Changeset 78f02c3 in sasview for src/sas/fit

Timestamp:

Feb 14, 2015 12:12:40 PM (10 years ago)

Author:

smk78

Branches:

master, ESS_GUI, ESS_GUI_Docs, ESS_GUI_batch_fitting, ESS_GUI_bumps_abstraction, ESS_GUI_iss1116, ESS_GUI_iss879, ESS_GUI_iss959, ESS_GUI_opencl, ESS_GUI_ordering, ESS_GUI_sync_sascalc, costrafo411, magnetic_scatt, release-4.1.1, release-4.1.2, release-4.2.2, release_4.0.1, ticket-1009, ticket-1094-headless, ticket-1242-2d-resolution, ticket-1243, ticket-1249, ticket885, unittest-saveload

Children:

898a8b9

Parents:

3e2ebbb

Message:

Level 1 sphinx-ready commit of remaining help files

File:

• src/sas/fit/media/fitting_help.rst (modified) (1 diff)

src/sas/fit/media/fitting_help.rst

@@ -1 +1 @@
 ..fitting_help.rst
+
+.. This is a port of the original SasView html help file to ReSTructured text
+.. by S King, ISIS, during SasView CodeCamp-III in Feb 2015.
+
+.. |beta| unicode:: U+03B2
+.. |gamma| unicode:: U+03B3
+.. |mu| unicode:: U+03BC
+.. |sigma| unicode:: U+03C3
+.. |phi| unicode:: U+03C6
+.. |theta| unicode:: U+03B8
 
