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Millepede-II V04-16-02
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Millepede-II V04-16-02
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Test case with a simple silicon strip tracker with ten equidistant, parallel planes in a beam telescope like configuration without magnetic field (implementation → More). The strip sensor have a size of 2 cm in X and 4 cm in Y and a thickness corresponding to 2% of a radiation length. The planes are 10 cm apart and oriented perpendicular to the Z-axis (as average beam direction). Each plane (1..10) has a layer of 50 sensors (0..49, 10 columns(X), 5 rows(Y)) measuring in the X-direction (with 20 µm resolution). Every third plane (1,4,7,10) has an additional ±5° stereo layer. Ten thousand tracks are simulated (with 
uniform in 10..100 GeV/c).
The broken lines track model is used to describe the multiple scattering in the silicon sensors [ref 4,6]. For the seed trajectory the true track parameters at the first layer (before any scattering) are used. Other models with different handling of multiple scattering are available too (see implementation → More).
As geometry reference the average corrections for some columns of modules in the first and last plane are forced to zero (using (four) linear equality constraints) to avoid correlations with the four degrees of freedom provided by the track model.
There are 700 alignment parameters in total:
50*#plane+#sensor)50*#plane+#sensor+1000)All modules (except those appearing in the constraints) are mislaligned with a RMS of 100 µm in X and Y.
The number of global parameters (here 700) and the number of constraints (NCGB, here 4) determine the (maximal) size of the global matrix. The actual (total) number of global parameters (identified by their global labels) appearing in the binary files (NTGB) may be smaller. In addition global parameters may have only few entries (number of appearances) producing possibly inaccurate results. An entries cut is available to fix parameters with too few entries. Only the (NVGB) variable global parameters are used by pede. The number of fit parameters (NFGB) is NVGB-NCGB for elimination of constraints or NVGB+NCGB for Lagrange multipliers.
gitlab server to target directory, e.g. (shallow clone): git clone --depth 1 --branch V04-12-01 \
https://gitlab.desy.de/claus.kleinwort/millepede-ii.git target
make pede
rm mp2???.???
./pede -t=BRLF > pede.dump
Creates the pede input binary (mp2tst.bin) and text files:
cksum mp2???.??? 2762434670 448 mp2con.txt 3457733667 1971 mp2str.txt 2736700272 14919648 mp2tst.bin
mp2con.txt
Constraint 0.0
54 1.00000
64 1.00000
74 1.00000
84 1.00000
94 1.00000
Constraint 0.0
1054 1.00000
1064 1.00000
1074 1.00000
1084 1.00000
1094 1.00000
Constraint 0.0
504 1.00000
514 1.00000
524 1.00000
534 1.00000
544 1.00000
Constraint 0.0
1504 1.00000
1514 1.00000
1524 1.00000
1534 1.00000
1544 1.00000
mp2str.txt
* *** Default test steering file ***
* Additinal files
fortranfiles ! following bin files are fortran
mp2con.txt ! constraints text file
mp2tst.bin ! binary data file
Cfiles ! following bin files are Cfiles
* Selection of variable global parameters
*entries 10 ! lower limit on number of entries/parameter
*entries 25 ! default limit on number of entries/parameter
*entries 50 ! higher limit on number of entries/parameter
* Initial parameter values, presigmas
*Parameter ! define parameter attributes (start of list)
*205 -0.01 0. ! start value
*206 0.01 0. ! start value
*215 0.01 -1. ! fix parameter at value
*216 0. -1. ! fix parameter at value
* Handling of outliers, tails etc
*hugecut 50.0 !cut factor in iteration 0
*chisqcut 30.0 6.0 ! cut factor in iterations 1 and 2
*outlierdownweighting 2 ! number of internal iterations (> 1)
*dwfractioncut 0.2 ! 0 < value < 0.5
*presigma 0.01 ! default value for presigma
*regularisation 1.0 ! regularisation factor
*regularisation 1.0 0.01 ! regularisation factor, pre-sigma
* Solution methods
method fullMINRES 3 0.01 ! (approximate) MINRES, full storage
method sparseMINRES 3 0.01 ! (approximate) MINRES, sparse storage
*mrestol 1.0D-8 ! epsilon for MINRES convergence
*bandwidth 0 ! width of MINRES precond. band matrix
method diagonalization 3 0.001 ! diagonalization (-> millepede.eve)
method decomposition 3 0.001 ! Cholesky decomposition
method inversion 3 0.001 ! Gauss matrix inversion
* last method is applied
* Additional output. monitoring
printcounts ! print number of entries
*monitorresiduals ! poor man's DMR (-> millepede.mon)
*printrecord 1 2 ! debug printout for records
*printrecord -1 -1 ! debug printout for bad data records
end ! optional for end-of-data
With the python2 script readMilleBinary.py binary files can be read and records printed in text form:
The broken lines track model defines at each (scattering) layer offsets in X (odd local labels) and Y-direction (even local labels) as fit parameeters. The measurement in each layer depends ("local derivatives") on a linear combination of the offsets in that layer depending on the orientation in the XY-plane (0.°, ±5°).
