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59           
60  <div class="section" id="sas-pr-package">
61<h1>sas.pr package</h1>
62<div class="section" id="subpackages">
63<h2>Subpackages</h2>
64<div class="toctree-wrapper compound">
65<ul>
66<li class="toctree-l1"><a class="reference internal" href="sas.pr.core.html">sas.pr.core package</a><ul>
67<li class="toctree-l2"><a class="reference internal" href="sas.pr.core.html#module-sas.pr.core">Module contents</a></li>
68</ul>
69</li>
70</ul>
71</div>
72</div>
73<div class="section" id="submodules">
74<h2>Submodules</h2>
75</div>
76<div class="section" id="module-sas.pr.distance_explorer">
77<span id="sas-pr-distance-explorer-module"></span><h2>sas.pr.distance_explorer module</h2>
78<p>Module to explore the P(r) inversion results for a range
79of D_max value. User picks a number of points and a range of
80distances, then get a series of outputs as a function of D_max
81over that range.</p>
82<dl class="class">
83<dt id="sas.pr.distance_explorer.DistExplorer">
84<em class="property">class </em><tt class="descclassname">sas.pr.distance_explorer.</tt><tt class="descname">DistExplorer</tt><big>(</big><em>pr_state</em><big>)</big><a class="reference internal" href="../../_modules/sas/pr/distance_explorer.html#DistExplorer"><span class="viewcode-link">[source]</span></a></dt>
85<dd><p>Bases: <tt class="xref py py-class docutils literal"><span class="pre">object</span></tt></p>
86<p>The explorer class</p>
87</dd></dl>
88
89<dl class="class">
90<dt id="sas.pr.distance_explorer.Results">
91<em class="property">class </em><tt class="descclassname">sas.pr.distance_explorer.</tt><tt class="descname">Results</tt><a class="reference internal" href="../../_modules/sas/pr/distance_explorer.html#Results"><span class="viewcode-link">[source]</span></a></dt>
92<dd><p>Class to hold the inversion output parameters
93as a function of D_max</p>
94</dd></dl>
95
96</div>
97<div class="section" id="module-sas.pr.invertor">
98<span id="sas-pr-invertor-module"></span><h2>sas.pr.invertor module</h2>
99<p>Module to perform P(r) inversion.
100The module contains the Invertor class.</p>
101<dl class="class">
102<dt id="sas.pr.invertor.Invertor">
103<em class="property">class </em><tt class="descclassname">sas.pr.invertor.</tt><tt class="descname">Invertor</tt><a class="reference internal" href="../../_modules/sas/pr/invertor.html#Invertor"><span class="viewcode-link">[source]</span></a></dt>
104<dd><p>Bases: <tt class="xref py py-class docutils literal"><span class="pre">Cinvertor</span></tt></p>
105<p>Invertor class to perform P(r) inversion</p>
106<p>The problem is solved by posing the problem as  Ax = b,
107where x is the set of coefficients we are looking for.</p>
108<p>Npts is the number of points.</p>
109<p>In the following i refers to the ith base function coefficient.
110The matrix has its entries j in its first Npts rows set to</p>
111<div class="highlight-python"><div class="highlight"><pre>A[j][i] = (Fourier transformed base function for point j)
112</pre></div>
113</div>
114<p>We them choose a number of r-points, n_r, to evaluate the second
115derivative of P(r) at. This is used as our regularization term.