 Fitting Perspective
 ===================
 
-Placeholder for fitting help
+Load_a_File_
+Single_Fit_
+Simultaneous_Fitting_
+Batch_Fitting_
+Model_Selection_
+Model_Category_Manager_
+Model_Functions_
+Custom_Model_Editor_
+Polydispersity_Distributions_
+Smearing_Computation_
+Polarisation/Magnetic_Scattering_
+Key_Combinations_
+Status_Bar_Help_
+
+.. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ
+
+..  _Load_a_File:
+
+Load a File
+-----------
+
+From Menu go to *Data* -> *Load Data File(or Folder)* . Select a file/folder 
+from the menu bar and click on Open button. Data contained in the file will be 
+displayed. To cancel the loading click on *cancel* . In case a file can not be 
+loaded, an error message will be displayed on the statusbar.
+
+.. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ
+
+.. _Single_Fit:
+
+Single Fit
+----------
+
+One of two fit-engines can be chosen from the Fitting menu bar. The Simple Fit-
+engine uses Scipy's leasqr and the Complex Fit-Engine is a custom optimizer 
+that provides a better chance to find the global minimum of the chi2 but that 
+requires longer computation time. In order to set a data to a control panel 
+(FitPage), see the "DataLoader Help". Once a data set to the FiPage, select a 
+model from the combo box. The default parameters of the model will be display. 
+Set initial parameters if need. Check and uncheck parameters to fit/fix. Click 
+the *'Fit'*  button. When the fitting is finished, the resultant parameter 
+values will be displayed with the errors. If a error is missing, it generally 
+means that the corresponding parameter is not very depending on the model. The 
+chisq/Npt_fit and the plot associated with the fit operation will be also 
+updated.
+
+.. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ
+
+..  _Simultaneous_Fitting:
+
+Simultaneous Fitting
+--------------------
+
+This fitting option enables to set a number of the constraints between the 
+parameters of fitting(s). It requires one or more FitPages with a data and a 
+model set for the fitting, and performs multiple fittings given by the 
+FitPage(s). The Complex (ParkMC) FitEngine will be used automatically.
+
+Simultaneous Fit without Constraint
+
+Assuming some FitPages are already set up, check the checkboxes of the 
+model_data rows to fit. And click the 'Fit' button. The results will return to 
+each FitPages.
+
+Note that the chi2/Npts returned is the sum of the chi2/Npts of each fits. If one needs the chi2 value only for a page, click the 'Compute' button in the FitPage to recalculate.
+
+Simultaneous Fit with Constraint
+
+Enter constraint in the text control next to *constraint fit*  button. 
+Constraint should be of type model1 parameter name = f(model2 parameter name) 
+for example, M0.radius=2*M1.radius. Many constraints can be entered for a 
+single fit. Each of them should be separated by a newline charater or ";" 
+The easy setup can generate many constraint inputs easily when the selected 
+two models are the same type.
+
+Note that the chi2/Npts returned is the sum of the chi2/Npts of each fits. 
+If one needs the chi2 value only for one fit, click the 'Compute' button in 
+the FitPage to recalculate.
+
+.. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ
+
+..  _Batch_Fitting:
+
+Batch Fitting
+-------------
+
+.. _Batch_Fit_
+.. _Batch_Window_
+.. _Edit_Grid_ 
+.. _Save_Grid_ 
+.. _Open_Batch_Results_ 
+.. _Plot_ 
+.. _View_Column/Cell(s)_ 
+
+.. _Batch_Fit:
+
+Batch Fit
+--------- 
+
+Create a *Batch Page* by selecting the *Batch* radio button on the DataExplorer
+(see figure below) and for a new control page select 'New FitPage' in the 
+Fitting menubar.
+
+.. image:: batch_button_area.bmp
+
+Figure 1: MenuBar: 
+
+Load Data to the DataExplorer if not already loaded.
+
+Select one or more data sets by checking the check boxes, and then make sure 
+that "Fitting" is selected in the dropdown menu next to the "Send To" button. 
+Once ready, click the 'Send To' button to set data to a BatchPage. If already 
+an empty batch page exists, it will be set there. Otherwise it will create a 
+new Batch Page. Set up the model and the parameter values as same as a single 
+fitting (see Single Fit help) <Single_Fit_>. Then use 'Fit' button to 
+perform the fitting.
+
+Unlike a single fit, the results of the fittings will not return to the 
+BatchPage'. Instead, a Grid window will be provided once the fitting is 
+completed. The Grid window is also accessible from the 'View' menu 
+(see Figure 2).
+
+Note that only one model is used for all the data. The initial parameter 
+values given in the control page will be used all the data fittings. If one 
