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Docu update

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Added information about the not yet documented functions for internal fields with Gaussian/Lorentzian broadening.
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suter_a 2019-01-21 13:36:15 +01:00
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@ -656,33 +656,39 @@ spinGlass spg :math:`\lambda (\mu \mathrm{s}^{-1})`, \ :math:`\fra
rdAnisoHf rahf :math:`\nu` (MHz), \ :math:`\frac{1}{6} (1-\nu t/2) \exp(-\nu t/2) +` [#n7]_
:math:`\lambda (\mu \mathrm{s}^{-1})` :math:`+ \frac{1}{3} (1 - \nu t/4) \exp(-\frac{\nu t + 2.44949 \lambda t}{4})`
TFieldCos tf :math:`\varphi (^\circ), \nu` (MHz) :math:`\cos\left(2\pi\nu t + \frac{\pi \varphi}{180}\right)`
internFld if :math:`\alpha (1), \varphi (^\circ)`, \ :math:`\alpha \cos\left(2\pi\nu t + \frac{\pi \varphi}{180}\right) \exp(\lambda_{\rm T}t) +`
internFld if :math:`\alpha (1), \varphi (^\circ)`, \ :math:`\alpha \cos\left(2\pi\nu t + \frac{\pi \varphi}{180}\right) \exp(-\lambda_{\rm T}t) +`
:math:`\nu` (MHz), \ :math:`+ (1-\alpha) \exp(-\lambda_{\rm L} t)`
:math:`\lambda_{\rm T} (\mu \mathrm{s}^{-1})`,\
:math:`\lambda_{\rm L} (\mu \mathrm{s}^{-1})`
Bessel b :math:`\varphi (^\circ), \nu` (MHz) :math:`j_0\left(2\pi\nu t + \frac{\pi \varphi}{180}\right)`
internbsl ib :math:`\alpha (1), \varphi (^\circ)`, \ :math:`\alpha j_0\left(2\pi\nu t + \frac{\pi \varphi}{180}\right) \exp(\lambda_{\rm T}t) +`
internbsl ib :math:`\alpha (1), \varphi (^\circ)`, \ :math:`\alpha j_0\left(2\pi\nu t + \frac{\pi \varphi}{180}\right) \exp(-\lambda_{\rm T}t) +`
:math:`\nu` (MHz), \ :math:`+ (1-\alpha) \exp(-\lambda_{\rm L} t)`
:math:`\lambda_{\rm T} (\mu \mathrm{s}^{-1})`,\
:math:`\lambda_{\rm L} (\mu \mathrm{s}^{-1})`
internFldGK ifgk :math:`\alpha (1), \nu` (MHz), \ :math:`\alpha\left[\cos(2\pi\nu t)-\frac{\sigma^2 t}{2\pi\nu}\sin(2\pi\nu t)\right]\exp(-\sigma^2 t^2/2)+`
:math:`\sigma (\mu \mathrm{s}^{-1})`, \ :math:`+ (1-\alpha) \exp(-(\lambda t)^\beta)` [#n8]_
:math:`\lambda (\mu\mathrm{s}^{-1}), \beta (1)`
internFldLL ifll :math:`\alpha (1), \nu` (MHz), \ :math:`\alpha\left[\cos(2\pi\nu t)-\frac{a}{2\pi\nu}\sin(2\pi\nu t)\right]\exp(-a t)+`
:math:`a (\mu \mathrm{s}^{-1})`, \ :math:`+ (1-\alpha) \exp(-(\lambda t)^\beta)` [#n9]_
:math:`\lambda (\mu\mathrm{s}^{-1}), \beta (1)`
abragam ab :math:`\sigma (\mu \mathrm{s}^{-1})`, \ :math:`\exp\left[-\frac{\sigma^2}{\gamma^2} (e^{-\gamma t} - 1 + \gamma t)\right]`
:math:`\gamma` (MHz)
skewedGss skg :math:`\varphi (^\circ), \nu` (MHz) \ :math:`\frac{\sigma_{-}}{\sigma_{+}+\sigma_{-}} \exp\left[\frac{\sigma_{-}^2 t^2}{2}\right] \left\{\cos(2\pi\nu t + \frac{\pi\varphi}{180}) + \sin(2\pi\nu t + \frac{\pi\varphi}{180}) \mathrm{Erfi}\left(\frac{\sigma_{-} t}{\sqrt{2}}\right)\right\} +` [#n8]_
