updated docu

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suter_a 2019-07-24 10:15:15 +02:00
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commit b68286761a
22 changed files with 170 additions and 238 deletions

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@ -1,4 +1,4 @@
# Sphinx build info version 1
# This file hashes the configuration used when building these files. When it is not found, a full rebuild will be done.
config: 20df816aeaa22714f2d1b51daabf53ca
config: b0f54e143f8f1d163af95476812112f7
tags: 645f666f9bcd5a90fca523b33c5a78b7

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@ -67,7 +67,8 @@ Additionally, *only* if ``musrfit`` should support reading of data files in the
.. index:: minixml
**minixml**
A small ``XML`` library that can be used to read and write ``XML`` and ``XML``-like data files. *Required version ≥ 2.2* (see `minixml <http://www.minixml.org/>`_).
A small ``XML`` library that can be used to read and write ``XML`` and ``XML``-like data files. *Required version ≥ 2.2* (see `minixml <http://www.minixml.org/>`_).
Currently the ``MXML`` support in ``NeXus`` is broken and hence you will **not** need to install ``minixml`` for the time being.
.. index:: nexus
@ -172,23 +173,20 @@ Installation of NeXus requirements (optional)
*Only* if ``musrfit`` should support reading/writing data files in the ``NeXus`` format the further required
software has to be set up. The required libraries and header files could either be available through the user's
GNU/Linux distribution or if this is not the case, the packages can be installed from the source code. The necessary
packages to build ``NeXus`` are ``MXML``, (``HDF4``), and ``HDF5``. This means, for a rpm-package based distro try something like:
GNU/Linux distribution or if this is not the case, the packages can be installed from the source code. In principle
NeXus should support ``MXML``, ``HDF4``, and ``HDF5``. At the time of this writing, the ``MXML`` support in the
NeXus project is broken, and ``HDF4`` is outdated on most platforms, hence currently only the ``HDF5`` binding is
used. Hence, the necessary package to build ``NeXus`` is ``HDF5``. This means, for a rpm-package based distro try something like:
.. code-block:: bash
$ yum install mxml-devel hdf-devel hdf5-devel
$ yum install hdf5-devel
and on a deb-package based distro try something like:
.. code-block:: bash
$ apt-get install libmxml-dev libhdf4-dev libhdf5-dev
.. note::
``HDF4`` support within ``NeXus`` will be dropped by ``musrfit`` in the near future. If you *not* urgently need
to read old ``ISIS NeXus`` files, you safely can drop it.
$ apt-get install libhdf5-dev
**Only NeXus Version ≥ 4.4 is support!**
@ -208,10 +206,7 @@ A brief instruction how to get ``NeXus`` compiled from source (lines starting wi
$ # next we will build NeXus out-of-source
$ mkdir build
$ cd build
$ # The next line only if HDF4 support is needed
$ cmake -DENABLE_HDF5=1 -DENABLE_HDF4=1 -DENABLE_MXML=1 ../code
$ # The next line if HDF4 support is NOT needed
$ cmake -DENABLE_HDF5=1 -DENABLE_MXML=1 ../code
$ cmake -DENABLE_HDF5=1 -DENABLE_HDF4=0 -DENABLE_MXML=0 ../code
$ cmake --build ./ --clean-first
$ # make install needs either to be carried out as root or sudo depending on your linux flavour.
$ sudo make install
@ -550,11 +545,7 @@ to be set up. Under ``Cygwin`` of all the required libraries only ``HDF5`` is av
``libhdf5-devel`` can be installed through the ``Cygwin`` setup. One should also make sure that ``bison``, ``flex``
and a package containing ``/usr/lib/librpc.a`` (*e.g.* ``sunrpc = 4.0-3``, but *not* ``sunrpc = 4.0-4``) are installed.
All other libraries have to be built from the sources. The following lines will track the installation of ``JPEG 6b``,
``MXML 2.9``, ``HDF 4.2.7-patch1``, and ``NeXus 4.3.2``. The version numbers and source-code locations might of
course change with time but should be easily adjustable.
*Only* ``NeXus`` version ≥ 4.4 is support!
**Only NeXus Version ≥ 4.4 is support!**
.. code-block:: bash
@ -567,18 +558,6 @@ course change with time but should be easily adjustable.
$ make
$ make install
$ cd ..
$ curl www.msweet.org/files/project3/mxml-2.9.tar.gz -G | tar xz
$ cd mxml-2.9
$ ./configure --prefix=/usr/local --enable-static
$ make
$ make install
$ cd ..
$ curl http://www.hdfgroup.org/ftp/HDF/HDF_Current/src/hdf-4.2.7-patch1.tar.gz -G | tar xz
$ cd hdf-4.2.7-patch1
$ ./configure --prefix=/usr/local --enable-static --disable-fortran --with-jpeg=/usr/local
$ make
$ make install
$ cd ..
$ # create a directory for the NeXus source code
$ mkdir nexus
$ cd nexus
@ -587,7 +566,7 @@ course change with time but should be easily adjustable.
$ # next we will build NeXus out-of-source
$ mkdir build
$ cd build
$ cmake -DENABLE_HDF5=1 -DENABLE_HDF4=1 -DENABLE_MXML=1 ../code
$ cmake -DENABLE_HDF5=1 -DENABLE_HDF4=0 -DENABLE_MXML=0 ../code
$ make
$ make install
@ -876,21 +855,14 @@ Installation of NeXus requirements (optional)
.. code-block:: bash
$ sudo port -v install hdf4 hdf5
$ sudo port -v install hdf5
Unfortunately, the ``minixml`` and ``NeXus`` libraries have to be compiled and installed directly from the source code.
Given the respective version numbers of 2.9 and 4.4.2 (which are subject to change with time.
