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| 50 | <h1>Source code for park.peaks</h1><div class="highlight"><pre> |
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| 51 | <span class="c"># This program is public domain</span> |
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| 52 | <span class="sd">""" </span> |
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| 53 | <span class="sd">A park model implementing a multipeak fitter.</span> |
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| 54 | |
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| 55 | <span class="sd">*** WARNING *** this example was used to inform the design process,</span> |
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| 56 | <span class="sd">and has not yet been updated to correspond to the current implementation.</span> |
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| 57 | <span class="sd">Do not use this as a tutorial.</span> |
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| 58 | |
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| 59 | <span class="sd">This is an example model showing how to put together a multi-part</span> |
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| 60 | <span class="sd">fit objective function.</span> |
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| 61 | |
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| 62 | <span class="sd">:group main: Peaks</span> |
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| 63 | <span class="sd">:group peaks: Gaussian, Lorentzian, Voigt</span> |
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| 64 | <span class="sd">:group backgrounds: Constant, Quadratic, Linear</span> |
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| 65 | <span class="sd">"""</span> |
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| 66 | <span class="kn">import</span> <span class="nn">numpy</span> |
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| 67 | <span class="kn">import</span> <span class="nn">park</span> |
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| 68 | |
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| 69 | <div class="viewcode-block" id="Peaks"><a class="viewcode-back" href="../../dev/api/park.html#park.peaks.Peaks">[docs]</a><span class="k">class</span> <span class="nc">Peaks</span><span class="p">(</span><span class="n">park</span><span class="o">.</span><span class="n">Model</span><span class="p">):</span> |
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| 70 | <span class="sd">"""Peak fitter"""</span> |
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| 71 | <span class="c"># Increment the minor version when adding new functions</span> |
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| 72 | <span class="c"># Increment the major version if refactoring the class</span> |
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| 73 | <span class="n">__version__</span> <span class="o">=</span> <span class="s">"0.9"</span> |
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| 74 | <span class="n">peak_types</span> <span class="o">=</span> <span class="p">{}</span> |
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| 75 | |
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| 76 | <span class="k">def</span> <span class="nf">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">datafile</span><span class="o">=</span><span class="bp">None</span><span class="p">):</span> |
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| 77 | <span class="sd">"""</span> |
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| 78 | <span class="sd"> Create a new multipeak model. If datafile is present it will</span> |
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| 79 | <span class="sd"> be loaded directly. If not, then it can be set later with</span> |
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| 80 | <span class="sd"> self.data.load(datafile), or replaced with a specialized</span> |
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| 81 | <span class="sd"> data loader for the particular instrument.</span> |
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| 82 | <span class="sd"> """</span> |
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| 83 | <span class="c"># The initializer creates self.parameterset which will hold</span> |
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| 84 | <span class="c"># the set of fitting parameters for all models. It will also</span> |
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| 85 | <span class="c"># define self.data = park.data.Data1D() which computes the</span> |
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| 86 | <span class="c"># residuals given an eval function.</span> |
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| 87 | <span class="n">park</span><span class="o">.</span><span class="n">Model</span><span class="o">.</span><span class="n">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span><span class="n">filename</span><span class="o">=</span><span class="n">datafile</span><span class="p">)</span> |
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| 88 | <span class="bp">self</span><span class="o">.</span><span class="n">parameterset</span> <span class="o">=</span> <span class="n">park</span><span class="o">.</span><span class="n">ParameterSet</span><span class="p">()</span> |
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| 89 | <span class="bp">self</span><span class="o">.</span><span class="n">peaks</span> <span class="o">=</span> <span class="p">{}</span> |
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| 90 | <span class="bp">self</span><span class="o">.</span><span class="n">peaknum</span> <span class="o">=</span> <span class="mi">0</span> |
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| 91 | |
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| 92 | <div class="viewcode-block" id="Peaks.eval"><a class="viewcode-back" href="../../dev/api/park.html#park.peaks.Peaks.eval">[docs]</a> <span class="k">def</span> <span class="nf">eval</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span> |
