fitting_help_v0.html @ 77d92cd

ESS_GUIESS_GUI_DocsESS_GUI_batch_fittingESS_GUI_bumps_abstractionESS_GUI_iss1116ESS_GUI_iss879ESS_GUI_iss959ESS_GUI_openclESS_GUI_orderingESS_GUI_sync_sascalccostrafo411magnetic_scattrelease-4.1.1release-4.1.2release-4.2.2ticket-1009ticket-1094-headlessticket-1242-2d-resolutionticket-1243ticket-1249ticket885unittest-saveload

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340	<body>
341	<div class="document" id="fitting-perspective">
342	<h1 class="title">Fitting Perspective</h1>
343
344	<!-- fitting_help.rst -->
345	<!-- This is a port of the original SasView html help file to ReSTructured text -->
346	<!-- by S King, ISIS, during SasView CodeCamp-III in Feb 2015. -->
347	<p><a class="reference internal" href="#load-a-file">Load_a_File</a></p>
348	<p><a class="reference internal" href="#single-fit">Single_Fit</a></p>
349	<p><a class="reference internal" href="#simultaneous-fitting">Simultaneous_Fitting</a></p>
350	<p><a class="reference internal" href="#batch-fitting">Batch_Fitting</a></p>
351	<p><a class="reference internal" href="#model-selection">Model_Selection</a></p>
352	<p><a class="reference internal" href="#model-category-manager">Model_Category_Manager</a></p>
353	<p><a class="reference internal" href="#model-functions">Model_Functions</a></p>
354	<p><a class="reference internal" href="#custom-model-editor">Custom_Model_Editor</a></p>
355	<p><a class="reference internal" href="#polydispersity-distributions">Polydispersity_Distributions</a></p>
356	<p><a class="reference internal" href="#smearing-computation">Smearing_Computation</a></p>
357	<p><a class="reference internal" href="#polarisation-magnetic-scattering">Polarisation_Magnetic_Scattering</a></p>
358	<p><a class="reference internal" href="#key-combinations">Key_Combinations</a></p>
359	<p><a class="reference internal" href="#status-bar-help">Status_Bar_Help</a></p>
360	<!-- ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ -->
361	<div class="section" id="id1">
362	<span id="load-a-file"></span><h1>Load a File</h1>
363	<p>From Menu go to <em>Data</em> -> <em>Load Data File(or Folder)</em> . Select a file/folder
364	from the menu bar and click on Open button. Data contained in the file will be
365	displayed. To cancel the loading click on <em>cancel</em> . In case a file can not be
366	loaded, an error message will be displayed on the statusbar.</p>
367	<!-- ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ -->
368	</div>
369	<div class="section" id="id2">
370	<span id="single-fit"></span><h1>Single Fit</h1>
371	<p>One of two fit-engines can be chosen from the Fitting menu bar. The Simple Fit-
372	engine uses Scipy's leasqr and the Complex Fit-Engine is a custom optimizer
373	that provides a better chance to find the global minimum of the <a href="#id3"><span class="problematic" id="id4">\|</span></a>chi\|2 but that
374	requires longer computation time. In order to set a data to a control panel
375	(FitPage), see the "DataLoader Help". Once a data set to the FiPage, select a
376	model from the combo box. The default parameters of the model will be display.
377	Set initial parameters if need. Check and uncheck parameters to fit/fix. Click
378	the <em>'Fit'</em> button. When the fitting is finished, the resultant parameter
379	values will be displayed with the errors. If a error is missing, it generally
380	means that the corresponding parameter is not very depending on the model. The
381	chisq/Npt_fit and the plot associated with the fit operation will be also
382	updated.</p>
383	<div class="system-message" id="id3">
384	<p class="system-message-title">System Message: WARNING/2 (<tt class="docutils">C:/Code/Eclipse_workspace/SasViewTrunk/src/sas/perspectives/fitting/media/fitting_help.rst</tt>, line 73); <em><a href="#id4">backlink</a></em></p>
385	Inline substitution_reference start-string without end-string.</div>
386	<!-- ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ -->
387	</div>
388	<div class="section" id="id5">
389	<span id="simultaneous-fitting"></span><h1>Simultaneous Fitting</h1>
390	<p>This fitting option enables to set a number of the constraints between the
391	parameters of fitting(s). It requires one or more FitPages with a data and a
392	model set for the fitting, and performs multiple fittings given by the
393	FitPage(s). The Complex (ParkMC) FitEngine will be used automatically.</p>
394	<p>Simultaneous Fit without Constraint</p>
395	<p>Assuming some FitPages are already set up, check the checkboxes of the
396	model_data rows to fit. And click the 'Fit' button. The results will return to
397	each FitPages.</p>
398	<p>Note that the chi2/Npts returned is the sum of the chi2/Npts of each fits. If
399	one needs the chi2 value only for a page, click the 'Compute' button in the
400	FitPage to recalculate.</p>
401	<p>Simultaneous Fit with Constraint</p>
402	<p>Enter constraint in the text control next to <em>constraint fit</em> button.