Only ``NeXus`` Version ≥ 4.4 is support!) this can be achieved for example by:
**Only NeXus Version ≥ 4.4 is support!**
To get things compiled do:
.. code-block:: bash
$ # get and instal Mini-XML
$ cd $HOME/Applications
$ git clone https://github.com/michaelrsweet/mxml.git
$ cd mxml
$ ./configure --prefix=/usr/local
$ make
$ sudo make install
$ # get and install NeXus
$ cd $HOME/Applications
$ # get the source code from the master repository
@ -899,7 +871,7 @@ Only ``NeXus`` Version ≥ 4.4 is support!) this can be achieved for example by:
$ cd nexus
$ mkdir build
$ cd build
$ cmake -DENABLE_HDF5=1 -DENABLE_HDF4=1 -DENABLE_MXML=1 ../code
$ cmake -DENABLE_HDF5=1 -DENABLE_HDF4=0 -DENABLE_MXML=0 ../code
$ make
$ sudo make install
@ -1101,27 +1073,20 @@ packages can be installed through Fink (check for the most recent versions):
libjpeg hdf hdf5-cpp11 hdf5-cpp11-shlibs
Unfortunately, the ``minixml`` and ``NeXus`` libraries have to be compiled and installed directly from
the source code. Given the respective version numbers of 2.9 and 4.3.2 (which are subject to change with time)
Unfortunately, the ``NeXus`` libraries have to be compiled and installed directly from
the source code. Given the respective version number 4.4 (which are subject to change with time)
this can be achieved for example by:
.. code-block:: bash
$ # first build Mini-XML
$ cd $HOME/Applications
$ git clone https://github.com/michaelrsweet/mxml.git
$ cd mxml
$ ./configure --prefix=/usr/local
$ make
$ sudo make install
$ # second build NeXus
$ # build NeXus
$ cd ..
$ git clone https://github.com/nexusformat/code.git nexus/code
$ cd nexus
$ # build NeXus out-of-source
$ mkdir build
$ cd build
$ cmake ../code -DENABLE_HDF4=1 -DENABLE_HDF5=1 -DENABLE_MXML=1
$ cmake ../code -DENABLE_HDF5=1 -DENABLE_HDF4=0 -DENABLE_MXML=0
$ cmake --build ./ --clean-first -- -j8
$ sudo make install

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@ -449,7 +449,7 @@ where :math:`\tau_{\mathrm{Li}}=1.21`\ s is the :math:`^8`\ Li lifetime.
Functions
^^^^^^^^^^^^
The ``libLineProfile`` library currently contains the following functions:
The ``libBNMR`` library currently contains the following functions:
@ -464,10 +464,10 @@ The ``libLineProfile`` library currently contains the following functions:
The parameters are:
#. pulse length :math:`t_0` (ms)
#. relaxation rate :math:`\sigma` (ms\ :math:`^{-1}`\ )
#. pulse length :math:`t_0` (s)
#. relaxation rate :math:`\lambda` (s\ :math:`^{-1}`\ )
This function implements :math:`f(t)=e^{-\sigma t}`.
This function implements :math:`f(t)=e^{-\lambda t}`.
.. index:: SExpRlx
@ -479,11 +479,11 @@ This function implements :math:`f(t)=e^{-\sigma t}`.
The parameters are:
#. pulse length :math:`t_0` (ms)
#. relaxation rate :math:`\sigma` (ms\ :math:`^{-1}`\ )
#. pulse length :math:`t_0` (s)
#. relaxation rate :math:`\lambda` (s\ :math:`^{-1}`\ )
#. stretching exponent :math:`\beta`
This function implements :math:`f(t)=e^{-(\sigma t)^{\beta}}`.
This function implements :math:`f(t)=e^{-(\lambda t)^{\beta}}`.

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@ -1064,7 +1064,7 @@ In order to describe the operations needed for fitting and plotting, quite some
.. _msr-alpha-beta:
**alpha, beta** (fit type 2, 3, 5)
These parameters are used to correct the asymmetry for different detector efficiencies, solid angles and initial asymmetries. They are defined as :math:`\alpha = N_{0,b}/N_{0,f}` and :math:`\beta = A_{0,b}/A_{0,f}`. If the parameters are not specified in the :ref:`RUN block <msr-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:
These parameters are used to correct the asymmetry for different detector efficiencies, solid angles and initial asymmetries. They are defined as :math:`\alpha = N_{0,b}/N_{0,f}` and :math:`\beta = A_{0,b}/A_{0,f}`. If the parameters are not specified in the :ref:`RUN block <msr-run-block>`, for each one the value of 1 is assumed (for fittype 5, alpha is estimated from the ratio of :math:`\sum_i \left( N_{\mathrm{bp}}(i)+N_{\mathrm{bm}}(i) \right)` and :math:`\sum_i \left( N_{\mathrm{fp}}(i)+N_{\mathrm{fm}}(i) \right)`). Example for alpha with fit parameter number 1:
::
@ -1868,12 +1868,12 @@ Since MuMinus is quite generic, the full functional depends has to be written in
beta-NMR Asymmetry Fit (fit type 5)
+++++++++++++++++++++++++++++++++++
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 :ref:`forward <msr-forward-backward>` and :ref:`backward <msr-forward-backward>` keywords
Four histograms are needed for a beta-NMR asymmetry fit (fit type 5), two for positive helecity and two for negative. These are given by the :ref:`forward <msr-forward-backward>` and :ref:`backward <msr-forward-backward>` keywords
in the :ref:`RUN block <msr-run-block>`. Additionally, the parameters :ref:`alpha <msr-alpha-beta>` and :ref:`beta <msr-alpha-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
:ref:`background-determined intervals <msr-background-asymmetry>` or specified through :ref:`backgr.fix <msr-backgr.fix>` in the :ref:`RUN-block <msr-run-block>`.
