[scilab-Users] Problem with Floating point and determinant of a matrix

[Prof. Dr. Reinaldo Golmia Dante]

Woww ... Manjsha, it works !

Interesting command !

Thnx.

Reinaldo.




________________________________
From: Manjusha Joshi <manjusha.joshi at gmail.com>
To: users at lists.scilab.org
Sent: Thu, December 30, 2010 4:33:37 AM
Subject: Re: [scilab-Users] Problem with Floating point and determinant of a 
matrix


Hello, 
 
> 
> 
>-->det(A)
> ans  =
> 
>    6.661D-16  <---------- it should be 0
> 
>-->inv(A)
> ans  =
> 
> 10^15 *
> 
>  - 4.5035996    9.0071993  - 4.5035996 
>    9.0071993  - 18.014399    9.0071993 
>  - 4.5035996    9.0071993  - 4.5035996            <---------- it should appear
>an error message because the matrix A is not invertible (or singular).
>
> 
>-->det(inv(A))
> ans  =
> 
>    9.007D+15     <-------------- The determinant of invertible matrix A^(-1)
>does not exist.
> 
>Other example:
>
>-->B = [1 1; 1 1]
>B  =
> 
>    1.    1. 
>    1.    1. 
> 
>-->det(B)
> ans  =
> 
>    0.  <-------- it is correct !!
> 
>-->inv(B)
>       !--error 19    <-------- it is correct !!
>
> 
>The previously examples show two integer matrices A and B. The determinant of
>matrix A is quite zero, but not,
>and this can propagate an error in case the Scilab developer uses that result
>into other future calculations or algorithms.
>The determinant of matrix B is equal to 0 and the answer is correct. In case 
the
>Scilab developer uses that value,
>he or she can use the simple statement for testing like to:
> if ( det(matrix) <> 0 ) then
><action 1>                     // The Scilab developer knows that the matrix is
>invertible (or nonsingular)
>else
><action 2>                     // The Scilab developer knows that the matrix is
>not invertible (or singular)
>end
> 
>My doubt: "How can I proceed to design any algorithm, which uses matrix, if the
>determinant of
>
>the matrix could not be zero and, as the same time, that matrix is not
>invertible ?".
>How can I manage this uncertainty ?
>  
>clean(det(A))
clean(inv(B))


This will return value  as zero if it is near to zero.
-- 
Manjusha S. Joshi  
P.I. of project on Use of Open source software for Teaching Maths,
 http://fossme.bprim.org
Lecturer in Computational  Mathematics, 
BIM, Pune, India. www.bprim.org
Mobile:  09822 319328
blog:http://manjushajoshi.wordpress.com/


      
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