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| 93 | <span class="sd">"""</span> |
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| 94 | <span class="sd"> Returns the raw theory value at x, unconvoluted and unweighted.</span> |
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| 95 | <span class="sd"> </span> |
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| 96 | <span class="sd"> The residuals will be calculated by park.Model.residuals by</span> |
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| 97 | <span class="sd"> calling </span> |
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| 98 | <span class="sd"> """</span> |
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| 99 | <span class="n">x</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">data</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> |
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| 100 | <span class="n">y</span> <span class="o">=</span> <span class="n">numpy</span><span class="o">.</span><span class="n">empty</span><span class="p">(</span><span class="n">x</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span> |
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| 101 | <span class="k">for</span> <span class="n">name</span><span class="p">,</span><span class="n">peak</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">peaks</span><span class="o">.</span><span class="n">itervalues</span><span class="p">():</span> |
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| 102 | <span class="n">y</span> <span class="o">+=</span> <span class="n">peak</span><span class="p">(</span><span class="n">x</span><span class="p">)</span> |
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| 103 | <span class="k">return</span> <span class="n">y</span> |
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| 104 | </div> |
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| 105 | <div class="viewcode-block" id="Peaks.add_peak"><a class="viewcode-back" href="../../dev/api/park.html#park.peaks.Peaks.add_peak">[docs]</a> <span class="k">def</span> <span class="nf">add_peak</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="nb">type</span><span class="p">,</span> <span class="n">name</span><span class="o">=</span><span class="bp">None</span><span class="p">,</span> <span class="o">**</span><span class="n">kw</span><span class="p">):</span> |
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| 106 | <span class="sd">""" </span> |
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| 107 | <span class="sd"> Add a peak to the model.</span> |
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| 108 | <span class="sd"> </span> |
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| 109 | <span class="sd"> The name of the peak is used to distinguish it from other peaks </span> |
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| 110 | <span class="sd"> in the model, and appears as part of the parameter name in</span> |
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| 111 | <span class="sd"> constraint expressions. For example, if name is 'P3' and this</span> |
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| 112 | <span class="sd"> is part of model 'M1' then the sigma parameter of a gaussian</span> |
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| 113 | <span class="sd"> peak would be 'M1.P3.sigma'.</span> |
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| 114 | |
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| 115 | <span class="sd"> The peak can be specified either by peak type and initial arguments</span> |
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| 116 | <span class="sd"> or by the peak itself, which is a function of x with a parameters </span> |
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| 117 | <span class="sd"> attribute.</span> |
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| 118 | <span class="sd"> </span> |
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| 119 | <span class="sd"> Available peak types include:</span> |
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| 120 | <span class="sd"> gaussian(scale=1, center=0, sigma=1) </span> |
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| 121 | <span class="sd"> = scale exp ( -0.5 (x-center)**2 / sigma**2 )</span> |
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| 122 | <span class="sd"> lorentzian(scale=1, center=0, gamma=1) </span> |
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| 123 | <span class="sd"> = scale/pi gamma / ((x-center)**2 + gamma**2))</span> |
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| 124 | <span class="sd"> voigt(scale=1, center=0, sigma=1, gamma=1)</span> |
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| 125 | <span class="sd"> = scale (lorentzian(mu,gamma) * gaussian(mu,sigma))(x-center)</span> |
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| 126 | <span class="sd"> where * represents convolution</span> |
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| 127 | <span class="sd"> </span> |
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| 128 | <span class="sd"> Available background functions include:</span> |
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| 129 | <span class="sd"> constant(C=0)</span> |
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| 130 | <span class="sd"> = C</span> |
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| 131 | <span class="sd"> slope(C=0, B=1)</span> |
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| 132 | <span class="sd"> = B x + C</span> |
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| 133 | <span class="sd"> quadratic(A=1, B=0, C=0)</span> |
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| 134 | <span class="sd"> = A x**2 + B x + C</span> |
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| 135 | |
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| 136 | <span class="sd"> Additional peak types can be registered. The complete dictionary</span> |
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| 137 | <span class="sd"> of available types is in Peaks.peak_types.</span> |
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| 138 | <span class="sd"> """</span> |
