Help with an error message: FUNC DOMAIN: x**y, x<0

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AB

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Apr 10, 2016, 6:28:35 AM4/10/16
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Hello All,

So i have read other or similar posts about this message and I have read about it online, but I still am not able to make sense of it. I think understand that the error is caused by the fact that taking the sqrt( NEG #) is what is supposed to cause this error, but what i dont understand with my code, is that I have the term squared to correct this. I am a programming newbie so this is probably an easily fixable syntax or input error. Would someone look at my code and tell me what they see?? I have included a picture of the equation i am trying to model.
When I run the code, I receive the following message: FUNC DOMAIN: x**y, x<0. There are no red error messages. Also, Im not exactly sure if I need to sum this for what I am trying to do so If that might be relevant information, there it is.

Also, I am aware that there is information in my code that does not actually get used, I just placed it in there because I am trying to compile everything I think is relevant information. Also, this model is far from being complete, I am just trying to fix one error at a time i guess and slowly build from there.


E2..  sum(i,((q1/K)*x)+(Q/4*pi*K)*log((((((x-xw)**2)+(y**2))/(((x+xw)**2)+(y**2))))))=e=phi_2;

Any information or insight that anyone may offer would be greatly appreciated.
Thank you!!


Enter code here...


Set i well /1/;
scalars
    K hydraulic conductivity m_d      /100/
    q1 uniform freshwater discharge   /0.6/
    d mean ocean SWE                  /14/
    Rs saltwater density              /1.025/
    Rf freshwater density             /1.000/
    s saltfreshwater ratio            /1.025/
    xw well distance from coast line  /1000/
    y distance between wells          /0/
    phi_1 saltwater head at tow       /2.5/;


positive variable   phi_2 freshwater head
                    Q     Optimal pumping rate
                    x     saltwater toe length;

free variable       obj   objective variable;

equations
E1 constraint on well pumping equation
E2 Equation for the Freshwater potential
E3 toe constraint
E4 objective fcn for max toe length;

E1..  phi_1=l=phi_2;
E2..  sum(i,((q1/K)*x)+(Q/4*pi*K)*log((((((x-xw)**2)+(y**2))/(((x+xw)**2)+(y**2))))))=e=phi_2;
E3..  x=l=xw;
E4..  obj=e=x;

model saltwater /all/;
solve saltwater using MINLP maximize obj;
* I dont know what execerror does
execerror=0;
display Q.l, x.l, obj.l;









AB

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Apr 21, 2016, 12:02:48 AM4/21/16
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So just in case anyone else reads this, I resolved this issue bu using the power function. I have no idea why it works but it does. so instead of using (x-xw)**2 and ) (x+xw)**2, i used power ((x-xw),2) and power((x+xw),2)

Steven Dirkse

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Apr 21, 2016, 10:03:02 AM4/21/16
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AB,

This link should give you a good idea why your change works as it does.


-Steve

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Steven Dirkse, Ph.D.
GAMS Development Corp.,  Washington DC
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