MPNlfit
The difference between MPNlfit and Nlfit is that Bailey’s Fortran 77 package[1] has been used to make some of the parameters in MPNlfit have 128 character accuracy. The fit being tested is to
The data for the fit was generated by repeating the time domain version of this in such a way as to make it 0 at both ends. This was then Fourier transformed using a double precision FFT and the appropriate section of the transform was saved as ..\TestData\Aigau.dat[2]. A number of the values in this data set for f’s in the neighborhood of 0 were repeated as a primitive way of increasing their weights in the fit.
In the
limit as f-∞, AiGauss
exp(-z2). To approximate this the value of Nnum in (1.1)
was kept 3 larger than Nden. The
parameters are added a few at a time.
Chi-squared is
(1.2)
This is minimized with respect to c using at first 3 parameters, then successively adding 1 to the numerator and one to the denominator. The ide’s, fortran, and data for this section are in mpaigau.zip
The first few parameters
Nlfit can be started with 5,2
File Aigau.dir
AIGAU2.DIR, OUTPUT FILE NAME
..\TestData\Aigau.DAT, DATA SET NAME
1, DIMENSION OF X IN F(X)
5,2 , NUMBER OF NUMERATOR TERMS, DENOMINATOR TERMS
1, 1 fits to exponential of a Pade, 0 to a Pade
1E-16,5E-18, err(i)= max(ep1,ep2*dat(i))
100000, NUMBER OF MINIMIZATION STEPS
.999, INITIAL FR DECREASE DESIRED
1 VARY O FIX FITTED CONS ERROR IN CONS
1 0
1 0
1 0
1 0
1 0
1 0
E:\PUBLIC~1\nlfit\Pade2>nlfit aigau.dir
NADIR=aigau.dir
NAOUT=AIGAU2.DIR
NADAT=..\TestData\Aigau.DAT
ND= 1
VORF CONS
1 0.000000E+00
1 0.000000E+00
1 0.000000E+00
1 0.000000E+00
1 0.000000E+00
1 0.000000E+00
1 0.000000E+00
FIT IS BEING MADE TO DATA IN FILE
..\TestData\Aigau.DAT
FR,CHI,CHB,CHL 0.999000000 0.366553940E+35 0.100000000E+67 0.500000000E+67
FR,CHI,CHB,CHL 0.997002999 0.365457531E+35 0.365455377E+35 0.366553940E+35
FR,CHI,CHB,CHL 0.991035916 0.362200708E+35 0.362181539E+35 0.365457531E+35
FR,CHI,CHB,CHL 0.973348092 0.352714058E+35 0.352547368E+35 0.362200708E+35
FR,CHI,CHB,CHL 0.922156318 0.326606065E+35 0.325257498E+35 0.352714058E+35
FR,CHI,CHB,CHL 0.784176167 0.264351314E+35 0.256116692E+35 0.326606065E+35
FR,CHI,CHB,CHL 0.533993701 0.155349433E+35 0.141161937E+35 0.264351314E+35
FR,CHI,CHB,CHL 0.237041124 0.531242478E+34 0.368242042E+34 0.155349433E+35
FR,CHI,CHB,CHL 0.111987085 0.115986155E+34 0.594922968E+33 0.531242478E+34
FR,CHI,CHB,CHL 0.109000000 0.218735116E+33 0.126424909E+33 0.115986155E+34
FR,CHI,CHB,CHL 0.100000000E-01 0.234062605E+32 0.218735116E+31 0.218735116E+33
FR,CHI,CHB,CHL 0.109000000 0.370683992E+31 0.255128239E+31 0.234062605E+32
FR,CHI,CHB,CHL 0.100000000E-01 0.212594025E+30 0.370683992E+29 0.370683992E+31
FR,CHI,CHB,CHL 0.100000000E-01 0.214264025E+29 0.212594025E+28 0.212594025E+30
FR,CHI,CHB,CHL 0.109000000 0.248773850E+28 0.233547787E+28 0.214264025E+29
from bnraph going low
FR,CHI,CHB,CHL 0.100000000E-01 0.139823643E+26 0.263037640E+26 0.248773850E+28