skewedGss skg :math:`\varphi (^\circ), \nu` (MHz) \ :math:`\frac{\sigma_{-}}{\sigma_{+}+\sigma_{-}} \exp\left[\frac{\sigma_{-}^2 t^2}{2}\right] \left\{\cos(2\pi\nu t + \frac{\pi\varphi}{180}) + \sin(2\pi\nu t + \frac{\pi\varphi}{180}) \mathrm{Erfi}\left(\frac{\sigma_{-} t}{\sqrt{2}}\right)\right\} +` [#n10]_
:math:`\sigma_{+} (\mu \mathrm{s}^{-1})`, \ :math:`+ \frac{\sigma_{+}}{\sigma_{+}+\sigma_{-}} \exp\left[\frac{\sigma_{+}^2 t^2}{2}\right] \left\{\cos(2\pi\nu t + \frac{\pi\varphi}{180}) - \sin(2\pi\nu t + \frac{\pi\varphi}{180}) \mathrm{Erfi}\left(\frac{\sigma_{+} t}{\sqrt{2}}\right)\right\}`
:math:`\sigma_{-} (\mu \mathrm{s}^{-1})`
staticNKZF snkzf :math:`\Delta_0 (\mu \mathrm{s}^{-1})`, \ :math:`\frac{1}{3} + \frac{2}{3}\left(\frac{1}{1+R_b^2\Delta_0^2 t^2}\right)^{3/2} \left(1 - \frac{\Delta_0^2 t^2}{1+R_b^2\Delta_0^2 t^2}\right) \exp\left[-\frac{\Delta_0^2 t^2}{2(1+R_b^2\Delta_0^2 t^2)}\right]` [#n9]_
staticNKZF snkzf :math:`\Delta_0 (\mu \mathrm{s}^{-1})`, \ :math:`\frac{1}{3} + \frac{2}{3}\left(\frac{1}{1+R_b^2\Delta_0^2 t^2}\right)^{3/2} \left(1 - \frac{\Delta_0^2 t^2}{1+R_b^2\Delta_0^2 t^2}\right) \exp\left[-\frac{\Delta_0^2 t^2}{2(1+R_b^2\Delta_0^2 t^2)}\right]` [#n11]_
:math:`R_b = \Delta_{\rm GbG}/\Delta_0 (1)`
staticNKTF snktf :math:`\varphi (^\circ), \nu` (MHz), \ :math:`\sqrt{\frac{1}{1+R_b^2 \Delta_0^2 t^2}} \exp\left[-\frac{\Delta_0^2 t^2}{2(1+R_b^2 \Delta_0^2 t^2)}\right] \cos(2\pi\nu t + \varphi)` see [11]
staticNKTF snktf :math:`\varphi (^\circ), \nu` (MHz), \ :math:`\sqrt{\frac{1}{1+R_b^2 \Delta_0^2 t^2}} \exp\left[-\frac{\Delta_0^2 t^2}{2(1+R_b^2 \Delta_0^2 t^2)}\right] \cos(2\pi\nu t + \varphi)` see [13]
:math:`\Delta_0 (\mu \mathrm{s}^{-1})`, \
:math:`R_b = \Delta_{\rm GbG}/\Delta_0 (1)`
dynamicNKZF dnkzf :math:`\Delta_0 (\mu \mathrm{s}^{-1})`, \ :math:`\sqrt{\frac{1}{1+4 R_b^2 \Delta_0^2 \Theta(t)}} \exp\left[-\frac{2\Delta_0^2 \Theta(t)}{1+4 R_b^2 \Delta_0^2 \Theta(t)}\right]`, see [11]
dynamicNKZF dnkzf :math:`\Delta_0 (\mu \mathrm{s}^{-1})`, \ :math:`\sqrt{\frac{1}{1+4 R_b^2 \Delta_0^2 \Theta(t)}} \exp\left[-\frac{2\Delta_0^2 \Theta(t)}{1+4 R_b^2 \Delta_0^2 \Theta(t)}\right]`, see [13]
:math:`R_b = \Delta_{\rm GbG}/\Delta_0 (1)`, \ :math:`\Theta(t) = \frac{\exp(-\nu_c t) -1 -\nu_c t}{\nu_c^2}`
:math:`\nu_c` (MHz)
dynamicNKTF dnktf :math:`\varphi (^\circ), \nu` (MHz), \ :math:`\sqrt{\frac{1}{1+2 R_b^2 \Delta_0^2 \Theta(t)}} \exp\left[-\frac{\Delta_0^2 \Theta(t)}{1+2 R_b^2 \Delta_0^2 \Theta(t)}\right] \cos(2\pi\nu t + \varphi)`, see [11]
