### Email Archive: maxima-bugs (read-only)

 [Maxima-bugs] [ maxima-Bugs-1963314 ] Fresnel integral - function romberg -error. From: SourceForge.net - 2008-05-13 19:35 ```Bugs item #1963314, was opened at 2008-05-13 12:35 Message generated for change (Tracker Item Submitted) made by Item Submitter You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1963314&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: Lisp Core - Integration Group: None Status: Open Resolution: None Priority: 5 Private: Yes Submitted By: Nobody/Anonymous (nobody) Assigned to: Nobody/Anonymous (nobody) Summary: Fresnel integral - function romberg -error. Initial Comment: Maxima 5.14.0 Linux and 5.15.0 Windows. Fresnel integral: http://en.wikipedia.org/wiki/Fresnel_integral http://upload.wikimedia.org/wikipedia/commons/thumb/8/8f/Fresnel_Integrals_%28Normalised%29.svg/250px-Fresnel_Integrals_%28Normalised%29.svg.png Maxima command: for i:1 thru 10 do display(romberg(sin(%pi/2*(x^2)),x,0,i)); .... romberg(sin((%pi*x^2)/2),x,0,7)=0.49970480390049 romberg(sin((%pi*x^2)/2),x,0,8)=-1.0449974219284286*10^-14 romberg(sin((%pi*x^2)/2),x,0,9)=0.49986104588168 also romberg(cos((%pi*x^2)/2),x,0,7)=0.54546705790348 romberg(cos((%pi*x^2)/2),x,0,8)=8.0 romberg(cos((%pi*x^2)/2),x,0,9)=0.53536612585252 in point x=8 is error. Thx ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1963314&group_id=4933 ```

 [Maxima-bugs] [ maxima-Bugs-1963314 ] Fresnel integral - function romberg -error. From: SourceForge.net - 2008-05-14 00:30 ```Bugs item #1963314, was opened at 2008-05-13 13:35 Message generated for change (Comment added) made by robert_dodier You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1963314&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: Share Libraries Group: None >Status: Pending >Resolution: Wont Fix Priority: 5 Private: Yes Submitted By: Nobody/Anonymous (nobody) Assigned to: Nobody/Anonymous (nobody) Summary: Fresnel integral - function romberg -error. Initial Comment: Maxima 5.14.0 Linux and 5.15.0 Windows. Fresnel integral: http://en.wikipedia.org/wiki/Fresnel_integral http://upload.wikimedia.org/wikipedia/commons/thumb/8/8f/Fresnel_Integrals_%28Normalised%29.svg/250px-Fresnel_Integrals_%28Normalised%29.svg.png Maxima command: for i:1 thru 10 do display(romberg(sin(%pi/2*(x^2)),x,0,i)); .... romberg(sin((%pi*x^2)/2),x,0,7)=0.49970480390049 romberg(sin((%pi*x^2)/2),x,0,8)=-1.0449974219284286*10^-14 romberg(sin((%pi*x^2)/2),x,0,9)=0.49986104588168 also romberg(cos((%pi*x^2)/2),x,0,7)=0.54546705790348 romberg(cos((%pi*x^2)/2),x,0,8)=8.0 romberg(cos((%pi*x^2)/2),x,0,9)=0.53536612585252 in point x=8 is error. Thx ---------------------------------------------------------------------- >Comment By: Robert Dodier (robert_dodier) Date: 2008-05-13 18:30 Message: Logged In: YES user_id=501686 Originator: NO romberg is easily fooled by oscillatory integrands: it evaluates the integrand at a few points and sees that they are the same, so it thinks the integrand is constant. Much better to use the Quadpack functions, namely quad_qags, etc. ?? quad at the input prompt should find them. You can fiddle with some parameters to make romberg succeed on this problem (?? romberg finds them), but romberg is just not a very strong algorithm; use quad_qags or some other Quadpack function instead. Marking this report as "won't fix"; the romberg function is a correct implementation of Romberg's method. Instead of closing it, I'll leave it pending, so it stays open for a while in case the original poster comes back. Note: please log in so that annotations on bug reports are automatically sent to you. ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1963314&group_id=4933 ```