from bnraph going low
FR,CHI,CHB,CHL 0.100000000E-01 0.262300682E+25 0.241566834E+25 0.139823643E+26
from bnraph going low
FR,CHI,CHB,CHL 0.100000000E-01 0.121145657E+24 0.178634232E+24 0.262300682E+25
from bnraph going low
FR,CHI,CHB,CHL 0.100000000E-01 0.625240320E+22 0.554863747E+22 0.121145657E+24
from bnraph going low
FR,CHI,CHB,CHL 0.100000000E-01 0.579747981E+22 0.575999370E+22 0.625240320E+22
from bnraph going low
FR,CHI,CHB,CHL 0.100000000E-01 0.576012490E+22 0.575573808E+22 0.579747981E+22
from bnraph going low
FR,CHI,CHB,CHL 0.109000000 0.574600105E+22 0.574769161E+22 0.576012490E+22
from bnraph going low
FR,CHI,CHB,CHL 0.100000000E-01 0.563393442E+22 0.568586544E+22 0.574600105E+22
from bnraph going low
FR,CHI,CHB,CHL 0.100000000E-01 0.905121477E+21 0.618343103E+21 0.563393442E+22
FR,CHI,CHB,CHL 0.100000000E-01 0.559633700E+20 0.905110935E+19 0.905121477E+21
from bnraph going low
FR,CHI,CHB,CHL 0.100000000E-01 0.242143142E+19 0.162502541E+19 0.559633700E+20
from bnraph going low
FR,CHI,CHB,CHL 0.100000000E-01 0.221806322E+19 0.221642220E+19 0.242143142E+19
from bnraph going low
FR,CHI,CHB,CHL 0.100000000E-01 0.221805181E+19 0.221805170E+19 0.221806322E+19
from bnraph going low
FR,CHI,CHB,CHL 0.100000000E-01 0.221805181E+19 0.221805181E+19 0.221805181E+19
AT END FR, CHI 0.100000000E-01 0.221805181E+19
TEMP2= 0.686816605E-09
NEW SECTION FR= 0.0100000000000000
FR,CHI,CHB,CHL 0.999999990 0.221805181E+19 0.100000000E+67 0.500000000E+67
from bnraph going low
FR,CHI,CHB,CHL 0.999999970 0.221805181E+19 0.221805181E+19 0.221805181E+19
AT END FR, CHI 0.999999970 0.221805181E+19
TEMP2= 0.110799936E-12
NEW SECTION FR= 0.9999999700000005
CHI AT END OF FIT 2.2180518137710760D+018
1 -0.6931472136515744 +- 5.0712402577507340D-009
1 1.5465969528564300 +- 0.0006335734587681
1 -1.4030769356107750 +- 0.0012197809092831
1 0.6259598796771734 +- 0.0008803302311293
1 -0.1221437276738046 +- 2.7621772374898270D-004
1 -0.6033653400846807 +- 0.0009142359135327
1 0.1234737788179483 +- 2.6958786391136100D-004
FINAL CHIT= 2.2180518137710760D+018
CHI/DEG OF FREE 5.3705855054989720D+015
RESULTS IN FILE AIGAU2.DIR
FINAL CHIT= 2.2180518157019170D+018
The routine begins by finding the λ for which chb, a quadratic expansion of χ2 about the present value using c(λ), is equal to Fr times chl the value of χ20 at the present parameters. This value is dependent on the smoothers for each parameter. On the first step these are all 1. They are re-determined between each step based on how the first derivatives compare to sums over the second derivatives. In a successful step the value of chi is below the last value chl, and close to the predicted chb. The phrase
“from bnraph going low” indicates that there is no λ for which the predicted chb is equal to Fr times chl so that λ has been set to near zero, exp(-600).
Figure 1 Single precision result. black data, blue fit, red abs(data-fit)
At this level MPNlfit simply reproduces the above.
