Re: how to avoid numeric error

*To*: mathgroup at smc.vnet.net*Subject*: [mg20364] Re: [mg20309] how to avoid numeric error*From*: BobHanlon at aol.com*Date*: Sun, 17 Oct 1999 02:45:39 -0400*Sender*: owner-wri-mathgroup at wolfram.com

Atul, (-5.2)^1208. 8.551437202665365431742222523666`12.6535*^864 - 2.4803091328936406321397756468`12.6535*^852*I Despite its large magnitude, the magnitude of the imaginary part is small compared to the magnitude of the real part (differ by 12 orders of magnitude). 10^864*Chop[(-5.2)^1208./10^864] == (-5.2)^1208 True Extending the concept of Chop relativeChop[x_ , delta_:10^-10] /; (Abs[x] == 0) = 0; relativeChop[x_, delta_:10^-10] := Module[{mag = Abs[x]}, mag*Chop[x/mag, delta]] relativeChop[(-5.2)^1208.] == (-5.2)^1208 True Bob Hanlon In a message dated 10/16/1999 12:38:51 AM, atulksharma at yahoo.com writes: >I am at a loss to explain this behavior, though I perhaps >misunderstand how Mathematica implements it's machine precision routines. >This is a simple example of a problem that cropped up during evaluation >of >constants of integration >in a WKB approximation, where I would get quite different results depending >on how the constant was evaluated. I have localized the discrepancy to >one >term of the form shown below: > > >testParameters = > {x1 -> 5.2, x2 -> 0.3, x3 -> 0.002, x4 -> -0.00025} > >(-x1)^(-(x2 + x3)/x4) /. testParameters > >In this case, as it turns out, x1 = -5.2, which is a floating point number, >and the exponent = 1208 (which may be integer or floating point, but is >floating point in this case). >I assumed that the result would be evaluated to machine precision in either >case, >since x1 is a float regardless. However, depending on whether the exponent >is integer or not, I get two different results, with a large imaginary >component > >In[27]:= >(-5.2)^1208. > >Out[27]= >8.55143720266536543174145`12.6535*^864 - > 2.48026735232231456274073`12.6535*^852*I > >In[28]:=(-5.2)^1208 > >Out[28]= >8.55143720266675767908621`12.8725*^864 > >I assume that this has some simple relationship to machine precision and >round-off error, but am I wrong in assuming that x1 should determine the >numeric precision of the entire operation? > >I am using Mathematica 3.01.1 on a PC/Win95 platform. > >I also encountered another problem, which bothers me because it's so >insidious. In moving a notebook from one machine to another by floppy (work >to home), a parsing error occurred buried deep inside about 30 pages of >code. A decimal number of the form 1.52356 was parsed as 1.5235 6 with >a >space inserted and interpreted as multiplication. The same error occured >in >the same place on several occasions (i.e. when I start getting bizarre >results, I know to go and correct this error). > >I know these sound minor, but they have a large effect on the solution >and >could easily go undetected. Thanks in advance. >

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