CubicSpline (FSharp.Stats)

CubicSpline Module

Namespace: FSharp.Stats
Assembly: FSharp.Stats.dll
Parent Module: Interpolation

Cubic splines interpolate two dimensional data by applying piecewise cubic polynomials that are continuous at the input coordinates (knots). The function itself, the first- and second derivative are continuous at the knots.

Types and nested modules

Type/Module	Description
Hermite	Hermite cubic splines are defined by the function values and their slopes (first derivatives). If the slopws are unknown, they must be estimated.
BoundaryCondition
CubicSplineCoef	Contains x data, y data (c0), slopes (c1), curvatures (c2), and the third derivative at each knot

Functions and values

Function or value	Description
`getFirstDerivative coefficients x` Full Usage: `getFirstDerivative coefficients x` Parameters: coefficients : `CubicSplineCoef` - Interpolation functions coefficients. x : `float` - X value of which the slope should be predicted. Returns: `float` Function that takes an x value and returns the function slope.	Returns function that takes x value and predicts the corresponding slope. x values outside of the xValue range are predicted by straight lines defined by the nearest knot! coefficients : `CubicSplineCoef` Interpolation functions coefficients. x : `float` X value of which the slope should be predicted. Returns: `float` Function that takes an x value and returns the function slope. Example `// e.g. days since a certain event let xData = vector [\|0.;1.;5.;4.;3.;\|] // some measured feature let yData = vector [\|1.;5.;4.;13.;17.\|] // get coefficients for piecewise interpolating cubic polynomials let coefficients = CubicSpline.interpolate CubicSpline.BoundaryConditions.Natural xData yData // get slope function let func = CubicSpline.getFirstDerivative(coefLinSpl) // get slope at x=3.4 func 3.4`
`getSecondDerivative coefficients x` Full Usage: `getSecondDerivative coefficients x` Parameters: coefficients : `CubicSplineCoef` - Interpolation functions coefficients. x : `float` - X value of which the curvature should be predicted. Returns: `float` Function that takes an x value and returns the function curvature.	Returns function that takes x value and predicts the corresponding curvature. x values outside of the xValue range are predicted by straight lines defined by the nearest knot! coefficients : `CubicSplineCoef` Interpolation functions coefficients. x : `float` X value of which the curvature should be predicted. Returns: `float` Function that takes an x value and returns the function curvature. Example `// e.g. days since a certain event let xData = vector [\|0.;1.;5.;4.;3.;\|] // some measured feature let yData = vector [\|1.;5.;4.;13.;17.\|] // get coefficients for piecewise interpolating cubic polynomials let coefficients = CubicSpline.interpolate CubicSpline.BoundaryConditions.Natural xData yData // get curvature function let func = CubicSpline.getSecondDerivative(coefLinSpl) // get curvature at x=3.4 func 3.4`
`getThirdDerivative coefficients x` Full Usage: `getThirdDerivative coefficients x` Parameters: coefficients : `CubicSplineCoef` - Interpolation functions coefficients. x : `float` - X value of which the y value should be predicted. Returns: `float` Function that takes an x value and returns the function third derivative.	Returns function that takes x value and predicts the corresponding third derivative. x values outside of the xValue range are predicted by straight lines defined by the nearest knot! coefficients : `CubicSplineCoef` Interpolation functions coefficients. x : `float` X value of which the y value should be predicted. Returns: `float` Function that takes an x value and returns the function third derivative. Example `// e.g. days since a certain event let xData = vector [\|0.;1.;5.;4.;3.;\|] // some measured feature let yData = vector [\|1.;5.;4.;13.;17.\|] // get coefficients for piecewise interpolating cubic polynomials let coefficients = CubicSpline.interpolate CubicSpline.BoundaryConditions.Natural xData yData // get third derivative function let func = CubicSpline.getThirdDerivative(coefLinSpl) // get third derivative at x=3.4 func 3.4`