Continuing to 6,3
Aigau2.dir
aigau.dir, OUTPUT FILE NAME
..\TestData\Aigau.DAT, DATA SET NAME
1, DIMENSION OF X IN F(X)
6,3 ,
NUMBER OF NUMERATOR TERMS, DEN TERMS changed from 5,2
1, 1 fits to exponential of a Pade, 0 to a Pade
1E-16,5E-18, err(i)= max(ep1,ep2*dat(i))
100000, NUMBER OF MINIMIZATION STEPS
.999, INITIAL FR DECREASE DESIRED
1 VARY O FIX FITTED CONS ERROR IN CONS
1 -0.6931472136515744 +- 0.507E-08
1 1.546596952856430 +- 0.634E-03
1 -1.403076935610775 +- 0.122E-02
1 0.6259598796771734 +- 0.880E-03
1 -0.1221437276738046 +- 0.276E-03
1 0 added by hand
1 -0.6033653400846807 +- 0.914E-03
1 0.1234737788179483 +- 0.270E-03
1 0 added by hand
CHIS=0.2218E+19 FOR 420 DATA POINTS
CHI USED IN CALCULATING ERRORS IS 0.2218E+19
The run
FIT IS BEING MADE TO DATA IN FILE
..\TestData\Aigau.DAT
FR,CHI,CHB,CHL 0.999000000 0.221805181E+19 0.100000000E+67 0.500000000E+67
FR,CHI,CHB,CHL 0.997002999 0.221140409E+19 0.221140431E+19 0.221805181E+19
FR,CHI,CHB,CHL 0.991035916 0.219157934E+19 0.219158088E+19 0.221140409E+19
FR,CHI,CHB,CHL 0.973348092 0.213319611E+19 0.213316957E+19 0.219157934E+19
FR,CHI,CHB,CHL 0.922156318 0.196718945E+19 0.196714028E+19 0.213319611E+19
FR,CHI,CHB,CHL 0.784176167 0.154226230E+19 0.154262280E+19 0.196718945E+19
FR,CHI,CHB,CHL 0.482215223 0.739341299E+18 0.743706693E+18 0.154226230E+19
FR,CHI,CHB,CHL 0.112130240 0.809121355E+17 0.828984351E+17 0.739341299E+18
FR,CHI,CHB,CHL 0.100000000E-01 0.551275089E+16 0.562949953E+15 0.809121355E+17
FR,CHI,CHB,CHL 0.100000000E-01 0.406755720E+14 0.000000000E+00 0.551275089E+16
from bnraph going low
FR,CHI,CHB,CHL 0.100000000E-01 0.151273947E+14 0.171111497E+14 0.406755720E+14
from bnraph going low
FR,CHI,CHB,CHL 0.100000000E-01 0.144409294E+14 0.143924354E+14 0.151273947E+14
from bnraph going low
FR,CHI,CHB,CHL 0.100000000E-01 0.144367023E+14 0.144376752E+14 0.144409294E+14
from bnraph going low
FR,CHI,CHB,CHL 0.100000000E-01 0.144365309E+14 0.144363676E+14 0.144367023E+14
...
