Download we include it here.

Advamced Regularisation and SVD-Assist
8-23
8.5.4.5 PEST
Upon commencement of an SVD-assisted parameter estimation run PEST reads the super
PEST control file, this being the file provided to it through its command line in the normal
manner. It then reads the base PEST control file and the Jacobian matrix file cited in the “svd
assist” section of the super PEST control file, checking for compatibility between these two
files. It then forms the matrix JtQJ where J is the base parameter Jacobian matrix and Q is
the observation weight matrix. Note that rows of the Jacobian matrix pertaining to any prior
information present in the base PEST control file are omitted in formulating this matrix. So
too are base parameters that are fixed and tied in the original PEST control file; hence these
base parameters remain fixed and tied through the SVD-assisted parameter estimation
process implemented by PEST.
PEST undertakes singular value decomposition of the JtQJ matrix, retaining only as many
singular values as were requested by the user. On the basis of the eigenvectors corresponding
to the retained singular values it writes a template file for the PARCALC input file
parcalc.in; the information in this file allows PARCALC to calculate base parameter values
when supplied with current super parameter values by PEST. This template file is re-written
at the beginning of every optimisation iteration. This is necessary because estimable
directions in parameter space are always calculated relative to current parameter values
(which change from iteration to iteration). Also, if any base parameters hit their bounds, the
SVD process is repeated, with new singular values and eigenvectors being calculated as a
consequence.
Thus as PEST alters the values of super parameters, either incrementally for the purpose of
derivatives calculation, or in response to the upgrading of these parameters, the values of
these super parameters are written to a model input file, as in normal PEST operations.
However on this occasion the model input file is parcalc.in. PARCALC then transforms
these super parameter values into base parameter values, writing all necessary model input
files using these parameters on PEST’s behalf. It also writes a PICALC input file on the basis
of these super parameters so that PICALC can undertake calculation of prior information
equations on PEST’s behalf. All model outputs, and all prior information equation results, are
then read directly by PEST after each model run.
8.5.5 Best Parameter Estimates
The values of super parameters estimated by PEST in the SVD-assisted parameter estimation
process have no inherent meaning. Even within a single parameter estimation run, the
calculation of base parameter values from super parameter values changes according to
current estimates of the latter parameters. A problem then arises as to how to use parameter
values estimated by PEST in a model that is run for predictive purposes, this requiring, of
course, optimised values of base parameters.
As is documented in Section 5.3.1 of this manual, in its normal mode of operation PEST
writes current best parameter estimates at any stage of the parameter estimation process to a
file named case.par where case is the filename base of the PEST control file. When
implementing SVD-assisted parameter estimation, PEST records another file named
bcase.bpa, where bcase is the filename base of the base PEST control file (that is the file
used by SVDAPREP in building the control file used for SVD-assisted parameter