`interpolate boundaryCondition xValues yValues` Full Usage: `interpolate boundaryCondition xValues yValues` Parameters: boundaryCondition : `BoundaryCondition` - Condition that defines how slopes and curvatures are defined at the left- and rightmost knot xValues : `Vector<float>` - Note: Must not contain duplicate x values (use Approximation.regularizeValues to preprocess data!) yValues : `Vector<float>` - function value at x values Returns: `CubicSplineCoef` Coefficients that define the interpolating function.	Computes coefficients for piecewise interpolating splines. In the form of [a0;b0;c0;d0;a1;b1;...;d(n-2)]. where: fn(x) = (an)x^3+(bn)x^2+(cn)x+(dn) boundaryCondition : `BoundaryCondition` Condition that defines how slopes and curvatures are defined at the left- and rightmost knot xValues : `Vector<float>` Note: Must not contain duplicate x values (use Approximation.regularizeValues to preprocess data!) yValues : `Vector<float>` function value at x values Returns: `CubicSplineCoef` Coefficients that define the interpolating function. Example `// e.g. days since a certain event let xData = vector [\|0.;1.;5.;4.;3.;\|] // some measured feature let yData = vector [\|1.;5.;4.;13.;17.\|] // get coefficients for piecewise interpolating cubic polynomials let coefficients = CubicSpline.interpolate CubicSpline.BoundaryConditions.Natural xData yData`
`interpolateWithCurvature x y curvatures` Full Usage: `interpolateWithCurvature x y curvatures` Parameters: x : `vector` y : `vector` curvatures : `vector` Returns: `CubicSplineCoef`	Interpolates x and y coordinates with given slopes at the knots. Probably makes no sense because slope isnt continuous anymore x : `vector` y : `vector` curvatures : `vector` Returns: `CubicSplineCoef`
`interpolateWithSlopes x y slopes` Full Usage: `interpolateWithSlopes x y slopes` Parameters: x : `vector` y : `vector` slopes : `vector` Returns: `CubicSplineCoef`	Interpolates x and y coordinates with given slopes at the knots. Curvature cannot be set anymore x : `vector` y : `vector` slopes : `vector` Returns: `CubicSplineCoef`
`predict coefficients x` Full Usage: `predict coefficients x` Parameters: coefficients : `CubicSplineCoef` - Interpolation functions coefficients. x : `float` - X value of which the y value should be predicted. Returns: `float` Function that takes an x value and returns function value.	Returns function that takes x value and predicts the corresponding interpolating y value. x values outside of the xValue range are predicted by straight lines defined by the nearest knot! coefficients : `CubicSplineCoef` Interpolation functions coefficients. x : `float` X value of which the y value should be predicted. Returns: `float` Function that takes an x value and returns function value. Example `// e.g. days since a certain event let xData = vector [\|0.;1.;5.;4.;3.;\|] // some measured feature let yData = vector [\|1.;5.;4.;13.;17.\|] // get coefficients for piecewise interpolating cubic polynomials let coefficients = CubicSpline.interpolate CubicSpline.BoundaryConditions.Natural xData yData // get interpolating function let func = CubicSpline.predict(coefLinSpl) // get function value at x=3.4 func 3.4`
`predictWithinRange coefficients x` Full Usage: `predictWithinRange coefficients x` Parameters: coefficients : `CubicSplineCoef` - Interpolation functions coefficients. x : `float` - X value of which the y value should be predicted. Returns: `float` Function that takes an x value and returns function value.	Returns function that takes x value (that lies within the range of input x values) and predicts the corresponding interpolating y value. Only defined within the range of the given xValues! coefficients : `CubicSplineCoef` Interpolation functions coefficients. x : `float` X value of which the y value should be predicted. Returns: `float` Function that takes an x value and returns function value. Example `// e.g. days since a certain event let xData = vector [\|0.;1.;5.;4.;3.;\|] // some measured feature let yData = vector [\|1.;5.;4.;13.;17.\|] // get coefficients for piecewise interpolating cubic polynomials let coefficients = CubicSpline.interpolate CubicSpline.BoundaryConditions.Natural xData yData // get interpolating value let func = CubicSpline.predictWithinRange(coefLinSpl) // get function value at x=3.4 func 3.4`