dynamicNKTF dnktf :math:`\varphi (^\circ), \nu` (MHz), \ :math:`\sqrt{\frac{1}{1+2 R_b^2 \Delta_0^2 \Theta(t)}} \exp\left[-\frac{\Delta_0^2 \Theta(t)}{1+2 R_b^2 \Delta_0^2 \Theta(t)}\right] \cos(2\pi\nu t + \varphi)`, see [13]
:math:`\Delta_0 (\mu \mathrm{s}^{-1})`, \ :math:`\Theta(t) = \frac{\exp(-\nu_c t) -1 -\nu_c t}{\nu_c^2}`
:math:`R_b = \Delta_{\rm GbG}/\Delta_0 (1)`, \
:math:`\nu_c` (MHz)
muMinusExpTF mmsetf :math:`N_0 (1), \tau (\mu \mathrm{s}^{-1})`, \ :math:`N_0 \exp(-t/\tau) \left[ 1 + A \exp(-\lambda t) \cos(2 \pi \nu t + \varphi) \right]` [#n10]_
muMinusExpTF mmsetf :math:`N_0 (1), \tau (\mu \mathrm{s}^{-1})`, \ :math:`N_0 \exp(-t/\tau) \left[ 1 + A \exp(-\lambda t) \cos(2 \pi \nu t + \varphi) \right]` [#n12]_
:math:`A (1), \lambda (\mu \mathrm{s}^{-1})`, \
:math:`\varphi (^\circ), \nu` (MHz)
polynom p :math:`t_0 ([t]), a_0 (1)`, \ :math:`\sum_{k=0}^n a_k (t-t_0)^k`
@ -700,12 +706,16 @@ polynom p :math:`t_0 ([t]), a_0 (1)`, \ :math:`\sum
.. [#n5] R.S. Hayano *et al.*, Phys. Rev. B **20**, 850 (1979)., P. Dalmas de Réotier and A. Yaouanc, J. Phys.: Condens. Matter **4**, 4533 (1992). -- **not** DKS ready.
.. [#n6] `M.R. Crook <http://dx.doi.org/10.1088/0953-8984/9/5/018>`_ and R. Cywinski, J. Phys.: Condens. Matter **9** 1149 (1997).
.. [#n7] `R.E. Turner <http://link.aps.org/doi/10.1103/PhysRevB.34.4467>`_ and D.R. Harshman, Phys. Rev. B **34**, 4467 (1986).
.. [#n8] `see memo <http://lmu.web.psi.ch/musrfit/memos/skewedGaussian.pdf>`_ -- **not** DKS ready.
.. [#n9] `D.R. Noakes <http://link.aps.org/doi/10.1103/PhysRevB.56.2352>`_ and G.M. Kalvius, Phys. Rev. B **56**, 2352 (1997);
.. [#n8] `E.I. Kornilov <https://doi.org/10.1016/0375-9601(91)90959-C>`_ and V.Yu. Pomjakushin, Physics Letters A **153**, 364, (1991).
In the original work, :math:`\alpha=2/3,\, \lambda=0,\, \beta=1`. If you find values strongly deviating from these values you should question your analysis approach.
.. [#n9] `M.I. Larkin <https://doi.org/10.1016/S0921-4526(00)00337-9>`_ *et al.*, Physica B: Condensed Matter **289-290**, 153 (2000).
In the original work, :math:`\alpha=2/3,\, \lambda=0,\, \beta=1`. If you find values strongly deviating from these values you should question your analysis approach.
.. [#n10] `see memo <http://lmu.web.psi.ch/musrfit/memos/skewedGaussian.pdf>`_ -- **not** DKS ready.
.. [#n11] `D.R. Noakes <http://link.aps.org/doi/10.1103/PhysRevB.56.2352>`_ and G.M. Kalvius, Phys. Rev. B **56**, 2352 (1997);
A. Yaouanc and P. Dalmas de Réotier "Muon Spin Rotation, Relaxation, and Resonance" Oxford Scientific Publication;
simplifying the original formulae by eliminating :math:`\Delta_{\rm eff}` via the identity
:math:`\Delta_{\rm eff}^2 = (1+R_b^2)\Delta_0`.
.. [#n10] This function is explicit for :math:`\mu^-`! Do not try to use it for :math:`\mu^+`!
