On May 29, 3:32 pm, Junum <junshi...@gmail.com> wrote:
> On May 29, 1:33 am, Craig Markwardt <craig.markwa...@gmail.com> wrote:
>
>
>
>> Greetings--
>
>> On May 29, 1:54 am, Junum <junshi...@gmail.com> wrote:
>
>>> 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?
>
>> You don't say how the code "does not work" so it is difficult to
>> comment. The example is not complete, so I can't test it.
>
>> I think you need to define better what you are trying to do. I guess
>> that you are trying to solve your two equations in a least squares
>> sense using all the data jointly, but that is not clear.
>
>> Your equation has 11 coefficients, so I don't understand why 14 or 15
>> are important. If I misinterpreted your intent, and you want to solve
>> each equation separately, then you can just run MPFIT*() 40000 times
>> and achieve your goal. I don't know why you need to join them
>> together into an expression. I doubt any IDL program will be able to
>> solve an equation with 40000 parameters, if that is really what you
>> are attempting.
>
>> MPFITEXPR() is not the ideal solution for your problem; it is better
>> for quick jobs. MPFITEXPR has limitations because it needs to parse
>> the user expression many times. IDL cannot parse or evaluate
>> infinitely long expressions. For solving equations, MPFIT() is the
>> desirable method, especially since you have already expressed your
>> equations as (function) = 0. That is exactly what MPFIT() solves.
>
>> If my initial suspicion was right, it should be as simple as something
>> like this (untested),
>> function myfunc, p, a=a, b=b, c=c, d=d
>> return, [p[0]* a * b^p[1] + p[2]*c^p[3] + p[4]*exp(d^p[5]), $
>> p[6] * (a/b)^p[7] + p[8]*(1/c)^p[9] ]
>> end
>> The [ ... ] notation will glue the two residual arrays together.
>> MPFIT() will try to solve for parameters which drive all equations to
>> zero.
>
>> p0 = [ ... initial guess of parameters ... ]
>> p = mpfit('myfunc', p0, functargs={a:a, b:b, c:c, d:d})
>
>> Your equations look a little troublesome. You may have to worry about
>> whether they are linearly independent, and whether certain parameters
>> will be strongly correlated. You also don't define whether the
>> equations should be weighted equally or not. The above formulation
>> gives equal weight.
>
>> Craig
>
> Craig, thank you very much.
> Let me explain my problem.
> I have two equations, f, g.
> These are function of 4 parameters (A, B, C, and D), so f(A,B,C,D) and
> g(A,B,C,D).
> I can guess how these equations should be.
> For example,
> 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
> Here, I don't know constants (c1 through c6 and d1 through d4).
> From lab experiments, I have measurements of A, B, C, and D.
> Therefore, my goal is to find optimum coefficients (c1 through c6 and
> d1 through d4) using measurements of A, B, C, and D.
> I have approximately 40000 datasets of A, B, C, D and want to find
> coefficients that satisfy eqs. 1 and 2 with minimum residual error.
> To make a problem simple, I may combine two equations together, so it
> becomes c1 * A * B^c2 + c3*C^c4 + c5*exp(D^c6) + d1*(A/B)^d2 + d3*(1/
> C)^d4 = 0.
> This is one equation with 11 unknowns (i.e., coefficient).
> Theoretically, I need 10 more equation to solve them.
> But, I have 40000 equations and want to find optimum coefficients that
> satisfy 40000 equations with some residuals.
> It is clear that there will be exact solution (coefficient) that
> satisfy 40000 equations.
> In summary, my goal is to find coefficients that make minimum residual
> error across 40000 equations.
> I need this because we need to find empirical relationship based on
> experiment and more data give us more higher confidence level.
>
> "Does not work" means that I got "% MPFITEXPR: check syntax and
> parameter usage" message when I add more expressions on "my
> function".
> Since my function ('expr' in original posting) is defined as a string,
> I think that this is problem of length of string, as you indicated.
>
> Does your suggestion associated with MPFIT solve equations 40000
> times?
> Do you have any suggestion?
> Please let me know any question or comment.
>
> I really thank for your help.
> Thank you very much again.
MPFIT() solves equations of the sort you described, in a least squares
sense - if that is what you want??!?!? I can't define your
optimization problem, you need to do that.
Your problem areas are:
* using MPFITEXPR
* trying to write an expression string with 40000 terms (!)
I gave you an example using MPFIT() that
* uses a user function, not an expression
* uses IDL vector notation to make the expression shorter and faster
to evaluate
* keeps the original equations
You are free to adapt it to see if it produces what you want.
Also, the "IDL Visualize 2009" presentation I did last year is
relevant since it talks about equation solving. Please see the link
from my web page.
http://cow.physics.wisc.edu/~craigm/idl/fitting.html
Craig
|
comp.lang.idl-pvwave archive
Members
Search
Help
Login
Home