+wants the FitEngine to use the initial values from the results of the 
+previous data fitting (if any), choose the 'Chain Fitting' option in the 
+Fitting menubar, which will speed up the fitting especially when you have 
+lots of, and similar, data sets.
+
+.. _Batch_Window:
+
+Batch Window
+------------
+Batch Window provides an easy way to view the fit results, i.e., plot data, 
+fits, and residuals. Batch window will be automatically shown after a batch 
+fit is finished.
+
+Once closed, it can be opened anytime from the "View" menubar item (see 
+Figure 2).
+
+.. image:: restore_batch_window.bmp
+
+Figure 2: Edit Menu: 
+
+.. _Edit_Grid:
+
+Edit Grid
+---------
+
+Once a batch fit is completed, all fitted and fixed model parameters are 
+displayed to the current sheet of the batch window except the errors of the 
+parameters. To view the errors, click on a given column then under *Edit*  
+menubar item, and insert the desired parameter by selecting a menu item with 
+the appropriated label. Empty column can be inserted in the same way. A 
+column value can be customized by editing an existing empty column.
+
+To Remove column from the grid, select it, choose edit menu, and click the 
+*'remove'*  menu item. Any removed column should reinserted whenever needed.
+
+All above options are also available when right clicking on a given column 
+label(see Figure 3).
+
+*Note:*  A column always needs to be selected in order to remove or insert a 
+column in the grid.
+
+.. image:: edit_menu.bmp
+
+Figure 3: Edit Menu:
+
+.. _Save_Grid:
+
+Save Grid
+---------
+To save the current page on the batch window, select the *'File'*  menubar 
+item(see Figure 4), then choose the *'Save as'*  menu item to save it as a 
+.csv file.
+
+ *Note:* The grid doesn't save the data array, fits, and the array residuals. 
+ As a result, the 'View (fit) Results' functionality will be lost when 
+ reloading the saved file.
+
+Warning! To ensure accuracy of saved fit results, it is recommended to save 
+the current grid before modifying it .
+
+.. _Open_Batch_Results:
+
+Open Batch Results 
+------------------
+
+Any *csv*  file can be opened in the grid by selecting the *'Open'*  under 
+the *'File'*  menu in the Grid Window(see Figure 4). All columns in the file 
+will be displayed but insertion will not available. Insertion will be 
+available only when at least one column will be removed from the grid.
+
+.. image:: file_menu.bmp
+
+Figure 4: MenuBar:
+
+.. _Plot:
+
+Plot
+----
+
+To *plot*  a column versus another, select one column at the time, click the 
+*'Add'*  button next to the text control of X/Y -axis *Selection Range*  to 
+plot the value of this column on the X/Y axis. Alternatively, all available 
+range can be selected by clicking the column letter (eg. B). Repeat the same 
+procedure the next axis. Finally, click the *'Plot'*  button. When clicking 
+on *Add*  button, the grid will automatically fill the axis label, but 
+different labels and units can be entered in the correct controls before 
+clicking on the plot button.
+
+ *X/Y -Axis Selection Range* can be edited manually. These text controls 
+ allow the following types of expression (operation can be + - * /, or pow)
+ 
+1) if the current axis label range is a function of 1 or more columns, write 
+this type of expression
+
+constant1  * column_name1 [minimum row index :  maximum  row index] operator 
+constant2 * column_name2 [minimum row index :  maximum  row index] 
+
+Example: radius [2 : 5] -3 * scale [2 : 5] 
+
+2) if only some values of a given column are need but the range between the 
+first row and the last row used is not continuous, write the following 
+expression in the text control
+
+column_name1 [minimum row index1 :  maximum  row index1] , column_name1 
+[minimum row index2 :  maximum  row index2] 
+
+Example : radius [2 : 5] , radius [10 : 25] 
+
+Note: Both text controls ( X and Y-axis Selection Ranges) need to be filled 
+with valid entries for plotting to work. The dY-bar is optional (see Figure 5).
+
+.. image::plot_button.bmp
+
+Figure 5: Plotting
+
+.. _View_Column/Cell(s):
+
+View Column/Cell(s)
+-------------------
+
+Select 1 or more cells from the same column, click the 'View Fits' button to 
+display available curves. 
+
+For example, select the cells of the  'Chi2'  column, then click the  'View Fits'  
+button. The plots generates will represent the residuals  plots. 
+ 
+If you select any cells of the 'Data' column and click the 'View Fits' button. 
+It generates both  data and fits in the graph (see Figure 6). 
+
+Alternatively, just click the column letter (eg. B) to choose all the 
