# MUSR :: MusrFit

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# `musrfit` User Manual

# 1 Introduction

`musrfit` is a software tool for analyzing time-differential μSR data. The program suite is free software and licensed under the GNU GPL version 2 or any later version (at your option). It is implemented in `C++/ROOT` and uses the MINUIT2 libraries developed at CERN for fitting data. Installation instructions for GNU/Linux, MS Windows, and Mac OS X can be found here. For people familiar with the μSR data analysis program `WKM` there is a short quick start page explaining the major differences between `WKM` and `musrfit`. Recent changes of the program are listed in the ChangeLog.

# 2 Available Executables, Configuration Files and their Basic Usage

## 2.1 musrfit

`musrfit` is the actual fitting program. It defines the FCN routine passed to `MINUIT2` and performs χ2 or log-likelihood fitting. If called from within a shell it accepts several parameters:

<msr_file>
  filename of the msr input file defining all the details needed for performing a fit to a specified set of data—the only mandatory parameter
-k, --keep-mn2-output
  selects the option for keeping the output of `MINUIT2` including the correlation coefficients between different parameters and renaming the files `MINUIT2.OUTPUT` and `MINUIT2.root` to `<msr_file_without_extension>-mn2.output` and `<msr_file_without_extension>-mn2.root`, repectively, e.g. <msr_file> = `8472.msr` → `8472-mn2.output` , `8472-mn2.root`
-c, --chisq-only
  Instead of fitting the model, `musrfit` calculates χ2 only once and sends the result to the standard output if called with this option. This might be useful for the adjustment of the initial values of the fit parameters.
-t, --title-from-data-file
  If this option is given `musrfit` will replace the title in the <msr_file> by the run title in the data file of the first run appearing in a RUN block. In case there is no run title in the data file no substitution is done.
--dump <type>
  is writing a data file with the fit data and the theory; <type> can be ascii (data in columns) or root (data in `ROOT` histograms)
--timeout <timeout_tag>
  overwrites the predefined timeout of 3600 sec. <timeout_tag><=0 means the timeout facility is not enabled. <timeout_tag> > 0, e.g. `nn` will set the timeout to `nn` (sec). If during a fit this timeout is reached, `musrfit` will terminate. This is used to prevent orphan musrfit process to jam the system.
--help
  displays a small help notice in the shell explaining the basic usage of the program
--version
  prints the version number of `musrfit`

If called with a msr input file, e.g.

    musrfit 8472.msr

the fit described in the input file will be executed and the results will be written to a mlog output file—in the example `8472.mlog`. When the fitting has terminated the msr file and the mlog file are swapped, so that the resultant parameter values can be found in the msr file and the mlog file contains a copy of the input file. The format of the mlog file is the same as that of the msr file. For a detailed description of the msr file format refer to the corresponding section.

## 2.2 musrview

`musrview` is an interactive graphical user interface for the presentation of the analyzed data and the corresponding fits. If called from within a shell it accepts the following parameters:

<msr_file>
  name of the msr input or output file to be displayed—this parameter is mandatory
--<graphic_format_extension>
  will produce a graphics output file without starting a `ROOT` session. The filename is based on the name of the <msr_file>, e.g. `8472.msr` → `8472_0.png`
  Supported values for <graphic_format_extension> are eps, pdf, gif, jpg, png, svg, xpm, root
--timeout <timeout>
  <timeout> given in seconds after which `musrview` terminates. If <timeout> <= 0, no timeout will take place. Default for <timeout> is 0.
--help
  displays a small help notice in the shell explaining the basic usage of the program
--version
  prints the version number of `musrview`

If called with a msr file and the --<graphic_format_extension> option, e.g.

    musrview 8472.msr --jpg

for each PLOT block in the the msr file a file 8472_X.jpg is produced where X counts the PLOT blocks starting from zero.

If called only with a msr file, e.g.

    musrview 8472.msr

a `ROOT` canvas is drawn; it contains all experimental data and fits specified in the PLOT block of the msr file. For a description of the various plotting types refer to the corresponding section.

Within the drawn canvas all standard actions applicable to `ROOT` canvases might be performed. In the menu bar the Musrfit menu can be found. From there some `musrfit`-specific actions might be taken:

Fourier
  performs the Fourier transformation of the selected data and shows the result
Difference
  shows the difference between the selected data and the fit
Save Data
  saves the selected data in a simple multi-column ASCII file

Additionally, some functions can be accessed using key-shortcuts:

q
  quits `musrview`
d
  shows the difference between the selected data and the fit
f
  performs the Fourier transformation of the selected data and shows the result
u
  reset the plotting range to the area given in the msr file ("unzoom")

## 2.3 musrt0

`musrt0` is a user interface for the determination of t0 and the time windows of data and background needed to be specified in the RUN blocks of the msr file. It can be operated either as an interactive program or in a non-interactive mode. In the non-interactive mode it accepts the following parameters:

<msr_file>
  name of an msr file
-g, --getT0FromPromptPeak [<firstGoodBinOffset>]
  tries to estimate t0 from the prompt peak (maximum entry) in each histogram and writes the corresponding values to the t0 lines in the RUN blocks of the msr file. If an optional number <firstGoodBinOffset> is given, the lower limit of the data range will be set to t0 + <firstGoodBinOffset>.
--timeout <timeout>
  <timeout> given in seconds after which `musrview` terminates. If <timeout> <= 0, no timeout will take place. Default for <timeout> is 0.
--help
  displays a small help notice in the shell explaining the basic usage of the program
--version
  prints the version number of `musrt0`

The interactive mode of `musrt0` is started if the program is called with a sole msr-file argument, e.g.

    musrt0 8472.msr

Then a `ROOT` canvas depicting the histogram of the data set mentioned first in the RUN block is drawn in different colors:
The colors of the data points represent the choice of the time windows of data (blue) and background (red), as well as t0 (green line). In order to change these ranges the mouse cross-hair is moved to a channel of choice and one of the following keys is pressed:

q
  close the currently open histogram and opens the next (see also below)
Q
  quit `musrt0` without writing into the msr file
z
  zoom into the region about the t0
u
  unzoom to the full range
t
  set t0
T
  automatically set t0, i.e. jump to the maximum of the histogram
b
  set the lower limit of the background range
B
  set the upper limit of the background range
d
  set the lower limit of the data range
D
  set the upper limit of the data range

When all channels have been set correctly for the first histogram, pressing of the key q opens the subsequent histogram listed in a RUN block and the respective channels can be updated there. This procedure is repeated until all histograms given in the RUN blocks are processed.

Using the key Q, `musrt0` can be interrupted. No changes to the msr file are applied in this case.
Closing a window by clicking the X button is equivalent to pressing Q, i.e. `musrt0` is simply terminated.