Detected Fortran binary file
=== NR 1 185
-g- meas. 1 73 1 1 -0.00794364139438 0.00200000009499
local [1]
local [1.0]
global [73]
global [1.0]
-g- meas. 2 73 2 2 -0.0057476432994 0.00200000009499
local [3, 4]
local [0.9961847066879272, 0.08726999908685684]
global [73, 1073]
global [0.9961847066879272, 0.08726999908685684]
...
-l- meas. 15 1 3 0 0.0 2.02223127417e-05
local [1, 3, 5]
local [2.0, -2.1052632331848145, 0.10526315867900848]
-l- meas. 16 2 3 0 0.0 2.02223127417e-05
local [2, 4, 6]
local [2.0, -2.1052632331848145, 0.10526315867900848]
...
Kinks constructed from three adjacent layers are describing the multiple scattering in the middle layer and are connecting the layers (in the XZ and YZ planes). The local derivatives depend on the distances between the layers.
python2 tools/readMilleBinary.py mp2tst.bin 3 > mp2binary.txt
The first three tracks are printed into mp2binary.txt.
Runs pede and creates output files (millepede.???):
pede.dump: Redirected standard output, large overlap with millepede.log. Information from the preparation and execution of the global fit. E.g.:
($Id: cc523e423547ec1e335b86a2ead55e4b2e6b3040 $)
using OpenMP (TM)
compiled with gcc 12.2.0
< Millepede II-P starting ... Tue Nov 22 10:20:58 2022
HOSTNAME
head -8 pede.dump
NTGB = 700 = total number of parameters
(all parameters, appearing in binary files)
NVGB = 683 = number of variable parameters
(appearing in fit matrix/vectors)
NAGB = 683 = number of all parameters
(including Lagrange multiplier or reduced)
NTPGRP = 700 = total number of parameter groups
NVPGRP = 683 = number of variable parameter groups
NFGB = 679 = number of fit parameters
NOFF = 232903 = max number of off-diagonal elements
NCGB = 4 = number of constraints
NAGBN = 18 = max number of global parameters in an event
NALCN = 28 = max number of local parameters in an event
NAEQN = 38 = max number of equations in an event
NCACHE = 25000000 = number of words for caching
cache splitting 56.7 % 3.0 % 40.2 %
Solution method and matrix-storage mode:
METSOL = 1: matrix inversion
with 3 iterations
MATSTO = 1: full symmetric matrix, (n*n+n)/2 elements
Convergence assumed, if expected dF < 0.1000E-02
Constraints handled by elimination
Rank of product matrix of constraints is 4 for 4 constraint equations
QL decomposition of constraints matrix
largest |eigenvalue| of L: -2.2360679774997898
smallest |eigenvalue| of L: -2.2360679774997898
Size of global matrix: 1 MB
_______________________________LOOP2-end__________________________________
grep -B33 "LOOP2-end" pede.dumpFor sparse storage information about the sparsity structure is added (use
-B48).
00000 S
2 3 0.10259E+06 0.28E-14 0 0 0.0 0 00000 F
Sum(Chi^2)/Sum(Ndf) = 102589.35168164221
/ ( 99992 - 679 )
= 1.0329901592101960
_____________________________Iteration-end________________________________
grep -A5 -B3 "/Sum(Ndf)" pede.dump
< Millepede II-P ending ... Tue Nov 22 10:20:58 2022
Peak dynamic memory allocation: 0.102192 GB
tail -5 pede.dump
grep -A708 "Misalignment test Si tracker" pede.dumpFrom this a steering file (fragment)
mp2param.txt defining the simulated values as start values ("starting from truth") can be created, e.g.: grep -A708 ... | awk 'BEGIN {print "Parameter"} NR>9 {print $2,$3,0.}' > mp2param.txt
millepede.end: Single line text file with exit code and message. Be careful with results for exit code > 1.millepede.log: Log file, large overlap with pede.dump.millepede.his: Internal histogram file. Script for viewing with ROOT available.millepede.res: Result file with alignment corrections from global fit.