.. [#n12] This function is explicit for :math:`\mu^-`! Do not try to use it for :math:`\mu^+`!
.. _msr-map-intro:

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@ -6,7 +6,7 @@
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@ -108,12 +108,12 @@ extremely competent way to deal with his projects as well as to deal with the ch
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@ -6,7 +6,7 @@
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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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@ -6,7 +6,7 @@
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@ -93,12 +93,12 @@ or send an e-mail to A. Suter at PSI.</p>
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@ -6,7 +6,7 @@
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@ -114,12 +114,12 @@
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@ -7,7 +7,7 @@
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@ -982,12 +982,12 @@
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@ -6,7 +6,7 @@
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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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@ -354,12 +354,12 @@ The only thing you need <tt class="docutils literal"><span class="pre">DKS</span
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@ -1481,12 +1481,12 @@ $ musrview test-histo-ROOT-NPP.msr
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@ -132,7 +132,7 @@ TFieldCos map1 fun2 (phase frequency)
</pre></div>
</div>
<p>The THEORY block is used to define a fit-parameter-dependent theory function used to model
the decay asymmetry. Different <a class="reference internal" href="user-manual.html#msr-theory-block"><em>predefined</em></a> and <a class="reference internal" href="user-manual.html#id20"><em>user-defined</em></a>
the decay asymmetry. Different <a class="reference internal" href="user-manual.html#msr-theory-block"><em>predefined</em></a> and <a class="reference internal" href="user-manual.html#id22"><em>user-defined</em></a>
functions can be combined here. Theory lines following each other are <em>multiplied</em> and the <strong>+</strong> sign
is used to add different (here: two) signal contributions. The numbers are the parameter numbers
according to the <tt class="docutils literal"><span class="pre">FITPARAMETER</span> <span class="pre">block</span></tt>. <tt class="docutils literal"><span class="pre">map</span></tt> and <tt class="docutils literal"><span class="pre">fun</span></tt> are used to refer to
@ -443,12 +443,12 @@ For a complete description please refer to the manuals of <a class="reference in
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@ -58,7 +58,7 @@
<span id="index-2"></span><h3>libFitPofB<a class="headerlink" href="#libfitpofb" title="Permalink to this headline"></a></h3>
<div class="section" id="introduction">
<h4>Introduction<a class="headerlink" href="#introduction" title="Permalink to this headline"></a></h4>
<p><tt class="docutils literal"><span class="pre">libFitPofB</span></tt> is a collection of <tt class="docutils literal"><span class="pre">C++</span></tt> classes using the <tt class="docutils literal"><span class="pre">musrfit</span></tt> <a class="reference internal" href="user-manual.html#id20"><em>user-functions</em></a>
<p><tt class="docutils literal"><span class="pre">libFitPofB</span></tt> is a collection of <tt class="docutils literal"><span class="pre">C++</span></tt> classes using the <tt class="docutils literal"><span class="pre">musrfit</span></tt> <a class="reference internal" href="user-manual.html#id22"><em>user-functions</em></a>
interface in order to facilitate the usage in conjunction with <tt class="docutils literal"><span class="pre">musrfit</span></tt>. The classes contained in this
library generally implement calculations of one-dimensional static magnetic field distributions
<span class="math">\(p(B)\)</span> which lead to the muon-spin depolarization functions</p>
@ -372,7 +372,7 @@ The expected name of the <tt class="docutils literal"><span class="pre">RGE</spa
</div>
<div class="section" id="functions-to-analyze-bgr-nmr-data-bnmr-libs">
<span id="bnmr-libs"></span><span id="index-14"></span><h2>Functions to analyze β-NMR data (BNMR libs)<a class="headerlink" href="#functions-to-analyze-bgr-nmr-data-bnmr-libs" title="Permalink to this headline"></a></h2>
<p>This is a collection of <tt class="docutils literal"><span class="pre">C++</span></tt> classes using the <tt class="docutils literal"><span class="pre">musrfit</span></tt> <a class="reference internal" href="user-manual.html#id20"><em>user-functions</em></a>
<p>This is a collection of <tt class="docutils literal"><span class="pre">C++</span></tt> classes using the <tt class="docutils literal"><span class="pre">musrfit</span></tt> <a class="reference internal" href="user-manual.html#id22"><em>user-functions</em></a>
interface in order to facilitate the usage in conjunction with <tt class="docutils literal"><span class="pre">musrfit</span></tt>. It consists of two libraries:</p>
<ul class="simple">
<li><tt class="docutils literal"><span class="pre">libBNMR</span></tt> contains functions to fit spin lattice relaxation (SLR) data.</li>
@ -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 1.4.0 documentation</a> &raquo;</li>
<li><a href="index.html">musrfit 1.4.1 documentation</a> &raquo;</li>
</ul>
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&copy; Copyright 2018, Andreas Suter.
