Hermite (FSharp.Stats)

Hermite Module

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

Hermite cubic splines are defined by the function values and their slopes (first derivatives). If the slopws are unknown, they must be estimated.

Types

Type	Description
HermiteCoef

Functions and values

Function or value	Description
`interpolate xData yData` Full Usage: `interpolate xData yData` Parameters: xData : `Vector<float>` - Note: Must not contain duplicate x values (use Approximation.regularizeValues to preprocess data!) yData : `Vector<float>` - function value at x values Returns: `HermiteCoef` Coefficients that define the interpolating function.	Computes coefficients for piecewise interpolating splines. Second derivative (curvature) is NOT necessarily continuous at knots to allow higher flexibility to reduce oscillations! xData : `Vector<float>` Note: Must not contain duplicate x values (use Approximation.regularizeValues to preprocess data!) yData : `Vector<float>` function value at x values Returns: `HermiteCoef` 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.Hermite.interpolate xData yData`
`interpolatePreserveMonotonicity xData yData` Full Usage: `interpolatePreserveMonotonicity xData yData` Parameters: xData : `Vector<float>` yData : `Vector<float>` - function value at x values Returns: `HermiteCoef` Coefficients that define the interpolating function.	Computes coefficients for piecewise interpolating splines. If the knots are monotone in/decreasing, the spline also is monotone (CJC Kruger method) The x data has to be sorted ascending Second derivative (curvature) is NOT necessarily continuous at knots to allow higher flexibility to reduce oscillations!Constrained Cubic Spline Interpolation for Chemical Engineering Applications by CJC Kruger xData : `Vector<float>` yData : `Vector<float>` function value at x values Returns: `HermiteCoef` 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.;6.;13.;13.1\|] // get coefficients for piecewise interpolating cubic polynomials let coefficients = CubicSpline.Hermite.interpolatePreserveMonotonicity xData yData`
`interpolateSorted xData yData` Full Usage: `interpolateSorted xData yData` Parameters: xData : `Vector<float>` - Note: Must not contain duplicate x values (use Approximation.regularizeValues to preprocess data!) yData : `Vector<float>` - function value at x values Returns: `HermiteCoef` Coefficients that define the interpolating function.	Computes coefficients for piecewise interpolating splines. The x data has to be sorted ascending. Second derivative (curvature) is NOT necessarily continuous at knots to allow higher flexibility to reduce oscillations! xData : `Vector<float>` Note: Must not contain duplicate x values (use Approximation.regularizeValues to preprocess data!) yData : `Vector<float>` function value at x values Returns: `HermiteCoef` 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.Hermite.interpolateSorted xData yData`
`interpolateWithSlopes xData yData slopes` Full Usage: `interpolateWithSlopes xData yData slopes` Parameters: xData : `Vector<float>` - Note: Must not contain duplicate x values (use Approximation.regularizeValues to preprocess data!) yData : `Vector<float>` - function value at x values slopes : `Vector<float>` - slopes at x values Returns: `HermiteCoef` Coefficients that define the interpolating function.	Computes coefficients for piecewise interpolating splines. The x data has to be sorted ascending. Second derivative (curvature) is NOT necessarily continuous at knots to allow higher flexibility to reduce oscillations! xData : `Vector<float>` Note: Must not contain duplicate x values (use Approximation.regularizeValues to preprocess data!) yData : `Vector<float>` function value at x values slopes : `Vector<float>` slopes at x values Returns: `HermiteCoef` Coefficients that define the interpolating function.
`predict coef x` Full Usage: `predict coef x` Parameters: coef : `HermiteCoef` 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! coef : `HermiteCoef` 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.Hermite.interpolate xData yData // get interpolating function let func = CubicSpline.Hermite.predict coefLinSpl // get function value at x=3.4 func 3.4`