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| 139 | <span class="bp">self</span><span class="o">.</span><span class="n">peaknum</span> |
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| 140 | <span class="k">if</span> <span class="n">name</span> <span class="o">==</span> <span class="bp">None</span><span class="p">:</span> <span class="n">name</span> <span class="o">=</span> <span class="s">'P'</span><span class="o">+</span><span class="nb">str</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">peaknum</span><span class="p">)</span> |
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| 141 | <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="nb">type</span><span class="p">,</span><span class="nb">basestring</span><span class="p">):</span> |
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| 142 | <span class="n">peak</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">peak_types</span><span class="p">[</span><span class="nb">type</span><span class="p">](</span><span class="o">**</span><span class="n">kw</span><span class="p">)</span> |
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| 143 | <span class="k">else</span><span class="p">:</span> |
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| 144 | <span class="nb">type</span> <span class="o">=</span> <span class="n">peak</span> |
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| 145 | <span class="bp">self</span><span class="o">.</span><span class="n">peaks</span><span class="p">[</span><span class="n">name</span><span class="p">]</span> <span class="o">=</span> <span class="n">peak</span> |
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| 146 | <span class="bp">self</span><span class="o">.</span><span class="n">parameters</span><span class="p">[</span><span class="n">name</span><span class="p">]</span> <span class="o">=</span> <span class="n">peak</span><span class="o">.</span><span class="n">parameters</span> |
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| 147 | <span class="nb">setattr</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span><span class="n">name</span><span class="p">,</span><span class="n">peak</span><span class="p">)</span> |
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| 148 | </div> |
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| 149 | <div class="viewcode-block" id="Peaks.remove_peak"><a class="viewcode-back" href="../../dev/api/park.html#park.peaks.Peaks.remove_peak">[docs]</a> <span class="k">def</span> <span class="nf">remove_peak</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">name</span><span class="p">):</span> |
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| 150 | <span class="sd">"""</span> |
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| 151 | <span class="sd"> Remove the named peak from the model.</span> |
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| 152 | <span class="sd"> """</span> |
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| 153 | <span class="k">del</span> <span class="bp">self</span><span class="o">.</span><span class="n">peaks</span><span class="p">[</span><span class="n">name</span><span class="p">]</span> |
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| 154 | <span class="k">del</span> <span class="bp">self</span><span class="o">.</span><span class="n">parameterset</span><span class="p">[</span><span class="n">name</span><span class="p">]</span> |
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| 155 | </div> |
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| 156 | <span class="nd">@classmethod</span> |
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| 157 | <div class="viewcode-block" id="Peaks.register_peak_generator"><a class="viewcode-back" href="../../dev/api/park.html#park.peaks.Peaks.register_peak_generator">[docs]</a> <span class="k">def</span> <span class="nf">register_peak_generator</span><span class="p">(</span><span class="n">cls</span><span class="p">,</span> <span class="nb">type</span><span class="p">,</span> <span class="n">factory</span><span class="p">):</span> |
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| 158 | <span class="sd">"""</span> |
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| 159 | <span class="sd"> Register a new peak generator. This will return a callable</span> |
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| 160 | <span class="sd"> object with a parameter set that can be used in the peak</span> |
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| 161 | <span class="sd"> fitting class.</span> |
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| 162 | |
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| 163 | <span class="sd"> The individual peak functions a number of attributes:</span> |
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| 164 | <span class="sd"> </span> |
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| 165 | <span class="sd"> __name__</span> |
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| 166 | <span class="sd"> the name to be displayed in the list of peaks; the</span> |
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| 167 | <span class="sd"> default is __class__.__name__</span> |
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| 168 | <span class="sd"> __factory__</span> |
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| 169 | <span class="sd"> the name of a factory function in the python</span> |
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| 170 | <span class="sd"> namespace which returns a new peak. These parameters</span> |
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| 171 | <span class="sd"> will be set from the stored parameter list when the</span> |
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| 172 | <span class="sd"> peak model is reloaded. This can be omitted if it</span> |
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| 173 | <span class="sd"> is simply the module and name of the class.</span> |
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| 174 | <span class="sd"> __doc__</span> |
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| 175 | <span class="sd"> the tool tip to be displayed with the peak</span> |
