[ec392464] | 1 | .. fitting_help.rst |
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| 3 | .. This is a port of the original SasView html help file to ReSTructured text |
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| 4 | .. by S King, ISIS, during SasView CodeCamp-III in Feb 2015. |
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| 23 | |
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[ec392464] | 24 | |
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| 25 | Fitting Perspective |
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| 26 | =================== |
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| 27 | |
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| 28 | Load_a_File_ |
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| 29 | |
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| 30 | Single_Fit_ |
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| 31 | |
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| 32 | Simultaneous_Fitting_ |
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| 33 | |
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| 34 | Batch_Fitting_ |
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| 35 | |
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| 36 | Model_Selection_ |
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| 37 | |
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| 38 | Model_Category_Manager_ |
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| 39 | |
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| 40 | Model_Functions_ |
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| 41 | |
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| 42 | Custom_Model_Editor_ |
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| 43 | |
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| 44 | Polydispersity_Distributions_ |
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| 45 | |
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| 46 | Smearing_Computation_ |
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| 47 | |
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| 48 | Polarisation_Magnetic_Scattering_ |
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| 49 | |
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| 50 | Key_Combinations_ |
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| 51 | |
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| 52 | Status_Bar_Help_ |
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| 53 | |
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| 54 | .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ |
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| 55 | |
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| 56 | .. _Load_a_File: |
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| 57 | |
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| 58 | Load a File |
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| 59 | ----------- |
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| 60 | |
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| 61 | From Menu go to *Data* -> *Load Data File(or Folder)* . Select a file/folder |
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| 62 | from the menu bar and click on Open button. Data contained in the file will be |
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| 63 | displayed. To cancel the loading click on *cancel* . In case a file can not be |
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| 64 | loaded, an error message will be displayed on the statusbar. |
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| 65 | |
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| 66 | .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ |
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| 67 | |
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| 68 | .. _Single_Fit: |
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| 69 | |
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| 70 | Single Fit |
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| 71 | ---------- |
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| 72 | |
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| 73 | One of two fit-engines can be chosen from the Fitting menu bar. The Simple Fit- |
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| 74 | engine uses Scipy's leasqr and the Complex Fit-Engine is a custom optimizer |
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[98b30b4] | 75 | that provides a better chance to find the global minimum of the |chi| 2 but that |
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[ec392464] | 76 | requires longer computation time. In order to set a data to a control panel |
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| 77 | (FitPage), see the "DataLoader Help". Once a data set to the FiPage, select a |
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| 78 | model from the combo box. The default parameters of the model will be display. |
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| 79 | Set initial parameters if need. Check and uncheck parameters to fit/fix. Click |
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| 80 | the *'Fit'* button. When the fitting is finished, the resultant parameter |
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| 81 | values will be displayed with the errors. If a error is missing, it generally |
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| 82 | means that the corresponding parameter is not very depending on the model. The |
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| 83 | chisq/Npt_fit and the plot associated with the fit operation will be also |
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| 84 | updated. |
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| 85 | |
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| 86 | .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ |
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| 87 | |
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| 88 | .. _Simultaneous_Fitting: |
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| 89 | |
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| 90 | Simultaneous Fitting |
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| 91 | -------------------- |
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| 92 | |
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| 93 | This fitting option enables to set a number of the constraints between the |
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| 94 | parameters of fitting(s). It requires one or more FitPages with a data and a |
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| 95 | model set for the fitting, and performs multiple fittings given by the |
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| 96 | FitPage(s). The Complex (ParkMC) FitEngine will be used automatically. |
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| 97 | |
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| 98 | Simultaneous Fit without Constraint |
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| 99 | |
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| 100 | Assuming some FitPages are already set up, check the checkboxes of the |
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| 101 | model_data rows to fit. And click the 'Fit' button. The results will return to |
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| 102 | each FitPages. |
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| 103 | |
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| 104 | Note that the chi2/Npts returned is the sum of the chi2/Npts of each fits. If |
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| 105 | one needs the chi2 value only for a page, click the 'Compute' button in the |
