## [Maxima-bugs] [ maxima-Bugs-3337674 ] Symmetric matrix yields complex eigenvalues

 [Maxima-bugs] [ maxima-Bugs-3337674 ] Symmetric matrix yields complex eigenvalues From: SourceForge.net - 2012-09-21 05:48:00 ```Bugs item #3337674, was opened at 2011-06-27 08:46 Message generated for change (Settings changed) made by rtoy You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3337674&group_id=4933 Please note that this message will contain a full copy of the comment thread, including the initial issue submission, for this request, not just the latest update. Category: None Group: None >Status: Closed Resolution: Wont Fix Priority: 5 Private: No Submitted By: Dženan Zukić (dzenanz) Assigned to: Nobody/Anonymous (nobody) Summary: Symmetric matrix yields complex eigenvalues Initial Comment: When using eigenvectors command in wxMaxima, the following symmetric matrix yields complex eigenvalues: matrix([2621.4397,-7823.3599,-1111.2726],[-7823.3599,23347.842,3316.4543],[-1111.2726,3316.4543,471.08722]) All eigenvalues of a symmetric matrix should be real: http://en.wikipedia.org/wiki/Symmetric_matrix Maxima version: 5.24.0 Maxima build date: 20:39 4/5/2011 Host type: i686-pc-mingw32 Lisp implementation type: GNU Common Lisp (GCL) Lisp implementation version: GCL 2.6.8 ---------------------------------------------------------------------- Comment By: Raymond Toy (rtoy) Date: 2012-08-18 16:52 Message: In addition, I think algorithms for symmetric matrices should be used, instead of a general eigen solver. I don't consider this a bug in maxima. Marking as pending/wontfix. ---------------------------------------------------------------------- Comment By: Barton Willis (willisbl) Date: 2011-06-28 21:00 Message: For a floating point evaluation of eigenvalues, you should use a purely numeric method, not a symbolic method. One (not the only) option is eigens_by_jacobi (symmetric and either binary64 or bigfloat entries). ---------------------------------------------------------------------- Comment By: Dženan Zukić (dzenanz) Date: 2011-06-28 05:37 Message: Thanks for suggestions, but I was using Maxima trying to verify some results obtained using numeric library. However after getting this nonsensical result from Maxima I used another numeric library and obtained similar results (difference was after some decimal points). I am not a frequent user of Maxima, and this problem has significantly lowered my faith in it. ---------------------------------------------------------------------- Comment By: Barton Willis (willisbl) Date: 2011-06-28 05:23 Message: I think the problem is that the default value of ratepsilon is too small; try this: (also do this same with ratepsilon : 1.0e-8) (%i1) load(hypergeometric)\$ (%i2) ratepsilon : 1.0e-18\$ (%i3) m : matrix([2621.4397,-7823.3599,-1111.2726],[-7823.3599,23347.842,3316.4543],[-1111.2726,3316.4543,471.08722])\$ (%i4) first(eigenvalues(m)), ratprint : false\$ (%i5) nfloat(% - conjugate(%),[],100); (%o5) [8.0266455652163197256568351091[46 digits]5913348171925384517960952b-197*%i-1.3377742608693866209428058515[46 digits]0985558028654230752993492b-197,-5.3510970434775464837712234061[46 digits]3942232114616923011973968b-197*%i-1.3377742608693866209428058515[46 digits]0985558028654230752993492b-197,-1.9934389902195135071021405630[46 digits]0374693317196116973450023b-205*%i-2.6755485217387732418856117030[46 digits]1971116057308461505986984b-197] See also http://en.wikipedia.org/wiki/Casus_irreducibilis ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3337674&group_id=4933 ```

