Module LeastSquares
Non-linear least squares fitting
Usage example:
from Scientific.N import exp
def f(param, t):
return param[0]*exp(-param[1]/t)
data_quantum = [(100, 3.445e+6),(200, 2.744e+7),
(300, 2.592e+8),(400, 1.600e+9)]
data_classical = [(100, 4.999e-8),(200, 5.307e+2),
(300, 1.289e+6),(400, 6.559e+7)]
print leastSquaresFit(f, (1e13,4700), data_classical)
def f2(param, t):
return 1e13*exp(-param[0]/t)
print leastSquaresFit(f2, (3000.,), data_quantum)
(list, float)
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leastSquaresFit(model,
parameters,
data,
max_iterations=None,
stopping_limit=0.005)
General non-linear least-squares fit using the Levenberg-Marquardt algorithm and automatic differentiation. |
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polynomialLeastSquaresFit(parameters,
data)
Least-squares fit to a polynomial whose order is defined by the
number of parameter values. |
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leastSquaresFit(model,
parameters,
data,
max_iterations=None,
stopping_limit=0.005)
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General non-linear least-squares fit using the Levenberg-Marquardt algorithm and automatic
differentiation.
- Parameters:
model (callable) - the function to be fitted. It will be called with two parameters:
the first is a tuple containing all fit parameters, and the
second is the first element of a data point (see below). The
return value must be a number. Since automatic differentiation
is used to obtain the derivatives with respect to the parameters,
the function may only use the mathematical functions known to the
module FirstDerivatives.parameters (tuple of numbers) - a tuple of initial values for the fit parametersdata (list) - a list of data points to which the model is to be fitted. Each
data point is a tuple of length two or three. Its first element
specifies the independent variables of the model. It is passed to
the model function as its first parameter, but not used in any
other way. The second element of each data point tuple is the
number that the return value of the model function is supposed to
match as well as possible. The third element (which defaults to
1.) is the statistical variance of the data point, i.e. the
inverse of its statistical weight in the fitting procedure. - Returns:
(list, float)
- a list containing the optimal parameter values and the
chi-squared value describing the quality of the fit
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polynomialLeastSquaresFit(parameters,
data)
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Least-squares fit to a polynomial whose order is defined by the number
of parameter values.
- Parameters:
parameters (tuple) - a tuple of initial values for the polynomial coefficientsdata (list) - the data points, as for leastSquaresFit
Note:
This could also be done with a linear least squares fit from Scientific.LA
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