403	Constraint should be of type model1 parameter name = f(model2 parameter name)
404	for example, M0.radius=2*M1.radius. Many constraints can be entered for a
405	single fit. Each of them should be separated by a newline charater or ";"
406	The easy setup can generate many constraint inputs easily when the selected
407	two models are the same type.</p>
408	<p>Note that the chi2/Npts returned is the sum of the chi2/Npts of each fits.
409	If one needs the chi2 value only for one fit, click the 'Compute' button in
410	the FitPage to recalculate.</p>
411	<!-- ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ -->
412	</div>
413	<div class="section" id="id6">
414	<span id="batch-fitting"></span><h1>Batch Fitting</h1>
415	<p><a class="reference internal" href="#batch-fit">Batch_Fit</a></p>
416	<p><a class="reference internal" href="#batch-window">Batch_Window</a></p>
417	<p><a class="reference internal" href="#edit-grid">Edit_Grid</a></p>
418	<p><a class="reference internal" href="#save-grid">Save_Grid</a></p>
419	<p><a class="reference internal" href="#open-batch-results">Open_Batch_Results</a></p>
420	<p><a class="reference internal" href="#plot">Plot</a></p>
421	<p><a class="reference internal" href="#view-column-cell">View_Column_Cell</a></p>
422	</div>
423	<div class="section" id="id7">
424	<span id="batch-fit"></span><h1>Batch Fit</h1>
425	<p>Create a <em>Batch Page</em> by selecting the <em>Batch</em> radio button on the DataExplorer
426	(see figure below) and for a new control page select 'New FitPage' in the
427	Fitting menubar.</p>
428	<img alt="batch_button_area.bmp" src="batch_button_area.bmp" />
429	<p>Figure 1: MenuBar:</p>
430	<p>Load Data to the DataExplorer if not already loaded.</p>
431	<p>Select one or more data sets by checking the check boxes, and then make sure
432	that "Fitting" is selected in the dropdown menu next to the "Send To" button.
433	Once ready, click the 'Send To' button to set data to a BatchPage. If already
434	an empty batch page exists, it will be set there. Otherwise it will create a
435	new Batch Page. Set up the model and the parameter values as same as a single
436	fitting (see Single Fit help) <<a class="reference internal" href="#single-fit">Single_Fit</a>>. Then use 'Fit' button to
437	perform the fitting.</p>
438	<p>Unlike a single fit, the results of the fittings will not return to the
439	BatchPage'. Instead, a Grid window will be provided once the fitting is
440	completed. The Grid window is also accessible from the 'View' menu
441	(see Figure 2).</p>
442	<p>Note that only one model is used for all the data. The initial parameter
443	values given in the control page will be used all the data fittings. If one
444	wants the FitEngine to use the initial values from the results of the
445	previous data fitting (if any), choose the 'Chain Fitting' option in the
446	Fitting menubar, which will speed up the fitting especially when you have
447	lots of, and similar, data sets.</p>
448	</div>
449	<div class="section" id="id8">
450	<span id="batch-window"></span><h1>Batch Window</h1>
451	<p>Batch Window provides an easy way to view the fit results, i.e., plot data,
452	fits, and residuals. Batch window will be automatically shown after a batch
453	fit is finished.</p>
454	<p>Once closed, it can be opened anytime from the "View" menubar item (see
455	Figure 2).</p>
456	<img alt="restore_batch_window.bmp" src="restore_batch_window.bmp" />
457	<p>Figure 2: Edit Menu:</p>
458	</div>
459	<div class="section" id="id9">
460	<span id="edit-grid"></span><h1>Edit Grid</h1>
461	<p>Once a batch fit is completed, all fitted and fixed model parameters are
462	displayed to the current sheet of the batch window except the errors of the
463	parameters. To view the errors, click on a given column then under <em>Edit</em>
464	menubar item, and insert the desired parameter by selecting a menu item with
465	the appropriated label. Empty column can be inserted in the same way. A
466	column value can be customized by editing an existing empty column.</p>
467	<p>To Remove column from the grid, select it, choose edit menu, and click the
468	<em>'remove'</em> menu item. Any removed column should reinserted whenever needed.</p>
469	<p>All above options are also available when right clicking on a given column
470	label(see Figure 3).</p>
471	<p><em>Note:</em> A column always needs to be selected in order to remove or insert a
472	column in the grid.</p>
473	<img alt="edit_menu.bmp" src="edit_menu.bmp" />
474	<p>Figure 3: Edit Menu:</p>
475	</div>
476	<div class="section" id="id10">
477	<span id="save-grid"></span><h1>Save Grid</h1>
478	<p>To save the current page on the batch window, select the <em>'File'</em> menubar
479	item(see Figure 4), then choose the <em>'Save as'</em> menu item to save it as a
480	.csv file.</p>
481	<p><em>Note:</em> The grid doesn't save the data array, fits, and the array residuals.
