Scilab Function
Last update : 28/12/2008
datafit - Parameter identification based on measured data
Calling Sequence
- [p,err]=datafit([imp,] G [,DG],Z [,W],[contr],p0,[algo],[df0,[mem]],
- [work],[stop],['in'])
Parameters
-
imp: scalar argument used to set the trace mode. imp=0 nothing (execpt errors) is reported, imp=1 initial and final reports, imp=2 adds a report per iteration, imp>2 add reports on linear search. Warning, most of these reports are written on the Scilab standard output.
-
G: function descriptor (e=G(p,z), e: ne x 1, p: np x 1, z: nz x 1)
-
DG: partial of G wrt p function descriptor (optional; S=DG(p,z), S: ne x np)
-
Z: matrix [z_1,z_2,...z_n] where z_i (nz x 1) is the ith measurement
-
W: weighting matrix of size ne x ne (optional; defaut no ponderation)
-
contr: 'b',binf,bsup with binf and bsup real vectors with same dimension as p0. binf and bsup are lower and upper bounds on p.
-
p0: initial guess (size np x 1)
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algo: 'qn' or 'gc' or 'nd' . This string stands for quasi-Newton (default), conjugate gradient or non-differentiable respectively. Note that 'nd' does not accept bounds on x ).
-
df0: real scalar. Guessed decreasing of f at first iteration. (df0=1 is the default value).
-
mem : integer, number of variables used to approximate the Hessian, (algo='gc' or 'nd'). Default value is around 6.
-
stop: sequence of optional parameters controlling the convergence of the algorithm. stop= 'ar',nap, [iter [,epsg [,epsf [,epsx]]]]
-
"ar" : reserved keyword for stopping rule selection defined as follows:
-
nap: maximum number of calls to fun allowed.
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iter: maximum number of iterations allowed.
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epsg: threshold on gradient norm.
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epsf: threshold controlling decreasing of f
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epsx: threshold controlling variation of x. This vector (possibly matrix) of same size as x0 can be used to scale x.
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"in" : reserved keyword for initialization of parameters used when fun in given as a Fortran routine (see below).
-
p: Column vector, optimal solution found
-
err: scalar, least square error.
Description
datafit is used for fitting data to a model.
For a given function G(p,z), this function finds the best vector
of parameters p for approximating G(p,z_i)=0 for a set of measurement
vectors z_i. Vector p is found by minimizing
G(p,z_1)'WG(p,z_1)+G(p,z_2)'WG(p,z_2)+...+G(p,z_n)'WG(p,z_n)
datafit is an improved version of fit_dat.
Examples
//generate the data
function y=FF(x,p),y=p(1)*(x-p(2))+p(3)*x.*x,endfunction
X=[];Y=[];
pg=[34;12;14] //parameter used to generate data
for x=0:.1:3, Y=[Y,FF(x,pg)+100*(rand()-.5)];X=[X,x];end
Z=[Y;X];
//The criterion function
function e=G(p,z),
y=z(1),x=z(2);
e=y-FF(x,p),
endfunction
//Solve the problem
p0=[3;5;10]
[p,err]=datafit(G,Z,p0);
scf(0);clf()
plot2d(X,FF(X,pg),5) //the curve without noise
plot2d(X,Y,-1) // the noisy data
plot2d(X,FF(X,p),12) //the solution
//the gradient of the criterion function
function s=DG(p,z),
a=p(1),b=p(2),c=p(3),y=z(1),x=z(2),
s=-[x-b,-a,x*x]
endfunction
[p,err]=datafit(G,DG,Z,p0);
scf(1);clf()
plot2d(X,FF(X,pg),5) //the curve without noise
plot2d(X,Y,-1) // the noisy data
plot2d(X,FF(X,p),12) //the solution
See Also
lsqrsolve, optim, leastsq,