The experimental asymmetry :math:`a(k)` then is calculated from the four histograms:
The experimental asymmetry :math:`a(k)` is then calculated from the four histograms:
.. math::
@ -1884,12 +1884,12 @@ with
* :math:`N_{\mathrm{fp}}(k)`: counts in the **forward** histogram channel with positive helicity :math:`k`
* :math:`N_{\mathrm{bp}}(k)`: counts in the **backward** histogram channel with positive helicity :math:`k`
* :math:` B_{\mathrm{fp}}`: constant background in the **forward** histogram with positive helicity (RUN block: :ref:`backgr.fix <msr-backgr.fix>` or :ref:`background <msr-background-asymmetry>`)
* :math:` B_{\mathrm{bp}}`: constant background in the **backward** histogram with positive helicity (RUN block: :ref:`backgr.fix <msr-backgr.fix>` or :ref:`background <msr-background-asymmetry>`)
* :math:`B_{\mathrm{fp}}`: constant background in the **forward** histogram with positive helicity (RUN block: :ref:`backgr.fix <msr-backgr.fix>` or :ref:`background <msr-background-asymmetry>`)
* :math:`B_{\mathrm{bp}}`: constant background in the **backward** histogram with positive helicity (RUN block: :ref:`backgr.fix <msr-backgr.fix>` or :ref:`background <msr-background-asymmetry>`)
* :math:`N_{\mathrm{fm}}(k)`: counts in the **forward** histogram channel with negative helicity :math:`k`
* :math:`N_{\mathrm{bm}}(k)`: counts in the **backward** histogram channel with negative helicity :math:`k`
* :math:` B_{\mathrm{fm}}`: constant background in the **forward** histogram with negative helicity (RUN block: :ref:`backgr.fix <msr-backgr.fix>` or :ref:`background <msr-background-asymmetry>`)
* :math:` B_{\mathrm{bm}}`: constant background in the **backward** histogram with negative helicity (RUN block: :ref:`backgr.fix <msr-backgr.fix>` or :ref:`background <msr-background-asymmetry>`)
* :math:`B_{\mathrm{fm}}`: constant background in the **forward** histogram with negative helicity (RUN block: :ref:`backgr.fix <msr-backgr.fix>` or :ref:`background <msr-background-asymmetry>`)
* :math:`B_{\mathrm{bm}}`: constant background in the **backward** histogram with negative helicity (RUN block: :ref:`backgr.fix <msr-backgr.fix>` or :ref:`background <msr-background-asymmetry>`)
This theoretical asymmetry :math:`a(t)` is used to fit the function
@ -1907,7 +1907,8 @@ For the graphical representation in plot type 5 the equation above is rearranged
.. math::
A(t)=\frac{(\alpha -1)+(\alpha +1)a(t)}{(\alpha\beta +1)+(\alpha\beta -1)a(t)}-\frac{(\alpha +1)a(t)-(\alpha -1)}{(\alpha\beta +1)+(1-\alpha\beta)a(t)}=\frac{\alpha\left[N_{\mathrm{fp}}(t)-B_{\mathrm{fp}}\right]-\left[N_{\mathrm{bp}}(t)-B_{\mathrm{bp}}\right]}{\alpha\beta\left[N_{\mathrm{fp}}(t)-B_{\mathrm{fp}}\right]+\left[N_{\mathrm{bp}}(t)-B_{\mathrm{bp}}\right]} -\frac{\alpha\left[N_{\mathrm{fm}}(t)-B_{\mathrm{fm}}\right]-\left[N_{\mathrm{bm}}(t)-B_{\mathrm{bm}}\right]}{\alpha\beta\left[N_{\mathrm{fm}}(t)-B_{\mathrm{fm}}\right]+\left[N_{\mathrm{bm}}(t)-B_{\mathrm{bm}}\right]}
A(t) &= \frac{(\alpha -1)+(\alpha +1)a(t)}{(\alpha\beta+1)+(\alpha\beta -1)a(t)}-\frac{(\alpha +1)a(t)-(\alpha-1)}{(\alpha\beta +1)+(1-\alpha\beta)a(t)} \\
&= \frac{\alpha\left[N_{\mathrm{fp}}(t)-B_{\mathrm{fp}}\right]-\left[N_{\mathrm{bp}}(t)-B_{\mathrm{bp}}\right]}{\alpha\beta\left[N_{\mathrm{fp}}(t)-B_{\mathrm{fp}}\right]+\left[N_{\mathrm{bp}}(t)-B_{\mathrm{bp}}\right]} -\frac{\alpha\left[N_{\mathrm{fm}}(t)-B_{\mathrm{fm}}\right]-\left[N_{\mathrm{bm}}(t)-B_{\mathrm{bm}}\right]}{\alpha\beta\left[N_{\mathrm{fm}}(t)-B_{\mathrm{fm}}\right]+\left[N_{\mathrm{bm}}(t)-B_{\mathrm{bm}}\right]}
and plotted together with the function given in the THEORY block.

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@ -6,7 +6,7 @@
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@ -112,12 +112,12 @@ extremely competent way to deal with his projects as well as to deal with the ch
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@ -102,12 +102,12 @@ For a detailed description see <a class="reference internal" href="user-manual.h
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@ -37,7 +37,7 @@
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@ -93,12 +93,12 @@ or send an e-mail to A. Suter at PSI.</p>
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@ -974,12 +974,12 @@
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@ -434,12 +434,12 @@ fit serves as template for the second and so on. The template field stays empty
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@ -252,12 +252,12 @@ SCRIPT COMMANDS:
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@ -923,12 +923,12 @@ the entry has been added. The last token, <tt class="docutils literal"><span cla
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@ -550,12 +550,12 @@ the corresponding fit parameter value, except the phases where the step will be
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@ -321,12 +321,12 @@ The only thing you need <tt class="docutils literal"><span class="pre">DKS</span
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@ -96,7 +96,8 @@ their header packages:</p>
</dl>
<dl class="docutils" id="index-9">
<dt><strong>minixml</strong></dt>
<dd>A small <tt class="docutils literal"><span class="pre">XML</span></tt> library that can be used to read and write <tt class="docutils literal"><span class="pre">XML</span></tt> and <tt class="docutils literal"><span class="pre">XML</span></tt>-like data files. <em>Required version ≥ 2.2</em> (see <a class="reference external" href="http://www.minixml.org/">minixml</a>).</dd>
<dd>A small <tt class="docutils literal"><span class="pre">XML</span></tt> library that can be used to read and write <tt class="docutils literal"><span class="pre">XML</span></tt> and <tt class="docutils literal"><span class="pre">XML</span></tt>-like data files. <em>Required version ≥ 2.2</em> (see <a class="reference external" href="http://www.minixml.org/">minixml</a>).