Last updated on Oct 15, 2018.
Last updated on Jan 21, 2019.
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@ -584,7 +584,7 @@ in case a <span class="math">\(\chi^2\)</span> single-histogram fit is done, als
<col width="2%" />
<col width="14%" />
<col width="77%" />
<col width="2%" />
<col width="3%" />
</colgroup>
<thead valign="bottom">
<tr class="row-odd"><th class="head">name</th>
@ -721,7 +721,7 @@ in case a <span class="math">\(\chi^2\)</span> single-histogram fit is done, als
<td>if</td>
<td><span class="math">\(\alpha (1), \varphi (^\circ)\)</span>, <span class="math">\(\nu\)</span> (MHz), <span class="math">\(\lambda_{\rm T} (\mu \mathrm{s}^{-1})\)</span>,<span class="math">\(\lambda_{\rm L} (\mu \mathrm{s}^{-1})\)</span></td>
<td><dl class="first last docutils">
<dt><span class="math">\(\alpha \cos\left(2\pi\nu t + \frac{\pi \varphi}{180}\right) \exp(\lambda_{\rm T}t) +\)</span></dt>
<dt><span class="math">\(\alpha \cos\left(2\pi\nu t + \frac{\pi \varphi}{180}\right) \exp(-\lambda_{\rm T}t) +\)</span></dt>
<dd><span class="math">\(+ (1-\alpha) \exp(-\lambda_{\rm L} t)\)</span></dd>
</dl>
</td>
@ -737,12 +737,32 @@ in case a <span class="math">\(\chi^2\)</span> single-histogram fit is done, als
<td>ib</td>
<td><span class="math">\(\alpha (1), \varphi (^\circ)\)</span>, <span class="math">\(\nu\)</span> (MHz), <span class="math">\(\lambda_{\rm T} (\mu \mathrm{s}^{-1})\)</span>,<span class="math">\(\lambda_{\rm L} (\mu \mathrm{s}^{-1})\)</span></td>
<td><dl class="first last docutils">
<dt><span class="math">\(\alpha j_0\left(2\pi\nu t + \frac{\pi \varphi}{180}\right) \exp(\lambda_{\rm T}t) +\)</span></dt>
<dt><span class="math">\(\alpha j_0\left(2\pi\nu t + \frac{\pi \varphi}{180}\right) \exp(-\lambda_{\rm T}t) +\)</span></dt>
<dd><span class="math">\(+ (1-\alpha) \exp(-\lambda_{\rm L} t)\)</span></dd>
</dl>
</td>
<td>&nbsp;</td>
</tr>
<tr class="row-odd"><td>internFldGK</td>
<td>ifgk</td>
<td><span class="math">\(\alpha (1), \nu\)</span> (MHz), <span class="math">\(\sigma (\mu \mathrm{s}^{-1})\)</span>, <span class="math">\(\lambda (\mu\mathrm{s}^{-1}), \beta (1)\)</span></td>
<td><dl class="first last docutils">
<dt><span class="math">\(\alpha\left[\cos(2\pi\nu t)-\frac{\sigma^2 t}{2\pi\nu}\sin(2\pi\nu t)\right]\exp(-\sigma^2 t^2/2)+\)</span></dt>
<dd><span class="math">\(+ (1-\alpha) \exp(-(\lambda t)^\beta)\)</span></dd>
</dl>
</td>
<td><a class="footnote-reference" href="#n8" id="id16">[10]</a></td>
</tr>
<tr class="row-even"><td>internFldLL</td>
<td>ifll</td>
<td><span class="math">\(\alpha (1), \nu\)</span> (MHz), <span class="math">\(a (\mu \mathrm{s}^{-1})\)</span>, <span class="math">\(\lambda (\mu\mathrm{s}^{-1}), \beta (1)\)</span></td>
<td><dl class="first last docutils">
<dt><span class="math">\(\alpha\left[\cos(2\pi\nu t)-\frac{a}{2\pi\nu}\sin(2\pi\nu t)\right]\exp(-a t)+\)</span></dt>
<dd><span class="math">\(+ (1-\alpha) \exp(-(\lambda t)^\beta)\)</span></dd>
</dl>
</td>
<td><a class="footnote-reference" href="#n9" id="id17">[11]</a></td>
</tr>
<tr class="row-odd"><td>abragam</td>
<td>ab</td>
<td><span class="math">\(\sigma (\mu \mathrm{s}^{-1})\)</span>, <span class="math">\(\gamma\)</span> (MHz)</td>
@ -757,19 +777,19 @@ in case a <span class="math">\(\chi^2\)</span> single-histogram fit is done, als