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| 176 | <span class="sd"> __call__(x)</span> |
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| 177 | <span class="sd"> evaluate the peak function at x</span> |
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| 178 | <span class="sd"> """</span> |
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| 179 | <span class="n">cls</span><span class="o">.</span><span class="n">peak_types</span><span class="p">[</span><span class="nb">type</span><span class="p">]</span><span class="o">=</span><span class="n">factory</span> |
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| 180 | |
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| 181 | |
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| 182 | |
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| 183 | <span class="c"># ================== Peaks and backgrounds ===================</span></div></div> |
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| 184 | <div class="viewcode-block" id="Gaussian"><a class="viewcode-back" href="../../dev/api/park.html#park.peaks.Gaussian">[docs]</a><span class="k">class</span> <span class="nc">Gaussian</span><span class="p">(</span><span class="nb">object</span><span class="p">):</span> |
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| 185 | <span class="sd">"""Gaussian peak: scale exp ( -0.5 (x-center)**2 / sigma**2 )"""</span> |
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| 186 | <span class="k">def</span> <span class="nf">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">name</span><span class="p">,</span> <span class="n">scale</span><span class="o">=</span><span class="mf">1.</span><span class="p">,</span> <span class="n">center</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">sigma</span><span class="o">=</span><span class="mi">1</span><span class="p">):</span> |
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| 187 | <span class="n">park</span><span class="o">.</span><span class="n">define_parameters</span><span class="p">(</span><span class="n">name</span><span class="p">,</span> <span class="p">[</span><span class="s">'scale'</span><span class="p">,</span><span class="s">'center'</span><span class="p">,</span><span class="s">'sigma'</span><span class="p">],</span> |
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| 188 | <span class="n">scale</span><span class="o">=</span><span class="n">scale</span><span class="p">,</span><span class="n">center</span><span class="o">=</span><span class="n">center</span><span class="p">,</span><span class="n">sigma</span><span class="o">=</span><span class="n">sigma</span><span class="p">)</span> |
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| 189 | <span class="bp">self</span><span class="o">.</span><span class="n">parameters</span><span class="p">[</span><span class="s">'scale'</span><span class="p">]</span><span class="o">.</span><span class="n">deriv</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">dscale</span> |
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| 190 | <span class="bp">self</span><span class="o">.</span><span class="n">parameters</span><span class="p">[</span><span class="s">'center'</span><span class="p">]</span><span class="o">.</span><span class="n">deriv</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">dcenter</span> |
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| 191 | <span class="bp">self</span><span class="o">.</span><span class="n">parameters</span><span class="p">[</span><span class="s">'sigma'</span><span class="p">]</span><span class="o">.</span><span class="n">deriv</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">dsigma</span> |
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| 192 | <span class="k">def</span> <span class="nf">__call__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span> |
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| 193 | <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">scale</span> <span class="o">*</span> <span class="n">numpy</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="o">-</span><span class="p">((</span><span class="n">x</span><span class="o">-</span><span class="bp">self</span><span class="o">.</span><span class="n">center</span><span class="p">)</span><span class="o">/</span><span class="bp">self</span><span class="o">.</span><span class="n">sigma</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span> |
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| 194 | <div class="viewcode-block" id="Gaussian.dscale"><a class="viewcode-back" href="../../dev/api/park.html#park.peaks.Gaussian.dscale">[docs]</a> <span class="k">def</span> <span class="nf">dscale</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span> |
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| 195 | <span class="k">return</span> <span class="bp">self</span><span class="p">(</span><span class="n">x</span><span class="p">)</span><span class="o">/</span><span class="bp">self</span><span class="o">.</span><span class="n">scale</span></div> |
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| 196 | <div class="viewcode-block" id="Gaussian.dcenter"><a class="viewcode-back" href="../../dev/api/park.html#park.peaks.Gaussian.dcenter">[docs]</a> <span class="k">def</span> <span class="nf">dcenter</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span> |
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| 197 | <span class="k">return</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="bp">self</span><span class="o">.</span><span class="n">center</span><span class="p">)</span><span class="o">/</span><span class="bp">self</span><span class="o">.</span><span class="n">sigma</span><span class="o">*</span><span class="bp">self</span><span class="p">(</span><span class="n">x</span><span class="p">)</span></div> |
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| 198 | <div class="viewcode-block" id="Gaussian.dsigma"><a class="viewcode-back" href="../../dev/api/park.html#park.peaks.Gaussian.dsigma">[docs]</a> <span class="k">def</span> <span class="nf">dsigma</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span> |
