MagicPlot Manual

Plotting and nonlinear fitting software

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new [Sun Nov 8 12:21:24 2015] (current)
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-  * in [[image_preview]]+  * In [[joining]] - new topic from [[fitting]]
  
-Upload new screenshot+  * In [[cloning]] new topic
  
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-  * in [[table from curves]] 
  
-Upload new screenshot of Table from curves +  In [[fitting]]
----- +    * about changing curves order by dragging 
-  in [[fitting]]+    * about adjusting parameters with mouse wheel 
 +    * fit has not converged, suspicious curve
  
-Extract 'Specifying Custom Fit Curve (Fit Formula) (Pro edition only)' 
-Create subsection 'Nonlinear Curve Fitting' in contents 
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-====== Coping Fit Curves between Fit Plots ====== 
-You can copy and paste Fit Curves as usual. Use context menu in curves table or press ''Ctrl+C'', ''Ctrl+V'' on PC and ''Cmd C'', ''Cmd V'' on Mac. When you paste Fit Curves parameters values and style are copied. 
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-  * in [[guess peaks]] 
-====== Guess Peaks (Pro only) ====== 
-MagicPlot can approximately locate peaks in spectrum. To locate peaks click on ''Guess'' button in ''Fit Curves'' tab of Fit Plot. Peak guessing is performed by looking for local minimums of second derivative of data-baseline. 
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-While ''Guess Peaks'' window is open you can see the preview of guessed peaks on Fit Plot. This preview is updated every time you change the parameters in the window. 
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-{{:guess-peaks-dialog.png|Guess peaks dialog}} 
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-===== Smoothing of Data and 2nd Derivative ===== 
-Smoothing is used in order to filter narrow peaks which can be guessed from noise. MagicPlot peak guess tool is capable of smoothing both data and second derivative before finding local minimums. Smoothing is used only to find peaks and does not affect the data on Fit Plot. 
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-[[wp>Savitzky–Golay_smoothing_filter|Savitzky–Golay method]] is used for smoothing. This algorithm performs a local polynomial regression of specified degree on specified number of points. The more points, the stronger is smoothing. 
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-===== The Number of Peaks ===== 
-MagicPlot sorts found peaks by amplitude and suggests only a specified number of greatest peaks. You can change the number of guessed peaks with slider or by entering value in the text field with spinner. 
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-  * in [[spline]] 
-====== Using Spline for Baseline Subtraction (Pro only) ====== 
-You can use cubic spline to fit and subtract baseline on Fit Plot. To create spline curve click on ''Add'' button in ''Fit Curves'' tab of Fit Plot.  
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-Don't use splines to subtract baselines which can be fit well enough with line curve (line or constant baseline). You can subtract wide peaks by mistake using spline. 
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-===== Editing Spline ===== 
-Created spline has 3 anchor points by default. You can move, add and remove anchor points: 
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-  * Move anchor point with mouse 
-  * Double click on spline curve to add new anchor point 
-  * Double click on anchor point to remove it 
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-{{:spline1.png|Using spline for baseline fitting}} 
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-===== Fitting with Spline ===== 
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-Spline anchor point (//x//, //y//) coordinates are treated as fit parameters so you can perform fitting with spline. Note that the anchor point coordinates will be varied but the number of point will remain. You also can lock some parameters (usually //x// coordinates) by setting ''Lock'' check boxes in parameters table.  
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-It is recommended to set appropriate fit intervals which contain only baseline without peaks. In such case ''Fit One Curve'' button is more acceptable than ''Fit by Sum'' button, because the individual interval for current curve will be used and the interval from ''Fit Interval'' tab (which is used to fit by sum of curves) is ignored. Select spline curve and check ''Set Interval'' check box in the bottom of the panel to edit spline interval, then click on ''Fit One Curve'' button.  
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-Set ''Baseline'' check box in spline row in curves table to subtract spline from data. 
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-{{:spline2.png|Setting Fit Interval for spline curve}} {{:spline3.png|Spline subtraction result}} 
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-  * in [[interval statistics]] 
-====== Integrals and Statistics on Intervals ====== 
-Setting intervals in ''Fit interval'' tab of Fit Plot is initially intended for setting data range which is used for fitting by sum of fit curves. However, this tab can also be used to calculate integrals and statistics on these intervals (Statistics is only available in Pro edition). Data-Baseline is used to calculate the results. 
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-MagicPlot can integrate data on selected intervals and calculate peak moments (x mean, variance, skewness, kurtosis). Spectrum line is treated as probability distribution curve: //x// values are treated as 'independent variable' and //y// values are treated as 'probability'. Standard statistical formulas are used to calculate moments.  
