282214147
Amsub – bli-ftbm
The Amoeba Routines and their visualization are in
for\AMSUB.ZIP for\BLIFTBM.ZIP
cpp\AMSUB.ZIP cpp\BLIFTBM.ZIP
Error estimation in principle is in
../class2K/optimization/amoeba/Errinfun.htm
The random distributions are reproduced below.
1/2
iy, pulling a value from a randomly selected table
entry and replacing that with a new value.
This can be re-initialized by printing out ix
and iy and then calling rseed. This wastes 128
random numbers, but gives a completely determined
new set of random numbers.
Gaussian distribution3
Rgauss=-6;
For(i=0;i<12;++i){Rgauss+=rndmf();}
1
1
f  xdx 
0
2
1
1
f 2  x 2 dx 
0
3
Psuedo Random numbers
Random numbers are not wanted. What is
desired is a set of completely reproducible numbers
that are the same on all computers and in both C and
Fortran. In addition, it must be true that the numbers
give all averages the same as would be given by
actual random numbers. In practice the numbers
should be re-initialized with the numbers needed to
recreate the desired set written out as
17894561 3678991
18345899 234567899
...
In this way, when the code bombs after 23 hours of
running, the situation just before the bomb can be
recreated by simply entering these numbers.
With this many random numbers, the
"randomness" of the set can be a problem for some
calculations1. The method used here, first suggested
by MacLaren and Marsaglia2, is to insert numbers
into a table with a multiplicative congruential method
with one multiplier and seed and to extract them from
the table with a multiplicative congruential method
with a different multiplier and seed. random.for
contains the common
COMMON/RAN/IX,IY,ITAB(128)
RANDOM.CPP RANDOM.H
The file random.h contains
struct {int ix,iy,itab[128];} ran;
int rseed(int ix,int iy);
double rndmf();
z
z
Equation 1
Thus
2  f
2
 f
2

1 1 1
 
3 4 12
Equation 2
or
12
12 f  6   rndmf
i 1
bg 6  1
Equation 3
This means that the above sum is 0 +- 1. If I
want to produce a peak of height P = 36 +- beta with
a Gaussian distribution of beta. I simply take
12


P  36  beta * 6   rndmf   
i 1


Equation 4
This is implemented in ..\ArtDat\for\FUNWE.ZIP
and ..\ArtDat\cpp\FUNWE.ZIP
The seeds are ix and iy. The random number set is
initialized by calling rseed(ix,iy). This call causes
128 numbers to be fed into the table itab[128] with
one random number generator. The call x=rndmf()
gives a random number base on ix,iy and itab,
between 0 and 1. It selects this by advancing ix and
Figure 1 Black is Fortran, Blue is C
1
R. L. Coldwell, "Correlational Defects in the Standard IBM 360 Random
Number Generator and the Classical Ideal Gas Correlation Function", J.
Computational Phys. 14, 223 (1974).
2
M. D. MacLaren and G. Marsaglia, J. Assoc. Comput. Mach. 12 (1965),83
3
J. M Hammersley and D. C. Handscomb, Monte Carlo
Methods, John Wiley (1964) p.39
282214147
2/2
completed assignments or four + the hello code earn
an A. Do as many as you like, but leave time for your
other homework. – Good Luck!
Assignment 05-3
Figure 2 Funwe.
Assignment 05-4
Zips
For
01/31/2005 TLORENT.ZIP appears in
Feb1.htm - Feb3.htm - Feb10.htm
(Assign03_02
01/31/2005 TLOCATE.ZIP appears in
Feb1.htm - Feb3.htm
02/09/2005 LAGRANGE.ZIP
Feb3.htm - Feb8.htm - Feb10.htm
Assign03_02
02/23/2005
02/23/2005
02/23/2005
1. Change funwe to generate a two bump
Gaussian with error – one extra line in the file.
2. Modify ftbm2 in AMSUB to read the file
produced by funwe on the first pass then to
calculate a CHI = I ((fI-fA(xI;cons))/errI)2
with fA(xI;cons) – the same function as in 1.
3. Use the code in BLIFTBM to make a file of
the fit. Plot the fit and the “data” – note the E
and e as symbols in gplot produce error bars.
4. Find the limits – vary the spacing between the
bumps and the errors until the Amoeba
cannot, even with coaxing find the peaks.
AMSUB.ZIP - here
BLIFTBM.ZIP- here
FUNWE.ZIP- here
Cpp
02/01/2005 TLOCATE.ZIP
Feb1.htm - Feb3.htm
02/08/2005 CTLAG.ZIP
Feb8.htm - Feb10.htm Assign03_02
Feb17.htm
02/17/2005 CLOREN.ZIP
Feb17.htm
02/17/2005 TSPLINE.ZIP
Feb17.htm
02/17/2005 TSPLINE2.ZIP
Feb17.htm
02/23/2005 AMSUB.ZIP - here
02/23/2005 BLIFTBM.ZIP - here
02/23/2005 FUNWE.ZIP – here
Assignments
You are welcome to do any of the assignments
in ..\class2K\Homework\Homework3.htm. Five
This is the same as the assignment above, except in
step 2, the fA(xI,cons) is a small set of values of xbar
and ybar. That is fA(xI;cons) is a cubic Lagrange
interpolating the values xbar and ybar.
1. Set a reasonable grid of xbar values and let the
cons be the ybar values on this grid.
2. Let both xbar and ybar be free constants.
Note the need to resort the xbar values to keep
them in ascending order before calculating
chi.
Assignment 05-5
This is the same as the assignment above, except that
fA(xI;cons) is a spline interpolating the values xbar
and ybar.
1. Set a reasonable grid of xbar values and let the
cons be the ybar values on this grid.
2. Let both xbar and ybar be free constants.
Note the need to resort the xbar values to keep
them in ascending order before calculating
chi.
3. Note that spline needs to be called before
splint.