R help - Jan 2009 - Matlab inv() and R solve() differences

I submit the following matrix to both MATLAB and R

x=  0.133 0.254 -0.214 0.116
    0.254 0.623 -0.674 0.139
   -0.214 -0.674 0.910 0.011
    0.116 0.139  0.011 0.180

MATLAB's inv(x) provides the following
 137.21 -50.68 -4.70 -46.42
-120.71  27.28 -8.94 62.19
-58.15   6.93  -7.89  36.94
  8.35   11.17 10.42 -14.82

R's solve(x) provides:
261.94 116.22 150.92 -267.78
116.22 344.30 286.68 -358.30
150.92 286.68 252.96 -334.09
-267.78 =358.30 -334.09 475.22

inv(x)*x = I(4)
and solve(x)%*%x = I(4)

Is there a way to obtain the MATLAB result in R?

Thanks for any help.


Pat Gray

I suppose the solution is unstable because x is ill-conditioned:
> x
       [,1]   [,2]   [,3]  [,4]
[1,]  0.133  0.254 -0.214 0.116
[2,]  0.254  0.623 -0.674 0.139
[3,] -0.214 -0.674  0.910 0.011
[4,]  0.116  0.139  0.011 0.180
> cor(x)
           [,1]       [,2]       [,3]       [,4]
[1,]  1.0000000  0.9963557 -0.9883690  0.8548065
[2,]  0.9963557  1.0000000 -0.9976663  0.8084090
[3,] -0.9883690 -0.9976663  1.0000000 -0.7663847
[4,]  0.8548065  0.8084090 -0.7663847  1.0000000
> kappa(x)
[1] 2813.326

hth,

Kingsford Jones

On Thu, Jan 29, 2009 at 7:00 PM, Joseph P Gray <jpgray at uwm.edu>
wrote:
> I submit the following matrix to both MATLAB and R
>
> x=  0.133 0.254 -0.214 0.116
>    0.254 0.623 -0.674 0.139
>   -0.214 -0.674 0.910 0.011
>    0.116 0.139  0.011 0.180
>
> MATLAB's inv(x) provides the following
>  137.21 -50.68 -4.70 -46.42
> -120.71  27.28 -8.94 62.19
> -58.15   6.93  -7.89  36.94
>  8.35   11.17 10.42 -14.82
>
> R's solve(x) provides:
> 261.94 116.22 150.92 -267.78
> 116.22 344.30 286.68 -358.30
> 150.92 286.68 252.96 -334.09
> -267.78 =358.30 -334.09 475.22
>
> inv(x)*x = I(4)
> and solve(x)%*%x = I(4)
>
> Is there a way to obtain the MATLAB result in R?
>
> Thanks for any help.
>
>
> Pat Gray
>
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>

Joseph P Gray wrote:
> I submit the following matrix to both MATLAB and R
> 
> x=  0.133 0.254 -0.214 0.116
>     0.254 0.623 -0.674 0.139
>    -0.214 -0.674 0.910 0.011
>     0.116 0.139  0.011 0.180
> 
> MATLAB's inv(x) provides the following
>  137.21 -50.68 -4.70 -46.42
> -120.71  27.28 -8.94 62.19
> -58.15   6.93  -7.89  36.94
>   8.35   11.17 10.42 -14.82
> 
> R's solve(x) provides:
> 261.94 116.22 150.92 -267.78
> 116.22 344.30 286.68 -358.30
> 150.92 286.68 252.96 -334.09
> -267.78 =358.30 -334.09 475.22
> 
> inv(x)*x = I(4)
> and solve(x)%*%x = I(4)
> 
> Is there a way to obtain the MATLAB result in R?
Multiply x[3,4] by 10:

 > xx <- x
 > xx[3,4]<-0.11
 > solve(xx)
            [,1]      [,2]      [,3]      [,4]
[1,]  137.20892 -50.67500 -4.705127 -46.41581
[2,] -120.71445  27.27570 -8.937571  62.19270
[3,]  -58.15073   6.93474 -7.886343  36.93919
[4,]    8.34851  11.17053 10.415928 -14.81602



-- 
    O__  ---- Peter Dalgaard             ?ster Farimagsgade 5, Entr.B
   c/ /'_ --- Dept. of Biostatistics     PO Box 2099, 1014 Cph. K
  (*) \(*) -- University of Copenhagen   Denmark      Ph:  (+45) 35327918
~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk)              FAX: (+45) 35327907

Joseph P Gray wrote:
> 
> I submit the following matrix to both MATLAB and R
> 
> x=  0.133 0.254 -0.214 0.116
>     0.254 0.623 -0.674 0.139
>    -0.214 -0.674 0.910 0.011
>     0.116 0.139  0.011 0.180
> 
> MATLAB's inv(x) provides the following
>  137.21 -50.68 -4.70 -46.42
> -120.71  27.28 -8.94 62.19
> -58.15   6.93  -7.89  36.94
>   8.35   11.17 10.42 -14.82
> 
> R's solve(x) provides:
> 261.94 116.22 150.92 -267.78
> 116.22 344.30 286.68 -358.30
> 150.92 286.68 252.96 -334.09
> -267.78 =358.30 -334.09 475.22
> 
> 
The matrix x is clearly symmetric. Therefore I expect a symmetric inverse of
x.
The result of Matlab's inv(x) is clearly not symmetric.
R's result is symmetric.

I find  what is shown as Matlab's result difficult to believe.

Berend


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