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| 199 | <span class="k">return</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="bp">self</span><span class="o">.</span><span class="n">center</span><span class="p">)</span><span class="o">/</span><span class="bp">self</span><span class="o">.</span><span class="n">sigma</span><span class="o">**</span><span class="mi">3</span><span class="o">*</span><span class="bp">self</span><span class="p">(</span><span class="n">x</span><span class="p">)</span> |
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| 200 | </div></div> |
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| 201 | <div class="viewcode-block" id="Lorentzian"><a class="viewcode-back" href="../../dev/api/park.html#park.peaks.Lorentzian">[docs]</a><span class="k">class</span> <span class="nc">Lorentzian</span><span class="p">(</span><span class="nb">object</span><span class="p">):</span> |
---|
| 202 | <span class="sd">"""Lorentzian peak (HWHM): scale/pi gamma/((x-center)**2 + gamma**2)"""</span> |
---|
| 203 | <span class="k">def</span> <span class="nf">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">name</span><span class="p">,</span> <span class="n">scale</span><span class="o">=</span><span class="mf">1.</span><span class="p">,</span> <span class="n">center</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">gamma</span><span class="o">=</span><span class="mi">1</span><span class="p">):</span> |
---|
| 204 | <span class="n">park</span><span class="o">.</span><span class="n">define_parameters</span><span class="p">(</span><span class="n">name</span><span class="p">,</span> <span class="p">[</span><span class="s">'scale'</span><span class="p">,</span><span class="s">'center'</span><span class="p">,</span><span class="s">'gamma'</span><span class="p">],</span> |
---|
| 205 | <span class="n">scale</span><span class="o">=</span><span class="n">scale</span><span class="p">,</span><span class="n">center</span><span class="o">=</span><span class="n">center</span><span class="p">,</span><span class="n">gamma</span><span class="o">=</span><span class="n">gamma</span><span class="p">)</span> |
---|
| 206 | <span class="bp">self</span><span class="o">.</span><span class="n">parameters</span><span class="p">[</span><span class="s">'scale'</span><span class="p">]</span><span class="o">.</span><span class="n">deriv</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">dscale</span> |
---|
| 207 | <span class="bp">self</span><span class="o">.</span><span class="n">parameters</span><span class="p">[</span><span class="s">'center'</span><span class="p">]</span><span class="o">.</span><span class="n">deriv</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">dcenter</span> |
---|
| 208 | <span class="bp">self</span><span class="o">.</span><span class="n">parameters</span><span class="p">[</span><span class="s">'gamma'</span><span class="p">]</span><span class="o">.</span><span class="n">deriv</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">dgamma</span> |
---|
| 209 | <span class="k">def</span> <span class="nf">__call__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span> |
---|
| 210 | <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">scale</span><span class="o">/</span><span class="n">numpy</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">gamma</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">center</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">gamma</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span> |
---|
| 211 | <div class="viewcode-block" id="Lorentzian.dscale"><a class="viewcode-back" href="../../dev/api/park.html#park.peaks.Lorentzian.dscale">[docs]</a> <span class="k">def</span> <span class="nf">dscale</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span> |
---|
| 212 | <span class="k">return</span> <span class="bp">self</span><span class="p">(</span><span class="n">x</span><span class="p">)</span><span class="o">/</span><span class="bp">self</span><span class="o">.</span><span class="n">scale</span></div> |
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| 213 | <div class="viewcode-block" id="Lorentzian.dcenter"><a class="viewcode-back" href="../../dev/api/park.html#park.peaks.Lorentzian.dcenter">[docs]</a> <span class="k">def</span> <span class="nf">dcenter</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span> |
---|
| 214 | <span class="k">return</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="bp">self</span><span class="o">.</span><span class="n">center</span><span class="p">)</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">center</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span><span class="o">+</span><span class="bp">self</span><span class="o">.</span><span class="n">gamma</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span><span class="o">*</span><span class="bp">self</span><span class="p">(</span><span class="n">x</span><span class="p">)</span></div> |
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| 215 | <div class="viewcode-block" id="Lorentzian.dgamma"><a class="viewcode-back" href="../../dev/api/park.html#park.peaks.Lorentzian.dgamma">[docs]</a> <span class="k">def</span> <span class="nf">dgamma</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span> |
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| 216 | <span class="k">return</span> <span class="bp">self</span><span class="p">(</span><span class="n">x</span><span class="p">)</span><span class="o">*</span><span class="p">(</span><span class="mi">1</span><span class="o">/</span><span class="bp">self</span><span class="o">.</span><span class="n">gamma</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">gamma</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">center</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">gamma</span><span class="o">**</span><span class="mi">2</span><span class="p">))</span> |
---|
| 217 | </div></div> |
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| 218 | <div class="viewcode-block" id="Voigt"><a class="viewcode-back" href="../../dev/api/park.html#park.peaks.Voigt">[docs]</a><span class="k">class</span> <span class="nc">Voigt</span><span class="p">(</span><span class="nb">object</span><span class="p">):</span> |