482	As a result, the 'View (fit) Results' functionality will be lost when
483	reloading the saved file.</p>
484	<p>Warning! To ensure accuracy of saved fit results, it is recommended to save
485	the current grid before modifying it .</p>
486	</div>
487	<div class="section" id="id11">
488	<span id="open-batch-results"></span><h1>Open Batch Results</h1>
489	<p>Any <em>csv</em> file can be opened in the grid by selecting the <em>'Open'</em> under
490	the <em>'File'</em> menu in the Grid Window(see Figure 4). All columns in the file
491	will be displayed but insertion will not available. Insertion will be
492	available only when at least one column will be removed from the grid.</p>
493	<img alt="file_menu.bmp" src="file_menu.bmp" />
494	<p>Figure 4: MenuBar:</p>
495	</div>
496	<div class="section" id="id12">
497	<span id="plot"></span><h1>Plot</h1>
498	<p>To <em>plot</em> a column versus another, select one column at the time, click the
499	<em>'Add'</em> button next to the text control of X/Y -axis <em>Selection Range</em> to
500	plot the value of this column on the X/Y axis. Alternatively, all available
501	range can be selected by clicking the column letter (eg. B). Repeat the same
502	procedure the next axis. Finally, click the <em>'Plot'</em> button. When clicking
503	on <em>Add</em> button, the grid will automatically fill the axis label, but
504	different labels and units can be entered in the correct controls before
505	clicking on the plot button.</p>
506	<p><em>X/Y -Axis Selection Range</em> can be edited manually. These text controls
507	allow the following types of expression (operation can be + - * /, or pow)</p>
508	<p>1) if the current axis label range is a function of 1 or more columns, write
509	this type of expression</p>
510	<p>constant1 * column_name1 [minimum row index : maximum row index] operator
511	constant2 * column_name2 [minimum row index : maximum row index]</p>
512	<p>Example: radius [2 : 5] -3 * scale [2 : 5]</p>
513	<p>2) if only some values of a given column are need but the range between the
514	first row and the last row used is not continuous, write the following
515	expression in the text control</p>
516	<p>column_name1 [minimum row index1 : maximum row index1] , column_name1
517	[minimum row index2 : maximum row index2]</p>
518	<p>Example : radius [2 : 5] , radius [10 : 25]</p>
519	<p>Note: Both text controls ( X and Y-axis Selection Ranges) need to be filled
520	with valid entries for plotting to work. The dY-bar is optional (see Figure 5).</p>
521	<img alt="plot_button.bmp" src="plot_button.bmp" />
522	<p>Figure 5: Plotting</p>
523	</div>
524	<div class="section" id="view-column-cell-s">
525	<span id="view-column-cell"></span><h1>View Column/Cell(s)</h1>
526	<p>Select 1 or more cells from the same column, click the 'View Fits' button to
527	display available curves.</p>
528	<p>For example, select the cells of the 'Chi2' column, then click the 'View Fits'
529	button. The plots generates will represent the residuals plots.</p>
530	<p>If you select any cells of the 'Data' column and click the 'View Fits' button.
531	It generates both data and fits in the graph (see Figure 6).</p>
532	<p>Alternatively, just click the column letter (eg. B) to choose all the
533	available data sets, then simply click the 'View Fits' button to plot the
534	data and fits.</p>
535	<img alt="view_button.bmp" src="view_button.bmp" />
536	<p>Figure 6: View Fits</p>
537	<!-- ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ -->
538	<p id="model-selection"><a class="reference internal" href="#model-type">Model_Type</a></p>
539	<p><a class="reference internal" href="#change-model-parameters">Change_Model_Parameters</a></p>
540	<p><a class="reference internal" href="#write-your-own-model">Write_your_Own_Model</a></p>
541	</div>
542	<div class="section" id="id13">
543	<span id="model-type"></span><h1>Model Type</h1>
544	<p>Models are grouped into three classes</p>
545	<ul class="simple">
546	<li><em>Shapes</em></li>
547	<li><em>Shape-Independent</em></li>
548	<li><em>Uncategorised</em></li>
549	<li><em>Customized Models</em></li>
550	<li><em>Structure Factor</em></li>
551	</ul>
552	</div>
553	<div class="section" id="id14">
554	<span id="change-model-parameters"></span><h1>Change Model Parameters</h1>
555	<p>To visualize model in a different window, from menu click on <em>Model</em>. Select
556	a type of model and then the name of your model.A new window will appear with
557	the plot of your model with default values. Change model's parameters on
558	<em>model view</em> tab and view the plotted model with its new parameters.</p>
559	</div>
560	<div class="section" id="id15">
561	<span id="write-your-own-model"></span><h1>Write your Own Model</h1>
562	<p>The custom model editors are provided from 'Fitting' menu in the menu bar.
