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[MUG] Re: why the plot is not consistent with evaluated value?
| [MUG] Re: why the plot is not consistent with evaluated value? |
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Author: Maple User Group
Posted: Wed, 27 Nov 2002 10:34:48 -0500
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>> From: Maple User Group "maple_gr"
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Date: Fri, 22 Nov 2002 00:37:28 -0400
From: C W "sylvester7"
To: "maple-list"
Subject: why the plot is not consistent with evaluated value?
You might observe a difference with the following code :
g := Pi*((2*R-x)^2-R^2);
Fx := exp(-m*g*(1-exp(-n*2)));
fx := diff(Fx,x);
Ex := (int)(x*fx,x=0..R);
Ex2:=collect(expand(Ex),exp,factor);
plot((evalf@subs)(m=1/Pi,n=0.2,[Ex,Ex2]),R=0..40,view=[DEFAULT,0..40]);
With my version of Maple, that is Maple V R4, Ex and Ex2 do not evaluate to the
same.
Chris
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Date: Fri, 22 Nov 2002 00:41:22 -0400
From: C W "sylvester7"
To: "maple-list"
Subject: why the plot is not consistent with evaluated value?
Hi !
Also try changing Digits and You will see that Ex evaluates differently. There
is a round off error someplace here...
Chris
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Date: Sat, 23 Nov 2002 10:54:45 -0400
From: Vladimir Bondarenko "vvb"
To: "maple-list"
Subject: why the plot is not consistent with evaluated value?
You have just come across a treacherous loss of accuracy (10 digits
by default). Add Digits := 15: before your plot() and enjoy ;-)
Best wishes,
Vladimir Bondarenko
Mathematical and Production Director
Symbolic Testing Group
Email: "vvb"
Web : http://www.CAS-testing.org/ (under development, 95% ready)
http://maple.bug-list.org/ (under development, 20% ready)
Voice: (380)-652-447325 Mon-Fri 6 a.m. - 3 p.m. GMT
Mail : 76 Zalesskaya Str, Simferopol, Crimea, Ukraine
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From: "Dr Francis J. Wright" "F.J.Wright"
To: "xili"
Subject: why the plot is not consistent with evaluated value?
Date: Tue, 26 Nov 2002 17:10:43 -0000
It appears to be a problem of numerical error caused by the cancellation of
large terms in tmpEx. By default, plot uses hardware floating point (for
speed), which is not quite sufficiently precise to handle the numerical
cancellation in this particular problem. One easy way to avoid this is to
set a high enough value for Digits; on my system Digits := 15 was enough to
give the almost-straight-line plot that you (presumably) expect. Setting
Digits to a value larger than evalhf(Digits) forces plot to use software
floating point, and on my system evalhf(Digits) is 14. But for safety I
suggest setting Digits to 20 for this problem.
Francis
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