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51  <h1>Source code for sas.models.BEPolyelectrolyte</h1><div class="highlight"><pre>
52<span class="sd">&quot;&quot;&quot;    </span>
53<span class="sd"> Provide F(x) = K*1/(4*pi*Lb*(alpha)^(2))*(q^(2)+k2)/(1+(r02)^(2))*(q^(2)+k2)\</span>
54<span class="sd">                       *(q^(2)-(12*h*C/b^(2)))</span>
55<span class="sd"> BEPolyelectrolyte as a BaseComponent model</span>
56<span class="sd">&quot;&quot;&quot;</span>
57
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="BEPolyelectrolyte"><a class="viewcode-back" href="../../../dev/api/sas.models.html#sas.models.BEPolyelectrolyte.BEPolyelectrolyte">[docs]</a><span class="k">class</span> <span class="nc">BEPolyelectrolyte</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 BEPolyelectrolyte.</span>
64<span class="sd">        </span>
65<span class="sd">        F(x) = K*1/(4*pi*Lb*(alpha)^(2))*(q^(2)+k2)/(1+(r02)^(2))*(q^(2)+k2)\</span>
66<span class="sd">                       *(q^(2)-(12*h*C/b^(2))) </span>
67<span class="sd">        </span>
68<span class="sd">        The model has Eight parameters: </span>
69<span class="sd">            K        =  Constrast factor of the polymer</span>
70<span class="sd">            Lb       =  Bjerrum length</span>
71<span class="sd">            H        =  virial parameter</span>
72<span class="sd">            B        =  monomer length</span>
73<span class="sd">            Cs       =  Concentration of monovalent salt </span>
74<span class="sd">            alpha    =  ionazation degree </span>
75<span class="sd">            C        = polymer molar concentration</span>
76<span class="sd">            bkd      = background</span>
77<span class="sd">    &quot;&quot;&quot;</span>
78       
79    <span class="k">def</span> <span class="nf">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
80        <span class="sd">&quot;&quot;&quot; Initialization &quot;&quot;&quot;</span>
81       
82        <span class="c"># Initialize BaseComponent first, then sphere</span>
83        <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>
84       
85        <span class="c">## Name of the model</span>
86        <span class="bp">self</span><span class="o">.</span><span class="n">name</span> <span class="o">=</span> <span class="s">&quot;BEPolyelectrolyte&quot;</span>
87        <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>
88<span class="s">        F(x) = K*1/(4*pi*Lb*(alpha)^(2))*(q^(2)+k^(2))/(1+(r02)^(2))</span>
89<span class="s">            *(q^(2)+k^(2))*(q^(2)-(12*h*C/b^(2)))+bkd</span>
90<span class="s">                </span>
91<span class="s">        The model has Eight parameters: </span>
92<span class="s">        K        =  Constrast factor of the polymer</span>
93<span class="s">        Lb       =  Bjerrum length</span>
94<span class="s">        H        =  virial parameter</span>
95<span class="s">        B        =  monomer length</span>
96<span class="s">        Cs       =  Concentration of monovalent salt </span>
97<span class="s">        alpha    =  ionazation degree </span>
98<span class="s">        C        = polymer molar concentration</span>
99<span class="s">        bkd      = background</span>
100<span class="s">        &quot;&quot;&quot;</span>
101        <span class="c">## Define parameters</span>
102        <span class="bp">self</span><span class="o">.</span><span class="n">params</span> <span class="o">=</span> <span class="p">{}</span>
103        <span class="bp">self</span><span class="o">.</span><span class="n">params</span><span class="p">[</span><span class="s">&#39;k&#39;</span><span class="p">]</span>     <span class="o">=</span> <span class="mi">10</span>
104        <span class="bp">self</span><span class="o">.</span><span class="n">params</span><span class="p">[</span><span class="s">&#39;lb&#39;</span><span class="p">]</span>    <span class="o">=</span> <span class="mf">7.1</span>
105        <span class="bp">self</span><span class="o">.</span><span class="n">params</span><span class="p">[</span><span class="s">&#39;h&#39;</span><span class="p">]</span>     <span class="o">=</span> <span class="mi">12</span>
106        <span class="bp">self</span><span class="o">.</span><span class="n">params</span><span class="p">[</span><span class="s">&#39;b&#39;</span><span class="p">]</span>     <span class="o">=</span> <span class="mi">10</span>
107        <span class="bp">self</span><span class="o">.</span><span class="n">params</span><span class="p">[</span><span class="s">&#39;cs&#39;</span><span class="p">]</span>    <span class="o">=</span> <span class="mf">0.0</span>
108        <span class="bp">self</span><span class="o">.</span><span class="n">params</span><span class="p">[</span><span class="s">&#39;alpha&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="mf">0.05</span>
109        <span class="bp">self</span><span class="o">.</span><span class="n">params</span><span class="p">[</span><span class="s">&#39;c&#39;</span><span class="p">]</span>     <span class="o">=</span> <span class="mf">0.7</span>
110        <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>
111
112        <span class="c">## Parameter details [units, min, max]</span>
113        <span class="bp">self</span><span class="o">.</span><span class="n">details</span> <span class="o">=</span> <span class="p">{}</span>
