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| 46 | |
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| 49 | <div class="bodywrapper"> |
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| 50 | <div class="body"> |
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| 51 | |
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| 52 | <div class="section" id="invariant"> |
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| 53 | <h1>invariant<a class="headerlink" href="#invariant" title="Permalink to this headline">¶</a></h1> |
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| 54 | <div class="section" id="module-sans.invariant.invariant"> |
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| 55 | <span id="sans-invariant-invariant"></span><h2><a class="reference internal" href="#module-sans.invariant.invariant"><tt class="xref py py-mod docutils literal"><span class="pre">sans.invariant.invariant</span></tt></a><a class="headerlink" href="#module-sans.invariant.invariant" title="Permalink to this headline">¶</a></h2> |
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| 56 | <p>This module implements invariant and its related computations.</p> |
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| 57 | <table class="docutils field-list" frame="void" rules="none"> |
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| 58 | <col class="field-name" /> |
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| 59 | <col class="field-body" /> |
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| 60 | <tbody valign="top"> |
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| 61 | <tr class="field"><th class="field-name">author:</th><td class="field-body">Gervaise B. Alina/UTK</td> |
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| 62 | </tr> |
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| 63 | <tr class="field"><th class="field-name">author:</th><td class="field-body">Mathieu Doucet/UTK</td> |
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| 64 | </tr> |
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| 65 | <tr class="field"><th class="field-name">author:</th><td class="field-body">Jae Cho/UTK</td> |
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| 66 | </tr> |
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| 67 | </tbody> |
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| 68 | </table> |
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| 69 | <dl class="class"> |
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| 70 | <dt id="sans.invariant.invariant.Extrapolator"> |
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| 71 | <em class="property">class </em><tt class="descclassname">sans.invariant.invariant.</tt><tt class="descname">Extrapolator</tt><big>(</big><em>data</em>, <em>model=None</em><big>)</big><a class="headerlink" href="#sans.invariant.invariant.Extrapolator" title="Permalink to this definition">¶</a></dt> |
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| 72 | <dd><p>Extrapolate I(q) distribution using a given model</p> |
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| 73 | <dl class="method"> |
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| 74 | <dt id="sans.invariant.invariant.Extrapolator.fit"> |
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| 75 | <tt class="descname">fit</tt><big>(</big><em>power=None</em>, <em>qmin=None</em>, <em>qmax=None</em><big>)</big><a class="headerlink" href="#sans.invariant.invariant.Extrapolator.fit" title="Permalink to this definition">¶</a></dt> |
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| 76 | <dd><p>Fit data for y = ax + b return a and b</p> |
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| 77 | <table class="docutils field-list" frame="void" rules="none"> |
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| 78 | <col class="field-name" /> |
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| 79 | <col class="field-body" /> |
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| 80 | <tbody valign="top"> |
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| 81 | <tr class="field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first last simple"> |
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| 82 | <li><strong>power</strong> – a fixed, otherwise None</li> |
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| 83 | <li><strong>qmin</strong> – Minimum Q-value</li> |
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| 84 | <li><strong>qmax</strong> – Maximum Q-value</li> |
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| 85 | </ul> |
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| 86 | </td> |
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| 87 | </tr> |
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| 88 | </tbody> |
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| 89 | </table> |
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| 90 | </dd></dl> |
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| 91 | |
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| 92 | </dd></dl> |
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| 93 | |
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| 94 | <dl class="class"> |
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| 95 | <dt id="sans.invariant.invariant.Guinier"> |
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| 96 | <em class="property">class </em><tt class="descclassname">sans.invariant.invariant.</tt><tt class="descname">Guinier</tt><big>(</big><em>scale=1</em>, <em>radius=60</em><big>)</big><a class="headerlink" href="#sans.invariant.invariant.Guinier" title="Permalink to this definition">¶</a></dt> |
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| 97 | <dd><p>Bases: <a class="reference internal" href="#sans.invariant.invariant.Transform" title="sans.invariant.invariant.Transform"><tt class="xref py py-class docutils literal"><span class="pre">sans.invariant.invariant.Transform</span></tt></a></p> |
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| 98 | <p>class of type Transform that performs operations related to guinier |
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| 99 | function</p> |
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| 100 | <dl class="method"> |
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| 101 | <dt id="sans.invariant.invariant.Guinier.evaluate_model"> |
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| 102 | <tt class="descname">evaluate_model</tt><big>(</big><em>x</em><big>)</big><a class="headerlink" href="#sans.invariant.invariant.Guinier.evaluate_model" title="Permalink to this definition">¶</a></dt> |
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| 103 | <dd>return F(x)= scale* e-((radius*x)**2/3)</dd></dl> |
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| 104 | |
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| 105 | <dl class="method"> |
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| 106 | <dt id="sans.invariant.invariant.Guinier.evaluate_model_errors"> |
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| 107 | <tt class="descname">evaluate_model_errors</tt><big>(</big><em>x</em><big>)</big><a class="headerlink" href="#sans.invariant.invariant.Guinier.evaluate_model_errors" title="Permalink to this definition">¶</a></dt> |
