`flrti` <-
function(Y,X,sigma,deriv=2,weight=1,int=T,wrap=F,plot=F){
    p <- ncol(X)
    beta.zero <- 0
    extra.con <- NULL
    if (length(weight)>1)
      deriv <- (1:4)[weight[-1]>0]  else{
      weight <- c(weight,0,0,0,0)
      weight[deriv+1] <- 1}
### different weights when there is intercept ###   
    if(int){
      X <- cbind(1,X)  
      weights<-c(0,rep(weight[1],p),0,rep(weight[1],p))
    } else 
    weights <- rep(weight[1],2*p)
    for (i in 2:5)
      if (weight[i]>0)
        weights <- c(weights,rep(weight[i],2*(p-i+1)))
    A <- makeA(p,deriv,int)
    colscale <- apply(X,2,function(x){sqrt(sum(x^2))})
    newX <- t(t(X)/colscale)
    if (wrap)
      if (int)
        extra.con <- c(0,1/colscale[2],rep(0,p-2),-1/colscale[p+1],0,-1/colscale[2],rep(0,p-2),1/colscale[p+1],rep(0,2*nrow(A)))
      else
        extra.con <- c(1/colscale[1],rep(0,p-2),-1/colscale[p],-1/colscale[1],rep(0,p-2),1/colscale[p],rep(0,2*nrow(A)))

    lin.fit <- linearoptim(Y,newX,sigma,sqrt(2*p),weights,A%*%diag(1/colscale),extra.con)
    beta <- lin.fit$eta/colscale
    fit <- X%*%beta
    residuals <- Y-fit
    Rsq <- 1- sum(residuals^2)/sum((Y-mean(Y))^2)
    if (int){
      beta.zero <- beta[1]
      beta <- beta[-1]}
    beta <- p*beta
    if (plot)
      plot(seq(0,1,length=p),beta,type='l',ylab="FLRTI Estimate", xlab="X axis")
    list(beta=beta,gamma=lin.fit$gamma,sol=lin.fit$sol,
lin.fit=lin.fit$lpout,code=lin.fit$code,sigma=sigma,weight=weight[1],
deriv=deriv,int=int,beta.zero=beta.zero,Rsq=Rsq,fitted.values=fit,residuals=residuals)
}

`flrti.boot` <-
function(Y=NULL,X=NULL,obj=NULL,B=100,CI=.95,bootfit=NULL){
    if (is.null(bootfit)){
       n <- length(Y)
      sigma <- obj$sigma
      weight <- obj$weight
      int <- obj$int
      wrap <- obj$wrap
      deriv <- obj$deriv
      bootbeta <- matrix(0,B,ncol(X))
      for (b in 1:B){
        status <- 1
        while (status!=0){
        s <- sample(n,n,replace=T)
        bootY <- Y[s]
        bootX <- X[s,]
        bootfit <- flrti(bootY,bootX,sigma,deriv,weight,int,wrap)
        status <- bootfit$code}
        bootbeta[b,] <- bootfit$beta
        }}
    else{
      obj <- bootfit$obj
      bootbeta <- bootfit$bootbeta}
    uci <- apply(bootbeta,2,function(x)quantile(x,1-(1-CI)/2))
    lci <- apply(bootbeta,2,function(x)quantile(x,(1-CI)/2))
    p <- length(uci)
    plot(seq(0,1,length=p),obj$beta,ylim=c(min(lci),max(uci)),type='l',lwd=3,        xlab="X axis", ylab="Beta Confidence Intervals")
    lines(seq(0,1,length=p),lci,col=2)
    lines(seq(0,1,length=p),uci,col=2)
    list(obj=obj,bootbeta=bootbeta,uci=uci,lci=lci)}

`flrti.cv` <-
function(Y,X,sigma,cv=2,deriv=2,weight=1,s=NULL,int=T,wrap=F){
    n <- length(Y)
    if (is.null(s))
      s <- sample(n,replace=T)
    siglen <- length(sigma)
    wlen <- length(weight)
    error <- matrix(0,wlen,siglen)
    allerrors <- array(0,c(cv,wlen,siglen))
    for (j in 1:siglen)
      for (k in 1:wlen){
        for (i in 1:cv){
          test.index <-  s[(1+(i-1)*floor(n/cv)):(i*floor(n/cv))]
          if (i==cv)
            test.index <- s[(1+(i-1)*floor(n/cv)):n]
          testY <- Y[test.index]
          testX <- X[test.index,]
          trainY <- Y[-test.index]
