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51  <h1>Source code for sas.models.GuinierPorodModel</h1><div class="highlight"><pre>
52<span class="sd">&quot;&quot;&quot; </span>
53<span class="sd">    I(q) = scale/q^s* exp ( - R_g^2 q^2 / (3-s) ) for q&lt;= ql</span>
54<span class="sd">        = scale/q^m*exp((-ql^2*Rg^2)/(3-s))*ql^(m-s) for q&gt;=ql</span>
55<span class="sd">    Guinier function as a BaseComponent model</span>
56<span class="sd">&quot;&quot;&quot;</span>
57<span class="kn">from</span> <span class="nn">sas.models.BaseComponent</span> <span class="kn">import</span> <span class="n">BaseComponent</span>
58<span class="kn">from</span> <span class="nn">math</span> <span class="kn">import</span> <span class="n">sqrt</span><span class="p">,</span><span class="n">exp</span>
59
60<div class="viewcode-block" id="GuinierPorodModel"><a class="viewcode-back" href="../../../dev/api/sas.models.html#sas.models.GuinierPorodModel.GuinierPorodModel">[docs]</a><span class="k">class</span> <span class="nc">GuinierPorodModel</span><span class="p">(</span><span class="n">BaseComponent</span><span class="p">):</span>
61    <span class="sd">&quot;&quot;&quot; </span>
62<span class="sd">    Class that evaluates a GuinierPorod model.</span>
63
64<span class="sd">    I(q) = scale/q^s* exp ( - R_g^2 q^2 / (3-s) ) for q&lt;= ql</span>
65<span class="sd">        = scale/q^m*exp((-ql^2*Rg^2)/(3-s))*ql^(m-s) for q&gt;=ql</span>
66<span class="sd">    &quot;&quot;&quot;</span>
67    <span class="k">def</span> <span class="nf">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
68        <span class="sd">&quot;&quot;&quot; Initialization &quot;&quot;&quot;</span>
69       
70        <span class="c"># Initialize BaseComponent first, then sphere</span>
71        <span class="n">BaseComponent</span><span class="o">.</span><span class="n">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span>
72       
73        <span class="c">## Name of the model</span>
74        <span class="bp">self</span><span class="o">.</span><span class="n">name</span> <span class="o">=</span> <span class="s">&quot;GuinierPorod&quot;</span>
75        <span class="bp">self</span><span class="o">.</span><span class="n">description</span> <span class="o">=</span> <span class="s">&quot;&quot;&quot;</span>
76<span class="s">         I(q) = scale/q^s* exp ( - R_g^2 q^2 / (3-s) ) for q&lt;= ql</span>
77<span class="s">         = scale/q^m*exp((-ql^2*Rg^2)/(3-s))*ql^(m-s) for q&gt;=ql</span>
78<span class="s">                        where ql = sqrt((m-s)(3-s)/2)/Rg.</span>
79<span class="s">                        List of parameters:</span>
80<span class="s">                        scale = Guinier Scale</span>
81<span class="s">                        s = Dimension Variable</span>
82<span class="s">                        Rg = Radius of Gyration [A] </span>
83<span class="s">                        m = Porod Exponent</span>
84<span class="s">                        background  = Background [1/cm]&quot;&quot;&quot;</span>
85        <span class="c">## Define parameters</span>
86        <span class="bp">self</span><span class="o">.</span><span class="n">params</span> <span class="o">=</span> <span class="p">{}</span>
87        <span class="bp">self</span><span class="o">.</span><span class="n">params</span><span class="p">[</span><span class="s">&#39;scale&#39;</span><span class="p">]</span>  <span class="o">=</span> <span class="mf">1.0</span>
88        <span class="bp">self</span><span class="o">.</span><span class="n">params</span><span class="p">[</span><span class="s">&#39;dim&#39;</span><span class="p">]</span>  <span class="o">=</span> <span class="mf">1.0</span>
89        <span class="bp">self</span><span class="o">.</span><span class="n">params</span><span class="p">[</span><span class="s">&#39;rg&#39;</span><span class="p">]</span>     <span class="o">=</span> <span class="mf">100.0</span>
90        <span class="bp">self</span><span class="o">.</span><span class="n">params</span><span class="p">[</span><span class="s">&#39;m&#39;</span><span class="p">]</span>     <span class="o">=</span> <span class="mf">3.0</span>
91        <span class="bp">self</span><span class="o">.</span><span class="n">params</span><span class="p">[</span><span class="s">&#39;background&#39;</span><span class="p">]</span>     <span class="o">=</span> <span class="mf">0.1</span>
92        <span class="c">## Parameter details [units, min, max]</span>
93        <span class="bp">self</span><span class="o">.</span><span class="n">details</span> <span class="o">=</span> <span class="p">{}</span>
94        <span class="bp">self</span><span class="o">.</span><span class="n">details</span><span class="p">[</span><span class="s">&#39;scale&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="p">[</span><span class="s">&#39;&#39;</span><span class="p">,</span> <span class="bp">None</span><span class="p">,</span> <span class="bp">None</span><span class="p">]</span>
95        <span class="bp">self</span><span class="o">.</span><span class="n">details</span><span class="p">[</span><span class="s">&#39;dim&#39;</span><span class="p">]</span>  <span class="o">=</span> <span class="p">[</span><span class="s">&#39;&#39;</span><span class="p">,</span> <span class="bp">None</span><span class="p">,</span> <span class="bp">None</span><span class="p">]</span>