 [Maxima-bugs] [ maxima-Bugs-3337674 ] Symmetric matrix yields complex eigenvalues From: SourceForge.net - 2011-06-27 15:46:55 ```Bugs item #3337674, was opened at 2011-06-27 17:46 Message generated for change (Tracker Item Submitted) made by dzenanz You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3337674&group_id=4933 Please note that this message will contain a full copy of the comment thread, including the initial issue submission, for this request, not just the latest update. Category: None Group: None Status: Open Resolution: None Priority: 5 Private: No Submitted By: Dženan Zukić (dzenanz) Assigned to: Nobody/Anonymous (nobody) Summary: Symmetric matrix yields complex eigenvalues Initial Comment: When using eigenvectors command in wxMaxima, the following symmetric matrix yields complex eigenvalues: matrix([2621.4397,-7823.3599,-1111.2726],[-7823.3599,23347.842,3316.4543],[-1111.2726,3316.4543,471.08722]) All eigenvalues of a symmetric matrix should be real: http://en.wikipedia.org/wiki/Symmetric_matrix Maxima version: 5.24.0 Maxima build date: 20:39 4/5/2011 Host type: i686-pc-mingw32 Lisp implementation type: GNU Common Lisp (GCL) Lisp implementation version: GCL 2.6.8 ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3337674&group_id=4933 ```
 [Maxima-bugs] [ maxima-Bugs-3337674 ] Symmetric matrix yields complex eigenvalues From: SourceForge.net - 2011-06-28 12:23:49 ```Bugs item #3337674, was opened at 2011-06-27 10:46 Message generated for change (Comment added) made by willisbl You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3337674&group_id=4933 Please note that this message will contain a full copy of the comment thread, including the initial issue submission, for this request, not just the latest update. Category: None Group: None Status: Open Resolution: None Priority: 5 Private: No Submitted By: Dženan Zukić (dzenanz) Assigned to: Nobody/Anonymous (nobody) Summary: Symmetric matrix yields complex eigenvalues Initial Comment: When using eigenvectors command in wxMaxima, the following symmetric matrix yields complex eigenvalues: matrix([2621.4397,-7823.3599,-1111.2726],[-7823.3599,23347.842,3316.4543],[-1111.2726,3316.4543,471.08722]) All eigenvalues of a symmetric matrix should be real: http://en.wikipedia.org/wiki/Symmetric_matrix Maxima version: 5.24.0 Maxima build date: 20:39 4/5/2011 Host type: i686-pc-mingw32 Lisp implementation type: GNU Common Lisp (GCL) Lisp implementation version: GCL 2.6.8 ---------------------------------------------------------------------- >Comment By: Barton Willis (willisbl) Date: 2011-06-28 07:23 Message: I think the problem is that the default value of ratepsilon is too small; try this: (also do this same with ratepsilon : 1.0e-8) (%i1) load(hypergeometric)\$ (%i2) ratepsilon : 1.0e-18\$ (%i3) m : matrix([2621.4397,-7823.3599,-1111.2726],[-7823.3599,23347.842,3316.4543],[-1111.2726,3316.4543,471.08722])\$ (%i4) first(eigenvalues(m)), ratprint : false\$ (%i5) nfloat(% - conjugate(%),[],100); (%o5) [8.0266455652163197256568351091[46 digits]5913348171925384517960952b-197*%i-1.3377742608693866209428058515[46 digits]0985558028654230752993492b-197,-5.3510970434775464837712234061[46 digits]3942232114616923011973968b-197*%i-1.3377742608693866209428058515[46 digits]0985558028654230752993492b-197,-1.9934389902195135071021405630[46 digits]0374693317196116973450023b-205*%i-2.6755485217387732418856117030[46 digits]1971116057308461505986984b-197] See also http://en.wikipedia.org/wiki/Casus_irreducibilis ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3337674&group_id=4933 ```
 [Maxima-bugs] [ maxima-Bugs-3337674 ] Symmetric matrix yields complex eigenvalues From: SourceForge.net - 2011-06-28 12:37:57 ```Bugs item #3337674, was opened at 2011-06-27 17:46 Message generated for change (Comment added) made by dzenanz You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3337674&group_id=4933 Please note that this message will contain a full copy of the comment thread, including the initial issue submission, for this request, not just the latest update. Category: None Group: None Status: Open Resolution: None Priority: 5 Private: No Submitted By: Dženan Zukić (dzenanz) Assigned to: Nobody/Anonymous (nobody) Summary: Symmetric matrix yields complex eigenvalues Initial Comment: When using eigenvectors command in wxMaxima, the following symmetric matrix yields complex eigenvalues: matrix([2621.4397,-7823.3599,-1111.2726],[-7823.3599,23347.842,3316.4543],[-1111.2726,3316.4543,471.08722]) All