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| 106 | FitPage to recalculate. |
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| 107 | |
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| 108 | Simultaneous Fit with Constraint |
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| 109 | |
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| 110 | Enter constraint in the text control next to *constraint fit* button. |
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| 111 | Constraint should be of type model1 parameter name = f(model2 parameter name) |
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| 112 | for example, M0.radius=2*M1.radius. Many constraints can be entered for a |
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| 113 | single fit. Each of them should be separated by a newline charater or ";" |
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| 114 | The easy setup can generate many constraint inputs easily when the selected |
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| 115 | two models are the same type. |
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| 116 | |
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| 117 | Note that the chi2/Npts returned is the sum of the chi2/Npts of each fits. |
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| 118 | If one needs the chi2 value only for one fit, click the 'Compute' button in |
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| 119 | the FitPage to recalculate. |
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| 120 | |
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| 121 | .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ |
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| 122 | |
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| 123 | .. _Batch_Fitting: |
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| 124 | |
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| 125 | Batch Fitting |
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| 126 | ------------- |
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| 127 | |
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| 128 | Batch_Fit_ |
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| 129 | |
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| 130 | Batch_Window_ |
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| 131 | |
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| 132 | Edit_Grid_ |
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| 133 | |
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| 134 | Save_Grid_ |
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| 135 | |
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| 136 | Open_Batch_Results_ |
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| 137 | |
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| 138 | Plot_ |
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| 139 | |
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| 140 | View_Column_Cell_ |
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| 141 | |
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| 142 | .. _Batch_Fit: |
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| 143 | |
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| 144 | Batch Fit |
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| 145 | --------- |
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| 146 | |
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| 147 | Create a *Batch Page* by selecting the *Batch* radio button on the DataExplorer |
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| 148 | (see figure below) and for a new control page select 'New FitPage' in the |
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| 149 | Fitting menubar. |
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| 150 | |
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| 151 | .. image:: batch_button_area.bmp |
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| 152 | |
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| 153 | Figure 1: MenuBar: |
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| 154 | |
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| 155 | Load Data to the DataExplorer if not already loaded. |
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| 156 | |
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| 157 | Select one or more data sets by checking the check boxes, and then make sure |
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| 158 | that "Fitting" is selected in the dropdown menu next to the "Send To" button. |
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| 159 | Once ready, click the 'Send To' button to set data to a BatchPage. If already |
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| 160 | an empty batch page exists, it will be set there. Otherwise it will create a |
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| 161 | new Batch Page. Set up the model and the parameter values as same as a single |
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| 162 | fitting (see Single Fit help) <Single_Fit_>. Then use 'Fit' button to |
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| 163 | perform the fitting. |
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| 164 | |
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| 165 | Unlike a single fit, the results of the fittings will not return to the |
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| 166 | BatchPage'. Instead, a Grid window will be provided once the fitting is |
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| 167 | completed. The Grid window is also accessible from the 'View' menu |
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| 168 | (see Figure 2). |
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| 169 | |
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| 170 | Note that only one model is used for all the data. The initial parameter |
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| 171 | values given in the control page will be used all the data fittings. If one |
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| 172 | wants the FitEngine to use the initial values from the results of the |
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| 173 | previous data fitting (if any), choose the 'Chain Fitting' option in the |
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| 174 | Fitting menubar, which will speed up the fitting especially when you have |
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| 175 | lots of, and similar, data sets. |
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| 176 | |
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| 177 | .. _Batch_Window: |
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| 178 | |
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| 179 | Batch Window |
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| 180 | ------------ |
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| 181 | Batch Window provides an easy way to view the fit results, i.e., plot data, |
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| 182 | fits, and residuals. Batch window will be automatically shown after a batch |
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| 183 | fit is finished. |
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| 184 | |
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| 185 | Once closed, it can be opened anytime from the "View" menubar item (see |
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| 186 | Figure 2). |
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| 187 | |
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| 188 | .. image:: restore_batch_window.bmp |
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| 189 | |
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| 190 | Figure 2: Edit Menu: |
