Interpolate2

Interpolate2 [flags ] [ xWave , ] yWave

The Interpolate2 operation performs linear, cubic spline and smoothing cubic spline interpolation on 1D waveform or XY data. It produces output in the form of a waveform or an XY pair.

The cubic spline interpolation is based on a routine from "Numerical Recipes in C".

The smoothing spline is based on "Smoothing by Spline Functions", Christian H. Reinsch, Numerische Mathematic 10, 177-183 (1967).

For background information, see The Interpolate2 Operation.

Parameters

xWave specifies the wave which supplies the X coordinates for the input curve. If you omit it, X coordinates are taken from the X values of yWave.

yWave specifies the wave which supplies the Y coordinates for the input curve.

Flags

/A=a	Controls pre-averaging. Pre-averaging is deprecated - use the smoothing spline (/T=3) instead.
	If a is zero, Interpolate2 does no pre-averaging. If a is greater than one, it specifies the number of nodes through which you want the output curve to go. Interpolate2 creates the nodes by averaging the raw input data.
	Pre-averaging does not work correctly with the log-spaced output mode (/I=2). This is because the pre-averaging is done on linearly-spaced intervals but the input data is log-spaced.
/E=e	Controls how the end points are determined for cubic spline interpolation only.
	e =1: Match first derivative (default) e =2: Match second derivative (natural)
/F=f	f is the smoothing factor used for the smoothing spline.
	f =0 is nearly identical to the cubic spline.
	f >0 gives increasing amounts of smoothing as f increases.
	See Smoothing Spline Parameters for details.
/FREE	Creates output waves as free waves (see Free Waves).
	/FREE is allowed only in functions. If you use /FREE then the output waves specified by /X and /Y must be either simple names or valid wave references.
	/FREE was added in Igor Pro 9.00.
/I[=i]	Determines at what X coordinates the interpolation is done.
	i =0: Gives output values at evenly-spaced X coordinates that span the X range of the input data. This is the default setting if /I is omitted. i =1: Same as i=0 except that the X input values are included in the list of X coordinates at which to interpolate. This is rarely needed and is not available if no X destination wave is specified. /I is equivalent to /I=1. Both are not recommended. i =2: Gives output values at X coordinates evenly-spaced on a logarithmic scale. Use this if your data is plotted on a logarithmic X axis. Ignores any non-positive values in your input X data. This mode is not recommended. See Interpolating Exponential Data for an alternative. i =3: Gives output values at X coordinates that you specify by setting the X coordinates of the destination wave before calling Interpolate2. You must create your destination wave or waves before doing the interpolation for this mode.
	If you omit /X=xDest then the X coordinates come from the X values of the output waveform designated by /Y=yDest .
	If you include /X=xDest then the X coordinates come from the data values of the specified X output wave.
	When using /I=3, the number of output points is determined by the destination wave and the /N flag is ignored.
	See Destination X Coordinates from Destination Wave for further details.
/J=j	Controls the use of end nodes with pre-averaging (/A). Pre-averaging is deprecated - use the smoothing spline (/T=3) instead.
	j =0: Turns end nodes off. j =1: Creates end nodes by cubic extrapolation. j =2: Creates end nodes equal to the first and last data points of the input data set, not counting points that contain NaNs or INFs.
/N=n	Controls the number of points in the output wave or waves. n defaults to the larger of 200 and the number of points in the source waves. This value is ignored if you /I=3 (X from dest mode).
/S=s	s is the estimated standard deviation of the noise of the Y data. It is used for the smoothing spline only. s is used as the estimated standard deviation for all points in the Y data.
	If neither /S nor /SWAV are present, Interpolate2 arbitrarily assumes an s equal to .05 times the amplitude of the Y data.
/SWAV=stdDevWave	stdDevWave is a wave containing the standard deviation of the noise of the Y data on a point-by-point basis. It is used for the smoothing spline only. stdDevWave must have the same number of points as the Y data wave.
	If neither /S nor /SWAV are present, Interpolate2 arbitrarily assumes an s equal to .05 times the amplitude of the Y data.
/T=t	Controls the type of interpolation performed.
	t =1: Linear interpolation t =2: Cubic spline interpolation (default) t =3: Smoothing spline interpolation
/X=xDest	Specifies the X destination wave name.
	If /X is present the output is an XY pair.
	If /X is omitted the output is a waveform.
	The X destination wave may or may not exist when Interpolate2 is called except for "X from dest" mode (/I=3) when it must exist. Interpolate2 overwrites it if it exists.
/Y=yDest	Specifies the Y destination wave name.
	If you omit /Y, a default wave name is generated. The name of the default wave is the name of the source Y wave plus "_L" for linear interpolation, "_CS" for cubic spline or "_SS" for smoothing spline.
	The Y destination wave may or may not exist when Interpolate2 is called. Interpolate2 overwrites it if it exists.

See Also

The Interpolate2 Operation

Demos

Open Interpolate2 Log Demo

References

"Numerical Recipes in C " for cubic spline.

"Smoothing by Spline Functions", Christian H. Reinsch, Numerische Mathematic 10, 177-183 (1967).