Currently the <tt class="docutils literal"><span class="pre">MXML</span></tt> support in <tt class="docutils literal"><span class="pre">NeXus</span></tt> is broken and hence you will <strong>not</strong> need to install <tt class="docutils literal"><span class="pre">minixml</span></tt> for the time being.</dd>
</dl>
<dl class="docutils" id="index-10">
<dt><strong>NeXus</strong></dt>
@ -177,24 +178,21 @@ the source code from the corresponding website, or to clone the git repo. If you
<span id="index-15"></span><h4>Installation of NeXus requirements (optional)<a class="headerlink" href="#installation-of-nexus-requirements-optional" title="Permalink to this headline"></a></h4>
<p><em>Only</em> if <tt class="docutils literal"><span class="pre">musrfit</span></tt> should support reading/writing data files in the <tt class="docutils literal"><span class="pre">NeXus</span></tt> format the further required
software has to be set up. The required libraries and header files could either be available through the user&#8217;s
GNU/Linux distribution or if this is not the case, the packages can be installed from the source code. The necessary
packages to build <tt class="docutils literal"><span class="pre">NeXus</span></tt> are <tt class="docutils literal"><span class="pre">MXML</span></tt>, (<tt class="docutils literal"><span class="pre">HDF4</span></tt>), and <tt class="docutils literal"><span class="pre">HDF5</span></tt>. This means, for a rpm-package based distro try something like:</p>
GNU/Linux distribution or if this is not the case, the packages can be installed from the source code. In principle
NeXus should support <tt class="docutils literal"><span class="pre">MXML</span></tt>, <tt class="docutils literal"><span class="pre">HDF4</span></tt>, and <tt class="docutils literal"><span class="pre">HDF5</span></tt>. At the time of this writing, the <tt class="docutils literal"><span class="pre">MXML</span></tt> support in the
NeXus project is broken, and <tt class="docutils literal"><span class="pre">HDF4</span></tt> is outdated on most platforms, hence currently only the <tt class="docutils literal"><span class="pre">HDF5</span></tt> binding is
used. Hence, the necessary package to build <tt class="docutils literal"><span class="pre">NeXus</span></tt> is <tt class="docutils literal"><span class="pre">HDF5</span></tt>. This means, for a rpm-package based distro try something like:</p>
<blockquote>
<div><div class="highlight-bash"><div class="highlight"><pre><span></span>$ yum install mxml-devel hdf-devel hdf5-devel
<div><div class="highlight-bash"><div class="highlight"><pre><span></span>$ yum install hdf5-devel
</pre></div>
</div>
</div></blockquote>
<p>and on a deb-package based distro try something like:</p>
<blockquote>
<div><div class="highlight-bash"><div class="highlight"><pre><span></span>$ apt-get install libmxml-dev libhdf4-dev libhdf5-dev
<div><div class="highlight-bash"><div class="highlight"><pre><span></span>$ apt-get install libhdf5-dev
</pre></div>
</div>
</div></blockquote>
<div class="admonition note">
<p class="first admonition-title">Note</p>
<p class="last"><tt class="docutils literal"><span class="pre">HDF4</span></tt> support within <tt class="docutils literal"><span class="pre">NeXus</span></tt> will be dropped by <tt class="docutils literal"><span class="pre">musrfit</span></tt> in the near future. If you <em>not</em> urgently need
to read old <tt class="docutils literal"><span class="pre">ISIS</span> <span class="pre">NeXus</span></tt> files, you safely can drop it.</p>
</div>
<p><strong>Only NeXus Version ≥ 4.4 is support!</strong></p>
<p>Even though there might exist binary packages for the <tt class="docutils literal"><span class="pre">NeXus</span></tt> library, it is best to build and
install it directly from the source code which can be found <a class="reference external" href="https://github.com/nexusformat/code">here</a>.</p>
@ -208,10 +206,7 @@ $ git clone https://github.com/nexusformat/code.git
$ <span class="c1"># next we will build NeXus out-of-source</span>
$ mkdir build
$ <span class="nb">cd</span> build
$ <span class="c1"># The next line only if HDF4 support is needed</span>
$ cmake -DENABLE_HDF5<span class="o">=</span><span class="m">1</span> -DENABLE_HDF4<span class="o">=</span><span class="m">1</span> -DENABLE_MXML<span class="o">=</span><span class="m">1</span> ../code
$ <span class="c1"># The next line if HDF4 support is NOT needed</span>
$ cmake -DENABLE_HDF5<span class="o">=</span><span class="m">1</span> -DENABLE_MXML<span class="o">=</span><span class="m">1</span> ../code
$ cmake -DENABLE_HDF5<span class="o">=</span><span class="m">1</span> -DENABLE_HDF4<span class="o">=</span><span class="m">0</span> -DENABLE_MXML<span class="o">=</span><span class="m">0</span> ../code
$ cmake --build ./ --clean-first
$ <span class="c1"># make install needs either to be carried out as root or sudo depending on your linux flavour.</span>
$ sudo make install
@ -500,10 +495,7 @@ the later handling will be easier if a symbolic link to these files is created n
to be set up. Under <tt class="docutils literal"><span class="pre">Cygwin</span></tt> of all the required libraries only <tt class="docutils literal"><span class="pre">HDF5</span></tt> is available. The packages <tt class="docutils literal"><span class="pre">hdf5</span></tt> and
<tt class="docutils literal"><span class="pre">libhdf5-devel</span></tt> can be installed through the <tt class="docutils literal"><span class="pre">Cygwin</span></tt> setup. One should also make sure that <tt class="docutils literal"><span class="pre">bison</span></tt>, <tt class="docutils literal"><span class="pre">flex</span></tt>
and a package containing <tt class="docutils literal"><span class="pre">/usr/lib/librpc.a</span></tt> (<em>e.g.</em> <tt class="docutils literal"><span class="pre">sunrpc</span> <span class="pre">=</span> <span class="pre">4.0-3</span></tt>, but <em>not</em> <tt class="docutils literal"><span class="pre">sunrpc</span> <span class="pre">=</span> <span class="pre">4.0-4</span></tt>) are installed.</p>
<p>All other libraries have to be built from the sources. The following lines will track the installation of <tt class="docutils literal"><span class="pre">JPEG</span> <span class="pre">6b</span></tt>,
<tt class="docutils literal"><span class="pre">MXML</span> <span class="pre">2.9</span></tt>, <tt class="docutils literal"><span class="pre">HDF</span> <span class="pre">4.2.7-patch1</span></tt>, and <tt class="docutils literal"><span class="pre">NeXus</span> <span class="pre">4.3.2</span></tt>. The version numbers and source-code locations might of
course change with time but should be easily adjustable.</p>
<p><em>Only</em> <tt class="docutils literal"><span class="pre">NeXus</span></tt> version ≥ 4.4 is support!</p>
<p><strong>Only NeXus Version ≥ 4.4 is support!</strong></p>
<div class="highlight-bash"><div class="highlight"><pre><span></span>$ <span class="nb">cd</span>
$ mkdir nexus
$ <span class="nb">cd</span> nexus
@ -513,18 +505,6 @@ $ ./configure --prefix<span class="o">=</span>/usr/local --enable-static
$ make
$ make install
$ <span class="nb">cd</span> ..
$ curl www.msweet.org/files/project3/mxml-2.9.tar.gz -G <span class="p">|</span> tar xz
$ <span class="nb">cd</span> mxml-2.9
$ ./configure --prefix<span class="o">=</span>/usr/local --enable-static
$ make
$ make install
$ <span class="nb">cd</span> ..