+available data sets, then simply click the 'View Fits' button to plot the 
+data and fits. 
+
+.. image::view_button.bmp
+
+Figure 6: View Fits
+
+.. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ
+
+..  _Model_Selection:
+
+Model_Type_ 
+Change_Model_Parameters_ 
+Write_your_Own_Model_ 
+
+.. _Model_Type:
+
+Model Type
+----------
+
+Models are grouped into three classes
+
+*  *Shapes* 
+*  *Shape-Independent* 
+*  *Uncategorised*
+*  *Customized Models* 
+*  *Structure Factor*
+
+.. _Change_Model_Parameters:
+
+Change Model Parameters
+-----------------------
+
+To visualize model in a different window, from menu click on *Model*. Select 
+a type of model and then the name of your model.A new window will appear with 
+the plot of your model with default values. Change model's parameters on 
+*model view*  tab and view the plotted model with its new parameters.
+
+.. _Write_your_Own_Model:
+
+Write your Own Model
+--------------------
+
+The custom model editors are provided from 'Fitting' menu in the menu bar. 
+See 'Custom model editor' in the side menu on left. Advanced users can write 
+your own model and save it (in .py format) into *plugin_models*  directory in 
+.sasview of your home directory (eg., username\.sasview>\plugin_models). Your 
+plugin model will be added into "<>Customized Models" on the next model 
+selection.
+
+.. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ
+
+..  _Model_Category_Manager:
+
+Model Category Manager
+----------------------
+
+Our SAS models are, by default, classified into 5 categories; shapes, 
+shape-independent, structure factor, and customized models, where these 
+categories (except the customized models) can be reassigned, added, and 
+removed using 'Category Manager'. Each models can also be enabled(shown)/
+disabled(hidden) from the category that they belong. The Category Manager 
+panel is accessible from the model category 'Modify' button in the fitting 
+panel or the 'View/Category Manager' menu in the menu bar (Fig. 1).
+
+1) Enable/Disable models: Check/uncheck the check boxes to enable/disable the 
+models (Fig. 2).
+
+2) Change category: Highlight a model in the list by left-clicking and click 
+the 'Modify' button. In the 'Change Category' panel, one can create/use a 
+category for the model, then click the 'Add' button. In order to delete a 
+category, select a category name and click the 'Remove Selected' button 
+(Fig. 3).
+
+3) To apply the changes made, hit the OK button. Otherwise, click the 'Cancel' 
+button (Fig. 2).
+
+.. image:: cat_fig0.bmp
+
+Fig.1
+
+.. image:: cat_fig1.bmp
+
+Fig.2
+
+.. image:: cat_fig2.bmp
+
+Fig.3
+
+.. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ
+
+..  _Model_Functions:
+
+Model Functions
+---------------
+
+Model Documentation <models/model_functions>
+
+.. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ
+
+..  _Custom_Model_Editor:
+
+Custom Model Editor
+-------------------
+
+Description_ 
+New_ 
+Sum|Multi(p1,p2)_ 
+Advanced_ 
+Delete_ 
+
+.. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ
+
+.. _Description:
+
+Description
+-----------
+
+This menu (Fitting/Edit Custom Model in the menu bar) interface is to provide 
+you an easy way to write your own custom models. The changes in a model 
+function are effective after it is re-selected from the combo-box menu.
+
+.. image:: edit_model_menu.bmp
+
+.. _New:
+
+New
+---
+
+This option is used to make a new model. A model code generated by this option 
+can be viewed and further modified by the 'Advanced' option below.
+
+.. image:: new_model.bmp
+
+.. _Sum|Multi(p1,p2):
+
+Sum|Multi(p1,p2)
+----------------
+
+This option create a new sum (or multiplication) model. Fill up the (sum 
+model function) name and the description. The description will show up on 
+details button in the application. Then select the p1 or p2 model for the 
+sum/multi model, select an operator as necessary and click the Apply button 
+for activation. Hit the 'Close' button when it's done.
+
+.. image:: sum_model.bmp
+
+.. _Advanced:
+
+Advanced
+--------
+
+The menu option shows all the files in the plugin_models folder. You can edit, 
+modify, and save it. It is recommended to modify only the lines with arrow 
+(--`-----). In the end of edit, 'Compile' and 'Run' from the menu bar to 
+activate or to see the model working properly.
+
+.. _Delete:
+
+Delete
+------
+
+The menu option is to delete the custom models. Just select the file name to 
+delete.
+
+.. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ
+
+..  _Polydispersity_Distributions:
+
+Polydispersity Distributions
+----------------------------
