R : Copyright 2005, The R Foundation for Statistical Computing
Version 2.1.1 Patched (2005-08-04), ISBN 3-900051-07-0

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> 
>  library(aster)
> 
>  set.seed(42)
>  nind <- 25
>  nnode <- 5
>  ncoef <- nnode + 1
> 
>  famnam <- families()
>  fam <- c(1, 1, 2, 3, 3)
>  print(famnam[fam])
[1] "bernoulli"        "bernoulli"        "poisson"          "non.zero.poisson"
[5] "non.zero.poisson"
> 
>  pred <- c(0, 1, 1, 2, 3)
>  print(pred)
[1] 0 1 1 2 3
> 
>  modmat <- array(0, c(nind, nnode, ncoef))
>  modmat[ , , 1] <- 1
>  for (i in 2:nnode)
+      modmat[ , i, i] <- 1
>  modmat[ , , ncoef] <- rnorm(nind * nnode)
> 
>  beta <- rnorm(ncoef) / 10
> 
>  phi <- matrix(modmat, ncol = ncoef) %*% beta
>  phi <- matrix(phi, ncol = nnode)
> 
>  theta <- .C("aster_phi2theta",
+      nind = as.integer(nind),
+      nnode = as.integer(nnode),
+      pred = as.integer(pred),
+      fam = as.integer(fam),
+      phi = as.double(phi),
+      theta = matrix(as.double(0), nind, nnode))$theta
> 
>  root <- sample(1:3, nind * nnode, replace = TRUE)
>  root <- matrix(root, nind, nnode)
> 
>  x <- raster(theta, pred, fam, root)
>  
>  out <- mlogl(beta, pred, fam, x, root, modmat, deriv = 2,
+      type = "unco")
>  print(out)
$value
[1] 123.9680

$gradient
[1] 41.9553321  0.5679575 12.9399758 -1.4608417 28.3767383 27.9290757

$hessian
          [,1]      [,2]       [,3]      [,4]       [,5]       [,6]
[1,] 618.58754 40.278506 173.359839 72.121848 305.696826  26.306053
[2,]  40.27851 11.702546   3.353047 17.380877   5.231394  -2.212379
[3,] 173.35984  3.353047  61.948882  4.980101  96.895585  10.514502
[4,]  72.12185 17.380877   4.980101 38.114502   7.770363  -1.323664
[5,] 305.69683  5.231394  96.895585  7.770363 186.157029  20.455780
[6,]  26.30605 -2.212379  10.514502 -1.323664  20.455780 303.041693

> 
>  my.value <- 0
>  for (j in 1:nnode) {
+      k <- pred[j]
+      if (k > 0)
+          xpred <- x[ , k]
+      else
+          xpred <- root[ , j]
+      for (i in 1:nind)
+          my.value <- my.value -
+              sum(x[i, j] * theta[i, j] -
+              xpred[i] * famfun(fam[j], 0, theta[i, j]))
+  }
>  all.equal(out$value, my.value)
[1] TRUE
> 
>  my.grad <- NaN * out$gradient
>  epsilon <- 1e-9
>  for (i in 1:ncoef) {
+      beta.eps <- beta
+      beta.eps[i] <- beta[i] + epsilon
+      out.eps <- mlogl(beta.eps, pred, fam, x, root, modmat, deriv = 0,
+          type = "unco")
+      my.grad[i] <- (out.eps$value - out$value) / epsilon
+  }
> 
>  all.equal(out$gradient, my.grad, tolerance = sqrt(epsilon))
[1] TRUE
> 
>  ##########
> 
>  objfun <- function(beta) {
+      out <- mlogl(beta, pred, fam, x, root, modmat, deriv = 1,
+          type = "unco")
+      result <- out$value
+      attr(result, "gradient") <- out$gradient
+      return(result)
+  }
>  nout <- nlm(objfun, beta, fscale = nind)
Warning message:
NA/Inf replaced by maximum positive value 
>  print(nout)
$minimum
[1] 119.1048

$estimate
[1] -0.06808120 -0.30707635  0.18622920  0.07756716 -0.37637382 -0.08436003

$gradient
[1]  9.348637e-06 -3.147490e-05 -6.786827e-06 -5.396298e-06  9.976263e-06
[6] -5.169924e-06

$code
[1] 1

$iterations
[1] 34

>  nout <- nlm(objfun, nout$estimate, fscale = nind)
>  print(nout)
$minimum
[1] 119.1048

$estimate
[1] -0.06808120 -0.30707635  0.18622920  0.07756716 -0.37637382 -0.08436003

$gradient
[1]  9.348637e-06 -3.147490e-05 -6.786827e-06 -5.396298e-06  9.976263e-06
[6] -5.169924e-06

$code
[1] 1

$iterations
[1] 0

> 
>  ##########
> 
>  my.hess <- matrix(NaN, ncoef, ncoef)
>  for (i in 1:ncoef) {
+      beta.eps <- beta
+      beta.eps[i] <- beta[i] + epsilon
+      out.eps <- mlogl(beta.eps, pred, fam, x, root, modmat, deriv = 1,
+          type = "unco")
+      my.hess[ , i] <- (out.eps$gradient - out$gradient) / epsilon
+  }
> 
>  all.equal(out$hessian, my.hess, tolerance = sqrt(epsilon))
[1] TRUE
> 
>  ##########
> 
>  objfun <- function(beta) {
+      out <- mlogl(beta, pred, fam, x, root, modmat, deriv = 2,
+          type = "unco")
+      result <- out$value
+      attr(result, "gradient") <- out$gradient
+      attr(result, "hessian") <- out$hessian
+      return(result)
+  }
>  nout <- try(nlm(objfun, beta, fscale = nind))
>  print(nout)
$minimum
[1] 119.1066

$estimate
[1] -0.08160559 -0.28811978  0.18178346  0.09066000 -0.34973178 -0.08345522

$gradient
[1] -0.027848502  0.008147191 -0.078372174  0.004814663  0.103718207
[6]  0.050151163

$code
[1] 4

$iterations
[1] 100

>  nout <- nlm(objfun, nout$estimate, fscale = nind, iterlim = 1000)
>  print(nout)
$minimum
[1] 119.1048

$estimate
[1] -0.06817031 -0.30695488  0.18633158  0.07765277 -0.37628604 -0.08435880

$gradient
[1] -1.186810e-04  2.504815e-05  7.096403e-05  3.026907e-05  8.608913e-05
[6]  6.624982e-05

$code
[1] 1

$iterations
[1] 920

> 
>  ##########
> 
>  objfun <- function(beta)
+      mlogl(beta, pred, fam, x, root, modmat, deriv = 0, type = "unco")$value
>  gradfun <- function(beta)
+      mlogl(beta, pred, fam, x, root, modmat, deriv = 1, type = "unco")$gradient
>  oout <- optim(beta, objfun, gradfun, method = "L-BFGS-B")
>  print(oout)
$par
[1] -0.06830710 -0.30690581  0.18662418  0.07786878 -0.37623632 -0.08435202

$value
[1] 119.1048

$counts
function gradient 
      38       38 

$convergence
[1] 0

$message
[1] "CONVERGENCE: REL_REDUCTION_OF_F <= FACTR*EPSMCH"

> 
>