$ curl http://www.hdfgroup.org/ftp/HDF/HDF_Current/src/hdf-4.2.7-patch1.tar.gz -G <span class="p">|</span> tar xz
$ <span class="nb">cd</span> hdf-4.2.7-patch1
$ ./configure --prefix<span class="o">=</span>/usr/local --enable-static --disable-fortran --with-jpeg<span class="o">=</span>/usr/local
$ make
$ make install
$ <span class="nb">cd</span> ..
$ <span class="c1"># create a directory for the NeXus source code</span>
$ mkdir nexus
$ <span class="nb">cd</span> nexus
@ -533,7 +513,7 @@ $ git clone https://github.com/nexusformat/code.git
$ <span class="c1"># next we will build NeXus out-of-source</span>
$ mkdir build
$ <span class="nb">cd</span> build
$ cmake -DENABLE_HDF5<span class="o">=</span><span class="m">1</span> -DENABLE_HDF4<span class="o">=</span><span class="m">1</span> -DENABLE_MXML<span class="o">=</span><span class="m">1</span> ../code
$ cmake -DENABLE_HDF5<span class="o">=</span><span class="m">1</span> -DENABLE_HDF4<span class="o">=</span><span class="m">0</span> -DENABLE_MXML<span class="o">=</span><span class="m">0</span> ../code
$ make
$ make install
</pre></div>
@ -770,20 +750,12 @@ please change over to <tt class="docutils literal"><span class="pre">musredit</s
<div class="section" id="index-28">
<span id="id14"></span><h4>Installation of NeXus requirements (optional)<a class="headerlink" href="#index-28" title="Permalink to this headline"></a></h4>
<p><em>Only</em> if <tt class="docutils literal"><span class="pre">musrfit</span></tt> should support reading data files in the <tt class="docutils literal"><span class="pre">NeXus</span></tt> format the further required packages are set up:</p>
<div class="highlight-bash"><div class="highlight"><pre><span></span>$ sudo port -v install hdf4 hdf5
<div class="highlight-bash"><div class="highlight"><pre><span></span>$ sudo port -v install hdf5
</pre></div>
</div>
<p>Unfortunately, the <tt class="docutils literal"><span class="pre">minixml</span></tt> and <tt class="docutils literal"><span class="pre">NeXus</span></tt> libraries have to be compiled and installed directly from the source code.
Given the respective version numbers of 2.9 and 4.4.2 (which are subject to change with time.
Only <tt class="docutils literal"><span class="pre">NeXus</span></tt> Version ≥ 4.4 is support!) this can be achieved for example by:</p>
<div class="highlight-bash"><div class="highlight"><pre><span></span>$ <span class="c1"># get and instal Mini-XML</span>
$ <span class="nb">cd</span> <span class="nv">$HOME</span>/Applications
$ git clone https://github.com/michaelrsweet/mxml.git
$ <span class="nb">cd</span> mxml
$ ./configure --prefix<span class="o">=</span>/usr/local
$ make
$ sudo make install
$ <span class="c1"># get and install NeXus</span>
<p><strong>Only NeXus Version ≥ 4.4 is support!</strong></p>
<p>To get things compiled do:</p>
<div class="highlight-bash"><div class="highlight"><pre><span></span>$ <span class="c1"># get and install NeXus</span>
$ <span class="nb">cd</span> <span class="nv">$HOME</span>/Applications
$ <span class="c1"># get the source code from the master repository</span>
$ git clone https://github.com/nexusformat/code.git nexus/code
@ -791,7 +763,7 @@ $ <span class="c1"># next we will build NeXus out-of-source</span>
$ <span class="nb">cd</span> nexus
$ mkdir build
$ <span class="nb">cd</span> build
$ cmake -DENABLE_HDF5<span class="o">=</span><span class="m">1</span> -DENABLE_HDF4<span class="o">=</span><span class="m">1</span> -DENABLE_MXML<span class="o">=</span><span class="m">1</span> ../code
$ cmake -DENABLE_HDF5<span class="o">=</span><span class="m">1</span> -DENABLE_HDF4<span class="o">=</span><span class="m">0</span> -DENABLE_MXML<span class="o">=</span><span class="m">0</span> ../code
$ make
$ sudo make install
</pre></div>
@ -956,24 +928,17 @@ packages can be installed through Fink (check for the most recent versions):</p>
<div class="highlight-python"><div class="highlight"><pre><span></span>libjpeg hdf hdf5-cpp11 hdf5-cpp11-shlibs
</pre></div>
</div>
<p>Unfortunately, the <tt class="docutils literal"><span class="pre">minixml</span></tt> and <tt class="docutils literal"><span class="pre">NeXus</span></tt> libraries have to be compiled and installed directly from
the source code. Given the respective version numbers of 2.9 and 4.3.2 (which are subject to change with time)
<p>Unfortunately, the <tt class="docutils literal"><span class="pre">NeXus</span></tt> libraries have to be compiled and installed directly from
the source code. Given the respective version number 4.4 (which are subject to change with time)
this can be achieved for example by:</p>
<div class="highlight-bash"><div class="highlight"><pre><span></span>$ <span class="c1"># first build Mini-XML</span>
$ <span class="nb">cd</span> <span class="nv">$HOME</span>/Applications
$ git clone https://github.com/michaelrsweet/mxml.git
$ <span class="nb">cd</span> mxml
$ ./configure --prefix<span class="o">=</span>/usr/local
$ make
$ sudo make install
$ <span class="c1"># second build NeXus</span>
<div class="highlight-bash"><div class="highlight"><pre><span></span>$ <span class="c1"># build NeXus</span>
$ <span class="nb">cd</span> ..
$ git clone https://github.com/nexusformat/code.git nexus/code
$ <span class="nb">cd</span> nexus
$ <span class="c1"># build NeXus out-of-source</span>
$ mkdir build
$ <span class="nb">cd</span> build
$ cmake ../code -DENABLE_HDF4<span class="o">=</span><span class="m">1</span> -DENABLE_HDF5<span class="o">=</span><span class="m">1</span> -DENABLE_MXML<span class="o">=</span><span class="m">1</span>
$ cmake ../code -DENABLE_HDF5<span class="o">=</span><span class="m">1</span> -DENABLE_HDF4<span class="o">=</span><span class="m">0</span> -DENABLE_MXML<span class="o">=</span><span class="m">0</span>
$ cmake --build ./ --clean-first -- -j8
$ sudo make install
</pre></div>
@ -1315,12 +1280,12 @@ $ musrview test-histo-ROOT-NPP.msr
<li class="right" >
<a href="user-libs.html" title="Documentation of user libs (user functions)"
>previous</a> |</li>
<li><a href="index.html">musrfit 1.5.0 documentation</a> &raquo;</li>
<li><a href="index.html">musrfit 1.5.1 documentation</a> &raquo;</li>
</ul>
</div>
<div class="footer">
&copy; Copyright 2019, Andreas Suter.
