y <- matrix(scan(file = "../data/Y.dat"),nrow=n,ncol=M.H,byrow=TRUE) ## kernel matricies for spatial model K1 <- matrix(scan(file = "../data/K1.dat"),nrow=n,ncol=J,byrow=TRUE) K2 <- matrix(scan(file = "../data/K2.dat"),nrow=n,ncol=J,byrow=TRUE) ## covariate vectors for fixed effects N <- matrix(scan(file = "../data/N.dat"),nrow=n,ncol=3,byrow=TRUE) X.temp <- matrix(scan(file = "../data/X.dat"),nrow=n,ncol=4,byrow=TRUE) HI2 <- X.temp[,3] HI3 <- X.temp[,4] ## covariate vectors for random effects block <- X.temp[,1] family <- X.temp[,2] ## center the columns of the kernel matrices to improve covergence of intercept temp.K1 <- colMeans(K1) temp.K2 <- colMeans(K2) for (j in 1:J) { K1[,j] <- K1[,j] - temp.K1[j] K2[,j] <- K2[,j] - temp.K2[j] } ########################## ## INITIALIZE PARAMETERS## ########################## beta.int <- -20 beta.time <- 21.4 beta.N <- -18 beta.HI2 <- 5.5 beta.HI3 <- 11 b.block <- c(-0.154327904784824, 0.392774259671583, -1.03416714910166, 1.04318164922975, -0.71871658614699, -0.154696303305651, -0.690351136280786, 1.31630317051107) b.family <- c(-0.105739639277800, -1.65578969661945, 0.963960274971922, -0.229408248050438, 0.750817842793139, -0.431543865799455, -0.59775756178601, 0.779214214077133, 0.0620507478477045, -4.1683480525725, -1.31456628702112, -3.1601023807461, -2.0490284086076, 1.0670259639956, 1.85521940072053, 0.307382770056423, 2.13861469974605, -0.720600819300007, -0.0508332633523969, 2.7575298363077, -1.51651490913607, 0.257207399309748, 0.090851618543596, 2.60511275970788, -0.356866686830333, 0.101937260427824, 0.277428165537277, 0.0579177959178775, 0.45815864180718, 0.944921316496419, 1.74778505800614, 1.88871763245300, -2.60421600217518, 1.43472652200686, -0.744857295394778, -1.04057562883566, -2.21924693852106, -2.14920610573910, 0.123959096660439, -0.0344459294989469, 0.731896047802949, 0.92428509760875, 1.70496950734237, 1.56844646913807, 1.77694158648017, -2.48052314523393, -0.213936728523652, 1.22998374711347, -2.38917382885456, 1.29918700079135, 0.244398001535968, -2.77002301980107, 0.100498857740044, 0.815580778494278, -1.01301573707541, -1.0029553748719, 1.20253666233106, -1.05370813800671, -1.23275368557282, -1.19715726987850, 0.565967598298127, 1.49612705205631, 0.98698909766583, -1.07723589493791, -0.305922186521898, 0.686387597672107, 2.89391293192919, 0.199292253832065, -1.16869937149275, -1.46811178185330, 0.465513058873785, -0.223627314467404, 2.03936643883732, 2.28896578001666, -2.43218013623255, 0.219813317315558, -0.759552171123955, 1.86691529280883, 1.16421519641069, 0.573569844190085, 1.38093931053797, 2.03995851333347, 0.234097485024822, 1.99725178915011, 3.24942385078111, -0.434529339299985, -1.01852494366032, 0.312921312720424, 1.84163224527155, 1.73496606967762, -0.634141740215574, 1.91713373550730, -0.605653846744036, 0.367716520105131, 0.344428343278782, 