| Finding coefficients in multiple nonlinear equations using MPFIT [message #71071] |
Fri, 28 May 2010 22:54  |
Junum
Messages: 13
Registered: May 2010
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Junior Member |
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Hi all,
I got a problem that I have spent several days, but did not solve.
I have two nonlinear equations.
Equation 1 has 6 coefficients (c1 through c6) and Eq. 2 has 5
equations (d1 through d5).
Eq. 1 : c1 * A * B^c2 + c3*C^c4 + c5*exp(D^c6) = 0
Eq. 2 : d1*(A/B)^d2 + d3*(1/C)^d4 = 0
Actually, original equations are much complex.
From lab experiments I have data sets of A, B, C, and D, more than
40000.
My goal is to find optimum coefficients using these large data sets.
I've tried to use MPFIT, but it seems that MPFIT has limit to define a
function.
What I did is
expr = '[ '
st = 31
en = 44
FOR j=st,en DO BEGIN
s_L = STRING(FORMAT='( D9.3)',L[j]) + 'D'
s_Lapp = STRING(FORMAT='( D9.3)',Lapp[j]) + 'D'
s_Z = STRING(FORMAT='(D11.6)',Z[j]) + 'D'
s_foc = STRING(FORMAT='( D8.3)',foc[j]) + 'D'
s_rnd = STRING(FORMAT='( D8.3)',round[j]) + 'D'
s_bg = STRING(FORMAT='(D11.5)',bg[j]) + 'D'
exp1 = '( -1.*' + s_foc + ' )'
exp2 = '( (ABS(' + s_L + '/' + s_rnd + '))^P[5] )'
exp3 = '(' + s_bg + ')'
exp4 = '( -1.*ABS(P[1]*(' + exp3 + '^P[3] )) )'
exp5 = '( ABS(' + s_Z + ' + ABS(' + s_Z + ')*P[2] )^P[4] )'
exp6 = '( EXP(' + exp4 + ' * ' + exp5 + ') )'
expr1 = exp1 + ' + ' + exp2 + ' * ' + exp3 + ' * ' +
exp6 + ' * P[0]'
exp7 = '( -1.*(' + s_Lapp + '/' + s_L + ') )'
exp8 = '(' + s_Z + '/((' + s_L + '*'+ s_rnd + ')^(2.)) )'
exp9 = '(ABS(' + exp8 + '))'
exp10 = '( ' + exp8 + ' * P[7] )'
exp11 = '( (' + exp9 + ' + ' + exp10 + ')^P[8] )'
exp12 = '( ((' + s_L + ')^P[10])*P[9] )'
exp13 = '( ' + exp11 + ' * ' + exp3 + ' )'
expr2 = exp7 + ' + ' + exp13 + ' * P[6] + ' + exp12
IF ( j eq st ) THEN BEGIN
expr = expr + expr1 + ', ' + expr2
ENDIF ELSE BEGIN
expr = expr + ', ' + expr1 + ', ' + expr2
ENDELSE
ENDFOR
expr = expr + ' ]'
fit_status = 0
num_iter = 0
resid = 0.D
st_gs = [-10., -10., -10., -10., -10., -10., -10., -10., -10.,
-10., -10. ]
P = mpfitexpr(expr, 1, 1, 0.1, st_gs, MAXITER=900)
14 (so 28 elements on defined function) is ok, but 15 (so 30 elements
on defined function) does not work.
How can I solve this problem?
Can any one help me?
Thank you.
Jun
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