          trainX <- X[-test.index,]
          trainfit <-flrti(trainY,trainX,sigma[j],deriv,weight[k],int=int,wrap=wrap)
          if (trainfit$code==0)
            allerrors[i,k,j]<-sum((testY-predict.flrti(trainfit,testX))^2)*n/length(testY)
          error[k,j] <- error[k,j]+allerrors[i,k,j]*length(testY)/n
        }
        code.errors <- sum(allerrors[,k,j]==0)
        if (code.errors<cv)
          error[k,j] <- error[k,j]*cv/(cv-code.errors)
        else
          error[k,j] <- 10^40
        print(c(j,k))}
    print(paste("Min sigma = ",rep(sigma,rep(wlen,siglen))[order(error)[1]]))
    print(paste("Min weight = ",rep(weight,siglen)[order(error)[1]]))                               
    list(sigma=sigma,weight=weight,error=error,allerrors=allerrors,s=s)}

`flrti.perm` <-
function(Y=NULL,X=NULL,obj,B=100,permfit=NULL,plot=T){
    if (is.null(permfit)){
       n <- length(Y)
       sigma <- obj$sigma
      weight <- obj$weight
      int <- obj$int
      wrap <- obj$wrap
      deriv <- obj$deriv
      SSE <- sum(obj$res^2)
      permSSE <- rep(0,B)
      for (b in 1:B){
        status <- 1
        while (status!=0){
        s <- sample(n,n,replace=F)
        permY <- Y[s]
        permfit <- flrti(permY,X,sigma,deriv,weight,int,wrap)
        status <- permfit$code}
        permSSE[b] <- sum(permfit$res^2)
        }
     permRsq <- 1-permSSE/sum((Y-mean(Y))^2)}
    else{
      obj <- permfit$obj
      SSE <- permfit$SSE
      permSSE <- permfit$permSSE
      permRsq <- permfit$permRsq}
    Rsq <- obj$Rsq 
    if (plot){
      plot(permRsq,ylim=c(min(permRsq),max(c(Rsq,permRsq))),ylab="Rsq",
       xlab ="Permutation")
      abline(Rsq,0,col=2,lwd=2)}
    p <- mean(Rsq<permRsq)
    print(paste("p-value = ",p))
    list(obj=obj,SSE=SSE,permSSE=permSSE,p=p,Rsq=Rsq,permRsq=permRsq)}

`linearoptim` <-
function(Y,X,sigma,lambdap,weights=1,A,extra.con=NULL){
    p <- ncol(X)
    K <- nrow(A)
    f.obj <- weights
    XX <- t(X)%*%X
    b1 <- lambdap*sigma+as.vector(t(X)%*%Y)
    b2 <- lambdap*sigma-as.vector(t(X)%*%Y)
    f.con1 <- cbind(XX,-XX,matrix(0,p,2*K))
    f.con2 <- cbind(-XX,XX,matrix(0,p,2*K))
    f.con3 <- cbind(A,-A,diag(K),-diag(K))
    f.con <- rbind(f.con1,f.con2,f.con3)
    f.rhs <- c(b1,b2,rep(0,K))
    f.dir <- c(rep("<=",2*p),rep("==",K))
    if (!is.null(extra.con)){
      f.con <- rbind(f.con,extra.con)
      f.rhs <- c(f.rhs,0)
      f.dir <- c(f.dir,"==")
    }
    lpout <- lp("min",f.obj,f.con,f.dir,f.rhs)
    eta <- lpout$sol[1:p]-lpout$sol[(p+1):(2*p)]
    gamma <-lpout$sol[(2*p+1):(2*p+K)]-lpout$sol[(2*p+K+1):(2*p+2*K)]#gamma here is acutally -gamma
    if (lpout$status!=0){
      print(paste("Error: Code = ",lpout$status))
    }
    list(eta=eta,gamma=gamma,lpfit=lpout,code=lpout$status)}

`makeA` <-
function(p,deriv=2,int=F){
    A <- NULL
    if (!is.na(match(1,deriv))){
      a <- c(-1,1,rep(0,p-1))
      K <- p-1
      A <- rbind(A,matrix(rep(a,K)[1:(K*p)],K,p,byrow=T))
    }
    if (!is.na(match(2,deriv))){
      a <- c(1,-2,1,rep(0,p-2))
      K <- p-2
      A <- rbind(A,matrix(rep(a,K)[1:(K*p)],K,p,byrow=T))
    }
    if (!is.na(match(3,deriv))){
      a <- c(-1,3,-3,1,rep(0,p-3))
      K <- p-3
      A <- rbind(A,matrix(rep(a,K)[1:(K*p)],K,p,byrow=T))
    }
