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MPNlfit
The difference between MPNlfit and Nlfit is that Bailey’s Fortran 77 package1 has been used to make
some of the parameters in MPNlfit have 128 character accuracy. The fit being tested is to
 Nnum

cI f I 1 
f


1
I 1
 (1.1)
AiGauss( f ) 
exp  t 2  dt  f A  f i , c   exp  Nden

 
I 
 1
cI  Nnum f 



I 1

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.dat2. 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
 AiGauss  f i   f A  f i , c  
 c    
 (1.2)
1016
i 1 

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
420
2
2
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
../../class2K/optimization/mpcholesky/Quadruple/Welcome.htm
2
..\AiGaussPgen\Welcome.htm
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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
2/11
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The routine begins by finding the  for which chb, a quadratic expansion of 2 about the present value using
c(), is equal to Fr times chl the value of 20 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  for which the predicted chb is equal to Fr times chl so that
 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
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1 -0.6033653400846807
1 0.1234737788179483
1 0  added by hand
CHIS=0.2218E+19 FOR
420 DATA
CHI USED IN CALCULATING ERRORS
5/28/2016
4/11
+- 0.914E-03
+- 0.270E-03
POINTS
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
FR,CHI,CHB,CHL 0.997002999
0.221140409E+19
FR,CHI,CHB,CHL 0.991035916
0.219157934E+19
FR,CHI,CHB,CHL 0.973348092
0.213319611E+19
FR,CHI,CHB,CHL 0.922156318
0.196718945E+19
FR,CHI,CHB,CHL 0.784176167
0.154226230E+19
FR,CHI,CHB,CHL 0.482215223
0.739341299E+18
FR,CHI,CHB,CHL 0.112130240
0.809121355E+17
FR,CHI,CHB,CHL 0.100000000E-01 0.551275089E+16
FR,CHI,CHB,CHL 0.100000000E-01 0.406755720E+14
from bnraph going low
FR,CHI,CHB,CHL 0.100000000E-01 0.151273947E+14
from bnraph going low
FR,CHI,CHB,CHL 0.100000000E-01 0.144409294E+14
from bnraph going low
FR,CHI,CHB,CHL 0.100000000E-01 0.144367023E+14
from bnraph going low
FR,CHI,CHB,CHL 0.100000000E-01 0.144365309E+14
...
0.100000000E+67
0.221140431E+19
0.219158088E+19
0.213316957E+19
0.196714028E+19
0.154262280E+19
0.743706693E+18
0.828984351E+17
0.562949953E+15
0.000000000E+00
0.500000000E+67
0.221805181E+19
0.221140409E+19
0.219157934E+19
0.213319611E+19
0.196718945E+19
0.154226230E+19
0.739341299E+18
0.809121355E+17
0.551275089E+16
0.171111497E+14 0.406755720E+14
0.143924354E+14 0.151273947E+14
0.144376752E+14 0.144409294E+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
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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
FR,CHI,CHB,CHL 0.997002999
0.143932570E+14 0.143932563E+14
FR,CHI,CHB,CHL 0.991035916
0.142642177E+14 0.142642347E+14
FR,CHI,CHB,CHL 0.973348092
0.138844742E+14 0.138839683E+14
FR,CHI,CHB,CHL 0.922156318
0.127929892E+14 0.128051766E+14
FR,CHI,CHB,CHL 0.784176167
0.100168961E+14 0.100201587E+14
FR,CHI,CHB,CHL 0.482215223
0.445442849E+13 0.475882376E+13
FR,CHI,CHB,CHL 0.112130240
0.119148160E+13 0.309237645E+12
from bnraph going low
FR,CHI,CHB,CHL 0.109000000
0.104923272E+13 0.107266808E+13
from bnraph going low
FR,CHI,CHB,CHL 0.100000000E-01 0.102782228E+13 0.101307541E+13
FR,CHI,CHB,CHL 0.109000000
0.102588416E+13 0.000000000E+00
from bnraph going low
FR,CHI,CHB,CHL 0.110692900
0.102443278E+13 0.102421548E+13
FR,CHI,CHB,CHL 0.109000000
0.102431094E+13 0.000000000E+00
from bnraph going low
FR,CHI,CHB,CHL 0.110692900
0.102388285E+13 0.102357795E+13
FR,CHI,CHB,CHL 0.109000000
0.101330808E+13 0.194347270E+12
from bnraph going low
FR,CHI,CHB,CHL 0.110692900
0.101392219E+13 0.101245465E+13
IREV=
1 IEND=99985
from bnraph going low
FR,CHI,CHB,CHL 0.911069290
0.101392219E+13 0.101245465E+13
IREV=
2 IEND=99985
from bnraph going low
FR,CHI,CHB,CHL 0.991106929
0.101392219E+13 0.101245465E+13
IREV=
20 IEND=99985
...
FR,CHI,CHB,CHL 0.999999999
0.101330946E+13 0.101330466E+13
IREV=
19 IEND=99980
FR,CHI,CHB,CHL 0.999999999
0.101330516E+13 0.101330466E+13
IREV=
20 IEND=99980