## 2.4 musrfit_startup.xml

`musrfit_startup.xml` is a configuration file located at the `musrfit` binary path. In this file the following XML tags are allowed to define settings:

<data_path>PATH_TO_DATA</data_path>
  add the new path PATH_TO_DATA where `musrfit` and `musrview` will search for data files
<write_per_run_block_chisq>y/n</write_per_run_block_chisq>
  if enabled χ2 for each RUN block will be written to the STATISTIC block of the resulting `msr` file. Additionally, in case a χ2 single-histogram fit is done, also Pearson's χ2 will be added.
<fourier_settings></fourier_settings>
  set the default parameters for the Fourier transform in `musrview`. For further details refer to the description of the msr file.
  <units>UNITS</units>
    specify the units of the frequency or field-domain. Valid units are Gauss, MHz and Mc/s (inside a <fourier_settings> environment)
  <fourier_power>n</fourier_power>
    specify the number of points 2n (n < 21) to be used for the Fourier transform (inside a <fourier_settings> environment)
  <apodization>APOD</apodization>
    set the default apodization method. Valid apodizations are none, weak, medium and strong (inside a <fourier_settings> environment)
  <plot>PLOT</plot>
    specify which part of the Fourier transform is plotted by default. You can choose between real, imag, real_and_imag, power and phase (inside a <fourier_settings> environment)
  <phase>PH</phase>
    set the initial phase shift PH (in degrees) of the data to be Fourier transformed (inside a <fourier_settings> environment)
  <phase_increment>PHINCR</phase_increment>
    change the default value of the phase increment (in degrees) used for the phase optimization to PHINCR (inside a <fourier_settings> environment)
<root_settings></root_settings>
  change the default `ROOT` settings
  <marker_list></marker_list>
    specify the order in which `musrview` should use markers when plotting data (inside a <root_settings> environment)
    <marker>X</marker>
      use the `ROOT` marker number X (inside a <marker_list> environment)
  <color_list></color_list>
    specify the order in which `musrview` should use colors when plotting data (inside a <root_settings> environment)
    <color>R,G,B</color>
      use the RGB coded color (inside a <color_list> environment)

An example would look like:

       <?xml version="1.0" encoding="UTF-8"?>
       <musrfit xmlns="https://intranet.psi.ch/MUSR/MusrFit">
           <data_path>/mnt/data/nemu/his</data_path>
           <write_per_run_block_chisq>y</write_per_run_block_chisq>
           <fourier_settings>
               <units>Gauss</units>
               <fourier_power>0</fourier_power>
               <apodization>none</apodization>
               <plot>real_and_imag</plot>
               <phase>0.0</phase>
               <phase_increment>1.0</phase_increment>
           </fourier_settings>
           <root_settings>
               <marker_list>
                   <!-- Root marker numbers -->
                   <marker>24</marker>
                   <marker>25</marker>
                   <marker>26</marker>
                   <marker>27</marker>
               </marker_list>
               <color_list>
                   <!-- Color as RGB coded string -->
                   <color>0,0,0</color>
                   <color>255,0,0</color>
                   <color>0,255,0</color>
                   <color>0,0,255</color>
               </color_list>
           </root_settings>
       </musrfit>

## 2.5 msr2msr

`msr2msr` is a small utility for converting existing `WKM` msr files into `musrfit` msr files. It accepts the following parameters:

<msr_file_in>
  input `WKM` msr file (mandatory first parameter)
<msr_file_out>
  converted output `musrfit` msr file (mandatory second parameter)
--help
  displays a small help notice in the shell explaining the basic usage of the program

A typical example then looks like:

    msr2msr 8472-WKM.msr 8472-musrfit.msr

If the input file has already the `musrfit` msr file structure, the output file will be just a copy of the input file.

## 2.6 any2many

`any2many` is a muSR data file converter. Currently different facilities (PSI, TRIUMF, ISIS, J-PARC) are saving their muSR data files in different formats, or even worse some instruments are using other muSR data formats than others. The aim of `any2many` is that these files can be converted into each other. Of course only a subset of header information can be converted.

Currently `any2many` can convert the following muSR data file formats:

- input formats: `MusrRoot`, `PSI-BIN` (PSI bulk), `ROOT` (PSI LEM), `MUD` (TRIUMF), `NeXus IDF1` and `NeXus IDF2` (ISIS), PSI-MDU (PSI bulk internal only), `WKM` (outdated ascii file format).
- output formats: `MusrRoot`, `PSI-BIN`, `ROOT`, `MUD`, `NeXus1-HDF4`, `NeXus1-HDF5`, `NeXus1-XML`, `NeXus2-HDF4`, `NeXus2-HDF5`, `NeXus2-XML`, `WKM`, `ASCII`

Since the goal was to create a very flexible converter tool, it has ample of options which will listed below, followed by many examples showing how to use it. The options:

-f <filenameList-input>
  where `<filenameList-input>` is a space separated list of file names (not starting with a '-'), e.g. `2010/lem10_his_0111.root 2010/lem10_his_0113.root`.
-o <outputFileName>
  this option allows to given an output-file-name for the converted file. This option only makes sense if `<filenameList-input>` is a single input-file-name!
-r <runList-input>
  where `<runList-input>` is a list of run numbers separated by spaces of the form: `<run1> <run2> <run3>` etc., or a sequence of runs `<runStart>-<runEnd>`, e.g. `111-123`. This option cannot be combined with `-f` and vice versa.
-t <in-template> <out-template>
  where `<in-/out-template>` are templates to generate real file names from run numbers. The following template tags can be used: `[yy]` for year, and `[rrrr]` for the run number. If the run number tag is used, the number of `'r'` will give the number of digits used with leading zeros, e.g. `[rrrrrr]` and run `123` will result in `000123`. Similarly `[yyyy]` will result in something like `1999`, whereas `[yy]` into something like `99`. For more details best check the examples below.
-c <in-Format> <out-Format>
  this is used to tell `any2many` what is the input-file-format and into which output-file-format the data shall be converted. The possible input-/output-file-formats are listed above.
-p <output-path>
  where `<output-path>` is the output path for the converted files. If no `<output-path>` is given, the current directory will be used, unless the option `-s` is used.
-y <year>
  here a `<year>` in the form `yy` or `yyyy` can be given. If this is the case, any automatic file name generation which needs a year will use this given one.
-s
  with this option the output data file will be sent to the stdout. It is intended to be used together with web applications.
-rebin <n>
  where `<n>` is the number of bins to be packed/rebinned.
-z [g|b] <compressed>
  where `<compressed>` is the output file name (without extension) of the compressed data collection, and `'g'` will result in `.tar.gz`, and `'b'` in `.tar.bz2` files.
--help
  displays a help notice in the shell explaining the basic usage of the program.
--version
  shows the current `SVN` version of `any2many`.

If the template option `'-t'` is absent, the output file name will be generated according to the input data file name (not possible with `<runList-input>`), and the output data format.

Here now a couple of examples which should help to understand the switches.

    any2many -f 2010/lem10_his_0123.root -c ROOT ASCII -rebin 25

Will take the LEM ROOT file `'2010/lem10_his_0123.root'` rebin it by 25 and convert it to ASCII. The output file name will be `lem10_his_0123.ascii`, and the file will be saved in the current directory. The data in `lem10_his_0123.ascii` are written in columns.

    any2many -f 2010/lem10_his_0123.root -c ROOT NEXUS2-HDF5 -o 2010/lem10_his_0123_v2.nxs

Will take the LEM ROOT file `'2010/lem10_his_0123.root'` and convert it to NeXus IDF V2. The output file name will be `lem10_his_0123_v2.nxs`, and will be saved in the current directory.

    any2many -r 123 137 -c PSI-BIN MUD -t d[yyyy]/deltat_tdc_gps_[rrrr].bin [rrrrrr].msr -y 2001

Will take the run 123 and 137, will generate the input file names: `d2001/deltat_tdc_gps_0123.bin` and `d2001/deltat_tdc_gps_0137.bin`, read these files, and convert them to the output files with names `000123.msr` and `000137.msr`, respectively.

    any2many -r 100-117 -c PSI-MDU ASCII -t d[yyyy]/deltat_tdc_alc_[rrrr].mdu [rrr].ascii -y 2011 -s

Will take the runs 100 through 117 and convert the `PSI-MDU` input files to `ASCII` output and instead of saving them into a file, they will be spit to the standard output.

    any2many -r 100-117 -c NEXUS ROOT -t d[yyyy]/psi_gps_[rrrr].NXS psi_[yyyy]_gps_[rrrr].root -z b psi_gps_run_100to117

Will take the runs 100 through 117 and convert the `NeXus` input files to `ROOT` output. Afterwards these new files will be collected in a compressed archive `psi_gps_run_100to117.tar.bz2`.

    any2many -f 2010/lem10_his_0123.root 2010/lem10_his_0012.root -c ROOT ROOT -rebin 25

Will read the two files `'2010/lem10_his_0123.root'` and `'2010/lem10_his_0012.root'`, rebin them with 25 and export them as `LEM ROOT` files with adding `rebin25` to the name, e.g. `2010/lem10_his_0123_rebin25.root`.