1.72777133190868, -0.613848226313207, 0.223042776842526, -3.25256758661658, 0.227225810970268, 0.088157019344018, -0.0521343617184185, -2.51844968986229, -2.93654137651462, -0.211378487505051, -2.27945347547712, 0.603875342716323, -2.28533610734698, -2.16193035481350, -1.20379137741464, -2.65688892937836, -3.93646490894968, 0.914884221931755, -1.43589853428689, 0.199806418184949, 0.943191333679058, -2.43045979664716, 0.158146657914322, -0.923602119652592, 0.665040964381182, -0.659973204422559, -0.430483241421050, 0.259282437889026, 2.62962994220367, 0.88439485503315, 1.98526337212497, 0.580496814142895, 0.703243639481994, 0.894547959431248, 0.398992423477968, 2.07322864216606, 0.168571834758988, 0.612726018532289, -1.46755526637555, -1.00592887815648, 0.298470812436063, 1.59148438482662, 0.0170402830436841, -0.891523409985896) alpha <- .68 nu <- 4.5 sigma <- 16 sigma2.block <- .95^2 sigma2.family <- 2^2 sigma2.X <-structure(c(1451.54950623055, -735.342979734541, -735.342979734541, 484.499970021059), .Dim = c(2, 2)) X1 <- c(0.724863009802043, 1.04438384206630, 1.83588494515537, -1.51342830001172, -4.79298241277743, 43.9455268805402, 11.7201458629409, -64.1647917924087, 29.0552619382893, -6.39050401926177, 1.48989669062707, 7.42230988188248, 10.8531659733688, -7.5022138285536, -2.20612434733787, 6.48295815038078, 8.52109985475473, -0.375439179365485, 21.0295493432215, -37.0380560009782, 9.55314584368972, -54.9908089653012, -4.23876539611617, 2.04688798128512, 6.68960011308596, -3.289944407091, -30.1312830239265, 3.76750347279146, -19.0272388320341, 22.4940400421848, -19.2924438364082, -19.9506565465194, -1.31207437439058, 23.066814542673, -6.7241095771104, 45.2941995657206, 16.0015822602408, -0.935292655905247, -43.554884747384, 15.4569718790331, -1.22034637872971, -19.9965704134644, 37.4076578101491, -28.0995543061898, -48.7622047908226, 23.7985850926121, 39.3046259220605, 14.2651739686861, -11.8105762270899, 85.0818124449961, 48.6469887832523, -72.59934441969, 29.8849770747271, 13.1193895409306, -9.57979284498301, 46.1855992615784, 55.7418657993218, 62.971599775132, -44.4494913514402, 3.07782350580271, 57.633898312856, 13.3911719697174, 77.0306069543372, -31.4419840691264, 42.1180269338110, -6.68577946242373, -1.68984665264424, -11.1428610972603, -7.74742778098567, -5.64383042395133, -38.5696885613131, -48.0019718878948, -34.1793773150862, -88.8255199214418, -6.88511862618801, -1.71217031483324, -53.3394568632865, 168.067487520848, 61.2065911259273, 13.8609236062366, -12.7906988834706, -13.3160537776899, -52.1979926753983, -30.4711185226477, -42.7307635473854, -12.5504158196579, -55.8851469677737, 1.65323994269325, -57.1285541502944, -12.3818611761319, 81.683571447922, 46.3369933513472, -20.7456676252002, 6.45902924446736, -12.3485942727343, -36.3828939882792, -43.1999224351874, -33.2815248438698, -9.5850075101226, -58.6777458258227, 