[Bugzilla] [Bug 13810] New: householder function fails with division by zero

[bugzilla.admin at scilab.org]

http://bugzilla.scilab.org/show_bug.cgi?id=13810
--------- Bug Summary -----------
householder function fails with division by zero

---------- Changed by ------------
adelson.oliveira at gmail.com

---------- What changed ----------
bug_id, short_desc, product, version, rep_platform, op_sys, bug_status, bug_severity, priority, component, assigned_to, reporter


            Bug ID: 13810
           Summary: householder function fails with division by zero
           Product: Scilab software
           Version: 5.5.2 final version
          Hardware: PC
                OS: All OS
            Status: NEW
          Severity: Blocker
          Priority: P5
         Component: Numerical Math
          Assignee: bugzilla.admin at scilab.org
          Reporter: adelson.oliveira at gmail.com

Description:
Scilab function householder fails to operate on vectors with just the first line positive and different of zero like [1;0;0]


Log: scilab returns division by zero for,

householder([1;0;0])


Reproduce the error simply defining vector x=[x1;x2;x3;.....;xn] with all xi=0 except x1>0 and try householder(x);


OTHER INFORMATION:
------------------
A possible solution.
Householder of a general vector x admits two possible solutions based on (x-|x|e1) and (x+|x|e1) where e1 is [1;0;0;.....;0]. If x = Const*e1, one of
these two choices is zero, depending on x1 being positive or negative, thus rendering normalization impossible. A safe choice for this would be,

x + SIGN(x1) x1 e1.

Scilab implements only x-|x|e1 thus if x1 is positive and x=Const*e1 this vector is zero.

Thanks.

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