## 2.7 dump_header

`dump_header` is a little program which tries to read a μSR data file and sends the relevant information (required header info, start of the histos, etc.) to the standard output. Currently the following μSR data file formats are supported: `MusrROOT`, `ROOT` (old LEM format), `PSI-BIN`, `PSI-MDU`, `NeXus` (IDF1 and IDF2), `MUD`, and `WKM`.

# 3 Auxiliary Programs

Additionally to the programs mentioned above editor front ends called `musrgui/musredit` and another tool named `msr2data` are available. The purpose of `msr2data` is to process multiple msr files with the same parameters and to summarize the fitting results either in a DB or a column ASCII file. Also, new msr files can be generated from a template. For details refer to its manual.

Before going to use `musrgui` / `musredit` it is strongly recommended to read this manual first!

# 4 Description of the msr File Format

The programs are using an input file to control their action. This input file has the extension .msr (msr file). The msr file is built up from different blocks. Each block starts with a keyword and is—with the exception of the title—terminated by an empty line. Comments start with the character #. The various input blocks are described below.

## 4.1 The Title

The first line of the msr file is the title line. Unlike all the other input blocks, it does not start with a block keyword. It is just a simple text line, in which any information can be placed. The title text will be used in the graphical representation of the data as a headline.

## 4.2 The FITPARAMETER Block

The FITPARAMETER block is used to define the fit parameters in a `MINUIT` typical style. There are various possible parameter definitions which are listed here:

       1. <no> <name> <value> <step>
       2. <no> <name> <value> <step> <lower_boundary> <upper_boundary>
       3. <no> <name> <value> <step> <pos_error> <lower_boundary> <upper_boundary>

where <no> is the parameter number, <name> is the parameter name (1), <value> is the initial guess of the parameter, <step> the inital step width, <lower/upper_boundary> is the lower/upper boundary for the parameter (2).

In the output file, <value> will be the `MINUIT` fit value, <step> will contain the error estimate (or the negative error estimate if `MINOS` was successfully used), <pos_error> will have the value none if `MINOS` has not been used, otherwise it will show the positive error estimate.

A typical example looks like this:

       FITPARAMETER
       #       No   Name      Value     Step        Pos_Error    Boundaries
               1   alpha     1          0.02       none         0       1.8
               2   asy       0.1042     0.004713   none         0       0.33
               3   phase     15         1.0        none
               4   freq      0.9        0.0379     none
               5   rate      0.03       0.00579    none

There is also the possibility to constrain the parameters to semi-defined intervals (like par > a or par < b). The syntax is as follows:

       FITPARAMETER
       #       No   Name      Value     Step        Pos_Error    Boundaries
       # Specify only a lower boundary for the parameter
               1   Asy1      0.04501   -0.00208    0.00211      0       none

       # Specify only an upper boundary for the parameter
               2   Rate1     0.14245   -0.02501    0.02279      none    10

       # Specify lower and upper boundaries for the parameter
               3   Asy2      0.14501   -0.00208    0.00211      0       0.33

       # Do not specify boundaries at all
               4   Field2    343.212   -2.27960    2.27885
               5   Rate2     0.42045   -0.02501    0.02279      none    none

Notes

1 : a standard string without whitespace

2 : According to the `MINUIT` manual this should be avoided whenever possible!

## 4.3 The THEORY Block

The THEORY block is used to define the fit function. There is a set of predefined functions available. It is also possible to use externally defined functions. How to use them will be explained afterwards, here only the predefined functions are described.

name | abbreviation | parameters | mathematical expression | reference
--- | --- | --- | --- | ---
const | c |  |
asymmetry | a |  |
simplExpo | se |  |
generExpo | ge | , |
simpleGss | sg |  |
statGssKT | stg |  |  |
statGssKTLF | sgktlf | , |  | (4)
dynGssKTLF | dgktlf | , , |  | (5)
statExpKT | sekt |  |  | (6)
statExpKTLF | sektlf | , |  | (7)
dynExpKTLF | dektlf | , , |  | (8)
combiLGKT | lgkt | , |  |
strKT | skt | , |  | (9)
spinGlass | spg | , , |  |
rdAnisoHf | rahf | , |  | (9)
TFieldCos | tf | , |  |
internFld | if | , , , , |  |
Bessel | b | , |  |
internBsl | ib | , , , , |  |
abragam | ab | , |  |
skewedGss | skg | , , , |  | memo
staticNKZF | snkzf | , |  | (10)
staticNKTF | snktf | , , , |  | see note 10
dynamicNKZF | dnkzf | , , |  | see note 10
dynamicNKTF | dnktf | , , , , |  | see note 10
polynom | p | , |  |

Every theory function has to be written on a single line. It starts with the theory function name or its abbreviation followed by the parameters. Consecutive lines of theory functions will be multiplied. If theory functions need to be added, a line with a + has to separate them. The parameters are given as the numbers assigned to them in the FITPARAMETER block. The order of the parameters is given in the table above. As an example

       simplExpo 4

defines an exponential function with a depolarization rate λ given by the parameter 4 of the FITPARAMETER-block. A full fetched THEORY block could be

       THEORY
       asymmetry 2
       simplExpo 3
       TFieldCos 4 5
       +
       asymmetry 6
       simplExpo 7

which means A(t) = p2 e-p3t cos(2π p5t + p4 π/180) + p6 e-p7t, where pα is the parameter α.

Notes

4 : R. S. Hayano et al., Phys. Rev. B 20 (1979) 850

5 : R. S. Hayano et al., Phys. Rev. B 20 (1979) 850; P. Dalmas de Réotier and A. Yaouanc, J. Phys.: Condens. Matter 4 (1992) 4533; A. Keren, Phys. Rev. B 50 (1994) 10039

6 , 7 : Y. J. Uemura et al., Phys. Rev. B 31 (1985) 546

8 : R. S. Hayano et al., Phys. Rev. B 20 (1979) 850; P. Dalmas de Réotier and A. Yaouanc, J. Phys.: Condens. Matter 4 (1992) 4533

9 : M.R. Crook and R. Cywinski, J. Phys.: Condens. Matter 9 (1997) 1149

9 : R. E. Turner and D. R. Harshman, Phys. Rev. B 34 (1986) 4467

10 : D.R. Noakes and G.M. Kalvius, Phys. Rev. B 56 (1997) 2352; A. Yaouanc and P. Dalmas de Réotier "Muon Spin Rotation, Relaxation, and Resonance" Oxford Scientific Publication; simplifying the original formulae by eliminating via the identity

### 4.3.1 Maps

In case different runs are fitted simultaneously, it is very often necessary that for a given theory function, some parameters are run-dependent. An example could be a temperature scan, where the parameters (asymmetry, depolarization rates, etc.) will depend on the temperature. In order to handle such situations, a mapping of parameters in the THEORY block is possible. That means, instead of a parameter number, the mapping of the parameter is given. The definition of the mapping block is part of the RUN block and will be described there. For example

       THEORY
       asymmetry 2
       simplExpo 3
       TFieldCos 4 5
       +
       asymmetry map1
       simplExpo map2

means that the first part of this theory function is common to all runs, as for instance the background, and the second part is changing from run to run, i.e. `map1/2` will point to different parameters depending on the run.