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| 191 | |
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| 192 | .. _Edit_Grid: |
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| 193 | |
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| 194 | Edit Grid |
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| 195 | --------- |
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| 196 | |
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| 197 | Once a batch fit is completed, all fitted and fixed model parameters are |
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| 198 | displayed to the current sheet of the batch window except the errors of the |
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| 199 | parameters. To view the errors, click on a given column then under *Edit* |
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| 200 | menubar item, and insert the desired parameter by selecting a menu item with |
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| 201 | the appropriated label. Empty column can be inserted in the same way. A |
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| 202 | column value can be customized by editing an existing empty column. |
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| 203 | |
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| 204 | To Remove column from the grid, select it, choose edit menu, and click the |
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| 205 | *'remove'* menu item. Any removed column should reinserted whenever needed. |
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| 206 | |
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| 207 | All above options are also available when right clicking on a given column |
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| 208 | label(see Figure 3). |
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| 209 | |
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| 210 | *Note:* A column always needs to be selected in order to remove or insert a |
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| 211 | column in the grid. |
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| 212 | |
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| 213 | .. image:: edit_menu.bmp |
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| 214 | |
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| 215 | Figure 3: Edit Menu: |
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| 216 | |
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| 217 | .. _Save_Grid: |
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| 218 | |
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| 219 | Save Grid |
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| 220 | --------- |
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| 221 | To save the current page on the batch window, select the *'File'* menubar |
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| 222 | item(see Figure 4), then choose the *'Save as'* menu item to save it as a |
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| 223 | .csv file. |
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| 224 | |
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| 225 | *Note:* The grid doesn't save the data array, fits, and the array residuals. |
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| 226 | As a result, the 'View (fit) Results' functionality will be lost when |
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| 227 | reloading the saved file. |
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| 228 | |
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| 229 | Warning! To ensure accuracy of saved fit results, it is recommended to save |
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| 230 | the current grid before modifying it . |
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| 231 | |
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| 232 | .. _Open_Batch_Results: |
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| 233 | |
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| 234 | Open Batch Results |
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| 235 | ------------------ |
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| 236 | |
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| 237 | Any *csv* file can be opened in the grid by selecting the *'Open'* under |
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| 238 | the *'File'* menu in the Grid Window(see Figure 4). All columns in the file |
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| 239 | will be displayed but insertion will not available. Insertion will be |
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| 240 | available only when at least one column will be removed from the grid. |
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| 241 | |
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| 242 | .. image:: file_menu.bmp |
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| 243 | |
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| 244 | Figure 4: MenuBar: |
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| 245 | |
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| 246 | .. _Plot: |
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| 247 | |
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| 248 | Plot |
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| 249 | ---- |
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| 250 | |
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| 251 | To *plot* a column versus another, select one column at the time, click the |
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| 252 | *'Add'* button next to the text control of X/Y -axis *Selection Range* to |
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| 253 | plot the value of this column on the X/Y axis. Alternatively, all available |
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| 254 | range can be selected by clicking the column letter (eg. B). Repeat the same |
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| 255 | procedure the next axis. Finally, click the *'Plot'* button. When clicking |
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| 256 | on *Add* button, the grid will automatically fill the axis label, but |
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| 257 | different labels and units can be entered in the correct controls before |
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| 258 | clicking on the plot button. |
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| 259 | |
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| 260 | *X/Y -Axis Selection Range* can be edited manually. These text controls |
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| 261 | allow the following types of expression (operation can be + - * /, or pow) |
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| 262 | |
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| 263 | 1) if the current axis label range is a function of 1 or more columns, write |
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| 264 | this type of expression |
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| 265 | |
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| 266 | constant1 * column_name1 [minimum row index : maximum row index] operator |
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| 267 | constant2 * column_name2 [minimum row index : maximum row index] |
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| 268 | |
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| 269 | Example: radius [2 : 5] -3 * scale [2 : 5] |
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| 270 | |
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| 271 | 2) if only some values of a given column are need but the range between the |