    if (!is.na(match(4,deriv))){
      a <- c(-1,4,-6,4,-1,rep(0,p-4))
      K <- p-4
      A <- rbind(A,matrix(rep(a,K)[1:(K*p)],K,p,byrow=T))
    }
    if (int)
      A <- cbind(0,A)
    A}

`predict.flrti` <-
function(obj,newdata){
  p <- ncol(newdata)
  newfit <- obj$beta.zero+newdata%*%obj$beta/p
  newfit}

`testdata` <-
structure(list(Y = structure(c(-0.815145534387887, -3.14144988029276, 
-1.17889070028366, -1.92000648729773, -4.00607094094585, -1.13838605961241, 
4.36197994265646, 0.91546100249255, 1.11867943280704, 3.77936296013858, 
3.78059768781644, -0.315260211545767, -3.1798608293741, -1.27438975810178, 
-1.66575030588019, 8.01122524476408, -0.621476863364219, -1.65282239499654, 
1.44021484935303, -3.43161831140547, 2.37115618450104, -6.09465599811645, 
4.12542446865918, 1.44816335084864, -2.23086628080267, -0.0487323943777446, 
-4.51453347068487, 0.351985185246913, -4.51161150580738, -1.53181208297211, 
-5.62310440471725, -3.59397203942069, 0.622413280487798, 0.277528124561617, 
3.36964836085444, -2.6540072535501, 3.56624777098862, -3.52358536114513, 
2.27823612085242, -0.0560067503762269, 4.98077105212989, 4.22476860559161, 
-4.52237696289909, -1.68289137702390, -1.91179936309872, 2.71002196772100, 
3.80221853934983, 2.59483490200912, 0.587630319289851, 0.918219602519564
), .Dim = c(50L, 1L)), X = structure(c(1.04572628748922, -0.374387810147261, 
-0.225742022036369, -0.672275230178074, -0.337225347245522, -1.48825701204109, 
-0.0535173074463828, 0.225916721924019, -0.325654301826846, -0.662364306439466, 
0.31745748934134, 1.15916971392317, -1.20828946881141, 0.766310625509267, 
0.279305195069077, 2.42132744413313, 2.92896711296337, -0.521130932969204, 
0.0260643416220976, 0.185928615139413, -0.986431709710492, 0.547058784796922, 
2.08618666233191, -0.479582217064465, -1.19875952311062, -0.232820244947758, 
-1.7557814195664, -1.61925654956430, -0.198619828428786, 2.2112489814007, 
-1.57573607259429, -2.05503245300679, 1.76648785393917, -1.00948248693956, 
-0.203117118081569, 0.542147557211439, 0.0575524477809679, -0.348572608156526, 
0.081533875545654, -1.28794359480924, -0.919101523303744, 1.57542322700504, 
-0.196837845017551, 0.728280860157142, -0.716536493576101, 0.0845973269464789, 
1.75059685191408, -0.832920904198932, -0.302940521334382, 0.25236418435019, 
0.611087349120662, -0.177969860459613, 0.00885775646850853, -0.376856047558266, 
-0.537662278253643, -1.02884574193418, 0.244396817786217, 0.178922357422303, 
-0.0522103705965416, -0.68864232369818, 0.256226193131231, 0.697104694672958, 
-1.20422581372589, 0.680396960972931, 0.180523790223787, 2.17258012091202, 
1.73584545934100, -0.433994031375091, -0.101608277777448, 0.0590561649259232, 
-1.17856344684005, 0.205949909280188, 1.58673993784206, -0.365023491203659, 
-0.917314671472458, -0.189132015274164, -1.48798189642819, -1.09413672802087, 
-0.504715864397716, 1.67200763721133, -1.72591437846908, -1.65791471456763, 
1.33618162933776, -0.81678150934002, 0.0845470235821452, 0.104235031305627, 
0.110160719668687, -0.489741047409908, 0.211378357164854, -1.01200260718075, 
-0.723807210593691, 1.32818262482808, -0.221309326766070, 0.438362219351182, 
-0.569112693698301, -0.0727683369670075, 1.92462218946647, -0.831000180520812, 
