Correction¶

Entry Points Correction¶

Module correction.correct¶

Created on ??

Single beam correction of phase, beta and horizontal dispersion. TODO: get better description (vimaier)

Usage example:

python correct_coupleDy.py  --accel=LHCB1
                            --Variables=Q
                            --ncorr=5
                            --rpath=C:\eclipse_4_2_2_python\workspace\Beta-Beat.src
                            --modelcut=0.3,0.3
                            --weight=1,1,0,0,0,10
                            --MinStr=0.00003
                            --path=C:\eclipse_4_2_2_python\workspace\Beta-Beat.src\Correction\test\correct\data\input\run1
                            --errorcut=0.5,0.5
                            --cut=0.01
                            --tech=SVD
                            --opt=C:\eclipse_4_2_2_python\workspace\Beta-Beat.src\Correction\test\correct\data\input

Hint: JustOneBeam is not used in the script except of a print. The reason is possibly the author wanted to have the same set of arguments for all correction scripts due to GUI compatibility(vimaier).

Options:

-h, --help            show this help message and exit
-a ACCEL, --accel=ACCEL
                      What accelerator: LHCB1 LHCB2 SPS RHIC
-t TECH, --tech=TECH  Which algorithm: SVD MICADO
-n NCORR, --ncorr=NCORR
                      Number of Correctors for MICADO
-p PATH, --path=PATH  Path to experimental files
-c CUT, --cut=CUT     Singular value cut for the generalized inverse
-e ERRORCUT, --errorcut=ERRORCUT
                      Maximum error allowed for the phase and dispersion
                      measurements, separated by commas; e.g. -e 0.013,0.2
-m MODELCUT, --modelcut=MODELCUT
                      Maximum difference allowed between model and measured
                      phase and dispersion, separated by commas; e.g. -e
                      0.02,0.2
-r RPATH, --rpath=RPATH
                      Path to BetaBeat repository (default is the afs
                      repository)
-o opt, --optics=opt  optics
-s MinStr, --MinStr=MinStr
                      Minimum strength of correctors in SVD correction
                      (default is 1e-6)
-v var, --Variables=var
                      variables split with ,
-j JUSTONEBEAM, --JustOneBeam=JUSTONEBEAM
                      0 Just quads from one beam are used, 1 all quads
                      (default is 0)
-w WGT, --weight=WGT  Weighting factor (phasex, phasey, betax, betay,
                      dispersion, tunes)

Module correction.correct_ChromCoup¶

Created on ??

Single beam correction of chromatic coupling using skew sextupoles at dispersive locations. TODO: get better description (vimaier)

Usage example:

python correct_ChromCoup.py --accel=LHCB1
                            --Variables=kss
                            --rpath=/afs/cern.ch/work/v/vimaier/public/Beta-Beat.src
                            --modelcut=100,100
                            --MinStr=0.000001
                            --path=/afs/cern.ch/work/v/vimaier/public/Beta-Beat.src/Correction/test/chrom_coup/data/input/run2
                            --errorcut=20,20
                            --Dy=1,1,0,0,0
                            --cut=0.01
                            --opt=/afs/cern.ch/work/v/vimaier/public/Beta-Beat.src/Correction/test/chrom_coup/data/input/run2

Hint: The latter parts of modelcut and errorcut and MinStr are not used in the script except of a print. The reason is possibly the author wanted to have the same set of arguments for all correction scripts due to GUI compatibility(vimaier).

Options:

-a ACCEL, --accelerator=ACCEL
                      What accelerator: LHCB1 LHCB2
-p PATH, --path=PATH  Path to experimental files
-c CUT, --cut=CUT     Singular value cut for the generalised inverse
-e ERRORCUT, --errorcut=ERRORCUT
                      Maximum error allowed for the coupling measurement and
                      Dy measurement
-m MODELCUT, --modelcut=MODELCUT
                      Maximum difference allowed between model and measured
                      phase
-r RPATH, --rpath=RPATH
                      Path to BetaBeat repository (default is the afs
                      repository)
-s MinStr, --MinStr=MinStr
                      Minimum strength of correctors in SVD correction
-d Dy, --Dy=Dy        weight on corrections (f1001.re, f1001.im, f1010.re,
                      f1010.im, Dy)
-o OPT, --opt=OPT     To specify the optics
-v var, --Variables=var
                      variables split with , - if coupling_knobs is given,
                      the modelcut will be calculated automatically

Module correction.correct_coupleDy¶

Created on ??