 [Maxima-bugs] [ maxima-Bugs-1963314 ] Fresnel integral - function romberg -error. From: SourceForge.net - 2008-05-14 00:31 ```Bugs item #1963314, was opened at 2008-05-13 13:35 Message generated for change (Settings changed) made by robert_dodier You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1963314&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: Share Libraries Group: None Status: Pending Resolution: Wont Fix Priority: 5 >Private: No Submitted By: Nobody/Anonymous (nobody) Assigned to: Nobody/Anonymous (nobody) Summary: Fresnel integral - function romberg -error. Initial Comment: Maxima 5.14.0 Linux and 5.15.0 Windows. Fresnel integral: http://en.wikipedia.org/wiki/Fresnel_integral http://upload.wikimedia.org/wikipedia/commons/thumb/8/8f/Fresnel_Integrals_%28Normalised%29.svg/250px-Fresnel_Integrals_%28Normalised%29.svg.png Maxima command: for i:1 thru 10 do display(romberg(sin(%pi/2*(x^2)),x,0,i)); .... romberg(sin((%pi*x^2)/2),x,0,7)=0.49970480390049 romberg(sin((%pi*x^2)/2),x,0,8)=-1.0449974219284286*10^-14 romberg(sin((%pi*x^2)/2),x,0,9)=0.49986104588168 also romberg(cos((%pi*x^2)/2),x,0,7)=0.54546705790348 romberg(cos((%pi*x^2)/2),x,0,8)=8.0 romberg(cos((%pi*x^2)/2),x,0,9)=0.53536612585252 in point x=8 is error. Thx ---------------------------------------------------------------------- Comment By: Robert Dodier (robert_dodier) Date: 2008-05-13 18:30 Message: Logged In: YES user_id=501686 Originator: NO romberg is easily fooled by oscillatory integrands: it evaluates the integrand at a few points and sees that they are the same, so it thinks the integrand is constant. Much better to use the Quadpack functions, namely quad_qags, etc. ?? quad at the input prompt should find them. You can fiddle with some parameters to make romberg succeed on this problem (?? romberg finds them), but romberg is just not a very strong algorithm; use quad_qags or some other Quadpack function instead. Marking this report as "won't fix"; the romberg function is a correct implementation of Romberg's method. Instead of closing it, I'll leave it pending, so it stays open for a while in case the original poster comes back. Note: please log in so that annotations on bug reports are automatically sent to you. ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1963314&group_id=4933 ```
 [Maxima-bugs] [ maxima-Bugs-1963314 ] Fresnel integral - function romberg -error. From: SourceForge.net - 2008-05-14 00:32 ```Bugs item #1963314, was opened at 2008-05-13 13:35 Message generated for change (Comment added) made by robert_dodier You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1963314&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: Share Libraries Group: None >Status: Open Resolution: Wont Fix Priority: 5 Private: No Submitted By: Nobody/Anonymous (nobody) Assigned to: Nobody/Anonymous (nobody) Summary: Fresnel integral - function romberg -error. Initial Comment: Maxima 5.14.0 Linux and 5.15.0 Windows. Fresnel integral: http://en.wikipedia.org/wiki/Fresnel_integral http://upload.wikimedia.org/wikipedia/commons/thumb/8/8f/Fresnel_Integrals_%28Normalised%29.svg/250px-Fresnel_Integrals_%28Normalised%29.svg.png Maxima command: for i:1 thru 10 do display(romberg(sin(%pi/2*(x^2)),x,0,i)); .... romberg(sin((%pi*x^2)/2),x,0,7)=0.49970480390049 romberg(sin((%pi*x^2)/2),x,0,8)=-1.0449974219284286*10^-14 romberg(sin((%pi*x^2)/2),x,0,9)=0.49986104588168 also romberg(cos((%pi*x^2)/2),x,0,7)=0.54546705790348 romberg(cos((%pi*x^2)/2),x,0,8)=8.0 romberg(cos((%pi*x^2)/2),x,0,9)=0.53536612585252 in point x=8 is error. Thx ---------------------------------------------------------------------- >Comment By: Robert Dodier (robert_dodier) Date: 2008-05-13 18:32 Message: Logged In: YES user_id=501686 Originator: NO Changing status back to open so it appears in the default browsing mode. ---------------------------------------------------------------------- Comment