mode    : one of the names mean or linear; specifies the method used to detrend the data. The mode mean removes the mean value of the data from the data. The mode linear removes the line of best-fit from the data. The default is linear.

If the argument XY is a 2-column rtable or DataFrame, the first column is used as the independent variables and the Detrend command is applied to the dependent values in the second column. Note that values in the first column do not need to be equally spaced.

If the argument Y is a 1-column rtable or DataSeries and there is no specified value for X, the Detrend command uses the index positions for each value in Y as the independent values and the Detrend command is applied to the dependent values in Y.

If the argument X and argument Y are 1-column rtables or DataSeries, the values in X are treated as the independent variables and the Detrend command is applied to the dependent values in Y.

$\mathrm{with}\left(\mathrm{Statistics}\right)\:$

$\mathrm{data}≔\mathrm{Matrix}\left(\left[\left[0\,1.8\right]\,\left[1\,0.7\right]\,\left[2.5\,2.8\right]\,\left[4\,4.2\right]\,\left[6.2\,3\right]\right]\right)$

$\mathrm{data}≔\left[\right]$

$\mathrm{lm}≔\mathrm{LinearFit}\left(a+bx\,\mathrm{data}\,x\right)$

$\mathrm{lm}≔1.49598376946009+0.366429281218947x$

$\mathrm{plots}:-\mathrm{display}\left(\left[\mathrm{ScatterPlot}\left(\mathrm{data}\,\mathrm{symbol}=\mathrm{solidcircle}\,\mathrm{symbolsize}=15\,\mathrm{color}=''Black''\,\mathrm{legend}=''Original\; Data''\right)\,\mathrm{plot}\left(\mathrm{lm}\,\mathrm{color}=''Black''\,\mathrm{legend}=''Trend''\,\mathrm{linestyle}=\mathrm{dash}\right)\right]\,\mathrm{view}=\left[\min \left(\mathrm{data}\left[..,1\right]\right)-0.1..\max \left(\mathrm{data}\left[..,1\right]\right)+0.1\,\min \left(\mathrm{data}\left[..,2\right]\right)-0.1..\max \left(\mathrm{data}\left[..,2\right]\right)+0.1\right]\right)$

$\mathrm{detrend\_data}≔\mathrm{Detrend}\left(\mathrm{data}\right)$

$\mathrm{detrend\_data}≔\left[\right]$

$\mathrm{plots}:-\mathrm{display}\left(\left[\mathrm{ScatterPlot}\left(\mathrm{data}\,\mathrm{color}=''Black''\,\mathrm{legend}=''Original\; Data''\,\mathrm{symbol}=\mathrm{solidcircle}\,\mathrm{symbolsize}=15\right)\,\mathrm{plot}\left(\mathrm{lm}\,\mathrm{color}=''Black''\,\mathrm{legend}=''Trend''\,\mathrm{linestyle}=\mathrm{dash}\right)\,\mathrm{ScatterPlot}\left(\mathrm{data}\left[..,1\right]\,\mathrm{detrend\_data}\,\mathrm{color}=''Red''\,\mathrm{legend}=''Detrended\; Data''\,\mathrm{symbol}=\mathrm{diamond}\,\mathrm{symbolsize}=15\right)\,\mathrm{plot}\left(\mathrm{Mean}\left(\mathrm{detrend\_data}\right)\,\mathrm{color}=''Red''\,\mathrm{legend}=''Mean\; of\; Detrended\; Data''\,\mathrm{linestyle}=\mathrm{dot}\right)\right]\,\mathrm{view}=\left[\min \left(\mathrm{data}\left[..,1\right]\right)-0.1..\max \left(\mathrm{data}\left[..,1\right]\right)+0.1\,\mathrm{default}\right]\right)$

$\mathrm{with}\left(\mathrm{SignalProcessing}\right)\:$

$\mathrm{signal\_data}≔\mathrm{GenerateGaussian}\left(100\,0.5\,0.3\right)+⟨\mathrm{seq}\left(i\,i=0.01..1\,0.01\right)⟩$

$\mathrm{signal\_data}≔\left[\right]$

$\mathrm{plots}:-\mathrm{display}\left(\left[\mathrm{SignalPlot}\left(\mathrm{signal\_data}\,\mathrm{legend}=''Data''\right)\,\mathrm{plot}\left(\mathrm{LinearFit}\left(a+bx\,⟨\mathrm{seq}\left(1..100\right)⟩\,\mathrm{signal\_data}\,x\right)\,x=1..100\,\mathrm{color}=''Black''\,\mathrm{legend}=''Trend''\,\mathrm{linestyle}=\mathrm{dash}\right)\right]\right)$

$\mathrm{plots}:-\mathrm{display}\left(\left[\mathrm{SignalPlot}\left(\mathrm{signal\_data}\,\mathrm{legend}=''Original\; Data''\right)\,\mathrm{plot}\left(\mathrm{LinearFit}\left(a+bx\,⟨\mathrm{seq}\left(1..100\right)⟩\,\mathrm{signal\_data}\,x\right)\,x=1..100\,\mathrm{color}=''Black''\,\mathrm{legend}=''Trend''\,\mathrm{linestyle}=\mathrm{dash}\right)\,\mathrm{SignalPlot}\left(\mathrm{signal\_data}\,\mathrm{detrend}\,\mathrm{color}=''Red''\,\mathrm{legend}=''Detrended\; Data''\right)\,\mathrm{plot}\left(\mathrm{Mean}\left(\mathrm{Detrend}\left(\mathrm{signal\_data}\right)\right)\,x=1..100\,\mathrm{color}=''Red''\,\mathrm{legend}=''Mean\; of\; Detrended\; Data''\,\mathrm{linestyle}=\mathrm{dot}\right)\right]\right)$

The Statistics[Detrend] command was introduced in Maple 2019.

For more information on Maple 2019 changes, see Updates in Maple 2019.