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<th>Reporter</th>
<td>adelson.oliveira@gmail.com</td>
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<th>Bug ID</th>
<td><a class="bz_bug_link
bz_status_NEW "
title="NEW - householder function fails with division by zero"
href="http://bugzilla.scilab.org/show_bug.cgi?id=13810">13810</a>
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<th>Summary</th>
<td>householder function fails with division by zero
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<th>Product</th>
<td>Scilab software
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<th>Version</th>
<td>5.5.2 final version
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<th>OS</th>
<td>All OS
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<th>Status</th>
<td>NEW
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<th>Severity</th>
<td>Blocker
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<th>Component</th>
<td>Numerical Math
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<th>Assignee</th>
<td>bugzilla.admin@scilab.org
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<pre>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.</pre>
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