sandy.gls module

This module contains all classes and functions specific for processing GLS and assessment of adjustment. It handles only numpy.ndarray.

sandy.gls.chi_diag(x_prior, S, Vx_prior, Vy_extra, y_extra)

Function to calculate diagonal chi-value $chi_{ind,i}$>>1 according to https://www.oecd-nea.org/jcms/pl_19760/intermediate-report-on-methods-and-approaches-to-provide-feedback-from-nuclear-and-covariance-data-adjustment-for-improvement-of-nuclear-data-files (page 9, equation (4.3))

Parameters:

x_prior: 1D iterable: Vector in which we are going to apply GLS (M,)
S2D iterable: 2D sensitivity of the model y=f(x) (M, N).
Vx_prior2D iterable: 2D covariance matrix of x_prior (M, N).
Vy_extra2D iterable: 2D covariance matrix for y_extra (M, N).
y_extra1D iterable: 1D extra info on output (N,)

Returns:

numpy.ndarray: diagonal chi-value
Results:

chi diagonal >> 1: Inconsistency may exist between |y_extra - y_calc| and covariance matrix, S*Vx_prior*S.T, and Vy_extra.

sandy.gls.chi_individual(x_prior, S, Vx_prior, Vy_extra, y_extra)

Function to calculate individual chi-value measured in sigmas according to https://www.oecd-nea.org/jcms/pl_19760/intermediate-report-on-methods-and-approaches-to-provide-feedback-from-nuclear-and-covariance-data-adjustment-for-improvement-of-nuclear-data-files (page 9, equation (4.2))

Parameters:

x_prior: 1D iterable: Vector in which we are going to apply GLS (M,)
S2D iterable: 2D sensitivity of the model y=f(x) (M, N).
Vx_prior2D iterable: 2D covariance matrix of x_prior (M, N).
Vy_extra2D iterable: 2D covariance matrix for y_extra (M, N).
y_extra1D iterable: 1D extra info on output (N,).

Returns:

numpy.ndarray: individual chi-value measured in sigmas.
Results:

chi individual >> 1: Inconsistency may exist between |y_extra - y_calc| and covariance matrix, S*Vx_prior*S.T, and Vy_extra.

sandy.gls.chi_square(x_prior, S, Vx_prior, Vy_extra, y_extra, N_e)

Function to calculate contribution to chi-square value according to https://www.oecd-nea.org/jcms/pl_19760/intermediate-report-on-methods-and-approaches-to-provide-feedback-from-nuclear-and-covariance-data-adjustment-for-improvement-of-nuclear-data-files (page 10, equation (4.4))

Parameters:

x_prior: 1D iterable: Vector in which we are going to apply GLS (M,)
S2D iterable: 2D sensitivity of the model y=f(x) (M, N).
Vx_prior2D iterable: 2D covariance matrix of x_prior (M, N).
Vy_extra2D iterable: 2D covariance matrix for y_extra (M, N).
y_extra1D iterable: 1D extra info on output (N,)
N_eint: Number of experimental values used in adjustment.

Returns:

numpy.ndarray: contribution to chi-square value
Results:

chi square < 0: The experiment is very effective in the adjustment.

sandy.gls.gls_update(x_prior, S, Vx_prior, y_extra, Vy_extra=None)

Perform the GlS update of a prior vector and its related covariance matrix, according with https://www.tandfonline.com/action/journalInformation?journalCode=tnst2 .. math:
$$
x_{post} = x_{prior} + V_{x_{prior}}\cdot S^T \cdot \left(S\cdot V_{x_{prior}}\cdot S^T + V_{y_{extra}}

ight)^{-1} cdot left(y_{extra} - y_{calc} ight)

V_{x_{post}} = V_{x_{prior}} - V_{x_{prior}}cdot S^T cdot left(Scdot V_{x_{prior}}cdot S^T + V_{y_{extra}}

ight)^{-1} cdot S cdot V_{x_{prior}}: $$

Parameters:

x_prior1D iterable: Vector to be updated (N,)
S2D or 1D iterable: Sensitivity matrix (M, N) or sensitivity vector(N,)
Vx_prior2D iterable: 2D covariance matrix of x_prior (N, N)
y_extra1D iterable: 1D extra info on output (M,)
Vy_extra2D iterable or sigle element 1D iterable, optional, default is None: covariance matrix with the uncertainties of the extra information, (M, M) or (1,).

Returns:

numpy.ndarray: updated vector adjusted with the GLS technique
numpy.ndarray: updated covariance matrix adjusted with the GLS technique

Notes

Note

If Vy_extra=None the constraint GLS update technique

will be performed

sandy.gls.ishikawa_factor(S, Vx_prior, Vy_extra)

Function to obtain Ishikawa factor according to https://www.oecd-nea.org/jcms/pl_19760/intermediate-report-on-methods-and-approaches-to-provide-feedback-from-nuclear-and-covariance-data-adjustment-for-improvement-of-nuclear-data-files (page 10, equation (4.5))

Parameters:

S2D iterable: 2D sensitivity of the model y=f(x) (M, N).
Vx_prior2D iterable: 2D covariance matrix of x_prior (M, N).
Vy_extra2D iterable: 2D covariance matrix for y_extra (M, N).

Returns:

numpy.ndarray: Ishikawa factor.
Results:

Ishikawa factor << 1: The extra data is not so useful and the data remain unchanged.
Ishikawa factor >> 1: The extra data very useful and the ‘posteriori’ covariance will be reduced to the same level as the integral parameter covariance.
Ishikawa factor ~ 1: The experiment is useful and the ‘posteriori’ covariance will be reduced by approximately half