| @@ -970,12 +974,12 @@ |
For a detailed discussion of these entries see the section RUN block.
The single histo RRF fit and asymmetry RRF fit related entries (fittype 1 and 3 only) have the following syntax:
@@ -1217,6 +1217,8 @@ etc.These parameters are used to correct the asymmetry for different detector efficiencies, solid angles and initial asymmetries. They are defined as \(\alpha = N_{0,b}/N_{0,f}\) and \(\beta = A_{0,b}/A_{0,f}\). If the parameters are not specified in the RUN block, for each one the value of 1 is assumed. Example for alpha with fit parameter number 1:
+These parameters are used to correct the asymmetry for different detector efficiencies, solid angles and initial asymmetries. They are defined as \(\alpha = N_{0,b}/N_{0,f}\) and \(\beta = A_{0,b}/A_{0,f}\). If the parameters are not specified in the RUN block, for each one the value of 1 is assumed (for fittype 5 alpha is estimated from the ration of sum of Bp+Bm and Fp+Fm). Example for alpha with fit parameter number 1:
alpha 1
Numbers of the histograms in the data file that should be taken to calculate the asymmetry. Two forward and backward histograms should be given indicationg positive and negative helicities. The asymmetry from opposite helicities will be subtracted. Examples:
+# build forward/backward asymmetry with histogram 1 and 3 then subtract asymmetry built with histograms 2 and 4
+forward 1 2
+backward 3 4
+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: \(k_{f,\rm first} k_{f,\rm last} k_{b,\rm first} k_{b, \rm last} [k_{r,\rm first} k_{r,\rm last} k_{l,\rm first} k_{l,\rm last}]\). In case histograms are being grouped, the specified channels are interpreted with respect to the first histograms. Example:
@@ -1327,7 +1337,7 @@ Typically these channels are referred to asThe numbers of the first and the last channel of an interval from which the data is taken are specified here. Typically these channels are referred to as first good bin / last good bin (fgb/lgb). For all the histograms this is done together in the following order: \(k_{f,\rm first} k_{f,\rm last} k_{b,\rm first} k_{b, \rm last} [k_{r,\rm first} k_{r,\rm last} k_{l,\rm first} k_{l,\rm last}]\). @@ -1347,8 +1357,8 @@ t0 3419 3434 # t0 channels for groupings: forward f1 f2. 3419 t0 for f1, 3434
The numbers of time-zero channels of the histograms in the order \(t_{0,f} t_{0,b}\). Example:
+The numbers of time-zero channels of the histograms in the order \(t_{0,f} t_{0,b}\). For fit type 5, the time-zero is the channel of the start of beam pulse. 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)
Since MuMinus is quite generic, the full functional depends has to be written in the THEORY Block.
+For a beta-NMR asymmetry fit (fit type 5) four histograms are needed, two for positive and two for negative helicities. 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 \(a(k)\) then is calculated from the four histograms:
+with
++++
+- \(N_{\mathrm{fp}}(k)\): counts in the forward histogram channel with positive helicity \(k\)
+- \(N_{\mathrm{bp}}(k)\): counts in the backward histogram channel with positive helicity \(k\)
+- :math:` B_{mathrm{fp}}`: constant background in the forward histogram with positive helicity (RUN block: backgr.fix or background)
+- :math:` B_{mathrm{bp}}`: constant background in the backward histogram with positive helicity (RUN block: backgr.fix or background)
+- \(N_{\mathrm{fm}}(k)\): counts in the forward histogram channel with negative helicity \(k\)
+- \(N_{\mathrm{bm}}(k)\): counts in the backward histogram channel with negative helicity \(k\)
+- :math:` B_{mathrm{fm}}`: constant background in the forward histogram with negative helicity (RUN block: backgr.fix or background)
+- :math:` B_{mathrm{bm}}`: constant background in the backward histogram with negative helicity (RUN block: backgr.fix or background)
+
This theoretical asymmetry \(a(t)\) is used to fit the function
+where
++++
+- \(\alpha\): accounts for the different detector efficiencies and solid angles (RUN block: alpha).
+- \(\beta\): accounts for the different detector asymmetries (RUN block: beta).
+- \(A(t)\): is the depolarization function as given in the THEORY block.
+
For the graphical representation in plot type 5 the equation above is rearranged to get \(A(t)\):
+and plotted together with the function given in the THEORY block.
+In the case of a non-μSR fit (fit type 8) the fitting function is
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:
@@ -1896,7 +1945,7 @@ In order to do so, basically two things are needed:
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.
In the following it is explained in detail how the implementation of a user function is done using the simple example of \(f_a(x) = \sin(a x)/(a x)\), 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 @@ -1999,7 +2048,7 @@ refer to the remark at the end of this section.
Before explaining how to use global objects within user functions, it will be shortly explained where is the 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 @@ -2139,7 +2188,7 @@ In case this cannot be ensured, the parallelization can be disabled by ̵
A technical description of the musrfit framework can be found on its own docu.