Non-Linear Models
A series of pre-defined models exist that are classified into different categories. For almost all of these models, the partial derivatives are specified so that they can be calculated analytically and no approximation of the derivatives is necessary.
EXPONENTIAL FUNCTIONS
Box and Lucas (variant 1)
2 Parameters
Constant: MODEL_EXP_BOXLUCAS1
Box and Lucas (variant 2)
2 Parameters
Constant: MODEL_EXP_BOXLUCAS2
Box and Lucas (variant 3)
2 Parameters
Constant: MODEL_EXP_BOXLUCAS3
Chapman model
3 Parameters
Constant: MODEL_EXP_CHAPMAN
Exponential function
3 Parameters
Constant: MODEL_EXP_EXPONENTIAL
Exponential associate
5 Parameters
Constant: MODEL_EXP_EXPONENTIAL_ASSOCIATE
Exponential decay function (variant 1)
3 Parameters
Constant: MODEL_EXP_EXPONENTIAL_DECAY1
Exponential decay function (variant 2)
5 Parameters
Constant: MODEL_EXP_EXPONENTIAL_DECAY2
Exponential decay function (variant 3)
7 Parameters
Constant: MODEL_EXP_EXPONENTIAL_DECAY3
Exponential decay function (variant 4)
4 Parameters
Constant: MODEL_EXP_EXPONENTIAL_DECAY4
Exponential decay function (variant 5)
6 Parameters
Constant: MODEL_EXP_EXPONENTIAL_DECAY5
Exponential decay function (variant 6)
8 Parameters
Constant: MODEL_EXP_EXPONENTIAL_DECAY6
Exponential growth function (variant 1)
3 Parameters
Constant: MODEL_EXP_EXPONENTIAL_GROW1
Exponential growth function (variant 2)
5 Parameters
Constant: MODEL_EXP_EXPONENTIAL_GROW2
Exponential growth function (variant 3)
7 Parameters
Constant: MODEL_EXP_EXPONENTIAL_GROW3
Exponential growth function (variant 4)
4 Parameters
Constant: MODEL_EXP_EXPONENTIAL_GROW4
Exponential growth function (variant 5)
6 Parameters
Constant: MODEL_EXP_EXPONENTIAL_GROW5
Exponential growth function (variant 6)
8 Parameters
Constant: MODEL_EXP_EXPONENTIAL_GROW6
Exponential linear combination
4 Parameters
Constant: MODEL_EXP_EXPONENTIAL_LINEAR
Exponential function with 1 parameter (variant 1)
1 Parameter
Constant: MODEL_EXP_EXPONENTIAL_ONEPARA1
Exponential function with 1 parameter (variant 2)
1 Parameter
Constant: MODEL_EXP_EXPONENTIAL_ONEPARA2
Exponential function with 1 parameter (variant 3)
1 Parameter
Constant: MODEL_EXP_EXPONENTIAL_ONEPARA3
Exponential function with 1 parameter (variant 4)
1 Parameter
Constant: MODEL_EXP_EXPONENTIAL_ONEPARA4
Exponential function with 1 parameter (variant 5)
1 Parameter
Constant: MODEL_EXP_EXPONENTIAL_ONEPARA5
Exponential function with 1 parameter (variant 6)
1 Parameter
Constant: MODEL_EXP_EXPONENTIAL_ONEPARA6
Exponential function with 1 parameter (variant 7)
1 Parameter
Constant: MODEL_EXP_EXPONENTIAL_ONEPARA7
Exponential function with 2 parameters (variant 1)
2 Parameters
Constant: MODEL_EXP_EXPONENTIAL_TWOPARA1
Exponential function with 2 parameters (variant 2)
2 Parameters
Constant: MODEL_EXP_EXPONENTIAL_TWOPARA2
Exponential function with 2 parameters (variant 3)
2 Parameters
Constant: MODEL_EXP_EXPONENTIAL_TWOPARA3
Exponential function with 3 parameters (variant 1)
3 Parameters
Constant: MODEL_EXP_EXPONENTIAL_THREEPARA1
Exponential function with 3 parameters (variant 2)
3 Parameters
Constant: MODEL_EXP_EXPONENTIAL_THREEPARA2
Exponential function with 3 parameters
(variant 3)
3 Parameters
Constant: MODEL_EXP_EXPONENTIAL_THREEPARA3
Monomolecular growth model (variant 1)
3 Parameters
Constant: MODEL_EXP_MONOMOLECULAR1
Monomolecular growth model (variant 2)
3 Parameters
Constant: MODEL_EXP_MONOMOLECULAR2
Shaw model
4 Parameters
Constant: MODEL_EXP_SHAW
Stirling model
3 Parameters
Constant: MODEL_EXP_STIRLING
Time-power model
3 Parameters
Constant: MODEL_EXP_TIMEPOWER