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| 108 | <dd><p>Returns the error on I(q) for the given array of q-values</p> |
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| 109 | <table class="docutils field-list" frame="void" rules="none"> |
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| 110 | <col class="field-name" /> |
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| 111 | <col class="field-body" /> |
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| 112 | <tbody valign="top"> |
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| 113 | <tr class="field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first last simple"> |
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| 114 | <li><strong>x</strong> – array of q-values</li> |
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| 115 | </ul> |
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| 116 | </td> |
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| 117 | </tr> |
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| 118 | </tbody> |
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| 119 | </table> |
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| 120 | </dd></dl> |
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| 121 | |
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| 122 | <dl class="method"> |
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| 123 | <dt id="sans.invariant.invariant.Guinier.extract_model_parameters"> |
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| 124 | <tt class="descname">extract_model_parameters</tt><big>(</big><em>constant</em>, <em>slope</em>, <em>dconstant=0</em>, <em>dslope=0</em><big>)</big><a class="headerlink" href="#sans.invariant.invariant.Guinier.extract_model_parameters" title="Permalink to this definition">¶</a></dt> |
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| 125 | <dd>assign new value to the scale and the radius</dd></dl> |
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| 126 | |
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| 127 | <dl class="method"> |
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| 128 | <dt id="sans.invariant.invariant.Guinier.get_allowed_bins"> |
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| 129 | <tt class="descname">get_allowed_bins</tt><big>(</big><em>data</em><big>)</big><a class="headerlink" href="#sans.invariant.invariant.Guinier.get_allowed_bins" title="Permalink to this definition">¶</a></dt> |
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| 130 | <dd><p>Goes through the data points and returns a list of boolean values |
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| 131 | to indicate whether each points is allowed by the model or not.</p> |
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| 132 | <table class="docutils field-list" frame="void" rules="none"> |
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| 133 | <col class="field-name" /> |
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| 134 | <col class="field-body" /> |
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| 135 | <tbody valign="top"> |
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| 136 | <tr class="field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first last simple"> |
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| 137 | <li><strong>data</strong> – Data1D object</li> |
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| 138 | </ul> |
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| 139 | </td> |
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| 140 | </tr> |
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| 141 | </tbody> |
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| 142 | </table> |
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| 143 | </dd></dl> |
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| 144 | |
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| 145 | <dl class="method"> |
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| 146 | <dt id="sans.invariant.invariant.Guinier.linearize_data"> |
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| 147 | <tt class="descname">linearize_data</tt><big>(</big><em>data</em><big>)</big><a class="headerlink" href="#sans.invariant.invariant.Guinier.linearize_data" title="Permalink to this definition">¶</a></dt> |
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| 148 | <dd><p>Linearize data so that a linear fit can be performed. |
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| 149 | Filter out the data that can’t be transformed.</p> |
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| 150 | <table class="docutils field-list" frame="void" rules="none"> |
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| 151 | <col class="field-name" /> |
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| 152 | <col class="field-body" /> |
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| 153 | <tbody valign="top"> |
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| 154 | <tr class="field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first last simple"> |
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| 155 | <li><strong>data</strong> – LoadData1D instance</li> |
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| 156 | </ul> |
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| 157 | </td> |
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| 158 | </tr> |
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| 159 | </tbody> |
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| 160 | </table> |
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| 161 | </dd></dl> |
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| 162 | |
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| 163 | <dl class="method"> |
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| 164 | <dt id="sans.invariant.invariant.Guinier.linearize_q_value"> |
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| 165 | <tt class="descname">linearize_q_value</tt><big>(</big><em>value</em><big>)</big><a class="headerlink" href="#sans.invariant.invariant.Guinier.linearize_q_value" title="Permalink to this definition">¶</a></dt> |
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| 166 | <dd><p>Transform the input q-value for linearization</p> |
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| 167 | <table class="docutils field-list" frame="void" rules="none"> |
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| 168 | <col class="field-name" /> |
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| 169 | <col class="field-body" /> |
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| 170 | <tbody valign="top"> |
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| 171 | <tr class="field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first simple"> |
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| 172 | <li><strong>value</strong> – q-value</li> |
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| 173 | </ul> |
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| 174 | </td> |
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| 175 | </tr> |
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| 176 | <tr class="field"><th class="field-name">Returns:</th><td class="field-body"><p class="first last">q*q</p> |
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| 177 | </td> |
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| 178 | </tr> |
