# [R] Reversing the Equation to find value of variable

Frede Aakmann Tøgersen frtog at vestas.com
Mon Jan 6 13:01:15 CET 2014

```Hi

Reading the error message carefully you can see that f() is not defined at 0:

> uniroot(f, c(0, 1))
Error in uniroot(f, c(0, 1)) : f.lower = f(lower) is NA
> f(0)
[1] NaN

If you plot f() in the interval (0,1) then you'll see there is two solutions:

> uniroot(f, c(0.0001, 1))
Error in uniroot(f, c(1e-04, 1)) :
f() values at end points not of opposite sign
> uniroot(f, c(0.0001, 0.2))
\$root
[1] 0.1533901

\$f.root
[1] 0.3414232

\$iter
[1] 6

\$estim.prec
[1] 6.103516e-05

> uniroot(f, c(0.3, 1))
\$root
[1] 0.4699984

\$f.root
[1] -0.04112121

\$iter
[1] 8

\$estim.prec
[1] 6.103516e-05

>

Yours sincerely / Med venlig hilsen

Frede Aakmann Tøgersen
Specialist, M.Sc., Ph.D.
Plant Performance & Modeling

Technology & Service Solutions
T +45 9730 5135
M +45 2547 6050
frtog at vestas.com
http://www.vestas.com

Company reg. name: Vestas Wind Systems A/S
This e-mail is subject to our e-mail disclaimer statement.

> -----Original Message-----
> From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org]
> On Behalf Of Katherine Gobin
> Sent: 6. januar 2014 12:42
> To: r-help at r-project.org
> Subject: [R] Reversing the Equation to find value of variable
>
> Dear R forum
>
> I have following variables -
>
> LGD = 0.45
> PD = 0.47
> M = 3
>
> # Equation 1
>
> R = 0.12*(1-exp(-50*PD))/(1-exp(-50)) + 0.24*(1-(1-exp(-50*PD))/(1-exp(-
> 50)))
>
> b = (0.11852 - 0.05478 * log(PD))^2
>
> K = (LGD * pnorm((1 - R)^(-0.5) * qnorm(PD) + (R / (1 - R))^0.5 *
> qnorm(0.999)) - PD * LGD) * (1 - 1.5 * b)^(-1) * (1 + (M - 2.5) * b)
>
> RWA = K * 12.5 * EAD
>
>
> > RWA
> [1] 22845.07
>
> #
> __________________________________________________________
> _______
>
> # MY Problem
>
> In the above part, knowing values of LGD, EAD, M and PD, the value of RWA
> was calculated. However, I need to go reverse way in the sense knowing the
> values of LGD, EAD, M and RWA, I need to find value of PD.
>
> So I have tried to use uniroot as (RWA - K * 12.5 * EAD and used the above
> equations i place of K and R)
>
> RWA = 22845.07
> LGD = 0.45
> M = 3
>
> f = function(x) RWA -  (LGD*pnorm((1-(0.12*(1-exp(-50*x))/(1-exp(-
> 50))+0.24*(1-(1-exp(-50*x))/(1-exp(-50)))))^(-0.5)*qnorm(x)+((0.12*(1-
> exp(-50*x))/(1-exp(-50))+0.24*(1-(1-exp(-50*x))/(1-exp(-50))))/(1-(0.12*(1-
> exp(-50*x))/(1-exp(-50))+0.24*(1-(1-exp(-50*x))/(1-exp(-
> 50))))))^0.5*qnorm(0.999))-x*LGD) * (1-1.5*((0.11852-0.05478 *
>
> uniroot(f, c(0,1), tol = 0.0000000001)
>
> I get following error -
>
> > uniroot(f, c(0,1), tol = 0.0000000001)
> Error in uniroot(f, c(0, 1), tol = 1e-10) : f.lower = f(lower) is NA
>
> Kindly guide as I am not sure if uniroot is the correct way of doing it or not.
> Ideally, I should be getting the PD value of 0.47.
>
> With regards
>
> Katherine
> 	[[alternative HTML version deleted]]

```