96        <span class="bp">self</span><span class="o">.</span><span class="n">details</span><span class="p">[</span><span class="s">&#39;rg&#39;</span><span class="p">]</span>    <span class="o">=</span> <span class="p">[</span><span class="s">&#39;[A]&#39;</span><span class="p">,</span> <span class="bp">None</span><span class="p">,</span> <span class="bp">None</span><span class="p">]</span>
97        <span class="bp">self</span><span class="o">.</span><span class="n">details</span><span class="p">[</span><span class="s">&#39;m&#39;</span><span class="p">]</span>     <span class="o">=</span> <span class="p">[</span><span class="s">&#39;&#39;</span><span class="p">,</span> <span class="bp">None</span><span class="p">,</span> <span class="bp">None</span><span class="p">]</span>
98        <span class="bp">self</span><span class="o">.</span><span class="n">details</span><span class="p">[</span><span class="s">&#39;background&#39;</span><span class="p">]</span>     <span class="o">=</span> <span class="p">[</span><span class="s">&#39;[1/cm]&#39;</span><span class="p">,</span> <span class="bp">None</span><span class="p">,</span> <span class="bp">None</span><span class="p">]</span>
99
100        <span class="c">#list of parameter that cannot be fitted</span>
101        <span class="bp">self</span><span class="o">.</span><span class="n">fixed</span> <span class="o">=</span> <span class="p">[]</span> 
102       
103    <span class="k">def</span> <span class="nf">_guinier_porod</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span>
104        <span class="sd">&quot;&quot;&quot;</span>
105<span class="sd">        Guinier-Porod Model</span>
106<span class="sd">        &quot;&quot;&quot;</span>
107        <span class="c"># parameters</span>
108        <span class="n">G</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">params</span><span class="p">[</span><span class="s">&#39;scale&#39;</span><span class="p">]</span>
109        <span class="n">s</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">params</span><span class="p">[</span><span class="s">&#39;dim&#39;</span><span class="p">]</span>
110        <span class="n">Rg</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">params</span><span class="p">[</span><span class="s">&#39;rg&#39;</span><span class="p">]</span>
111        <span class="n">m</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">params</span><span class="p">[</span><span class="s">&#39;m&#39;</span><span class="p">]</span>
112        <span class="n">bgd</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">params</span><span class="p">[</span><span class="s">&#39;background&#39;</span><span class="p">]</span>
113        <span class="n">n</span> <span class="o">=</span> <span class="mf">3.0</span> <span class="o">-</span> <span class="n">s</span>
114        <span class="n">qval</span> <span class="o">=</span> <span class="n">x</span>
115        <span class="c"># take care of the singular points</span>
116        <span class="k">if</span> <span class="n">Rg</span> <span class="o">&lt;=</span> <span class="mf">0.0</span><span class="p">:</span>
117            <span class="k">return</span> <span class="n">bgd</span>
118        <span class="k">if</span> <span class="p">(</span><span class="n">n</span><span class="o">-</span><span class="mf">3.0</span><span class="o">+</span><span class="n">m</span><span class="p">)</span> <span class="o">&lt;=</span> <span class="mf">0.0</span><span class="p">:</span>
119            <span class="k">return</span> <span class="n">bgd</span>
120        <span class="c">#do the calculation and return the function value</span>
121        <span class="n">q1</span> <span class="o">=</span> <span class="n">sqrt</span><span class="p">((</span><span class="n">n</span><span class="o">-</span><span class="mf">3.0</span><span class="o">+</span><span class="n">m</span><span class="p">)</span><span class="o">*</span><span class="n">n</span><span class="o">/</span><span class="mf">2.0</span><span class="p">)</span><span class="o">/</span><span class="n">Rg</span>
122        <span class="k">if</span> <span class="n">qval</span> <span class="o">&lt;</span> <span class="n">q1</span><span class="p">:</span>
123            <span class="n">F</span> <span class="o">=</span> <span class="p">(</span><span class="n">G</span><span class="o">/</span><span class="nb">pow</span><span class="p">(</span><span class="n">qval</span><span class="p">,(</span><span class="mf">3.0</span><span class="o">-</span><span class="n">n</span><span class="p">)))</span><span class="o">*</span><span class="n">exp</span><span class="p">((</span><span class="o">-</span><span class="n">qval</span><span class="o">*</span><span class="n">qval</span><span class="o">*</span><span class="n">Rg</span><span class="o">*</span><span class="n">Rg</span><span class="p">)</span><span class="o">/</span><span class="n">n</span><span class="p">)</span> 
124        <span class="k">else</span><span class="p">:</span>