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| 179 | </tbody> |
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| 180 | </table> |
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| 181 | </dd></dl> |
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| 182 | |
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| 183 | </dd></dl> |
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| 184 | |
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| 185 | <dl class="class"> |
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| 186 | <dt id="sans.invariant.invariant.InvariantCalculator"> |
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| 187 | <em class="property">class </em><tt class="descclassname">sans.invariant.invariant.</tt><tt class="descname">InvariantCalculator</tt><big>(</big><em>data</em>, <em>background=0</em>, <em>scale=1</em><big>)</big><a class="headerlink" href="#sans.invariant.invariant.InvariantCalculator" title="Permalink to this definition">¶</a></dt> |
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| 188 | <dd><p>Bases: <tt class="xref py py-class docutils literal"><span class="pre">object</span></tt></p> |
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| 189 | <p>Compute invariant if data is given. |
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| 190 | Can provide volume fraction and surface area if the user provides |
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| 191 | Porod constant and contrast values.</p> |
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| 192 | <table class="docutils field-list" frame="void" rules="none"> |
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| 193 | <col class="field-name" /> |
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| 194 | <col class="field-body" /> |
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| 195 | <tbody valign="top"> |
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| 196 | <tr class="field"><th class="field-name">Precondition :</th><td class="field-body">the user must send a data of type DataLoader.Data1D |
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| 197 | the user provide background and scale values.</td> |
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| 198 | </tr> |
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| 199 | <tr class="field"><th class="field-name">Note :</th><td class="field-body">Some computations depends on each others.</td> |
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| 200 | </tr> |
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| 201 | </tbody> |
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| 202 | </table> |
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| 203 | <dl class="method"> |
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| 204 | <dt id="sans.invariant.invariant.InvariantCalculator.get_data"> |
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| 205 | <tt class="descname">get_data</tt><big>(</big><big>)</big><a class="headerlink" href="#sans.invariant.invariant.InvariantCalculator.get_data" title="Permalink to this definition">¶</a></dt> |
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| 206 | <dd><table class="docutils field-list" frame="void" rules="none"> |
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| 207 | <col class="field-name" /> |
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| 208 | <col class="field-body" /> |
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| 209 | <tbody valign="top"> |
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| 210 | <tr class="field"><th class="field-name">Returns:</th><td class="field-body">self._data</td> |
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| 211 | </tr> |
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| 212 | </tbody> |
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| 213 | </table> |
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| 214 | </dd></dl> |
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| 215 | |
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| 216 | <dl class="method"> |
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| 217 | <dt id="sans.invariant.invariant.InvariantCalculator.get_extra_data_high"> |
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| 218 | <tt class="descname">get_extra_data_high</tt><big>(</big><em>npts_in=None</em>, <em>q_end=10</em>, <em>npts=20</em><big>)</big><a class="headerlink" href="#sans.invariant.invariant.InvariantCalculator.get_extra_data_high" title="Permalink to this definition">¶</a></dt> |
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| 219 | <dd><p>Returns the extrapolated data used for the high-Q invariant calculation. |
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| 220 | By default, the distribution will cover the data points used for the |
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| 221 | extrapolation. The number of overlap points is a parameter (npts_in). |
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| 222 | By default, the maximum q-value of the distribution will be Q_MAXIMUM, |
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| 223 | the maximum q-value used when extrapolating for the purpose of the |
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| 224 | invariant calculation.</p> |
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| 225 | <table class="docutils field-list" frame="void" rules="none"> |
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| 226 | <col class="field-name" /> |
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| 227 | <col class="field-body" /> |
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| 228 | <tbody valign="top"> |
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| 229 | <tr class="field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first last simple"> |
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| 230 | <li><strong>npts_in</strong> – number of data points for which the extrapolated data overlap</li> |
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| 231 | <li><strong>q_end</strong> – is the maximum value to uses for extrapolated data</li> |
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| 232 | <li><strong>npts</strong> – the number of points in the extrapolated distribution</li> |
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| 233 | </ul> |
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| 234 | </td> |
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| 235 | </tr> |
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| 236 | </tbody> |
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| 237 | </table> |
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| 238 | </dd></dl> |
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| 239 | |
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| 240 | <dl class="method"> |
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| 241 | <dt id="sans.invariant.invariant.InvariantCalculator.get_extra_data_low"> |
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| 242 | <tt class="descname">get_extra_data_low</tt><big>(</big><em>npts_in=None</em>, <em>q_start=None</em>, <em>npts=20</em><big>)</big><a class="headerlink" href="#sans.invariant.invariant.InvariantCalculator.get_extra_data_low" title="Permalink to this definition">¶</a></dt> |