Last updated on May 15, 2019.
Last updated on Jul 24, 2019.
Created using <a href="http://sphinx-doc.org/">Sphinx</a> 1.2.3.
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@ -6,7 +6,7 @@
<head>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
<title>Tutorial for musrfit &mdash; musrfit 1.5.0 documentation</title>
<title>Tutorial for musrfit &mdash; musrfit 1.5.1 documentation</title>
<link rel="stylesheet" href="_static/nature.css" type="text/css" />
<link rel="stylesheet" href="_static/pygments.css" type="text/css" />
@ -14,7 +14,7 @@
<script type="text/javascript">
var DOCUMENTATION_OPTIONS = {
URL_ROOT: './',
VERSION: '1.5.0',
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COLLAPSE_INDEX: false,
FILE_SUFFIX: '.html',
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@ -24,7 +24,7 @@
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<link rel="prev" title="How to Cite musrfit?" href="cite.html" />
</head>
@ -41,7 +41,7 @@
<li class="right" >
<a href="cite.html" title="How to Cite musrfit?"
accesskey="P">previous</a> |</li>
<li><a href="index.html">musrfit 1.5.0 documentation</a> &raquo;</li>
<li><a href="index.html">musrfit 1.5.1 documentation</a> &raquo;</li>
</ul>
</div>
@ -443,12 +443,12 @@ For a complete description please refer to the manuals of <a class="reference in
<li class="right" >
<a href="cite.html" title="How to Cite musrfit?"
>previous</a> |</li>
<li><a href="index.html">musrfit 1.5.0 documentation</a> &raquo;</li>
<li><a href="index.html">musrfit 1.5.1 documentation</a> &raquo;</li>
</ul>
</div>
<div class="footer">
&copy; Copyright 2019, Andreas Suter.
Last updated on May 15, 2019.
Last updated on Jul 24, 2019.
Created using <a href="http://sphinx-doc.org/">Sphinx</a> 1.2.3.
</div>
</body>

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@ -6,7 +6,7 @@
<head>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
<title>Documentation of user libs (user functions) &mdash; musrfit 1.5.0 documentation</title>
<title>Documentation of user libs (user functions) &mdash; musrfit 1.5.1 documentation</title>
<link rel="stylesheet" href="_static/nature.css" type="text/css" />
<link rel="stylesheet" href="_static/pygments.css" type="text/css" />
@ -14,7 +14,7 @@
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var DOCUMENTATION_OPTIONS = {
URL_ROOT: './',
VERSION: '1.5.0',
VERSION: '1.5.1',
COLLAPSE_INDEX: false,
FILE_SUFFIX: '.html',
HAS_SOURCE: true
@ -24,7 +24,7 @@
<script type="text/javascript" src="_static/underscore.js"></script>
<script type="text/javascript" src="_static/doctools.js"></script>
<script type="text/javascript" src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script>
<link rel="top" title="musrfit 1.5.0 documentation" href="index.html" />
<link rel="top" title="musrfit 1.5.1 documentation" href="index.html" />
<link rel="next" title="Setting up musrfit on Different Platforms" href="setup-standard.html" />
<link rel="prev" title="User manual" href="user-manual.html" />
</head>
@ -41,7 +41,7 @@
<li class="right" >
<a href="user-manual.html" title="User manual"
accesskey="P">previous</a> |</li>
<li><a href="index.html">musrfit 1.5.0 documentation</a> &raquo;</li>
<li><a href="index.html">musrfit 1.5.1 documentation</a> &raquo;</li>
</ul>
</div>
@ -394,28 +394,28 @@ The asymmetry is measured both during the pulse and afterwards. For a a general
<p>where <span class="math">\(\tau_{\mathrm{Li}}=1.21\)</span>s is the <span class="math">\(^8\)</span>Li lifetime.</p>
<div class="section" id="functions">
<h4>Functions<a class="headerlink" href="#functions" title="Permalink to this headline"></a></h4>
<p>The <tt class="docutils literal"><span class="pre">libLineProfile</span></tt> library currently contains the following functions:</p>
<p>The <tt class="docutils literal"><span class="pre">libBNMR</span></tt> library currently contains the following functions:</p>
<p id="index-17"><strong>Exponential relaxation</strong></p>
<div class="highlight-python"><div class="highlight"><pre><span></span>userFcn libBNMR ExpRlx 1 2
</pre></div>
</div>
<p>The parameters are:</p>
<ol class="arabic simple">
<li>pulse length <span class="math">\(t_0\)</span> (ms)</li>
<li>relaxation rate <span class="math">\(\sigma\)</span> (ms<span class="math">\(^{-1}\)</span>)</li>
<li>pulse length <span class="math">\(t_0\)</span> (s)</li>
<li>relaxation rate <span class="math">\(\lambda\)</span> (s<span class="math">\(^{-1}\)</span>)</li>
</ol>
<p>This function implements <span class="math">\(f(t)=e^{-\sigma t}\)</span>.</p>
<p>This function implements <span class="math">\(f(t)=e^{-\lambda t}\)</span>.</p>
<p id="index-18"><strong>Stretched exponential relaxation</strong></p>
<div class="highlight-python"><div class="highlight"><pre><span></span>userFcn libBNMR SExpRlx 1 2 3
</pre></div>
</div>
<p>The parameters are:</p>
<ol class="arabic simple">
<li>pulse length <span class="math">\(t_0\)</span> (ms)</li>
<li>relaxation rate <span class="math">\(\sigma\)</span> (ms<span class="math">\(^{-1}\)</span>)</li>
<li>pulse length <span class="math">\(t_0\)</span> (s)</li>
<li>relaxation rate <span class="math">\(\lambda\)</span> (s<span class="math">\(^{-1}\)</span>)</li>
<li>stretching exponent <span class="math">\(\beta\)</span></li>
</ol>
<p>This function implements <span class="math">\(f(t)=e^{-(\sigma t)^{\beta}}\)</span>.</p>
<p>This function implements <span class="math">\(f(t)=e^{-(\lambda t)^{\beta}}\)</span>.</p>
</div>
</div>
<div class="section" id="liblineprofile">
@ -662,12 +662,12 @@ K(m)&amp;=\int_0^{\pi/2}\frac{\mathrm d\varphi}{\sqrt{1-m^2\sin^2{\varphi}}},\en
<li class="right" >
<a href="user-manual.html" title="User manual"
>previous</a> |</li>
<li><a href="index.html">musrfit 1.5.0 documentation</a> &raquo;</li>
<li><a href="index.html">musrfit 1.5.1 documentation</a> &raquo;</li>
</ul>
</div>
<div class="footer">
&copy; Copyright 2019, Andreas Suter.