116For a vector r of length n_r, the following n_r rows are set to</p>
117<div class="highlight-python"><div class="highlight"><pre>A[j+Npts][i] = (2nd derivative of P(r), d**2(P(r))/d(r)**2,
118evaluated at r[j])
119</pre></div>
120</div>
121<p>The vector b has its first Npts entries set to</p>
122<div class="highlight-python"><div class="highlight"><pre>b[j] = (I(q) observed for point j)
123</pre></div>
124</div>
125<p>The following n_r entries are set to zero.</p>
126<p>The result is found by using scipy.linalg.basic.lstsq to invert
127the matrix and find the coefficients x.</p>
128<p>Methods inherited from Cinvertor:</p>
129<ul class="simple">
130<li><tt class="docutils literal"><span class="pre">get_peaks(pars)</span></tt>: returns the number of P(r) peaks</li>
131<li><tt class="docutils literal"><span class="pre">oscillations(pars)</span></tt>: returns the oscillation parameters for the output P(r)</li>
132<li><tt class="docutils literal"><span class="pre">get_positive(pars)</span></tt>: returns the fraction of P(r) that is above zero</li>
133<li><tt class="docutils literal"><span class="pre">get_pos_err(pars)</span></tt>: returns the fraction of P(r) that is 1-sigma above zero</li>
134</ul>
135<dl class="attribute">
136<dt id="sas.pr.invertor.Invertor.background">
137<tt class="descname">background</tt><em class="property"> = 0</em></dt>
138<dd></dd></dl>
139
140<dl class="attribute">
141<dt id="sas.pr.invertor.Invertor.chi2">
142<tt class="descname">chi2</tt><em class="property"> = 0</em></dt>
143<dd></dd></dl>
144
145<dl class="method">
146<dt id="sas.pr.invertor.Invertor.clone">
147<tt class="descname">clone</tt><big>(</big><big>)</big><a class="reference internal" href="../../_modules/sas/pr/invertor.html#Invertor.clone"><span class="viewcode-link">[source]</span></a></dt>
148<dd><p>Return a clone of this instance</p>
149</dd></dl>
150
151<dl class="attribute">
152<dt id="sas.pr.invertor.Invertor.cov">
153<tt class="descname">cov</tt><em class="property"> = None</em></dt>
154<dd></dd></dl>
155
156<dl class="attribute">
157<dt id="sas.pr.invertor.Invertor.elapsed">
158<tt class="descname">elapsed</tt><em class="property"> = 0</em></dt>
159<dd></dd></dl>
160
161<dl class="method">
162<dt id="sas.pr.invertor.Invertor.estimate_alpha">
163<tt class="descname">estimate_alpha</tt><big>(</big><em>nfunc</em><big>)</big><a class="reference internal" href="../../_modules/sas/pr/invertor.html#Invertor.estimate_alpha"><span class="viewcode-link">[source]</span></a></dt>
164<dd><p>Returns a reasonable guess for the
165regularization constant alpha</p>
166<table class="docutils field-list" frame="void" rules="none">
167<col class="field-name" />
168<col class="field-body" />
169<tbody valign="top">
170<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>nfunc</strong> &#8211; number of terms to use in the expansion.</td>
171</tr>
172<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body">alpha, message, elapsed</td>
173</tr>
174</tbody>
175</table>
176<p>where alpha is the estimate for alpha,
177message is a message for the user,
178elapsed is the computation time</p>
179</dd></dl>
180
181<dl class="method">
182<dt id="sas.pr.invertor.Invertor.estimate_numterms">
183<tt class="descname">estimate_numterms</tt><big>(</big><em>isquit_func=None</em><big>)</big><a class="reference internal" href="../../_modules/sas/pr/invertor.html#Invertor.estimate_numterms"><span class="viewcode-link">[source]</span></a></dt>
184<dd><p>Returns a reasonable guess for the
185number of terms</p>
186<table class="docutils field-list" frame="void" rules="none">
187<col class="field-name" />
188<col class="field-body" />
189<tbody valign="top">