563	See 'Custom model editor' in the side menu on left. Advanced users can write
564	your own model and save it (in .py format) into <em>plugin_models</em> directory in
565	.sasview of your home directory (eg., username.sasview>plugin_models). Your
566	plugin model will be added into "<>Customized Models" on the next model
567	selection.</p>
568	<!-- ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ -->
569	</div>
570	<div class="section" id="id16">
571	<span id="model-category-manager"></span><h1>Model Category Manager</h1>
572	<p>Our SAS models are, by default, classified into 5 categories; shapes,
573	shape-independent, structure factor, and customized models, where these
574	categories (except the customized models) can be reassigned, added, and
575	removed using 'Category Manager'. Each models can also be enabled(shown)/
576	disabled(hidden) from the category that they belong. The Category Manager
577	panel is accessible from the model category 'Modify' button in the fitting
578	panel or the 'View/Category Manager' menu in the menu bar (Fig. 1).</p>
579	<p>1) Enable/Disable models: Check/uncheck the check boxes to enable/disable the
580	models (Fig. 2).</p>
581	<p>2) Change category: Highlight a model in the list by left-clicking and click
582	the 'Modify' button. In the 'Change Category' panel, one can create/use a
583	category for the model, then click the 'Add' button. In order to delete a
584	category, select a category name and click the 'Remove Selected' button
585	(Fig. 3).</p>
586	<p>3) To apply the changes made, hit the OK button. Otherwise, click the 'Cancel'
587	button (Fig. 2).</p>
588	<img alt="cat_fig0.bmp" src="cat_fig0.bmp" />
589	<p>Fig.1</p>
590	<img alt="cat_fig1.bmp" src="cat_fig1.bmp" />
591	<p>Fig.2</p>
592	<img alt="cat_fig2.bmp" src="cat_fig2.bmp" />
593	<p>Fig.3</p>
594	<!-- ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ -->
595	</div>
596	<div class="section" id="id17">
597	<span id="model-functions"></span><h1>Model Functions</h1>
598	<p>Model Documentation <models/model_functions></p>
599	<!-- ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ -->
600	</div>
601	<div class="section" id="id18">
602	<span id="custom-model-editor"></span><h1>Custom Model Editor</h1>
603	<p><a class="reference internal" href="#description">Description</a></p>
604	<p><a class="reference internal" href="#new">New</a></p>
605	<p><a class="reference internal" href="#sum-multi-p1-p2">Sum_Multi_p1_p2</a></p>
606	<p><a class="reference internal" href="#advanced">Advanced</a></p>
607	<p><a class="reference internal" href="#delete">Delete</a></p>
608	<!-- ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ -->
609	</div>
610	<div class="section" id="id19">
611	<span id="description"></span><h1>Description</h1>
612	<p>This menu (Fitting/Edit Custom Model in the menu bar) interface is to provide
613	you an easy way to write your own custom models. The changes in a model
614	function are effective after it is re-selected from the combo-box menu.</p>
615	<img alt="edit_model_menu.bmp" src="edit_model_menu.bmp" />
616	</div>
617	<div class="section" id="id20">
618	<span id="new"></span><h1>New</h1>
619	<p>This option is used to make a new model. A model code generated by this option
620	can be viewed and further modified by the 'Advanced' option below.</p>
621	<img alt="new_model.bmp" src="new_model.bmp" />
622	</div>
623	<div class="section" id="id21">
624	<span id="sum-multi-p1-p2"></span><h1>Sum\|Multi(p1,p2)</h1>
625	<p>This option create a new sum (or multiplication) model. Fill up the (sum
626	model function) name and the description. The description will show up on
627	details button in the application. Then select the p1 or p2 model for the
628	sum/multi model, select an operator as necessary and click the Apply button
629	for activation. Hit the 'Close' button when it's done.</p>
630	<img alt="sum_model.bmp" src="sum_model.bmp" />
631	</div>
632	<div class="section" id="id22">
633	<span id="advanced"></span><h1>Advanced</h1>
634	<p>The menu option shows all the files in the plugin_models folder. You can edit,
635	modify, and save it. It is recommended to modify only the lines with arrow
636	(-------). In the end of edit, 'Compile' and 'Run' from the menu bar to
637	activate or to see the model working properly.</p>
638	</div>
639	<div class="section" id="id23">
640	<span id="delete"></span><h1>Delete</h1>
641	<p>The menu option is to delete the custom models. Just select the file name to
642	delete.</p>
643	<!-- ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ -->
644	</div>
645	<div class="section" id="id24">
646	<span id="polydispersity-distributions"></span><h1>Polydispersity Distributions</h1>
647	<p>Calculates the form factor for a polydisperse and/or angular population of
648	particles with uniform scattering length density. The resultant form factor
649	is normalized by the average particle volume such that</p>
650	<p>P(q) = scale<FF>/Vol + bkg</p>
651	<p>where F is the scattering amplitude and the<>denote an average over the size
652	distribution. Users should use PD (polydispersity: this definition is
653	different from the typical definition in polymer science) for a size
654	distribution and Sigma for an angular distribution (see below).</p>
655	<p>Note that this computation is very time intensive thus applying polydispersion/
656	angular distrubtion for more than one paramters or increasing Npts values
657	might need extensive patience to complete the computation. Also note that
658	even though it is time consuming, it is safer to have larger values of Npts
659	and Nsigmas.</p>
660	<p>The following five distribution functions are provided</p>
661	<ul class="simple">
662	<li><em>Rectangular_Distribution_</em></li>
663	<li><em>Array_Distribution_</em></li>
664	<li><em>Gaussian_Distribution_</em></li>
665	<li><em>Lognormal_Distribution_</em></li>
666	<li><em>Schulz_Distribution_</em></li>
667	</ul>
668	</div>
669	<div class="section" id="id25">
670	<span id="rectangular-distribution"></span><h1>Rectangular Distribution</h1>
671	<img alt="pd_image001.png" src="pd_image001.png" />
672	<p>The xmean is the mean of the distribution, w is the half-width, and Norm is a
673	normalization factor which is determined during the numerical calculation.