+
+Calculates the form factor for a polydisperse and/or angular population of 
+particles with uniform scattering length density. The resultant form factor 
+is normalized by the average particle volume such that 
+
+P(q) = scale*\<F*F\>/Vol + bkg
+
+where F is the scattering amplitude and the\<\>denote an average over the size 
+distribution.  Users should use PD (polydispersity: this definition is 
+different from the typical definition in polymer science) for a size 
+distribution and Sigma for an angular distribution (see below).
+
+Note that this computation is very time intensive thus applying polydispersion/
+angular distrubtion for more than one paramters or increasing Npts values 
+might need extensive patience to complete the computation. Also note that 
+even though it is time consuming, it is safer to have larger values of Npts 
+and Nsigmas.
+
+The following five distribution functions are provided
+
+*  *Rectangular_Distribution_*
+*  *Array_Distribution_*
+*  *Gaussian_Distribution_*
+*  *Lognormal_Distribution_*
+*  *Schulz_Distribution_*
+
+.. _Rectangular_Distribution:
+
+Rectangular Distribution
+------------------------
+
+.. image:: img/pd_image001.png
+
+The xmean is the mean of the distribution, w is the half-width, and Norm is a 
+normalization factor which is determined during the numerical calculation. 
+Note that the Sigma and the half width *w*  are different.
+
+The standard deviation is
+
+.. image:: img/pd_image002.png
+
+The PD (polydispersity) is
+
+.. image:: img/pd_image003.png
+
+.. image:: img/pd_image004.jpg
+
+.. _Array_Distribution:
+
+Array Distribution
+------------------
+
+This distribution is to be given by users as a txt file where the array 
+should be defined by two columns in the order of x and f(x) values. The f(x) 
+will be normalized by SasView during the computation.
+
+Example of an array in the file
+
+30        0.1
+32        0.3
+35        0.4
+36        0.5
+37        0.6
+39        0.7
+41        0.9
+
+We use only these array values in the computation, therefore the mean value 
+given in the control panel, for example ‘radius = 60’, will be ignored.
+
+.. _Gaussian_Distribution:
+
+Gaussian Distribution
+---------------------
+
+.. image:: img/pd_image005.png
+
+The xmean is the mean of the distribution and Norm is a normalization factor 
+which is determined during the numerical calculation.
+
+The PD (polydispersity) is
+
+.. image:: img/pd_image003.png
+
+.. image:: img/pd_image006.jpg
+
+.. _Lognormal_Distribution:
+
+Lognormal Distribution
+----------------------
+
+.. image:: img/pd_image007.png
+
+The /mu/=ln(xmed), xmed is the median value of the distribution, and Norm is a 
+normalization factor which will be determined during the numerical calculation. 
+The median value is the value given in the size parameter in the control panel, 
+for example, “radius = 60”.
+
+The PD (polydispersity) is given by /sigma/
+
+.. image:: img/pd_image008.png
+
+For the angular distribution
+
+.. image:: img/pd_image009.png
+
+The mean value is given by xmean=exp(/mu/+p2/2). The peak value is given by 
+xpeak=exp(/mu/-p2).
+
+.. image:: img/pd_image010.jpg
+
+This distribution function spreads more and the peak shifts to the left as the 
+p increases, requiring higher values of Nsigmas and Npts.
+
+.. _Schulz_Distribution:
+
+Schulz Distribution
+-------------------
+
+.. image:: img/pd_image011.png
+
+The xmeanis the mean of the distribution and Norm is a normalization factor 
+which is determined during the numerical calculation.
+
+The z = 1/p2– 1.
+
+The PD (polydispersity) is
+
+.. image:: img/pd_image012.png
+
+Note that the higher PD (polydispersity) might need higher values of Npts and 
+Nsigmas. For example, at PD = 0.7 and radisus = 60 A, Npts >= 160, and 
+Nsigmas >= 15 at least.
+
+.. image:: img/pd_image013.jpg
+
+.. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ
+
+.. _Smearing_Computation:
+
+Smearing Computation
+--------------------
+
+Slit_Smearing_ 
+Pinhole_Smearing_ 
+2D_Smearing_ 
+
+.. _Slit_Smearing:
+
+Slit Smearing
+-------------
+
+The sit smeared scattering intensity for SAS is defined by
+
+.. image:: img/sm_image002.gif
+
+where Norm =
+
+.. image:: img/sm_image003.gif
+
+Equation 1
+
+The functions .. image:: img/sm_image004.gif and .. image:: img/sm_image005.gif
+refer to the slit width weighting function and the slit height weighting 
+determined at the q point, respectively. Here, we assumes that the weighting 
+function is described by a rectangular function, i.e.,
+
+.. image:: img/sm_image006.gif
+
+Equation 2
+
+and
+
+.. image:: img/sm_image007.gif
+
+Equation 3
+