Parameter ! first 3 elements per line are significant (if used as input)
50 0.12387E-01 0.0000 0.12387E-01 0.38268E-03 185
51 -0.10100E-02 0.0000 -0.10100E-02 0.31170E-03 350
52 0.35959E-02 0.0000 0.35959E-02 0.28972E-03 366
53 0.10121E-01 0.0000 0.10121E-01 0.28810E-03 331
...
150 0.0000 0.0000
...
(Output text files in draft manual.)
Save steering and output files:
mkdir run0; cp mp2???.txt run0; cp pede.dump run0; cp millepede.??? run0
Run pede in special mode to check input only (no solution calculated):
./pede -C mp2str.txt > pede.dump
The standard output in pede.dump contains now a lot of information about the (linear equality) constraints:
LOOP2" start: For each constraint (in order of appearance in steering files) the number of all and of variable global parameters involved. _________________________________LOOP2____________________________________ constraint 1 : 5 parameters, 5 variable constraint 2 : 5 parameters, 5 variable constraint 3 : 5 parameters, 5 variable constraint 4 : 5 parameters, 5 variable PRPCON: 4 constraints acceptedEmpty constraints (without variable global parameters) will cause singularities.
grep -A6 '_LOOP2_' pede.dump
PRPCON: constraints split": The constraints are sorted by (global) label range, split into disjoint groups and combined into non overlapping blocks.
Cons. sorted index file: index, first line first label last label
Cons. group index first cons. last cons. first label last label
Cons. block index first group last group first label last label
Cons. sorted 1 1 1 54 94
Cons. group 1 1 1 54 94
Cons. block 1 1 1 54 94
Cons. sorted 2 3 13 504 544
Cons. group 2 2 2 504 544
Cons. block 2 2 2 504 544
Cons. sorted 3 2 7 1054 1094
Cons. group 3 3 3 1054 1094
Cons. block 3 3 3 1054 1094
Cons. sorted 4 4 19 1504 1544
Cons. group 4 4 4 1504 1544
Cons. block 4 4 4 1504 1544
PRPCON: constraints split into 4 (disjoint) groups,
groups combined into 4 (non overlapping) blocks
max group size (cons., par.) 1 41
max block size (cons., par.) 1 41
total block matrix sizes 164 4
grep -A4 -B16 'PRPCON: constraints' pede.dump
Rank of product": For each constraint group the size and the rank of the product matrix ( 
in equation (11)) to verify linear independence. Constraint group, #con, rank 1 1 1 Constraint group, #con, rank 2 1 1 Constraint group, #con, rank 3 1 1 Constraint group, #con, rank 4 1 1 Rank of product matrix of constraints is 4 for 4 constraint equations
grep -B6 'Rank of product' pede.dumpThe results file
millepede.res contains now several different sections:! === global parameters === ! fixed-1: by pre-sigma, -2: by entries cut, -3: by iterated entries cut ! Label Value Pre-sigma Entries Cons. group Status !> 50 0.0000 0.0000 185 0 variable !> 51 0.0000 0.0000 350 0 variable !> 52 0.0000 0.0000 366 0 variable !> 53 0.0000 0.0000 331 0 variable !> 54 0.0000 0.0000 357 1 variable !> 55 0.0000 0.0000 373 0 variable !> 56 0.0000 0.0000 376 0 variable ... !> 150 0.0000 0.0000 18 0 fixed-2 ...
grep -e"\! " -e "\!>" millepede.res
!. !.Appearance statistics !. Label First file and record Last file and record #files #paired-par !. 50 1 169 1 9931 1 1 !. 51 1 63 1 9976 1 1 !. 52 1 15 1 9914 1 1 !. 53 1 64 1 9992 1 1 !. 54 1 132 1 9968 1 1 !. 55 1 22 1 9984 1 1 !. 56 1 2 1 9984 1 1 ... !. 100 1 550 1 9931 1 0 !. 101 1 63 1 9925 1 0 !. 102 1 58 1 9976 1 0 ...The first plane (labels 50..99) contains a stereo layer. There each alignment offset in X or Y is paired with one in the other (Y or X) direction.
