id summary reporter owner description type status priority milestone component resolution keywords cc merged author reviewer upstream work_issues branch commit dependencies stopgaps
10791 Fix and upgrade Gram-Schmidt rbeezer jason was "If a set of vectors has a linearly dependent subset, followed by a vector outside the span of that subset, then the presence of a zero vector in the orthogonal set causes division by a zero dot product.
There are various other improvements that can be made in this routine.
{{{
sage: A=matrix(QQ, [[1,2],[2,4],[1,1]])
sage: A.gram_schmidt()
---------------------------------------------------------------------------
ZeroDivisionError Traceback (most recent call last)
/sage/sage-4.6.2.alpha4/ in ()
/sage/sage-4.6.2.alpha4/local/lib/python2.6/site-packages/sage/matrix/matrix2.so in sage.matrix.matrix2.Matrix.gram_schmidt (sage/matrix/matrix2.c:31979)()
/sage/sage-4.6.2.alpha4/local/lib/python2.6/site-packages/sage/modules/misc.pyc in gram_schmidt(B)
55 for i in range(1,n):
56 for j in range(i):
---> 57 mu[i,j] = B[i].dot_product(Bstar[j]) / (Bstar[j].dot_product(Bstar[j]))
58 Bstar.append(B[i] - sum(mu[i,j]*Bstar[j] for j in range(i)))
59 return Bstar, mu
/sage/sage-4.6.2.alpha4/local/lib/python2.6/site-packages/sage/structure/element.so in sage.structure.element.RingElement.__div__ (sage/structure/element.c:11981)()
/sage/sage-4.6.2.alpha4/local/lib/python2.6/site-packages/sage/rings/rational.so in sage.rings.rational.Rational._div_ (sage/rings/rational.c:15177)()
ZeroDivisionError: Rational division by zero
}}}" defect new major sage-4.7.1 linear algebra N/A