From Pensak@UDEL.EDU Wed Mar 25 05:29:37 1987
Received: from UDEL.EDU (dewey.udel.edu.ARPA) by anl-mcs.ARPA (4.12/4.9)
	id AA24156; Wed, 25 Mar 87 05:29:31 cst
Date:     Wed, 25 Mar 87 6:29:12 EST
From: Pensak@UDEL.EDU
To: dongarra@anl-mcs.arpa
Subject:  Diagonalization
Message-Id:  <8703250629.a024836@Dewey.UDEL.EDU>
Status: R

Treeql is performing exactly as advertised.  I have inserted it into three
of my molecular orbital codes and it is getting significantly more accurate
norms and running about 2.5x faster than the routines that I used to use.

Would it be possible to get a copy of your parallelized version ?  I would
like to convert it to run on our BBN Butterfly and on our array of INMOS
Transputers.

Thank you very much.

From Pensak@UDEL.EDU Wed Mar 25 18:55:58 1987
Received: from UDEL.EDU (dewey.udel.edu.ARPA) by anl-mcs.ARPA (4.12/4.9)
	id AA09644; Wed, 25 Mar 87 18:55:46 cst
Date:     Wed, 25 Mar 87 19:47:57 EST
From: Pensak@UDEL.EDU
To: Jack Dongarra <dongarra@anl-mcs.arpa>
Subject:  Re:  Diagonalization
Message-Id:  <8703251947.a008865@Dewey.UDEL.EDU>
Status: R

The matrices are running between 150 and 350.  They are somewhat dense, since
the off diagonal elements reflect atomic orbital overlap (which is non-zero
except at distances above several angstroms, though the vast majority of
elements are close to zero [i.e. less than .1] ).  The place where the
improvement was most notable was in highly symmetrical chemical structures
where there are several degenerate eigenvalues (molecular orbitals).  The
orthogonality was about 2 digits closer to 0 than the old givens routine that
I had been using.

I do, in fact, need all vectors and values.  One wierd result that I wanted to
share with you, since I am befuddled is:

I modified your test program to work with matrices of size 2,4,8,16... rather 
than 50,100,etc.  For those cases up through size 128 the ratio of tql to
treeql vaired between 2.9 and 3.4 for the pathological cases (for fun I
modified the twos on the diagonal case to 0's on the diagonal, but I know
it wont make a difference) and between 1.8 and 2.9 for the random case.  For
dimension 256 however the 0's test gave 3.3, but the random gave 6.33.  I
plan to run other cases to see if there is something special about a 2**N
size matrix, but from what I understand of your algorithm, there should not
be such a massive effect.  I will keep you posted on the testing.


.