674	Note that the Sigma and the half width <em>w</em> are different.</p>
675	<p>The standard deviation is</p>
676	<img alt="pd_image002.png" src="pd_image002.png" />
677	<p>The PD (polydispersity) is</p>
678	<img alt="pd_image003.png" src="pd_image003.png" />
679	<img alt="pd_image004.jpg" src="pd_image004.jpg" />
680	</div>
681	<div class="section" id="id26">
682	<span id="array-distribution"></span><h1>Array Distribution</h1>
683	<p>This distribution is to be given by users as a txt file where the array
684	should be defined by two columns in the order of x and f(x) values. The f(x)
685	will be normalized by SasView during the computation.</p>
686	<p>Example of an array in the file</p>
687	<p>30 0.1
688	32 0.3
689	35 0.4
690	36 0.5
691	37 0.6
692	39 0.7
693	41 0.9</p>
694	<p>We use only these array values in the computation, therefore the mean value
695	given in the control panel, for example Ã¢â¬Ëradius = 60Ã¢â¬â¢, will be ignored.</p>
696	</div>
697	<div class="section" id="id27">
698	<span id="gaussian-distribution"></span><h1>Gaussian Distribution</h1>
699	<img alt="pd_image005.png" src="pd_image005.png" />
700	<p>The xmean is the mean of the distribution and Norm is a normalization factor
701	which is determined during the numerical calculation.</p>
702	<p>The PD (polydispersity) is</p>
703	<img alt="pd_image003.png" src="pd_image003.png" />
704	<img alt="pd_image006.jpg" src="pd_image006.jpg" />
705	</div>
706	<div class="section" id="id28">
707	<span id="lognormal-distribution"></span><h1>Lognormal Distribution</h1>
708	<img alt="pd_image007.png" src="pd_image007.png" />
709	<p>The /mu/=ln(xmed), xmed is the median value of the distribution, and Norm is a
710	normalization factor which will be determined during the numerical calculation.
711	The median value is the value given in the size parameter in the control panel,
712	for example, Ã¢â¬Åradius = 60Ã¢â¬ï¿œ.</p>
713	<p>The PD (polydispersity) is given by /sigma/</p>
714	<img alt="pd_image008.png" src="pd_image008.png" />
715	<p>For the angular distribution</p>
716	<img alt="pd_image009.png" src="pd_image009.png" />
717	<p>The mean value is given by xmean=exp(/mu/+p2/2). The peak value is given by
718	xpeak=exp(/mu/-p2).</p>
719	<img alt="pd_image010.jpg" src="pd_image010.jpg" />
720	<p>This distribution function spreads more and the peak shifts to the left as the
721	p increases, requiring higher values of Nsigmas and Npts.</p>
722	</div>
723	<div class="section" id="id29">
724	<span id="schulz-distribution"></span><h1>Schulz Distribution</h1>
725	<img alt="pd_image011.png" src="pd_image011.png" />
726	<p>The xmean is the mean of the distribution and Norm is a normalization factor
727	which is determined during the numerical calculation.</p>
728	<p>The z = 1/p2Ã¢â¬â 1.</p>
729	<p>The PD (polydispersity) is</p>
730	<img alt="pd_image012.png" src="pd_image012.png" />
731	<p>Note that the higher PD (polydispersity) might need higher values of Npts and
732	Nsigmas. For example, at PD = 0.7 and radisus = 60 A, Npts >= 160, and
733	Nsigmas >= 15 at least.</p>
734	<img alt="pd_image013.jpg" src="pd_image013.jpg" />
735	<!-- ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ -->
736	</div>
737	<div class="section" id="id30">
738	<span id="smearing-computation"></span><h1>Smearing Computation</h1>
739	<p><a class="reference internal" href="#slit-smearing">Slit_Smearing</a></p>
740	<p><a class="reference internal" href="#pinhole-smearing">Pinhole_Smearing</a></p>
741	<p><a class="reference internal" href="#d-smearing">2D_Smearing</a></p>
742	</div>
743	<div class="section" id="id31">
744	<span id="slit-smearing"></span><h1>Slit Smearing</h1>
745	<p>The sit smeared scattering intensity for SAS is defined by</p>
746	<img alt="sm_image002.gif" src="sm_image002.gif" />
747	<p>where Norm =</p>
748	<img alt="sm_image003.gif" src="sm_image003.gif" />
749	<p>Equation 1</p>
750	<p>The functions <img alt="inlineimage004" src="sm_image004.gif" /> and <img alt="inlineimage005" src="sm_image005.gif" />
751	refer to the slit width weighting function and the slit height weighting
752	determined at the q point, respectively. Here, we assumes that the weighting
753	function is described by a rectangular function, i.e.,</p>
754	<img alt="sm_image006.gif" src="sm_image006.gif" />
