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Plotting and nonlinear fitting software

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integration [Tue May 11 13:16:15 2010]
Alexander created
integration [Sun Nov 8 12:21:24 2015] (current)
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-====== Integration =====+====== Integration (Pro edition only) ===== 
 +Open Table or Figure or Fit Plot with initial data and select ''Processing -> Integrate'' menu item.
  
-Open Table or Figure or Plot with initial data and use ''Analysis → Integrate'' menu item.+{{:integrate.png?nolink|}}
  
-===== Formula ===== +===== Baseline Correction ===== 
-To perform integration you should specify two columns: //x// and //y//+If your initial data to be integrated contains a baseline (usually constant or linear), you may want to subtract it from data **before** integrating(A constant baseline will result in linearly growing integral.) 
  
-The result of integration is the column with integral valuesIntegration is performed using the formula:+In such case the algorithm may be the following: 
 +  - Create Fit Plot with your initial table data 
 +  - Add a Fit Curve which simulates the baselineYou may specify a custom equation (Pro edition only) 
 +  - Specify Fit Interval so that it contains only noise points 
 +  - Fit the data by clicking ''Fit Sum'' button 
 +  - Subtract the baseline fitting curve from data by checking ''Baseline'' checkbox in curves list 
 +  - Use menu ''Processing → Integrate'' to integrate the plotted data without baseline.
  
-<m>I_n sum{i=1}{n − 1}{ {1/2} (y_{i+1} + y_i) (x_{i+1} − x_i)}</m>+===== Algorithm ===== 
 +To perform integration you should specify two columns: //x// and //y//. Missing values are ignored.
  
 +MagicPlot uses [[wp>Trapezoidal_rule|trapezoidal rule]] to compute the integral:
 +
 +<m>I_n = 1/2 sum{i=2}{n}{(x_i} − x_{i − 1}) ({y_i + y_{i − 1})},~ n=2...N;~~ I_1=0</m>
 +
 +===== See Also =====
 +  * [[processing]]
 +  * [[Differentiation]]
integration.1273569375.txt.gz · Last modified: Sun Nov 8 12:20:32 2015 (external edit)