### 4.3.2 Functions

Yet another useful feature is the possibility to define functions in the FUNCTIONS block. Within the THEORY block these functions can be addressed as `funα`, where α is the function number, e.g. `fun2`.

### 4.3.3 User Functions

In the case complicated and not predefined functions are needed to fit data, `musrfit` offers the possibility to implement external functions and introduce them to `musrfit` through the `ROOT` dictionary mechanism. The detailed rules these user-defined functions have to obey will be discussed in the according section. Here only the syntax for the msr file is provided. To call a user function in the THEORY block the keyword `userFcn` is used. It is followed by the name of the shared library which holds the `C++` class where the function is implemented and the name of the class. Finally, all parameters are given in the order needed by the class. Of course it is also possible to use mapped parameters or functions instead of specifying the parameters directly.

A THEORY block including a user function may then look like

       THEORY
       asymmetry 1
       userFcn libMyLibrary.so TMyFunction 2 3 4 map1 fun1
       +
       ...

## 4.4 The FUNCTIONS Block

`musrfit` utilizes a powerful parser. Therefore, it is possible to define even rather complicated functional relations between the fit parameters and use these in the THEORY block (and in one exceptional case also in the RUN-block). Supported is the use of basic arithmetics:

+
  Addition
-
  Subtraction
*
  Multiplication
/
  Division
()
  Parentheses

The following functions are built-in and can be used in a function definition: cos(), sin(), tan(), acos(), asin(), atan(), cosh(), sinh(), tanh(), acosh(), asinh(), atanh(), exp(), log(), ln(), sqrt(), pow(base, exponent)

Furthermore, some constants are predefined and might also be used:

- gamma_mu = γμ/2π = 0.0135538817 MHz/G
- pi = π = 3.14159265358979323846

The fit parameters are accessed either directly through `parα`, where α is the number of the parameter in the FITPARAMETER block, e.g. `par5` or through a mapping with `mapδ`, where δ specifies the mapping number in the RUN block as explained below.

The defined functions are denoted as `funα`, where α is the function number, i.e. `fun1`, `fun2`, etc. and have to be placed separately on one line each. Afterwards they might be used in the THEORY block.

It follows an example to illustrate the usage of functions in the THEORY block. The total asymmetry of a signal consisting of two parts should be a fit parameter. The fraction of each of the parts will then be expressed as a function of the total asymmetry.

       FITPARAMETER
       #       No   Name      Value     Step        Pos_Error    Boundaries
               1   alpha     1          0.02       none         0       1.8
               2   phase     15         1.0        none
               3   asy       0.2542     0.004713   none         0       0.33
               4   rate1     15         1.0        none         0       none
               5   frac1     0.33       0.0379     none         0       1
               6   rate2     0.13       0.00579    none         0       10

       ###############################################################
       THEORY
       asymmetry   fun1
       simplExpo      4                   (rate)
       +
       asymmetry   fun2
       simplExpo      6                   (rate)

       ###############################################################
       FUNCTIONS
       fun1 = par3 * par5
       fun2 = par3 * ( 1.0 - par5 )

In the case that functions have to be fitted which cannot be defined in the FUNCTIONS block, the functions can be implemented externally and made usable through the userFunc mechanism.

## 4.5 The RUN Block

The RUN block is used to collect the data needed for a particular run to be fitted. This includes the run name, fit type, data format, etc. The RUN block is slightly differently organized than the other blocks. The information is collected via labels followed by the information. Each run to be fitted has its own RUN block. A RUN block starts with a run-file line which has the structure

       RUN <run_file_name> <beamline> <facility> <file_format>

RUN-block tag | comment
--- | ---
<run_file_name> | sub path and filename without extension
<beamline> | name of the beamline where the data were taken, e.g. MUE4. Used to generate a default path.
<facility> | name of the facility where the data were recorded, e.g. PSI. Used to generate a default path.
<file_format> | file format: MUSR-ROOT, NEXUS, ROOT-NPP, ROOT-PPC, PSI-BIN, PSI-MDU, WKM, MUD, MDU-ASCII, ASCII, DB

The tokens following the RUN statement are used to identify the run, the potential location where the run might be found, and the file format in which the run data has been saved. In order to understand the meaning of all the above tokens, a short digression is needed.

Where is `musrfit` looking for data files? There is a specific order how this is done:

- Check if the file is found in the current directory
- Check if the path (or multiple paths) was (were) given in the XML startup file.
- Check if there is a system variable MUSRFULLDATAPATH. This system variable can contain multiple search paths separated by colons, e.g.

      export MUSRFULLDATAPATH=/mnt/data/nemu/wkm/:/mnt/data/nemu/his/:/afs/psi.ch/user/s/smith/

- Construct the search path from the RUN-block information in the following way: Based on the RUN line in the RUN block, default paths will be generated, e.g. for

      RUN lem07_his_2018 MUE4 PSI ROOT-NPP

  the generated search path will look like

      musrFullDataPathToken/DATA/Facility/Beamline/Year/runName.ext

  where musrFullDataPathToken is extracted from the MUSRFULLDATAPATH token by token, for the above example this might lead to the path

      /afs/psi.ch/user/s/smith/DATA/PSI/MUE4/2007/lem07_his_2018.root

Here are some valid examples for the first line of a RUN block:

    RUN 2007/lem07_his_2018 MUE4 PSI ROOT-NPP
    RUN 2007/lem07_2018_rb1_npp MUE4 PSI WKM
    RUN d2007/deltat_pta_gps_2650 PIM3 PSI PSI-BIN
    RUN d2010/tdc/deltat_tdc_gpd_8472 MUE1 PSI PSI-BIN
    RUN beautiful-data MUE4 PSI DB

After this short digression back to the RUN-block description.

In order to describe the operations needed for fitting and plotting, quite some information are needed. These information are following the RUN statement and are listed below. Depending on the fit type these information vary and hence it is indicated for which fit/plot type the information is applicable.

ADDRUN <run_file_name> <beamline> <facility> <file_format> (optional)
  If an ADDRUN is just following after a RUN statement, these runs will be added. More than one ADDRUN statements are possible, i.e. adding up as many runs as wished. It is also possible to add runs with different file formats. If the t0's are given in the data files, the ADDRUN statement is all what is needed, otherwise just add the t0's with the addt0 statement.

For a 'Single Histogram Fit' or a 'MuMinus Fit' it will be

    addt0 t0AddRun1
    addt0 t0AddRun2
    etc.

For an 'Asymmetry Fit' this reads

    addt0 t0AddRun1Forward t0AddRun1Backward
    addt0 t0AddRun2Forward t0AddRun2Backward
    etc.

