Re: [Mplapack-devel] Can I compute eigenvalues of ill-conditioned matrix less than 10^-156 ?
Status: Pre-Alpha
Brought to you by:
nakatamaho
From: Maho N. <ch...@ma...> - 2011-09-22 14:41:40
|
Hi Gang Yan, sorry for long delay. From: Gang Yan <ee...@gm...> Subject: Re: [Mplapack-devel] Can I compute eigenvalues of ill-conditioned matrix less than 10^-156 ? Date: Tue, 13 Sep 2011 01:35:22 -0400 > Many thanks, Maho. Attached please find the source code. > > A20.dat is the input matrix, eigenvalue_mpfr.cpp is the source code modified > from your example code. ok, > Place the two files into the folder mpack-0.6.7/examples/mlapack/ and use > commands "make" and "./eigenvalue_mpfr", it will show the results of the > largest and smallest eigenvalues. done. > It is shown that when the variable tt (a time variable in my program) is > very small, the matrix will become extremely ill-conditioned, and the > smallest eigenvalue will be less than 1e-156 and thus become negative. following output is correct wrong result? --- OK [ [ 1.644791426e1]; [ 1.722920009e1]; [ 1.747945946e1]; [ 1.766113939e1]; [ 1.776131407e1]; [ 1.810655068e1]; [ 1.869304632e1]; [ 1.913033628e1]; [ 1.941946805e1]; [ 1.992760133e1]; [ 2.000190806e1]; [ 2.041030420e1]; [ 2.073058106e1]; [ 2.092543236e1]; [ 2.108105957e1]; [ 2.166945660e1]; [ 2.212463197e1]; [ 2.255747777e1]; [ 2.281199141e1]; [ 2.583112709e1] ] OK 1.000000000e-4 9.980027172e-5 9.980027105e-5 -3.323972836e-158 2.000000000e-4 1.992021715e-4 1.992021662e-4 -8.891981975e-159 4.000000000e-4 3.968173357e-4 3.968172935e-4 -1.165480641e-159 8.000000000e-4 7.873381119e-4 7.873377765e-4 3.018299932e-160 1.600000000e-3 1.549895802e-3 1.549893166e-3 -2.121601048e-158 3.200000000e-3 3.003823837e-3 3.003803478e-3 5.848200770e-153 6.400000000e-3 5.647598950e-3 5.647447187e-3 3.014126150e-141 1.280000000e-2 1.002517109e-2 1.002411737e-2 1.456356388e-129 2.560000000e-2 1.606256118e-2 1.605621952e-2 6.184498678e-118 5.120000000e-2 2.193695924e-2 2.190825888e-2 2.028549225e-106 1.024000000e-1 2.495037779e-2 2.487359809e-2 3.969087087e-95 2.048000000e-1 2.545631687e-2 2.535104125e-2 2.761963837e-84 4.096000000e-1 2.546875365e-2 2.536157283e-2 2.427716249e-74 8.192000000e-1 2.546876239e-2 2.536157891e-2 3.411560868e-66 1.638400000 2.546876239e-2 2.536157891e-2 1.315185105e-61 3.276800000 2.546876239e-2 2.536157891e-2 2.514747138e-61 6.553600000 2.546876239e-2 2.536157891e-2 2.514747138e-61 1.310720000e1 2.546876239e-2 2.536157891e-2 2.514747138e-61 2.621440000e1 2.546876239e-2 2.536157891e-2 2.514747138e-61 5.242880000e1 2.546876239e-2 2.536157891e-2 2.514747138e-61 --- thanks -- Nakata Maho http://accc.riken.jp/maho/ , JA OOO http://ja.openoffice.org/ http://blog.goo.ne.jp/nakatamaho/ ,GPG: http://accc.riken.jp/maho/maho.pgp.txt |