<dd><span class="math">\(+ \frac{\sigma_{+}}{\sigma_{+}+\sigma_{-}} \exp\left[\frac{\sigma_{+}^2 t^2}{2}\right] \left\{\cos(2\pi\nu t + \frac{\pi\varphi}{180}) - \sin(2\pi\nu t + \frac{\pi\varphi}{180}) \mathrm{Erfi}\left(\frac{\sigma_{+} t}{\sqrt{2}}\right)\right\}\)</span></dd>
</dl>
</td>
<td><a class="footnote-reference" href="#n8" id="id16">[10]</a></td>
<td><a class="footnote-reference" href="#n10" id="id18">[12]</a></td>
</tr>
<tr class="row-odd"><td>staticNKZF</td>
<td>snkzf</td>
<td><span class="math">\(\Delta_0 (\mu \mathrm{s}^{-1})\)</span>, <span class="math">\(R_b = \Delta_{\rm GbG}/\Delta_0 (1)\)</span></td>
<td><span class="math">\(\frac{1}{3} + \frac{2}{3}\left(\frac{1}{1+R_b^2\Delta_0^2 t^2}\right)^{3/2} \left(1 - \frac{\Delta_0^2 t^2}{1+R_b^2\Delta_0^2 t^2}\right) \exp\left[-\frac{\Delta_0^2 t^2}{2(1+R_b^2\Delta_0^2 t^2)}\right]\)</span></td>
<td><a class="footnote-reference" href="#n9" id="id17">[11]</a></td>
<td><a class="footnote-reference" href="#n11" id="id19">[13]</a></td>
</tr>
<tr class="row-even"><td>staticNKTF</td>
<td>snktf</td>
<td><span class="math">\(\varphi (^\circ), \nu\)</span> (MHz), <span class="math">\(\Delta_0 (\mu \mathrm{s}^{-1})\)</span>, <span class="math">\(R_b = \Delta_{\rm GbG}/\Delta_0 (1)\)</span></td>
<td><span class="math">\(\sqrt{\frac{1}{1+R_b^2 \Delta_0^2 t^2}} \exp\left[-\frac{\Delta_0^2 t^2}{2(1+R_b^2 \Delta_0^2 t^2)}\right] \cos(2\pi\nu t + \varphi)\)</span></td>
<td>see [11]</td>
<td>see [13]</td>
</tr>
<tr class="row-odd"><td>dynamicNKZF</td>
<td>dnkzf</td>
@ -779,7 +799,7 @@ in case a <span class="math">\(\chi^2\)</span> single-histogram fit is done, als
<dd><span class="math">\(\Theta(t) = \frac{\exp(-\nu_c t) -1 -\nu_c t}{\nu_c^2}\)</span></dd>
</dl>
</td>
<td>see [11]</td>
<td>see [13]</td>
</tr>
<tr class="row-even"><td>dynamicNKTF</td>
<td>dnktf</td>
@ -789,13 +809,13 @@ in case a <span class="math">\(\chi^2\)</span> single-histogram fit is done, als
<dd><span class="math">\(\Theta(t) = \frac{\exp(-\nu_c t) -1 -\nu_c t}{\nu_c^2}\)</span></dd>
</dl>
</td>
<td>see [11]</td>
<td>see [13]</td>
</tr>
<tr class="row-odd"><td>muMinusExpTF</td>
<td>mmsetf</td>
<td><span class="math">\(N_0 (1), \tau (\mu \mathrm{s}^{-1})\)</span>, <span class="math">\(A (1), \lambda (\mu \mathrm{s}^{-1})\)</span>, <span class="math">\(\varphi (^\circ), \nu\)</span> (MHz)</td>
<td><span class="math">\(N_0 \exp(-t/\tau) \left[ 1 + A \exp(-\lambda t) \cos(2 \pi \nu t + \varphi) \right]\)</span></td>
<td><a class="footnote-reference" href="#n10" id="id18">[12]</a></td>
<td><a class="footnote-reference" href="#n12" id="id20">[14]</a></td>
</tr>
<tr class="row-even"><td>polynom</td>
<td>p</td>
@ -853,22 +873,36 @@ in case a <span class="math">\(\chi^2\)</span> single-histogram fit is done, als
<table class="docutils footnote" frame="void" id="n8" rules="none">
<colgroup><col class="label" /><col /></colgroup>
<tbody valign="top">
<tr><td class="label"><a class="fn-backref" href="#id16">[10]</a></td><td><a class="reference external" href="http://lmu.web.psi.ch/musrfit/memos/skewedGaussian.pdf">see memo</a> &#8211; <strong>not</strong> DKS ready.</td></tr>
<tr><td class="label"><a class="fn-backref" href="#id16">[10]</a></td><td><a class="reference external" href="https://doi.org/10.1016/0375-9601(91)90959-C">E.I. Kornilov</a> and V.Yu. Pomjakushin, Physics Letters A <strong>153</strong>, 364, (1991).