How will the background and data ranges be handled in this situation? First, the ADDRUN's will be shifted in time such that all the t0's have the same channel/bin number. Subsequently, the runs will be added. The background/data range is applied to this summed up new histogram. ADDRUN is not available for the fit type 'Non-μSR Fit' (sorry ).

fittype (required)
  This tag is used to indicate which type of fit is wished. The supported fit types are:
  0
    Single Histogram Fit
  2
    Asymmetry Fit
  4
    MuMinus Fit. This is a single histogram fit especially for negative muon μSR
  8
    Non-μSR Fit

The description of these fit types can be found in the corresponding section.

alpha, beta (fit types 2)
  These parameters are used to correct the asymmetry for different detector efficiencies, solid angles and initial asymmetries. They are defined as α≡N0,b/N0,f and β≡|A0,b/A0,f|. If the parameters are not specified in the RUN block, for each one the value of 1 is assumed.

norm (fit type 0)
  Number of the fit parameter that represents the normalization constant N0 of the histogram; the value of this parameter is given either per nanosecond or per bin (see below). It is possible to substitute the parameter number by a function here (and only here in a RUN block), for instance to relate N0s of different histograms through an α parameter.

backgr.fit (fit type 0)
  Parameter number specifying the constant background in a histogram. Its value is given either per nanosecond or per bin (see below). If this keyword is present, any information on a background line are ignored.

lifetime (fit type 0)
  Fit parameter representing the lifetime of the muon. If it is not specified the value τμ=2.197019 μs is used in the calculations.

lifetimecorrection (fit type 0)
  Does not accept any arguments. If present, the output in `musrview` is corrected for the exponential decay of the muon.

map
  On this line the mapping of run-dependent parameters is done. Parameter numbers given here may be accessed through `map1`, `map2`, etc. in the THEORY and FUNCTIONS blocks (see also here). The first ten maps are always present and have the value 0 if not used; however, the total number of maps is not restricted!

forward (fit type 0, 4)
  Number of the histogram in the data file to be processed. If histograms shall be grouped, all the numbers which shall be grouped. Examples:

        forward 3       # no grouping, take histogram number 3
        forward 1 2     # group histogram number 1 and 2
        forward 1-10 12 # group histograms with numbers from 1 to 10 and additionally histogram 12

forward, backward (fit types 2)
  Numbers of the histograms in the data file that should be taken to calculate the asymmetry. If histograms shall be grouped, all the numbers which shall be grouped. Examples:

        # build forward/backward asymmetry with histogram 1 and 3
        forward  1
        backward 3
        # build forward/backward asymmetry with groupings 1+2+3 and 7+8+9
        forward   1 2 3
        backward  7 8 9
        # build forward/backward asymmetry with groupings 1+2+3 and 7+8+9 (alternative notation)
        forward   1-3
        backward  7-9

backgr.fix (fit types 0, 2)
  A fixed constant background in counts per nanosecond or per bin (see below) may be given at this point. The background is specified for all histograms in the order Bf Bb [Br Bl]. If this keyword is present, any information on a background line is ignored.

background (fit type 0)
  The numbers of the first and the last channel of an interval from which the constant background should be calculated are specified here. In case histograms are being grouped, the specified channels are interpreted with respect to the first histogram.

background (fit types 2)
  The numbers of the first and the last channel of an interval from which the constant background should be calculated are specified here. For all the histograms this is done together in the following order: kf,first kf,last kb,first kb,last [kr,first kr,last kl,first kl,last]. In case histograms are being grouped, the specified channels are interpreted with respect to the first histograms.

data (fit type 0, 4)
  The numbers of the first and the last channel of an interval from which the data is taken are specified here. In case histograms are being grouped, the specified channels are interpreted with respect to the first histogram.

data (fit types 2)
  The numbers of the first and the last channel of an interval from which the data is taken are specified here. For all the histograms this is done together in the following order: kf,first kf,last kb,first kb,last [kr,first kr,last kl,first kl,last]. In case histograms are being grouped, the specified channels are interpreted with respect to the first histograms.

t0 (fit type 0, 4)
  The number of the time-zero channel of the histogram. Example:

        t0 3419        # t0 channel = 3419
        t0 3419 3434   # t0 channels for groupings: forward f1 f2. 3419 t0 for f1, 3434 t0 for f2.

t0 (fit types 2)
  The numbers of time-zero channels of the histograms in the order t0,f t0,b. Example:

        t0 3419 3418           # t0 channels: forward (3419), backward (3418)
        t0 3419 3418 3417 3416 # t0 channels (assuming forward f1 f2, backward b1 b2): forward (3419, f1), backward (3418, b1); forward (3417, f2), backward (3416, b2)

addt0 (fit type 0, 4)
  The number of the time-zero channel of the histogram. If grouping of histograms is present (see forward) the same syntax as for t0 applies. If one addt0 is given, the total number of addt0's needs to be equal to the total number of ADDRUN's!

addt0 (fit types 2)
  The numbers of time-zero channels of the histograms in the order t0,f t0,b [t0,r t0,l]. If grouping of histograms is present (see forward) the same syntax as for t0 applies. If one addt0 is given, the total number of addt0's needs to be equal to the total number of ADDRUN's!

xy-data (fit type 8)
  Specification of the data from an ASCII or DB file which should be used as x and y data (in this order). For a simple ASCII file the column numbers are used, in the case of a DB file one can either specify the variable numbers or the name of the variables as given in the DB header.

fit
  The range of data that should be considered when the fitting is done. For the μSR fit types 0, 2, and 4 here the starting and end times are given in microseconds. For the non-μSR fit type 8 the starting and end points of the fitting range are given in the units of the x data.
  In case the fit range specified here is larger than the data range (in any direction), eventually the data range will be used as fit range. An example for a μSR fit:

      fit 0.2 8.5

  Which means that the fitting window will span from 0.2 to 8.5 microseconds.
  Another possibility for the μSR fits is to give the fit range in bins, rather than time. The syntax is then:

      fit fgb+<n0> lgb-<n1>,

  where fgb and lgb are label tags which refer to the 'first good bin' and the 'last good bin' defined either in the `data` tag of the run block, data file, are estimated based on T0. <n0> and <n1> are offsets (given in bins) allowing to change the fit window compared to the data window. An example:

      fit fgb+150 lgb-1332

packing
  Number of data channels to be binned together. For the non-μSR fit type 8 the binning is supposed to be 1.

## 4.6 The COMMANDS Block

The COMMANDS block is used to specify the commands which are passed from `musrfit` to `MINUIT2`. The supported commands after the COMMANDS keyword are STRATEGY, MIGRAD, SIMPLEX, MINIMIZE, MINOS, HESSE, SAVE, some additional commands described below, and for compatibility reasons SET BATCH and END RETURN. The last two commands may appear in the COMMANDS block but are simply ignored. A detailed description of all of these commands can be found in the MINUIT2 users guide .

A standard COMMANDS block then looks like this:

       COMMANDS
       MINIMIZE
       MINOS
       SAVE

Additional to the commands listed above also the command MAX_LIKELIHOOD is valid. This keyword can be placed anywhere in the block and switches from the default χ2 minimization to the log-likelihood maximization which can be advantageous if one is dealing with low-statistics data.

