"dd" <-
function(y,X,lambda=1,tol=0.001,maxit=10,family=binomial,int=T,lambda2=.001,tol.zero=10^-6,gauss=T){
    # Add column to X for intercept.
    if (int)
      X <- cbind(1,X)
    p <- ncol(X)
    gds.beta <- dd.beta <- gauss.beta <- rep(0,p)
    # Compute GDS estimates for beta.
    gdsfit <- gds(y,X,lambda,tol,maxit,family,int=F)
    gds.beta <- gdsfit$beta
    sig.vars <- NULL
    if (sum(abs(gds.beta)>tol.zero)>0){
    # Determine non-zero betas and compute design matrix for the
    # corresponding variables.
      sig.vars <- (1:p)[abs(gds.beta)>tol]
      sig.X <- cbind(X[,sig.vars])
    # Compute the DD estimates.
      ddfit <- gds(y,sig.X,lambda2,tol,maxit,family,int=F)
      dd.beta[sig.vars] <- ddfit$beta
    # Compute the Gauss-Dantzig estimates.
      if (gauss)
      gauss.beta[sig.vars] <- glm(y~sig.X-1,family=family)$coef
    }
    list(gds.beta=gds.beta,dd.beta=dd.beta,gauss.beta=gauss.beta,lambda=lambda,lambda2=lambda2,iterations=gdsfit$iterations)}

"dd.cv" <-
function(Y,X,lambda,cv=10,s=NULL,int=T,family=binomial,lambda2=.001,trace=F){
    if (is.character(family)) 
      family <- get(family, mode = "function", envir = parent.frame())
    if (int)
      X <- cbind(1,X)
    n <- length(Y)
    # Determine the randomization of the data.
    if (is.null(s))
      s <- sample(n,replace=F)
    lambdalen <- length(lambda)
    error <- rep(0,lambdalen)
    for (j in 1:lambdalen){
      for (i in 1:cv){
    # Produce the left out portion of the data.
        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,]
    # Produce the training data.
        trainY <- Y[-test.index]
        trainX <- X[-test.index,]
    # Compute the DD estimates for beta on the training data.
        trainfit <-dd(trainY,trainX,lambda[j],int=F,family=family,lambda2=lambda2,gauss=F)$dd.beta
    # Compute the deviance on the left out portion of the data.
        muhat <- family()$linkinv(testX%*%trainfit)
        error[j] <- error[j]+sum(family()$dev(testY,muhat,1))
      }
      if (trace)
        print(paste("Finished lambda = ",lambda[j]))
    }
    # Print the optimal value of lambda.
    if (trace)
      print(paste("Min lambda = ",lambda[which.min(error)]))      
    list(lambda=lambda,error=error,s=s,optimal=lambda[which.min(error)])}

"gds" <-
function(y,X,lambda=1,tol=0.001,maxit=10,family=binomial,int=T){
    if (is.character(family)) 
      family <- get(family, mode = "function", envir = parent.frame())
    # Add column to X for intercept.
    if (int)
      X <- cbind(1,X)
    weights <- 1
    p <- ncol(X)
    nobs <- length(y)
    # Set initial values for X*beta 
    if (family()$family!="gaussian")
    eval(family()$initialize)
    else
      mustart <- y
    muzero <- mustart
    xbeta <- family()$linkfun(muzero)
    # Initialize the beta vector
    beta.old <- rep(2,p)
    beta.new <- rep(1,p)
    num.it <- 1
    # Start iterative weighted Dantzig Algorithm
    while(sum(abs(beta.new-beta.old))/(tol+sum(abs(beta.old)))>tol &
          num.it<=maxit){
      beta.old <- beta.new
      V <- family()$var(muzero)
      Z <- xbeta+(y-muzero)/V
      # Zstar and Xstar correspond to the weighted new response and design
      # matrix. 
      Zstar <- sqrt(V)*Z
      Xstar <- sqrt(V)*X
      # Rescale the design matrix to have columns of norm one.
      colscale <- apply(X,2,function(x){sqrt(sum(x^2))})
      Xstar <- t(t(Xstar)/colscale)