grep -e"\!\." millepede.res
* === constraint groups === * Group #Cons. Entries First label Last label Paired label range * 1 1 2231 54 94 *: 1054 .. 1054 *: 1064 .. 1064 *: 1074 .. 1074 *: 1084 .. 1084 *: 1094 .. 1094 * 2 1 2049 504 544 *: 1504 .. 1504 *: 1514 .. 1514 *: 1524 .. 1524 *: 1534 .. 1534 *: 1544 .. 1544 ...
grep -e"* " -e"*:" millepede.res
*. *.Appearance statistics *. Group First file and record Last file and record files *. 1 1 13 1 9998 1 *. 2 1 5 1 9963 1 *. 3 1 13 1 9998 1 *. 4 1 5 1 9963 1
grep -e"*\." millepede.res
Save steering and output files:
mkdir run1; cp mp2???.txt run1; cp pede.dump run1; cp millepede.??? run1
Depending on the quality of the local (track) fit very bad tracks are rejected ( 
) automatically and bad tracks can be removed by the user with the "chisqcut f1 f2" option. The scaling factor 
should start with a large value 
to allow for initial misalignment and be further reduced (to 1.) in the internal iterations of the global fit.
Uncomment "
chisqcut" option in the steering file.
chisqcut 30.0 6.0 ! cut factor in iterations 1 and 2
./pede mp2str.txt > pede.dump
Watch the pede exit code in
millepede.end.
2 Ended with severe warnings (insufficient measurements)
The severe warnings indicate a major problem. More details are in pede.dump.
3 4 0.10086E+06 0.17E+02 0 0 1.6 33 00000 F
00000 S
... warning ...
global parameters with too few (< MREQENA) accepted entries: 2
minimum entries: 7 for label 209
4 5 0.10013E+06 0.53E+01 0.781 0.062 0 0 -1 1.000 1.0 79 00000 F
...
After rejection of bad tracks there are only 7 entries left for the global parameter with the label "209". This is less than the minumum required by MREQENA (default 10, second parameter of entries cut). grep -C3 '... warning ...' pede.dump
ngWarningWarningWarningWarningWarningWarningWarningWarningW
gWarningWarningWarningWarningWarningWarningWarningWarningWa
Possible bad elements = 6 in global vector
(too few accepted entries)
(indicated in millepede.res by counts<0)
=> please check mille data and ENTRIES cut
WarningWarningWarningWarningWarningWarningWarningWarningWar
During the iterations six times a global parameter had too few accepted entries. All those parameters are flagged in millepede.res by an negative count value (-(#entries+1)). grep -C4 'too few accepted' pede.dump
Get affected global parameter from result file millepede.res.
Select lines with negative count value, e.g.:
209 0.76209E-02 0.0000 0.76209E-02 0.54649E-03 -8
249 -0.11705E-01 0.0000 -0.11705E-01 0.51044E-03 -9
The global parameters with labels 209/249 have finally less than 10 entries.
awk 'NF==6 && $6<0' millepede.res
!> 209 0.0000 0.0000 35 0 variable !> 249 0.0000 0.0000 40 0 variableThe global parameters with labels 209/249 have initialy more than 25 entries.
awk '($1=="!>" || $1=="! ") && ($2==209 || $2==249)' run1/millepede.res
!. 209 1 39 1 9867 1 1 !. 249 1 637 1 9547 1 1The global parameters with labels 209/249 describe offsets in a stereo layer. Therefore the X and Y offsets for each sensor are paired (appearing together for each measurement). The number of paired parameters (last column) is 1.
awk '$1=="!." && ($2==209 || $2==249)' run1/millepede.res
Options to resolve the severe warnings for problematic labels 209/249:
Parameter
209 0. -1.
249 0. -1.
Save steering and output files:
mkdir run2; cp mp2???.txt run2; cp pede.dump run2; cp millepede.??? run2
Uncomment "
entries 25" option in the steering file and add mreqena with value 5.
entries 25 5 ! default limit on number of entries/parameter, reduced accepted entries
./pede mp2str.txt > pede.dump
Watch the pede exit code in
millepede.end.
0 Ended normally
No warnings are reported. More details are in pede.dump.
Quality of global fit.
Data rejected in last loop:
0 (rank deficit/NaN) 0 (Ndf=0) 0 (huge) 79 (large)
Sum(Chi^2)/Sum(Ndf) = 100125.94658222546
/ ( 99992 - 679 )
= 1.0081857015921929
_____________________________Iteration-end________________________________
The final Sum(Chi^2)/Sum(Ndf) is very close to 1, the rejection rate less than 1% (79/10000) and 679 (of maximal 696) parameters have been fitted.
grep -A5 -B3 "/Sum(Ndf)" pede.dump
The quality is fine.