In the original work, <span class="math">\(\alpha=2/3,\, \lambda=0,\, \beta=1\)</span>. If you find values strongly deviating from these values you should question your analysis approach.</td></tr>
</tbody>
</table>
<table class="docutils footnote" frame="void" id="n9" rules="none">
<colgroup><col class="label" /><col /></colgroup>
<tbody valign="top">
<tr><td class="label"><a class="fn-backref" href="#id17">[11]</a></td><td><a class="reference external" href="http://link.aps.org/doi/10.1103/PhysRevB.56.2352">D.R. Noakes</a> and G.M. Kalvius, Phys. Rev. B <strong>56</strong>, 2352 (1997);
A. Yaouanc and P. Dalmas de Réotier &#8220;Muon Spin Rotation, Relaxation, and Resonance&#8221; Oxford Scientific Publication;
simplifying the original formulae by eliminating <span class="math">\(\Delta_{\rm eff}\)</span> via the identity
<span class="math">\(\Delta_{\rm eff}^2 = (1+R_b^2)\Delta_0\)</span>.</td></tr>
<tr><td class="label"><a class="fn-backref" href="#id17">[11]</a></td><td><a class="reference external" href="https://doi.org/10.1016/S0921-4526(00)00337-9">M.I. Larkin</a> <em>et al.</em>, Physica B: Condensed Matter <strong>289-290</strong>, 153 (2000).
In the original work, <span class="math">\(\alpha=2/3,\, \lambda=0,\, \beta=1\)</span>. If you find values strongly deviating from these values you should question your analysis approach.</td></tr>
</tbody>
</table>
<table class="docutils footnote" frame="void" id="n10" rules="none">
<colgroup><col class="label" /><col /></colgroup>
<tbody valign="top">
<tr><td class="label"><a class="fn-backref" href="#id18">[12]</a></td><td>This function is explicit for <span class="math">\(\mu^-\)</span>! Do not try to use it for <span class="math">\(\mu^+\)</span>!</td></tr>
<tr><td class="label"><a class="fn-backref" href="#id18">[12]</a></td><td><a class="reference external" href="http://lmu.web.psi.ch/musrfit/memos/skewedGaussian.pdf">see memo</a> &#8211; <strong>not</strong> DKS ready.</td></tr>
</tbody>
</table>
<table class="docutils footnote" frame="void" id="n11" rules="none">
<colgroup><col class="label" /><col /></colgroup>
<tbody valign="top">
<tr><td class="label"><a class="fn-backref" href="#id19">[13]</a></td><td><a class="reference external" href="http://link.aps.org/doi/10.1103/PhysRevB.56.2352">D.R. Noakes</a> and G.M. Kalvius, Phys. Rev. B <strong>56</strong>, 2352 (1997);
A. Yaouanc and P. Dalmas de Réotier &#8220;Muon Spin Rotation, Relaxation, and Resonance&#8221; Oxford Scientific Publication;
simplifying the original formulae by eliminating <span class="math">\(\Delta_{\rm eff}\)</span> via the identity
<span class="math">\(\Delta_{\rm eff}^2 = (1+R_b^2)\Delta_0\)</span>.</td></tr>
</tbody>
</table>
<table class="docutils footnote" frame="void" id="n12" rules="none">
<colgroup><col class="label" /><col /></colgroup>
<tbody valign="top">
<tr><td class="label"><a class="fn-backref" href="#id20">[14]</a></td><td>This function is explicit for <span class="math">\(\mu^-\)</span>! Do not try to use it for <span class="math">\(\mu^+\)</span>!</td></tr>
</tbody>
</table>
<div class="section" id="maps">
@ -901,7 +935,7 @@ Whereas the theory is operating on the parameters and the time, functions curren
<span id="msr-theory-block-user-functions"></span><h4>User Functions<a class="headerlink" href="#user-functions" title="Permalink to this headline"></a></h4>
<p>In the case complicated and not predefined functions are needed to fit data, <tt class="docutils literal"><span class="pre">musrfit</span></tt> offers the possibility to implement external functions
and introduce them to <tt class="docutils literal"><span class="pre">musrfit</span></tt> through the ROOT dictionary mechanism. The detailed rules these user-defined functions have to obey will be discussed