Single beam correction of coupling resonances and vertical dispersion. TODO: get better description (vimaier)

Usage example:

python correct_coupleDy.py --accel=LHCB1
                            --path=C:\MyTemp\correct_coupleDy_out\
                            --cut=0.01
                            --errorcut=0.02,0.02
                            --modelcut=0.0,0.01
                            --rpath=H:\work/v/vimaier/public/Beta-Beat.src/
                            --MinStr=0.000001
                            --Dy=1,1,0,0,1
                            --opt=C:\MyTemp\correct_coupleDy_out\
                            --Variables=coupling_knobs

Hint: MinStr is not used in the script except of a print. The reason is possibly the author wanted to have the same set of arguments for all correction scripts due to GUI compatibility(vimaier).

Options:

-a ACCEL, --accelerator=ACCEL
                      What accelerator: LHCB1 LHCB2 SPS RHIC
-p PATH, --path=PATH  Path to experimental files
-c CUT, --cut=CUT     Singular value cut for the generalised inverse
-e ERRORCUT, --errorcut=ERRORCUT
                      Maximum error allowed for the coupling measurement and
                      Dy measurement
-m MODELCUT, --modelcut=MODELCUT
                      Maximum difference allowed between model and measured
                      phase
-r RPATH, --rpath=RPATH
                      Path to BetaBeat repository (default is the afs
                      repository)
-s MinStr, --MinStr=MinStr
                      Minimum strength of correctors in SVD correction
-d Dy, --Dy=Dy        weight on corrections (f1001.re, f1001.im, f1010.re,
                      f1010.im, Dy)
-o OPT, --opt=OPT     To specify the optics
-v var, --Variables=var
                      variables split with , - if coupling_knobs is given,
                      the modelcut will be calculated automatically

Helpers Correction¶

Module correction.GenMatrix¶

Module correction.GenMatrix_chromcouple¶

Created on ??

TODO: description

correction.GenMatrix_chromcouple.make_list(x, m, modelcut, errorcut, CorD)[source]¶: Makes list in coupling correction

Module correction.GenMatrix_coupleDy¶

Created on ??

TODO: description

correction.GenMatrix_coupleDy.make_list(x, m, modelcut, errorcut, CorD)[source]¶: Makes list in coupling correction

Module correction.getdiff¶

module:	correction.getdiff

Created on 24/02/18

author:	Lukas Malina

Calculates the difference between GetLLM output and correction plugged in the model. Provide as first argument the path to the output files of GetLLM.

model inputs:

twiss_cor.dat and twiss_no.dat

outputs in measurement directory:

phasex.out and phasey.out bbx.out and bby.out dx.out, dy.out and ndx.out couple.out and chromatic_coupling.out

TODOs and Notes:

OpticsMeasurement: possibly extend and use with measurement filters from global correction: to be used in sbs, new corrections, getdiff, plot_export

Expected values after correction to be put in, little tricky with phase column names No coupling in twiss_no.dat? not used

Some hints:

MEA, MODEL, EXPECT are usually the names for the differences between the values and the model. Apart from phase, where these differences are called DIFF and DIFF_MDL (EXPECT is still the same) while MEA and MODEL are the actual measurement and model values respectively.

Don’t look into the coupling and chromatic coupling namings.

correction.getdiff.getdiff(meas_path=None, beta_file_name='getbeta')[source]¶

Calculates the differences between measurement, corrected and uncorrected model.

After running madx and creating the model with (twiss_cor) and without (twiss_no) corrections, run this functions to get tfs-files with the differences between measurements and models.

Parameters:	meas_path (str) -- Path to the measurement folder. to contain twiss_cor.dat and twiss_no.dat. (Needs) --

Helpers Response Creation¶

Module correction.fullresponse.response_madx¶

Provides a function to create the responses of beta, phase, dispersion, tune and coupling via iterative madx calls.

The variables under investigation need to be provided as a list (which can be gotten from accelerator class).

For now, the response matrix is stored in a ‘pickled’ file.

author:	Lukas Malina, Joschua Dilly, Jaime (…) Coello de Portugal

correction.fullresponse.response_madx.generate_fullresponse(accel_inst, variable_categories, delta_k=2e-05, num_proc=2, temp_dir=None)[source]¶

Generate a dictionary containing response matrices for beta, phase, dispersion, tune and coupling and saves it to a file.

Parameters:	accel_inst -- Accelerator Instance. variable_categories (list) -- Categories of the variables/knobs to use. (from .json) delta_k (float) -- delta K1L to be applied to quads for sensitivity matrix num_proc (int) -- Number of processes to use in parallel. temp_dir (str) -- temporary directory. If `None`, uses folder of original_jobfile.

Module correction.fullresponse.response_twiss¶

Provides Class to get response matrices from Twiss parameters.