      # linearoptim computes the linear programming solution for the new
      # beta estimate. 
      beta.new <-linearoptim(Zstar,Xstar,lambda,sqrt(2*log(p)))/colscale
      # Update X*beta and muhat.
      xbeta <- as.vector(X%*%beta.new)
      muzero <- family()$linkinv(xbeta)
      if (sum(abs(beta.new))==0) warning("Beta all zero")
      num.it <- num.it+1
    }
    list(beta=beta.new,iterations=num.it-1,L1=sum(abs(beta.new*colscale)),lambda=lambda)
  }

"linearoptim" <-
function(Y,X,sigma,lambdap){
    p <- ncol(X)
    f.obj <- rep(1,2*p)
    XX <- t(X)%*%X
    b1 <- lambdap*sigma-as.vector(t(X)%*%Y)
    b2 <- lambdap*sigma+as.vector(t(X)%*%Y)
    f.con <- rbind(-XX,XX)
    f.con <- cbind(f.con,-f.con)
    f.rhs <- c(b1,b2)
    f.dir <- rep("<=",2*p)
    lpout <- lp("min",f.obj,f.con,f.dir,f.rhs)
    gamma <- lpout$solution[1:p]-lpout$solution[-(1:p)]
    if (lpout$status==2)
      print("Warning: No Solution Found")
    gamma}

"X" <-
structure(c(-2.32879318448734, 2.21544653343575, 1.01662353277786, 
0.729874909060432, -0.820929218005718, 1.72572271810397, 1.32695724646609, 
-0.468377747920094, 0.675998730182393, 1.36875458475311, 0.21997066381779, 
0.620282999691934, -2.22811563010229, 1.80101066313167, 1.41577816035736, 
-1.20038458454913, -0.575412349920434, -0.0140030966667093, -0.221561827746805, 
0.726123181379953, -0.0523449935370128, 0.685936286251573, 0.0808797886196207, 
0.446442247345510, -0.564660602974651, -0.598100226496101, -1.04175217323897, 
2.51979450885922, -0.138309433489977, 1.42446905750012, 0.392657190867863, 
0.0650140720041818, 0.696456329865136, 0.31263157283462, 2.07432986102694, 
-0.184574123861624, -1.35466573933667, 0.916481481293875, 0.537293704616908, 
-0.690261724893343, 0.903100043887345, -0.791875519476372, 1.23435123229575, 
0.537818918874935, -0.665349380910091, 0.421467295165087, -0.692635958702744, 
1.62300186537167, 0.174022187551898, 0.057759749738413, -0.499990869324146, 
-0.619996520150812, 0.643853236948264, -0.418555154241308, 0.0253133492550712, 
-0.323837761799265, -2.38810992769837, -0.407980614612721, -0.236650473617717, 
1.73947105934868, 1.57133992419121, 2.02233197793502, 1.82168128568298, 
0.391279479244774, -0.32171323880592, 1.14086195999397, 0.271753856377144, 
-1.36728562709877, 0.797978773212606, -0.486947212072696, -1.15496941141718, 
-0.0484786494013809, -1.11936549313623, -1.05586946950875, -0.455797569508131, 
0.63035922828248, -1.11354592632429, 0.313799595317743, -0.616965280953186, 
-0.404226652908102, 0.530372623035164, -0.702831080582944, -0.752815578779642, 
1.29054586675973, -0.732520389898227, -0.537644164106454, -0.89584077421562, 
-1.17389056423862, -0.944686418476437, 0.144560826046175, -0.163361422893306, 
0.213017842110982, -0.653028431980568, -0.116298523068096, -0.886712767780863, 
-0.134799937390872, 0.596024459857607, 0.922736855155713, -0.561042759463318, 
0.936705721101377, -0.431805893186004, 0.219572013711018, 0.106731778174903, 
0.733646459325024, -0.539051990461157, 1.27730465439259, 0.411595397835077, 
0.866731072387015, -0.302949817912798, -0.764655232295964, -0.697444077906182, 
0.904440220438481, 0.240817480416544, 0.143991372238938, 0.300558654608085, 
-0.0340755700026112, -1.31758719187134, -0.617899615637195, 0.153609033349740, 
0.549745906889739, 0.937512382614595, 0.223198587652608, 1.34923531136694, 
1.56790373648252, 0.306788994552756, 0.666452326917032, 0.295924470587600, 
-0.883517797614564, 0.790918540919896, -1.80248767711325, 1.35638314572398, 
-0.615507254059989, 1.23205299431026, -0.0347108881096039, 0.460050424696302, 
0.789678201700174, 2.01995748055608, -0.416196797753661, 0.320954963874743, 
-0.662260319208222, 1.64698424304247, -0.0542850119201105, 1.45757576640545, 
0.340198142721445, -1.41217165932499, -0.0142714878355667, 0.6151986883652, 
-0.929627671763573, 1.63146542476703, 0.0385974734358371, -0.396098750563441, 
0.580115419821961, 0.188455259500988, -0.558149583554868, 1.21131382743368, 
-0.238351059163313, 1.31266401780783, 0.264783490157525, 1.03780208169579, 
0.423617804286210, 1.08282380983675, -0.0517826702974574, -1.17434464861673, 
0.417697310571988, -0.768149019137103, -0.888473909689998, 2.14220546560758, 
-1.07015639196376, -0.631603604995248, -1.29619087029133, 1.48481145905179, 
0.0192212223038742, -0.855741005987011, -1.07841936568715, -0.539156994059163, 
-0.192323359923102, 0.593248379136963, 0.419683667575279, -0.970026844765552, 
0.270486455084178, -0.802306110997362, 1.05356370332693, -0.145548059785189, 
0.969671924748243, -1.99825004386812, -0.135176544009973, 0.449357443413167, 
0.544919408761955, 1.28299830895204, -2.04445688655824, -0.153441543158741, 
-0.935028994142539, 0.566594175218874, -1.09540849237205, 0.0204916346815683, 
0.503063959007974, -1.61676473049726, 1.13242119189494, -1.78561606153664, 