in the according <a class="reference internal" href="#id20"><em>section</em></a>. Here only the syntax for the msr file is provided. To call a user function in the <a class="reference internal" href="#msr-theory-block"><em>THEORY block</em></a> the
in the according <a class="reference internal" href="#id22"><em>section</em></a>. Here only the syntax for the msr file is provided. To call a user function in the <a class="reference internal" href="#msr-theory-block"><em>THEORY block</em></a> the
keyword <tt class="docutils literal"><span class="pre">userFcn</span></tt> 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.</p>
@ -1732,7 +1766,7 @@ If enabled in the <a class="reference internal" href="#musrfit-startup"><em>XML
</div>
</div>
<div class="section" id="fit-types">
<span id="index-63"></span><span id="id19"></span><h2>Fit Types<a class="headerlink" href="#fit-types" title="Permalink to this headline"></a></h2>
<span id="index-63"></span><span id="id21"></span><h2>Fit Types<a class="headerlink" href="#fit-types" title="Permalink to this headline"></a></h2>
<div class="section" id="single-histogram-fit-fit-type-0">
<span id="single-histogram-fit"></span><span id="index-64"></span><h3>Single Histogram Fit (fit type 0)<a class="headerlink" href="#single-histogram-fit-fit-type-0" title="Permalink to this headline"></a></h3>
<p>The single-histogram fit (fit type 0) is used to fit a function directly to the raw data using</p>
@ -1843,8 +1877,8 @@ the single histogram RRF fit apply: <strong>if you not urgently need it: do not
<p>The same applies for the plot with plot type 8.</p>
</div>
</div>
<div class="section" id="id20">
<span id="index-70"></span><span id="id21"></span><h2>User Functions<a class="headerlink" href="#id20" title="Permalink to this headline"></a></h2>
<div class="section" id="id22">
<span id="index-70"></span><span id="id23"></span><h2>User Functions<a class="headerlink" href="#id22" title="Permalink to this headline"></a></h2>
<p><tt class="docutils literal"><span class="pre">musrfit</span></tt> offers the possibility to plug-in user-defined functions implemented in <tt class="docutils literal"><span class="pre">C++</span></tt> classes to the fitting and plotting routines.
In order to do so, basically two things are needed:</p>
<blockquote>
@ -2154,7 +2188,7 @@ In case this cannot be ensured, the parallelization can be disabled by <em>&#821
<li><a class="reference internal" href="#non-mgrsr-fit-fit-type-8">Non-μSR Fit (fit type 8)</a></li>
</ul>
</li>
<li><a class="reference internal" href="#id20">User Functions</a><ul>
<li><a class="reference internal" href="#id22">User Functions</a><ul>
<li><a class="reference internal" href="#user-function-without-global-user-function-object-access">User Function without global user-function-object access</a></li>
<li><a class="reference internal" href="#user-function-with-global-user-function-object-access">User Function with global user-function-object access</a></li>
</ul>
@ -2204,12 +2238,12 @@ In case this cannot be ensured, the parallelization can be disabled by <em>&#821
<li class="right" >
<a href="tutorial.html" title="Tutorial for musrfit"
>previous</a> |</li>
<li><a href="index.html">musrfit 1.4.0 documentation</a> &raquo;</li>
<li><a href="index.html">musrfit 1.4.1 documentation</a> &raquo;</li>
</ul>
</div>
<div class="footer">
&copy; Copyright 2018, Andreas Suter.
Last updated on Nov 13, 2018.
Last updated on Jan 21, 2019.
Created using <a href="http://sphinx-doc.org/">Sphinx</a> 1.2.3.
</div>
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