"anim1" <- function(N=200, dt=.02){
  yr<- c(-8,15)  
  xr<- c(1,40) 
  plot( xr, yr, type="n", xlab="LONGITUDE", ylab="VARIABLE")
  loc<- 1:40
  xl<- seq( 1,40,,300)
  temp<- L96()
  lines( xl, splint(1:40, temp, xl),col=2, lwd=1.5) 
  tt<- -dt
  for ( k in 1:N){
    tt<- tt + dt
    text( 3,-8, round( tt,2), col=4, cex=2, adj=0)
    lines( xl, splint(1:40, temp, xl),col="#FFFFFF", lwd=1.5) 
    temp<- L96(temp, dt=dt)
    lines( xl, splint(1:40, temp, xl), col=4, lwd=1.5) 
    junk<- 0
    for ( j in 1:10000){junk <- sqrt(j)}
    
    xline( 10, col=3)
    text( 3,-8, round( tt,2), col="#FFFFFF", cex=2, adj=0) 
#system( "sleep 0")
  }
}
"anim2" <- function(N=15, MM=5, dt=.02){
# MM is number of ensemble members
  set.seed( 123)
  yr<- c(-8,15)
  xr<- c(1,40)
  plot( xr, yr, type="n", xlab="LONGITUDE", ylab="VARIABLE")
  loc<- 1:40
  xl<- seq( 1,40,,150)
  temp<- L96()

# generate MM perturbations from starting state.

  X<-matrix( temp, ncol=MM, nrow=40) + matrix( rnorm(MM*40)*.05, nrow=40)

#
#
  tt<- -dt
  for ( k in 1:N){
    tt<- tt + dt
    text( 3,-8, round( tt,2), col=4, cex=2, adj=0)
    for ( jj in 1: MM){
      lines( xl, splint(1:40, X[,jj], xl),col="#FFFFFF", lwd=1) }
    lines( xl,  splint(1:40, temp, xl),col="#FFFFFF", lwd=1)
    X<- L96(X, dt=dt)
    temp<- L96( temp, dt=dt)
    for ( jj in 1: MM){
      lines( xl, splint(1:40, X[,jj], xl),col=2, lwd=1) }
    lines( xl,  splint(1:40, temp, xl),col=4, lwd=1)

    junk<- 0
#for ( jj in 1:1000) { junk<- sqrt(jj)}
    if( k ==1) { system( "sleep 1")}
    system( "sleep 0.2")
    text( 3,-8, round( tt,2), col="#FFFFFF", cex=2, adj=0)
}


}
"EKF" <- function(N=25, MM=15, dt=.2/5, sige=.5,tempo=T){
  set.seed( 123)
  yr<- c(-8,15)
  xr<- c(1,40)
  plot( xr, yr, type="n", xlab="LONGITUDE", ylab="VARIABLE")
  loc<- 1:40
  ind<- ( 1:20)*2
  xl<- seq( 1,40,,300)
  temp<- L96()
  
  X<-matrix( temp, ncol=MM, nrow=40) + matrix( rnorm(MM*40)*.5, nrow=40)
  tt<- 0
#
#
  for ( k in 1:N){
    tt<- tt + dt
    text( 3,-8, round( tt,2), col=4, cex=2, adj=0)
    for ( jj in 1: MM){
      lines( xl, splint(1:40, X[,jj], xl),col="#FFFFFF", lwd=1) }
    lines( xl,  splint(1:40, temp, xl),col="#FFFFFF", lwd=2)
    X<- L96(X, dt=dt)

    temp<- L96( temp, dt=dt)
    cat (k, " ")

    for ( jj in 1: MM){
      lines( xl, splint(1:40, X[,jj], xl),col=2, lwd=1) }
    lines( xl,  splint(1:40, temp, xl),col=4, lwd=2)