190<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>isquit_func</strong> &#8211; reference to thread function to call to check whether the computation needs to
191be stopped.</td>
192</tr>
193<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body">number of terms, alpha, message</td>
194</tr>
195</tbody>
196</table>
197</dd></dl>
198
199<dl class="method">
200<dt id="sas.pr.invertor.Invertor.from_file">
201<tt class="descname">from_file</tt><big>(</big><em>path</em><big>)</big><a class="reference internal" href="../../_modules/sas/pr/invertor.html#Invertor.from_file"><span class="viewcode-link">[source]</span></a></dt>
202<dd><p>Load the state of the Invertor from a file,
203to be able to generate P(r) from a set of
204parameters.</p>
205<table class="docutils field-list" frame="void" rules="none">
206<col class="field-name" />
207<col class="field-body" />
208<tbody valign="top">
209<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>path</strong> &#8211; path of the file to load</td>
210</tr>
211</tbody>
212</table>
213</dd></dl>
214
215<dl class="attribute">
216<dt id="sas.pr.invertor.Invertor.info">
217<tt class="descname">info</tt><em class="property"> = {}</em></dt>
218<dd></dd></dl>
219
220<dl class="method">
221<dt id="sas.pr.invertor.Invertor.invert">
222<tt class="descname">invert</tt><big>(</big><em>nfunc=10</em>, <em>nr=20</em><big>)</big><a class="reference internal" href="../../_modules/sas/pr/invertor.html#Invertor.invert"><span class="viewcode-link">[source]</span></a></dt>
223<dd><p>Perform inversion to P(r)</p>
224<p>The problem is solved by posing the problem as  Ax = b,
225where x is the set of coefficients we are looking for.</p>
226<p>Npts is the number of points.</p>
227<p>In the following i refers to the ith base function coefficient.
228The matrix has its entries j in its first Npts rows set to</p>
229<div class="highlight-python"><div class="highlight"><pre>A[i][j] = (Fourier transformed base function for point j)
230</pre></div>
231</div>
232<p>We them choose a number of r-points, n_r, to evaluate the second
233derivative of P(r) at. This is used as our regularization term.
234For a vector r of length n_r, the following n_r rows are set to</p>
235<div class="highlight-python"><div class="highlight"><pre>A[i+Npts][j] = (2nd derivative of P(r), d**2(P(r))/d(r)**2, evaluated at r[j])
236</pre></div>
237</div>
238<p>The vector b has its first Npts entries set to</p>
239<div class="highlight-python"><div class="highlight"><pre>b[j] = (I(q) observed for point j)
240</pre></div>
241</div>
242<p>The following n_r entries are set to zero.</p>
243<p>The result is found by using scipy.linalg.basic.lstsq to invert
244the matrix and find the coefficients x.</p>
245<table class="docutils field-list" frame="void" rules="none">
246<col class="field-name" />
247<col class="field-body" />
248<tbody valign="top">
249<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first simple">
250<li><strong>nfunc</strong> &#8211; number of base functions to use.</li>
251<li><strong>nr</strong> &#8211; number of r points to evaluate the 2nd derivative at for the reg. term.</li>
252</ul>
253</td>
254</tr>
255<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first last">c_out, c_cov - the coefficients with covariance matrix</p>
256</td>
257</tr>
258</tbody>
259</table>
260</dd></dl>
261
262<dl class="method">
263<dt id="sas.pr.invertor.Invertor.invert_optimize">
264<tt class="descname">invert_optimize</tt><big>(</big><em>nfunc=10</em>, <em>nr=20</em><big>)</big><a class="reference internal" href="../../_modules/sas/pr/invertor.html#Invertor.invert_optimize"><span class="viewcode-link">[source]</span></a></dt>
265<dd><p>Slower version of the P(r) inversion that uses scipy.optimize.leastsq.</p>
266<p>This probably produce more reliable results, but is much slower.
