Very Small Numbers

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Sanborn, Mike

• May 01, 2023 21:59

I am trying to run a lateral dispersion model which includes a complimentary error function.  As the complimentary error function gets smaller and smaller, Goldsim stops calculating is at 2.2e-16  

Is 2.2e-16 the smallest (i.e. most precise) number that the software works at?  

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  Rick Kossik

  • May 01, 2023 22:01

  What version are you running?

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  Sanborn, Mike

  • May 01, 2023 22:00

  I realize that I don't have e-16 precision, so it's just a theoretical number, but it makes my outputs a little ownky. 

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  Sanborn, Mike

  • May 01, 2023 22:02

  I am running 14.0

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  Rick Kossik

  • May 01, 2023 22:03

  The issue is with the math library for the calculation of erfc.  However, we added a  new function for erfc (more accurate) in GoldSim 14, so I am surprised by this

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  Rick Kossik

  • May 01, 2023 22:05

  Can you add an if statement that sets it to 0 when it gets very small?  The erfc is tricky.  But in 14 we used a different function that was as accurate as Excel's representation

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  Rick Kossik

  • May 01, 2023 22:06

  Do you realize that GoldSim can compute lateral dispersion using the Plume function?

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  Sanborn, Mike

  • May 01, 2023 22:21

  When I set to 0 I get a divide by zero error, so I have an if then that puts in 1e-16.  It works well enough, now that I now the limitations of that particular set of calculations.    
  Unfortunately, I am obligated to use this particular model implementation.  Thanks for the prompt response.  GoldSim RULES!!!!!!!

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  Rick Kossik

  • May 01, 2023 22:23

  Just out of curiosity, what is the value of the argument to erfc when it hits the limit?

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  Sanborn, Mike

  • May 01, 2023 22:26

  

   

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  Rick Kossik

  • May 01, 2023 22:29

  Not surprised.  You are WAAAAAAY at the tail of that function

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  Sanborn, Mike

  • May 01, 2023 22:32

  Yeah.  It was a hidden issue for a while, because we weren't ever calculating way out there.  The end result of these calculations predict a theoretical concentration of a contaminant  min soil that cannot physically exist, so it's really a non issue.  Thanks for your help

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