    if( (k %% 5)==0){

      y <- temp[ind] + rnorm( 20)*sige
      update( X, y, ind=ind, sige=sige)-> Xnew

      points( ind, y, cex=2, pch="o")
      if (tempo) system( "sleep 1")
      for ( jj in 1: MM){
        lines( xl, splint(1:40, Xnew[,jj], xl),col=3, lwd=1) }
      lines( xl,  splint(1:40, temp, xl),col=4, lwd=2)
      points( ind, y, cex=2, pch="o")
      if (k<N){
        if (tempo) system( "sleep 2")
        points( ind, y, cex=2, pch="o", col="#FFFFFF")

        for ( jj in 1: MM){
          lines( xl, splint(1:40, X[,jj], xl),col="#FFFFFF", lwd=1) 
        }
        for ( jj in 1: MM){
          lines( xl, splint(1:40, Xnew[,jj], xl),col=2, lwd=1) 
        }
        
        lines( xl,  splint(1:40, temp, xl),col=4, lwd=2)
      }
      
      X<- Xnew
      
    }
    
    if (k<N){
      if (tempo) system( "sleep 1")
      text( 3,-8, round( tt,2), col="#FFFFFF", cex=2, adj=0)
    }
  }
}
"fig1" <- function(kk=16 ){
  set.panel( 1,2)
  par( pty="s")

  X<- xens[,,kk]

  plot( X[,2], X[,1], xlab="X2", ylab="X1")
  points( xtrue[kk,2], xtrue[kk,1], pch="+", col=3, cex=2)
  lines( sreg(  X[,2], X[,1], df=400/25) $predicted, col=2, lwd=2)
  lm(  X[,1]~ X[,2])-> hold
  abline( coefficients(hold), col=4, lwd=2)

  plot( X[,2], X[,3], xlab="X2", ylab="X3")
  points( xtrue[kk,2], xtrue[kk,3], pch="+", col=3, cex=2)
  lines( sreg(  X[,2], X[,3], df=400/25) $predicted, col=2, lwd=2)
  lm(  X[,3]~ X[,2])-> hold
  abline( coefficients(hold), col=4, lwd=2)

}

"L96" <- function( z0=z0.start.L96,dt=.4,F=8, delta=.001){
  MM <- nrow( z0)
  nstep <- round( dt/delta)
  delta <- dt/nstep
  ind <- (1:MM)+2
  for( k in 1:nstep){
    z0 <- rbind( z0[MM-1,], z0[MM,], z0,z0[1,])
    z0 <- matrix(z0[ind,]+delta*((z0[ind+1,]-z0[ind-2,])*z0[ind-1,]-z0[ind,] 
                                 +F), nrow=MM)
  }
  z0
}

"sim.EKF" <- function( N=25,true.state=z0.start.L96,X=NULL,
                      dt=.2, sige=.5, M=15, ind= (1:20)*2, alpha=1.0)
{
  
  if( is.null( X)){
    n<- nrow( true.state)
    X<- matrix( true.state, nrow=n, ncol=M) + .5*sige*matrix( 
                                      rnorm(M*n), nrow=n,ncol=M)
  }

  n<- nrow(X)

  set.seed( 123)

  xhat<- (X%*% rep( 1/M, M))
  rmse<- sqrt(mean( ( xhat- true.state)**2) )
  cat( rmse, fill=T)

  for ( k in 1:N){
# update/analysis 
    y<- true.state[ind] + rnorm( length( ind))*sige
    update( X, y, ind=ind, sige=sige, alpha=alpha)-> X
    xhat<- stats( t(X))[2,]
    rmse1<- sqrt(mean( ( xhat- true.state)**2) )
# forecast 
    true.state<- L96( true.state, dt=dt)
    X<- L96(X, dt=dt)
    xhat<- stats( t(X))[2,]
    rmse2<- sqrt(mean( (xhat- true.state)**2) )
    rmse3<- sqrt(mean(stats( t( X))[3,]**2))
    cat( k,rmse1,rmse2, rmse3,fill=T)
  }
  list( true.state= true.state, X=X)
}
"update" <-
  function(X,y, ind,sige=2, window=20, alpha =1.0){
    R<- diag( sige**2, 20)
    M<- ncol( X)
    dd<- c(0:19,20:1)
    phi<- matrix( dd, ncol=40, nrow=40)
    for ( k in 1:40){
      phi[k,]<- dd
      dd<- c( dd[40], dd[1:39])
    }
    M<- ncol( X)
    
