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See the recommended documentation of this function
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'])
Arguments
- 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
withbinf
andbsup
real vectors with same dimension asp0
.binf
andbsup
are lower and upper bounds onp
.- p0
initial guess (size np x 1)
- 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 onx
).- 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.- iter
maximum number of iterations allowed.
- epsg
threshold on gradient norm.
- epsf
threshold controlling decreasing of
f
- epsx
threshold controlling variation of
x
. This vector (possibly matrix) of same size asx0
can be used to scalex
.
- "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)
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
//generate the data function y=FF(x, p) y=p(1)*(x-p(2))+p(3)*x.*x endfunction //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 function e=G(p, z), y=z(1),x=z(2); e=y-FF(x,p), endfunction X=[];Y=[]; pg=[34;12;14] for x=0:.1:3 Y=[Y,FF(x,pg)+100*(rand()-.5)]; X=[X,x]; end Z=[Y;X]; p0=[3;5;10] [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
//generate the data function y=FF(x, p) y=p(1)*(x-p(2))+p(3)*x.*x endfunction //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 function e=G(p, z), y=z(1),x=z(2); e=y-FF(x,p), endfunction X=[];Y=[]; pg=[34;12;14] for x=0:.1:3 Y=[Y,FF(x,pg)+100*(rand()-.5)]; X=[X,x]; end Z=[Y;X]; p0=[3;5;10] // 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
See Also
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