The calculation is based on formulas in [1], [2].

Only works properly for on-orbit twiss files.

Beta Response: Eq. A35 inserted into Eq. B45 in [1]

\[\delta \beta_{z,j} = \mp \beta_{z,j} \sum_m \delta K_{1,m} \frac{\beta_{z,m}}{2} \frac{cos(2\tau_{z,mj})}{sin(2\pi Q_z)}\]

Dispersion Response: Eq. 25-27 in [1] + K1 (see Eq. B17)

\[\begin{split}\delta D_{x,j} =&+ \sqrt{\beta_{x,j}} \sum_m (\delta K_{0,m} + \delta K_{1S,m} D_{y,m} - \delta K_{1,m} D_{x,m}) \frac{\sqrt{\beta_{x,m}}}{2} \frac{cos(\tau_{x,mj})}{sin(\pi Q_x)} \\ \delta D_{y,j} =&- \sqrt{\beta_{y,j}} \sum_m (\delta K_{0S,m} - \delta K_{1S,m} D_{x,m} - \delta K_{1,m} D_{y,m}) \frac{\sqrt{\beta_{y,m}}}{2} \frac{cos(\tau_{y,mj})}{sin(\pi Q_y)}\end{split}\]

Norm. Dispersion Response: similar as above but with \(\frac{1}{\sqrt{\beta}}\) linearized

\[\begin{split}\delta \frac{D_{x,j}}{\sqrt{\beta_{x,j}}} =&+ \sum_m (\delta K_{0,m} + \delta K_{1S,m} D_{y,m} - \delta K_{1,m} D_{x,m} ) \frac{\sqrt{\beta_{x,m}}}{2} \frac{cos(\tau_{x,mj})}{sin(\pi Q_x)} &&+ \frac{D_{x,j}}{\sqrt{\beta_{x,j}}} \delta K_{1,m} \frac{\beta_{x,m}}{4}\frac{cos(2\tau_{x,mj})}{2sin(\pi Q_x)} \\ \delta \frac{D_{y,j}}{\sqrt{\beta_{y,j}}} =&- \sum_m (\delta K_{0S,m} - \delta K_{1S,m} D_{x,m} - \delta K_{1,m} D_{y,m}) \frac{\sqrt{\beta_{y,m}}}{2} \frac{cos(\tau_{y,mj})}{sin(\pi Q_y)} &&- \frac{D_{y,j}}{\sqrt{\beta_{y,j}}} \delta K_{1,m} \frac{\beta_{y,m}}{4}\frac{cos(2\tau_{y,mj})}{2sin(\pi Q_y)}\end{split}\]

Phase Advance Response: Eq. 28 in [1]

\[\delta \Phi_{z,wj} = \pm \sum_m \delta K_{1,m} \frac{\beta_{z,m}}{4} \left\{ 2\left[ \Pi_{mj} - \Pi_{mw} + \Pi_{jw} \right] + \frac{sin(2\tau_{z,mj}) - sin(2\tau_{z,mw})}{sin(2\pi Q_z)} \right\}\]

Tune Response: Eq. 7 in [2]

\[\delta Q_z = \pm \sum_m \delta K_{1,m} \frac{\beta_{z,m}}{4\pi}\]

Coupling Response: Eq. 10 in [1]

\[\begin{split}\delta f_{\substack{\scriptscriptstyle 1001 \\ \scriptscriptstyle 1010},j} = \sum_m \delta J_{1,m} \, \frac{\sqrt{\beta_{x,m}\beta_{y,m}}}{4} \, \frac{\exp{(i(\Delta\Phi_{x,mj} \mp \Delta\Phi_{y,mj}))}}{1-\exp({2\pi i (Q_x \mp Q_y}))}\end{split}\]

For people reading the code, the response matrices are first calculated like:

|  Elements of interest (j) --> ... |
|Magnets (m)                        |
|  |                                |
|  v                                |
|  .                                |
|  .                                |
|  .                                |
|                                   |

This avoids transposing all vectors individually in the beginning. At the end (of the calculation) the matrix is then transposed to fit the \(M \cdot \delta K\) orientation.

Also \(\Delta \Phi_{z,wj}\) needs to be multiplied by \(2\pi\) to be consistent.

References

[1]	(1, 2, 3, 4, 5) A. Franchi et al., Analytic formulas for the rapid evaluation of the orbit response matrix and chromatic functions from lattice parameters in circular accelerators https://arxiv.org/abs/1711.06589

[2]	(1, 2) R. Tomas, et al., ‘Review of linear optics measurement and correction for charged particle accelerators.’ Physical Review Accelerators and Beams, 20(5), 54801. (2017) https://doi.org/10.1103/PhysRevAccelBeams.20.054801

class correction.fullresponse.response_twiss.TwissResponse(accel_inst, variable_categories, varmap_or_path, at_elements='bpms')[source]¶

Provides Response Matrices calculated from sequence, model and given variables.

