Simplex function in R

re pseudo inverse

On the point of generalised inverses - GINV is usually taken to mean the
moore-penrose pseudo inverse - this is the least squares projection.
There are others - e.g. the Drazin inverse which amounts to diagonalisation
- of course this inverse may not be available in R.

Gerard




                                                                           
             "Gabor                                                        
             Grothendieck"                                                 
             <ggrothendieck at gm                                          To 
             ail.com>                  "Chris Line"                        
             Sent by:                  <chris.line at tibra.com.au>           
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             project.org               "r-help at r-project.org"              
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                                                                   Subject 
             11/12/2008 12:14          Re: [R] Simplex function in R       
                                                                           
                                                                           
                                                                           
                                                                           
                                                                           
                                                                           




Try the pseudo inverse:

m <- rbind(c(1, 1, 1), c(1, 0, 1), c(0, 1, 0))
b <- c(5, 2, 3)

library(MASS)
ginv(m) %*% b


On Thu, Dec 11, 2008 at 2:20 AM, Chris Line <chris.line at tibra.com.au>
wrote:

I have a set of linear equations and would like to find any feasible

solution.  A simplex solution works in Case 1 below, but not in Case 2.  I
would be grateful for any help.

Case 1: Find any feasible solution for the set of linear equations:
 a  +   b   +   c  = 5
 a  +   b  +  0c  = 4
0a +   b   +   c  =  4

Solution - a feasible (and unique) solution is a=1, b=3, c=1.

The following R code returns a feasible solution:
A3M = matrix(c(1,1,0,1,1,1,1,0,1),nrow=3)
b3M = matrix(c(5,4,4),ncol=1)
A1M = matrix(c(1,0,0,0,1,0,0,0,1),nrow=3)
b1M = matrix(c(10,10,10),ncol=1)
AM = matrix(c(1,1,1),nrow=1)
simplex(a = AM, A1 = A1M, b1 = b1M, A2 = NULL, b2 = NULL, A3 = A3M, b3 =

b3M, maxi = TRUE)

Case 2: Find any feasible solution for the set of linear equations
  a +   b   +   c  = 5
  a + 0b  +   c  = 2
0a +   b   + 0c  = 3

Solution - one feasible solution of many is a=1, b=3, c=1.  There are

infinite possible solutions in Case 2.

However, the following R code fails to return any feasible solution:
A3M = matrix(c(1,1,0,1,0,1,1,1,0),nrow=3)
b3M = matrix(c(5,2,3),ncol=1)
A1M = matrix(c(1,0,0,0,1,0,0,0,1),nrow=3)
b1M = matrix(c(10,10,10),ncol=1)
AM = matrix(c(1,1,1),nrow=1)
simplex(a = AM, A1 = A1M, b1 = b1M, A2 = NULL, b2 = NULL, A3 = A3M, b3 =

b3M, maxi = TRUE)

The code returns the error:
Error in A.out[, basic] <- iden(M) : subscript out of bounds

Am I using the Simplex function incorrectly?  There may be a better way

to approach the problem of finding a feasible solution.

Cheers,
Chris.

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