85.5588134199878, 18.3490330350249, 0.6469910836776, 31.6801544583398, -14.2937962307507, -25.4639545549927, -52.3317659684662, -63.4606100761937, -55.2036951089484, -71.6422171573315, -20.5738342629688, -13.8547922849018, -12.3523088708975, 149.135550445419, 104.013643750684, 12.2566947983565, -13.1405481559627, -9.39676334612957, 36.2192689090373, 42.1380261469973, 39.8430852771662, -15.8731918247898, -6.47327429673065, 16.5586728981484, -13.1430168300115, -26.8963211264258, 37.7597819710676, 70.0642022391324, 4.71172262393074, 2.7804346809211, -17.5951486096899, 19.0394086848346, 53.6168614459115, 67.3861472799418, 0.00961642995429255, -9.81632652049684, -1.20033119362427, -14.7772883784266, -1.44374810634621, 57.0926703144478, 13.9733711656857, -72.6300675962072, 1.53735140313113, -1.52652095808364, 0.480251133054604, -21.3828325292082, -15.2944479093155, -2.75003573176319, -0.921484563707578, 2.19091120351644, 0.928357036544768, -24.8789293133563, -47.1742422022339, -49.4756777091106, -13.3292666222640, 7.58568136972644, -0.784483374136152, 2.14472671713154, -4.81154006089481, -19.8871231502694, -30.3775841570554, -43.5780566840745, -30.7831250706626, -20.53255189707, 11.1288061012215, -2.65085261689034, 6.93244868370388, -21.3795685470829, -18.3133632229568, -18.5330634188051) X2 <- c(-0.272531873985738, -12.6732113465296, -7.0931189482588, 13.9568934481434, 3.12307597528903, -30.6872547341677, 6.96785336991028, 26.5733424060205, -13.7875472203734, -4.43056952269522, -2.05233412528771, -2.80543420582175, -0.210512891712975, -3.36050574307093, 1.64899189720122, -15.9146656047332, 6.08730659071286, 2.05788274350682, -14.0374653146842, 24.3976142257943, -15.3567835645471, 20.660448085985, 8.04580089948749, -3.22851786522769, -10.5090245691133, 4.13636215094978, 15.4087225434774, -5.05261274019493, 17.9188552441247, -10.8633568056978, 5.27989674352352, 15.5489461117556, -3.3926800286214, -10.6067117078695, 6.45607499487954, -23.9189943306969, -12.0339492480188, 1.16734318279936, 13.9803617438012, -22.2638135679493, 1.60882676358479, 0.902986687342542, -3.05130596356946, 7.55949581072743, 22.4261656643831, -23.8115947549491, -13.1122629565943, 2.99476318284071, 18.5603488067114, -36.8243492221321, -26.2464627264416, 52.3023217879052, -20.3048787588799, 10.6320930711397, 16.8531169716702, -22.2132273207110, -6.10087145027055, -46.37057361062, 31.7787192163125, -18.1199299701944, -36.9382901149086, -6.4937244203413, -50.6381592502502, 16.2297005876901, -11.8249892985755, 5.78125967637133, -5.44838814623478, 32.5474691538385, 19.5543810309836, 17.0322493275024, 12.7877299206322, 15.9472693206416, 13.3270817228587, 41.2775887836998, 23.7505133377825, 15.5970411635691, 38.7238185364050, -82.1533220155762, -42.3511097982348, 7.27714759250505, -7.64643913066041, -6.7529744375802, 20.7759340986725, 2.92095000312944, 