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| 272 | first row and the last row used is not continuous, write the following |
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| 273 | expression in the text control |
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| 274 | |
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| 275 | column_name1 [minimum row index1 : maximum row index1] , column_name1 |
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| 276 | [minimum row index2 : maximum row index2] |
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| 277 | |
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| 278 | Example : radius [2 : 5] , radius [10 : 25] |
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| 279 | |
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| 280 | Note: Both text controls ( X and Y-axis Selection Ranges) need to be filled |
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| 281 | with valid entries for plotting to work. The dY-bar is optional (see Figure 5). |
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| 282 | |
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| 283 | .. image:: plot_button.bmp |
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| 284 | |
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| 285 | Figure 5: Plotting |
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| 286 | |
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| 287 | .. _View_Column_Cell: |
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| 288 | |
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| 289 | View Column/Cell(s) |
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| 290 | ------------------- |
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| 291 | |
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| 292 | Select 1 or more cells from the same column, click the 'View Fits' button to |
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| 293 | display available curves. |
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| 294 | |
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| 295 | For example, select the cells of the 'Chi2' column, then click the 'View Fits' |
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| 296 | button. The plots generates will represent the residuals plots. |
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| 297 | |
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| 298 | If you select any cells of the 'Data' column and click the 'View Fits' button. |
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| 299 | It generates both data and fits in the graph (see Figure 6). |
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| 300 | |
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| 301 | Alternatively, just click the column letter (eg. B) to choose all the |
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| 302 | available data sets, then simply click the 'View Fits' button to plot the |
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| 303 | data and fits. |
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| 304 | |
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| 305 | .. image:: view_button.bmp |
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| 306 | |
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| 307 | Figure 6: View Fits |
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| 308 | |
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| 309 | .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ |
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| 310 | |
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| 311 | .. _Model_Selection: |
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| 312 | |
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| 313 | Model_Type_ |
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| 314 | |
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| 315 | Change_Model_Parameters_ |
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| 316 | |
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| 317 | Write_your_Own_Model_ |
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| 318 | |
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| 319 | .. _Model_Type: |
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| 320 | |
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| 321 | Model Type |
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| 322 | ---------- |
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| 323 | |
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| 324 | Models are grouped into three classes |
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| 325 | |
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| 326 | * *Shapes* |
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| 327 | * *Shape-Independent* |
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| 328 | * *Uncategorised* |
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| 329 | * *Customized Models* |
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| 330 | * *Structure Factor* |
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| 331 | |
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| 332 | .. _Change_Model_Parameters: |
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| 333 | |
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| 334 | Change Model Parameters |
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| 335 | ----------------------- |
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| 336 | |
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| 337 | To visualize model in a different window, from menu click on *Model*. Select |
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| 338 | a type of model and then the name of your model.A new window will appear with |
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| 339 | the plot of your model with default values. Change model's parameters on |
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| 340 | *model view* tab and view the plotted model with its new parameters. |
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| 341 | |
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| 342 | .. _Write_your_Own_Model: |
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| 343 | |
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| 344 | Write your Own Model |
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| 345 | -------------------- |
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| 346 | |
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| 347 | The custom model editors are provided from 'Fitting' menu in the menu bar. |
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| 348 | See 'Custom model editor' in the side menu on left. Advanced users can write |
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| 349 | your own model and save it (in .py format) into *plugin_models* directory in |
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| 350 | .sasview of your home directory (eg., username\.sasview>\plugin_models). Your |
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| 351 | plugin model will be added into "<>Customized Models" on the next model |
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| 352 | selection. |
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| 353 | |
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| 354 | .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ |
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| 355 | |
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| 356 | .. _Model_Category_Manager: |
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| 357 | |
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| 358 | Model Category Manager |