FR,CHI,CHB,CHL 0.999999999 0.144365273E+14 0.144365225E+14 0.144365225E+14
IREV= 19 IEND=99980
FR,CHI,CHB,CHL 0.999999999 0.144365302E+14 0.144365225E+14 0.144365225E+14
IREV= 20 IEND=99980
FR,CHI,CHB,CHL 0.999999999 0.144365225E+14 0.144365225E+14 0.144365225E+14
AT END FR, CHI 0.999999999 0.144365225E+14
TEMP2= 0.000000000E+00
NEW SECTION FR= 0.9999999990000000
CHI AT END OF FIT 1.4436522507135110D+013
1 -0.6931471804701830 +- 1.4458288071061270D-011
1 1.6782935992035770 +- 2.4399095520258720D-004
1 -1.7306560107488270 +- 0.0005542303927824
1 0.9585173224247970 +- 0.0005130575505448
1 -0.2889648246510679 +- 2.3426955394895050D-004
1 0.0389247666961553 +- 4.7531861341660710D-005
1 -0.7933588041493399 +- 3.5200369163025530D-004
1 0.2868467339113511 +- 2.2663656170199130D-004
1 -0.0389560008101865 +- 4.7924832490854800D-005
FINAL CHIT= 1.4436522507135110D+013
CHI/DEG OF FREE 3.5125358898138950D+010
RESULTS IN FILE aigau.dir
First sign of trouble
Nlfit 7,4
FIT IS BEING MADE TO DATA IN FILE
..\TestData\Aigau.DAT
FR,CHI,CHB,CHL 0.999000000 0.144365226E+14 0.100000000E+67 0.500000000E+67
FR,CHI,CHB,CHL 0.997002999 0.143932570E+14 0.143932563E+14 0.144365226E+14
FR,CHI,CHB,CHL 0.991035916 0.142642177E+14 0.142642347E+14 0.143932570E+14
FR,CHI,CHB,CHL 0.973348092 0.138844742E+14 0.138839683E+14 0.142642177E+14
FR,CHI,CHB,CHL 0.922156318 0.127929892E+14 0.128051766E+14 0.138844742E+14
FR,CHI,CHB,CHL 0.784176167 0.100168961E+14 0.100201587E+14 0.127929892E+14
FR,CHI,CHB,CHL 0.482215223 0.445442849E+13 0.475882376E+13 0.100168961E+14
FR,CHI,CHB,CHL 0.112130240 0.119148160E+13 0.309237645E+12 0.445442849E+13
from bnraph going low
FR,CHI,CHB,CHL 0.109000000 0.104923272E+13 0.107266808E+13 0.119148160E+13
from bnraph going low
FR,CHI,CHB,CHL 0.100000000E-01 0.102782228E+13 0.101307541E+13 0.104923272E+13
FR,CHI,CHB,CHL 0.109000000 0.102588416E+13 0.000000000E+00 0.102782228E+13
from bnraph going low
FR,CHI,CHB,CHL 0.110692900 0.102443278E+13 0.102421548E+13 0.102588416E+13
FR,CHI,CHB,CHL 0.109000000 0.102431094E+13 0.000000000E+00 0.102443278E+13
from bnraph going low
FR,CHI,CHB,CHL 0.110692900 0.102388285E+13 0.102357795E+13 0.102431094E+13
FR,CHI,CHB,CHL 0.109000000 0.101330808E+13 0.194347270E+12 0.102388285E+13
from bnraph going low
FR,CHI,CHB,CHL 0.110692900 0.101392219E+13 0.101245465E+13 0.101330808E+13
IREV= 1 IEND=99985
from bnraph going low
FR,CHI,CHB,CHL 0.911069290 0.101392219E+13 0.101245465E+13 0.101330808E+13
IREV= 2 IEND=99985
from bnraph going low
FR,CHI,CHB,CHL 0.991106929 0.101392219E+13 0.101245465E+13 0.101330808E+13
IREV= 20 IEND=99985
...
FR,CHI,CHB,CHL 0.999999999 0.101330946E+13 0.101330466E+13 0.101330466E+13
IREV= 19 IEND=99980
FR,CHI,CHB,CHL 0.999999999 0.101330516E+13 0.101330466E+13 0.101330466E+13
IREV= 20 IEND=99980
FR,CHI,CHB,CHL 0.999999999 0.101330466E+13 0.101330466E+13 0.101330466E+13
AT END FR, CHI 0.999999999 0.101330466E+13
TEMP2= 0.000000000E+00
NEW SECTION FR= 0.9999999990000000
CHI AT END OF FIT 1.0133046600254290D+012
1 -0.6931471805392518 +- 4.1581938793687670D-012
1 1.6774212588784540 +- 2.9712392197654640D-004
1 -1.7352176175778950 +- 0.0005834587395913
1 0.9718528295887369 +- 4.4826849846264450D-004
1 -0.3024947110641524 +- 1.9006602201471140D-004
1 0.0454785560315660 +- 7.9304690450917410D-005
1 -0.0014240809655113 +- 2.1808937763341420D-005
1 -0.7921002978159773 +- 4.2865887261788370D-004
1 0.2954761546357216 +- 1.7315498921803580D-004
1 -0.0453056386094508 +- 7.6205898104717990D-005
1 0.0014333125421946 +- 2.2003970143109860D-005
FINAL CHIT= 1.0133046600254290D+012
CHI/DEG OF FREE 2.4775175061746440D+009
RESULTS IN FILE aigau2.dir
The last two coefficients are possibly small. The matrix has an inverse even with λ =0, but the routine is on a saddle point.