eigenvalues of a symmetric matrix should be real: http://en.wikipedia.org/wiki/Symmetric_matrix Maxima version: 5.24.0 Maxima build date: 20:39 4/5/2011 Host type: i686-pc-mingw32 Lisp implementation type: GNU Common Lisp (GCL) Lisp implementation version: GCL 2.6.8 ---------------------------------------------------------------------- >Comment By: Dženan Zukić (dzenanz) Date: 2011-06-28 14:37 Message: Thanks for suggestions, but I was using Maxima trying to verify some results obtained using numeric library. However after getting this nonsensical result from Maxima I used another numeric library and obtained similar results (difference was after some decimal points). I am not a frequent user of Maxima, and this problem has significantly lowered my faith in it. ---------------------------------------------------------------------- Comment By: Barton Willis (willisbl) Date: 2011-06-28 14:23 Message: I think the problem is that the default value of ratepsilon is too small; try this: (also do this same with ratepsilon : 1.0e-8) (%i1) load(hypergeometric)\$ (%i2) ratepsilon : 1.0e-18\$ (%i3) m : matrix([2621.4397,-7823.3599,-1111.2726],[-7823.3599,23347.842,3316.4543],[-1111.2726,3316.4543,471.08722])\$ (%i4) first(eigenvalues(m)), ratprint : false\$ (%i5) nfloat(% - conjugate(%),[],100); (%o5) [8.0266455652163197256568351091[46 digits]5913348171925384517960952b-197*%i-1.3377742608693866209428058515[46 digits]0985558028654230752993492b-197,-5.3510970434775464837712234061[46 digits]3942232114616923011973968b-197*%i-1.3377742608693866209428058515[46 digits]0985558028654230752993492b-197,-1.9934389902195135071021405630[46 digits]0374693317196116973450023b-205*%i-2.6755485217387732418856117030[46 digits]1971116057308461505986984b-197] See also http://en.wikipedia.org/wiki/Casus_irreducibilis ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3337674&group_id=4933 ```
 [Maxima-bugs] [ maxima-Bugs-3337674 ] Symmetric matrix yields complex eigenvalues From: SourceForge.net - 2011-06-29 04:00:22 ```Bugs item #3337674, was opened at 2011-06-27 10:46 Message generated for change (Comment added) made by willisbl You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3337674&group_id=4933 Please note that this message will contain a full copy of the comment thread, including the initial issue submission, for this request, not just the latest update. Category: None Group: None Status: Open Resolution: None Priority: 5 Private: No Submitted By: Dženan Zukić (dzenanz) Assigned to: Nobody/Anonymous (nobody) Summary: Symmetric matrix yields complex eigenvalues Initial Comment: When using eigenvectors command in wxMaxima, the following symmetric matrix yields complex eigenvalues: matrix([2621.4397,-7823.3599,-1111.2726],[-7823.3599,23347.842,3316.4543],[-1111.2726,3316.4543,471.08722]) All eigenvalues of a symmetric matrix should be real: http://en.wikipedia.org/wiki/Symmetric_matrix Maxima version: 5.24.0 Maxima build date: 20:39 4/5/2011 Host type: i686-pc-mingw32 Lisp implementation type: GNU Common Lisp (GCL) Lisp implementation version: GCL 2.6.8 ---------------------------------------------------------------------- >Comment By: Barton Willis (willisbl) Date: 2011-06-28 23:00 Message: For a floating point evaluation of eigenvalues, you should use a purely numeric method, not a symbolic method. One (not the only) option is eigens_by_jacobi (symmetric and either binary64 or bigfloat entries). ---------------------------------------------------------------------- Comment By: Dženan Zukić (dzenanz) Date: 2011-06-28 07:37 Message: Thanks for suggestions, but I was using Maxima trying to verify some results obtained using numeric library. However after getting this nonsensical result from Maxima I used another numeric library and obtained similar results (difference was after some decimal points). I am not a frequent user of Maxima, and this problem has significantly lowered my faith in