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PEST RUN RECORD: CASE test
PEST Version: 17.1
PEST run mode:-
Parameter estimation mode
Case dimensions:-
Number of parameters : 4
Number of adjustable parameters : 4
Number of parameter groups : 4
Number of observations : 43
Number of prior estimates : 0
Model command line(s):-
test
Jacobian command line:-
na
Model interface files:-
Templates:
in_1.tpl
for model input files:
in_1.dat
(Parameter values written using single precision protocol.)
(Decimal point always included.)
Instruction files:
output.ins
for reading model output files:
output.dat
PEST-to-model message file:-
na
Derivatives calculation:-
Param Increment Increment Increment Forward or Multiplier Method
group type low bound central (central) (central)
qsl relative 1.0000E-02 none switch 2.000 parabolic
alphaim relative 1.0000E-02 none switch 2.000 parabolic
alphasf relative 1.0000E-02 none switch 2.000 parabolic
alpha relative 1.0000E-02 none switch 2.000 parabolic
Parameter definitions:-
Name Trans- Change Initial Lower Upper
formation limit value bound bound
qsl none relative 0.364000 -1.000000E+10 1.000000E+10
alphaim none relative 5.000000E-05 -1.000000E+10 1.000000E+10
alphasf none relative 1.000000E-02 -1.000000E+10 1.000000E+10
alpha none relative 0.400000 -1.000000E+10 1.000000E+10
Name Group Scale Offset Model command number
qsl qsl 1.00000 0.00000 1
alphaim alphaim 1.00000 0.00000 1
alphasf alphasf 1.00000 0.00000 1
alpha alpha 1.00000 0.00000 1
Prior information:-
No prior information supplied
Observations:-
Observation name Observation Weight Group
o1 7.000000E-03 1.000 obsgroup
o2 4.600000E-02 1.000 obsgroup
o3 7.500000E-02 1.000 obsgroup
o4 0.117000 1.000 obsgroup
o5 0.154000 1.000 obsgroup
o6 0.174000 1.000 obsgroup
o7 0.211000 1.000 obsgroup
o8 0.240000 1.000 obsgroup
o9 0.264000 1.000 obsgroup
o10 0.288000 1.000 obsgroup
o11 0.321000 1.000 obsgroup
o12 0.351000 1.000 obsgroup
o13 0.376000 1.000 obsgroup
o14 0.412000 1.000 obsgroup
o15 0.433000 1.000 obsgroup
o16 0.486000 1.000 obsgroup
o17 0.516000 1.000 obsgroup
o18 0.563000 1.000 obsgroup
o19 0.610000 1.000 obsgroup
o20 0.656000 1.000 obsgroup
o21 0.699000 1.000 obsgroup
o22 0.738000 1.000 obsgroup
o23 0.796000 1.000 obsgroup
o24 0.830000 1.000 obsgroup
o25 0.850000 1.000 obsgroup
o26 0.885000 1.000 obsgroup
o27 0.915000 1.000 obsgroup
o28 0.934000 1.000 obsgroup
o29 0.935000 1.000 obsgroup
o30 0.964000 1.000 obsgroup
o31 0.977000 1.000 obsgroup
o32 0.987000 1.000 obsgroup
o33 0.979000 1.000 obsgroup
o34 0.982000 1.000 obsgroup
o35 0.999000 1.000 obsgroup
o36 0.989000 1.000 obsgroup
o37 1.01500 1.000 obsgroup
o38 1.00500 1.000 obsgroup
o39 1.00600 1.000 obsgroup
o40 1.01100 1.000 obsgroup
o41 1.00500 1.000 obsgroup
o42 0.997000 1.000 obsgroup
o43 0.992000 1.000 obsgroup
Control settings:-
Initial lambda : 5.0000
Lambda adjustment factor : 2.0000
Sufficient new/old phi ratio per optimisation iteration : 0.30000
Limiting relative phi reduction between lambdas : 3.00000E-02
Maximum trial lambdas per iteration : 10
Forgive model run failure during lamda testing : no
Forgive model run failure during Jacobian runs : no
Perform Broyden's update of Jacobian matrix : no
Undertake observation re-referencing : no
Maximum factor parameter change (factor-limited changes) : na
Maximum relative parameter change (relative-limited changes) : 3.0000
