NR {lmfor}

Solve a Nonlinear Equation Using Newton-Raphson algorithm.

Description

Solves an equation equation of form f(x)=0, for scalar x using the Newton-Raphson algorithm.

Usage

NR(init, fn, gr, crit = 6, range = c(-Inf, Inf))

Arguments

init

Numeric scalar, The initial guess for x.

fn

An R-function returning the scalar value of f(x), with x as the only argument.

gr

An R-function returning the first derivative of f(x), with x as the only argument.

crit

Convergence criteria. The upper limit for the absolute value of f(x) at an accepted the solution.

range

A two-unit vector giving the upper and lower bounds for x. The solution is searched from within this range.

Details

The function is a straightforward implementation of the well-known Newton-Raphson algorithm.

Value

A list of components

par

the value of x in the solution

crit

the value of f(x) at the solution

If estimation fails (no solution is found during 100000 iterations), both e lements of the solution are NA's.

Author(s)

Lauri Mehtatalo <[e-mail]>

See Also

See NRnum for a vector-valued x without analytical gradients.

Examples

## Numerically solve Weibull shape for a stand
## where DGM=15cm, G=15m^2/ha and N=1000 trees per ha
func<-function(shape,G,N,DGM) {
##      print(G,DGM,N)
      val<-pi/(4*gamma(1-2/shape)*log(2)^(2/shape))-G/(N*DGM^2)
      val
      }

grad<-function(shape) {
      pi/4*(-1)*                                                            
      (gamma(1-2/shape)*log(2)^(2/shape))^(-2)*                             
      (gamma(1-2/shape)*digamma(1-2/shape)*2*shape^(-2)*log(2)^(2/shape)+   
      log(2)^(2/shape)*log(log(2))*(-2)*shape^(-2)*gamma(1-2/shape))         
      }
      
shape<-NR(5,fn=function(x) func(x,G=10000*15,1000,15),gr=grad,crit=10,range=c(2.1,Inf))$par