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MathGroup Archive 2007

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Why I got inumr??

  • To: mathgroup at smc.vnet.net
  • Subject: [mg80987] Why I got inumr??
  • From: "hj.gegewu" <chiron1201 at 163.com>
  • Date: Fri, 7 Sep 2007 02:03:46 -0400 (EDT)

Hi all!
I have a problem when I try to Nintegrate following code:

a = 0;  b = 2; 

P = (Max[0, (Min[b, #2*Cos[#3] + Sqrt[#1^2 - (#2*Sin[#3])^2]] - 
        Max[a, #2*Cos[#3] - Sqrt[#1^2 - (#2*Sin[#3])^2]])/(b - 
        a)]) &;

ProbR1 = (NIntegrate[
     P[(-#1*Cos[z] + Sqrt[#2^2 - (#1 *Sin[z])^2])/#3, x, 
       y]/(4*Pi^2*(b - a)), {z, Pi - ArcSin[#2/#1], 
      Pi + ArcSin[#2/#1]}, {y, 0, 2*Pi}, {x, a, 
      Min[b, (-#1*Cos[z] + Sqrt[#2^2 - (#1 *Sin[z])^2])/(#3*
          Abs[Sin[y]])]}, 
     Method -> {"GlobalAdaptive", 
       "SingularityHandler" -> "DuffyCoordinates"}]) &;

ProbR2 = (NIntegrate[
     P[(-#1*Cos[z] - Sqrt[#2^2 - (#1 *Sin[z])^2])/#3, x, 
       y]/(4*Pi^2*(b - a)), {z, Pi - ArcSin[#2/#1], 
      Pi + ArcSin[#2/#1]}, {y, 0, 2*Pi}, {x, a, 
      Min[b, (-#1*Cos[z] + Sqrt[#2^2 - (#1 *Sin[z])^2])/(#3*
          Abs[Sin[y]])]}, 
     Method -> {"GlobalAdaptive", 
       "SingularityHandler" -> "DuffyCoordinates"}]) &;

ProbR1[130, 125, 50]
ProbR2[130, 125, 50]

while the line of "ProbR1[130, 125, 50]" can be caculated correctly, the line of "ProbR2[130, 125, 50]" keeps giving me the warning of

NIntegrate::inumr: "The integrand \
Max[0,1/2\(-Max[0,Times[<<2>>]+Times[<<2>>]]+Min[2,x\Cos[<<1>>]+Sqrt[\
Plus[<<2>>]]])]/(8\\[Pi]^2) has evaluated to non-numerical values for \
all sampling points in the region with boundaries \
{{0.5,0.75},{0.125,0.0625},{0.5,0.25}}."

The only difference of these two sentence is the sign of "Sqrt[#2^2 - (#1 *Sin[z])^2])". Why this happened?

Thanks!


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