Author: tlinnet
Date: Tue Aug 26 14:37:28 2014
New Revision: 25289
URL: http://svn.gna.org/viewcvs/relax?rev=25289&view=rev
Log:
Added initial documentation for multifit_covar.
task #7822(https://gna.org/task/index.php?7822): Implement user function to
estimate R2eff and associated errors for exponential curve fitting.
Modified:
trunk/specific_analyses/relax_disp/estimate_r2eff.py
Modified: trunk/specific_analyses/relax_disp/estimate_r2eff.py
URL:
http://svn.gna.org/viewcvs/relax/trunk/specific_analyses/relax_disp/estimate_r2eff.py?rev=25289&r1=25288&r2=25289&view=diff
==============================================================================
--- trunk/specific_analyses/relax_disp/estimate_r2eff.py (original)
+++ trunk/specific_analyses/relax_disp/estimate_r2eff.py Tue Aug 26
14:37:28 2014
@@ -422,6 +422,51 @@
return hessian_matrix
+ def multifit_cova(self, matrix_X_J=None, epsrel=None,
matrix_X_covar=None):
+ """This is the implementation of 'gsl_multifit_covar' from GNU
Scientific Library (GSL).
+
+ This function uses the Jacobian matrix J to compute the covariance
matrix of the best-fit parameters, covar.
+ The parameter 'epsrel' is used to remove linear-dependent columns
when J is rank deficient.
+
+ The covariance matrix is given by,
+
+ covar = (J^T J)^{-1}
+
+ and is computed by QR decomposition of J with column-pivoting. Any
columns of R which satisfy
+
+ |R_{kk}| <= epsrel |R_{11}|
+
+ are considered linearly-dependent and are excluded from the
covariance matrix (the corresponding rows and columns of the covariance
matrix are set to zero).
+
+ If the minimisation uses the weighted least-squares function:
+ f_i = (Y(x, t_i) - y_i) / \sigma_i
+ then the covariance matrix above gives the statistical error on
the best-fit parameters resulting from the Gaussian errors \sigma_i on the
underlying data y_i.
+ This can be verified from the relation \delta f = J \delta c and
the fact that the fluctuations in f from the data y_i are normalised by
\sigma_i and so satisfy <\delta f \delta f^T> = I.
+
+ For an unweighted least-squares function f_i = (Y(x, t_i) - y_i)
the covariance matrix above should be multiplied by the variance of the
residuals about the best-fit
+ \sigma^2 = \sum (y_i - Y(x,t_i))^2 / (n-p)
+ to give the variance-covariance matrix \sigma^2 C.
+ This estimates the statistical error on the best-fit parameters
from the scatter of the underlying data.
+
+ See:
+ U{GSL - GNU Scientific Library<http://www.gnu.org/software/gsl/>}
+ U{Manual: Computing the covariance matrix of best fit
parameters<http://www.gnu.org/software/gsl/manual/gsl-ref_38.html#SEC528>}
+ U{Manual: Computing the covariance matrix of best fit
parameters<http://www.gnu.org/software/gsl/manual/gsl-ref_38.html#SEC528>}
+ U{Manual:
Overview<http://www.gnu.org/software/gsl/manual/gsl-ref_37.html#SEC510>}
+
+ @param matrix_X_J: The vector of parameter values.
+ @type matrix_X_J: numpy rank-1 float array
+ @param epsrel: The vector of parameter values.
+ @type epsrel: numpy rank-1 float array
+ @param matrix_X_covar: The vector of parameter values.
+ @type matrix_X_covar: numpy rank-1 float array
+ @return: ?
+ @rtype: ?
+ """
+
+
+
+
# 'minfx'
# 'scipy.optimize.leastsq'
def estimate_r2eff(spin_id=None, ftol=1e-15, xtol=1e-15, maxfev=10000000,
factor=100.0, method='minfx', verbosity=1):
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Re: r25289 - /trunk/specific_analyses/relax_disp/estimate_r2eff.py