#taper
    phi<- exp( -(dd/window)**2)
#
    Sigma<- var( t(X))*phi
    N<- length( ind)
#perturbed obs. 
    Y<- matrix( y, ncol=M, nrow=N) + 
      matrix( sige*rnorm(M*N), nrow=N, ncol=M)
#
#print(stats( sqrt(diag( Sigma))))

    X + Sigma[,ind] %*% solve( alpha*Sigma[ind, ind] + R)%*%(Y - X[ind,])

  }
"Xstart" <-
  structure(c(3.5886628854236, 9.00624508024815, 0.91216532710636, 
-2.49452610267489, 0.376274678815257, 6.31940649415671, 10.0424654460794, 
1.69970472610699, 4.55080130549106, 6.19769977130194, -1.39848173920306, 
1.70244951165189, 5.24763939220236, -0.511615517190156, -0.899444456883006, 
-1.14336384883213, 8.13135492877022, 0.459242460002726, -2.27360643666785, 
0.81155124031871, 8.11450833383125, -1.56879461907277, 2.70517443310065, 
2.05655129540688, 3.8827495075211, 5.91599581311795, -3.94825514073419, 
0.470819911388634, -0.388112956206747, -0.0300068555728339, 1.51659977098393, 
10.3267825060747, -0.0540411642573238, -1.59363333849404, 4.36169331576214, 
3.24393303614042, 3.65986208977533, 7.42651621834744, 2.59956625568726, 
-1.16906381111526, 3.57938889507908, 8.96848718654208, 0.915804777104896, 
-2.54113511018364, 0.348494274992999, 6.26285843336328, 10.0956936175605, 
1.68897167009638, 4.52077157377994, 6.24025286196749, -1.37177306121797, 
1.69450478519280, 5.2385304459191, -0.513191698092321, -0.922123572559479, 
-1.19680509887942, 8.13260335044882, 0.440829085547306, -2.26670743937208, 
0.734822727977626, 8.13352680954609, -1.50364280654973, 2.65680502840963, 
2.00934779337989, 3.84826883001686, 5.94025842712253, -3.93808507387177, 
0.42091615469333, -0.378826992955367, -0.0162828071716654, 1.55009647824534, 
10.3269531506400, -0.0870878712821183, -1.59786513295941, 4.36213354657957, 
3.25149823263019, 3.66178460231708, 7.42097453321074, 2.62611956158932, 
-1.16766606482741, 3.57910072884731, 8.95925135201058, 0.9568920510816, 
-2.5501817339215, 0.358631440620915, 6.27932204105812, 10.0985406935179, 
1.68780420776536, 4.50624812049762, 6.21248714836927, -1.34523032958614, 
1.69078673388398, 5.2298743574397, -0.510940985830208, -0.918613663444734, 
-1.18630977487884, 8.10508496812112, 0.477227760311891, -2.30530031804778, 
0.772129619937146, 8.12916681973384, -1.54206743485495, 2.66544271445616, 
2.02599539834539, 3.88786396213374, 5.91715996693164, -3.94996157146461, 
0.492649484957331, -0.390539609281357, -0.026431562942225, 1.50732578416481, 
10.3143910752110, -0.0418232317066048, -1.62439705537615, 4.36443019275413, 
3.2872231734962, 3.67737277384979, 7.41769746965387, 2.65681827085147, 
-1.16658667135825, 3.57464109596479, 8.98329355597953, 0.943184234303938, 
-2.53076819299595, 0.368680242953335, 6.30535614601534, 10.0523700414710, 
1.68089002497658, 4.54243267723579, 6.22322522923874, -1.40721167704944, 
1.68528388839313, 5.24651653474041, -0.490108297612888, -0.961153457731673, 
-1.19865937341070, 8.14779460984442, 0.436851596298397, -2.24177411514551, 
0.767519499110138, 8.13117980520931, -1.51683558447025, 2.68375783222005, 
2.03209747458321, 3.86568464050477, 5.92626769962339, -3.94528931283847, 
0.470286148536007, -0.394480051939058, -0.041392769223082, 1.48904211900571, 
10.3336462771788, -0.0168964417523443, -1.62023626073614, 4.35938395480228, 