Asymptotic regression model (variant 1)
3 Parameters
Constant: MODEL_EXP_YIELDFERTILIZER1
Asymptotic regression model (variant 2)
3 Parameters
Constant: MODEL_EXP_YIELDFERTILIZER2
GROWTH FUNCTIONS
Boltzmann model
4 Parameters
Constant: MODEL_GROWTH_BOLTZMANN
Gompertz model
3 Parameters
Constant: MODEL_GROWTH_GOMPERTZ
Hill model
3 Parameters
Constant: MODEL_GROWTH_HILL
Logistic Dose response model
4 Parameters
Constant: MODEL_GROWTH_LOGISTICDOSERESPONSE
Logistic model (variant 1)
3 Parameters
Constant: MODEL_GROWTH_SIGMOIDALLOGISTIC1
Logistic model (variant 2)
3 Parameters
Constant: MODEL_GROWTH_SIGMOIDALLOGISTIC2
Logistic model (variant 3)
3 Parameters
Constant: MODEL_GROWTH_SIGMOIDALLOGISTIC3
Richards model
4 Parameters
Constant: MODEL_GROWTH_SIGMOIDALRICHARDS2
Weibull model (variant 1)
4 Parameters
Constant: MODEL_GROWTH_SIGMOIDALWEIBULL1
Weibull model (variant 2)
4 Parameters
Constant: MODEL_GROWTH_SIGMOIDALWEIBULL2
HYPERBOLA FUNCTIONS
Hyperbola function (variant 1)
2 Parameters
Constant: MODEL_HYPERBOLA_HYPERBOLA1
Hyperbola function (variant 2)
5 Parameters
Constant: MODEL_HYPERBOLA_HYPERBOLA2
Hyperbola function (variant 3)
4 Parameters
Constant: MODEL_HYPERBOLA_HYPERBOLA3
Hyperbola function (variant 4)
2 Parameters
Constant: MODEL_HYPERBOLA_HYPERBOLA4
Hyperbola function (variant 5)
2 Parameters
Constant: MODEL_HYPERBOLA_HYPERBOLA5
LOGARITHM FUNCTIONS
Bradley function
2 Parameters
Constant: MODEL_LOGARITHM_BRADLEY
Logarithm function (variant 1)
2 Parameters
Constant: MODEL_LOGARITHM_LOG1
Logarithm function (variant 2)
2 Parameters
Constant: MODEL_LOGARITHM_LOG2
Logarithm function (variant 3)
3 Parameters
Constant: MODEL_LOGARITHM_LOG3
Logarithm function (variant 4)
1 Parameters
Constant: MODEL_LOGARITHM_LOG4
PEAK FUNCTIONS
Asymmetric double sigmoidal model
5 parameters + baseline parameter
Peak Function
Constant: MODEL_PEAK_ASYMMETRICDOUBLESIG
Beta function
5 parameters + baseline parameter
Peak Function
Constant: MODEL_PEAK_BETA
Extreme function
3 parameters + baseline parameter
Peak Function
Constant: MODEL_PEAK_EXTREME
Gauss model (variant 1)
3 parameters + baseline parameter
Peak Function
Constant: MODEL_PEAK_GAUSS
Gauss model (variant 2)
3 parameters + baseline parameter
Peak Function
Constant: MODEL_PEAK_GAUSSAMPLITUDE
Gram-Charlier model
5 parameters + baseline parameter
Peak Function
Constant: MODEL_PEAK_GRAMCHARLIER
Inverse polynomial function
6 parameters + baseline parameter
Peak Function
Constant: MODEL_PEAK_INVERSEPOLYNOMIAL
Logistic peak function
5 parameters + baseline parameter
Peak Function
Constant: MODEL_PEAK_LOGISTICPEAK
3 parameters + baseline parameter
Peak Function
Constant: MODEL_PEAK_LOGNORMAL
Lorentz peak function
3 parameters + baseline parameter
Peak Function
Constant: MODEL_PEAK_LORENTZIANPEAK
Pseudo-Voigt function (variant 1)
4 parameters + baseline parameter
Peak Function
Constant: MODEL_PEAK_PSEUDOVOIGT1
Pseudo-Voigt function (variant 2)
5 parameters + baseline parameter
Peak Function
Constant: MODEL_PEAK_PSEUDOVOIGT2
Weibull model
4 parameters + baseline parameter
Peak Function
Constant: MODEL_PEAK_WEIBULL
POWER FUNCTIONS
Belehradek model
3 Parameters
Constant: MODEL_POWER_BELEHRADEK
Bleasdale Nelder model
4 Parameters
Constant: MODEL_POWER_BLEASDALENELDER
Freundlich model (variant 1)
2 Parameters
Constant: MODEL_POWER_FREUNDLICH1
Freundlich model (variant 2)
3 Parameters
Constant: MODEL_POWER_FREUNDLICH2
Freundlich model (variant 3)
3 Parameters
Constant: MODEL_POWER_FREUNDLICHEXT
Gunary model
3 Parameters
Constant: MODEL_POWER_GUNARY
Harris model
3 Parameters
Constant: MODEL_POWER_HARRIS