125            <span class="n">F</span> <span class="o">=</span> <span class="p">(</span><span class="n">G</span><span class="o">/</span><span class="nb">pow</span><span class="p">(</span><span class="n">qval</span><span class="p">,</span> <span class="n">m</span><span class="p">))</span><span class="o">*</span><span class="n">exp</span><span class="p">(</span><span class="o">-</span><span class="p">(</span><span class="n">n</span><span class="o">-</span><span class="mf">3.0</span><span class="o">+</span><span class="n">m</span><span class="p">)</span><span class="o">/</span><span class="mf">2.0</span><span class="p">)</span><span class="o">*</span><span class="nb">pow</span><span class="p">(((</span><span class="n">n</span><span class="o">-</span><span class="mf">3.0</span><span class="o">+</span><span class="n">m</span><span class="p">)</span><span class="o">*</span><span class="n">n</span><span class="o">/</span><span class="mf">2.0</span><span class="p">),</span>
126                                        <span class="p">((</span><span class="n">n</span><span class="o">-</span><span class="mf">3.0</span><span class="o">+</span><span class="n">m</span><span class="p">)</span><span class="o">/</span><span class="mf">2.0</span><span class="p">))</span><span class="o">/</span><span class="nb">pow</span><span class="p">(</span><span class="n">Rg</span><span class="p">,(</span><span class="n">n</span><span class="o">-</span><span class="mf">3.0</span><span class="o">+</span><span class="n">m</span><span class="p">))</span>
127        <span class="n">inten</span> <span class="o">=</span> <span class="n">F</span> <span class="o">+</span> <span class="n">bgd</span>
128   
129        <span class="k">return</span> <span class="n">inten</span>
130   
131<div class="viewcode-block" id="GuinierPorodModel.run"><a class="viewcode-back" href="../../../dev/api/sas.models.html#sas.models.GuinierPorodModel.GuinierPorodModel.run">[docs]</a>    <span class="k">def</span> <span class="nf">run</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">x</span> <span class="o">=</span> <span class="mf">0.0</span><span class="p">):</span>
132        <span class="sd">&quot;&quot;&quot; Evaluate the model</span>
133<span class="sd">            @param x: input q-value (float or [float, float] as [r, theta])</span>
134<span class="sd">            @return: (guinier value)</span>
135<span class="sd">        &quot;&quot;&quot;</span>
136        <span class="k">if</span> <span class="n">x</span><span class="o">.</span><span class="n">__class__</span><span class="o">.</span><span class="n">__name__</span> <span class="o">==</span> <span class="s">&#39;list&#39;</span><span class="p">:</span>
137            <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_guinier_porod</span><span class="p">(</span><span class="n">x</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
138        <span class="k">elif</span> <span class="n">x</span><span class="o">.</span><span class="n">__class__</span><span class="o">.</span><span class="n">__name__</span> <span class="o">==</span> <span class="s">&#39;tuple&#39;</span><span class="p">:</span>
139            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">,</span> <span class="s">&quot;Tuples are not allowed as input to models&quot;</span>
140        <span class="k">else</span><span class="p">:</span>
141            <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_guinier_porod</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
142   </div>
143<div class="viewcode-block" id="GuinierPorodModel.runXY"><a class="viewcode-back" href="../../../dev/api/sas.models.html#sas.models.GuinierPorodModel.GuinierPorodModel.runXY">[docs]</a>    <span class="k">def</span> <span class="nf">runXY</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">x</span> <span class="o">=</span> <span class="mf">0.0</span><span class="p">):</span>
144        <span class="sd">&quot;&quot;&quot; Evaluate the model</span>
145<span class="sd">            @param x: input q-value (float or [float, float] as [qx, qy])</span>
146<span class="sd">            @return: guinier value</span>
147<span class="sd">        &quot;&quot;&quot;</span>
148        <span class="k">if</span> <span class="n">x</span><span class="o">.</span><span class="n">__class__</span><span class="o">.</span><span class="n">__name__</span> <span class="o">==</span> <span class="s">&#39;list&#39;</span><span class="p">:</span>
149            <span class="n">q</span> <span class="o">=</span> <span class="n">sqrt</span><span class="p">(</span><span class="n">x</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">**</span><span class="mi">2</span> <span class="o">+</span> <span class="n">x</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span>
150            <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_guinier_porod</span><span class="p">(</span><span class="n">q</span><span class="p">)</span>
151        <span class="k">elif</span> <span class="n">x</span><span class="o">.</span><span class="n">__class__</span><span class="o">.</span><span class="n">__name__</span> <span class="o">==</span> <span class="s">&#39;tuple&#39;</span><span class="p">:</span>
152            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">,</span> <span class="s">&quot;Tuples are not allowed as input to models&quot;</span>
153        <span class="k">else</span><span class="p">:</span>
154            <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_guinier_porod</span><span class="p">(</span><span class="n">x</span><span class="p">)</span></div></div>
155</pre></div>
156
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