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## Re: Octave criterion for matrix singularity

**From**: |
Carlo De Falco |

**Subject**: |
Re: Octave criterion for matrix singularity |

**Date**: |
Tue, 26 Feb 2019 13:00:25 +0000 |

>* On 25 Feb 2019, at 19:34, mabalenk <address@hidden> wrote:*
>* *
>* Dear all,*
>* *
>* I'm repeatedly solving a linear system with a Vandermonde matrix. I'm using*
>* a "backslash" operator:*
>* *
>* y = -W'/b'*
>* *
>* At each iteration I'm increasing the matrix order by one. At some point*
>* Octave issues a warning:*
>* *
>* warning: matrix singular to machine precision, rcond = 1.56508e-17*
>* *
>* If possible, would you please direct me to the Octave source code, where*
>* this decision is made? I would like to understand the criterion, that*
>* triggers the warning. I found a post on StackOverflow that says MATLAB would*
>* issue a similar warning, once rcond < 1e-12. I would like to know, what*
>* threshold does Octave use and how is it defined. Thank you!*
>* *
>* --*
>* Best wishes,*
>* Maxim*
The code for solving A\b with A real double precision, full matrix is here :
http://hg.savannah.gnu.org/hgweb/octave/file/14815cb62fbe/liboctave/array/dMatrix.cc#l1445
the condition being checked is
rcond + 1.0 == 1.0
which means rcond is less or equal than eps(1.0)/2
HTH,
c.