Fraction of initial parameter values used in computing
change limit for near-zero parameters : 1.00000E-03
Allow bending of parameter upgrade vector : no
Allow parameters to stick to their bounds : no
Relative phi reduction below which to begin use of
central derivatives : 0.10000
Iteration at which to first consider derivatives switch : 1
Relative phi reduction indicating convergence : 0.10000E-01
Number of phi values required within this range : 3
Maximum number of consecutive failures to lower phi : 3
Minimal relative parameter change indicating convergence : 0.10000E-01
Number of consecutive iterations with minimal param change : 3
Maximum number of optimisation iterations : 30
Attempt automatic user intervention : no
Attempt reuse of parameter sensitivities : no
Scale parameters by their bounds : no
File saving options: -
Save best JCO file : yes
Save multiple JCO files : no
Save multiple REI files : no
Save multiple PAR files : no
OPTIMISATION RECORD
INITIAL CONDITIONS:
Sum of squared weighted residuals (ie phi) = 0.78441
Current parameter values
qsl 0.364000
alphaim 5.000000E-05
alphasf 1.000000E-02
alpha 0.400000
OPTIMISATION ITERATION NO. : 1
Model calls so far : 1
Starting phi for this iteration: 0.78441
Lambda = 5.0000 ----->
Phi = 3.85589E-02 ( 0.049 of starting phi)
No more lambdas: phi is less than 0.3000 of starting phi
Lowest phi this iteration: 3.85589E-02
Current parameter values Previous parameter values
qsl 0.233498 qsl 0.364000
alphaim 1.857238E-04 alphaim 5.000000E-05
alphasf 2.004466E-02 alphasf 1.000000E-02
alpha 0.453765 alpha 0.400000
Maximum relative change: 2.714 ["alphaim"]
OPTIMISATION ITERATION NO. : 2
Model calls so far : 6
Starting phi for this iteration: 3.85589E-02
Parameter "alphaim" has no effect on observations.
Lambda = 2.5000 ----->
Phi = 2.19455E-02 ( 0.569 of starting phi)
Lambda = 1.2500 ----->
Phi = 2.24320E-02 ( 0.582 of starting phi)
Lambda = 5.0000 ----->
Phi = 2.16690E-02 ( 0.562 of starting phi)
No more lambdas: relative phi reduction between lambdas less than 0.0300
Lowest phi this iteration: 2.16690E-02
Current parameter values Previous parameter values
qsl 0.267627 qsl 0.233498
alphaim 1.857238E-04 alphaim 1.857238E-04
alphasf 6.321475E-03 alphasf 2.004466E-02
alpha 0.430371 alpha 0.453765
Maximum relative change: 0.6846 ["alphasf"]
OPTIMISATION ITERATION NO. : 3
Model calls so far : 13
Starting phi for this iteration: 2.16690E-02
Lambda = 5.0000 ----->
Phi = 9.59787E-03 ( 0.443 of starting phi)
Lambda = 2.5000 ----->
Phi = 9.61169E-03 ( 0.444 of starting phi)
Lambda = 10.000 ----->
Phi = 9.59730E-03 ( 0.443 of starting phi)
No more lambdas: relative phi reduction between lambdas less than 0.0300
Lowest phi this iteration: 9.59730E-03
Current parameter values Previous parameter values
qsl 0.263327 qsl 0.267627
alphaim -3.014080E-05 alphaim 1.857238E-04
alphasf 8.844564E-03 alphasf 6.321475E-03
alpha 0.431161 alpha 0.430371
Maximum relative change: 1.162 ["alphaim"]
OPTIMISATION ITERATION NO. : 4
Model calls so far : 20
Starting phi for this iteration: 9.59730E-03
Lambda = 10.000 ----->
Phi = 9.22039E-03 ( 0.961 of starting phi)
Lambda = 5.0000 ----->
Phi = 9.22004E-03 ( 0.961 of starting phi)
No more lambdas: relative phi reduction between lambdas less than 0.0300
Lowest phi this iteration: 9.22004E-03