FR,CHI,CHB,CHL 0.999999999
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
0.500000000E+67
0.144365226E+14
0.143932570E+14
0.142642177E+14
0.138844742E+14
0.127929892E+14
0.100168961E+14
0.445442849E+13
0.119148160E+13
0.104923272E+13
0.102782228E+13
0.102588416E+13
0.102443278E+13
0.102431094E+13
0.102388285E+13
0.101330808E+13
0.101330808E+13
0.101330808E+13
0.101330466E+13
0.101330466E+13
0.101330466E+13
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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  =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
FR,CHI,CHB,CHL 0.997002999
0.101028396E+13 0.101026791E+13
FR,CHI,CHB,CHL 0.991035916
0.100123912E+13 0.100122769E+13
FR,CHI,CHB,CHL 0.973348092
0.974762607E+12 0.974554189E+12
FR,CHI,CHB,CHL 0.922156318
0.900217388E+12 0.898883497E+12
FR,CHI,CHB,CHL 0.784176167
0.714761239E+12 0.705929021E+12
FR,CHI,CHB,CHL 0.482215223
0.377349682E+12 0.344668750E+12
FR,CHI,CHB,CHL 0.112130240
0.759535608E+11 0.423123103E+11
from bnraph going low
FR,CHI,CHB,CHL 0.109000000
0.125289511E+11 0.876771260E+10
from bnraph going low
FR,CHI,CHB,CHL 0.100000000E-01 0.120839736E+11 0.120681258E+11
from bnraph going low
FR,CHI,CHB,CHL 0.100000000E-01 0.120831939E+11 0.120834280E+11
from bnraph going low
FR,CHI,CHB,CHL 0.100000000E-01 0.120833172E+11 0.120831923E+11
IREV=
1 IEND=99989
from bnraph going low
FR,CHI,CHB,CHL 0.901000000
0.120833172E+11 0.120831923E+11
IREV=
2 IEND=99989
from bnraph going low
FR,CHI,CHB,CHL 0.990100000
0.120833172E+11 0.120831923E+11
IREV=
20 IEND=99989
FR,CHI,CHB,CHL 0.999010000
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
FR,CHI,CHB,CHL 0.999999970
0.120832342E+11 0.120831936E+11
IREV=
1 IEND=99988
FR,CHI,CHB,CHL 0.999999997
0.120833903E+11 0.120831939E+11
IREV=
2 IEND=99988
0.500000000E+67
0.101330478E+13
0.101028396E+13
0.100123912E+13
0.974762607E+12
0.900217388E+12
0.714761239E+12
0.377349682E+12
0.759535608E+11
0.125289511E+11
0.120839736E+11
0.120831939E+11
0.120831939E+11
0.120831939E+11
0.120831939E+11
0.500000000E+67
0.120831939E+11
0.120831939E+11
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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
7/11
291195807
1 -0.2555450447973331E-01
1 0 insert
1 -1.385782751110020
1 0.7734070845891521
1 -0.2203181830673359
1 0.2558923427316152E-01
1 0 insert
CHIS=0.1208E+11 FOR
420 DATA
CHI USED IN CALCULATING ERRORS
5/28/2016
8/11
+- 0.209E-03
++++-
0.520E-02
0.417E-02
0.152E-02
0.210E-03
POINTS
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
FR,CHI,CHB,CHL 0.997002999
167351.072
FR,CHI,CHB,CHL 0.991932325
166471.657
FR,CHI,CHB,CHL 0.978392540
162726.772
FR,CHI,CHB,CHL 0.936568178
152536.354
FR,CHI,CHB,CHL 0.821520097
124590.566
FR,CHI,CHB,CHL 0.554440027
69341.3583
FR,CHI,CHB,CHL 0.170436940
11529.2788
from bnraph going low
FR,CHI,CHB,CHL 0.100000000E-01 813.365694
from bnraph going low
FR,CHI,CHB,CHL 0.100000000E-01 487.629930
from bnraph going low
FR,CHI,CHB,CHL 0.109000000
477.074349
from bnraph going low
FR,CHI,CHB,CHL 0.109000000
486.473559
IREV=
1 IEND=99989
from bnraph going low
FR,CHI,CHB,CHL 0.910900000
486.473559
IREV=
2 IEND=99989
FR,CHI,CHB,CHL 0.991090000
462.482141
FR,CHI,CHB,CHL 0.973507457
478.717817
IREV=
1 IEND=99988
FR,CHI,CHB,CHL 0.997350746
459.398413
FR,CHI,CHB,CHL 0.992073274
460.513413
IREV=
1 IEND=99987
FR,CHI,CHB,CHL 0.999207327
467.017521
IREV=
2 IEND=99987
FR,CHI,CHB,CHL 0.999920733
459.744471
IREV=
3 IEND=99987
0.100000000E+67 0.500000000E+67
167213.679
167716.325
166000.938
167351.072
162874.627
166471.657
152404.717
162726.772
125311.680
152536.354
69077.9969
124590.566
11818.3289
69341.3583
464.732345
11529.2788
433.555844
813.365694
474.550091
487.629930
465.008361
477.074349
465.008361
477.074349
472.823616
450.229813
477.074349
462.482141
461.256908
455.756887
462.482141
459.398413
459.034260
459.398413
459.361997
459.398413
291195807
5/28/2016
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
9/11
291195807
CHI USED IN CALCULATING ERRORS IS
5/28/2016
10/11
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.
291195807
5/28/2016
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).
11/11