755	<p>Equation 2</p>
756	<p>and</p>
757	<img alt="sm_image007.gif" src="sm_image007.gif" />
758	<p>Equation 3</p>
759	<p>so that <img alt="inlineimage008" src="sm_image008.gif" /> <img alt="inlineimage009" src="sm_image009.gif" /> for <img alt="inlineimage010" src="sm_image010.gif" /> and u.</p>
760	<p>The <img alt="inlineimage011" src="sm_image011.gif" /> and <img alt="inlineimage012" src="sm_image012.gif" /> stand for
761	the slit height (FWHM/2) and the slit width (FWHM/2) in the q space. Now the
762	integral of Equation 1 is simplified to</p>
763	<img alt="sm_image013.gif" src="sm_image013.gif" />
764	<p>Equation 4</p>
765	</div>
766	<div class="section" id="numerical-implementation-of-equation-4">
767	<h1>Numerical Implementation of Equation 4</h1>
768	</div>
769	<div class="section" id="case-1">
770	<h1>Case 1</h1>
771	<p>For <img alt="inlineimage012" src="sm_image012.gif" /> = 0 and <img alt="inlineimage011" src="sm_image011.gif" /> = constant.</p>
772	<img alt="sm_image016.gif" src="sm_image016.gif" />
773	<p>For discrete q values, at the q values from the data points and at the q
774	values extended up to qN= qi + <img alt="inlineimage011" src="sm_image011.gif" /> the smeared
775	intensity can be calculated approximately</p>
776	<img alt="sm_image017.gif" src="sm_image017.gif" />
777	<p>Equation 5</p>
778	<p><img alt="inlineimage018" src="sm_image018.gif" /> = 0 for <em>Is</em> in <em>j</em> < <em>i</em> or <em>j</em> > N-1*.</p>
779	</div>
780	<div class="section" id="case-2">
781	<h1>Case 2</h1>
782	<p>For <img alt="inlineimage012" src="sm_image012.gif" /> = constant and <img alt="inlineimage011" src="sm_image011.gif" /> = 0.</p>
783	<p>Similarly to Case 1, we get</p>
784	<p><img alt="inlineimage019" src="sm_image019.gif" /> for qp= qi- <img alt="inlineimage012" src="sm_image012.gif" /> and qN= qi+ <img alt="inlineimage012" src="sm_image012.gif" />. <img alt="inlineimage018" src="sm_image018.gif" /> = 0
785	for <em>Is</em> in <em>j</em> < <em>p</em> or <em>j</em> > <em>N-1</em>.</p>
786	</div>
787	<div class="section" id="case-3">
788	<h1>Case 3</h1>
789	<p>For <img alt="inlineimage011" src="sm_image011.gif" /> = constant and
790	<img alt="inlineimage011" src="sm_image011.gif" /> = constant.</p>
791	<p>In this case, the best way is to perform the integration, Equation 1,
792	numerically for both slit height and width. However, the numerical integration
793	is not correct enough unless given a large number of iteration, say at least
794	10000 by 10000 for each element of the matrix, W, which will take minutes and
795	minutes to finish the calculation for a set of typical SAS data. An
796	alternative way which is correct for slit width << slit hight, is used in
797	SasView. This method is a mixed method that combines method 1 with the
798	numerical integration for the slit width.</p>
799	<img alt="sm_image020.gif" src="sm_image020.gif" />
800	<p>Equation 7</p>
801	<p>for qp= qi- <img alt="inlineimage012" src="sm_image012.gif" /> and
802	qN= qi+ <img alt="inlineimage012" src="sm_image012.gif" />. <img alt="inlineimage018" src="sm_image018.gif" /> = 0 for
803	<em>Is</em> in <em>j</em> < <em>p</em> or <em>j</em> > <em>N-1</em>.</p>
804	</div>
805	<div class="section" id="id32">
806	<span id="pinhole-smearing"></span><h1>Pinhole Smearing</h1>
807	<p>The pinhole smearing computation is done similar to the case above except
808	that the weight function used is the Gaussian function, so that the Equation 6
809	for this case becomes</p>
810	<img alt="sm_image021.gif" src="sm_image021.gif" />
811	<p>Equation 8</p>
812	<p>For all the cases above, the weighting matrix <em>W</em> is calculated when the
813	smearing is called at the first time, and it includes the ~ 60 q values
814	(finely binned evenly) below (>0) and above the q range of data in order
815	to cover all data points of the smearing computation for a given model and
816	for a given slit size. The <em>Norm</em> factor is found numerically with the
817	weighting matrix, and considered on <em>Is</em> computation.</p>
818	</div>
819	<div class="section" id="id33">
820	<span id="d-smearing"></span><h1>2D Smearing</h1>
821	<p>The 2D smearing computation is done similar to the 1D pinhole smearing above
822	except that the weight function used was the 2D elliptical Gaussian function</p>
