[BLAST_ANAWARE] convergence of Newton fitter, and chi^2

From: Chris Crawford (chris2@lns.mit.edu)
Date: Tue Jun 03 2003 - 15:45:56 EDT


hi,
  there were some questions about how the newton fitter convergence
depended on the initial fast fit (also if it was possible to converge to
two different solutions), so i checked into the matter.
  first of all, i found a couple of bugs: the most important one was in
the determination of chi^2 = sum_18 (sim_i - data_i). the effect of the
bug was chi^2 = sum_18 ((sim_i-data_i)*2^(18-i)), so that the inner
hits were entirely discounted in the chi^2. also, we had previously
reported chi^2 ~ 1 (200micron resolution), but now, i am seeing between
30-50, which makes sense, seeing we need a better calibration of the
wire chambers.
  i am going to recrunch old data with the new fast fitter and bug
fixes, and see how this affects our resolution.
  there was also a bug in the magnetic field, allowing access to points
off the grid, causing segfaults, which has been fixed

  the result of my study was that the newton fitter will converge to the
same value starting from on the order of almost any valid track
parameter. the convergence can be fine-tuned with various parameters
labeled FitTrack.*, Newt.* and NewtDer.* in the blastrc file. in
particular, i think NewtDer.dZ0 was too small. that would be a good
project for someone to fine-tune all of these parameters.
  anyways, here are plots of convergence in the most dynamic variables,
(p,th) for an electron and proton, taken at random.
--chris

electron:
-----------
  // run 1070, event 8, nw 0
  float data[18] =
    { 89.3713, 90.2627, 91.1635, 97.8851, 98.8512, 99.7311,
      136.753, 138.067, 139.116, 147.394, 148.378, 149.558,
      193.022, 194.501, 196.027, 205.61, 207.085, 208.483 };
  float v[6] =
    { p=0.768798, theta=27.6792, phi=-169.675, x0=-59.1049, y0=-10.7683,
z0=110.499 };
  int pid=-1;

      0 theta 20 40 60 80 100
120 140
 p
+---------+---------+---------+---------+---------+---------+---------+-----
0.16:
......^.......^.....^^.^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^.^....^^^^^.^..^.:....
0.18:
.....^.^.........^^^...^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^......^^..^^^.^.......
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..........^...^^.^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^.^.........^...^.^^.^:....
0.22:
...^^^^.....^.^.^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^............^.......^.^..
0.24:
....^..^....^..^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^..........................:
0.26:
...^.^.^....^.^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^.^^................^...^....:^.
0.28:
...^......^^..^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^.......................^.....
0.30:
.^..^^.^.^^..^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^..............................
0.32:
.......^^^..^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^...............................
0.34:
.....^.^..^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^........................^.....:.
0.36:
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0.40:
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^^..^^^^^^^^^^^^^^^^^.......................................................

proton
---------
  run 3070, event 2, nw 1
  float data[18] =
    { 6.81864, 6.70208, 6.9777, 5.20358, 5.21103, 5.24986,
      7.26853, 7.25334, 7.18858, 4.13989, 3.92184, 4.33837,
      4.51546, 4.43925, 4.36508, 0.282379, 0.196165, 0.0577528 };
  float v[6] =
    {p= 0.34338, theta=71.1494, phi=172.919, x0=-82.72, y0=10.2755,
z0=30.5711 };
  int pid=1;

      0 theta 20 40 60 80 100
120 140
      
+---------+---------+---------+---------+---------+---------+---------+-----
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