-----BEGIN PGP SIGNED MESSAGE----- Hash: SHA1 It's been a while since I've done much linear algebra stuff, and I don't think I've ever used LAPACK before.
Recently, I was trying to duplicate the results in http://actifeld.com/A%20Possible%20Method.doc. In particular, Geoff Coyle gives a matrix on p. 6 and then shows the eigenvector (presumably the principal eigenvector) as (0.232, 0.402, 0.061, 0.305). I tried using dgeev_jlapack_ as in the lab (J5.04). Here are snippets of my work: ,----[ His Client Preference Matrix ] | m | 1 0.333333 5 1 | 3 1 5 1 | 0.2 0.2 1 0.2 | 1 1 5 1 `---- ,----[ Eigenvalues; the first is presumably the principal eigenvalues ] | > 1{ dgeev_jlapack_ m | 4.1545007 _0.077250375j0.79743768 _0.077250375j_0.79743768_5.5511151e_17 `---- ,----[ Left eigenvectors; the first is presumably the principal ] | > 0{ dgeev_jlapack_ m | 0.25760047 0.25043806j0.32061757 0.25043806j_0.32061757 0 | 0.14598546 0.11143426j_0.18169805 0.11143426j0.18169805 1.0965318e_17 | 0.93661124 _0.87103684 _0.87103684 _0.98058068 | 0.18732225 _0.17420737j_2.3592239e_16 _0.17420737j2.3592239e_16 0.19611614 | `---- ,----[ Right eigenvectors; the first is presumably the principal ] | > 2{ dgeev_jlapack_ m | 0.41429869 0.15147845j_0.40545658 0.15147845j0.40545658 4.86865e_17 | 0.73105594 _0.82614212 _0.82614212 _1.2962781e_15 | 0.10632205 0.043552657j0.055757287 0.043552657j_0.055757287 _0.19611614 | 0.53161023 0.21776329j0.27878644 0.21776329j_0.27878644 0.98058068 `---- ,----[ Principle left eigenvector, with components converted to magnitudes ] | {. | > 0{ dgeev_jlapack_ m | 0.25760047 0.40683516 0.40683516 0 `---- ,----[ Principal right eigenvector, with components converted to magnitudes ] | {. | > 2{ dgeev_jlapack_ m | 0.41429869 0.43282878 0.43282878 4.86865e_17 `---- None of those match his (0.232, 0.402, 0.061, 0.305). While I'm waiting on an answer from him, does anyone here see anything I'm doing dumb? Can anyone reproduce his result, perhaps using LAPACK? I do read that people tend to find principal eigenvectors using a power method, which only returns the principal eigenvector, but I neither see that in my skimming of the LAPACK docs nor do I (yet) know why it's better to go that way than to find them all, assuming it's not computationally costly to find them all. TIA, Bill - -- Bill Harris http://facilitatedsystems.com/weblog/ Facilitated Systems Everett, WA 98208 USA http://facilitatedsystems.com/ phone: +1 425 337-5541 -----BEGIN PGP SIGNATURE----- Version: GnuPG v1.4.1 (MingW32) Comment: For more information, see http://www.gnupg.org iD8DBQFEBgbc3J3HaQTDvd8RAtLpAJ9cJie7+cQQMjlX85oqlR485tDGoACfWquT 0WPlZFk3b+23JigaeowuKp0= =x1/P -----END PGP SIGNATURE----- ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