By: Robert Dodier (robert_dodier) Date: 2008-05-13 18:30 Message: Logged In: YES user_id=501686 Originator: NO romberg is easily fooled by oscillatory integrands: it evaluates the integrand at a few points and sees that they are the same, so it thinks the integrand is constant. Much better to use the Quadpack functions, namely quad_qags, etc. ?? quad at the input prompt should find them. You can fiddle with some parameters to make romberg succeed on this problem (?? romberg finds them), but romberg is just not a very strong algorithm; use quad_qags or some other Quadpack function instead. Marking this report as "won't fix"; the romberg function is a correct implementation of Romberg's method. Instead of closing it, I'll leave it pending, so it stays open for a while in case the original poster comes back. Note: please log in so that annotations on bug reports are automatically sent to you. ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1963314&group_id=4933 ```
 [Maxima-bugs] [ maxima-Bugs-1963314 ] Fresnel integral - function romberg -error. From: SourceForge.net - 2008-06-03 03:58 ```Bugs item #1963314, was opened at 2008-05-13 13:35 Message generated for change (Comment added) made by robert_dodier You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1963314&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: Share Libraries Group: None >Status: Closed Resolution: Wont Fix Priority: 5 Private: No Submitted By: Nobody/Anonymous (nobody) Assigned to: Nobody/Anonymous (nobody) Summary: Fresnel integral - function romberg -error. Initial Comment: Maxima 5.14.0 Linux and 5.15.0 Windows. Fresnel integral: http://en.wikipedia.org/wiki/Fresnel_integral http://upload.wikimedia.org/wikipedia/commons/thumb/8/8f/Fresnel_Integrals_%28Normalised%29.svg/250px-Fresnel_Integrals_%28Normalised%29.svg.png Maxima command: for i:1 thru 10 do display(romberg(sin(%pi/2*(x^2)),x,0,i)); .... romberg(sin((%pi*x^2)/2),x,0,7)=0.49970480390049 romberg(sin((%pi*x^2)/2),x,0,8)=-1.0449974219284286*10^-14 romberg(sin((%pi*x^2)/2),x,0,9)=0.49986104588168 also romberg(cos((%pi*x^2)/2),x,0,7)=0.54546705790348 romberg(cos((%pi*x^2)/2),x,0,8)=8.0 romberg(cos((%pi*x^2)/2),x,0,9)=0.53536612585252 in point x=8 is error. Thx ---------------------------------------------------------------------- >Comment By: Robert Dodier (robert_dodier) Date: 2008-06-02 21:58 Message: Logged In: YES user_id=501686 Originator: NO Closing this report as "won't fix" per earlier comment. ---------------------------------------------------------------------- Comment By: Robert Dodier (robert_dodier) Date: 2008-05-13 18:32 Message: Logged In: YES user_id=501686 Originator: NO Changing status back to open so it appears in the default browsing mode. ---------------------------------------------------------------------- Comment By: Robert Dodier (robert_dodier) Date: 2008-05-13 18:30 Message: Logged In: YES user_id=501686 Originator: NO romberg is easily fooled by oscillatory integrands: it evaluates the integrand at a few points and sees that they are the same, so it thinks the integrand is constant. Much better to use the Quadpack functions, namely quad_qags, etc. ?? quad at the input prompt should find them. You can fiddle with some parameters to make romberg succeed on this problem (?? romberg finds them), but romberg is just not a very strong algorithm; use quad_qags or some other Quadpack function instead. Marking this report as "won't fix"; the romberg function is a correct implementation of Romberg's method. Instead of closing it, I'll leave it pending, so it stays open for a while in case the original poster comes back. Note: please log in so that annotations on bug reports are automatically sent to you. ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1963314&group_id=4933 ```