267The minimization function is set to
268sum_i[ (I_obs(q_i) - I_theo(q_i))/err**2 ] + alpha * reg_term,
269where the reg_term is given by Svergun: it is the integral of
270the square of the first derivative
271of P(r), d(P(r))/dr, integrated over the full range of r.</p>
272<table class="docutils field-list" frame="void" rules="none">
273<col class="field-name" />
274<col class="field-body" />
275<tbody valign="top">
276<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first simple">
277<li><strong>nfunc</strong> &#8211; number of base functions to use.</li>
278<li><strong>nr</strong> &#8211; number of r points to evaluate the 2nd derivative at
279for the reg. term.</li>
280</ul>
281</td>
282</tr>
283<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first last">c_out, c_cov - the coefficients with covariance matrix</p>
284</td>
285</tr>
286</tbody>
287</table>
288</dd></dl>
289
290<dl class="method">
291<dt id="sas.pr.invertor.Invertor.iq">
292<tt class="descname">iq</tt><big>(</big><em>out</em>, <em>q</em><big>)</big><a class="reference internal" href="../../_modules/sas/pr/invertor.html#Invertor.iq"><span class="viewcode-link">[source]</span></a></dt>
293<dd><p>Function to call to evaluate the scattering intensity</p>
294<table class="docutils field-list" frame="void" rules="none">
295<col class="field-name" />
296<col class="field-body" />
297<tbody valign="top">
298<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>args</strong> &#8211; c-parameters, and q</td>
299</tr>
300<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body">I(q)</td>
301</tr>
302</tbody>
303</table>
304</dd></dl>
305
306<dl class="method">
307<dt id="sas.pr.invertor.Invertor.lstsq">
308<tt class="descname">lstsq</tt><big>(</big><em>nfunc=5</em>, <em>nr=20</em><big>)</big><a class="reference internal" href="../../_modules/sas/pr/invertor.html#Invertor.lstsq"><span class="viewcode-link">[source]</span></a></dt>
309<dd><p>The problem is solved by posing the problem as  Ax = b,
310where x is the set of coefficients we are looking for.</p>
311<p>Npts is the number of points.</p>
312<p>In the following i refers to the ith base function coefficient.
313The matrix has its entries j in its first Npts rows set to</p>
314<div class="highlight-python"><div class="highlight"><pre>A[i][j] = (Fourier transformed base function for point j)
315</pre></div>
316</div>
317<p>We them choose a number of r-points, n_r, to evaluate the second
318derivative of P(r) at. This is used as our regularization term.
319For a vector r of length n_r, the following n_r rows are set to</p>
320<div class="highlight-python"><div class="highlight"><pre>A[i+Npts][j] = (2nd derivative of P(r), d**2(P(r))/d(r)**2,
321evaluated at r[j])
322</pre></div>
323</div>
324<p>The vector b has its first Npts entries set to</p>
325<div class="highlight-python"><div class="highlight"><pre>b[j] = (I(q) observed for point j)
326</pre></div>
327</div>
328<p>The following n_r entries are set to zero.</p>
329<p>The result is found by using scipy.linalg.basic.lstsq to invert
330the matrix and find the coefficients x.</p>
331<table class="docutils field-list" frame="void" rules="none">
332<col class="field-name" />
333<col class="field-body" />
334<tbody valign="top">
335<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first last simple">
336<li><strong>nfunc</strong> &#8211; number of base functions to use.</li>
337<li><strong>nr</strong> &#8211; number of r points to evaluate the 2nd derivative at for the reg. term.</li>
338</ul>
339</td>
340</tr>
341</tbody>
342</table>
343<p>If the result does not allow us to compute the covariance matrix,
344a matrix filled with zeros will be returned.</p>
345</dd></dl>
346
347<dl class="attribute">
348<dt id="sas.pr.invertor.Invertor.nfunc">
349<tt class="descname">nfunc</tt><em class="property"> = 10</em></dt>
350<dd></dd></dl>
351
352<dl class="attribute">
