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version 1.67, 2023/05/23 12:25:36 version 1.68, 2024/04/24 20:53:06
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   2024-04-24  Nicolas Brouard   <brouard@ined.fr>
   
           * (Module): This version comes late after having tested
           successfully the praxis C version of Buckhardt.  But Buckardt's
           version was difficult to read and Gegenfurtner's version had a few
           typos which made its results less reliable than Buckhardt's
           results.  The most important work consisted in retyping the Brent
           original PRAXIS program written in Algol W (published with errors,
           ommitting the transposition of matrix V before its QR reduction
           from Golub. I used the recent "awe" compiler from Gkynn Webster.
           The awe library had errors, for example in arc tangent function
           which have been fixed.
   
           The main objective was to get identical results with the three
           versions: (1) Algol W, (2) Buckhardt'C version as well (3)
           Gegenfürtner C versions on the various test functions published by
           Brent in 1973 in Algol W.
   
           Also, in order to compare them, the random function had to produce
           the same sequence for the 3 softwares. The random function used in
           imach corresponds to original Brent's random function written in
           Algol W.  Other point, in Algol W, the arrays of dimension n are
           'normal' mathematical arrays starting from 1 to n. But this is a
           real issue in C where, by default, arrays are starting from 0 to
           n-1. In Buckhardt, as well as in Gegenfürtner C code, it can be
           seen that authors while trying to mimick original Brent Algol W
           code are hesitating by changing either a loop originally from 1 to
           n in a loop from 0 to n-1, or keeping Brent's loop from 1 to n and
           shifting the index from original X(I) in Algol W to x[i-1] in C.
           But as IMaCh is using, since the beginning, the Numerical Recipes
           functions vector or matrix, I changed Geggenfürtner code to mimick
           the original Algol W arrays. Thus the X(I) is translated in C as
           x[i] which minimizes the errors. The Golub QR algorithm was
           published in Algol with overflow errors which were reproduced in
           Brent's Algol W code. Buckhardt code fixed these errors which are
           much more problematic in C than in Algol W.  Thus Buckhardt code
           seems very safe, but i haven't chosen it for IMaCh because the C
           style is horrible and almost unreadable compared to Gegenfürtner
           CO code which is very close to Brent's original. Also what makes
           Buckhardt code more difficult to read is, instead of passing the
           minimum of parameters in the functions calls, as it is in Algol
           Brent's code or Gegenfürtner's code, the list of parameters is
           high. For example, the flin function LONG REAL PROCEDURE FLIN
           (LONG REAL VALUE L) has only one parameter in Algol W, the
           Gegenfürtner flin function had two parameters: static double
           flin(l, j) double l; { int i; double tflin[N];} but Buckhardt
           function has 14 parameters which makes the code unreadable and
           useless. Gegenfürtner used a lot of static variables or functions
           which I tried to minimize. Also in Gegefürtner, array dimensions
           were fixed to N. In my adaptation the flin is static double
           flin(double l, int j) and the parameter used are global variables.
   
   2023-06-14  Nicolas Brouard   <brouard@ined.fr>
   
           * imach.c (Module): Testing if conjugate gradient could be quicker
           when lot of variables POWELLORIGINCONJUGATE
   
 2023-05-23  Nicolas Brouard   <brouard@ined.fr>  2023-05-23  Nicolas Brouard   <brouard@ined.fr>
   
         * imach.c (Module): Fixed PROB_r           * imach.c (Module): Fixed PROB_r 
Removed from v.1.67  
changed lines
  Added in v.1.68

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