Last updated on May 15, 2019.
Last updated on Jul 24, 2019.
Created using <a href="http://sphinx-doc.org/">Sphinx</a> 1.2.3.
</div>
</body>

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@ -6,7 +6,7 @@
<head>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
<title>User manual &mdash; musrfit 1.5.0 documentation</title>
<title>User manual &mdash; musrfit 1.5.1 documentation</title>
<link rel="stylesheet" href="_static/nature.css" type="text/css" />
<link rel="stylesheet" href="_static/pygments.css" type="text/css" />
@ -14,7 +14,7 @@
<script type="text/javascript">
var DOCUMENTATION_OPTIONS = {
URL_ROOT: './',
VERSION: '1.5.0',
VERSION: '1.5.1',
COLLAPSE_INDEX: false,
FILE_SUFFIX: '.html',
HAS_SOURCE: true
@ -24,7 +24,7 @@
<script type="text/javascript" src="_static/underscore.js"></script>
<script type="text/javascript" src="_static/doctools.js"></script>
<script type="text/javascript" src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script>
<link rel="top" title="musrfit 1.5.0 documentation" href="index.html" />
<link rel="top" title="musrfit 1.5.1 documentation" href="index.html" />
<link rel="next" title="Documentation of user libs (user functions)" href="user-libs.html" />
<link rel="prev" title="Tutorial for musrfit" href="tutorial.html" />
</head>
@ -41,7 +41,7 @@
<li class="right" >
<a href="tutorial.html" title="Tutorial for musrfit"
accesskey="P">previous</a> |</li>
<li><a href="index.html">musrfit 1.5.0 documentation</a> &raquo;</li>
<li><a href="index.html">musrfit 1.5.1 documentation</a> &raquo;</li>
</ul>
</div>
@ -1230,7 +1230,7 @@ etc.
</dl>
<span id="index-20"></span><dl class="docutils" id="msr-alpha-beta">
<dt><strong>alpha, beta</strong> (fit type 2, 3, 5)</dt>
<dd><p class="first">These parameters are used to correct the asymmetry for different detector efficiencies, solid angles and initial asymmetries. They are defined as <span class="math">\(\alpha = N_{0,b}/N_{0,f}\)</span> and <span class="math">\(\beta = A_{0,b}/A_{0,f}\)</span>. If the parameters are not specified in the <a class="reference internal" href="#msr-run-block"><em>RUN block</em></a>, 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:</p>
<dd><p class="first">These parameters are used to correct the asymmetry for different detector efficiencies, solid angles and initial asymmetries. They are defined as <span class="math">\(\alpha = N_{0,b}/N_{0,f}\)</span> and <span class="math">\(\beta = A_{0,b}/A_{0,f}\)</span>. If the parameters are not specified in the <a class="reference internal" href="#msr-run-block"><em>RUN block</em></a>, for each one the value of 1 is assumed (for fittype 5, alpha is estimated from the ratio of <span class="math">\(\sum_i \left( N_{\mathrm{bp}}(i)+N_{\mathrm{bm}}(i) \right)\)</span> and <span class="math">\(\sum_i \left( N_{\mathrm{fp}}(i)+N_{\mathrm{fm}}(i) \right)\)</span>). Example for alpha with fit parameter number 1:</p>
<div class="last highlight-python"><div class="highlight"><pre><span></span>alpha 1
</pre></div>
</div>
@ -1880,11 +1880,11 @@ the single histogram RRF fit apply: <strong>if you not urgently need it: do not
</div>
<div class="section" id="beta-nmr-asymmetry-fit-fit-type-5">
<span id="bnmr-asymmetry-fit"></span><span id="index-69"></span><h3>beta-NMR Asymmetry Fit (fit type 5)<a class="headerlink" href="#beta-nmr-asymmetry-fit-fit-type-5" title="Permalink to this headline"></a></h3>
<p>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 <a class="reference internal" href="#msr-forward-backward"><em>forward</em></a> and <a class="reference internal" href="#msr-forward-backward"><em>backward</em></a> keywords
<p>Four histograms are needed for a beta-NMR asymmetry fit (fit type 5), two for positive helecity and two for negative. These are given by the <a class="reference internal" href="#msr-forward-backward"><em>forward</em></a> and <a class="reference internal" href="#msr-forward-backward"><em>backward</em></a> keywords
in the <a class="reference internal" href="#msr-run-block"><em>RUN block</em></a>. Additionally, the parameters <a class="reference internal" href="#msr-alpha-beta"><em>alpha</em></a> and <a class="reference internal" href="#msr-alpha-beta"><em>beta</em></a> 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
<a class="reference internal" href="#msr-background-asymmetry"><em>background-determined intervals</em></a> or specified through <a class="reference internal" href="#msr-backgr-fix"><em>backgr.fix</em></a> in the <a class="reference internal" href="#msr-run-block"><em>RUN-block</em></a>.</p>
<p>The experimental asymmetry <span class="math">\(a(k)\)</span> then is calculated from the four histograms:</p>
<p>The experimental asymmetry <span class="math">\(a(k)\)</span> is then calculated from the four histograms:</p>
<div class="math">
\[a(k)=\frac{\left[N_{\mathrm{fp}}(k)-B_{\mathrm{fp}}\right]-\left[N_{\mathrm{bp}}(k)-B_{\mathrm{bp}}\right]}{\left[N_{\mathrm{fp}}(k)-B_{\mathrm{fp}}\right]+\left[N_{\mathrm{bp}}(k)-B_{\mathrm{bp}}\right]}
- \frac{\left[N_{\mathrm{fm}}(k)-B_{\mathrm{fm}}\right]-\left[N_{\mathrm{bm}}(k)-B_{\mathrm{bm}}\right]}{\left[N_{\mathrm{fm}}(k)-B_{\mathrm{fm}}\right]+\left[N_{\mathrm{bm}}(k)-B_{\mathrm{bm}}\right]},\]</div>