Furthermore, it is possible to call the `MINUIT2` methods SCAN and CONTOURS. Exemplary invocations are as follows:

       COMMANDS
       SCAN 7
       MNPLOT

       COMMANDS
       MINIMIZE
       CONTOURS 8 9
       MNPLOT
       SAVE

Sometimes it is necessary to guide `MINUIT2` to the global optimum. For this purpose it is useful to have the commands FIX list_of_param_to_be_fixed, RELEASE list_of_param_to_be_fixed, and RESTORE at hand. list_of_param_to_be_fixed is a list of the parameters to be fixed/released. It is a space- or comma-separated list of either parameter numbers and/or parameter names. RESTORE releases all the fixed parameters. A typical example could look like:

       COMMANDS
       FIX Freq1, Freq2
       MINIMIZE
       RESTORE
       MINIMIZE
       MINOS
       SAVE

It is important to understand that before MINOS is called, all the fixed parameters need to be released and another minimizer command (MINIMIZE, MIGRAD, or SIMPLEX) needs to be in place, otherwise `musrfit` will assume that the still fixed parameters have to be handled as constant parameters, i.e. setting the <step> value of the parameter to zero.

For even more complex fitting the additional command FIT_RANGE RESET | tstart tend | ts1 te1 ts2 te2 ... tsn ten is provided. It allows to change the fit range during different iterations. The command FIT_RANGE tstart tend changes the current fit range for `all` the runs present in the msr file. FIT_RANGE RESET will restore to the original fit ranges as provided in the RUN block. If for each run of the msr file an individual fit range should be used, the third option applies. Here n has to correspond to the number of runs in the RUN block.

As for the run block, there is a 2nd flavor how the FIT_RANGE can be changed, namely giving the fit range in bins, i.e. FIT_RANGE RESET | fgb+<n0> lgb-<n1> | fgb+<n00> lgb-<n01> fgb+<n10> lgb-<n11> ... fgb+<nN0> lgb-<nN1> where N is the number of available run blocks. The idea is inline with the above syntax and the syntax describe for the fit range (fit) of the RUN block.

A typical example could look like:

       COMMANDS
       FIT_RANGE 0.0 0.8
       MINIMIZE
       FIT_RANGE RESET
       MINIMIZE
       MINOS
       SAVE

or

       COMMANDS
       FIT_RANGE fgb+15 lgb-1332 fgb+17 lgb-1330
       MINIMIZE
       FIT_RANGE RESET
       MINIMIZE
       MINOS
       SAVE

The last accepted command in the COMMAND block is SCALE_N0_BKG TRUE | FALSE. This command is only used in conjunction with single-histogram fits. The default is SCALE_N0_BKG TRUE which will result in a scaling of N(t) such that it is given in ns-1, whereas with SCALE_N0_BKG FALSE no scaling is performed and N(t) will be given in bin-1. If the command is not present at all, it will be interpreted as if SCALE_N0_BKG TRUE was present.

For debug purposes it is possible to force MINUIT2 to print out additional informations. The COMMAND block command is PRINT_LEVEL <n>, where <n> can have the values 0,1,2, or 3. A typical example could look like:

      COMMANDS
      MIGRAD
      SAVE
      PRINT_LEVEL 3
      MINOS
      SAVE

Here the `MINOS` command will print out lot of additional information to the standard output. Notice there are 2 `SAVE` commands here. This will write the result of `MIGRAD` to the `MINUIT2.OUTPUT` file and at the end append the `MINOS` results to this file.

## 4.7 The FOURIER Block

The Fourier transform is done and the results are plotted within `musrview` —as input data the actual data shown in `musrview` is used. In the FOURIER block of the msr file all necessary parameters for calculating and presenting the Fourier transform of the data specified in the PLOT block is given. If the FOURIER block is not present in the msr file, either the parameters set in the XML startup file or the system defaults are taken when the Fourier transform is performed. The block starts with the FOURIER keyword and may contain the following entries on the successive lines:

units
  Here is specified in which domain the Fourier-transformed data is presented. One may choose between the field (Gauss), the frequency (MHz), and the angular-frequency domain (Mc/s).
fourier_power
  It is possible (but not necessary) to set the number of data points used for the Fourier transform here. As argument the exponent n<21 of a power of 2 is accepted. The number of data points is then 2n. Attention: If the number of points given here is bigger than the actual number of available data points, the input data vector is filled with zeros until the number of requested points is reached (zero padding)!
dc-corrected
  a flag to remove a potential DC-offset of the signal. Allowed entries are `dc-corrected true | 1 | false | 0`.
apodization
  Here is decided if the data should be apodized before the Fourier transform is done and if yes, which apodization should be used (for further details about apodization of μSR data refer to the PhD thesis of T.M. Riseman). The argument to be put after the keyword is therefore one of the following: NONE, WEAK, MEDIUM or STRONG. If the data should be apodized, they are manipulated as follows: each data value is multiplied by the function , where is the data-point index and is the total number of data points. The coefficients for the different apodizations are given by:
  WEAK
  MEDIUM
  STRONG
plot
  At this point it is possible to set the part of the Fourier-transformed data which should be plotted by default if the Fourier transform is done by pressing the f-key in `musrview`. The argument may be one of the following:
  real
    The real part of the (complex) Fourier transform is plotted.
  imag
    The imaginary part of the Fourier transform is plotted.
  real_and_imag
    Both the real and the imaginary parts of the Fourier transform are shown.
  power
    The absolute value of the Fourier transform is depicted.
  phase
    The phase of the Fourier transform is plotted.
phase
  The initial phase of the input data is given here in degrees. Optionally the phase parameter from the FITPARAMETER block can be given, e.g. `par3`, which would take the value of parameter number 3.
range_for_phase_correction
  An interval within which the initial phase should be optimized automatically can be specified here. The interval is given by its start and end values in degrees.
range
  The plotting range is set here. The interval is specified through its start and end points given in the units set after the units tag.

Altogether, a possible FOURIER block might look like that:

       FOURIER
       units Mc/s
       fourier_power 12
       apodization NONE
       plot real_and_imag
       phase 22.6   # par3
       #range_for_phase_correction 10.0 40.0
       range 0.0 17.03

## 4.8 The PLOT Block

The PLOT block is intended to collect all the information needed for the graphical presentation of the data and fits using `musrview`. The PLOT keyword at the beginning of the block is followed by a number which indicates the plot type. The plot types match the fit types. Additionally, it is possible to provide information using the following keywords:

runs
  The numbers of the runs to be plotted have to be put here. The runs are numbered according to their appearance in the RUN block.
range
  Here it is possible to define the plotting range explicitly. Depending on the plot type the following settings are allowed where the times are given in microseconds and the N in counts (type 0, 4) or in counts/nsec (type 0):
  0 without lifetimecorrection, 4
    tmin tmax [ Nmin Nmax ]
  0 with lifetimecorrection, 2
    tmin tmax [ Amin Amax ]
  8
    xmin xmax [ ymin ymax ]
sub_ranges
  Here it is possible to define the plotting range for each run individually. For the different plot types the command has the structure
  0 without lifetimecorrection, 4
    tmin1 tmax1 tmin2 tmax2 ... tminn tmaxn [ Nmin Nmax ] (n = the number of runs to be plotted)
  0 with lifetimecorrection, 2
    tmin1 tmax1 tmin2 tmax2 ... tminn tmaxn [ Amin Amax ] (n = the number of runs to be plotted)
  8
    not yet implemented.
use_fit_ranges [ ymin ymax]
  The fit ranges of the individual runs are used to present the data. Optionally, an ordinate range can be provided.
view_packing
  The data are presented in the packing given here rather than the binning used for the fit. WARNING: This is a global option and applies to all PLOT-blocks.
logx
  Will present the time axis in a logarithmic scale. So far no checking of negative and zero-valued data is performed
logy
  Will present the axis of ordinates in a logarithmic scale. So far no checking of negative and zero-valued data is performed
rrf_packing `value`
  In the rotating-reference-frame (RRF) representation, this will be the value for the packing. WARNING: For the time being, this is a global option and applies to all PLOT blocks.
rrf_freq `value` `unit`
  This entry provides the RRF "frequency" given by the `value` and the `unit` which can be: `kHz`, `MHz`, `Mc/s`, `G`, or `T`.
rrf_phase `value`
  A phase of the RRF can be provided, either as a value in degrees, or as a `parX`, e.g. `par4`, where `X` is supposed to be the phase parameter number in the FITPARAMETER block.