it. ---------------------------------------------------------------------- Comment By: Barton Willis (willisbl) Date: 2011-06-28 07:23 Message: I think the problem is that the default value of ratepsilon is too small; try this: (also do this same with ratepsilon : 1.0e-8) (%i1) load(hypergeometric)\$ (%i2) ratepsilon : 1.0e-18\$ (%i3) m : matrix([2621.4397,-7823.3599,-1111.2726],[-7823.3599,23347.842,3316.4543],[-1111.2726,3316.4543,471.08722])\$ (%i4) first(eigenvalues(m)), ratprint : false\$ (%i5) nfloat(% - conjugate(%),[],100); (%o5) [8.0266455652163197256568351091[46 digits]5913348171925384517960952b-197*%i-1.3377742608693866209428058515[46 digits]0985558028654230752993492b-197,-5.3510970434775464837712234061[46 digits]3942232114616923011973968b-197*%i-1.3377742608693866209428058515[46 digits]0985558028654230752993492b-197,-1.9934389902195135071021405630[46 digits]0374693317196116973450023b-205*%i-2.6755485217387732418856117030[46 digits]1971116057308461505986984b-197] See also http://en.wikipedia.org/wiki/Casus_irreducibilis ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3337674&group_id=4933 ```
 [Maxima-bugs] [ maxima-Bugs-3337674 ] Symmetric matrix yields complex eigenvalues From: SourceForge.net - 2012-08-18 23:52:52 ```Bugs item #3337674, was opened at 2011-06-27 08:46 Message generated for change (Comment added) made by rtoy You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3337674&group_id=4933 Please note that this message will contain a full copy of the comment thread, including the initial issue submission, for this request, not just the latest update. Category: None Group: None >Status: Pending >Resolution: Wont Fix Priority: 5 Private: No Submitted By: Dženan Zukić (dzenanz) Assigned to: Nobody/Anonymous (nobody) Summary: Symmetric matrix yields complex eigenvalues Initial Comment: When using eigenvectors command in wxMaxima, the following symmetric matrix yields complex eigenvalues: matrix([2621.4397,-7823.3599,-1111.2726],[-7823.3599,23347.842,3316.4543],[-1111.2726,3316.4543,471.08722]) All eigenvalues of a symmetric matrix should be real: http://en.wikipedia.org/wiki/Symmetric_matrix Maxima version: 5.24.0 Maxima build date: 20:39 4/5/2011 Host type: i686-pc-mingw32 Lisp implementation type: GNU Common Lisp (GCL) Lisp implementation version: GCL 2.6.8 ---------------------------------------------------------------------- >Comment By: Raymond Toy (rtoy) Date: 2012-08-18 16:52 Message: In addition, I think algorithms for symmetric matrices should be used, instead of a general eigen solver. I don't consider this a bug in maxima. Marking as pending/wontfix. ---------------------------------------------------------------------- Comment By: Barton Willis (willisbl) Date: 2011-06-28 21:00 Message: For a floating point evaluation of eigenvalues, you should use a purely numeric method, not a symbolic method. One (not the only) option is eigens_by_jacobi (symmetric and either binary64 or bigfloat entries). ---------------------------------------------------------------------- Comment By: Dženan Zukić (dzenanz) Date: 2011-06-28 05:37 Message: Thanks for suggestions, but I was using Maxima trying to verify some results obtained using numeric library. However after getting this nonsensical result from Maxima I used another numeric library and obtained similar results (difference was after some decimal points). I am not a frequent user of Maxima, and this problem has significantly lowered my faith in it. ---------------------------------------------------------------------- Comment By: Barton Willis (willisbl) Date: 2011-06-28 05:23 Message: I think the problem is that the default value of ratepsilon is too small; try this: (also do this same with ratepsilon : 1.0e-8) (%i1) load(hypergeometric)\$ (%i2) ratepsilon : 1.0e-18\$ (%i3) m : matrix([2621.4397,-7823.3599,-1111.2726],[-7823.3599,23347.842,3316.4543],[-1111.2726,3316.4543,471.08722])\$ (%i4) first(eigenvalues(m)), ratprint : false\$ (%i5) nfloat(% - conjugate(%),[],100); (%o5) [8.0266455652163197256568351091[46 digits]5913348171925384517960952b-197*%i-1.3377742608693866209428058515[46 digits]0985558028654230752993492b-197,-5.3510970434775464837712234061[46 digits]3942232114616923011973968b-197*%i-1.3377742608693866209428058515[46 digits]0985558028654230752993492b-197,-1.9934389902195135071021405630[46 digits]0374693317196116973450023b-205*%i-2.6755485217387732418856117030[46 digits]1971116057308461505986984b-197] See also http://en.wikipedia.org/wiki/Casus_irreducibilis ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3337674&group_id=4933 ```