---|
| 219 | <span class="sd">"""Voigt peak (HWHM,sigma): A [G(sigma) * L(gamma)](x-center)"""</span> |
---|
| 220 | <span class="k">def</span> <span class="nf">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">name</span><span class="p">,</span> <span class="n">scale</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">center</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">sigma</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">gamma</span><span class="o">=</span><span class="mi">1</span><span class="p">):</span> |
---|
| 221 | <span class="n">park</span><span class="o">.</span><span class="n">define_parameters</span><span class="p">(</span><span class="n">name</span><span class="p">,</span> <span class="p">[</span><span class="s">'scale'</span><span class="p">,</span><span class="s">'center'</span><span class="p">,</span><span class="s">'sigma'</span><span class="p">,</span><span class="s">'gamma'</span><span class="p">],</span> |
---|
| 222 | <span class="n">scale</span><span class="o">=</span><span class="n">scale</span><span class="p">,</span> <span class="n">center</span><span class="o">=</span><span class="n">center</span><span class="p">,</span> <span class="n">sigma</span><span class="o">=</span><span class="n">sigma</span><span class="p">,</span> |
---|
| 223 | <span class="n">gamma</span><span class="o">=</span><span class="n">gamma</span><span class="p">)</span> |
---|
| 224 | <span class="k">def</span> <span class="nf">__call__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span> |
---|
| 225 | <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">scale</span><span class="o">*</span><span class="n">voigt</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">center</span><span class="p">,</span> |
---|
| 226 | <span class="n">sigma</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">sigma</span><span class="p">,</span> <span class="n">gamma</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">gamma</span><span class="p">)</span> |
---|
| 227 | </div> |
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| 228 | <div class="viewcode-block" id="Quadratic"><a class="viewcode-back" href="../../dev/api/park.html#park.peaks.Quadratic">[docs]</a><span class="k">class</span> <span class="nc">Quadratic</span><span class="p">(</span><span class="nb">object</span><span class="p">):</span> |
---|
| 229 | <span class="sd">"""Quadratic background: A x**2 + B x + C"""</span> |
---|
| 230 | <span class="n">name</span> <span class="o">=</span> <span class="s">"Background: quadratic"</span> |
---|
| 231 | <span class="k">def</span> <span class="nf">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">name</span><span class="p">,</span> <span class="n">A</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">B</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">C</span><span class="o">=</span><span class="mi">0</span><span class="p">):</span> |
---|
| 232 | <span class="n">park</span><span class="o">.</span><span class="n">define_parameters</span><span class="p">(</span><span class="n">name</span><span class="p">,</span> <span class="p">[</span><span class="s">'A'</span><span class="p">,</span> <span class="s">'B'</span><span class="p">,</span> <span class="s">'C'</span><span class="p">],</span> <span class="n">A</span><span class="o">=</span><span class="n">A</span><span class="p">,</span> <span class="n">B</span><span class="o">=</span><span class="n">B</span><span class="p">,</span> <span class="n">C</span><span class="o">=</span><span class="n">C</span><span class="p">)</span> |
---|
| 233 | <span class="bp">self</span><span class="o">.</span><span class="n">parameters</span><span class="p">[</span><span class="s">'A'</span><span class="p">]</span><span class="o">.</span><span class="n">deriv</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">dA</span> |
---|
| 234 | <span class="bp">self</span><span class="o">.</span><span class="n">parameters</span><span class="p">[</span><span class="s">'B'</span><span class="p">]</span><span class="o">.</span><span class="n">deriv</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">dB</span> |
---|
| 235 | <span class="bp">self</span><span class="o">.</span><span class="n">parameters</span><span class="p">[</span><span class="s">'C'</span><span class="p">]</span><span class="o">.</span><span class="n">deriv</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">dC</span> |
---|
| 236 | <span class="k">def</span> <span class="nf">__call__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span> |
---|
| 237 | <span class="k">return</span> <span class="n">numpy</span><span class="o">.</span><span class="n">polyval</span><span class="p">([</span><span class="bp">self</span><span class="o">.</span><span class="n">a</span><span class="o">.</span><span class="n">value</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">b</span><span class="o">.</span><span class="n">value</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">c</span><span class="o">.</span><span class="n">value</span><span class="p">],</span><span class="n">x</span><span class="p">)</span> |
---|
| 238 | <div class="viewcode-block" id="Quadratic.dA"><a class="viewcode-back" href="../../dev/api/park.html#park.peaks.Quadratic.dA">[docs]</a> <span class="k">def</span> <span class="nf">dA</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span> <span class="k">return</span> <span class="n">x</span><span class="o">**</span><span class="mi">2</span></div> |
---|
| 239 | <div class="viewcode-block" id="Quadratic.dB"><a class="viewcode-back" href="../../dev/api/park.html#park.peaks.Quadratic.dB">[docs]</a> <span class="k">def</span> <span class="nf">dB</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span> <span class="k">return</span> <span class="n">x</span></div> |
---|
| 240 | <div class="viewcode-block" id="Quadratic.dC"><a class="viewcode-back" href="../../dev/api/park.html#park.peaks.Quadratic.dC">[docs]</a> <span class="k">def</span> <span class="nf">dC</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span> <span class="k">return</span> <span class="n">numpy</span><span class="o">.</span><span class="n">ones</span><span class="p">(</span><span class="n">x</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span> |