Langmuir model (variant 1)
3 Parameters
Constant: MODEL_POWER_LANGMUIREXT1
Langmuir model (variant 2)
3 Parameters
Constant: MODEL_POWER_LANGMUIREXT2
Pareto model
1 Parameters
Constant: MODEL_POWER_PARETO
Exponential function (variant 1)
1 Parameters
Constant: MODEL_POWER_POWER1
Exponential function (variant 2)
2 Parameters
Constant: MODEL_POWER_POWER2
Exponential function (variant 3)
2 Parameters
Constant: MODEL_POWER_POWER3
Exponential function (variant 4)
2 Parameters
Constant: MODEL_POWER_POWER4
RATIONAL FUNCTIONS
BET model (variant 1)
2 Parameters
Constant: MODEL_RATIONAL_BET1
BET model (variant 2)
2 Parameters
Constant: MODEL_RATIONAL_BET2
Holliday model (variant 1)
3 Parameters
Constant: MODEL_RATIONAL_HOLLIDAY
Holliday model (variant 2)
3 Parameters
Constant: MODEL_RATIONAL_HOLLIDAYEXT
Nelder function
4 Parameters
Constant: MODEL_RATIONAL_NELDER
Rational function (variant 1)
3 Parameters
Constant: MODEL_RATIONAL_RATIONAL1
Rational function (variant 2)
3 Parameters
Constant: MODEL_RATIONAL_RATIONAL2
Rational function (variant 3)
3 Parameters
Constant: MODEL_RATIONAL_RATIONAL3
Rational function (variant 4)
3 Parameters
Constant: MODEL_RATIONAL_RATIONAL4
Rational function (variant 5)
3 Parameters
Constant: MODEL_RATIONAL_RATIONAL5
Reciprocal function (variant 1)
2 Parameters
Constant: MODEL_RATIONAL_RECI1
Reciprocal function (variant 2)
1 Parameters
Constant: MODEL_RATIONAL_RECI2
Reciprocal function (variant 3)
1 Parameters
Constant: MODEL_RATIONAL_RECI3
Reciprocal function (variant 4)
2 Parameters
Constant: MODEL_RATIONAL_RECI4
OTHER FUNCTIONS
Binding curve (variant 1)
2 Parameters
Constant: MODEL_PHARMA_BINDING1
Binding curve (variant 2)
4 Parameters
Constant: MODEL_PHARMA_BINDING2
Biphasic model
7 Parameters
Constant: MODEL_PHARMA_BIPHASIC
Competition curve (variant 1)
3 Parameters
Constant: MODEL_PHARMA_COMPETITION1
Competition curve (variant 2)
5 Parameters
Constant: MODEL_PHARMA_COMPETITION2
Dose response model
4 Parameters
Constant: MODEL_PHARMA_DOSERESPONSE
Sine function
3 Parameters
Constant: MODEL_WAVE_SINE
Damped sine function
4 Parameters
Constant: MODEL_WAVE_SINEDAMP
Square sine function
3 Parameters
Constant: MODEL_WAVE_SINESQUARE
NIST model Bennet5
3 Parameters
Constant: MODEL_NIST_BENNET5
NIST model Boxbod
2 Parameters
Constant: MODEL_NIST_BOXBOD
NIST model Chwirut
3 Parameters
Constant: MODEL_NIST_CHWIRUT
NIST model Danwood
2 Parameters
Constant: MODEL_NIST_DANWOOD
NIST model Eckerle4
3 Parameters
Constant: MODEL_NIST_ECKERLE4
NIST model Enso
9 Parameters
Constant: MODEL_NIST_ENSO
NIST model Gauss
8 Parameters
Constant: MODEL_NIST_GAUSS
NIST model Hahn1
7 Parameters
Constant: MODEL_NIST_HAHN1
NIST model Kirby2
6 Parameters
Constant: MODEL_NIST_KIRBY2
NIST model Lanczos
6 Parameters
Constant: MODEL_NIST_LANCZOS
NIST model MGH09
4 Parameters
Constant: MODEL_NIST_MGH09
NIST model MGH10
3 Parameters
Constant: MODEL_NIST_MGH10
NIST model MGH17
5 Parameters
Constant: MODEL_NIST_MGH17
NIST model Misra1A
2 Parameters
Constant: MODEL_NIST_MISRA1A
NIST model Misra1B
2 Parameters
Constant: MODEL_NIST_MISRA1B
NIST model Misra1C
2 Parameters
Constant: MODEL_NIST_MISRA1C
NIST model Misra1D
2 Parameters
Constant: MODEL_NIST_MISRA1D
NIST model RAT42
3 Parameters
Constant: MODEL_NIST_RAT42
NIST model RAT43
4 Parameters
Constant: MODEL_NIST_RAT43
NIST model Roszman1
4 Parameters
Constant: MODEL_NIST_ROSZMAN1
References
•Seber G. A. F., Wild C. J. Nonlinear Regression. Wiley, New York, 2003.
•The NIST models can be found on the Internet at: http://www.itl.nist.gov/div898/strd
See Also
Non-Linear Curve Fitting Analysis Object