823	<img alt="sm_image022.gif" src="sm_image022.gif" />
824	<p>Equation 9</p>
825	<p>In Equation 9, x0 = qcos/theta/ and y0 = qsin/theta/, and the primed axes
826	are in the coordinate rotated by an angle /theta/ around the z-axis (below)
827	so that xÃ¢â¬â¢0= x0cos/theta/+y0sin/theta/ and yÃ¢â¬â¢0= -x0sin/theta/+y0cos/theta/.</p>
828	<p>Note that the rotation angle is zero for x-y symmetric elliptical Gaussian
829	distribution. The A is a normalization factor.</p>
830	<img alt="sm_image023.gif" src="sm_image023.gif" />
831	<p>Now we consider a numerical integration where each bins in /theta/ and R are
832	<em>evenly</em> (this is to simplify the equation below) distributed by /delta//theta/
833	and /delta/R, respectively, and it is assumed that I(xÃ¢â¬â¢, yÃ¢â¬â¢) is constant
834	within the bins which in turn becomes</p>
835	<img alt="sm_image024.gif" src="sm_image024.gif" />
836	<p>Equation 10</p>
837	<p>Since we have found the weighting factor on each bin points, it is convenient
838	to transform xÃ¢â¬â¢-yÃ¢â¬â¢ back to x-y coordinate (rotating it by -/theta/ around z
839	axis). Then, for the polar symmetric smear</p>
840	<img alt="sm_image025.gif" src="sm_image025.gif" />
841	<p>Equation 11</p>
842	<p>where</p>
843	<img alt="sm_image026.gif" src="sm_image026.gif" />
844	<p>while for the x-y symmetric smear</p>
845	<img alt="sm_image027.gif" src="sm_image027.gif" />
846	<p>Equation 12</p>
847	<p>where</p>
848	<img alt="sm_image028.gif" src="sm_image028.gif" />
849	<p>Here, the current version of the SasView uses Equation 11 for 2D smearing
850	assuming that all the Gaussian weighting functions are aligned in the polar
851	coordinate.</p>
852	<p>In the control panel, the higher accuracy indicates more and finer binnng
853	points so that it costs more in time.</p>
854	<!-- ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ -->
855	</div>
856	<div class="section" id="id34">
857	<span id="polarisation-magnetic-scattering"></span><h1>Polarisation/Magnetic Scattering</h1>
858	<p>Magnetic scattering is implemented in five (2D) models</p>
859	<ul class="simple">
860	<li><em>SphereModel</em></li>
861	<li><em>CoreShellModel</em></li>
862	<li><em>CoreMultiShellModel</em></li>
863	<li><em>CylinderModel</em></li>
864	<li><em>ParallelepipedModel</em></li>
865	</ul>
866	<p>In general, the scattering length density (SLD) in each regions where the
867	SLD (=/beta/) is uniform, is a combination of the nuclear and magnetic SLDs and
868	depends on the spin states of the neutrons as follows. For magnetic scattering,
869	only the magnetization component, <em>M*perp, perpendicular to the scattering
870	vector *Q</em> contributes to the the magnetic scattering length.</p>
871	<img alt="mag_vector.bmp" src="mag_vector.bmp" />
872	<p>The magnetic scattering length density is then</p>
873	<img alt="dm_eq.gif" src="dm_eq.gif" />
874	<p>where /gamma/ = -1.913 the gyromagnetic ratio, /mu/B is the Bohr magneton, r0
875	is the classical radius of electron, and <em>/sigma/</em> is the Pauli spin. For
876	polarised neutron, the magnetic scattering is depending on the spin states.</p>
877	<p>Let's consider that the incident neutrons are polarized parallel (+)/
878	anti-parallel (-) to the x' axis (See both Figures above). The possible
879	out-coming states then are + and - states for both incident states</p>
880	<p>Non-spin flips: (+ +) and (- -)
881	Spin flips: (+ -) and (- +)</p>
882	<img alt="M_angles_pic.bmp" src="M_angles_pic.bmp" />
883	<p>Now, let's assume that the angles of the <em>Q</em> vector and the spin-axis (x')
884	against x-axis are /phi/ and /theta/up, respectively (See Figure above). Then,
885	depending upon the polarisation (spin) state of neutrons, the scattering length
886	densities, including the nuclear scattering length density (/beta/N) are given
887	as, for non-spin-flips</p>
888	<img alt="sld1.gif" src="sld1.gif" />
889	<p>for spin-flips</p>
890	<img alt="sld2.gif" src="sld2.gif" />
891	<p>where</p>
892	<img alt="mxp.gif" src="mxp.gif" />
893	<img alt="myp.gif" src="myp.gif" />
894	<img alt="mzp.gif" src="mzp.gif" />
895	<img alt="mqx.gif" src="mqx.gif" />
896	<img alt="mqy.gif" src="mqy.gif" />
897	<p>Here, the M0x, M0y and M0z are the x, y and z components of the magnetization
