Welcome to the multiple precision nlfit fortran folder

The folder formp contains the fortran files needed for nlfit.  These files were tested by fitting the complementary error function to a Pade approximate in ..\LogAigau\Welcome.doc htm

Fortran

01/05/2008  06:24 AM             9,702 nlfit.for

12/31/2007  07:38 PM            33,236 mpbob.for – see ..\..\..\MultiplePrecision\Bob\Welcome.htm

01/05/2008  06:04 AM            35,591 robmin.for

 

11/18/2007  06:06 PM               768 poly.for ß generic polynomial includes multiple precision

01/11/2008  09:31 AM             3,485 2Dpoly.for ß 2d polynomial tested in ..\2dPoly\Welcome.htm

12/31/2007  05:35 PM             1,840 pademp.for ß Pade form for fitting the log of the complementary error function ../LogAigau/Welcome.htm 

11/11/2007  09:50 AM             1,188 pademMP.for ß above with constants+diff in num and constants in denom ../LogAigau/PadeM/Welcome.htm

 

10/12/2007  09:34 AM             1,088 intelsys.for  <<intel-10ß These routines all contain the code needed to make different compilers and

10/12/2007  11:11 AM             2,830 openwsys.for << watcom ß operating systems behave the same way.  One only is needed for each compiler.

10/27/2007  12:16 PM             1,096 PSSYS.FOR <<power stationß These codes do not change with it, maxcon, or ndim.

10/12/2007  11:23 AM             2,801 unixsys.for << unix

10/18/2007  10:49 AM             5,743 WSYSTEM.FOR << watfor

10/30/2008  11:32 AM             2,024 Ishft.for ß for those systems that do not support the ISHFT command in the usual way.  This slows the calculation of the 2^nd derivative array, but has no other effect.  The data statement needed for arithmetic shifts is

      DATA IAA/-2147483648/

This is the largest integer and includes the sign.  In Watfor this need to be changed to the equivalent

      DATA IAA/Z80000000/  

On the original Vax compilers it would need to be

      DATA IAA/’80000000’X/

 

            The fortran is set up to fit 20 constants with it=63 for approximately 260 digit accuracy in the matrix inversion routine. 

            The maximum number of constants is determined by maxcon=20 in nlfit.for and robmin.for. 

            The precision is approximately 4.2 x it in decimal digits.  The time to form the storage matrix MPPPCC is almost independent of it.  Thus the time required when MPSMINV is not needed increases only slightly as it is increased.  When high precision is wanted for an almost linearly dependent system such as the Pade approximate form in LogAigau\Welcome.doc htm, MPSMINV matrix inversions dominate the code’s cpu time requirements.  These go as it².  An investigation of the accuracy effects of various values of it was carried out in LogAigau\The number of Multiple Precision integers.htm.  An it value of 15, is adequate, 31 is better and 63 introduces a minor problem in the early stages of converging on an undesired local minimum.  The multiplication algorithm does not contain intermediate normalizations which limits it to it=63.  The codes here all have it=63 and I recommend it owing to the fact that the time increase occurs only when the code is almost at its limits and it saves making a series of runs in which it is slowly increased.  The files containing it=63 are

1. nlfit.for
2. mpbob.for
3. robmin.for
4. poly – your version

If all it= parameters are not changed, some of the values are un-initialized.  Watfor finds this, but not the other compilers.

 

            The dimension of x in f_A(x) is set in nlfit on line [10] above. 

 [10]      parameter(maxcon=20,maxdim=2,it=63)

Compilers

            Watcom nlfit.wpj

            Watfor nlfit.for – change last 4 lines from # to $ and run.  Be sure to change back before using watcom again.  Best debugger, slow.

            Power Station nlfit-PS\nlfit.mdp – This like to have its own folder.

            Intel -10 nlfit.vfproj – mot modern and fastest code tested.