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| 243 | <dd><p>Returns the extrapolated data used for the loew-Q invariant calculation. |
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| 244 | By default, the distribution will cover the data points used for the |
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| 245 | extrapolation. The number of overlap points is a parameter (npts_in). |
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| 246 | By default, the maximum q-value of the distribution will be |
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| 247 | the minimum q-value used when extrapolating for the purpose of the |
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| 248 | invariant calculation.</p> |
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| 249 | <table class="docutils field-list" frame="void" rules="none"> |
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| 250 | <col class="field-name" /> |
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| 251 | <col class="field-body" /> |
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| 252 | <tbody valign="top"> |
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| 253 | <tr class="field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first last simple"> |
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| 254 | <li><strong>npts_in</strong> – number of data points for which the extrapolated data overlap</li> |
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| 255 | <li><strong>q_start</strong> – is the minimum value to uses for extrapolated data</li> |
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| 256 | <li><strong>npts</strong> – the number of points in the extrapolated distribution</li> |
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| 257 | </ul> |
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| 258 | </td> |
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| 259 | </tr> |
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| 260 | </tbody> |
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| 261 | </table> |
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| 262 | </dd></dl> |
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| 263 | |
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| 264 | <dl class="method"> |
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| 265 | <dt id="sans.invariant.invariant.InvariantCalculator.get_extrapolation_power"> |
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| 266 | <tt class="descname">get_extrapolation_power</tt><big>(</big><em>range='high'</em><big>)</big><a class="headerlink" href="#sans.invariant.invariant.InvariantCalculator.get_extrapolation_power" title="Permalink to this definition">¶</a></dt> |
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| 267 | <dd><table class="docutils field-list" frame="void" rules="none"> |
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| 268 | <col class="field-name" /> |
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| 269 | <col class="field-body" /> |
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| 270 | <tbody valign="top"> |
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| 271 | <tr class="field"><th class="field-name">Returns:</th><td class="field-body">the fitted power for power law function for a given extrapolation range</td> |
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| 272 | </tr> |
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| 273 | </tbody> |
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| 274 | </table> |
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| 275 | </dd></dl> |
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| 276 | |
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| 277 | <dl class="method"> |
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| 278 | <dt id="sans.invariant.invariant.InvariantCalculator.get_qstar"> |
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| 279 | <tt class="descname">get_qstar</tt><big>(</big><em>extrapolation=None</em><big>)</big><a class="headerlink" href="#sans.invariant.invariant.InvariantCalculator.get_qstar" title="Permalink to this definition">¶</a></dt> |
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| 280 | <dd><p>Compute the invariant of the local copy of data.</p> |
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| 281 | <table class="docutils field-list" frame="void" rules="none"> |
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| 282 | <col class="field-name" /> |
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| 283 | <col class="field-body" /> |
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| 284 | <tbody valign="top"> |
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| 285 | <tr class="field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first simple"> |
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| 286 | <li><strong>extrapolation</strong> – string to apply optional extrapolation</li> |
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| 287 | </ul> |
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| 288 | </td> |
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| 289 | </tr> |
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| 290 | <tr class="field"><th class="field-name">Return q_star:</th><td class="field-body"><p class="first">invariant of the data within data’s q range</p> |
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| 291 | </td> |
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| 292 | </tr> |
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| 293 | <tr class="field"><th class="field-name">Warning :</th><td class="field-body"><p class="first last">When using setting data to Data1D , the user is responsible of |
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| 294 | checking that the scale and the background are properly apply to the data</p> |
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| 295 | </td> |
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| 296 | </tr> |
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| 297 | </tbody> |
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| 298 | </table> |
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| 299 | </dd></dl> |
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| 300 | |
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| 301 | <dl class="method"> |
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| 302 | <dt id="sans.invariant.invariant.InvariantCalculator.get_qstar_high"> |
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| 303 | <tt class="descname">get_qstar_high</tt><big>(</big><big>)</big><a class="headerlink" href="#sans.invariant.invariant.InvariantCalculator.get_qstar_high" title="Permalink to this definition">¶</a></dt> |
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| 304 | <dd><p>Compute the invariant for extrapolated data at high q range.</p> |
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| 305 | <dl class="docutils"> |
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| 306 | <dt>Implementation:</dt> |
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| 307 | <dd>data = self._get_extra_data_high() |
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| 308 | return self._get_qstar()</dd> |
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| 309 | </dl> |