898	vector given in the xyz lab frame. The angles of the magnetization, /theta/M
899	and /phi/M as defined in the Figure (above)</p>
900	<img alt="m0x_eq.gif" src="m0x_eq.gif" />
901	<img alt="m0y_eq.gif" src="m0y_eq.gif" />
902	<img alt="m0z_eq.gif" src="m0z_eq.gif" />
903	<p>The user input parameters are M0_sld = DMM0, Up_theta = /theta/up,
904	M_theta = /theta/M, and M_phi = /phi/M. The 'Up_frac_i' and 'Up_frac_f' are
905	the ratio</p>
906	<p>(spin up)/(spin up + spin down)</p>
907	<p>neutrons before the sample and at the analyzer, respectively.</p>
908	<p><em>Note:</em> The values of the 'Up_frac_i' and 'Up_frac_f' must be in the range
909	between 0 and 1.</p>
910	<!-- ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ -->
911	</div>
912	<div class="section" id="id35">
913	<span id="key-combinations"></span><h1>Key Combinations</h1>
914	<p><a class="reference internal" href="#copy-paste">Copy_Paste</a></p>
915	<p><a class="reference internal" href="#bookmark">Bookmark</a></p>
916	<p><a class="reference internal" href="#graph-context-menu">Graph_Context_Menu</a></p>
917	<p><a class="reference internal" href="#ftolerance">FTolerance</a></p>
918	</div>
919	<div class="section" id="id36">
920	<span id="copy-paste"></span><h1>Copy & Paste</h1>
921	<p>To copy the parameter values in a Fit(Model) panel to the clipboard:</p>
922	<p><em>Ctrl(Cmd on MAC) + Left(Mouse)Click</em> on the panel.</p>
923	<p>To paste the parameter values to a Fit(Model)panel from the clipboard:</p>
924	<p><em>Ctrl(Cmd on MAC) + Shift + Left(Mouse)Click</em> on the panel.</p>
925	<p>If this operation is successful, it will say so in the info line at the
926	bottom of the SasView window.</p>
927	</div>
928	<div class="section" id="id37">
929	<span id="bookmark"></span><h1>Bookmark</h1>
930	<p>Bookmark of a fit-panel or model-panel status:</p>
931	<p><em>(Mouse)Right-Click</em> and select the bookmark in the popup list.</p>
932	</div>
933	<div class="section" id="id38">
934	<span id="graph-context-menu"></span><h1>Graph Context Menu</h1>
935	<p>To get the graph context menu to print, copy, save data, (2D)average, etc.:</p>
936	<p><em>Locate the mouse point on the plot to highlight and *(Mouse) Right Click</em>
937	to bring up the full menu.</p>
938	</div>
939	<div class="section" id="ftolerance-scipy">
940	<span id="ftolerance"></span><h1>FTolerance (SciPy)</h1>
941	<p>To change the ftol value of the Scipy FitEngine (leastsq):</p>
942	<p>First, make sure that the Fit panel has data and a model selected.</p>
943	<p><em>Ctrl(Cmd on MAC) + Shift + Alt + Right(Mouse)Click</em> on the panel.</p>
944	<p>Then, set up the value in the dialog panel.</p>
945	<p>If this operation is successful, the new ftol value will be displayed in the
946	info line at the bottom of the SV window.Note that increasing the ftol value
947	may cause for the fitting to terminate with higher <a href="#id39"><span class="problematic" id="id40">\|</span></a>chi\|sq.</p>
948	<div class="system-message" id="id39">
949	<p class="system-message-title">System Message: WARNING/2 (<tt class="docutils">C:/Code/Eclipse_workspace/SasViewTrunk/src/sas/perspectives/fitting/media/fitting_help.rst</tt>, line 947); <em><a href="#id40">backlink</a></em></p>
950	Inline substitution_reference start-string without end-string.</div>
951	<!-- ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ -->
952	</div>
953	<div class="section" id="id41">
954	<span id="status-bar-help"></span><h1>Status Bar Help</h1>
955	<p><a class="reference internal" href="#message-warning-hint">Message_Warning_Hint</a></p>
956	<p><a class="reference internal" href="#console">Console</a></p>
957	</div>
958	<div class="section" id="id42">
959	<span id="message-warning-hint"></span><h1>Message/Warning/Hint</h1>
960	<p>The status bar located at the bottom of the application frame, displays
961	messages, hints, warnings and errors.</p>
962	</div>
963	<div class="section" id="id43">
964	<span id="console"></span><h1>Console</h1>
965	<p>Select <em>light bulb/info icon</em> button in the status bar at the bottom of the
966	application window to display available history. During a long task, the
967	console can also help users to understand the status in progressing.</p>
968	</div>
969	</div>
970	</body>
971	</html>

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