-0.0124106718638141, 0.48252240001478, 0.250837244146622, -0.0183492506533708, 
0.171700600865819, -0.147107050178118, -0.679882634705122, -0.668542933676978, 
0.483702173729778, 0.132298482224804, 0.15906693345467, -0.660249571030787, 
0.219361899412791, 0.343164081149605, -1.19048188886199, 0.602988971136353, 
0.107364935041212, 1.95238078226065, 0.764550795423754, -0.352776259690006, 
-0.201919213956009, -0.0876666919646315, -1.27200827880814, -0.106310194733334, 
1.17817344685046, -0.272385751951982, -0.67354403993907, -0.146139966956744, 
-1.25372502824763, -0.645674250298313, -0.764800570985382, 1.25101299413337, 
-1.81665037756756, -1.31528422985618, 0.978972038132975, -0.64383064136629, 
0.306841959619862, -0.259242261092457, 0.156006125461689, -0.597380392882113, 
0.332474905193911, -0.801634278944397, -0.552909313389766, 1.12247207795297, 
-0.258200475007006, 0.171746875930453, -0.443049611896373, -0.188123560819529, 
2.04303471185469, -0.785712862059498, 0.222829647547024, 0.637383590491289, 
-0.0405896576027779, 0.106816308340321, 0.270083755832408, 0.0232948683355511, 
-0.769649089654605, -0.398115887086605, 0.669174316885293, 0.0862200200052433, 
0.314267162747985, -0.584610536388098, 0.204795216692533, 0.0863822458377656, 
-1.16789632700190, 0.533870290337102, 0.0570027974149741, 1.75880275490342, 
-0.00407825013938282, -0.277867833038626, -0.277832903901193, 
-0.250529229324971, -1.27903520905909, -0.389736033291201, 0.852663401595157, 
-0.199144283068357, -0.465035004539658, -0.103938033298772, -1.05033168142614, 
-0.268108255094358, -0.980993964477738, 0.936256027377165, -1.85391249376039, 
-1.02338299025013, 0.687953916700428, -0.489751664433526, 0.470097581268103, 
-0.554261029194989, 0.195535031386384, -0.674496594001262, 0.44449139544036, 
-0.649708445551194, -0.404107254258848, 0.954566289551722, -0.30506924826581, 
-0.0712104699687283, -0.337052980039724, -0.265493858867516, 
2.11023121214481, -0.702426937616906, 0.407544639015022, 0.724942029815468, 
-0.268758986297415, 0.199869105590318, 0.311304466045120, 0.14067281435592, 
-0.812724316156742, -0.208331901980200, 0.80558880375376, 0.0408618944373451, 
0.419479869704598, -0.46914970772093, 0.210456753476971, -0.0842064387779028, 
-1.13730776092779, 0.472824552912749, 0.0266115452386946, 1.58991936556470, 
-0.589203048699447, -0.209658966545625, -0.33231378460061, -0.425820720947813, 
-1.21191324103724, -0.64434211244097, 0.6023860143142, -0.142774368311708, 
-0.289374941303429, -0.0626201476035212, -0.875122722365125, 
0.0443221188932515, -1.15541606116074, 0.71572771215304, -1.84366915091820, 
-0.778452987127147, 0.456222101415753, -0.353666359956884, 0.580643779763388, 
-0.786797982214144, 0.229193803669181, -0.724095600195482, 0.547095703711737, 
-0.549094942452173, -0.275100455767818, 0.820739962796327, -0.359473605067933, 
-0.290155118210047, -0.249828529997763, -0.308904745367395, 2.13060848340291, 
-0.586510395994952, 0.546498504657069, 0.753191992023068, -0.439236372107165, 
0.263151430165475, 0.302659976180801, 0.211349894256169, -0.81487098726618, 
-0.0899582781748952, 0.897721190836172, -0.00360097080516742, 
0.480794606745707, -0.321291572980094, 0.234277118272619, -0.179567600212743, 