353<dt id="sas.pr.invertor.Invertor.out">
354<tt class="descname">out</tt><em class="property"> = None</em></dt>
355<dd></dd></dl>
356
357<dl class="method">
358<dt id="sas.pr.invertor.Invertor.pr_err">
359<tt class="descname">pr_err</tt><big>(</big><em>c</em>, <em>c_cov</em>, <em>r</em><big>)</big><a class="reference internal" href="../../_modules/sas/pr/invertor.html#Invertor.pr_err"><span class="viewcode-link">[source]</span></a></dt>
360<dd><p>Returns the value of P(r) for a given r, and base function
361coefficients, with error.</p>
362<table class="docutils field-list" frame="void" rules="none">
363<col class="field-name" />
364<col class="field-body" />
365<tbody valign="top">
366<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first simple">
367<li><strong>c</strong> &#8211; base function coefficients</li>
368<li><strong>c_cov</strong> &#8211; covariance matrice of the base function coefficients</li>
369<li><strong>r</strong> &#8211; r-value to evaluate P(r) at</li>
370</ul>
371</td>
372</tr>
373<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first last">P(r)</p>
374</td>
375</tr>
376</tbody>
377</table>
378</dd></dl>
379
380<dl class="method">
381<dt id="sas.pr.invertor.Invertor.pr_fit">
382<tt class="descname">pr_fit</tt><big>(</big><em>nfunc=5</em><big>)</big><a class="reference internal" href="../../_modules/sas/pr/invertor.html#Invertor.pr_fit"><span class="viewcode-link">[source]</span></a></dt>
383<dd><p>This is a direct fit to a given P(r). It assumes that the y data
384is set to some P(r) distribution that we are trying to reproduce
385with a set of base functions.</p>
386<p>This method is provided as a test.</p>
387</dd></dl>
388
389<dl class="attribute">
390<dt id="sas.pr.invertor.Invertor.suggested_alpha">
391<tt class="descname">suggested_alpha</tt><em class="property"> = 0</em></dt>
392<dd></dd></dl>
393
394<dl class="method">
395<dt id="sas.pr.invertor.Invertor.to_file">
396<tt class="descname">to_file</tt><big>(</big><em>path</em>, <em>npts=100</em><big>)</big><a class="reference internal" href="../../_modules/sas/pr/invertor.html#Invertor.to_file"><span class="viewcode-link">[source]</span></a></dt>
397<dd><p>Save the state to a file that will be readable
398by SliceView.</p>
399<table class="docutils field-list" frame="void" rules="none">
400<col class="field-name" />
401<col class="field-body" />
402<tbody valign="top">
403<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first last simple">
404<li><strong>path</strong> &#8211; path of the file to write</li>
405<li><strong>npts</strong> &#8211; number of P(r) points to be written</li>
406</ul>
407</td>
408</tr>
409</tbody>
410</table>
411</dd></dl>
412
413</dd></dl>
414
415<dl class="function">
416<dt id="sas.pr.invertor.help">
417<tt class="descclassname">sas.pr.invertor.</tt><tt class="descname">help</tt><big>(</big><big>)</big><a class="reference internal" href="../../_modules/sas/pr/invertor.html#help"><span class="viewcode-link">[source]</span></a></dt>
418<dd><p>Provide general online help text
419Future work: extend this function to allow topic selection</p>
420</dd></dl>
421
422</div>
423<div class="section" id="module-sas.pr.num_term">
424<span id="sas-pr-num-term-module"></span><h2>sas.pr.num_term module</h2>
425<dl class="class">
426<dt id="sas.pr.num_term.Num_terms">
427<em class="property">class </em><tt class="descclassname">sas.pr.num_term.</tt><tt class="descname">Num_terms</tt><big>(</big><em>invertor</em><big>)</big><a class="reference internal" href="../../_modules/sas/pr/num_term.html#Num_terms"><span class="viewcode-link">[source]</span></a></dt>
428<dd><dl class="method">
429<dt id="sas.pr.num_term.Num_terms.compare_err">
430<tt class="descname">compare_err</tt><big>(</big><big>)</big><a class="reference internal" href="../../_modules/sas/pr/num_term.html#Num_terms.compare_err"><span class="viewcode-link">[source]</span></a></dt>