Save steering and output files:
mkdir run3; cp mp2???.txt run3; cp pede.dump run3; cp millepede.??? run3
Comment "
entries 25" again and uncomment "entries 50" option in the steering file.
*entries 25 5 ! default limit on number of entries/parameter, reduced accepted entries entries 50 ! higher limit on number of entries/parameter
./pede mp2str.txt > pede.dump
Watch the pede exit code in
millepede.end.
1 Ended with warnings (bad measurements)
The warnings indicate some problem. More details are in pede.dump.
Data rejected in last loop:
0 (rank deficit/NaN) 0 (Ndf=0) 0 (huge) 276 (large)
Sum(Chi^2)/Sum(Ndf) = 104495.47920560479
/ ( 99992 - 645 )
= 1.0518231975359578
The final Sum(Chi^2)/Sum(Ndf) is close to 1, but the rejection rate is allmost 3% (276/10000) and only 645 (of maximal 696) parameters have been fitted. grep -A5 -B3 "/Sum(Ndf)" pede.dump
ngWarningWarningWarningWarningWarningWarningWarningWarningW
gWarningWarningWarningWarningWarningWarningWarningWarningWa
Fraction of rejects = 2.76 % (should be far below 1 %)
=> please provide correct mille data
WarningWarningWarningWarningWarningWarningWarningWarningWar
grep -C3 'Fraction of rejects' pede.dump
The result is not optimal. Too many globals parameters have been fixed at the misaligned values spoiling the local/track fit.
Save steering and output files:
mkdir run4; cp mp2???.txt run4; cp pede.dump run4; cp millepede.??? run4
Add text file "
mp2param.txt" with start values to the steering file (e.g. after constraints file).
mp2con.txt ! constraints text file mp2param.txt ! start values (from truth) mp2tst.bin ! binary data file
This defines a different starting geometry (in this case the "truth").
./pede mp2str.txt > pede.dump
Watch the pede exit code in
millepede.end.
0 Ended normally
No warnings are reported. More details are in pede.dump.
Quality of global fit.
Data rejected in last loop:
0 (rank deficit/NaN) 0 (Ndf=0) 0 (huge) 24 (large)
Sum(Chi^2)/Sum(Ndf) = 99050.817948768963
/ ( 99992 - 645 )
= 0.99701871167492695
_____________________________Iteration-end________________________________
The final Sum(Chi^2)/Sum(Ndf) is very close to 1 and the rejection rate less than 1% (24/10000) despite only 645 (of maximal 696) parameters have been fitted.
grep -A5 -B3 "/Sum(Ndf)" pede.dump
The quality is fine. Starting values matter for fixed parameters.
Save steering and output files:
mkdir run5; cp mp2???.txt run5; cp pede.dump run5; cp millepede.??? run5
With the python2 script compareResults.py two millepede result text files (millepede.res) can be compared. As only the first three columns are evaluated a steering file (fragment) defining start values can be used too, e.g:
python2 compareResults.py mp2param.txt run4/millepede.res
This compares the results from example 4 with the "truth".
output file mp2compare.txt total parameters 700 matched parameters 700 mean1, mean2 -0.000189471428571 -0.000542676439286 rms1, rms2 0.00994723953843 0.00994581992618 correlation 0.945525591556
For both sets of parameters the mean and RMS and the correlation of the sets is calculated.
A text file (default mp2compare.txt) is created.
It contains the parameter labels and values and can be directly used as ROOT input (with "
tree->ReadFile()"):
label/I:value_1/F:value_2/F
50 0.01339 0.012557
51 -0.00037 -0.00082443
52 0.00403 0.0037749
53 0.01061 0.010278
54 -0 0.00020854
55 -0.00712 -0.0075308
...
1545 -0.01218 -0.010553
1546 -0.0029 0.0032485
1547 -0.01605 -0.0082543
1548 -0.01081 -0.0027929
1549 0.00236 0.008585
For all labels appearing in boths files ("matched"): label value1 value2. For all labels appearing only in one file: -label, value, value
Other examples (C++, Python2 or Python3) are included in the GeneralBrokenLines package to explore track fitting and track based alignment with MP2. Those will produce binary files of type Cfiles.
1.9.3