[R] System of equations with unknowns in R

[Berend Hasselman]

> On 20 Jul 2016, at 19:20, Sachin Kuruvithadam <sacios at hotmail.it> wrote:
> 
> 
> 
> I have a 3x3 matrix Omega whose elements are unknown, and a defined 3x1 parameter vector alpha. I want to define a 3x1 vector delta whose elements are still unknown but depend on alpha and Omega as shown in this image (sorry, but when I write in Latex format it doesn't appear formatted in my preview):
> 
> https://www.dropbox.com/home/Public?preview=model.png
> 

I cannot access your image.

> The term in the brackets simplifies into a number K, so I wrote this function:
> 
> Alpha=c(-0.248,1.092,-0.518)
> K=function(gamma1,gamma2,gamma3,gamma12,gamma23,gamma13){
>    (1+Alpha[1]*(Alpha[1]+Alpha[2]*gamma12/(gamma1*gamma2)+Alpha[3]*gamma13/(gamma1*gamma3)))^(-1/2)
>    }
> 

This functions a scalar not a function

> gamma1, gamma2, gamma3 are the elements in the diagonal of the 3x3 matrix Omega, whereas gamma12, gamma13, gamma23 are the off-diagonal elements (each elements repeats itself twice, e.g. gamma12=gamma21). So, by putting 6 arbitrary values in K() I get the scalar. So far so clear.
> 
> The rest I'm not sure about. I want R to return me a vector delta defined as shown above. How can I write a function that would perform this algebraic calculation, and return a 3x1 vector delta whose elements are the same unknowns as in Omega, but shifted/multiplied by the numbers in alpha?
> 

You can simplify the gamma arguments of your function K by passing the matrix Omega.
Like this

<code>
K1 <- function(Omega,Alpha){
    gamma1 <- Omega[1,1]   
    gamma2 <- Omega[2,2]   
    gamma3 <- Omega[3,3]   
    gamma12 <- Omega[1,2]
    gamma13 <- Omega[1,2]
    gamma23 <- Omega[2,3]
    z <- 1+Alpha[1]*(Alpha[1]+Alpha[2]*gamma12/(gamma1*gamma2)+Alpha[3]*gamma13/(gamma1*gamma3))^(-1/2)
    z
}
</code>

Define as given in your mail

Alpha <- c(-0.248,1.092,-0.518)


Fake a symmetric matrix Omega 

<code>
set.seed(413:
library(Matrix)
x <- Matrix(round(runif(9),2), 3)
x

Omega <- forceSymmetric(x)
Omega

# and run the function

K1(Omega,Alpha)
</code>

The result is a scalar: 0.8149383

Depending on the contents of Omega the result of K1 may be NaN.

You will have to redefine your function if you want it to return a vector.
You have not given enough information to give an answer to your question.

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Berend Hasselman
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