r - Using rootSolve for non-linear system in matrix form -
for part of thesis have write programm, solves system of non-linear equations:
where $\lambda$ diagonal matrix $\lambda_1$ , $\lambda_2$ diagonal entries. thus, 6 equations 6 unknown parameters:
i tried use package rootsolve , found introduction document provided me example without explanation of steps. have been trying code according examples lost how can model this. tips or sources more information package helpful! in advance!
what did far:
i) tried solve system in non-matrix form, extended 'b' matrix row , used lampda , lampda2, x5 , x6 in code respectively! error matrix singular, should not possible. values choosen arbitrarily.
model <- function(x) { f1 <- x[1]^2+x[2]^2 f2 <- x[1]*x[3]+x[2]*x[4] f3 <- x[3]^2+x[4]^2 f4 <- x[5]*x[1]^2+x[6]*x[2]^2 f5 <- x[5]*x[1]*x[3]+x[6]*x[2]*x[4] f6 <- x[5]*x[3]^2+x[6]*x[4]^2 f7 <- x[5] (edit: how model free-variables?) f8 <- x[6] c(f1 = 3, f2 = 23, f3 = 21, f4=2, f5=1, f6=4, f7, f8) } multiroot(f = model, start = c(1, 1, 1, 2,2,2,3,3)) ii) tried model matrix form, error here number of derivatives returned not equal ones in initial condition.
f3 <- function(x){ x<-matrix(ncol=2,nrow=3) y1<-matrix(c(1,2,3,4),nrow=2,ncol=2) y2<-matrix(c(6,5,4,9),nrow=2,ncol=2) x[1:2,]%*%t(x[1:2,])-y1, x[1:2,]%*%(x[3,]*diag(2))%*%t(x[1:2,])-y2, ) } multiroot(f3, start<-c(1,1,1,1,2,2))
Comments
Post a Comment