3.26280561565268, 3.67598825932818, 7.42823081765178, 2.59822611119458, 
-1.17239101434459, 3.56790207013446, 9.00276293870764, 0.951422316445807, 
-2.51722899259250, 0.378452269317995, 6.34628128635469, 9.95698670371927, 
1.62042484080073, 4.59965936015942, 6.28227493059343, -1.45368913372098, 
1.68985780449076, 5.24301092889283, -0.511612847051196, -0.923580686631765, 
-1.20711684930065, 8.09305721997878, 0.503242883494385, -2.31410920516354, 
0.781093721760552, 8.12654856017364, -1.54734718491719, 2.70959707470663, 
2.04418356300407, 3.85417149807989, 5.93703742036182, -3.92775783668311, 
0.426769177139630, -0.391219894993665, -0.0365198339970235, 1.50313734243886, 
10.3174507118459, -0.00244845204531577, -1.61814904550720, 4.36236287053332, 
3.25598456893710, 3.67075823706483, 7.41473343647248, 2.55112807974729, 
-1.17090898587427, 3.57552203658087, 8.99667972153278, 0.93448677547692, 
-2.51932369849728, 0.376682660295546, 6.32494982610273, 10.0128023017008, 
1.67755754862559, 4.55371250814155, 6.2014620935137, -1.43206573123282, 
1.67578850935694, 5.24106627987226, -0.477649960320955, -0.954611748791632, 
-1.19053077503409, 8.12293164924048, 0.47086306210707, -2.27526819500192, 
0.796624039818382, 8.12014692312699, -1.54723426771054, 2.71966413356912, 
2.04898425706199, 3.85775189775298, 5.9362303003975, -3.94600485032587, 
0.460544137110443, -0.397025044155475, -0.0435844650389595, 1.50901844451275, 
10.3380889107486, -0.0582063195070083, -1.57706182686591, 4.35330680313339, 
3.22468716151317, 3.65613566600176, 7.41892481755941, 2.60556080116844, 
-1.17183546434534, 3.58828662229869, 8.96912888725662, 0.978980938554059, 
-2.52983825017792, 0.376340094063807, 6.30386356648892, 10.0433083148555, 
1.69117172936252, 4.54889467201753, 6.22859197897625, -1.41150394574118, 
1.68473147153701, 5.23895793665236, -0.4984375811986, -0.931076059374486, 
-1.18651101177178, 8.11552477630794, 0.474977794105953, -2.28863898739546, 
0.786079482493354, 8.12700779847831, -1.54394385685821, 2.6786329866871, 
2.04273463948536, 3.89737752630111, 5.90706317298865, -3.97050743869758, 
0.513716378714542, -0.394056308926811, -0.0274422937459723, 1.50059662542882, 
10.2999720962326, -0.0092598069378295, -1.65536107551215, 4.37028457567638, 
3.28204425416486, 3.67124310236945, 7.4209815949879, 2.65887892844428, 
-1.15697787393290, 3.59340422712074, 8.98613269201346, 0.901675198113306, 
-2.50970774937393, 0.361985075199115, 6.28864027566934, 10.0274952852132, 
1.67431092995953, 4.54963535271163, 6.2538314103973, -1.40884727837973, 
1.67990282724043, 5.24268255206099, -0.498092214749531, -0.935688459760882, 
-1.19816158412223, 8.10105222995099, 0.490416055931995, -2.30959653729074, 
0.789810295633347, 8.12631867092879, -1.54612231719317, 2.70077925456784, 
2.04595825423540, 3.86965169564741, 5.92375313163821, -3.93838486890817, 
0.46548127191322, -0.393518167305342, -0.0334082118924499, 1.48724865049521, 
10.3113861143059, -0.00340637500589349, -1.65041335755131, 4.36811632243878, 
3.26541232503123, 3.66662442145594, 7.42706983790196, 2.60207828294508, 
-1.15635869041787, 3.57207718665248, 8.97864795363092, 0.933111053557884, 
-2.54310869829461, 0.356347653468331, 6.27621006004972, 10.0490706737209, 
