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Bill Choi
Hong Kong
Posts |
 Posted - 10/16/2006 : 07:09:05 AM
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Hi all,
I've encounter problem again. When I try to perform fitting with my scripts(which can be complied) and the 'solver' plugin in excel, they give different responses. For examples, when K1=150000 and K2=120000, NLSF does not response ('errors in defined formula or parameter initialization) while the solver gives a convergent result. (The details of the calculation will be given as the reply of this post). So why there's a such difference? Thank you very much!
Bill |
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Bill Choi
Hong Kong
Posts |
Posted - 10/16/2006 : 07:30:08 AM
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1. Equations:
The equation used in my fitting is shown in the pic as equation (6), which in my script, A=C(tot)*E(tot)
The solution of Cm is calculated according to the resources on the web http://mathworld.wolfram.com/CubicFormula.html
2. Scripts for NLSF using Origin 7.5
Parameters: Kd ('K1'), Kt ('K2'), Em, Ed, Et
Independent variable: C 'C(tot)'
Dependent variable: A
if( Kt == 0.0 || Kd == 0.0)
{
A = NANUM;
return;
}
double a=2.0/(3.0*Kt);
double b=1.0/(3.0*Kd*Kt);
double c=-(C)/(3.0*Kd*Kt);
double Q=(3.0*b-(a^2.0))/9.0;
double R=(9.0*a*b-27.0*c-2.0*(a^3.0))/54.0;
double D=Q^3.0+R^2.0;
double t;
double S;
double T;
double Cm;
if (D<0.0)
{
t=acos(R/sqrt(-(Q^3.0)));
Cm=2.0*sqrt(-Q)*cos(t/3.0)-(a/3.0);
}
else
{
S=(R+sqrt(D))^(1.0/3.0);
T=(R-sqrt(D))^(1.0/3.0);
Cm=S+T-(a/3.0);
}
A=Cm*Em+2.0*Kd*(Cm^2.0)*Ed+3.0*Kd*Kt*(Cm^3.0)*Et;
3. Excel and Raw Data:
The sum of difference between A and A(calc) is minimized by varying K1 and K2. |
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Bill Choi
Hong Kong
Posts |
Posted - 10/16/2006 : 07:37:05 AM
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Data:
C(tot)
1.00E-06
2.00E-06
3.01E-06
4.01E-06
5.01E-06
6.01E-06
7.01E-06
8.02E-06
9.02E-06
1.00E-05
1.10E-05
1.20E-05
1.30E-05
1.40E-05
1.50E-05
1.75E-05
2.00E-05
A
0.069596171
0.18049413
0.277240485
0.367668748
0.427025646
0.494419694
0.526324153
0.551330388
0.58293289
0.605690002
0.606800854
0.622256041
0.674458563
0.68992275
0.705682695
0.757495046
0.77144444
Em 115000
Ed 35361
Et 7500
K1 153819.5216
K2 130000
Calculations
a = 2/(3*K2)
b = 1/(3*K2*K1)
c = -C(tot)/(3*K2*K1)
Q = (3*b-a^2)/9
R = (9*a*b-27*c+2*a^3)/54
D = Q^3+R^2
S = (R+sqrt(D))^(1/3)
T = (R+sqrt(D))^(1/3)
Cm = S+T-a/3
The fitting is performed by minimizing the sum of difference of square between A and A(cal.). |
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larry_lan
China
Posts |
Posted - 10/18/2006 : 12:17:51 AM
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Hi Bill:
The problem is the line:
T=(R-sqrt(D))^(1.0/3.0);
You can see the result of (R-sqrt(D)) is negative, actually you can not compute power (1/3) of a negative value. In fact, the value you calculated in Excel actually is:
T=-((sqrt(D)-R)^(1.0/3.0));
Try to modify this line and fit again.
Larry
OriginLab Technical Services |
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Topic |
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NLSF vs. Solver in Excel