spline

Syntax

spline(X, Y, resampleRule, [closed='left'], [origin='start_day'], [outputX=false])

Parameters

X is a strictly increasing vector of temporal type.

Y is a numeric vector of the same length as X.

resampleRule is a string. See the parameter rule of function resample for the optional values.

closed and origin (optional) are the same as the parameters closed and origin of function resample.

outputX (optional) is a Boolean value indicating whether to output the resampled X. The default value is false.

Details

Resample X based on the specified resampleRule, closed and origin. Perform cubic spline interpolation on Y based on the resampled X.

If outputX is unspecified, return a vector of Y after the interpolation.

If outputX=true, return a tuple where the first element is the vector of resampled X and the second element is a vector of Y after the interpolation.

Examples

Example 1

spline([2016.02.14 00:00:00, 2016.02.15 00:00:00, 2016.02.16 00:00:00], [1.0, 2.0, 4.0], resampleRule=`60min);

// output: [1,1.0313,1.0626,1.0942,1.1262,1.1585,1.1914,1.225,1.2593,1.2944,1.3306,1.3678,1.4062,1.446,1.4871,1.5298,1.5741,1.6201,1.668,1.7178
,1.7697,1.8237,1.8801,1.9388,2,2.0638,2.1301,2.1987,2.2697,2.3428,2.418,2.4951,2.5741,2.6548,2.7371,2.821,2.9062,2.9928,3.0806,3.1694
,3.2593,3.35,3.4414,3.5335,3.6262,3.7192,3.8126,3.9063,4]

Example 2 Different values of closed affect the result.

X = 2022.01.01T00:00:00 + [0, 3, 6, 9] * 60
Y = [1.0, 3.0, 7.0, 13.0]

// closed='left' (default): 00:03 belongs to the start of [00:03, 00:06)
spline(X, Y, `3min, closed=`left, outputX=true)

// closed='right': 00:03 belongs to the end of (00:00, 00:03]
// The starting points of resampled X differ, so the spline curve also changes
spline(X, Y, `3min, closed=`right, outputX=true)

Example 3 Different values of origin affect the result.

X = 2022.01.01T00:00:30 + (0..4) * 60
Y = [2.0, 4.0, 7.0, 11.0, 16.0]

// origin='start_day' (default): align to 00:00:00 of the same day
spline(X, Y, `1min, origin=`start_day, outputX=true)

// origin='start': align to the first data point 00:00:30
spline(X, Y, `1min, origin=`start, outputX=true)

// origin=custom timestamp: align to 00:00:10
spline(X, Y, `1min, origin=2022.01.01T00:00:10, outputX=true)

Example 4 Different values of outputX affect the result.

X = [2016.02.14T00:00:00, 2016.02.15T00:00:00, 2016.02.16T00:00:00]
Y = [1.0, 2.0, 4.0]

// outputX=false (default): return only the cubic spline interpolated Y vector
spline(X, Y, `60min)

// outputX=true: return a tuple; [0] is the resampled timestamp vector, [1] is the interpolated Y
result = spline(X, Y, `60min, outputX=true)
result[0]
result[1]