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-Statistical data and integrals are automatically updated if //x// or //y// data is changed or intervals are changed. 
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-{{:integration-on-intervals.png|Integration on intervals}} 
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-All statistical data is summarized in the intervals table: 
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-{{:statistics-on-intervals.png|Statistics on intervals}} 
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-===== Managing Intervals ===== 
-Move interval borders with mouse. Double click on interval to split it at desired position. Right click opens context menu from which new intervals can be created on free space and existing intervals can be deleted or split. 
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-===== Relative Integrals Calculation ===== 
-MagicPlot can calculate relative integrals to compare the relative intensity of spectrum lines. To compute relative integrals set ''Relative integrals'' check box. MagicPlot designate the smallest integral as 1 but you can enter a custom value. If you want to set not the smallest integral as reference point, enter 1 first and then enter the value of desired integral relative to 1 to this field, so that other integrals will be calculated relative to this new value. 
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-===== Formulas ===== 
-^  Property  ^  Formula  ^ 
-| Integral | Calculated using \\ [[integration|Trapezoidal rule]] | 
-| X Mean (expected value) | <m>mu = nu_1</m> | 
-| Variance | <m>sigma^2 = mu_2</m> | 
-| Standard deviation | <m>sigma = sqrt{mu_2}</m> | 
-| Skewness | <m>gamma_1 = {mu_3} / {sigma^3}</m> | 
-| Kurtosis | <m>gamma_2 = {mu_4} / {sigma^4} − 3</m> | 
-| Y Sum | <m>s = sum{k}{}{y_k}</m> | 
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-Intermediate values are calculated as follows: 
-^  Property  ^  Formula  ^ 
-| [[wp>Raw moment|Raw moments]] | <m>nu_n = 1/s sum{k}{}{y_k {x_k}^n}, ~ n = 1...4, ~ s = sum{k}{}{y_k}</m> | 
-| [[wp>Central moment|Central moments]] | <m>mu_2 = nu_2 − mu^2</m> \\ <m>mu_3 = nu_3 − 3 mu nu_2 + 2 mu^3</m> \\ <m>mu_4 = nu_4 − 4 mu nu_3 + 6 mu^2 nu_2 − 3 mu^4</m> | 
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-  * in [[table]] 
-Upload new menu screenshot 
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-===== Displaying Column Formulas in Table ===== 
-MagicPlot indicates columns for which formulas or other evaluators (FFT, integral, etc.) are set with blue header color. You can see the formula in column header tool tip. 
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-{{:table-highlighting.png|Table highlighting}} 
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-On the screenshot above: 
-  * Column A has no formula 
-  * Column B has formula, auto recalculation is off 
-  * Column C has formula, auto recalculation is on, so this column is not editable 
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-===== Fit Column Widths ===== 
-To fit the width of one column, double click on right separator line in table header. To fit selected columns widths, double click one of column separators in table header. 
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-  * in [[transform xy]] 
-====== Transform X or Y Column (Pro only) ====== 
-You can quickly transform X or Y data on Fit Plot by using ''Transform X/Y'' items in ''Processing'' menu. These menu items open set column formula dialog for table column which is used as X or Y. Note that this transformation affects the table with plot data. 
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-  * in [[shift_curves]] 
-''Make Waterfall'' menu item opens waterfall window in which you can specify shift increment. MagicPlot tries to guess handsome shift values on basis of the number of curves and current scale. 
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-{{:waterfall-dialog.png|Waterfall window}} 
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-  * in [[fft]] 
-Upload new screenshot, update formulas 
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-  * in [[calculator]] 
-Update screenshot. 
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-MagicPlot may be minimized to task bar while Calculator window is still on top 
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-  * in [[fit equations]] 
-====== Fit Curves Types ====== 
-This is the table of predefined fit curves. 
- 
-^ Name  ^ Formula ^ Additional Properties ^  
-| Line | <m>y = a x + b</m> | | 
-| Parabola | <m>y = a x^2 + b x + c</m> | Vertex: \\ <m>x_0 = − b / {2 a}</m> \\ <m>y_0 = c − {b^2} / {4 a}</m> | 
-| Gaussian | <m>y = a exp(− ln(2) ({x−x_0}/dx)^2)</m> | Area: \\ <m>S = sqrt{pi / {ln {2}}} ~ a dx</m> \\ Standard deviation: \\ <m>sigma = dx / sqrt{2 ln 2}</m> | 
-| Gaussian-A \\ (normalized) | <m>y = sqrt{{ln {2}} / pi} ~ a / dx exp(− ln(2) ({x−x_0}/dx)^2)</m> | Amplitude: \\ <m>A = sqrt{{ln 2} / pi} ~ a/dx</m> \\ Standard deviation: \\ <m>sigma = dx / sqrt{2 ln 2}</m> | 
-| Lorentzian | <m>y = a 1 / {1 + ({x−x_0} / dx)^2}</m> | Area: \\ <m>S = pi a dx</m> | 
-| Lorentzian-A \\ (normalized) | <m>y = a / {pi dx} 1 / {1 + ({x−x_0} / dx)^2}</m> | Amplitude: \\ <m>A = a / {pi dx}</m> | 
-| Gauss Derivative | <m>y = − 2 ln(2) ~ {a (x−x_0)} / {dx^2} exp(− ln(2) ({x−x_0}/dx)^2)</m> | Area (second integral): \\ <m>S = sqrt{pi / {ln {2}}} ~ a dx</m> \\ Standard deviation: \\ <m>sigma = dx / sqrt{2 ln 2}</m> \\ Peak-to-peak horizontal: \\ <m>p_x = sqrt{2/{ln {2}}} ~ dx</m> \\ Peak-to-peak vertical: \\ <m>p_y = 2 sqrt{{2 ln {2}} / e} ~ a / dx</m> | 
-| Lorentz Derivative | <m>y=−2 a {x−x_0}/{dx^2} {(1 + ({x−x_0} / dx)^2)^{−2}}</m> | Area (second integral): \\ <m>S = pi a dx</m> \\ Peak-to-peak horizontal: \\ <m>p_x = 2/{sqrt {3}} ~ dx</m> \\ Peak-to-peak vertical: \\ <m>p_y = {3 sqrt {3}} / 4 ~ a / dx</m> | 
new.1287992572.txt.gz · Last modified: Sun Nov 8 12:20:32 2015 (external edit)