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| 359 | ---------------------- |
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| 360 | |
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| 361 | Our SAS models are, by default, classified into 5 categories; shapes, |
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| 362 | shape-independent, structure factor, and customized models, where these |
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| 363 | categories (except the customized models) can be reassigned, added, and |
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| 364 | removed using 'Category Manager'. Each models can also be enabled(shown)/ |
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| 365 | disabled(hidden) from the category that they belong. The Category Manager |
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| 366 | panel is accessible from the model category 'Modify' button in the fitting |
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| 367 | panel or the 'View/Category Manager' menu in the menu bar (Fig. 1). |
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| 368 | |
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| 369 | 1) Enable/Disable models: Check/uncheck the check boxes to enable/disable the |
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| 370 | models (Fig. 2). |
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| 371 | |
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| 372 | 2) Change category: Highlight a model in the list by left-clicking and click |
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| 373 | the 'Modify' button. In the 'Change Category' panel, one can create/use a |
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| 374 | category for the model, then click the 'Add' button. In order to delete a |
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| 375 | category, select a category name and click the 'Remove Selected' button |
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| 376 | (Fig. 3). |
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| 377 | |
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| 378 | 3) To apply the changes made, hit the OK button. Otherwise, click the 'Cancel' |
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| 379 | button (Fig. 2). |
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| 380 | |
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| 381 | .. image:: cat_fig0.bmp |
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| 382 | |
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| 383 | Fig.1 |
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| 384 | |
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| 385 | .. image:: cat_fig1.bmp |
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| 386 | |
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| 387 | Fig.2 |
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| 388 | |
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| 389 | .. image:: cat_fig2.bmp |
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| 390 | |
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| 391 | Fig.3 |
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| 392 | |
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| 393 | .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ |
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| 394 | |
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| 395 | .. _Model_Functions: |
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| 396 | |
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| 397 | Model Functions |
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| 398 | --------------- |
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| 399 | |
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| 400 | Model Documentation <models/model_functions> |
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| 401 | |
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| 402 | .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ |
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| 403 | |
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| 404 | .. _Custom_Model_Editor: |
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| 405 | |
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| 406 | Custom Model Editor |
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| 407 | ------------------- |
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| 408 | |
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| 409 | Description_ |
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| 410 | |
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| 411 | New_ |
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| 412 | |
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| 413 | Sum_Multi_p1_p2_ |
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| 414 | |
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| 415 | Advanced_ |
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| 416 | |
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| 417 | Delete_ |
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| 418 | |
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| 419 | .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ |
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| 420 | |
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| 421 | .. _Description: |
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| 422 | |
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| 423 | Description |
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| 424 | ----------- |
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| 425 | |
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| 426 | This menu (Fitting/Edit Custom Model in the menu bar) interface is to provide |
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| 427 | you an easy way to write your own custom models. The changes in a model |
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| 428 | function are effective after it is re-selected from the combo-box menu. |
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| 429 | |
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| 430 | .. image:: edit_model_menu.bmp |
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| 431 | |
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| 432 | .. _New: |
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| 433 | |
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| 434 | New |
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| 435 | --- |
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| 436 | |
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| 437 | This option is used to make a new model. A model code generated by this option |
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| 438 | can be viewed and further modified by the 'Advanced' option below. |
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| 439 | |
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| 440 | .. image:: new_model.bmp |
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| 441 | |
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| 442 | .. _Sum_Multi_p1_p2: |
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| 443 | |
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| 444 | Sum|Multi(p1,p2) |
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| 445 | ---------------- |
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| 446 | |
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| 447 | This option create a new sum (or multiplication) model. Fill up the (sum |
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| 448 | model function) name and the description. The description will show up on |
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| 449 | details button in the application. Then select the p1 or p2 model for the |