MPNlfit 7,4
E:\PUBLIC~1\nlfit\Pade2>mpnlfit aigau2.dir
NADIR=aigau2.dir
NAOUT=aigau.dir
NADAT=..\TestData\Aigau.DAT
ND= 1
VORF CONS
1 -0.693147
1 1.67742
1 -1.73522
1 0.971853
1 -0.302495
1 0.454786E-01
1 -0.142408E-02
1 -0.792100
1 0.295476
1 -0.453056E-01
1 0.143331E-02
FIT IS BEING MADE TO DATA IN FILE
..\TestData\Aigau.DAT
FR,CHI,CHB,CHL 0.999000000 0.101330478E+13 0.100000000E+67 0.500000000E+67
FR,CHI,CHB,CHL 0.997002999 0.101028396E+13 0.101026791E+13 0.101330478E+13
FR,CHI,CHB,CHL 0.991035916 0.100123912E+13 0.100122769E+13 0.101028396E+13
FR,CHI,CHB,CHL 0.973348092 0.974762607E+12 0.974554189E+12 0.100123912E+13
FR,CHI,CHB,CHL 0.922156318 0.900217388E+12 0.898883497E+12 0.974762607E+12
FR,CHI,CHB,CHL 0.784176167 0.714761239E+12 0.705929021E+12 0.900217388E+12
FR,CHI,CHB,CHL 0.482215223 0.377349682E+12 0.344668750E+12 0.714761239E+12
FR,CHI,CHB,CHL 0.112130240 0.759535608E+11 0.423123103E+11 0.377349682E+12
from bnraph going low
FR,CHI,CHB,CHL 0.109000000 0.125289511E+11 0.876771260E+10 0.759535608E+11
from bnraph going low
FR,CHI,CHB,CHL 0.100000000E-01 0.120839736E+11 0.120681258E+11 0.125289511E+11
from bnraph going low
FR,CHI,CHB,CHL 0.100000000E-01 0.120831939E+11 0.120834280E+11 0.120839736E+11
from bnraph going low
FR,CHI,CHB,CHL 0.100000000E-01 0.120833172E+11 0.120831923E+11 0.120831939E+11
IREV= 1 IEND=99989
from bnraph going low
FR,CHI,CHB,CHL 0.901000000 0.120833172E+11 0.120831923E+11 0.120831939E+11
IREV= 2 IEND=99989
from bnraph going low
FR,CHI,CHB,CHL 0.990100000 0.120833172E+11 0.120831923E+11 0.120831939E+11
IREV= 20 IEND=99989
FR,CHI,CHB,CHL 0.999010000 0.120831939E+11 0.120831939E+11 0.120831939E+11
AT END FR, CHI 0.999010000 0.120831939E+11
TEMP2= 0.000000000E+00
NEW SECTION FR= 0.9990100000000001
FR,CHI,CHB,CHL 0.999999990 0.120831939E+11 0.100000000E+67 0.500000000E+67
FR,CHI,CHB,CHL 0.999999970 0.120832342E+11 0.120831936E+11 0.120831939E+11
IREV= 1 IEND=99988
FR,CHI,CHB,CHL 0.999999997 0.120833903E+11 0.120831939E+11 0.120831939E+11
IREV= 2 IEND=99988
FR,CHI,CHB,CHL 0.999999999 0.120831590E+11 0.120831939E+11 0.120831939E+11
FR,CHI,CHB,CHL 0.999999997 0.120831594E+11 0.120831589E+11 0.120831590E+11
IREV= 1 IEND=99987
FR,CHI,CHB,CHL 0.999999999 0.120831356E+11 0.120831590E+11 0.120831590E+11
FR,CHI,CHB,CHL 0.999999997 0.120830771E+11 0.120831356E+11 0.120831356E+11
FR,CHI,CHB,CHL 0.999999991 0.120833500E+11 0.120830770E+11 0.120830771E+11
IREV= 1 IEND=99985
FR,CHI,CHB,CHL 0.999999999 0.120832907E+11 0.120830771E+11 0.120830771E+11