14.4446554257903, -1.80828403750044, 24.4147348820056, 3.57723481615554, 53.2853964911132, 14.1227591028702, -34.3461425771073, -5.35600957556876, 11.2118001009274, -8.12625441223396, -5.81361570620547, -9.93095390890167, 9.80075980531042, 4.01220616598551, -13.4071248576922, 24.4760542972845, -55.1791204075326, 20.7122515140315, 14.9526614325378, -31.4668521910998, 10.8765408072777, 10.5582926924627, 36.5587828056955, 43.8222319676968, 18.5560227149101, 37.6010385306465, 3.21630641394690, -3.48657472918, 21.3483560912942, -76.5407695571773, -32.8897362479988, 2.82353563357743, 4.41650178123251, 12.1511930010507, -23.8589327592206, -18.7178738333025, -23.2704057776054, 6.11175475280951, -7.40743277318622, -14.7187122319453, -0.222825108730596, 27.9925262488002, -50.5661769629271, -35.1022795159195, 1.89902605980024, 4.67610423846604, 12.3888602979042, -16.5962916293541, -44.7391221318359, -58.6437843119999, 11.1687010802516, 7.90244740249326, -4.44600052863641, 7.10436543126574, 8.91503264727688, -44.6607195450111, -21.2464617123802, 33.4992870158698, 2.96721415572959, 0.521194305783759, -5.42887922352969, 2.25315888529839, 26.4818388036174, 22.6696695876108, 2.21920231839013, -9.96358236954472, -3.55684210761352, 13.1457872605569, 17.1867759685232, 12.9622489402124, -2.42313860764845, -16.1480638212884, 1.90904974046514, -9.42537034255124, 1.64141033906311, 13.5517974924939, -3.27011986058282, 10.2990572047796, 9.35514634729958, -1.03544041980337, -6.1260389030768, -2.84491401743449, -4.92381768532470, 20.0737786368934, 20.0196535478164, 16.3548704414098) # W are gamma(nu/2,nu/2) latent variables # initialize these at default value of 1 W <- matrix(1,nrow=4330,ncol=3) # Z are truncated-normal(0,W^-1) on (0,infty) # initialize these by simulating from their prior temp <- rtnorm(n=3*4330,mean=rep(0,3*4330),sd=sqrt(c(1/W[,1],1/W[,2],1/W[,3])),lower=0,upper=Inf) Z <- matrix(temp,nrow=4330,ncol=3,byrow=FALSE) ############################################ ### Now initialize logical nodes############ ############################################ b1 <- as.vector(K1%*%X1) # spatial intercept b2 <- as.vector(K2%*%X2) # spatial slope mu.star <- sqrt(nu/pi)*exp(lgamma(0.5*(nu-1)) - lgamma(0.5*nu)) ################################################################################ #####log full conditional densities for those parameters updated via MH steps#### ################################################################################ ## log full conditional for alpha and intercept lfc.alpha.beta <- function(alpha,beta.int,beta.time,beta.N,beta.HI2,beta.HI3,b.block,b.family,b1,b2,nu,sigma,Z,W,mu.star, Y,N,block,family,HI2,HI3,t,a1,a2) { ##prior SD a.alpha <- 10 a.beta <- 10 mu.Y <- beta.int + beta.N*N + beta.HI2*HI2 + beta.HI3*HI3 + beta.time*outer(rep(1,nrow(Y)),t)+b.block[block] + b.family[family] + b1+a1 + (b2+a2)*outer(rep(1,nrow(Y)),t) + (alpha*sigma/sqrt(1+alpha*alpha))*(Z-mu.star) sigma2.Y <- (sigma*sigma/(1+alpha*alpha))*(1/W) result <- sum(dnorm(x=Y,mean=mu.Y,sd=sqrt(sigma2.Y),log=TRUE)) + (-(alpha^2)/(2*a.alpha*a.alpha)) + (-(beta.int^2)/(2*a.beta*a.beta)) mu.y <- NULL sigma2.Y <- NULL result } ## log full conditional for sigma, assuming that sigma is in (a.sigma,b.sigma) lfc.sigma <- function(sigma,beta.int,beta.time,beta.N,beta.HI2,beta.HI3,b.block,b.family,b1,b2,nu,alpha,Z,W,mu.star, Y,N,block,family,HI2,HI3,t,a1,a2) { mu.Y <- beta.int + beta.N*N + beta.HI2*HI2 + beta.HI3*HI3 + beta.time*outer(rep(1,nrow(Y)),t)+b.block[block] + b.family[family] + b1+a1 + (b2+a2)*outer(rep(1,nrow(Y)),t) + (alpha*sigma/sqrt(1+alpha*alpha))*(Z-mu.star) sigma2.Y <- (sigma*sigma/(1+alpha*alpha))*(1/W) result <- sum(dnorm(x=Y,mean=mu.Y,sd=sqrt(sigma2.Y),log=TRUE)) mu.Y <- NULL sigma2.Y <- NULL result } ## the function assumes that nu is in (a.nu,b.nu) -- the prior bounds ## the function assumes that the logical node mu.star corresponds to nu lfc.nu <- function(nu,beta.int,beta.time,beta.N,beta.HI2,beta.HI3,b.block,b.family,b1,b2,sigma,alpha,Z,W,mu.star, Y,N,block,family,HI2,HI3,t,a1,a2) { mu.Y <- beta.int + beta.N*N + beta.HI2*HI2 + beta.HI3*HI3 + beta.time*outer(rep(1,nrow(Y)),t)+b.block[block] + b.family[family] + b1+a1 + (b2+a2)*outer(rep(1,nrow(Y)),t) + (alpha*sigma/sqrt(1+alpha*alpha))*(Z-mu.star) sigma2.Y <- (sigma*sigma/(1+alpha*alpha))*(1/W) term1 <- sum(dnorm(x=Y,mean=mu.Y,sd=sqrt(sigma2.Y),log=TRUE)) term2 <- sum(dgamma(W,shape=nu/2,rate=nu/2,log=TRUE)) mu.Y <- NULL sigma2.Y <- NULL result <- term1+term2 result } ## log full conditional for X1,X2 ## It is assumed that b1 and b2 correspond to X1 and X2 respectively lfc.X <- function(X1,X2,beta.int,beta.time,beta.N,beta.HI2,beta.HI3,b.block,b.family,b1,b2,nu,sigma,alpha,Z,W,mu.star, Y,N,block,family,HI2,HI3,t,sigma2.X,a1,a2) { mu.Y <- beta.int + beta.N*N + beta.HI2*HI2 + beta.HI3*HI3 + beta.time*outer(rep(1,nrow(Y)),t)+b.block[block] + b.family[family] + b1+a1 + (b2+a2)*outer(rep(1,nrow(Y)),t) + (alpha*sigma/sqrt(1+alpha*alpha))*(Z-mu.star) sigma2.Y <- (sigma*sigma/(1+alpha*alpha))*(1/W) term1 <- sum(dnorm(x=Y,mean=mu.Y,sd=sqrt(sigma2.Y),log=TRUE)) sigma2.X.inv <- solve(sigma2.X) term2 <- -0.5*sigma2.X.inv[1,1]*sum(X1*X1)-0.5*sigma2.X.inv[2,2]*sum(X2*X2)-sigma2.X.inv[1,2]*sum(X1*X2) result <- term1+term2 mu.Y <- NULL sigma2.Y <- NULL result } gradient.X <- function(x,beta.int,beta.time,beta.N,beta.HI2,beta.HI3,b.block,b.family,nu,sigma,alpha,Z,W,mu.star, Y,N,block,family,HI2,HI3,t,sigma2.X,K1,K2,J,a1,a2) { gradient.x1 <- rep(0,J) gradient.x2 <- rep(0,J) X1 <- x[1:J] X2 <- x[(J+1):(J+J)] b1 <- as.vector(K1%*%X1) # spatial intercept b2 <- as.vector(K2%*%X2) # spatial slope mu.Y <- beta.int + beta.N*N + beta.HI2*HI2 + beta.HI3*HI3 + beta.time*outer(rep(1,nrow(Y)),t)+b.block[block] + b.family[family] + b1+a1 + (b2+a2)*outer(rep(1,nrow(Y)),t) + (alpha*sigma/sqrt(1+alpha*alpha))*(Z-mu.star) mat.sum1 <- W*(Y-mu.Y) mat.sum2 <- W*(Y-mu.Y)*outer(rep(1,nrow(Y)),t) for (j in 1:J) { gradient.x1[j] <- sum(mat.sum1*K1[,j]) gradient.x2[j] <- sum(mat.sum2*K2[,j]) } gradient.x1 <- ((1+alpha*alpha)/(sigma^2))*gradient.x1 gradient.x2 <- ((1+alpha*alpha)/(sigma^2))*gradient.x2 sigma2.X.inv <- solve(sigma2.X) gradient.x1 <- gradient.x1 - sigma2.X.inv[1,1]*X1 - sigma2.X.inv[1,2]*X2 gradient.x2 <- gradient.x2 - sigma2.X.inv[2,2]*X2 - sigma2.X.inv[1,2]*X1 result <- c(gradient.x1,gradient.x2) mu.Y <- NULL mat.sum1 <- NULL mat.sum2 <- NULL b1 <- NULL b2 <- NULL result } ## moore-penrose inverse mpinv <- function(X) { # Moore-Penrose inverse Eps <- 100 * .Machine$double.eps; # singular value decomposition s <- svd(X); d <- s$d; m <- length(d); if (!(is.vector(d))) return(t(s$v%*%(1/d)%*%t(s$u))); # remove eigenvalues equal zero d <- d[d > Eps]; notnull <- length(d); if (notnull == 1) { inv <- 1/d; } else { inv <- solve(diag(d)); } # add rows, columns of zeros if needed if (notnull != m) { inv <- cbind(inv, matrix(0, nrow=notnull, ncol=(m - notnull))); inv <- rbind(inv, matrix(0, nrow=(m-notnull), ncol=m)); } # compute Moore-Penrose mp <- s$v%*%inv%*%t(s$u); # set very small values to zero mp[abs(mp) < Eps] <- 0; return(mp); }; ## inital values for uncorrelated random slopes and intercepts a1 <- c(5.530829, -9.377366, -2.960568, 4.919659, -5.823069, 0.077153, -31.951033, -34.672691, 11.802348, 6.8992, 4.300014, -13.498802, 5.604104, 10.295424, 1.041724, -2.654834, 17.567763, 8.793761, 16.720376, 19.038746, 8.772481, 8.894833, 19.308411, 12.031612, -10.826456, 6.997631, -6.174195, -11.663993, -6.713927, -9.355704, -11.830963, -10.713225, -11.920077, 22.973979, -9.56889, -5.603988, 0.803613, -26.386207, -12.362163, -2.947003, 12.763505, 7.603684, -0.199837, 18.647319, 5.510261, -2.852885, 5.62626, 8.118342, -4.698671, -11.496593, -2.899646, -8.716137, 9.938144, -0.665485, 2.329143, 10.922582, 2.923155, -1.500961, 6.976016, 2.879105, 9.024552, 14.546127, 4.32178, 6.377708, 7.141057, 32.198772, -6.575482, 5.074525, -2.583718, -28.764025, -18.464653, -7.756083, -6.575944, 1.001514, -10.537732, 2.070862, 3.069925, -18.842274, -6.397313, 13.630384, -7.062129, -4.496808, 6.046205, -12.635665, -2.781529, 13.586624, -5.007827, -0.202754, -10.002944, 1.575455, -2.334977, 0.323465, -0.113897, -0.261082, -10.836797, -13.20687, 3.266612, 6.684926, 11.881257, 8.669888, 2.339208, -24.065431, 2.804878, 10.005059, -1.660878, 7.564901, 8.397539, 0.26488, 0.475573, 0.051251, -2.595726, 11.893657, 1.884682, 10.992791, 11.629336, 37.191257, -2.178975, 10.95018, -22.61417, -15.99495, 4.316402, -1.466278, 6.751373, -5.016725, -3.278169, -5.853571, 2.958197, 0.226031, -26.232845, -4.375442, -10.625755, 15.55721, 2.233292, 7.757404, -0.114446, 11.842892, 15.453005, -0.601276, 28.104389, 9.526244, -3.657062, -10.758275, 