1.67762033063438, 4.53472992400223, 6.26584795829408, -1.36149176884973, 
1.68076234821678, 5.22138876858846, -0.494623794163789, -0.933749913892013, 
-1.19439763256650, 8.10544388822517, 0.488107163744845, -2.30914134570176, 
0.787357280517801, 8.12964563265103, -1.55267422518318, 2.70008869614286, 
2.04699611141881, 3.87651780393486, 5.91315573026106, -3.95226651437142, 
0.459497337867362, -0.396772061016497, -0.0364742464569593, 1.50374410803573, 
10.3239206234582, -0.0337548041510575, -1.62273298116874, 4.36113787734345, 
3.26009852111937, 3.67429500155293, 7.42886060664337, 2.58823040819705, 
-1.16979877782456, 3.58177576194406, 8.97169784357791, 0.869133789155431, 
-2.53352371868066, 0.339593241441268, 6.23531670635163, 10.1325196540807, 
1.74175623907841, 4.49063332495016, 6.19525870215361, -1.35757525249835, 
1.68338300326479, 5.23681123921195, -0.499088124542346, -0.936247024717168, 
-1.18449000932106, 8.11106177381788, 0.474750660503953, -2.28561869610939, 
0.789604736386097, 8.12982125311483, -1.53979512376745, 2.69024265183237, 
2.04665116203833, 3.89071674039723, 5.91499360219541, -3.94999572814982, 
0.490122616614236, -0.393422364031845, -0.0225788913640503, 1.52180887155122, 
10.32194672829, -0.0452910961322234, -1.61514926884999, 4.37045244031226, 
3.28744247548040, 3.67211411598504, 7.39426034978587, 2.58507600246729, 
-1.15584051015957, 3.59130891842504, 8.97893590296225, 0.837003550848066, 
-2.51903854497782, 0.344322722375214, 6.2578988819912, 10.0999675556903, 
1.72095157728377, 4.50143000725315, 6.19543995561749, -1.35955167472186, 
1.68301074593991, 5.24137350812758, -0.47679699404784, -0.940661114962958, 
-1.1451869706359, 8.14611100458802, 0.455637746633101, -2.25990598595806, 
0.839777469132654, 8.11064163997182, -1.59175128909765, 2.70702224161599, 
2.05517910877320, 3.89284580038674, 5.90313427154329, -3.95647035642411, 
0.502635701505425, -0.389767818701813, -0.0343994563760371, 1.49461915992625, 
10.3282801272051, -0.000628573050208053, -1.61752206262229, 4.37908590947073, 
3.29563524127976, 3.69200308261191, 7.41238458765042, 2.57198838904449, 
-1.14533935328128, 3.57479511809659, 8.99357319971203, 0.931846177850437, 
-2.53348846636988, 0.359794744359578, 6.28799364166256, 10.0795348565944, 
1.68464290276681, 4.53063159886003, 6.26084307316232, -1.35147624704390, 
1.68821130840205, 5.22657100700884, -0.521860677686214, -0.89752493127047, 
-1.18528786889114, 8.09176744845625, 0.49806574388304, -2.33057847690127, 
0.775355330588283, 8.13806184181105, -1.55097817195881, 2.69953128712899, 
2.04240749782631, 3.86923321295406, 5.92581848411625, -3.94506789849943, 
0.450980117556763, -0.392521730100564, -0.0357088747094665, 1.50695025217193, 
10.3159853728404, -0.0132592496271875, -1.61689345693137, 4.36183092035476, 
3.23142899608347, 3.65841594613564, 7.43298140238943, 2.58434978500472, 
-1.17743853033504, 3.56738547081377, 8.9902737875175, 0.8711722598328, 
-2.54093190810701, 0.349258262555684, 6.30641133820278, 10.0248557147782, 
1.64346532535304, 4.55280479683024, 6.26506835524738, -1.37716433066004, 
1.69029948465351, 5.24050930130652, -0.502481203235434, -0.922716591558376, 
-1.17394269456955, 8.14309216775566, 0.432713575108224, -2.25502205996873, 