If no plot range is given at all, the fit range of the first run also serves as time window for the plot. In the case no information on the axis of ordinates is available, the plotting range is chosen so that all data can be presented.

It is possible to define multiple PLOT blocks. Each PLOT block generates its own `ROOT` canvas.

A few comments concerning the rotating reference frame (rrf) plot option: the idea of the rrf is to transform a high frequency μSR spectrum into a low frequency spectrum. This is essentially done by multiplying the original asymmetry by . This leads to two frequency shifted copies of the original , one shifted downwards in frequency by (to wanted one) and one upwards (unwanted one). In order to get rid of the upward shifted spectrum, the `rrf_packing` is used, we just over-bin the high frequency copy (for now. In the future this will be dealt with FIR filtering)! The theory, however, is filtered via Kaiser filter. Here a short example:

        ###############################################################
        PLOT 0   (single histo plot)
        runs     1
        range    0   10   -0.3   0.3
        rrf_freq 13900 G
        rrf_packing 75

## 4.9 The STATISTIC Block

The STATISTIC block is the last block of a msr file. It contains some information on the fit: the date and time as well as the absolute and normalized values of χ2 and the number of degrees of freedom in the fit.
If enabled in the XML file for χ2-single-histogram fits also Pearson's χ2 will be written to the STATISTIC block.
These information only have a meaning if the fitting procedure has been executed at least once and the fit has converged!

# 5 The Fit Types

## 5.1 Single Histogram Fit

The single-histogram fit (fit type 0) is used to fit a function directly to the raw data using
The parameters are given by:

  rebinned decay histogram
  normalization constant of the histogram (RUN block: norm)
  lifetime of the muon (RUN block: lifetime)
  constant background (RUN block: backgr.fit or background)
  decay asymmetry/depolarization function as given in the THEORY block

In the plot type 0 without lifetimecorrection the rebinned histogram and the function written above are presented. If the option lifetimecorrection is set in the RUN block the asymmetry is plotted:

## 5.2 Asymmetry Fit

For an asymmetry fit (fit type 2) two histograms are needed. These are given by the forward and backward keywords in the RUN block. Additionally, the parameters alpha and beta which relate the detector efficiencies, solid angles and initial asymmetries of the two detectors can be supplied. The constant background for the two histograms is either given by background-determined intervals or specified through backgr.fix in the RUN-block.

The experimental asymmetry then is inferred from the two histograms:
with

  counts in the forward histogram channel
  counts in the backward histogram channel
  constant background in the forward histogram (RUN block: backgr.fix or background)
  constant background in the backward histogram (RUN block: backgr.fix or background).

This asymmetry is used to fit the function
where

  accounts for the different detector efficiencies and solid angles (RUN block: alpha)
  accounts for the different detector asymmetries (RUN block: beta)
  is the depolarization function as given in the THEORY block.

For the graphical representation in plot type 2 the equation above is rearranged to get :
and plotted together with the function given in the THEORY block.

## 5.3 Negative Muon μSR Fit

The negative muon μSR fit (fit type 4) is used for single histogram fits of MuMinus, i.e.
where runs over the different lifetime channels of , and

  counts of lifetime channel
  lifetime of lifetime channel
  depolarization function of lifetime channel
  the background

Since MuMinus is quite generic, the full functional depends has to be written in the THEORY Block.

## 5.4 Non-μSR Fit

In the case of a non-μSR fit (fit type 8) the fitting function is
where

  are given by xy-data in the RUN block
  is the function defined in the THEORY block.

The same is valid for the plot with plot type 8.

# 6 User Functions

`musrfit` offers the possibility to plug-in user-defined functions implemented in `C++` classes to the fitting and plotting routines. In order to do so, basically two things are needed:

1. a shared library containing the compiled class with the defined function
2. a ROOT dictionary that contains information about the functions in the shared library

There are two possible ways to implement user functions and both will be explained below:

1. a user function without global user-function-object access
2. a user function with global user-function-object access

Since the first is simpler this will be explained using an explicit example, before it is discussed why the second option is needed and how it can be used.

## 6.1 User Function without global user-function-object access

In the following it is explained in detail how the implementation of a user function is done using the simple example of fa(x) = sin(ax)/ax, where the parameter a should be determined by the fit. Although not necessary for this simple example, the source code is split into two parts, namely a header file TMyFunction.h containing the class declaration and a second file TMyFunction.cpp including the function implementation.

To plug in the class to `musrfit`, it is necessary that the class derives from the base class PUserFcnBase defined in the header file PUserFcnBase.h. In this abstract base class a function operator is defined that takes two arguments: the point where the function should be evaluated and a reference to a vector with all parameters of the function. Therefore, the user's header file could look like the following:

    /***************************************************************************

      TMyFunction.h

    ***************************************************************************/

    #include "PUserFcnBase.h"
    #include <cassert>
    #include <cmath>
    #include <vector>

    using namespace std;

    class TMyFunction : public PUserFcnBase {

    public:
      // default constructor and destructor
      TMyFunction(){}
      ~TMyFunction(){}

      // global user-function-access functions, here without any functionality
      Bool_t NeedGlobalPart() const { return false; }
      void SetGlobalPart(vector<void*> &globalPart, UInt_t idx) { }
      Bool_t GlobalPartIsValid() const { return true; }

      // function operator
      Double_t operator()(Double_t, const vector<Double_t>&) const;

      // definition of the class for the ROOT dictionary
      ClassDef(TMyFunction,1)
    };

In the header file above the constructor (destructor) of the class is empty. This is not necessary. Any code that should be executed when the RUN block is read and the class object is created (destroyed) may be implemented in the constructor (destructor). Another peculiarity is the ClassDef statement at the end of the class definition. It is needed for the `ROOT` dictionary generation and has as arguments the class name and a revision number.

Please also be aware of the const-ness of the operator(). For an introductory discussion on that topic look for example here and the links herein.

The actual implementation of the user function is done in the second source file. In this example it only contains the definition of the function operator() declared in the header file and might look like:

    /***************************************************************************

      TMyFunction.cpp

    ***************************************************************************/

    #include "TMyFunction.h"

    ClassImp(TMyFunction)  // for the ROOT dictionary

    Double_t TMyFunction::operator()(Double_t x, const vector<Double_t> &par) const {
      assert(par.size()==1); // make sure the number of parameters handed to the function is correct

      Double_t arg(par[0]*x);

      if(!arg)
        return 1.0;
      return sin(arg)/arg;
    }

Also this file contains a special statement for the `ROOT` dictionary generation (ClassImp), which is placed before the definition of the function. If functions of more than one class are defined in the file, the ClassImp statements for the other classes follow right after the first one.