114        <span class="bp">self</span><span class="o">.</span><span class="n">details</span><span class="p">[</span><span class="s">&#39;k&#39;</span><span class="p">]</span>     <span class="o">=</span> <span class="p">[</span><span class="s">&#39;[barns]&#39;</span><span class="p">,</span> <span class="bp">None</span><span class="p">,</span> <span class="bp">None</span><span class="p">]</span>
115        <span class="bp">self</span><span class="o">.</span><span class="n">details</span><span class="p">[</span><span class="s">&#39;lb&#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>
116        <span class="bp">self</span><span class="o">.</span><span class="n">details</span><span class="p">[</span><span class="s">&#39;h&#39;</span><span class="p">]</span>     <span class="o">=</span> <span class="p">[</span><span class="s">&#39;[1/A^(2)]&#39;</span><span class="p">,</span> <span class="bp">None</span><span class="p">,</span> <span class="bp">None</span><span class="p">]</span>
117        <span class="bp">self</span><span class="o">.</span><span class="n">details</span><span class="p">[</span><span class="s">&#39;b&#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>
118        <span class="bp">self</span><span class="o">.</span><span class="n">details</span><span class="p">[</span><span class="s">&#39;cs&#39;</span><span class="p">]</span>    <span class="o">=</span> <span class="p">[</span><span class="s">&#39;[mol/L]&#39;</span><span class="p">,</span> <span class="bp">None</span><span class="p">,</span> <span class="bp">None</span><span class="p">]</span>
119        <span class="bp">self</span><span class="o">.</span><span class="n">details</span><span class="p">[</span><span class="s">&#39;alpha&#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>
120        <span class="bp">self</span><span class="o">.</span><span class="n">details</span><span class="p">[</span><span class="s">&#39;c&#39;</span><span class="p">]</span>     <span class="o">=</span> <span class="p">[</span><span class="s">&#39;[mol/L]&#39;</span><span class="p">,</span> <span class="bp">None</span><span class="p">,</span> <span class="bp">None</span><span class="p">]</span>
121        <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>
122        <span class="c">#list of parameter that cannot be fitted</span>
123        <span class="bp">self</span><span class="o">.</span><span class="n">fixed</span> <span class="o">=</span> <span class="p">[]</span>
124               
125    <span class="k">def</span> <span class="nf">_BEPoly</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span>
126        <span class="sd">&quot;&quot;&quot;</span>
127<span class="sd">            Evaluate  </span>
128<span class="sd">            F(x) = K*1/(4*pi*Lb*(alpha)^(2))*(q^(2)+k2)/(1+(r02)^(2))</span>
129<span class="sd">                *(q^(2)+k2)*(q^(2)-(12*h*C/b^(2)))</span>
130<span class="sd">        </span>
131<span class="sd">            has 3 internal parameters :</span>
132<span class="sd">                   The inverse Debye Length: K2 = 4*pi*Lb*(2*Cs+alpha*C)</span>
133<span class="sd">                   r02 =1/alpha/Ca^(0.5)*(B/(48*pi*Lb)^(0.5))</span>
134<span class="sd">                   Ca = C*6.022136e-4</span>
135<span class="sd">        &quot;&quot;&quot;</span>
136        <span class="n">Ca</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;c&#39;</span><span class="p">]</span> <span class="o">*</span> <span class="mf">6.022136e-4</span>
137        <span class="c">#remove singulars</span>
138        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">params</span><span class="p">[</span><span class="s">&#39;alpha&#39;</span><span class="p">]</span><span class="o">&lt;=</span><span class="mi">0</span> <span class="ow">or</span> <span class="bp">self</span><span class="o">.</span><span class="n">params</span><span class="p">[</span><span class="s">&#39;c&#39;</span><span class="p">]</span><span class="o">&lt;=</span><span class="mi">0</span>\
139            <span class="ow">or</span> <span class="bp">self</span><span class="o">.</span><span class="n">params</span><span class="p">[</span><span class="s">&#39;b&#39;</span><span class="p">]</span><span class="o">==</span><span class="mi">0</span> <span class="ow">or</span> <span class="bp">self</span><span class="o">.</span><span class="n">params</span><span class="p">[</span><span class="s">&#39;lb&#39;</span><span class="p">]</span><span class="o">&lt;=</span><span class="mi">0</span><span class="p">:</span>
140            <span class="k">return</span> <span class="mi">0</span>
141        <span class="k">else</span><span class="p">:</span>
142           
143            <span class="n">K2</span> <span class="o">=</span> <span class="mf">4.0</span> <span class="o">*</span> <span class="n">math</span><span class="o">.</span><span class="n">pi</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;lb&#39;</span><span class="p">]</span> <span class="o">*</span> <span class="p">(</span><span class="mi">2</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;cs&#39;</span><span class="p">]</span> <span class="o">+</span> \
144                     <span class="bp">self</span><span class="o">.</span><span class="n">params</span><span class="p">[</span><span class="s">&#39;alpha&#39;</span><span class="p">]</span> <span class="o">*</span> <span class="n">Ca</span><span class="p">)</span>
