cheb (version 0.3)

chebR: chebR

Description

Discrete Linear Chebyshev Approximation

Usage

chebR(a, b, tol = 1e-15, relerr = 0)

Arguments

a

matrix with left-hand sides

b

vector with right-hand sides

tol

a small positive tolerance

relerr

relative error

Value

A list with the following components:

coefs

regression coefficients

resids

signed residuals

rank

rank of coefficient matrix

iter

number of simplex iterations performed

ocode

error code: ocode=0 for a probably non-unique solution, ocode=1 for a unique solution, ocode=2 for premature termination due to rounding errors

Details

R Interface to the CHEB code by Barrodale and Philips for Discrete Linear Chebyshev Approximation. Computes the Chebyshev solution to an overdetermined system of linear equations.

relerr is a real variable which on entry must have the value 0.0 if a Chebyshev solution is required. If relerr is positive, the subroutine calculates an approximate solution with relerr as an upper bound on the relative error of its largest residual.

References

I. Barrodale and C. Philips. Algorithm 495 – Solutions of an Overdetermined System of Linear Equations in the Chebyshev Norm. ACM Transactions on Mathematical Software, 1:264–270, 1975.d

Examples

a<-matrix(rnorm(20),10,2)
b<-rnorm(10)
chebR(a,b)
## The function is currently defined as
function(a,b,tol=1e-15,relerr=0.0) {
m<-nrow(a); n<-ncol(a); ndim<-n+3; mdim<-m+1
if (n > m) stop("number of equations exceeds number of unknowns")
aa<-matrix(0,ndim,mdim); bb<-rep(0,mdim); xx<-rep(0,ndim)
aa[1:n,1:m]<-t(a); bb[1:m]<-b
rlist<-.Fortran("cheb",as.integer(m),as.integer(n),as.integer(m+1),as.integer(n+3),
	as.single(aa),bb=as.single(bb),as.single(tol),as.single(relerr),xx=as.single(xx),
	rank=as.integer(0),resmax=as.single(0.0),iter=as.integer(0),ocode=as.integer(0))
return(list(coefs=rlist$xx[1:n],resids=rlist$bb[1:m],rank=rlist$rank,iter=rlist$iter,ocode=rlist$ocode))
  }