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| 450 | sum/multi model, select an operator as necessary and click the Apply button |
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| 451 | for activation. Hit the 'Close' button when it's done. |
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| 452 | |
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| 453 | .. image:: sum_model.bmp |
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| 454 | |
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| 455 | .. _Advanced: |
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| 456 | |
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| 457 | Advanced |
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| 458 | -------- |
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| 459 | |
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| 460 | The menu option shows all the files in the plugin_models folder. You can edit, |
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| 461 | modify, and save it. It is recommended to modify only the lines with arrow |
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| 462 | (-------). In the end of edit, 'Compile' and 'Run' from the menu bar to |
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| 463 | activate or to see the model working properly. |
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| 464 | |
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| 465 | .. _Delete: |
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| 466 | |
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| 467 | Delete |
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| 468 | ------ |
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| 469 | |
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| 470 | The menu option is to delete the custom models. Just select the file name to |
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| 471 | delete. |
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| 472 | |
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| 473 | .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ |
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| 474 | |
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| 475 | .. _Polydispersity_Distributions: |
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| 476 | |
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| 477 | Polydispersity Distributions |
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| 478 | ---------------------------- |
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| 479 | |
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| 480 | Calculates the form factor for a polydisperse and/or angular population of |
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| 481 | particles with uniform scattering length density. The resultant form factor |
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| 482 | is normalized by the average particle volume such that |
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| 483 | |
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| 484 | P(q) = scale*\<F*F\>/Vol + bkg |
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| 485 | |
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| 486 | where F is the scattering amplitude and the\<\>denote an average over the size |
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| 487 | distribution. Users should use PD (polydispersity: this definition is |
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| 488 | different from the typical definition in polymer science) for a size |
---|
| 489 | distribution and Sigma for an angular distribution (see below). |
---|
| 490 | |
---|
| 491 | Note that this computation is very time intensive thus applying polydispersion/ |
---|
| 492 | angular distrubtion for more than one paramters or increasing Npts values |
---|
| 493 | might need extensive patience to complete the computation. Also note that |
---|
| 494 | even though it is time consuming, it is safer to have larger values of Npts |
---|
| 495 | and Nsigmas. |
---|
| 496 | |
---|
| 497 | The following five distribution functions are provided |
---|
| 498 | |
---|
| 499 | * *Rectangular_Distribution_* |
---|
| 500 | * *Array_Distribution_* |
---|
| 501 | * *Gaussian_Distribution_* |
---|
| 502 | * *Lognormal_Distribution_* |
---|
| 503 | * *Schulz_Distribution_* |
---|
| 504 | |
---|
| 505 | .. _Rectangular_Distribution: |
---|
| 506 | |
---|
| 507 | Rectangular Distribution |
---|
| 508 | ------------------------ |
---|
| 509 | |
---|
| 510 | .. image:: pd_image001.png |
---|
| 511 | |
---|
| 512 | The xmean is the mean of the distribution, w is the half-width, and Norm is a |
---|
| 513 | normalization factor which is determined during the numerical calculation. |
---|
| 514 | Note that the Sigma and the half width *w* are different. |
---|
| 515 | |
---|
| 516 | The standard deviation is |
---|
| 517 | |
---|
| 518 | .. image:: pd_image002.png |
---|
| 519 | |
---|
| 520 | The PD (polydispersity) is |
---|
| 521 | |
---|
| 522 | .. image:: pd_image003.png |
---|
| 523 | |
---|
| 524 | .. image:: pd_image004.jpg |
---|
| 525 | |
---|
| 526 | .. _Array_Distribution: |
---|
| 527 | |
---|
| 528 | Array Distribution |
---|
| 529 | ------------------ |
---|
| 530 | |
---|
| 531 | This distribution is to be given by users as a txt file where the array |
---|
| 532 | should be defined by two columns in the order of x and f(x) values. The f(x) |
---|
| 533 | will be normalized by SasView during the computation. |
---|
| 534 | |
---|
| 535 | Example of an array in the file |
---|
| 536 | |
---|
| 537 | 30 0.1 |
---|
| 538 | 32 0.3 |
---|
| 539 | 35 0.4 |
---|
| 540 | 36 0.5 |
---|
| 541 | 37 0.6 |
---|
| 542 | 39 0.7 |
---|
| 543 | 41 0.9 |
---|
| 544 | |
---|
| 545 | We use only these array values in the computation, therefore the mean value |
---|
[98b30b4] | 546 | given in the control panel, for example ââ¬Ëradius = 60ââ¬â¢, will be ignored. |
---|
[ec392464] | 547 | |
---|
| 548 | .. _Gaussian_Distribution: |
---|
| 549 | |
---|
| 550 | Gaussian Distribution |
---|
| 551 | --------------------- |
---|
| 552 | |
---|
| 553 | .. image:: pd_image005.png |
---|
| 554 | |
---|
| 555 | The xmean is the mean of the distribution and Norm is a normalization factor |
---|
| 556 | which is determined during the numerical calculation. |
---|
| 557 | |
---|
| 558 | The PD (polydispersity) is |
---|
| 559 | |
---|
| 560 | .. image:: pd_image003.png |
---|
| 561 | |
---|
| 562 | .. image:: pd_image006.jpg |
---|
| 563 | |
---|
| 564 | .. _Lognormal_Distribution: |
---|
| 565 | |
---|
| 566 | Lognormal Distribution |
---|
| 567 | ---------------------- |
---|
| 568 | |
---|
| 569 | .. image:: pd_image007.png |
---|
| 570 | |
---|
| 571 | The /mu/=ln(xmed), xmed is the median value of the distribution, and Norm is a |
---|
| 572 | normalization factor which will be determined during the numerical calculation. |
---|
| 573 | The median value is the value given in the size parameter in the control panel, |
---|
[98b30b4] | 574 | for example, ââ¬Åradius = 60ââ¬ï¿œ. |
---|
[ec392464] | 575 | |
---|
| 576 | The PD (polydispersity) is given by /sigma/ |
---|
| 577 | |
---|
| 578 | .. image:: pd_image008.png |
---|
| 579 | |
---|
| 580 | For the angular distribution |
---|
| 581 | |
---|
| 582 | .. image:: pd_image009.png |
---|
| 583 | |
---|
| 584 | The mean value is given by xmean=exp(/mu/+p2/2). The peak value is given by |
---|
| 585 | xpeak=exp(/mu/-p2). |
---|
| 586 | |
---|
| 587 | .. image:: pd_image010.jpg |
---|
| 588 | |
---|
| 589 | This distribution function spreads more and the peak shifts to the left as the |
---|
| 590 | p increases, requiring higher values of Nsigmas and Npts. |
---|
| 591 | |
---|
| 592 | .. _Schulz_Distribution: |
---|
| 593 | |
---|
