Hi list,
I am running the following R code, the answer should be zero. But R gives
a very small negative number, what should I do?
##R code
library(numDeriv)
h_x <- function(x){
a = x[1]
b = x[2]
c = x[3]
d = x[4]
(a^2 + c^2 + d^2) * (b^2 + c^2 + d^2)
}
x1 = 10
x2 = 1
x3 = 0
x4 = 10
x = c(x1, x2, x3, x4)
hess.h <- hessian(func = h_x, x)
mat <- h_x(x)*hess.h - grad(h_x, x) %o% grad(h_x, x)
> mat
[,1] [,2] [,3] [,4]
[1,] 4.059961e-05 -3.038031e-04 -1.307195e-02 -4.080400e+06
[2,] -3.038031e-04 7.920000e+06 -2.663690e-02 -1.600000e+06
[3,] -1.307195e-02 -2.663690e-02 1.216065e+07 1.331894e-02
[4,] -4.080400e+06 -1.600000e+06 1.331894e-02 -7.920000e+06
# A lot of the elements should be zero, for example the first one. I will
change them manually.
m = ifelse(abs(mat)< 0.1, 0, mat)
eigen(m)$val
[1] 12160648 8103268 1665782 -9769050
> sum(eigen(m)$val[2:4])
[1] -0.0005430793
## End of R code
The last answer above should be zero, but it's appearing as a very small
negative number. How should I deal with it?
Thanks lots,
Mike
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