e04bb {NAGFWrappers} R Documentation

## e04bb: Minimum, function of one variable, using first derivative

### Description

e04bb searches for a minimum, in a given finite interval, of a continuous function of a single variable, using function and first derivative values. The method (based on cubic interpolation) is intended for functions which have a continuous first derivative (although it will usually work if the derivative has occasional discontinuities).

### Usage

```e04bb(funct, e1, e2, a, b, maxcal)
```

### Arguments

 `funct` function You must supply this function to calculate the values of F(x) and (dF)/(dx) at any point x in [ab]. ```(FC,GC) = funct(xc) ``` `e1` double The relative accuracy to which the position of a minimum is required. (Note that, since e1 is a relative tolerance, the scaling of x is automatically taken into account.) `e2` double The absolute accuracy to which the position of a minimum is required. e2 should be no smaller than 2ε. `a` double The lower bound a of the interval containing a minimum. `b` double The upper bound b of the interval containing a minimum. `maxcal` integer The maximum number of calls of funct to be allowed.

### Details

R interface to the NAG Fortran routine E04BBF.

### Value

 `E1` double If you set e1 to 0.0 (or to any value less than ε), e1 will be reset to the default value sqrt(ε) before starting the minimization process. `E2` double If you set e2 to 0.0 (or to any value less than ε), e2 will be reset to the default value sqrt(ε). `A` double An improved lower bound on the position of the minimum. `B` double An improved upper bound on the position of the minimum. `MAXCAL` integer The total number of times that funct was actually called. `X` double The estimated position of the minimum. `F` double The function value at the final point given in x. `G` double The value of the first derivative at the final point 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
funct = function(xc) {

fc <- sin(xc)/xc
gc <- (cos(xc) - fc)/xc
list(FC = fc, GC = gc)
}

e1 <- 0

e2 <- 0

a <- 3.5

b <- 5

maxcal <- 30

e04bb(funct, e1, e2, a, b, maxcal)

```

[Package NAGFWrappers version 24.0 Index]