R/MakeJ.R

In CorReg: Linear Regression Based on Linear Structure Between Variables

#  '  Constructs the jacobian for the constrained likelihood
#  ' @param B matrice p+1 x p
# ' @param X dataset n x p
# ' @param A Fixed p+1 coefficient vector for the main regression
#  ' @param Z p squared binary matrix describing the structure (adjacency matrix)
# ' @param Sigma p2 vector of standard deviations for each subregression
# '@export
MakeJ <- function(X = X, Z = Z, B = B, Sigma = Sigma, A = A) {
   X = cbind(1, X)
   I2 = which(colSums(Z) != 0)
   p2 = length(I2)
   Z = rbind(0, Z)
   Z[1, I2] = 1 # on ajoute une constante a chaque ssreg
   Z = cbind(0, Z)
   I2 = I2 + 1
   pz = sum(Z != 0)
   p1 = length(which(rowSums(Z[-I2, ]) != 0)) # I3 ne doit pas intervenir
   n = nrow(X)
   J = matrix(0, ncol = (p1 + p2 + pz), nrow = (p1 + p2 + pz))
   barZ = which(Z != 0, arr.ind = TRUE)
   for (j in 1:p2) {
      I1j = barZ[barZ[, 2] == I2[j], 1]
      J[pz + p1 + j, pz + p1 + j] = 2 * Sigma[j] # bloc J9
      debcolj = nrow(barZ[barZ[, 2] < I2[j], ])
      colonne = (debcolj + 1):(debcolj + sum(Z[, I2[j]])) # sous-reg precedentes+
      J[pz + p1 + j, colonne] = (2 / n) * t(X[, I2[j]] - X[, I1j] %*% B[I1j, I2[j] - 1]) %*% X[, I1j] # bloc J7
      diag(J[pz + (1:p1), which(barZ[, 2] == I2[j])]) = A[I2[j]] # attention on compte l'intercept #blocJ4
      J[colonne, pz + p1 + j] = (-2 / (Sigma[j]^3)) * t(X[, I1j]) %*% (X[, I2[j]] - X[, I1j] %*% B[I1j, I2[j] - 1]) # bloc J3
      diag(J[which(barZ[, 2] == I2[j]), pz + (1:p1)]) = A[I2[j]] # attention on compte l'intercept #bloc J2
      diag(J[colonne, colonne]) = (-1 / (Sigma[j]^2)) * diag(t(X[, I1j]) %*% (X[, I1j])) # bloc J1
   }
   return(J)
}