+so that .. image:: img/sm_image008.gif .. image::img/sm_image009.gif for 
+.. image:: img/sm_image010.gif and u.
+
+The .. image::img/sm_image011.gif and .. image::img/sm_image012.gif stand for 
+the slit height (FWHM/2) and the slit width (FWHM/2) in the q space. Now the 
+integral of Equation 1 is simplified to
+
+.. image:: img/sm_image013.gif
+
+Equation 4
+
+Numerical Implementation of Equation 4
+--------------------------------------
+
+Case 1
+------
+
+For .. image:: img/sm_image012.gif = 0 and .. image:: img/sm_image011.gif = 
+constant.
+
+.. image:: img/sm_image016.gif
+
+For discrete q values, at the q values from the data points and at the q 
+values extended up to qN= qi + .. image:: img/sm_image011.gif the smeared 
+intensity can be calculated approximately
+
+.. image:: img/sm_image017.gif
+
+Equation 5
+
+.. image:: img/sm_image018.gif = 0 for *Is* in *j* < *i* or *j* > N-1*.
+
+Case 2
+------
+
+For .. image:: img/sm_image012.gif = constant and 
+.. image:: img/sm_image011.gif = 0.
+
+Similarly to Case 1, we get
+
+.. image:: img/sm_image019.gif for qp= qi-.. image:: img/sm_image012.gif 
+and qN= qi+.. image:: img/sm_image012.gif. .. image:: img/sm_image018.gif = 0 
+for *Is* in *j* < *p* or *j* > *N-1*.
+
+Case 3
+------
+
+For .. image:: img/sm_image011.gif = constant and 
+.. image:: img/sm_image011.gif = constant.
+
+In this case, the best way is to perform the integration, Equation 1, 
+numerically for both slit height and width. However, the numerical integration 
+is not correct enough unless given a large number of iteration, say at least 
+10000 by 10000 for each element of the matrix, W, which will take minutes and 
+minutes to finish the calculation for a set of typical SAS data. An 
+alternative way which is correct for slit width << slit hight, is used in 
+SasView. This method is a mixed method that combines method 1 with the 
+numerical integration for the slit width.
+
+.. image:: img/sm_image020.gif
+
+Equation 7
+
+for qp= qi-.. image:: img/sm_image012.gif and 
+qN= qi+.. image:: img/sm_image012.gif. .. image:: img/sm_image018.gif = 0 for 
+*Is* in *j* < *p* or *j* > *N-1*.
+
+.. Pinhole_Smearing:
+
+Pinhole Smearing
+----------------
+
+The pinhole smearing computation is done similar to the case above except 
+that the weight function used is the Gaussian function, so that the Equation 6 
+for this case becomes
+
+.. image:: img/sm_image021.gif
+
+Equation 8
+
+For all the cases above, the weighting matrix *W* is calculated when the 
+smearing is called at the first time, and it includes the ~ 60 q values 
+(finely binned evenly) below (\>0) and above the q range of data in order 
+to cover all data points of the smearing computation for a given model and 
+for a given slit size. The *Norm*  factor is found numerically with the 
+weighting matrix, and considered on *Is* computation.
+
+.. _2D_Smearing:
+
+2D Smearing
+----------- 
+
+The 2D smearing computation is done similar to the 1D pinhole smearing above 
+except that the weight function used was the 2D elliptical Gaussian function
+
+.. image:: img/sm_image022.gif
+
+Equation 9
+
+In Equation 9, x0 = qcos/theta/ and y0 = qsin/theta/, and the primed axes 
+are in the coordinate rotated by an angle /theta/ around the z-axis (below) 
+so that x’0= x0cos/theta/+y0sin/theta/ and y’0= -x0sin/theta/+y0cos/theta/.
+
+Note that the rotation angle is zero for x-y symmetric elliptical Gaussian 
+distribution. The A is a normalization factor.
+
+.. image:: img/sm_image023.gif
+
+Now we consider a numerical integration where each bins in /theta/ and R are 
+*evenly* (this is to simplify the equation below) distributed by /delta//theta/ 
+and /delta/R, respectively, and it is assumed that I(x’, y’) is constant 
+within the bins which in turn becomes
+
+.. image:: img/sm_image024.gif
+
+Equation 10
+
+Since we have found the weighting factor on each bin points, it is convenient 
+to transform x’-y’ back to x-y coordinate (rotating it by -/theta/ around z 
+axis). Then, for the polar symmetric smear
+
+.. image:: img/sm_image025.gif
+
+Equation 11
+
+where
+
+.. image:: img/sm_image026.gif
+
+while for the x-y symmetric smear
+
+.. image:: img/sm_image027.gif
+
+Equation 12
+
+where
+
+.. image:: img/sm_image028.gif
+
+Here, the current version of the SasView uses Equation 11 for 2D smearing 
+assuming that all the Gaussian weighting functions are aligned in the polar 
+coordinate.
+
+In the control panel, the higher accuracy indicates more and finer binnng 
+points so that it costs more in time.
+
+.. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ
+
+.. _Polarisation/Magnetic_Scattering:
+