| 594 | Schulz Distribution |
---|
| 595 | ------------------- |
---|
| 596 | |
---|
| 597 | .. image:: pd_image011.png |
---|
| 598 | |
---|
| 599 | The xmean is the mean of the distribution and Norm is a normalization factor |
---|
| 600 | which is determined during the numerical calculation. |
---|
| 601 | |
---|
[98b30b4] | 602 | The z = 1/p2ââ¬â 1. |
---|
[ec392464] | 603 | |
---|
| 604 | The PD (polydispersity) is |
---|
| 605 | |
---|
| 606 | .. image:: pd_image012.png |
---|
| 607 | |
---|
| 608 | Note that the higher PD (polydispersity) might need higher values of Npts and |
---|
| 609 | Nsigmas. For example, at PD = 0.7 and radisus = 60 A, Npts >= 160, and |
---|
| 610 | Nsigmas >= 15 at least. |
---|
| 611 | |
---|
| 612 | .. image:: pd_image013.jpg |
---|
| 613 | |
---|
| 614 | .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ |
---|
| 615 | |
---|
| 616 | .. _Smearing_Computation: |
---|
| 617 | |
---|
| 618 | Smearing Computation |
---|
| 619 | -------------------- |
---|
| 620 | |
---|
| 621 | Slit_Smearing_ |
---|
| 622 | |
---|
| 623 | Pinhole_Smearing_ |
---|
| 624 | |
---|
| 625 | 2D_Smearing_ |
---|
| 626 | |
---|
| 627 | .. _Slit_Smearing: |
---|
| 628 | |
---|
| 629 | Slit Smearing |
---|
| 630 | ------------- |
---|
| 631 | |
---|
| 632 | The sit smeared scattering intensity for SAS is defined by |
---|
| 633 | |
---|
| 634 | .. image:: sm_image002.gif |
---|
| 635 | |
---|
| 636 | where Norm = |
---|
| 637 | |
---|
| 638 | .. image:: sm_image003.gif |
---|
| 639 | |
---|
| 640 | Equation 1 |
---|
| 641 | |
---|
[98b30b4] | 642 | The functions |inlineimage004| and |inlineimage005| |
---|
[ec392464] | 643 | refer to the slit width weighting function and the slit height weighting |
---|
| 644 | determined at the q point, respectively. Here, we assumes that the weighting |
---|
| 645 | function is described by a rectangular function, i.e., |
---|
| 646 | |
---|
| 647 | .. image:: sm_image006.gif |
---|
| 648 | |
---|
| 649 | Equation 2 |
---|
| 650 | |
---|
| 651 | and |
---|
| 652 | |
---|
| 653 | .. image:: sm_image007.gif |
---|
| 654 | |
---|
| 655 | Equation 3 |
---|
| 656 | |
---|
[98b30b4] | 657 | so that |inlineimage008| |inlineimage009| for |inlineimage010| and u. |
---|
[ec392464] | 658 | |
---|
[98b30b4] | 659 | The |inlineimage011| and |inlineimage012| stand for |
---|
[ec392464] | 660 | the slit height (FWHM/2) and the slit width (FWHM/2) in the q space. Now the |
---|
| 661 | integral of Equation 1 is simplified to |
---|
| 662 | |
---|
| 663 | .. image:: sm_image013.gif |
---|
| 664 | |
---|
| 665 | Equation 4 |
---|
| 666 | |
---|
| 667 | Numerical Implementation of Equation 4 |
---|
| 668 | -------------------------------------- |
---|
| 669 | |
---|
| 670 | Case 1 |
---|
| 671 | ------ |
---|
| 672 | |
---|
[98b30b4] | 673 | For |inlineimage012| = 0 and |inlineimage011| = constant. |
---|
[ec392464] | 674 | |
---|
| 675 | .. image:: sm_image016.gif |
---|
| 676 | |
---|
| 677 | For discrete q values, at the q values from the data points and at the q |
---|
[98b30b4] | 678 | values extended up to qN= qi + |inlineimage011| the smeared |
---|
[ec392464] | 679 | intensity can be calculated approximately |
---|
| 680 | |
---|
| 681 | .. image:: sm_image017.gif |
---|
| 682 | |
---|
| 683 | Equation 5 |
---|
| 684 | |
---|
[98b30b4] | 685 | |inlineimage018| = 0 for *Is* in *j* < *i* or *j* > N-1*. |
---|
[ec392464] | 686 | |
---|
| 687 | Case 2 |
---|
| 688 | ------ |
---|
| 689 | |
---|
[98b30b4] | 690 | For |inlineimage012| = constant and |inlineimage011| = 0. |
---|
[ec392464] | 691 | |
---|
| 692 | Similarly to Case 1, we get |
---|
| 693 | |
---|
[98b30b4] | 694 | |inlineimage019| for qp= qi- |inlineimage012| and qN= qi+ |inlineimage012|. |inlineimage018| = 0 |
---|
[ec392464] | 695 | for *Is* in *j* < *p* or *j* > *N-1*. |
---|
| 696 | |
---|
| 697 | Case 3 |
---|
| 698 | ------ |
---|
| 699 | |
---|
[98b30b4] | 700 | For |inlineimage011| = constant and |
---|
| 701 | |inlineimage011| = constant. |
---|
[ec392464] | 702 | |
---|
| 703 | In this case, the best way is to perform the integration, Equation 1, |
---|
| 704 | numerically for both slit height and width. However, the numerical integration |
---|
| 705 | is not correct enough unless given a large number of iteration, say at least |
---|
| 706 | 10000 by 10000 for each element of the matrix, W, which will take minutes and |
---|
| 707 | minutes to finish the calculation for a set of typical SAS data. An |
---|
| 708 | alternative way which is correct for slit width << slit hight, is used in |
---|
| 709 | SasView. This method is a mixed method that combines method 1 with the |
---|
| 710 | numerical integration for the slit width. |
---|
| 711 | |
---|
| 712 | .. image:: sm_image020.gif |
---|
| 713 | |
---|
| 714 | Equation 7 |
---|
| 715 | |
---|
[98b30b4] | 716 | for qp= qi- |inlineimage012| and |
---|
| 717 | qN= qi+ |inlineimage012|. |inlineimage018| = 0 for |
---|
[ec392464] | 718 | *Is* in *j* < *p* or *j* > *N-1*. |
---|
| 719 | |
---|
| 720 | .. _Pinhole_Smearing: |
---|
| 721 | |
---|
| 722 | Pinhole Smearing |
---|
| 723 | ---------------- |
---|
| 724 | |
---|
| 725 | The pinhole smearing computation is done similar to the case above except |
---|
| 726 | that the weight function used is the Gaussian function, so that the Equation 6 |
---|
| 727 | for this case becomes |
---|
| 728 | |
---|
| 729 | .. image:: sm_image021.gif |
---|
| 730 | |
---|
| 731 | Equation 8 |
---|
| 732 | |
---|
| 733 | For all the cases above, the weighting matrix *W* is calculated when the |
---|
| 734 | smearing is called at the first time, and it includes the ~ 60 q values |
---|
| 735 | (finely binned evenly) below (\>0) and above the q range of data in order |
---|
| 736 | to cover all data points of the smearing computation for a given model and |
---|
| 737 | for a given slit size. The *Norm* factor is found numerically with the |
---|
| 738 | weighting matrix, and considered on *Is* computation. |
---|
| 739 | |
---|
| 740 | .. _2D_Smearing: |
---|
| 741 | |
---|
| 742 | 2D Smearing |
---|
| 743 | ----------- |
---|
| 744 | |
---|
| 745 | The 2D smearing computation is done similar to the 1D pinhole smearing above |
---|
| 746 | except that the weight function used was the 2D elliptical Gaussian function |
---|
| 747 | |
---|
| 748 | .. image:: sm_image022.gif |
---|
| 749 | |
---|
| 750 | Equation 9 |
---|
| 751 | |
---|
| 752 | In Equation 9, x0 = qcos/theta/ and y0 = qsin/theta/, and the primed axes |
---|
| 753 | are in the coordinate rotated by an angle /theta/ around the z-axis (below) |
---|
[98b30b4] | 754 | so that xââ¬â¢0= x0cos/theta/+y0sin/theta/ and yââ¬â¢0= -x0sin/theta/+y0cos/theta/. |
---|
[ec392464] | 755 | |
---|
| 756 | Note that the rotation angle is zero for x-y symmetric elliptical Gaussian |
---|
| 757 | distribution. The A is a normalization factor. |
---|
| 758 | |
---|
| 759 | .. image:: sm_image023.gif |
---|
| 760 | |
---|
| 761 | Now we consider a numerical integration where each bins in /theta/ and R are |
---|
| 762 | *evenly* (this is to simplify the equation below) distributed by /delta//theta/ |
---|
[98b30b4] | 763 | and /delta/R, respectively, and it is assumed that I(xââ¬â¢, yââ¬â¢) is constant |
---|
[ec392464] | 764 | within the bins which in turn becomes |
---|
| 765 | |
---|
| 766 | .. image:: sm_image024.gif |
---|
| 767 | |
---|
| 768 | Equation 10 |
---|
| 769 | |
---|
| 770 | Since we have found the weighting factor on each bin points, it is convenient |
---|
[98b30b4] | 771 | to transform xââ¬â¢-yââ¬â¢ back to x-y coordinate (rotating it by -/theta/ around z |
---|
[ec392464] | 772 | axis). Then, for the polar symmetric smear |
---|
| 773 | |
---|
| 774 | .. image:: sm_image025.gif |
---|
| 775 | |
---|
| 776 | Equation 11 |
---|
| 777 | |
---|
| 778 | where |
---|
| 779 | |
---|
| 780 | .. image:: sm_image026.gif |
---|