0.484825125251108, -0.0782748018720911, -0.445194006853718, 0.367666071377939, 
-2.16103480728696, -1.49979069569815, 0.486625949413924, -0.350473206437820, 
-0.347107302296917, 0.596116306392842, 0.0452341244080496, 1.25187535868746, 
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-0.156323306607294, -0.241219858452594, 1.73825558212255, 0.365409158863655, 
-0.748192969256712, 0.632957638230113, -1.54317725391535, 0.784690205416667, 
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-0.576371286626616, -0.630304404353771, 1.27980343936840, -0.691667637086334, 
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0.475648476656072, 1.58029724152961, -1.32379196355471, -0.981829643329212, 
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-0.0384840743289531, 0.583806038792608, -1.42305449880838, -0.72265025280224, 
-1.03992870917191, 0.0739739394620606, 0.324096118249759, -1.19712324403347, 
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-0.810233905520656, -0.716911353402793, 1.66325247199496, -0.513265169825234, 
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-0.382993517211973, -0.641214555178291, -0.0285266096186368, 
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-0.480938174427491, -0.460745110229635, -0.0970444048711286, 
-0.113100765995651, -2.35267907727568, 1.71100114825487, -0.763118661806805, 
-0.658953688732989, 0.207761542961540, -1.21194659867965, -1.52240233488241, 
0.215665913605225, 0.741659854453683, 0.182016674042254, 0.636746643276828, 
-0.96257971321646, -0.80598963113916, -0.503643945676312, 0.256218541041034, 
-0.102568248418714, 0.0102866797161375, 0.307849140711101, 0.597827096583711, 
0.553539208864078, 2.3255325169045, 1.26119363804960, -0.41307921974452, 
-0.667926267410786, 0.0157750508422494, -1.13493716490660, 1.08830745118744, 
1.35278688336712, 1.02708754414484, 0.58218483761059, -1.01378603298639, 
-0.938159650952002, -0.0336367667507330, 0.0649002971933338, 
-0.215235534882975, 1.54276448825337, 1.08888642071526, 0.541866890605418, 
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-0.511741504096861, 0.654443941446116, 1.02526715454372, -0.214328423831622, 
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-2.80520243864212, -0.147345378546930, -1.1293382450648, -1.85523652631410, 
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-1.60458234100780, -0.446137022253272, 0.20410175643411, 0.677979040183188, 
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-0.0991431012187625, -2.65039282617326, -1.60126401582609, 2.44905313660311, 
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-1.49112386070500, 0.518146249275876, 0.404006870238268, 1.15984800634436, 
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-0.851243586565548, 1.17581233652973, 0.852084912309662, -1.3562580916361, 
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-0.776709988151919, -1.05950227578534, -2.33499151319719, 0.0395247992390896, 
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-1.72948724357147, 0.189613139113561, 0.689073113763994, 0.564613763071743, 
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-1.06892201880083, 3.31892272519127, 1.44606348372735, 0.800726785999269, 
-1.08311554016510, -1.30509099635020, -1.26787472146628, -0.791989544846194, 
-0.59755916453328, -1.60043445670179, 1.79586320845268, 0.53057828067517, 
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-0.400161897521362, 0.555889979631658, 1.14677438577066, 0.748552151107001, 
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0.696003587905484, -0.0929813210164307, -0.781772239076215, 0.866600088097931, 
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0.837500685624244, -2.52480812211321, 1.74438170318462, -0.411257795488144, 
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0.152757292235777, 1.53997443683171, 0.137185398510527, 0.99239673897036, 
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0.034649092431275, -0.0269341446690613, 0.438280148041560, 0.621527582243276, 
0.158412016415774, 0.328530504802913, 0.607268962024232, -0.158354595087638, 
0.177156641275047, -0.326118129700421, 1.64840014990480, -1.24813810687968, 
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-1.27066455218853, -1.50077986431725, 0.942536005247458, -0.856950606238877, 
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-1.54332155812310, 0.100299201273349, -1.13228938130509, -0.342863487715928, 
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0.35788819232612, -0.158334240845491, -1.55892009279792), .Dim = as.integer(c(100, 
20)))
"ybinom" <-
c(0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 
1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 
0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 
1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 
1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1)