---|
| 241 | </div></div> |
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| 242 | <div class="viewcode-block" id="Linear"><a class="viewcode-back" href="../../dev/api/park.html#park.peaks.Linear">[docs]</a><span class="k">class</span> <span class="nc">Linear</span><span class="p">(</span><span class="nb">object</span><span class="p">):</span> |
---|
| 243 | <span class="sd">"""Linear background: B x**2 + C"""</span> |
---|
| 244 | <span class="n">name</span> <span class="o">=</span> <span class="s">"Background: linear"</span> |
---|
| 245 | <span class="k">def</span> <span class="nf">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">name</span><span class="p">,</span> <span class="n">B</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">C</span><span class="o">=</span><span class="mi">0</span><span class="p">):</span> |
---|
| 246 | <span class="n">park</span><span class="o">.</span><span class="n">define_parameters</span><span class="p">(</span><span class="n">name</span><span class="p">,</span> <span class="p">[</span><span class="s">'B'</span><span class="p">,</span> <span class="s">'C'</span><span class="p">],</span> <span class="n">B</span><span class="o">=</span><span class="n">B</span><span class="p">,</span> <span class="n">C</span><span class="o">=</span><span class="n">C</span><span class="p">)</span> |
---|
| 247 | <span class="bp">self</span><span class="o">.</span><span class="n">parameters</span><span class="p">[</span><span class="s">'B'</span><span class="p">]</span><span class="o">.</span><span class="n">deriv</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">dB</span> |
---|
| 248 | <span class="bp">self</span><span class="o">.</span><span class="n">parameters</span><span class="p">[</span><span class="s">'C'</span><span class="p">]</span><span class="o">.</span><span class="n">deriv</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">dC</span> |
---|
| 249 | <span class="k">def</span> <span class="nf">__call__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span> |
---|
| 250 | <span class="k">return</span> <span class="n">numpy</span><span class="o">.</span><span class="n">polyval</span><span class="p">([</span><span class="bp">self</span><span class="o">.</span><span class="n">a</span><span class="o">.</span><span class="n">value</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">b</span><span class="o">.</span><span class="n">value</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">c</span><span class="o">.</span><span class="n">value</span><span class="p">],</span><span class="n">x</span><span class="p">)</span> |
---|
| 251 | <div class="viewcode-block" id="Linear.dB"><a class="viewcode-back" href="../../dev/api/park.html#park.peaks.Linear.dB">[docs]</a> <span class="k">def</span> <span class="nf">dB</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span> <span class="k">return</span> <span class="n">x</span></div> |
---|
| 252 | <div class="viewcode-block" id="Linear.dC"><a class="viewcode-back" href="../../dev/api/park.html#park.peaks.Linear.dC">[docs]</a> <span class="k">def</span> <span class="nf">dC</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span> <span class="k">return</span> <span class="n">numpy</span><span class="o">.</span><span class="n">ones</span><span class="p">(</span><span class="n">x</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span> |
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| 253 | </div></div> |
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| 254 | <div class="viewcode-block" id="Constant"><a class="viewcode-back" href="../../dev/api/park.html#park.peaks.Constant">[docs]</a><span class="k">class</span> <span class="nc">Constant</span><span class="p">(</span><span class="nb">object</span><span class="p">):</span> |
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| 255 | <span class="sd">"""Constant background: C"""</span> |
---|
| 256 | <span class="n">name</span> <span class="o">=</span> <span class="s">"Background: constant"</span> |
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| 257 | <span class="k">def</span> <span class="nf">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">name</span><span class="p">,</span> <span class="n">C</span><span class="o">=</span><span class="mi">0</span><span class="p">):</span> |
---|
| 258 | <span class="n">park</span><span class="o">.</span><span class="n">define_parameters</span><span class="p">(</span><span class="n">name</span><span class="p">,</span> <span class="p">[</span><span class="s">'C'</span><span class="p">],</span> <span class="n">C</span><span class="o">=</span><span class="n">C</span><span class="p">)</span> |
---|
| 259 | <span class="bp">self</span><span class="o">.</span><span class="n">parameters</span><span class="p">[</span><span class="s">'C'</span><span class="p">]</span><span class="o">.</span><span class="n">deriv</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">dC</span> |
---|
| 260 | <span class="k">def</span> <span class="nf">__call__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span> |
---|
| 261 | <span class="k">return</span> <span class="n">numpy</span><span class="o">.</span><span class="n">polyval</span><span class="p">([</span><span class="bp">self</span><span class="o">.</span><span class="n">a</span><span class="o">.</span><span class="n">value</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">b</span><span class="o">.</span><span class="n">value</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">c</span><span class="o">.</span><span class="n">value</span><span class="p">],</span><span class="n">x</span><span class="p">)</span> |
---|
| 262 | <div class="viewcode-block" id="Constant.dC"><a class="viewcode-back" href="../../dev/api/park.html#park.peaks.Constant.dC">[docs]</a> <span class="k">def</span> <span class="nf">dC</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span> <span class="k">return</span> <span class="n">numpy</span><span class="o">.</span><span class="n">ones</span><span class="p">(</span><span class="n">x</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span> |