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| 310 | <table class="docutils field-list" frame="void" rules="none"> |
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| 311 | <col class="field-name" /> |
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| 312 | <col class="field-body" /> |
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| 313 | <tbody valign="top"> |
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| 314 | <tr class="field"><th class="field-name">Return q_star:</th><td class="field-body">the invariant for data extrapolated at high q.</td> |
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| 315 | </tr> |
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| 316 | </tbody> |
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| 317 | </table> |
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| 318 | </dd></dl> |
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| 319 | |
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| 320 | <dl class="method"> |
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| 321 | <dt id="sans.invariant.invariant.InvariantCalculator.get_qstar_low"> |
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| 322 | <tt class="descname">get_qstar_low</tt><big>(</big><big>)</big><a class="headerlink" href="#sans.invariant.invariant.InvariantCalculator.get_qstar_low" title="Permalink to this definition">¶</a></dt> |
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| 323 | <dd><p>Compute the invariant for extrapolated data at low q range.</p> |
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| 324 | <dl class="docutils"> |
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| 325 | <dt>Implementation:</dt> |
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| 326 | <dd>data = self._get_extra_data_low() |
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| 327 | return self._get_qstar()</dd> |
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| 328 | </dl> |
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| 329 | <table class="docutils field-list" frame="void" rules="none"> |
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| 330 | <col class="field-name" /> |
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| 331 | <col class="field-body" /> |
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| 332 | <tbody valign="top"> |
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| 333 | <tr class="field"><th class="field-name">Return q_star:</th><td class="field-body">the invariant for data extrapolated at low q.</td> |
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| 334 | </tr> |
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| 335 | </tbody> |
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| 336 | </table> |
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| 337 | </dd></dl> |
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| 338 | |
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| 339 | <dl class="method"> |
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| 340 | <dt id="sans.invariant.invariant.InvariantCalculator.get_qstar_with_error"> |
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| 341 | <tt class="descname">get_qstar_with_error</tt><big>(</big><em>extrapolation=None</em><big>)</big><a class="headerlink" href="#sans.invariant.invariant.InvariantCalculator.get_qstar_with_error" title="Permalink to this definition">¶</a></dt> |
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| 342 | <dd><p>Compute the invariant uncertainty. |
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| 343 | This uncertainty computation depends on whether or not the data is |
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| 344 | smeared.</p> |
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| 345 | <table class="docutils field-list" frame="void" rules="none"> |
---|
| 346 | <col class="field-name" /> |
---|
| 347 | <col class="field-body" /> |
---|
| 348 | <tbody valign="top"> |
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| 349 | <tr class="field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first simple"> |
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| 350 | <li><strong>extrapolation</strong> – string to apply optional extrapolation</li> |
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| 351 | </ul> |
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| 352 | </td> |
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| 353 | </tr> |
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| 354 | <tr class="field"><th class="field-name">Returns:</th><td class="field-body"><p class="first last">invariant, the invariant uncertainty</p> |
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| 355 | </td> |
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| 356 | </tr> |
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| 357 | </tbody> |
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| 358 | </table> |
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| 359 | </dd></dl> |
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| 360 | |
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| 361 | <dl class="method"> |
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| 362 | <dt id="sans.invariant.invariant.InvariantCalculator.get_surface"> |
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| 363 | <tt class="descname">get_surface</tt><big>(</big><em>contrast</em>, <em>porod_const</em>, <em>extrapolation=None</em><big>)</big><a class="headerlink" href="#sans.invariant.invariant.InvariantCalculator.get_surface" title="Permalink to this definition">¶</a></dt> |
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| 364 | <dd><p>Compute the specific surface from the data.</p> |
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| 365 | <p>Implementation:</p> |
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| 366 | <div class="highlight-python"><pre>V = self.get_volume_fraction(contrast, extrapolation) |
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| 367 | |
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| 368 | Compute the surface given by: |
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| 369 | surface = (2*pi *V(1- V)*porod_const)/ q_star</pre> |
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| 370 | </div> |
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| 371 | <table class="docutils field-list" frame="void" rules="none"> |
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| 372 | <col class="field-name" /> |
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| 373 | <col class="field-body" /> |
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| 374 | <tbody valign="top"> |
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| 375 | <tr class="field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first simple"> |
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| 376 | <li><strong>contrast</strong> – contrast value to compute the volume</li> |
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| 377 | <li><strong>porod_const</strong> – Porod constant to compute the surface</li> |
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| 378 | <li><strong>extrapolation</strong> – string to apply optional extrapolation</li> |
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| 379 | </ul> |
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| 380 | </td> |