0.765694709506847, 8.13002086044722, -1.50995163350029, 2.70199010293640, 
2.03755799295182, 3.84278294748495, 5.9610897999749, -3.92191388385506, 
0.426899583169161, -0.398675846316236, -0.0431741709128175, 1.55457671271451, 
10.3595341618967, -0.116904448310821, -1.52684083795944, 4.33654660478494, 
3.19762284298860, 3.67126364992046, 7.44330998861644, 2.56928454269515, 
-1.17946875916657, 3.57214154197628, 8.96502508621775, 0.988700765724875, 
-2.52897696693634, 0.379069512452316, 6.30600158243911, 10.0436943569792, 
1.69206493658555, 4.54107110743661, 6.21484324109845, -1.39896819701824, 
1.68648859029258, 5.23712133367277, -0.510241021503656, -0.920895336558857, 
-1.19193075138483, 8.08901136481816, 0.51164993370563, -2.33079270703429, 
0.798688823392473, 8.12370133038955, -1.56599451374116, 2.71572502424098, 
2.04714172200428, 3.87347661733167, 5.92969443886643, -3.94447208436692, 
0.508102321126094, -0.405480848927354, -0.0396414461598930, 1.51437315314789, 
10.3357814904163, -0.0803187699358443, -1.58657159190307, 4.35797906028930, 
3.28625206206110, 3.68937837164411, 7.41201292760469, 2.60167213923568, 
-1.16472767513381, 3.57966500731912, 8.97871159356436, 0.967596740968215, 
-2.5131820152094, 0.380171459721766, 6.32405237030259, 9.99244967212638, 
1.64136762829026, 4.56892493035955, 6.26467476889497, -1.42468662854452, 
1.68191786983328, 5.24545063768508, -0.494766774233497, -0.932879951405183, 
-1.17843705293250, 8.10913916139761, 0.481956158285795, -2.29472453491392, 
0.802015601104673, 8.11970742093663, -1.56679709769000, 2.70272484980587, 
2.04628913106856, 3.8834547969144, 5.91617528968715, -3.93941277708879, 
0.479466710258234, -0.388880263206644, -0.0358219366499144, 1.51337171250138, 
10.3376073689365, -0.0503963593239808, -1.58443414480112, 4.35699962492181, 
3.23972952150101, 3.67047191389912, 7.4284483587123, 2.60510303920686, 
-1.16495459770245, 3.57889586582707, 8.96760774991983, 0.950509319195662, 
-2.54624407369143, 0.360892311998556, 6.28621654910153, 10.0741989119029, 
1.70578579320935, 4.53558940133195, 6.22308396618897, -1.37589020314274, 
1.70032319677306, 5.23624696031308, -0.521454379061984, -0.903092665142604, 
-1.17998089697146, 8.13435194348829, 0.455436441964713, -2.28079041251113, 
0.768497323950685, 8.13044873091208, -1.53052967985906, 2.69797000714331, 
2.05367532635228, 3.89142486521916, 5.90374771718195, -3.94539881757474, 
0.445032481017304, -0.392765031859338, -0.0401487407436118, 1.51256842670191, 
10.3423356263124, -0.0724450077220064, -1.58411787341062, 4.34960283035293, 
3.25791476333207, 3.67503061676745, 7.41001409755322, 2.6298834089826, 
-1.15633188965754, 3.58501893955447, 8.98463357886494, 0.948099046374076, 
-2.51058524401054, 0.372068814256134, 6.29910495780984, 10.0114015440082, 
1.68698980566184, 4.56580540878926, 6.2677888120226, -1.40834592463325, 
1.67795928386683, 5.24017191091754, -0.496618227632365, -0.907095109883997, 
-1.15929043410800, 8.11602344722961, 0.446731050615418, -2.29433724770334, 
0.749578583259613, 8.14734370119425, -1.52252887083349, 2.67074486536737, 
2.03936260952430, 3.89743266013084, 5.9116000858378, -3.94719090371743, 
0.482637648702742, -0.396922912327686, -0.0380812717615176, 1.54177054643852, 