-1.09955482342182, 0.41963539320086, 0.0133653464059949, 1.44380394096888, 
-1.00998497160747, -0.148539875335678, -0.368326293041865, -0.609830440625878, 
-1.08291137818692, -0.870142938230197, 0.419517497245639, -0.100751291440958, 
-0.144151226259586, -0.0222802431742648, -0.725419017465989, 
0.297377732966776, -1.29018687732035, 0.577419023671336, -1.79188877291165, 
-0.57673621186492, 0.276871428654581, -0.234696509351522, 0.644810446342236, 
-0.962829829362099, 0.257428808536491, -0.749183360892895, 0.639955705815578, 
-0.492663605098361, -0.163588340483553, 0.717267800858791, -0.418971503938825, 
-0.484732368657189, -0.180081993639898, -0.322381734575597, 2.10856331869506, 
-0.443331225995553, 0.644455446590054, 0.730127751149842, -0.557587445201907, 
0.299005571134647, 0.251447530916297, 0.241649214409476, -0.781851776037568, 
-0.0337623154878226, 0.950347034633524, -0.046993652048571, 0.504300926292505, 
-0.148460620116406, 0.274186919585991, -0.210666865982099, -1.05547614726618, 
0.374086445539006, 0.0144383688104964, 1.31852980784035, -1.28558539021448, 
-0.0949007745334619, -0.388834866212568, -0.798847662151886, 
-0.904298623952465, -1.06715301670644, 0.296234062627521, -0.0705503362150292, 
-0.0269512354373345, 0.0169877466857240, -0.598541433130142, 
0.496819448428475, -1.38742642924252, 0.509320937142388, -1.70453978361139, 
-0.414474655841127, 0.14299673479254, -0.131963894032598, 0.668927472241168, 
-1.08833327985103, 0.280686412214723, -0.752765825521626, 0.722739277559418, 
-0.473284268940786, -0.0672703309729344, 0.640424506911116, -0.481120903403938, 
-0.654587521173837, -0.126519102835536, -0.309950340748549, 2.04849251108733, 
-0.278257416420624, 0.706179666930866, 0.66374358123154, -0.629377835751517, 
0.309773817566689, 0.164964374928451, 0.237893881189022, -0.719429355525553, 
-0.0305113137361155, 0.968241891646813, -0.0891412256191422, 
0.496088380766190, 0.0419186629193211, 0.328116765923599, -0.188469863601314, 
-1.00591036524303, 0.335961344264756, 0.0270047803458205, 1.2121702929035, 
-1.43516567587151, -0.0491318792636508, -0.396803941100327, -0.989161659318554, 
-0.68834398177821, -1.23538685391725, 0.224711922697895, -0.0496467863928447, 
0.0646376551341199, 0.0550898886731718, -0.49181083575899, 0.648408126580608, 
-1.44925473321321, 0.499424427776533, -1.58759060688806, -0.287910310433451, 
0.047692856205261, -0.0445902954152663, 0.659324748696703, -1.16928504289311, 
0.299412980930288, -0.737848943509799, 0.795114294750794, -0.483826769430473, 
0.0161541501971588, 0.586484784125304, -0.543479761988723, -0.799365875623677, 
-0.0878455894540869, -0.275636078142682, 1.9547928536458, -0.096656956072082, 
0.736435367796396, 0.562033756303913, -0.660173173925873, 0.297798458530458, 
0.0505077528941108, 0.206407000967986, -0.633366398784783, -0.0709725727369067, 
0.956181318377032, -0.129868767843158, 0.462246522587958, 0.242421788176274, 
0.393997265791957, -0.123942220585730, -0.951696110134547, 0.305043723715677, 
0.0482387489055885, 1.12279872288271, -1.47788719992959, -0.0116234046509205, 
-0.395197954692749, -1.17706170591860, -0.447316455108489, -1.37485895591019, 
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