Relative phi reduction between optimisation iterations less than 0.1000
Switch to higher order derivatives calculation
Current parameter values Previous parameter values
qsl 0.263246 qsl 0.263327
alphaim -1.205630E-04 alphaim -3.014080E-05
alphasf 8.869438E-03 alphasf 8.844564E-03
alpha 0.431108 alpha 0.431161
Maximum relative change: 3.000 ["alphaim"]
OPTIMISATION ITERATION NO. : 5
Model calls so far : 26
Starting phi for this iteration: 9.22004E-03
Lambda = 2.5000 ----->
Phi = 9.15293E-03 ( 0.993 of starting phi)
Lambda = 1.2500 ----->
Phi = 9.17101E-03 ( 0.995 of starting phi)
Lambda = 5.0000 ----->
Phi = 9.16887E-03 ( 0.994 of starting phi)
No more lambdas: phi rising
Lowest phi this iteration: 9.15293E-03
Current parameter values Previous parameter values
qsl 0.261964 qsl 0.263246
alphaim -1.707220E-04 alphaim -1.205630E-04
alphasf 9.110885E-03 alphasf 8.869438E-03
alpha 0.432086 alpha 0.431108
Maximum relative change: 0.4160 ["alphaim"]
OPTIMISATION ITERATION NO. : 6
Model calls so far : 37
Starting phi for this iteration: 9.15293E-03
Lambda = 2.5000 ----->
Phi = 9.15486E-03 ( 1.000 times starting phi)
Lambda = 1.2500 ----->
Phi = 9.15808E-03 ( 1.001 times starting phi)
Lambda = 5.0000 ----->
Phi = 9.14422E-03 ( 0.999 of starting phi)
No more lambdas: relative phi reduction between lambdas less than 0.0300
Lowest phi this iteration: 9.14422E-03
Current parameter values Previous parameter values
qsl 0.261646 qsl 0.261964
alphaim -1.723260E-04 alphaim -1.707220E-04
alphasf 9.198813E-03 alphasf 9.110885E-03
alpha 0.431451 alpha 0.432086
Maximum relative change: 9.6508E-03 ["alphasf"]
Optimisation complete: the 3 lowest phi's are within a relative distance
of eachother of 1.000E-02
Total model calls: 48
The model has been run one final time using best parameters.
Thus all model input files contain best parameter values, and model
output files contain model results based on these parameters.
OPTIMISATION RESULTS
Parameters ----->
Parameter Estimated 95% percent confidence limits
value lower limit upper limit
qsl 0.261646 0.253698 0.269594
alphaim -1.723260E-04 -5.938624E-04 2.492104E-04
alphasf 9.198813E-03 6.926382E-03 1.147124E-02
alpha 0.431451 0.318534 0.544368
Note: confidence limits provide only an indication of parameter uncertainty.
They rely on a linearity assumption which may not extend as far in
parameter space as the confidence limits themselves - see PEST manual.
See file test.sen for parameter sensitivities.
Observations ----->
Observation Measured Calculated Residual Weight Group
value value
o1 7.000000E-03 5.619880E-04 6.438012E-03 1.000 obsgroup
o2 4.600000E-02 1.399467E-02 3.200533E-02 1.000 obsgroup
o3 7.500000E-02 6.104460E-02 1.395540E-02 1.000 obsgroup
o4 0.117000 0.129212 -1.221180E-02 1.000 obsgroup
o5 0.154000 0.182672 -2.867170E-02 1.000 obsgroup
o6 0.174000 0.218306 -4.430640E-02 1.000 obsgroup
o7 0.211000 0.244996 -3.399580E-02 1.000 obsgroup
o8 0.240000 0.268546 -2.854600E-02 1.000 obsgroup
o9 0.264000 0.289888 -2.588830E-02 1.000 obsgroup
o10 0.288000 0.312250 -2.424970E-02 1.000 obsgroup
o11 0.321000 0.333781 -1.278100E-02 1.000 obsgroup
o12 0.351000 0.357335 -6.334900E-03 1.000 obsgroup
o13 0.376000 0.382649 -6.648500E-03 1.000 obsgroup
o14 0.412000 0.410899 1.101500E-03 1.000 obsgroup
o15 0.433000 0.442217 -9.216700E-03 1.000 obsgroup
o16 0.486000 0.478307 7.692700E-03 1.000 obsgroup