@ -1893,12 +1893,12 @@ efficiencies, solid angles and initial asymmetries of the two detectors can be s
<div><ul class="simple">
<li><span class="math">\(N_{\mathrm{fp}}(k)\)</span>: counts in the <strong>forward</strong> histogram channel with positive helicity <span class="math">\(k\)</span></li>
<li><span class="math">\(N_{\mathrm{bp}}(k)\)</span>: counts in the <strong>backward</strong> histogram channel with positive helicity <span class="math">\(k\)</span></li>
<li>:math:` B_{mathrm{fp}}`: constant background in the <strong>forward</strong> histogram with positive helicity (RUN block: <a class="reference internal" href="#msr-backgr-fix"><em>backgr.fix</em></a> or <a class="reference internal" href="#msr-background-asymmetry"><em>background</em></a>)</li>
<li>:math:` B_{mathrm{bp}}`: constant background in the <strong>backward</strong> histogram with positive helicity (RUN block: <a class="reference internal" href="#msr-backgr-fix"><em>backgr.fix</em></a> or <a class="reference internal" href="#msr-background-asymmetry"><em>background</em></a>)</li>
<li><span class="math">\(B_{\mathrm{fp}}\)</span>: constant background in the <strong>forward</strong> histogram with positive helicity (RUN block: <a class="reference internal" href="#msr-backgr-fix"><em>backgr.fix</em></a> or <a class="reference internal" href="#msr-background-asymmetry"><em>background</em></a>)</li>
<li><span class="math">\(B_{\mathrm{bp}}\)</span>: constant background in the <strong>backward</strong> histogram with positive helicity (RUN block: <a class="reference internal" href="#msr-backgr-fix"><em>backgr.fix</em></a> or <a class="reference internal" href="#msr-background-asymmetry"><em>background</em></a>)</li>
<li><span class="math">\(N_{\mathrm{fm}}(k)\)</span>: counts in the <strong>forward</strong> histogram channel with negative helicity <span class="math">\(k\)</span></li>
<li><span class="math">\(N_{\mathrm{bm}}(k)\)</span>: counts in the <strong>backward</strong> histogram channel with negative helicity <span class="math">\(k\)</span></li>
<li>:math:` B_{mathrm{fm}}`: constant background in the <strong>forward</strong> histogram with negative helicity (RUN block: <a class="reference internal" href="#msr-backgr-fix"><em>backgr.fix</em></a> or <a class="reference internal" href="#msr-background-asymmetry"><em>background</em></a>)</li>
<li>:math:` B_{mathrm{bm}}`: constant background in the <strong>backward</strong> histogram with negative helicity (RUN block: <a class="reference internal" href="#msr-backgr-fix"><em>backgr.fix</em></a> or <a class="reference internal" href="#msr-background-asymmetry"><em>background</em></a>)</li>
<li><span class="math">\(B_{\mathrm{fm}}\)</span>: constant background in the <strong>forward</strong> histogram with negative helicity (RUN block: <a class="reference internal" href="#msr-backgr-fix"><em>backgr.fix</em></a> or <a class="reference internal" href="#msr-background-asymmetry"><em>background</em></a>)</li>
<li><span class="math">\(B_{\mathrm{bm}}\)</span>: constant background in the <strong>backward</strong> histogram with negative helicity (RUN block: <a class="reference internal" href="#msr-backgr-fix"><em>backgr.fix</em></a> or <a class="reference internal" href="#msr-background-asymmetry"><em>background</em></a>)</li>
</ul>
</div></blockquote>
<p>This theoretical asymmetry <span class="math">\(a(t)\)</span> is used to fit the function</p>
@ -1914,7 +1914,8 @@ efficiencies, solid angles and initial asymmetries of the two detectors can be s
</div></blockquote>
<p>For the graphical representation in plot type 5 the equation above is rearranged to get <span class="math">\(A(t)\)</span>:</p>
<div class="math">
\[A(t)=\frac{(\alpha -1)+(\alpha +1)a(t)}{(\alpha\beta +1)+(\alpha\beta -1)a(t)}-\frac{(\alpha +1)a(t)-(\alpha -1)}{(\alpha\beta +1)+(1-\alpha\beta)a(t)}=\frac{\alpha\left[N_{\mathrm{fp}}(t)-B_{\mathrm{fp}}\right]-\left[N_{\mathrm{bp}}(t)-B_{\mathrm{bp}}\right]}{\alpha\beta\left[N_{\mathrm{fp}}(t)-B_{\mathrm{fp}}\right]+\left[N_{\mathrm{bp}}(t)-B_{\mathrm{bp}}\right]} -\frac{\alpha\left[N_{\mathrm{fm}}(t)-B_{\mathrm{fm}}\right]-\left[N_{\mathrm{bm}}(t)-B_{\mathrm{bm}}\right]}{\alpha\beta\left[N_{\mathrm{fm}}(t)-B_{\mathrm{fm}}\right]+\left[N_{\mathrm{bm}}(t)-B_{\mathrm{bm}}\right]}\]</div>
\[\begin{split}A(t) &amp;= \frac{(\alpha -1)+(\alpha +1)a(t)}{(\alpha\beta+1)+(\alpha\beta -1)a(t)}-\frac{(\alpha +1)a(t)-(\alpha-1)}{(\alpha\beta +1)+(1-\alpha\beta)a(t)} \\
&amp;= \frac{\alpha\left[N_{\mathrm{fp}}(t)-B_{\mathrm{fp}}\right]-\left[N_{\mathrm{bp}}(t)-B_{\mathrm{bp}}\right]}{\alpha\beta\left[N_{\mathrm{fp}}(t)-B_{\mathrm{fp}}\right]+\left[N_{\mathrm{bp}}(t)-B_{\mathrm{bp}}\right]} -\frac{\alpha\left[N_{\mathrm{fm}}(t)-B_{\mathrm{fm}}\right]-\left[N_{\mathrm{bm}}(t)-B_{\mathrm{bm}}\right]}{\alpha\beta\left[N_{\mathrm{fm}}(t)-B_{\mathrm{fm}}\right]+\left[N_{\mathrm{bm}}(t)-B_{\mathrm{bm}}\right]}\end{split}\]</div>
<p>and plotted together with the function given in the THEORY block.</p>
</div>
<div class="section" id="non-mgrsr-fit-fit-type-8">
@ -2288,12 +2289,12 @@ In case this cannot be ensured, the parallelization can be disabled by <em>&#821
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Last updated on May 15, 2019.
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