10.3497857608516, -0.0792641075459913, -1.53621509442878, 4.35308515193635, 
3.22008708711401, 3.67083472990137, 7.42860318517401, 2.58302270990452, 
-1.16011485366081, 3.58378313440414, 8.97014663369128, 0.954155548126827, 
-2.52367004951773, 0.367507165453721, 6.28783331360862, 10.0683211180525, 
1.69053902463801, 4.53437572490392, 6.2383468359201, -1.39048856518222, 
1.68740697365807, 5.24312258745768, -0.513924386870897, -0.920869583083037, 
-1.19658395124974, 8.1213519803947, 0.471625869912617, -2.28396877459994, 
0.772454915287329, 8.13073617501588, -1.52823478987795, 2.68347541336019, 
2.04257615815792, 3.89086444592276, 5.91300616088377, -3.94707899843214, 
0.483471320243221, -0.399327384915899, -0.0430860768722755, 1.48735013427939, 
10.3363034783202, -0.0164485379161002, -1.60486011541253, 4.36756232746421, 
3.27441170744395, 3.68677448500513, 7.42516819419455, 2.58432194501936, 
-1.15570410236681, 3.56431287418927, 9.00032150425199, 0.962346760494096, 
-2.53002787609522, 0.375644003363508, 6.3345200108944, 10.0163192716606, 
1.63345517766218, 4.56486611979551, 6.26978274553159, -1.38517400152390, 
1.69521420679176, 5.2383879029904, -0.520765109267363, -0.894772709355562, 
-1.16695674565124, 8.10012299226234, 0.486869586697904, -2.31662358178627, 
0.783246667843503, 8.14023940988072, -1.53936414266488, 2.71184557194026, 
2.07169013315185, 3.91229519570189, 5.89069892297196, -3.95499209335274, 
0.510420375294293, -0.4016176794294, -0.0316082358754505, 1.48388319379660, 
10.3071770958998, -0.0123519490812328, -1.66830110923894, 4.37800507162268, 
3.3055698941547, 3.6780418773979, 7.41746769241518, 2.5699300784364, 
-1.18118836929105, 3.58223745448811, 8.9683216796244, 0.942191881797062, 
-2.52468429866380, 0.367706473682345, 6.29963282798902, 10.0460316498397, 
1.68092345162286, 4.53650639576282, 6.21917470754471, -1.38869175112889, 
1.68769992404551, 5.242689237075, -0.489208554423239, -0.942946659914716, 
-1.17956445545372, 8.16345209176016, 0.414483272892043, -2.22470245727078, 
0.761535074346666, 8.12141219113283, -1.5076913150129, 2.66014359302256, 
2.02021741098971, 3.86983896704179, 5.93511546942066, -3.92303500475998, 
0.460337682738017, -0.401243078442422, -0.0352708567091407, 1.50123100527901, 
10.3166682048386, -0.0404311550551306, -1.63020655155515, 4.35863448457459, 
3.26093641823467, 3.66412039011181, 7.42104226761469, 2.63730259792516, 
-1.16227484027), .Dim = c(40, 20))
"z0.start.L96" <-
structure(c(1.60886541272225, 0.598943818848781, 5.71558743579969, 
6.43818839970195, -1.37236989200768, 5.04694234905259, 3.77690464433516, 
2.77797372863299, 3.2443764829296, 6.01040684639448, 6.31334785536396, 
1.65992639277626, 4.50695304398058, 3.75284568615516, -4.16903368619754, 
2.6975476769102, 4.96669831827152, 8.06939581158632, -1.38527087180471, 
3.16621135654676, 3.69622951239341, 5.29476944887165, -0.602734785374163, 
-1.87902422944466, 2.06358287353776, 5.02493521757799, 5.10165605262604, 
3.53573128791433, -5.24267431401288, -0.862857214667616, 1.14780953621480, 
8.77843769919082, 2.86080839361846, 3.6996599666903, 5.45194829931056, 
-3.12047911973242, 0.152176331893935, 0.965414577296707, 7.42775977891734, 
-1.4204503591615), .Dim = c(40, 1))