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51  <h1>Source code for sas.models.DebyeModel</h1><div class="highlight"><pre>
52<span class="sd">&quot;&quot;&quot; </span>
53<span class="sd">    Provide F(x) = 2( exp(-x) + x - 1 )/x**2</span>
54<span class="sd">    with x = (q*R_g)**2</span>
55<span class="sd">    </span>
56<span class="sd">    Debye function as a BaseComponent model</span>
57<span class="sd">&quot;&quot;&quot;</span>
58<span class="kn">from</span> <span class="nn">sas.models.BaseComponent</span> <span class="kn">import</span> <span class="n">BaseComponent</span>
59<span class="kn">import</span> <span class="nn">math</span>
60
61<div class="viewcode-block" id="DebyeModel"><a class="viewcode-back" href="../../../dev/api/sas.models.html#sas.models.DebyeModel.DebyeModel">[docs]</a><span class="k">class</span> <span class="nc">DebyeModel</span><span class="p">(</span><span class="n">BaseComponent</span><span class="p">):</span>
62    <span class="sd">&quot;&quot;&quot;</span>
63<span class="sd">        Class that evaluates a Debye model.</span>
64<span class="sd">        </span>
65<span class="sd">        F(x) = 2( exp(-x) + x - 1 )/x**2</span>
66<span class="sd">        with x = (q*R_g)**2</span>
67<span class="sd">        </span>
68<span class="sd">        The model has three parameters: </span>
69<span class="sd">            Rg     =  radius of gyration</span>
70<span class="sd">            scale  =  scale factor</span>
71<span class="sd">            bkd    =  Constant background</span>
72<span class="sd">    &quot;&quot;&quot;</span>
73       
74    <span class="k">def</span> <span class="nf">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
75        <span class="sd">&quot;&quot;&quot; Initialization &quot;&quot;&quot;</span>
76       
77        <span class="c"># Initialize BaseComponent first, then sphere</span>
78        <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>
79       
80        <span class="c">## Name of the model</span>
81        <span class="bp">self</span><span class="o">.</span><span class="n">name</span> <span class="o">=</span> <span class="s">&quot;Debye&quot;</span>
82        <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>
83<span class="s">        F(x) = 2( exp(-x) + x - 1 )/x**2</span>
84<span class="s">        with x = (q*R_g)**2</span>
85<span class="s">        </span>
86<span class="s">        The model has three parameters: </span>
87<span class="s">        Rg     =  radius of gyration</span>
88<span class="s">        scale  =  scale factor</span>
89<span class="s">        bkd    =  Constant background</span>
90<span class="s">        &quot;&quot;&quot;</span>
91        <span class="c">## Define parameters</span>
92        <span class="bp">self</span><span class="o">.</span><span class="n">params</span> <span class="o">=</span> <span class="p">{}</span>
93        <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">50.0</span>
94        <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>
95        <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">0.0</span>
96
97        <span class="c">## Parameter details [units, min, max]</span>
98        <span class="bp">self</span><span class="o">.</span><span class="n">details</span> <span class="o">=</span> <span class="p">{}</span>
99        <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>
100        <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>
101        <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>
102        <span class="c">#list of parameter that cannot be fitted</span>
103        <span class="bp">self</span><span class="o">.</span><span class="n">fixed</span> <span class="o">=</span> <span class="p">[]</span> 
104             
105    <span class="k">def</span> <span class="nf">_debye</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span>
106        <span class="sd">&quot;&quot;&quot;</span>
107<span class="sd">            Evaluate F(x)= scale * D + bkd</span>
108<span class="sd">            has 2 internal parameters :</span>
109<span class="sd">                    D = 2 * (exp(-y) + y - 1)/y**2 </span>
110<span class="sd">                    y = (x * Rg)^(2)</span>
111<span class="sd">        &quot;&quot;&quot;</span>
112        <span class="c"># Note that a zero denominator value will raise</span>
113        <span class="c"># an exception</span>
114        <span class="n">y</span> <span class="o">=</span> <span class="p">(</span><span class="n">x</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><span class="o">**</span><span class="mf">2.0</span>
115        <span class="k">if</span> <span class="n">x</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
116            <span class="n">D</span> <span class="o">=</span> <span class="mi">1</span>
117        <span class="k">else</span><span class="p">:</span>
118            <span class="n">D</span> <span class="o">=</span> <span class="mf">2.0</span><span class="o">*</span><span class="p">(</span> <span class="n">math</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="o">-</span><span class="n">y</span><span class="p">)</span> <span class="o">+</span> <span class="n">y</span> <span class="o">-</span><span class="mf">1.0</span> <span class="p">)</span><span class="o">/</span><span class="n">y</span><span class="o">**</span><span class="mf">2.0</span>
119        <span class="k">return</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> <span class="o">*</span> <span class="n">D</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>
120   
121<div class="viewcode-block" id="DebyeModel.run"><a class="viewcode-back" href="../../../dev/api/sas.models.html#sas.models.DebyeModel.DebyeModel.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>
122        <span class="sd">&quot;&quot;&quot; Evaluate the model</span>
123<span class="sd">            @param x: input q-value (float or [float, float] as [r, theta])</span>
124<span class="sd">            @return: (debye value)</span>
125<span class="sd">        &quot;&quot;&quot;</span>
126        <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>
127            <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_debye</span><span class="p">(</span><span class="n">x</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
128        <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>
129            <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>
130        <span class="k">else</span><span class="p">:</span>
131            <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_debye</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
132   </div>
133<div class="viewcode-block" id="DebyeModel.runXY"><a class="viewcode-back" href="../../../dev/api/sas.models.html#sas.models.DebyeModel.DebyeModel.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>
134        <span class="sd">&quot;&quot;&quot; Evaluate the model</span>
135<span class="sd">            @param x: input q-value (float or [float, float] as [qx, qy])</span>
136<span class="sd">            @return: debye value</span>
137<span class="sd">        &quot;&quot;&quot;</span>
138        <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>
139            <span class="n">q</span> <span class="o">=</span> <span class="n">math</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>
140            <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_debye</span><span class="p">(</span><span class="n">q</span><span class="p">)</span>
141        <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>
142            <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>
143        <span class="k">else</span><span class="p">:</span>
144            <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_debye</span><span class="p">(</span><span class="n">x</span><span class="p">)</span></div></div>
145</pre></div>
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