LevenbergMarquardt 法非线性回归函数文档格式.docx
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LevenbergMarquardt 法非线性回归函数文档格式.docx
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%y=vecofobsvalues,sameno.ofrowsasx.
%wt=vec(dim=1orlength(x))ofstatisticalweights.
Theseshouldbeset
tobeproportionalto(sqrtsofvar(y))^-1;
(Thatis,thecovaraince
matrixofthedataisassumedtobeproportionaltodiagonalwithdiagonal
equalto(wt.^2)^-1.
Theconstantofproportionalitywillbeestimated.),
default=1.
%pin=vectorofinitialparameterstobeadjustedbyleasqr.
%dp=fractionalincrofpfornumericalpartials,default=.001*ones(size(pin))
dp(j)>
0meanscentraldifferences.
dp(j)<
0meansone-sideddifferences.
%Note:
dp(j)=0holdsp(j)fixedi.e.leasqrwontchangeinitialguess:
pin(j)
%func=nameoffunctioninquotes,oftheformy=f(x,p)
%dfdp=nameofpartialsM-fileinquotesdefaultisprt=dfdp(x,f,p,dp,func)
%stol=scalartolerancesonfractionalimprovementinss,defaultstol=.0001
%niter=scalarmaxno.ofiterations,default=20
%options=matrixofnrows(samenumberofrowsaspin)containing
column1:
desiredfractionalprecisioninparameterestimates.
Iterationsareterminatedifchangeinparametervector(chg)ontwo
consecutiveiterationsislessthantheircorrespondingelements
inoptions(:
1).
[ie.all(abs(chg*currentparmest)<
options(:
1))
ontwoconsecutiveiterations.],default=zeros().
column2:
maximumfractionalstepchangeinparametervector.
Fractionalchangeinelementsofparametervectorisconstrainedtobe
atmostoptions(:
2)betweensucessiveiterations.
[ie.abs(chg(i))=abs(min([chg(i)options(i,2)*currentparamestimate])).],
default=Inf*ones().
OUTPUTVARIABLES
%f=vecfunctionvaluescomputedinfunctionfunc.
%p=vectrialorfinalparameters.i.e,thesolution.
%kvg=scalar:
=1ifconvergence,=0otherwise.
%iter=scalarno.ofinterationsused.
%corp=correlationmatrixforparameters
%covp=covariancematrixoftheparameters
%covr=diag(covariancematrixoftheresiduals)
%stdresid=standardizedresiduals
%Z=matrixthatdefinesconfidenceregion
%r2=coefficientofmultipledetermination
{}=optionalparameters
%ss=scalarsumofsquares=sum-over-i(wt(i)*(y(i)-f(i)))^2.
%AllZeroguessesnotacceptable
%RichardI.Shrager(301)-496-1122
%ModifiedbyA.Jutan(519)-679-2111
%ModifiedbyRayMuzic14-Jul-1992
1)addmaxstepfeatureforlimitingchangesinparameterestimates
ateachstep.
2)removeforcedcolumnizationofx(x=x(:
))atbeginning.xcouldbe
amatrixwiththeithrowofcontainingvaluesofthe
independentvariablesattheithobservation.
3)addverboseoption
4)addoptionalreturnargumentscovp,stdresid,chi2
5)reviseestimatesofcorp,stdev
%ModifiedbyRayMuzic11-Oct-1992
%1)reviseestimateofVy.
removechi2,addZasreturnvalues
%ModifiedbyRayMuzic7-Jan-1994
1)Replaceones(x)withaconstructthatiscompatiblewithversions
newerandolderthanv4.1.
2)Addedglobaldeclarationofverbose(neededfornewerthanv4.x)
3)Replacereturnvaluevar,thevarianceoftheresidualswithcovr,
thecovariancematrixoftheresiduals.
4)Introduceoptionsas10thinputargument.
Include
convergencecriteriaandmaxstepinit.
5)Correctcalculationofxtxwhichaffectscoverainceestimate.
6)Eliminatestdev(estimateofstandarddeviationofparameter
estimates)fromthereturnvalues.
Thecovpisamuchmore
meaningfulexpressionofprecisionbecauseitspecifiesaconfidence
regionincontrasttoaconfidenceinterval..
Ifneeded,however,
stdevmaybecalculatedasstdev=sqrt(diag(covp)).
7)Changetheorderofthereturnvaluestoamorelogicalorder.
8)ChangetomoreefficentalgorithmofBardforselectingepsL.
%Refrences:
%Bard,NonlinearParameterEstimation,AcademicPress,1974.
%DraperandSmith,AppliedRegressionAnalysis,JohnWileyandSons,1981.
%setdefaultargs
%argumentprocessing
plotcmd='
plot(x(:
1),y,'
'
o'
x(:
1),f);
shg'
;
if(sscanf(version,'
%f'
)>
=4),
globalverbose
figure(gcf)'
end;
if(exist('
verbose'
)~=1),verbose=1;
end;
if(nargin<
=8),dfdp='
dfdp'
=7),dp=.001*(pin*0+1);
%DT
if(nargin==6),wt=1.
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