What is further needed for the `ROOT` dictionary is a so-called LinkDef file which again contains the class names of all classes that should be accessible through the dictionary and has the following structure, where the "LinkDef.h" (or "linkdef.h" or "Linkdef.h") at the end of the file name is mandatory:

    /***************************************************************************

      TMyLibraryLinkDef.h

    ***************************************************************************/

    #ifdef __CINT__

    #pragma link off all globals;
    #pragma link off all classes;
    #pragma link off all functions;

    #pragma link C++ class TMyFunction+;

    #endif //__CINT__

For compiling and linking it is wise to use a Makefile as for example the attached Makefile.TMyLibrary. It assumes standard `ROOT` and `musrfit` installations and defines rules for the generation of the shared library libTMyLibrary.so including the class and the `ROOT` dictionary. In order to get the library built and installed on the standard `ROOT` path just call:

    make -f Makefile.TMyLibrary
    make -f Makefile.TMyLibrary install

In case of a custom installation some paths in the Makefile might have to be changed. For further information about the `ROOT` dictionary mechanism please refer to the documentation.

After installing the shared library the defined user function might be used in `musrfit` as described above.

Good luck!

Finally, please be aware of the remark at the end of this section.

## 6.2 User Function with global user-function-object access

Before explaining how to use global objects within user functions, it will be shortly explained where is problem and why this might be a sensible approach. In `musrfit` each RUN block (histogram, asymmetry, ...) is owning its own theory-function tree. An example is shown in the figure below. The bluish nodes are default `musrfit` functions, whereas the red nodes represent user functions (here labeled by `uF1` and `uF2`). Without global user-function object, these nodes are independent entities. This means if the msr file contains n run blocks, the user function `uF1` will be called n times for each step in the calculation. If the user function is performing CPU-demanding calculations this is rather inefficient.

Therefore, it is possible to associate to each user function (`uFx`) a global user-function object (`g_uFx`). The idea is the following: If `uFx` needs to perform very time-consuming calculations (e.g. calculate an Abrikosov vortex lattice or the nonlocal response of a superconductor in the Meissner state) this can be transferred to the global user-function object (`g_uFx`) and hence the time-consuming calculation is only performed once per cycle (compared to n times without `g_uFx`), thus speeding up the fit.

After explaining the purpose of the global user-function-object approach, some explanations how to interface it follow here. Since the interface is very close to the user function without global objects, only the additionally necessary overhead is explained here.

The user's header file could look like the following:

    /***************************************************************************

      TMyFunction.h

    ***************************************************************************/

    #include "PUserFcnBase.h"
    #include <cassert>
    #include <cmath>
    #include <vector>

    using namespace std;

    class TMyGlobalFunction {

    public:
      // default constructor and destructor
      TMyGlobalFunction(){}
      ~TMyGlobalFunction(){}

      Bool_t IsValid() { return fValid; }

      // the following function will check if something needs to be calculated, which
      // is the case if param != fPrevParam
      void CalcSomethingCPUExpensive(const vector<Double_t> &param);

      // this routine will return the calculated values, e.g. B(z,E) for TMyFunction::operator()()
      // (...) here sketches only that some parameters are likley to be fed
      Double_t GetWhatIsNeeded(...);

    private:
      Bool_t fValid;
      vector<Double_t> fPrevParam;

      // definition of the class for the ROOT-dictionary
      ClassDef(TMyGlobalFunction,1)
    };

    class TMyFunction : public PUserFcnBase {

    public:
      // default constructor and destructor
      TMyFunction(){}
      ~TMyFunction(){}

      // global user-function-access functions, here with some functionality
      Bool_t NeedGlobalPart() const { return true; }
      void SetGlobalPart(vector<void*> &globalPart, UInt_t idx);
      Bool_t GlobalPartIsValid() const;

      // function operator
      Double_t operator()(Double_t, const vector<Double_t>&) const;

    private:
      Bool_t fValid;
      Bool_t fInvokedGlobal;
      Int_t  fIdxGlobal;
      TMyGlobalFunction * fGlobalUserFcn;

      // definition of the class for the ROOT dictionary
      ClassDef(TMyFunction,1)
    };

Compared to the user function without global objects, here the `NeedGlobalPart()` method returns `true` meaning that a global user-function object will be needed. Furthermore, the methods `SetGlobalPart(vector<void*> &globalPart, UInt_t idx)` and `GlobalPartIsValid()` now need to be implemented. The method `SetGlobalPart(vector<void*> &globalPart, UInt_t idx)` is used to link the `fGlobalUserFcn` to the global user object. This routine will look like:

    void TMyFunction::SetGlobalPart(vector<void *> &globalPart, UInt_t idx)
    {
      fIdxGlobal = static_cast<Int_t>(idx);

      if ((Int_t)globalPart.size() <= fIdxGlobal) { // global user function not present, invoke it
        fGlobalUserFcn = new TMyGlobalFunction();
        if (fGlobalUserFcn == 0) { // global user function object couldn't be invoked -> error
          fValid = false;
          cerr << endl << ">> TMyFunction::SetGlobalPart(): **ERROR** Couldn't invoke global user function object, sorry ..." << endl;
        } else {  // global user function object could be invoked -> resize to global user function vector and keep the pointer to the corresponding object
          globalPart.resize(fIdxGlobal+1);
          globalPart[fIdxGlobal] = dynamic_cast<TMyGlobalFunction*>(fGlobalUserFcn);
          fValid = true;
          fInvokedGlobal = true;
        }
      } else { // global user function already present hence just retrieve a pointer to it
        fValid = true;
        fGlobalUserFcn = (TMyGlobalFunction*)globalPart[fIdxGlobal];
      }
    }

What it does is the following: it first checks if the object is already present in the global user-function-object vector and if not creates it. If it is already present, the pointer to the global object vector is just kept (see figure above).

A sketch of the method `operator()(Double_t, const vector<Double_t>&) const` will then look like (pseudo-code snippet):

    Double_t TMyFunction::operator()(Double_t t, const vector<Double_t> &param) const
    {
      Double_t result = 0.0;

      // do something, checking, etc.
      ...

      // call the global user function object (which will calculate something
      // if param has changed). Hence it will only be done once in a iteration,
      // and therefore only once for all run blocks.
      fGlobalUserFcn->CalcSomethingCPUExpensive(param);

      // extract the needed values from the global object
      value(s) = fGlobalUserFcn->GetWhatIsNeeded(...);

      // use 'value(s)' to do some run block specific calculations (not/less CPU demanding)
      ...

      return result;
    }

This way the efficiency of the user function can be increased by almost a factor of n (where n is the number of RUN blocks).

Important remark: If `musrfit` has been built with parallelization support (default for `GCC` ≥ 4.2) it should be taken care of the thread safety of the user-function operator(). During the function optimization of `musrfit` the operator() is called once for any given set of parameters in order to allow the safe execution of any calculation. Within the single-histogram and asymmetry fits the calculation of χ2 or the log-likelihood is parallelized and the operator() is expected to evaluate to reasonable values for a fixed set of parameters (but changing t) beginning with the second function call. In case this cannot be ensured, the parallelization can be disabled by --disable-omp on the configure level of the program installation.

# 7 Technical Description of the musrfit framework

A technical description of the musrfit framework can be found here.

# 8 Bugtracking

For reporting bugs or requesting new features and improvements please use the PSI Tracker or send an e-mail to A. Suter.

-- AS & BMW

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Topic revision: r113 - 16 Dec 2013, AndreasSuter

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