IREV= 2 IEND=99985
FR,CHI,CHB,CHL 0.999999999 0.120832907E+11 0.120830771E+11 0.120830771E+11
IREV= 3 IEND=99985
FR,CHI,CHB,CHL 0.999999999 0.120832907E+11 0.120830771E+11 0.120830771E+11
IREV= 20 IEND=99985
FR,CHI,CHB,CHL 0.999999999 0.120830771E+11 0.120830771E+11 0.120830771E+11
AT END FR, CHI 0.999999999 0.120830771E+11
TEMP2= 0.000000000E+00
NEW SECTION FR= 0.9999999990000000
FR,CHI,CHB,CHL 0.999999990 0.120830771E+11 0.100000000E+67 0.500000000E+67
FR,CHI,CHB,CHL 0.999999970 0.120831331E+11 0.120830767E+11 0.120830771E+11
IREV= 1 IEND=99984
FR,CHI,CHB,CHL 0.999999997 0.120831937E+11 0.120830771E+11 0.120830771E+11
IREV= 2 IEND=99984
FR,CHI,CHB,CHL 0.999999999 0.120833167E+11 0.120830771E+11 0.120830771E+11
IREV= 3 IEND=99984
FR,CHI,CHB,CHL 0.999999999 0.120833167E+11 0.120830771E+11 0.120830771E+11
IREV= 4 IEND=99984
FR,CHI,CHB,CHL 0.999999999 0.120833167E+11 0.120830771E+11 0.120830771E+11
IREV= 20 IEND=99984
FR,CHI,CHB,CHL 0.999999999 0.120830771E+11 0.120830771E+11 0.120830771E+11
AT END FR, CHI 0.999999999 0.120830771E+11
TEMP2= 0.000000000E+00
NEW SECTION FR= 0.9999999990000000
CHI AT END OF FIT 1.2083077093256680D+010
1 -0.6931471805615839 +- 4.4877629997768990D-013
1 2.0889305735056730 +- 0.0036028965000463
1 -2.7363931119040410 +- 0.0087573978356257
1 2.0103985094354060 +- 0.0090737802408966
1 -0.8819988829712878 +- 0.0050557641281230
1 0.2218974386819869 +- 0.0015362123680080
1 -0.0255545044797333 +- 2.0949939788925640D-004
1 -1.3857827511100200 +- 0.0051978809479565
1 0.7734070845891521 +- 0.0041726339981921
1 -0.2203181830673359 +- 0.0015241495234300
1 0.0255892342731615 +- 2.0971147757262310D-004
FINAL CHIT= 1.2083077093256680D+010
CHI/DEG OF FREE 2.9542975778133680D+007
RESULTS IN FILE aigau.dir
The continuing process
AIGAU.DIR
aigau2.dir, OUTPUT FILE NAME
..\TestData\Aigau.DAT, DATA SET NAME
1, DIMENSION OF X IN F(X)
8,5 ,
NUMBER OF NUMERATOR TERMS, DENOMINATOR TERMS from
7,4
1, 1 fits to exponential of a Pade, 0 to a Pade
1E-16,5E-18, err(i)= max(ep1,ep2*dat(i))
100000, NUMBER OF MINIMIZATION STEPS
.999, INITIAL FR DECREASE DESIRED
1 VARY O FIX FITTED CONS ERROR IN CONS
1 -0.6931471805615839 +- 0.449E-12
1 2.088930573505673 +- 0.360E-02
1 -2.736393111904041 +- 0.876E-02
1 2.010398509435406 +- 0.907E-02
1 -0.8819988829712878 +- 0.506E-02
1 0.2218974386819869 +- 0.154E-02
1 -0.2555450447973331E-01 +- 0.209E-03
1 0 insert
1 -1.385782751110020 +- 0.520E-02
1 0.7734070845891521 +- 0.417E-02
1 -0.2203181830673359 +- 0.152E-02