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| 381 | </tr> |
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| 382 | <tr class="field"><th class="field-name">Returns:</th><td class="field-body"><p class="first last">specific surface</p> |
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| 383 | </td> |
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| 384 | </tr> |
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| 385 | </tbody> |
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| 386 | </table> |
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| 387 | </dd></dl> |
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| 388 | |
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| 389 | <dl class="method"> |
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| 390 | <dt id="sans.invariant.invariant.InvariantCalculator.get_surface_with_error"> |
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| 391 | <tt class="descname">get_surface_with_error</tt><big>(</big><em>contrast</em>, <em>porod_const</em>, <em>extrapolation=None</em><big>)</big><a class="headerlink" href="#sans.invariant.invariant.InvariantCalculator.get_surface_with_error" title="Permalink to this definition">¶</a></dt> |
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| 392 | <dd><p>Compute uncertainty of the surface value as well as the surface value. |
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| 393 | The uncertainty is given as follow:</p> |
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| 394 | <div class="highlight-python"><pre>dS = porod_const *2*pi[( dV -2*V*dV)/q_star |
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| 395 | + dq_star(v-v**2) |
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| 396 | |
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| 397 | q_star: the invariant value |
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| 398 | dq_star: the invariant uncertainty |
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| 399 | V: the volume fraction value |
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| 400 | dV: the volume uncertainty</pre> |
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| 401 | </div> |
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| 402 | <table class="docutils field-list" frame="void" rules="none"> |
---|
| 403 | <col class="field-name" /> |
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| 404 | <col class="field-body" /> |
---|
| 405 | <tbody valign="top"> |
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| 406 | <tr class="field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first simple"> |
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| 407 | <li><strong>contrast</strong> – contrast value</li> |
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| 408 | <li><strong>porod_const</strong> – porod constant value</li> |
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| 409 | <li><strong>extrapolation</strong> – string to apply optional extrapolation</li> |
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| 410 | </ul> |
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| 411 | </td> |
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| 412 | </tr> |
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| 413 | <tr class="field"><th class="field-name">Return S, dS:</th><td class="field-body"><p class="first last">the surface, with its uncertainty</p> |
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| 414 | </td> |
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| 415 | </tr> |
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| 416 | </tbody> |
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| 417 | </table> |
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| 418 | </dd></dl> |
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| 419 | |
---|
| 420 | <dl class="method"> |
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| 421 | <dt id="sans.invariant.invariant.InvariantCalculator.get_volume_fraction"> |
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| 422 | <tt class="descname">get_volume_fraction</tt><big>(</big><em>contrast</em>, <em>extrapolation=None</em><big>)</big><a class="headerlink" href="#sans.invariant.invariant.InvariantCalculator.get_volume_fraction" title="Permalink to this definition">¶</a></dt> |
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| 423 | <dd><p>Compute volume fraction is deduced as follow:</p> |
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| 424 | <div class="highlight-python"><pre>q_star = 2*(pi*contrast)**2* volume( 1- volume) |
---|
| 425 | for k = 10^(-8)*q_star/(2*(pi*|contrast|)**2) |
---|
| 426 | we get 2 values of volume: |
---|
| 427 | with 1 - 4 * k >= 0 |
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| 428 | volume1 = (1- sqrt(1- 4*k))/2 |
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| 429 | volume2 = (1+ sqrt(1- 4*k))/2 |
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| 430 | |
---|
| 431 | q_star: the invariant value included extrapolation is applied |
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| 432 | unit 1/A^(3)*1/cm |
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| 433 | q_star = self.get_qstar() |
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| 434 | |
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| 435 | the result returned will be 0 <= volume <= 1</pre> |
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| 436 | </div> |
---|
| 437 | <table class="docutils field-list" frame="void" rules="none"> |
---|
| 438 | <col class="field-name" /> |
---|
| 439 | <col class="field-body" /> |
---|
| 440 | <tbody valign="top"> |
---|
| 441 | <tr class="field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first simple"> |
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| 442 | <li><strong>contrast</strong> – contrast value provides by the user of type float. |
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| 443 | contrast unit is 1/A^(2)= 10^(16)cm^(2)</li> |
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| 444 | <li><strong>extrapolation</strong> – string to apply optional extrapolation</li> |
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| 445 | </ul> |
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| 446 | </td> |
---|
| 447 | </tr> |
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| 448 | <tr class="field"><th class="field-name">Returns:</th><td class="field-body"><p class="first">volume fraction</p> |
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| 449 | </td> |
---|
| 450 | </tr> |
---|
| 451 | <tr class="field"><th class="field-name">Note :</th><td class="field-body"><p class="first last">volume fraction must have no unit</p> |
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| 452 | </td> |
---|
| 453 | </tr> |
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| 454 | </tbody> |
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| 455 | </table> |
---|
| 456 | </dd></dl> |
---|
| 457 | |
---|
| 458 | <dl class="method"> |
---|
| 459 | <dt id="sans.invariant.invariant.InvariantCalculator.get_volume_fraction_with_error"> |
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| 460 | <tt class="descname">get_volume_fraction_with_error</tt><big>(</big><em>contrast</em>, <em>extrapolation=None</em><big>)</big><a class="headerlink" href="#sans.invariant.invariant.InvariantCalculator.get_volume_fraction_with_error" title="Permalink to this definition">¶</a></dt> |