| 781 | |
---|
| 782 | while for the x-y symmetric smear |
---|
| 783 | |
---|
| 784 | .. image:: sm_image027.gif |
---|
| 785 | |
---|
| 786 | Equation 12 |
---|
| 787 | |
---|
| 788 | where |
---|
| 789 | |
---|
| 790 | .. image:: sm_image028.gif |
---|
| 791 | |
---|
| 792 | Here, the current version of the SasView uses Equation 11 for 2D smearing |
---|
| 793 | assuming that all the Gaussian weighting functions are aligned in the polar |
---|
| 794 | coordinate. |
---|
| 795 | |
---|
| 796 | In the control panel, the higher accuracy indicates more and finer binnng |
---|
| 797 | points so that it costs more in time. |
---|
| 798 | |
---|
| 799 | .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ |
---|
| 800 | |
---|
| 801 | .. _Polarisation_Magnetic_Scattering: |
---|
| 802 | |
---|
| 803 | Polarisation/Magnetic Scattering |
---|
| 804 | -------------------------------- |
---|
| 805 | |
---|
| 806 | Magnetic scattering is implemented in five (2D) models |
---|
| 807 | |
---|
| 808 | * *SphereModel* |
---|
| 809 | * *CoreShellModel* |
---|
| 810 | * *CoreMultiShellModel* |
---|
| 811 | * *CylinderModel* |
---|
| 812 | * *ParallelepipedModel* |
---|
| 813 | |
---|
| 814 | In general, the scattering length density (SLD) in each regions where the |
---|
| 815 | SLD (=/beta/) is uniform, is a combination of the nuclear and magnetic SLDs and |
---|
| 816 | depends on the spin states of the neutrons as follows. For magnetic scattering, |
---|
| 817 | only the magnetization component, *M*perp, perpendicular to the scattering |
---|
| 818 | vector *Q* contributes to the the magnetic scattering length. |
---|
| 819 | |
---|
| 820 | .. image:: mag_vector.bmp |
---|
| 821 | |
---|
| 822 | The magnetic scattering length density is then |
---|
| 823 | |
---|
| 824 | .. image:: dm_eq.gif |
---|
| 825 | |
---|
| 826 | where /gamma/ = -1.913 the gyromagnetic ratio, /mu/B is the Bohr magneton, r0 |
---|
| 827 | is the classical radius of electron, and */sigma/* is the Pauli spin. For |
---|
| 828 | polarised neutron, the magnetic scattering is depending on the spin states. |
---|
| 829 | |
---|
| 830 | Let's consider that the incident neutrons are polarized parallel (+)/ |
---|
| 831 | anti-parallel (-) to the x' axis (See both Figures above). The possible |
---|
| 832 | out-coming states then are + and - states for both incident states |
---|
| 833 | |
---|
| 834 | Non-spin flips: (+ +) and (- -) |
---|
| 835 | Spin flips: (+ -) and (- +) |
---|
| 836 | |
---|
| 837 | .. image:: M_angles_pic.bmp |
---|
| 838 | |
---|
| 839 | Now, let's assume that the angles of the *Q* vector and the spin-axis (x') |
---|
| 840 | against x-axis are /phi/ and /theta/up, respectively (See Figure above). Then, |
---|
| 841 | depending upon the polarisation (spin) state of neutrons, the scattering length |
---|
| 842 | densities, including the nuclear scattering length density (/beta/N) are given |
---|
| 843 | as, for non-spin-flips |
---|
| 844 | |
---|
| 845 | .. image:: sld1.gif |
---|
| 846 | |
---|
| 847 | for spin-flips |
---|
| 848 | |
---|
| 849 | .. image:: sld2.gif |
---|
| 850 | |
---|
| 851 | where |
---|
| 852 | |
---|
| 853 | .. image:: mxp.gif |
---|
| 854 | |
---|
| 855 | .. image:: myp.gif |
---|
| 856 | |
---|
| 857 | .. image:: mzp.gif |
---|
| 858 | |
---|
| 859 | .. image:: mqx.gif |
---|
| 860 | |
---|
| 861 | .. image:: mqy.gif |
---|
| 862 | |
---|
| 863 | Here, the M0x, M0y and M0z are the x, y and z components of the magnetization |
---|
| 864 | vector given in the xyz lab frame. The angles of the magnetization, /theta/M |
---|
| 865 | and /phi/M as defined in the Figure (above) |
---|
| 866 | |
---|
| 867 | .. image:: m0x_eq.gif |
---|
| 868 | |
---|
| 869 | .. image:: m0y_eq.gif |
---|
| 870 | |
---|
| 871 | .. image:: m0z_eq.gif |
---|
| 872 | |
---|
| 873 | The user input parameters are M0_sld = DMM0, Up_theta = /theta/up, |
---|
| 874 | M_theta = /theta/M, and M_phi = /phi/M. The 'Up_frac_i' and 'Up_frac_f' are |
---|
| 875 | the ratio |
---|
| 876 | |
---|
| 877 | (spin up)/(spin up + spin down) |
---|
| 878 | |
---|
| 879 | neutrons before the sample and at the analyzer, respectively. |
---|
| 880 | |
---|
| 881 | *Note:* The values of the 'Up_frac_i' and 'Up_frac_f' must be in the range |
---|
| 882 | between 0 and 1. |
---|
| 883 | |
---|
| 884 | .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ |
---|
| 885 | |
---|
| 886 | .. _Key_Combinations: |
---|
| 887 | |
---|
| 888 | Key Combinations |
---|
| 889 | ---------------- |
---|
| 890 | |
---|
| 891 | Copy_Paste_ |
---|
| 892 | |
---|
| 893 | Bookmark_ |
---|
| 894 | |
---|
| 895 | Graph_Context_Menu_ |
---|
| 896 | |
---|
| 897 | FTolerance_ |
---|
| 898 | |
---|
| 899 | .. _Copy_Paste: |
---|
| 900 | |
---|
| 901 | Copy & Paste |
---|
| 902 | ------------ |
---|
| 903 | |
---|
| 904 | To copy the parameter values in a Fit(Model) panel to the clipboard: |
---|
| 905 | |
---|
| 906 | *Ctrl(Cmd on MAC) + Left(Mouse)Click* on the panel. |
---|
| 907 | |
---|
| 908 | To paste the parameter values to a Fit(Model)panel from the clipboard: |
---|
| 909 | |
---|
| 910 | *Ctrl(Cmd on MAC) + Shift + Left(Mouse)Click* on the panel. |
---|
| 911 | |
---|
| 912 | If this operation is successful, it will say so in the info line at the |
---|
| 913 | bottom of the SasView window. |
---|
| 914 | |
---|
| 915 | .. _Bookmark: |
---|
| 916 | |
---|
| 917 | Bookmark |
---|
| 918 | -------- |
---|
| 919 | |
---|
| 920 | Bookmark of a fit-panel or model-panel status: |
---|
| 921 | |
---|
| 922 | *(Mouse)Right-Click* and select the bookmark in the popup list. |
---|
| 923 | |
---|
| 924 | .. _Graph_Context_Menu: |
---|
| 925 | |
---|
| 926 | Graph Context Menu |
---|
| 927 | ------------------ |
---|
| 928 | |
---|
| 929 | To get the graph context menu to print, copy, save data, (2D)average, etc.: |
---|
| 930 | |
---|
| 931 | *Locate the mouse point on the plot to highlight and *(Mouse) Right Click* |
---|
| 932 | to bring up the full menu. |
---|
| 933 | |
---|
| 934 | .. _FTolerance: |
---|
| 935 | |
---|
| 936 | FTolerance (SciPy) |
---|
| 937 | ------------------ |
---|
| 938 | |
---|
| 939 | To change the ftol value of the Scipy FitEngine (leastsq): |
---|
| 940 | |
---|
| 941 | First, make sure that the Fit panel has data and a model selected. |
---|
| 942 | |
---|
| 943 | *Ctrl(Cmd on MAC) + Shift + Alt + Right(Mouse)Click* on the panel. |
---|
| 944 | |
---|
| 945 | Then, set up the value in the dialog panel. |
---|
| 946 | |
---|
| 947 | If this operation is successful, the new ftol value will be displayed in the |
---|
| 948 | info line at the bottom of the SV window.Note that increasing the ftol value |
---|
[98b30b4] | 949 | may cause for the fitting to terminate with higher |chi| sq. |
---|
[ec392464] | 950 | |
---|
| 951 | .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ |
---|
| 952 | |
---|
| 953 | .. _Status_Bar_Help: |
---|
| 954 | |
---|
| 955 | Status Bar Help |
---|
| 956 | --------------- |
---|
| 957 | |
---|
| 958 | Message_Warning_Hint_ |
---|
| 959 | |
---|
| 960 | Console_ |
---|
| 961 | |
---|
| 962 | .. _Message_Warning_Hint: |
---|
| 963 | |
---|
| 964 | Message/Warning/Hint |
---|
| 965 | -------------------- |
---|
| 966 | |
---|
| 967 | The status bar located at the bottom of the application frame, displays |
---|
| 968 | messages, hints, warnings and errors. |
---|
| 969 | |
---|
| 970 | .. _Console: |
---|
| 971 | |
---|
| 972 | Console |
---|
| 973 | ------- |
---|
| 974 | |
---|
| 975 | Select *light bulb/info icon* button in the status bar at the bottom of the |
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| 976 | application window to display available history. During a long task, the |
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| 977 | console can also help users to understand the status in progressing. |
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