 [Maxima-bugs] [ maxima-Bugs-3337674 ] Symmetric matrix yields complex eigenvalues From: SourceForge.net - 2012-09-21 05:48:00 ```Bugs item #3337674, was opened at 2011-06-27 08:46 Message generated for change (Settings changed) made by rtoy You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3337674&group_id=4933 Please note that this message will contain a full copy of the comment thread, including the initial issue submission, for this request, not just the latest update. Category: None Group: None >Status: Closed Resolution: Wont Fix Priority: 5 Private: No Submitted By: Dženan Zukić (dzenanz) Assigned to: Nobody/Anonymous (nobody) Summary: Symmetric matrix yields complex eigenvalues Initial Comment: When using eigenvectors command in wxMaxima, the following symmetric matrix yields complex eigenvalues: matrix([2621.4397,-7823.3599,-1111.2726],[-7823.3599,23347.842,3316.4543],[-1111.2726,3316.4543,471.08722]) All eigenvalues of a symmetric matrix should be real: http://en.wikipedia.org/wiki/Symmetric_matrix Maxima version: 5.24.0 Maxima build date: 20:39 4/5/2011 Host type: i686-pc-mingw32 Lisp implementation type: GNU Common Lisp (GCL) Lisp implementation version: GCL 2.6.8 ---------------------------------------------------------------------- Comment By: Raymond Toy (rtoy) Date: 2012-08-18 16:52 Message: In addition, I think algorithms for symmetric matrices should be used, instead of a general eigen solver. I don't consider this a bug in maxima. Marking as pending/wontfix. ---------------------------------------------------------------------- Comment By: Barton Willis (willisbl) Date: 2011-06-28 21:00 Message: For a floating point evaluation of eigenvalues, you should use a purely numeric method, not a symbolic method. One (not the only) option is eigens_by_jacobi (symmetric and either binary64 or bigfloat entries). ---------------------------------------------------------------------- Comment By: Dženan Zukić (dzenanz) Date: 2011-06-28 05:37 Message: Thanks for suggestions, but I was using Maxima trying to verify some results obtained using numeric library. However after getting this nonsensical result from Maxima I used another numeric library and obtained similar results (difference was after some decimal points). I am not a frequent user of Maxima, and this problem has significantly lowered my faith in it. ---------------------------------------------------------------------- Comment By: Barton Willis (willisbl) Date: 2011-06-28 05:23 Message: I think the problem is that the default value of ratepsilon is too small; try this: (also do this same with ratepsilon : 1.0e-8) (%i1) load(hypergeometric)\$ (%i2) ratepsilon : 1.0e-18\$ (%i3) m : matrix([2621.4397,-7823.3599,-1111.2726],[-7823.3599,23347.842,3316.4543],[-1111.2726,3316.4543,471.08722])\$ (%i4) first(eigenvalues(m)), ratprint : false\$ (%i5) nfloat(% - conjugate(%),[],100); (%o5) [8.0266455652163197256568351091[46 digits]5913348171925384517960952b-197*%i-1.3377742608693866209428058515[46 digits]0985558028654230752993492b-197,-5.3510970434775464837712234061[46 digits]3942232114616923011973968b-197*%i-1.3377742608693866209428058515[46 digits]0985558028654230752993492b-197,-1.9934389902195135071021405630[46 digits]0374693317196116973450023b-205*%i-2.6755485217387732418856117030[46 digits]1971116057308461505986984b-197] See also http://en.wikipedia.org/wiki/Casus_irreducibilis ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3337674&group_id=4933 ```