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| 461 | <dd><p>Compute uncertainty on volume value as well as the volume fraction |
---|
| 462 | This uncertainty is given by the following equation:</p> |
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| 463 | <div class="highlight-python"><pre>dV = 0.5 * (4*k* dq_star) /(2* math.sqrt(1-k* q_star)) |
---|
| 464 | |
---|
| 465 | for k = 10^(-8)*q_star/(2*(pi*|contrast|)**2) |
---|
| 466 | |
---|
| 467 | q_star: the invariant value including extrapolated value if existing |
---|
| 468 | dq_star: the invariant uncertainty |
---|
| 469 | dV: the volume uncertainty</pre> |
---|
| 470 | </div> |
---|
| 471 | <p>The uncertainty will be set to -1 if it can’t be computed.</p> |
---|
| 472 | <table class="docutils field-list" frame="void" rules="none"> |
---|
| 473 | <col class="field-name" /> |
---|
| 474 | <col class="field-body" /> |
---|
| 475 | <tbody valign="top"> |
---|
| 476 | <tr class="field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first simple"> |
---|
| 477 | <li><strong>contrast</strong> – contrast value</li> |
---|
| 478 | <li><strong>extrapolation</strong> – string to apply optional extrapolation</li> |
---|
| 479 | </ul> |
---|
| 480 | </td> |
---|
| 481 | </tr> |
---|
| 482 | <tr class="field"><th class="field-name">Returns:</th><td class="field-body"><p class="first last">V, dV = volume fraction, error on volume fraction</p> |
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| 483 | </td> |
---|
| 484 | </tr> |
---|
| 485 | </tbody> |
---|
| 486 | </table> |
---|
| 487 | </dd></dl> |
---|
| 488 | |
---|
| 489 | <dl class="method"> |
---|
| 490 | <dt id="sans.invariant.invariant.InvariantCalculator.set_extrapolation"> |
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| 491 | <tt class="descname">set_extrapolation</tt><big>(</big><em>range</em>, <em>npts=4</em>, <em>function=None</em>, <em>power=None</em><big>)</big><a class="headerlink" href="#sans.invariant.invariant.InvariantCalculator.set_extrapolation" title="Permalink to this definition">¶</a></dt> |
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| 492 | <dd><p>Set the extrapolation parameters for the high or low Q-range. |
---|
| 493 | Note that this does not turn extrapolation on or off.</p> |
---|
| 494 | <table class="docutils field-list" frame="void" rules="none"> |
---|
| 495 | <col class="field-name" /> |
---|
| 496 | <col class="field-body" /> |
---|
| 497 | <tbody valign="top"> |
---|
| 498 | <tr class="field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first last simple"> |
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| 499 | <li><strong>range</strong> – a keyword set the type of extrapolation . type string</li> |
---|
| 500 | <li><strong>npts</strong> – the numbers of q points of data to consider for extrapolation</li> |
---|
| 501 | <li><strong>function</strong> – a keyword to select the function to use for extrapolation. |
---|
| 502 | of type string.</li> |
---|
| 503 | <li><strong>power</strong> – an power to apply power_low function</li> |
---|
| 504 | </ul> |
---|
| 505 | </td> |
---|
| 506 | </tr> |
---|
| 507 | </tbody> |
---|
| 508 | </table> |
---|
| 509 | </dd></dl> |
---|
| 510 | |
---|
| 511 | </dd></dl> |
---|
| 512 | |
---|
| 513 | <dl class="class"> |
---|
| 514 | <dt id="sans.invariant.invariant.PowerLaw"> |
---|
| 515 | <em class="property">class </em><tt class="descclassname">sans.invariant.invariant.</tt><tt class="descname">PowerLaw</tt><big>(</big><em>scale=1</em>, <em>power=4</em><big>)</big><a class="headerlink" href="#sans.invariant.invariant.PowerLaw" title="Permalink to this definition">¶</a></dt> |
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| 516 | <dd><p>Bases: <a class="reference internal" href="#sans.invariant.invariant.Transform" title="sans.invariant.invariant.Transform"><tt class="xref py py-class docutils literal"><span class="pre">sans.invariant.invariant.Transform</span></tt></a></p> |
---|
| 517 | <p>class of type transform that perform operation related to power_law |
---|
| 518 | function</p> |
---|
| 519 | <dl class="method"> |
---|
| 520 | <dt id="sans.invariant.invariant.PowerLaw.evaluate_model"> |
---|
| 521 | <tt class="descname">evaluate_model</tt><big>(</big><em>x</em><big>)</big><a class="headerlink" href="#sans.invariant.invariant.PowerLaw.evaluate_model" title="Permalink to this definition">¶</a></dt> |
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| 522 | <dd>given a scale and a radius transform x, y using a power_law |
---|
| 523 | function</dd></dl> |
---|
| 524 | |
---|
| 525 | <dl class="method"> |
---|
| 526 | <dt id="sans.invariant.invariant.PowerLaw.evaluate_model_errors"> |
---|
| 527 | <tt class="descname">evaluate_model_errors</tt><big>(</big><em>x</em><big>)</big><a class="headerlink" href="#sans.invariant.invariant.PowerLaw.evaluate_model_errors" title="Permalink to this definition">¶</a></dt> |
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| 528 | <dd>Returns the error on I(q) for the given array of q-values |
---|
| 529 | :param x: array of q-values</dd></dl> |
---|
| 530 | |
---|
| 531 | <dl class="method"> |
---|
| 532 | <dt id="sans.invariant.invariant.PowerLaw.extract_model_parameters"> |
---|
| 533 | <tt class="descname">extract_model_parameters</tt><big>(</big><em>constant</em>, <em>slope</em>, <em>dconstant=0</em>, <em>dslope=0</em><big>)</big><a class="headerlink" href="#sans.invariant.invariant.PowerLaw.extract_model_parameters" title="Permalink to this definition">¶</a></dt> |
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| 534 | <dd>Assign new value to the scale and the power</dd></dl> |
---|
| 535 | |
---|
| 536 | <dl class="method"> |
---|
| 537 | <dt id="sans.invariant.invariant.PowerLaw.get_allowed_bins"> |
---|
| 538 | <tt class="descname">get_allowed_bins</tt><big>(</big><em>data</em><big>)</big><a class="headerlink" href="#sans.invariant.invariant.PowerLaw.get_allowed_bins" title="Permalink to this definition">¶</a></dt> |
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| 539 | <dd><p>Goes through the data points and returns a list of boolean values |
---|
| 540 | to indicate whether each points is allowed by the model or not.</p> |
---|
| 541 | <table class="docutils field-list" frame="void" rules="none"> |
---|
| 542 | <col class="field-name" /> |
---|
| 543 | <col class="field-body" /> |
---|
| 544 | <tbody valign="top"> |
---|
| 545 | <tr class="field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first last simple"> |
---|
| 546 | <li><strong>data</strong> – Data1D object</li> |
---|
| 547 | </ul> |
---|
| 548 | </td> |
---|
| 549 | </tr> |
---|
| 550 | </tbody> |
---|
| 551 | </table> |
---|
| 552 | </dd></dl> |
---|
| 553 | |
---|
| 554 | <dl class="method"> |
---|
| 555 | <dt id="sans.invariant.invariant.PowerLaw.linearize_data"> |
---|
| 556 | <tt class="descname">linearize_data</tt><big>(</big><em>data</em><big>)</big><a class="headerlink" href="#sans.invariant.invariant.PowerLaw.linearize_data" title="Permalink to this definition">¶</a></dt> |
---|
| 557 | <dd><p>Linearize data so that a linear fit can be performed. |
---|
| 558 | Filter out the data that can’t be transformed.</p> |
---|
| 559 | <table class="docutils field-list" frame="void" rules="none"> |
