Akima (FSharp.Stats)

Akima Module

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

Module to create piecewise cubic polynomials (cubic subsplines) from x,y coordinates. Akima subsplines are more flexible than standard cubic splines because the are NOT continuous in the function curvature, thereby diminishing oscillating behaviour.

Types

Type	Description
SubSplineCoef	Subsplines differ from regular splines because they are discontinuous in the second derivative.

Functions and values

Function or value	Description
`definiteIntegral integrateF xVal1 xVal2` Full Usage: `definiteIntegral integrateF xVal1 xVal2` Parameters: integrateF : `float -> float` xVal1 : `float` - X value from where the integral should be calculated. xVal2 : `float` - X value up to which the integral should be calculated. Returns: `float` Integral (area under the curve) from x=xVal1 to x=xVal2	Returns integral from interpolating function from x=xVal1 to x=xVal2. integrateF : `float -> float` xVal1 : `float` X value from where the integral should be calculated. xVal2 : `float` X value up to which the integral should be calculated. Returns: `float` Integral (area under the curve) from x=xVal1 to x=xVal2
`getFirstDerivative splineCoeffs xVal` Full Usage: `getFirstDerivative splineCoeffs xVal` Parameters: splineCoeffs : `SubSplineCoef` - Interpolation functions coefficients. xVal : `float` - X value of which the slope should be predicted. Returns: `float` Function that takes an x value and returns slope.	Returns function that takes x value and predicts the corresponding slope. Second derivative (curvature) is NOT continuous at knots to allow higher flexibility to reduce oscillations! For reference see: http://www.dorn.org/uni/sls/kap06/f08_0204.htm. splineCoeffs : `SubSplineCoef` Interpolation functions coefficients. xVal : `float` X value of which the slope should be predicted. Returns: `float` Function that takes an x value and returns 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 = Akima.interpolate xData yData // get function to predict slope let interpolFunc = Akima.getFirstDerivative coefficients // get slope at x=3.4 interpolFunc 3.4`
`getSecondDerivative splineCoeffs xVal` Full Usage: `getSecondDerivative splineCoeffs xVal` Parameters: splineCoeffs : `SubSplineCoef` - Interpolation functions coefficients. xVal : `float` - X value of which the curvature should be predicted. Returns: `float` Function that takes an x value and returns curvature.	Returns function that takes x value and predicts the corresponding interpolating curvature. Second derivative (curvature) is NOT continuous at knots to allow higher flexibility to reduce oscillations! For reference see: http://www.dorn.org/uni/sls/kap06/f08_0204.htm. splineCoeffs : `SubSplineCoef` Interpolation functions coefficients. xVal : `float` X value of which the curvature should be predicted. Returns: `float` Function that takes an x value and returns 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 = Akima.interpolate xData yData // get function to predict curvature let interpolFunc = Akima.getSecondDerivative coefficients // get curvature at x=3.4 interpolFunc 3.4`
`integrate splineCoeffs xVal` Full Usage: `integrate splineCoeffs xVal` Parameters: splineCoeffs : `SubSplineCoef` - Interpolation functions coefficients. xVal : `float` - X value up to which the integral should be calculated. Returns: `float` Integral (area under the curve) from x=0 to x=xVal	Returns integral from interpolating function from x=0 to x=xVal. splineCoeffs : `SubSplineCoef` Interpolation functions coefficients. xVal : `float` X value up to which the integral should be calculated. Returns: `float` Integral (area under the curve) from x=0 to x=xVal
`interpolate xValues yValues` Full Usage: `interpolate xValues yValues` Parameters: xValues : `float[]` - Note: Must not contain duplicate x values (use Approximation.regularizeValues to preprocess data!) yValues : `float[]` - function value at x values Returns: `SubSplineCoef` Coefficients that define the interpolating function.	Computes coefficients for piecewise interpolating subsplines. Second derivative (curvature) is NOT continuous at knots to allow higher flexibility to reduce oscillations! For reference see: http://www.dorn.org/uni/sls/kap06/f08_0204.htm. xValues : `float[]` Note: Must not contain duplicate x values (use Approximation.regularizeValues to preprocess data!) yValues : `float[]` function value at x values Returns: `SubSplineCoef` 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 = Akima.interpolate xData yData`
`interpolateHermiteSorted xValues yValues firstDerivatives` Full Usage: `interpolateHermiteSorted xValues yValues firstDerivatives` Parameters: xValues : `float[]` - x values that are sorted ascending. Note: Must not contain duplicate x values (use Approximation.regularizeValues to preprocess data!) yValues : `float[]` - function value at x values firstDerivatives : `float[]` - first derivatives at x values Returns: `SubSplineCoef` Coefficients that define the interpolating function.	Computes coefficients for piecewise interpolating subsplines. Second derivative (curvature) is NOT continuous at knots to allow higher flexibility to reduce oscillations! For reference see: http://www.dorn.org/uni/sls/kap06/f08_0204.htm. xValues : `float[]` x values that are sorted ascending. Note: Must not contain duplicate x values (use Approximation.regularizeValues to preprocess data!) yValues : `float[]` function value at x values firstDerivatives : `float[]` first derivatives at x values Returns: `SubSplineCoef` 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 = Akima.interpolate xData yData`
`predict splineCoeffs xVal` Full Usage: `predict splineCoeffs xVal` Parameters: splineCoeffs : `SubSplineCoef` - Interpolation functions coefficients. xVal : `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. Second derivative (curvature) is NOT continuous at knots to allow higher flexibility to reduce oscillations! For reference see: http://www.dorn.org/uni/sls/kap06/f08_0204.htm. splineCoeffs : `SubSplineCoef` Interpolation functions coefficients. xVal : `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 = Akima.interpolate xData yData // get function to predict y value let interpolFunc = Akima.predict coefficients // get function value at x=3.4 interpolFunc 3.4`