LinearFit

class jwst.ami.leastsqnrm.LinearFit(dependent_variable, inverse_covariance_matrix, independent_variable)

Bases: object

Perform a general least-squares fit of a linear model using numpy matrix inversion.

Uncertainties in the dependent variables (but not in the independent variables) can be taken into account. All inputs have to be numpy matrices.

Math is based on Press’

• Numerical Recipes p661 : Section 15.2 Fitting Data to a Straight Line

• Numerical Recipes p671 : Section 15.4 General Linear Least Squares

Code is based on an early yorick implementation by Damien Segransan (University of Geneva) Python implementation and tools by Johannes Sahlmann 2009-2017 (University of Geneva, European Space Agency, STScI/AURA)

Parameters:

dependent_variablendarray (1xN)

Dependent_variables of the linear equation system (N equations, M unknown coefficients)

inverse_covariance_matrixndarray (NxN)

Inverse covariance matrix corresponding to the dependent_variable. i.e. data weights proportional to 1/sigma**2 where sigma=uncertainty

independent_variablendarray (MxN)

The independent_variables that are multiplied by the unknown coefficients

Attributes:

pndarray

Coefficients of the solution

p_formal_uncertaintyndarray

Formal uncertainty of the coefficients

p_formal_covariance_matrixndarray

Formal covariance matrix of the coefficients (not rescaled)

p_normalised_uncertaintyndarray

Normalised uncertainty (chi2 = 1) of the coefficients

p_normalised_covariance_matrixndarray

Normalised covariance matrix of the coefficients (rescaled to yield chi2=1)

p_correlation_matrixndarray

Coefficient correlation matrix

fitndarray

Perform the linear fit.

residualsndarray

Observed - Calculated (O-C) residuals

chi2float

Chi-square value of the best fit

Methods Summary

fit()

Perform the linear fit.

Methods Documentation

fit()

Perform the linear fit.