1 0.2558923427316152E-01 +- 0.210E-03
1 0 insert
CHIS=0.1208E+11 FOR 420 DATA POINTS
CHI USED IN CALCULATING ERRORS IS 0.1208E+11
Continuing with MPNlfit
9,6
I:\PUBLIC~1\nlfit\Pade2>mpnlfit aigau.dir
NADIR=aigau.dir
NAOUT=aigau2.dir
NADAT=..\TestData\Aigau.DAT
ND= 1
VORF CONS
1 -0.693147
1 1.91260
1 -2.35216
1 1.67321
1 -0.744051
1 0.206773
1 -0.331569E-01
1 0.234110E-02
1 0.000000E+00
1 -1.13140
1 0.633198
1 -0.195749
1 0.330629E-01
1 -0.234251E-02
1 0.000000E+00
FIT IS BEING MADE TO DATA IN FILE
..\TestData\Aigau.DAT
FR,CHI,CHB,CHL 0.999000000 167716.325 0.100000000E+67 0.500000000E+67
FR,CHI,CHB,CHL 0.997002999 167351.072 167213.679 167716.325
FR,CHI,CHB,CHL 0.991932325 166471.657 166000.938 167351.072
FR,CHI,CHB,CHL 0.978392540 162726.772 162874.627 166471.657
FR,CHI,CHB,CHL 0.936568178 152536.354 152404.717 162726.772
FR,CHI,CHB,CHL 0.821520097 124590.566 125311.680 152536.354
FR,CHI,CHB,CHL 0.554440027 69341.3583 69077.9969 124590.566
FR,CHI,CHB,CHL 0.170436940 11529.2788 11818.3289 69341.3583
from bnraph going low
FR,CHI,CHB,CHL 0.100000000E-01 813.365694 464.732345 11529.2788
from bnraph going low
FR,CHI,CHB,CHL 0.100000000E-01 487.629930 433.555844 813.365694
from bnraph going low
FR,CHI,CHB,CHL 0.109000000 477.074349 474.550091 487.629930
from bnraph going low
FR,CHI,CHB,CHL 0.109000000 486.473559 465.008361 477.074349
IREV= 1 IEND=99989
from bnraph going low
FR,CHI,CHB,CHL 0.910900000 486.473559 465.008361 477.074349
IREV= 2 IEND=99989
FR,CHI,CHB,CHL 0.991090000 462.482141 472.823616 477.074349
FR,CHI,CHB,CHL 0.973507457 478.717817 450.229813 462.482141
IREV= 1 IEND=99988
FR,CHI,CHB,CHL 0.997350746 459.398413 461.256908 462.482141
FR,CHI,CHB,CHL 0.992073274 460.513413 455.756887 459.398413
IREV= 1 IEND=99987
FR,CHI,CHB,CHL 0.999207327 467.017521 459.034260 459.398413
IREV= 2 IEND=99987
FR,CHI,CHB,CHL 0.999920733 459.744471 459.361997 459.398413
IREV= 3 IEND=99987
FR,CHI,CHB,CHL 0.999992073 459.398413 459.394771 459.398413
IREV= 4 IEND=99987
FR,CHI,CHB,CHL 0.999999207 459.398411 459.398048 459.398413
FR,CHI,CHB,CHL 0.999998573 459.398426 459.397756 459.398411
IREV= 1 IEND=99986
FR,CHI,CHB,CHL 0.999999857 459.398411 459.398346 459.398411
FR,CHI,CHB,CHL 0.999999743 459.398403 459.398293 459.398411
FR,CHI,CHB,CHL 0.999999538 459.398403 459.398190 459.398403
IREV= 1 IEND=99984
FR,CHI,CHB,CHL 0.999999954 459.398403 459.398381 459.398403
IREV= 2 IEND=99984
FR,CHI,CHB,CHL 0.999999995 459.398403 459.398400 459.398403
IREV= 20 IEND=99984
FR,CHI,CHB,CHL 0.999999999 459.398403 459.398403 459.398403
