e04hy {NAGFWrappers} R Documentation

## e04hy: Unconstrained minimum of a sum of squares, combined Gauss-Newton and modified Newton algorithm, using second derivatives (easy-to-use)

### Description

e04hy is an easy-to-use modified Gauss-Newton algorithm for finding an unconstrained minimum of a sum of squares of m nonlinear functions in n variables (m >= n). First and second derivatives are required.

It is intended for functions which are continuous and which have continuous first and second derivatives (although it will usually work even if the derivatives have occasional discontinuities).

### Usage

e04hy(m, lsfun2, lshes2, x,
n = nrow(x))


### Arguments

 m integer lsfun2 function You must supply this function to calculate the vector of values f_i(x) and the Jacobian matrix of first derivatives ( \partial f_i)/( \partial x_j) at any point x. It should be tested separately before being used in conjunction with e04hy (see the E04 chapter introduction in the Fortran Library documentation). (FVEC,FJAC) = lsfun2(m,n,xc,ldfjac)  lshes2 function You must supply this function to calculate the elements of the symmetric matrix B(x) = ∑_i = 1^mf_i(x)G_i(x), at any point x, where G_i(x) is the Hessian matrix of f_i(x). It should be tested separately before being used in conjunction with e04hy (see the E04 chapter introduction in the Fortran Library documentation). (B) = lshes2(m,n,fvec,xc,lb)  x double array x[j] must be set to a guess at the jth component of the position of the minimum for j=1 . . . n. The function checks lsfun2 and lshes2 at the starting point and so is more likely to detect any error in your functions if the initial x[j] are nonzero and mutually distinct. n integer: default = nrow(x) The number m of residuals, f_i(x), and the number n of variables, x_j.

### Details

R interface to the NAG Fortran routine E04HYF.

### Value

 X double array The lowest point found during the calculations. Thus, if ifail =0 on exit, x[j] is the jth component of the position of the minimum. FSUMSQ double The value of the sum of squares, F(x), corresponding to the final point stored in x. IFAIL integer ifail =0 unless the function detects an error or a warning has been flagged (see the Errors section in Fortran library documentation).

NAG

### Examples


ifail <- 0
lsfun2 = function(m, n, xc, ljc) {

fvec <- as.matrix(mat.or.vec(m, 1))
fjacc <- as.matrix(mat.or.vec(ljc, n))
for (i in c(1:m)) {
denom <- xc[2] %*% user(2)[i, 2] + xc[3] %*% user(2)[i,
3]

fvec[i] <- xc[1] + user(2)[i, 1]/denom - user(1)[i]

fjacc[i, 1] <- 1

dummy <- -1/(denom %*% denom)

fjacc[i, 2] <- user(2)[i, 1] %*% user(2)[i, 2] %*% dummy

fjacc[i, 3] <- user(2)[i, 1] %*% user(2)[i, 3] %*% dummy
}
list(FVEC = as.matrix(fvec), FJAC = as.matrix(fjacc))
}
lshes2 = function(m, n, fvec, xc, lb) {

b <- as.matrix(mat.or.vec(lb, 1))
sum22 <- 0
sum32 <- 0
sum33 <- 0
for (i in c(1:m)) {
dummy <- 2 %*% user(2)[i, 1]/(xc[2] %*% user(2)[i, 2] +
xc[3] %*% user(2)[i, 3])^3

sum22 <- sum22 + fvec[i] %*% dummy %*% user(2)[i, 2]^2

sum32 <- sum32 + fvec[i] %*% dummy %*% user(2)[i, 2] %*%
user(2)[i, 3]

sum33 <- sum33 + fvec[i] %*% dummy %*% user(2)[i, 3]^2
}
b[3] <- sum22
b[5] <- sum32
b[6] <- sum33
list(B = as.matrix(b))
}

m <- 15

x <- matrix(c(0.5, 1, 1.5), nrow = 3, ncol = 1, byrow = TRUE)

x <- matrix(c(0.5, 1, 1.5), nrow = 3, ncol = 1, byrow = TRUE)

y <- matrix(c(0.14, 0.18, 0.22, 0.25, 0.29, 0.32,
0.35, 0.39, 0.37, 0.58, 0.73, 0.96, 1.34, 2.1, 4.39), nrow = 1,
ncol = 15, byrow = TRUE)

t <- matrix(c(1, 15, 1, 2, 14, 2, 3, 13, 3, 4, 12,
4, 5, 11, 5, 6, 10, 6, 7, 9, 7, 8, 8, 8, 9, 7, 7, 10, 6,
6, 11, 5, 5, 12, 4, 4, 13, 3, 3, 14, 2, 2, 15, 1, 1), nrow = 15,
ncol = 3, byrow = TRUE)

user <- function(switch_integer) {
switch(switch_integer, y, t, 3)
}

e04hy(m, lsfun2, lshes2, x)



[Package NAGFWrappers version 24.0 Index]