145           
146            <span class="n">r02</span> <span class="o">=</span> <span class="mf">1.0</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;alpha&#39;</span><span class="p">]</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">Ca</span><span class="p">)</span> <span class="o">*</span> \
147                    <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">params</span><span class="p">[</span><span class="s">&#39;b&#39;</span><span class="p">]</span><span class="o">/</span>\
148                     <span class="n">math</span><span class="o">.</span><span class="n">sqrt</span><span class="p">((</span><span class="mf">48.0</span><span class="o">*</span><span class="n">math</span><span class="o">.</span><span class="n">pi</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;lb&#39;</span><span class="p">])))</span>
149           
150            <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;k&#39;</span><span class="p">]</span><span class="o">/</span><span class="p">(</span> <span class="mf">4.0</span> <span class="o">*</span> <span class="n">math</span><span class="o">.</span><span class="n">pi</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;lb&#39;</span><span class="p">]</span> \
151                                      <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;alpha&#39;</span><span class="p">]</span><span class="o">**</span><span class="mi">2</span> <span class="p">)</span> \
152                   <span class="o">*</span> <span class="p">(</span> <span class="n">x</span><span class="o">**</span><span class="mi">2</span> <span class="o">+</span> <span class="n">K2</span> <span class="p">)</span> <span class="o">/</span> <span class="p">(</span> <span class="mf">1.0</span> <span class="o">+</span> <span class="n">r02</span><span class="o">**</span><span class="mi">2</span> <span class="o">*</span> <span class="p">(</span> <span class="n">x</span><span class="o">**</span><span class="mi">2</span> <span class="o">+</span> <span class="n">K2</span> <span class="p">)</span> \
153                        <span class="o">*</span> <span class="p">(</span><span class="n">x</span><span class="o">**</span><span class="mi">2</span> <span class="o">-</span> <span class="p">(</span> <span class="mf">12.0</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;h&#39;</span><span class="p">]</span> \
154                        <span class="o">*</span> <span class="n">Ca</span><span class="o">/</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">params</span><span class="p">[</span><span class="s">&#39;b&#39;</span><span class="p">]</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span> <span class="p">)))</span> \
155                        <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>
156   
157<div class="viewcode-block" id="BEPolyelectrolyte.run"><a class="viewcode-back" href="../../../dev/api/sas.models.html#sas.models.BEPolyelectrolyte.BEPolyelectrolyte.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>
158        <span class="sd">&quot;&quot;&quot; Evaluate the model</span>
159<span class="sd">            @param x: input q-value (float or [float, float] as [r, theta])</span>
160<span class="sd">            @return: (debye value)</span>
161<span class="sd">        &quot;&quot;&quot;</span>
162        <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>
163            <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_BEPoly</span><span class="p">(</span><span class="n">x</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
164        <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>
165            <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 BaseComponent models&quot;</span>
166        <span class="k">else</span><span class="p">:</span>
167            <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_BEPoly</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
168   </div>
169<div class="viewcode-block" id="BEPolyelectrolyte.runXY"><a class="viewcode-back" href="../../../dev/api/sas.models.html#sas.models.BEPolyelectrolyte.BEPolyelectrolyte.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>
170        <span class="sd">&quot;&quot;&quot; Evaluate the model</span>
171<span class="sd">            @param x: input q-value (float or [float, float] as [qx, qy])</span>
172<span class="sd">            @return: debye value</span>
173<span class="sd">        &quot;&quot;&quot;</span>
174        <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>
175            <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>
176            <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_BEPoly</span><span class="p">(</span><span class="n">q</span><span class="p">)</span>
177        <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>
178            <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 BaseComponent models&quot;</span>
179        <span class="k">else</span><span class="p">:</span>
180            <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_BEPoly</span><span class="p">(</span><span class="n">x</span><span class="p">)</span></div></div>
181</pre></div>
182
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