431<dd></dd></dl>
432
433<dl class="method">
434<dt id="sas.pr.num_term.Num_terms.get0_out">
435<tt class="descname">get0_out</tt><big>(</big><big>)</big><a class="reference internal" href="../../_modules/sas/pr/num_term.html#Num_terms.get0_out"><span class="viewcode-link">[source]</span></a></dt>
436<dd></dd></dl>
437
438<dl class="method">
439<dt id="sas.pr.num_term.Num_terms.is_odd">
440<tt class="descname">is_odd</tt><big>(</big><em>n</em><big>)</big><a class="reference internal" href="../../_modules/sas/pr/num_term.html#Num_terms.is_odd"><span class="viewcode-link">[source]</span></a></dt>
441<dd></dd></dl>
442
443<dl class="method">
444<dt id="sas.pr.num_term.Num_terms.ls_osc">
445<tt class="descname">ls_osc</tt><big>(</big><big>)</big><a class="reference internal" href="../../_modules/sas/pr/num_term.html#Num_terms.ls_osc"><span class="viewcode-link">[source]</span></a></dt>
446<dd></dd></dl>
447
448<dl class="method">
449<dt id="sas.pr.num_term.Num_terms.median_osc">
450<tt class="descname">median_osc</tt><big>(</big><big>)</big><a class="reference internal" href="../../_modules/sas/pr/num_term.html#Num_terms.median_osc"><span class="viewcode-link">[source]</span></a></dt>
451<dd></dd></dl>
452
453<dl class="method">
454<dt id="sas.pr.num_term.Num_terms.num_terms">
455<tt class="descname">num_terms</tt><big>(</big><em>isquit_func=None</em><big>)</big><a class="reference internal" href="../../_modules/sas/pr/num_term.html#Num_terms.num_terms"><span class="viewcode-link">[source]</span></a></dt>
456<dd></dd></dl>
457
458<dl class="method">
459<dt id="sas.pr.num_term.Num_terms.sort_osc">
460<tt class="descname">sort_osc</tt><big>(</big><big>)</big><a class="reference internal" href="../../_modules/sas/pr/num_term.html#Num_terms.sort_osc"><span class="viewcode-link">[source]</span></a></dt>
461<dd></dd></dl>
462
463</dd></dl>
464
465<dl class="function">
466<dt id="sas.pr.num_term.load">
467<tt class="descclassname">sas.pr.num_term.</tt><tt class="descname">load</tt><big>(</big><em>path</em><big>)</big><a class="reference internal" href="../../_modules/sas/pr/num_term.html#load"><span class="viewcode-link">[source]</span></a></dt>
468<dd></dd></dl>
469
470</div>
471<div class="section" id="module-sas.pr">
472<span id="module-contents"></span><h2>Module contents</h2>
473<p>P(r) inversion for SAS</p>
474</div>
475</div>
476
477
478          </div>
479        </div>
480      </div>
481      <div class="sphinxsidebar">
482        <div class="sphinxsidebarwrapper">
483  <h3><a href="../../index.html">Table Of Contents</a></h3>
484  <ul>
485<li><a class="reference internal" href="#">sas.pr package</a><ul>
486<li><a class="reference internal" href="#subpackages">Subpackages</a></li>
487<li><a class="reference internal" href="#submodules">Submodules</a></li>
488<li><a class="reference internal" href="#module-sas.pr.distance_explorer">sas.pr.distance_explorer module</a></li>
489<li><a class="reference internal" href="#module-sas.pr.invertor">sas.pr.invertor module</a></li>
490<li><a class="reference internal" href="#module-sas.pr.num_term">sas.pr.num_term module</a></li>
491<li><a class="reference internal" href="#module-sas.pr">Module contents</a></li>
492</ul>
493</li>
494</ul>
495
496  <h4>Previous topic</h4>
497  <p class="topless"><a href="sas.plottools.html"
498                        title="previous chapter">sas.plottools package</a></p>
499  <h4>Next topic</h4>
500  <p class="topless"><a href="sas.pr.core.html"
501                        title="next chapter">sas.pr.core package</a></p>
502  <h3>This Page</h3>
503  <ul class="this-page-menu">
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505           rel="nofollow">Show Source</a></li>
506  </ul>
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516    Enter search terms or a module, class or function name.
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