---|
| 560 | <col class="field-name" /> |
---|
| 561 | <col class="field-body" /> |
---|
| 562 | <tbody valign="top"> |
---|
| 563 | <tr class="field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first last simple"> |
---|
| 564 | <li><strong>data</strong> – LoadData1D instance</li> |
---|
| 565 | </ul> |
---|
| 566 | </td> |
---|
| 567 | </tr> |
---|
| 568 | </tbody> |
---|
| 569 | </table> |
---|
| 570 | </dd></dl> |
---|
| 571 | |
---|
| 572 | <dl class="method"> |
---|
| 573 | <dt id="sans.invariant.invariant.PowerLaw.linearize_q_value"> |
---|
| 574 | <tt class="descname">linearize_q_value</tt><big>(</big><em>value</em><big>)</big><a class="headerlink" href="#sans.invariant.invariant.PowerLaw.linearize_q_value" title="Permalink to this definition">¶</a></dt> |
---|
| 575 | <dd><p>Transform the input q-value for linearization</p> |
---|
| 576 | <table class="docutils field-list" frame="void" rules="none"> |
---|
| 577 | <col class="field-name" /> |
---|
| 578 | <col class="field-body" /> |
---|
| 579 | <tbody valign="top"> |
---|
| 580 | <tr class="field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first simple"> |
---|
| 581 | <li><strong>value</strong> – q-value</li> |
---|
| 582 | </ul> |
---|
| 583 | </td> |
---|
| 584 | </tr> |
---|
| 585 | <tr class="field"><th class="field-name">Returns:</th><td class="field-body"><p class="first last">log(q)</p> |
---|
| 586 | </td> |
---|
| 587 | </tr> |
---|
| 588 | </tbody> |
---|
| 589 | </table> |
---|
| 590 | </dd></dl> |
---|
| 591 | |
---|
| 592 | </dd></dl> |
---|
| 593 | |
---|
| 594 | <dl class="class"> |
---|
| 595 | <dt id="sans.invariant.invariant.Transform"> |
---|
| 596 | <em class="property">class </em><tt class="descclassname">sans.invariant.invariant.</tt><tt class="descname">Transform</tt><a class="headerlink" href="#sans.invariant.invariant.Transform" title="Permalink to this definition">¶</a></dt> |
---|
| 597 | <dd><p>Bases: <tt class="xref py py-class docutils literal"><span class="pre">object</span></tt></p> |
---|
| 598 | <p>Define interface that need to compute a function or an inverse |
---|
| 599 | function given some x, y</p> |
---|
| 600 | <dl class="method"> |
---|
| 601 | <dt id="sans.invariant.invariant.Transform.evaluate_model"> |
---|
| 602 | <tt class="descname">evaluate_model</tt><big>(</big><em>x</em><big>)</big><a class="headerlink" href="#sans.invariant.invariant.Transform.evaluate_model" title="Permalink to this definition">¶</a></dt> |
---|
| 603 | <dd>Returns an array f(x) values where f is the Transform function.</dd></dl> |
---|
| 604 | |
---|
| 605 | <dl class="method"> |
---|
| 606 | <dt id="sans.invariant.invariant.Transform.evaluate_model_errors"> |
---|
| 607 | <tt class="descname">evaluate_model_errors</tt><big>(</big><em>x</em><big>)</big><a class="headerlink" href="#sans.invariant.invariant.Transform.evaluate_model_errors" title="Permalink to this definition">¶</a></dt> |
---|
| 608 | <dd>Returns an array of I(q) errors</dd></dl> |
---|
| 609 | |
---|
| 610 | <dl class="method"> |
---|
| 611 | <dt id="sans.invariant.invariant.Transform.extract_model_parameters"> |
---|
| 612 | <tt class="descname">extract_model_parameters</tt><big>(</big><em>constant</em>, <em>slope</em>, <em>dconstant=0</em>, <em>dslope=0</em><big>)</big><a class="headerlink" href="#sans.invariant.invariant.Transform.extract_model_parameters" title="Permalink to this definition">¶</a></dt> |
---|
| 613 | <dd>set private member</dd></dl> |
---|
| 614 | |
---|
| 615 | <dl class="method"> |
---|
| 616 | <dt id="sans.invariant.invariant.Transform.get_allowed_bins"> |
---|
| 617 | <tt class="descname">get_allowed_bins</tt><big>(</big><em>data</em><big>)</big><a class="headerlink" href="#sans.invariant.invariant.Transform.get_allowed_bins" title="Permalink to this definition">¶</a></dt> |
---|
| 618 | <dd><p>Goes through the data points and returns a list of boolean values |
---|
| 619 | to indicate whether each points is allowed by the model or not.</p> |
---|
| 620 | <table class="docutils field-list" frame="void" rules="none"> |
---|
| 621 | <col class="field-name" /> |
---|
| 622 | <col class="field-body" /> |
---|
| 623 | <tbody valign="top"> |
---|
| 624 | <tr class="field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first last simple"> |
---|
| 625 | <li><strong>data</strong> – Data1D object</li> |
---|
| 626 | </ul> |
---|
| 627 | </td> |
---|
| 628 | </tr> |
---|
| 629 | </tbody> |
---|
| 630 | </table> |
---|
| 631 | </dd></dl> |
---|
| 632 | |
---|
| 633 | <dl class="method"> |
---|
| 634 | <dt id="sans.invariant.invariant.Transform.linearize_data"> |
---|
| 635 | <tt class="descname">linearize_data</tt><big>(</big><em>data</em><big>)</big><a class="headerlink" href="#sans.invariant.invariant.Transform.linearize_data" title="Permalink to this definition">¶</a></dt> |
---|
| 636 | <dd><p>Linearize data so that a linear fit can be performed. |
---|
| 637 | Filter out the data that can’t be transformed.</p> |
---|
| 638 | <table class="docutils field-list" frame="void" rules="none"> |
---|
| 639 | <col class="field-name" /> |
---|
| 640 | <col class="field-body" /> |
---|
| 641 | <tbody valign="top"> |
---|
| 642 | <tr class="field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first last simple"> |
---|
| 643 | <li><strong>data</strong> – LoadData1D instance</li> |
---|
| 644 | </ul> |
---|
| 645 | </td> |
---|
| 646 | </tr> |
---|
| 647 | </tbody> |
---|
| 648 | </table> |
---|
| 649 | </dd></dl> |
---|
| 650 | |
---|
| 651 | <dl class="method"> |
---|
| 652 | <dt id="sans.invariant.invariant.Transform.linearize_q_value"> |
---|
| 653 | <tt class="descname">linearize_q_value</tt><big>(</big><em>value</em><big>)</big><a class="headerlink" href="#sans.invariant.invariant.Transform.linearize_q_value" title="Permalink to this definition">¶</a></dt> |
---|
| 654 | <dd>Transform the input q-value for linearization</dd></dl> |
---|
| 655 | |
---|
| 656 | </dd></dl> |
---|
| 657 | |
---|
| 658 | </div> |
---|
| 659 | </div> |
---|
| 660 | |
---|
| 661 | |
---|
| 662 | </div> |
---|
| 663 | </div> |
---|
| 664 | </div> |
---|
| 665 | <div class="sphinxsidebar"> |
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| 666 | <div class="sphinxsidebarwrapper"> |
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| 667 | <h3><a href="../index.html">Table Of Contents</a></h3> |
---|
| 668 | <ul> |
---|
| 669 | <li><a class="reference internal" href="#">invariant</a><ul> |
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| 670 | <li><a class="reference internal" href="#module-sans.invariant.invariant"><tt class="docutils literal"><span class="pre">sans.invariant.invariant</span></tt></a></li> |
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| 671 | </ul> |
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| 672 | </li> |
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| 673 | </ul> |
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| 674 | |
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| 675 | <h4>Previous topic</h4> |
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| 676 | <p class="topless"><a href="index.html" |
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| 677 | title="previous chapter">Reference</a></p> |
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| 678 | <h3>This Page</h3> |
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