o17 0.516000 0.518467 -2.467000E-03 1.000 obsgroup
o18 0.563000 0.562026 9.745000E-04 1.000 obsgroup
o19 0.610000 0.608316 1.683600E-03 1.000 obsgroup
o20 0.656000 0.654999 1.001100E-03 1.000 obsgroup
o21 0.699000 0.698794 2.059000E-04 1.000 obsgroup
o22 0.738000 0.745168 -7.168400E-03 1.000 obsgroup
o23 0.796000 0.785448 1.055220E-02 1.000 obsgroup
o24 0.830000 0.822080 7.920500E-03 1.000 obsgroup
o25 0.850000 0.855883 -5.883400E-03 1.000 obsgroup
o26 0.885000 0.884862 1.376000E-04 1.000 obsgroup
o27 0.915000 0.909693 5.307300E-03 1.000 obsgroup
o28 0.934000 0.929620 4.379700E-03 1.000 obsgroup
o29 0.935000 0.946066 -1.106610E-02 1.000 obsgroup
o30 0.964000 0.960056 3.944200E-03 1.000 obsgroup
o31 0.977000 0.970392 6.608300E-03 1.000 obsgroup
o32 0.987000 0.979264 7.736400E-03 1.000 obsgroup
o33 0.979000 0.985963 -6.962500E-03 1.000 obsgroup
o34 0.982000 0.991138 -9.138000E-03 1.000 obsgroup
o35 0.999000 0.995030 3.970100E-03 1.000 obsgroup
o36 0.989000 0.998130 -9.129700E-03 1.000 obsgroup
o37 1.01500 1.00035 1.465400E-02 1.000 obsgroup
o38 1.00500 1.00201 2.990000E-03 1.000 obsgroup
o39 1.00600 1.00327 2.726000E-03 1.000 obsgroup
o40 1.01100 1.00419 6.811000E-03 1.000 obsgroup
o41 1.00500 1.00489 1.070000E-04 1.000 obsgroup
o42 0.997000 1.00539 -8.387000E-03 1.000 obsgroup
o43 0.992000 1.00574 -1.373700E-02 1.000 obsgroup
See file test.res for more details of residuals in graph-ready format.
See file test.seo for composite observation sensitivities.
Objective function ----->
Sum of squared weighted residuals (ie phi) = 9.1442E-03
Correlation Coefficient ----->
Correlation coefficient = 0.99921
Analysis of residuals ----->
All residuals:-
Number of residuals with non-zero weight = 43
Mean value of non-zero weighted residuals = -3.8113E-03
Maximum weighted residual [observation "o2"] = 3.2005E-02
Minimum weighted residual [observation "o6"] = -4.4306E-02
Standard variance of weighted residuals = 2.3447E-04
Standard error of weighted residuals = 1.5312E-02
Note: the above variance was obtained by dividing the objective
function by the number of system degrees of freedom (ie. number of
observations with non-zero weight plus number of prior information
articles with non-zero weight minus the number of adjustable parameters.)
If the degrees of freedom is negative the divisor becomes
the number of observations with non-zero weight plus the number of
prior information items with non-zero weight.
K-L information statistics ----->
AIC = -353.6009
AICC = -351.9792
BIC = -344.7949
KIC = -320.1371
Parameter covariance matrix ----->
qsl alphaim alphasf alpha
qsl 1.5433E-05 2.5164E-07 -3.3823E-06 4.0724E-05
alphaim 2.5164E-07 4.3415E-08 4.6237E-08 -6.2017E-06
alphasf -3.3823E-06 4.6237E-08 1.2617E-06 -4.2769E-05
alpha 4.0724E-05 -6.2017E-06 -4.2769E-05 3.1152E-03
Parameter correlation coefficient matrix ----->
qsl alphaim alphasf alpha
qsl 1.000 0.3074 -0.7665 0.1857
alphaim 0.3074 1.000 0.1976 -0.5333
alphasf -0.7665 0.1976 1.000 -0.6822
alpha 0.1857 -0.5333 -0.6822 1.000
Normalized eigenvectors of parameter covariance matrix ----->
Vector_1 Vector_2 Vector_3 Vector_4
qsl -5.9283E-02 -0.1794 -0.9819 -1.3145E-02
alphaim 0.9786 -0.2047 -2.1700E-02 1.9889E-03
alphasf -0.1972 -0.9622 0.1875 1.3741E-02
alpha 1.6158E-05 -1.1272E-02 1.5444E-02 -0.9998
Eigenvalues ----->
1.8751E-08 1.3977E-07 1.5444E-05 3.1163E-03