datafit — Parameter identification based on measured data
[p,err]=datafit([imp,] G [,DG],Z [,W],[contr],p0,[algo],[df0,[mem]], [work],[stop],['in'])
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.
function descriptor (e=G(p,z), e: ne x 1, p: np x 1, z: nz x 1)
partial of G wrt p function descriptor (optional; S=DG(p,z), S: ne x np)
matrix [z_1,z_2,...z_n] where z_i (nz x 1) is the ith measurement
weighting matrix of size ne x ne (optional; defaut no ponderation)
: 'b',binf,bsup
with binf
and bsup
real vectors with same dimension as p0
. binf
and bsup
are lower and upper bounds on p
.
initial guess (size np x 1)
: '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
).
real scalar. Guessed decreasing of f
at first iteration. (df0=1
is the default value).
integer, number of variables used to approximate the Hessian, (algo='gc' or 'nd'
). Default value is around 6.
sequence of optional parameters controlling the convergence of the algorithm. stop= 'ar',nap, [iter [,epsg [,epsf [,epsx]]]]
reserved keyword for stopping rule selection defined as follows:
maximum number of calls to fun
allowed.
maximum number of iterations allowed.
threshold on gradient norm.
threshold controlling decreasing of f
threshold controlling variation of x
. This vector (possibly matrix) of same size as x0
can be used to scale x
.
reserved keyword for initialization of parameters used when fun
in given as a Fortran routine (see below).
Column vector, optimal solution found
scalar, least square error.
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
.
//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 // Add some bounds on the estimate of the parameters // We want positive estimation (the result will not change) [p,err]=datafit(G,DG,Z,'b',[0;0;0],[%inf;%inf;%inf],p0,algo='gc'); 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