AT END FR, CHI 0.999999999 459.398403
TEMP2= 0.000000000E+00
NEW SECTION FR= 0.9999999990000000
FR,CHI,CHB,CHL 0.999999990 459.398403 0.100000000E+67 0.500000000E+67
FR,CHI,CHB,CHL 0.999999970 459.398403 459.398389 459.398403
IREV= 20 IEND=99983
FR,CHI,CHB,CHL 0.999999997 459.398403 459.398403 459.398403
AT END FR, CHI 0.999999997 459.398403
TEMP2= 0.000000000E+00
NEW SECTION FR= 0.9999999970000002
CHI AT END OF FIT 459.3984025939595000
1 -0.6931471805599452 +- 9.2680844561023110D-017
1 1.9959157137768370 +- 0.0027346017020747
1 -2.5823106233410170 +- 0.0075428474861388
1 1.9536880925711240 +- 0.0092587844769758
1 -0.9387916412290680 +- 0.0065593672284100
1 0.2892445861593335 +- 0.0028952635649145
1 -0.0540078433082985 +- 0.0007942333019080
1 0.0050787392223134 +- 1.2442010185481990D-004
1 -1.0612517668379220D-004 +- 8.3772738126872600D-006
1 -1.2515906736869810 +- 0.0039451963143826
1 0.7695652871670581 +- 0.0044596182820735
1 -0.2680046704303274 +- 0.0024743211617132
1 0.0533212759681357 +- 0.0007543724951810
1 -0.0050795087997970 +- 1.2410151915342200D-004
1 1.0608506577952600D-004 +- 8.3818134220689910D-006
FINAL CHIT= 459.3984025939595000
CHI/DEG OF FREE 1.1343170434418750
RESULTS IN FILE aigau2.dir
Results
aigau.dir, OUTPUT FILE NAME
..\TestData\Aigau.DAT, DATA SET NAME
1, DIMENSION OF X IN F(X)
9,6 , NUMBER OF NUMERATOR TERMS, DENOMINATOR TERMS
1, 1 fits to exponential of a Pade, 0 to a Pade
1E-16,5E-18, err(i)= max(ep1,ep2*dat(i))
100000, NUMBER OF MINIMIZATION STEPS
.999, INITIAL FR DECREASE DESIRED
1 VARY O FIX FITTED CONS ERROR IN CONS
1 -0.6931471805599452 +- 0.927E-16
1 1.995915713776837 +- 0.273E-02
1 -2.582310623341017 +- 0.754E-02
1 1.953688092571124 +- 0.926E-02
1 -0.9387916412290680 +- 0.656E-02
1 0.2892445861593335 +- 0.290E-02
1 -0.5400784330829852E-01 +- 0.794E-03
1 0.5078739222313374E-02 +- 0.124E-03
1 -0.1061251766837922E-03 +- 0.838E-05
1 -1.251590673686981 +- 0.395E-02
1 0.7695652871670581 +- 0.446E-02
1 -0.2680046704303274 +- 0.247E-02
1 0.5332127596813570E-01 +- 0.754E-03
1 -0.5079508799796978E-02 +- 0.124E-03
1 0.1060850657795260E-03 +- 0.838E-05
CHIS= 459.4 FOR 420 DATA POINTS
CHI USED IN CALCULATING ERRORS IS 459.4
Figure 2 (AiGauss(f)-fA(f,c))
The dip at -4 is probably due to error in the FFT. The fit error is certainly less than 3x10-16 and arguably less than 1x10-16.
Figure 3 Black is "data". Blue is fit, fA(f,c). Red is abs(data-fit)
This will be the best fit to use for f>0 where
AiGauss(f)=1-AiGauss(-f).