Parameters:

accel_inst (accelerator) -- Accelerator Instance (needs to contain elements model).
variable_categories (list) -- List of variable categories to get from the accelerator class.
varmap_or_path (dict, string) -- mapping of the variables, either as dict-structure of Series or path to a pickled-file.
at_elements (str) -- Get response matrix for these elements. Can be: ‘bpms’: All BPMS (Default) ‘bpms+’: BPMS+ used magnets (== magnets defined by variables in varfile) ‘all’: All BPMS and Magnets given in the model (Markers are removed)

get_beta(mapped=True)[source]¶: Returns Response Matrix for Beta

get_beta_beat(mapped=True)[source]¶: Returns Response Matrix for Beta Beating

get_coupling(mapped=True)[source]¶: Returns Response Matrix for the coupling

get_dispersion(mapped=True)[source]¶: Returns Response Matrix for Dispersion

get_norm_dispersion(mapped=True)[source]¶: Returns Response Matrix for Normalized Dispersion

get_phase(mapped=True)[source]¶: Returns Response Matrix for Total Phase

get_phase_adv(mapped=True)[source]¶: Returns Response Matrix for Phase Advance

get_response_for(obs=None)[source]¶: Calculates and returns only desired response matrices

get_tune(mapped=True)[source]¶: Returns Response Matrix for the Tunes

correction.fullresponse.response_twiss.create_response(accel_inst, vars_categories, optics_params)[source]¶: Wrapper to create response via TwissResponse

correction.fullresponse.response_twiss.dict_mul(number, dictionary)[source]¶: Multiply an int with a dict of dataframes (or anything multiplyable)

correction.fullresponse.response_twiss.get_delta(response, delta_k)[source]¶

Returns the deltas of \(response_matrix \cdot delta_k\).

Parameters:	response -- Response dictionary delta_k -- Pandas Series of variables and their delta-value
Returns:	TFS_DataFrame with elements as indices and the calculated deltas in the columns

correction.fullresponse.response_twiss.response_add(*args)[source]¶: Merges two or more Response Matrix DataFrames

Module correction.fullresponse.generateFullResponse_parallel¶

Created on ??

This Python script produces the responses of the beta, phase and horizontal dispersion on the quadrupole strengths or on other variables as horizontal orbit bumps at sextupoles. The fullresponse.couple does the corresponding calculation for the coupling and the vertical dispersion.

The response matrices are stored it in the following ‘pickled’ files:

FullResponse
FullResponse_couple
FullResponse_chromcouple

The files are saved in option -p(output_path).

These response matrices are used to calculate the corrections by the correction scripts.

Parallel execution: multiprocessing from Python stdlib is used to spwan subprocesses and run MADX in parallel. Further the loading of the MADX outputfiles will be executed in parallel.

Possible improvements:

The order of the three _gen*_for_*() functions are irrelevant and they do not depend on each other. Thus the execution could be parallelized. Therefore the created iter.madx and twiss files need an unique prefix. E.g.: ‘beta_iter.madx’. All three functions would need own process pools and the handling of the input data have to be considered. For test_fullresponse_parallel.py the comparing of *iter.madx should then be avoided since the ‘valid’ script does not produce them.
The three functions in the main function do basically the same. A good pattern to handle this is the template method: http://en.wikipedia.org/wiki/Template_method_pattern
Removing of the exec statements. This is very ugly and could be replaced with a function get_variables_for_accel_and_fullresponse_type(accel, type). The function could import the corresponding module by checking function parameters in if/else statements and deliver the appropriate list.

Usage example:

python generateFullResponse_parallel.py --accel=LHCB1 --path=/afs/cern.ch/work/v/vimaier/public/betabeatGui/temp/2013-10-22/models/LHCB1/a_mod --core=/afs/cern.ch/work/v/vimaier/public/Beta-Beat.src/MODEL/LHCB1/fullresponse --deltak=0.00002

Options:

-a ACCEL, --accel=ACCEL
                      Which accelerator: LHCB1 LHCB2 SPS RHIC SOLEIL
-p PATH, --path=PATH  path to save. Have to contain 'job.iterate.madx' and 'modifiers.madx'
-c CORE, --core=CORE  core files
-k K, --deltak=K      delta k to be applied to quads for sensitivity matrix