---|
| 263 | |
---|
| 264 | </div></div> |
---|
| 265 | <div class="viewcode-block" id="voigt"><a class="viewcode-back" href="../../dev/api/park.html#park.peaks.voigt">[docs]</a><span class="k">def</span> <span class="nf">voigt</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">sigma</span><span class="p">,</span> <span class="n">gamma</span><span class="p">):</span> |
---|
| 266 | <span class="sd">"""</span> |
---|
| 267 | <span class="sd"> Return the voigt function, which is the convolution of a Lorentz</span> |
---|
| 268 | <span class="sd"> function with a Gaussian.</span> |
---|
| 269 | <span class="sd"> </span> |
---|
| 270 | <span class="sd"> :Parameters:</span> |
---|
| 271 | <span class="sd"> gamma : real</span> |
---|
| 272 | <span class="sd"> The half-width half-maximum of the Lorentzian</span> |
---|
| 273 | <span class="sd"> sigma : real</span> |
---|
| 274 | <span class="sd"> The 1-sigma width of the Gaussian, which is one standard deviation.</span> |
---|
| 275 | |
---|
| 276 | <span class="sd"> Ref: W.I.F. David, J. Appl. Cryst. (1986). 19, 63-64</span> |
---|
| 277 | <span class="sd"> </span> |
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| 278 | <span class="sd"> Note: adjusted to use stddev and HWHM rather than FWHM parameters</span> |
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| 279 | <span class="sd"> """</span> |
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| 280 | <span class="c"># wofz function = w(z) = Fad[d][e][y]eva function = exp(-z**2)erfc(-iz)</span> |
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| 281 | <span class="kn">from</span> <span class="nn">scipy.special</span> <span class="kn">import</span> <span class="n">wofz</span> |
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| 282 | <span class="n">z</span> <span class="o">=</span> <span class="p">(</span><span class="n">x</span><span class="o">+</span><span class="mi">1j</span><span class="o">*</span><span class="n">gamma</span><span class="p">)</span><span class="o">/</span><span class="p">(</span><span class="n">sigma</span><span class="o">*</span><span class="n">sqrt</span><span class="p">(</span><span class="mi">2</span><span class="p">))</span> |
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| 283 | <span class="n">V</span> <span class="o">=</span> <span class="n">wofz</span><span class="p">(</span><span class="n">z</span><span class="p">)</span><span class="o">/</span><span class="p">(</span><span class="n">sqrt</span><span class="p">(</span><span class="mi">2</span><span class="o">*</span><span class="n">pi</span><span class="p">)</span><span class="o">*</span><span class="n">sigma</span><span class="p">)</span> |
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| 284 | <span class="k">return</span> <span class="n">V</span><span class="o">.</span><span class="n">real</span> |
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| 285 | |
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| 286 | </div> |
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| 287 | <div class="viewcode-block" id="init"><a class="viewcode-back" href="../../dev/api/park.html#park.peaks.init">[docs]</a><span class="k">def</span> <span class="nf">init</span><span class="p">():</span> |
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| 288 | <span class="sd">"""</span> |
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| 289 | <span class="sd"> Register peak types with the Peaks model.</span> |
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| 290 | <span class="sd"> """</span> |
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| 291 | <span class="k">for</span> <span class="n">cls</span> <span class="ow">in</span> <span class="p">[</span><span class="n">Gaussian</span><span class="p">,</span> <span class="n">Lorentzian</span><span class="p">,</span> <span class="n">Voigt</span><span class="p">,</span> <span class="n">Quadratic</span><span class="p">,</span> <span class="n">Linear</span><span class="p">,</span> <span class="n">Constant</span><span class="p">]:</span> |
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| 292 | <span class="n">Peaks</span><span class="o">.</span><span class="n">register_peak_generator</span><span class="p">(</span><span class="n">cls</span><span class="o">.</span><span class="n">__name__</span><span class="p">,</span><span class="n">cls</span><span class="p">)</span></div> |
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| 293 | <span class="n">init</span><span class="p">()</span> |
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| 294 | |
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| 295 | <span class="c"># ========================================</span> |
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| 296 | |
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| 297 | <div class="viewcode-block" id="test"><a class="viewcode-back" href="../../dev/api/park.html#park.peaks.test">[docs]</a><span class="k">def</span> <span class="nf">test</span><span class="p">():</span> |
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| 298 | <span class="n">x</span> <span class="o">=</span> <span class="n">numpy</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="o">-</span><span class="mi">5</span><span class="p">,</span><span class="mi">5</span><span class="p">,</span><span class="mi">10</span><span class="p">)</span> |
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| 299 | |
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| 300 | <span class="k">pass</span> |
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| 301 | </div> |
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| 302 | <span class="k">if</span> <span class="n">__name__</span> <span class="o">==</span> <span class="s">"__main__"</span><span class="p">:</span> <span class="n">test</span><span class="p">()</span> |
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| 303 | </pre></div> |
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| 304 | |
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