+Polarisation/Magnetic Scattering
+--------------------------------
+
+Magnetic scattering is implemented in five (2D) models 
+
+*  *SphereModel*
+*  *CoreShellModel*
+*  *CoreMultiShellModel*
+*  *CylinderModel*
+*  *ParallelepipedModel*
+
+In general, the scattering length density (SLD) in each regions where the 
+SLD (=/beta/) is uniform, is a combination of the nuclear and magnetic SLDs and 
+depends on the spin states of the neutrons as follows. For magnetic scattering, 
+only the magnetization component, *M*perp, perpendicular to the scattering 
+vector *Q* contributes to the the magnetic scattering length.
+
+... image:: img/mag_vector.bmp
+
+The magnetic scattering length density is then
+
+.. image:: img/dm_eq.gif
+
+where /gamma/ = -1.913 the gyromagnetic ratio, /mu/B is the Bohr magneton, r0 
+is the classical radius of electron, and */sigma/* is the Pauli spin. For 
+polarised neutron, the magnetic scattering is depending on the spin states. 
+
+Let's consider that the incident neutrons are polarized parallel (+)/
+anti-parallel (-) to the x' axis (See both Figures above). The possible 
+out-coming states then are + and - states for both incident states
+
+Non-spin flips: (+ +) and (- -)
+Spin flips:     (+ -) and (- +)
+
+.. image:: img/M_angles_pic.bmp
+
+Now, let's assume that the angles of the *Q*  vector and the spin-axis (x') 
+against x-axis are /phi/ and /theta/up, respectively (See Figure above). Then, 
+depending upon the polarisation (spin) state of neutrons, the scattering length 
+densities, including the nuclear scattering length density (/beta/N) are given 
+as, for non-spin-flips
+
+.. image:: img/sld1.gif
+
+for spin-flips
+
+.. image:: img/sld2.gif
+
+where
+
+.. image:: img/mxp.gif
+
+.. image:: img/myp.gif
+
+.. image:: img/mzp.gif
+
+.. image:: img/mqx.gif
+
+.. image:: img/mqy.gif
+
+Here, the M0x, M0y and M0z are the x, y and z components of the magnetization 
+vector given in the xyz lab frame. The angles of the magnetization, /theta/M 
+and /phi/M as defined in the Figure (above)
+
+.. image:: img/m0x_eq.gif
+
+.. image:: img/m0y_eq.gif
+
+.. image:: img/m0z_eq.gif
+
+The user input parameters are M0_sld = DMM0, Up_theta = /theta/up, 
+M_theta = /theta/M, and M_phi = /phi/M. The 'Up_frac_i' and 'Up_frac_f' are 
+the ratio
+
+(spin up)/(spin up + spin down)
+
+neutrons before the sample and at the analyzer, respectively.
+
+*Note: The values of the 'Up_frac_i' and 'Up_frac_f' must be in the range 
+between 0 and 1.
+
+.. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ
+
+.. _Key_Combinations:
+
+Key Combinations
+----------------
+
+Copy&Paste_
+Bookmark_
+Graph_Context_Menu_
+FTolerance(SciPy)_
+
+.. _Copy&Paste:
+
+Copy & Paste
+------------
+
+To copy the parameter values in a Fit(Model) panel to the clipboard:
+
+*Ctrl(Cmd on MAC) + Left(Mouse)Click*  on the panel.
+
+To paste the parameter values to a Fit(Model)panel from the clipboard:
+
+*Ctrl(Cmd on MAC) + Shift + Left(Mouse)Click*  on the panel.
+
+If this operation is successful, it will say so in the info line at the 
+bottom of the SasView window.
+
+.. _Bookmark:
+
+Bookmark
+--------
+
+Bookmark of a fit-panel or model-panel status:
+
+*(Mouse)Right-Click*  and select the bookmark in the popup list.
+
+.. _Graph_Context_Menu:
+
+Graph Context Menu
+------------------
+
+To get the graph context menu to print, copy, save data, (2D)average, etc.:
+
+*Locate the mouse point on the plot to highlight and *(Mouse) Right Click* 
+to bring up the full menu.
+
+.. _FTolerance(SciPy): 
+
+FTolerance (SciPy)
+------------------
+
+To change the ftol value of the Scipy FitEngine (leastsq):
+
+First, make sure that the Fit panel has data and a model selected.
+
+*Ctrl(Cmd on MAC) + Shift + Alt + Right(Mouse)Click*  on the panel.
+
+Then, set up the value in the dialog panel.
+
+If this operation is successful, the new ftol value will be displayed in the 
+info line at the bottom of the SV window.Note that increasing the ftol value 
+may cause for the fitting to terminate with higher chisq.
+
+.. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ
+
+.. _Status_Bar_Help:
+
+Status Bar Help
+---------------
+
+Message/Warning/Hint_ 
+Console_ 
+
+.. _Message/Warning/Hint:
+
+Message/Warning/Hint
+--------------------
+
+The status bar located at the bottom of the application frame, displays 
+messages, hints, warnings and errors.
+
+.. _Console:
+
+Console
+-------
+
+Select *light bulb/info icon*  button in the status bar at the bottom of the 
+application window to display available history. During a long task, the 
+console can also help users to understand the status in progressing.