0.247526, -6.449835, 6.23085, -9.296505, -0.371483, -3.964297, -15.254804, 13.789209, 4.558614, -6.822449, -0.681116, 8.959604, 20.929781, 18.770371, -16.672286, -3.029051, 15.164464, -6.184787, -13.1063, -4.484583, 5.359876, 19.027496, 10.164677, 4.859785, -1.313472, -0.64555, -10.864876, -19.592762, -13.374351, -22.707019, -4.043963, -4.015614, -8.711936, -4.606528, 0.284594, -9.506994, -5.579769, -5.608603, 0.035297, 4.053093, 3.438843, 8.550799, 1.790329, -29.599047, 11.047218, -4.056669, -6.683567, 3.986853, -35.166838, -12.683565, 4.655535, -5.425353, 0.609637, -0.504936, -5.878914, -4.091789, -7.76341, -28.028102, -7.734854, -6.376251, -14.537282, -1.733905, 4.588305, 13.551415, 7.189791, 14.00857, 5.159054, 12.068666, 1.443296, 8.908, -12.115542, 2.452689, 17.571135, 19.075351, 10.984671, 2.421629, 8.067007, -1.987613, -3.549508, 2.351115, 5.002614, -3.988253, 10.285817, -13.202876, -5.654637, 8.195208, -5.365455, 3.464953, 8.875748, 13.245059, -3.625923, -35.312727, 15.472218, 22.864189, 2.713316, -14.777872, -5.771511, -17.319588, 2.629055, 12.000342, 5.202902, -5.999592, 7.04304, 12.574369, 4.05937, -13.510943, -7.428931, 0.428293, 3.320299, -14.488865, -9.741838, 1.935204, -3.62905, 6.778857, -5.404345, -4.676777, 5.059299, -15.683607, -13.076736, -3.1943, 3.420465, -5.383699, -5.848197, -11.803311, 10.826985, 3.415391, -1.232519, 14.708334, -2.948054, -1.84399, -34.215412, -3.413113, -3.862431, -13.202678, -27.381448, -4.402169, 15.632541, -32.867078, 3.248673, 30.3436, 17.318267, -17.083175, 1.042304, -2.578133, -2.17153, 4.316743, 5.97469, 1.236899, 14.016727, 27.962123, -2.580947, -2.13937, -19.101052, 0.154061, 0.701668, 4.044565, -8.914383, 11.821961, -7.908428, 5.444003, 16.798175, -7.567206, -3.952542, 0.938366, 3.32561, -6.961978, -1.850168, 2.73589, 5.211004, 1.494966, -17.402343, 4.692136, -1.347293, 0.09017, 19.3563, -9.894588, -2.536741, 8.041588, -3.662797, 4.277107, -13.906754, 12.427825, -14.30586, -6.507547, -6.486902, -5.317565, -33.859252, -26.24729, -14.99095, -5.53245, 10.10508, 5.185162, 7.637916, -2.027713, 4.917635, -9.225927, -23.637453, 3.660156, 12.162429, 8.604646, 15.16929, -5.744887, -6.825688, -1.488801, -2.813295, 14.220745, -14.179864, -4.085968, 22.33957, 0.872367, -7.769854, 1.468868, 1.256864, 7.737562, 6.812834, -0.52438, 1.814249, 5.359213, -24.492526, 3.252217, 8.040102, -8.035868, -7.179307, 4.157797, -19.292748, 1.410431, 11.011433, -5.489366, -8.015715, 8.077853, -5.376064, 6.80654, -21.830195, 25.011145, 1.45209, -16.217431, -23.268073, -37.248234, 8.284368, -4.705392, -12.912568, -25.360469, 0.95648, 16.495819, -16.985932, 7.304138, -30.426893, -28.25521, -9.458013, -11.720263, 12.159225, 13.262364, -0.094364, 2.509098, 4.518662, -4.873261, -15.1802, -5.258572, 11.853813, 17.823983, 10.74934, 9.044788, 1.512376, 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