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package interp

import "gonum.org/v1/gonum/interp"

Package interp implements 1-dimensional algorithms for interpolating values. Outside of the interpolation interval determined by the interpolated data, the returned value is undefined (but we do our best to return something reasonable).

Index

Examples

Types

type AkimaSpline

type AkimaSpline struct {
	// contains filtered or unexported fields
}

AkimaSpline is a piecewise cubic 1-dimensional interpolator with continuous value and first derivative, which can be fitted to (X, Y) value pairs without providing derivatives. See https://www.iue.tuwien.ac.at/phd/rottinger/node60.html for more details.

func (*AkimaSpline) Fit

func (as *AkimaSpline) Fit(xs, ys []float64) error

Fit fits a predictor to (X, Y) value pairs provided as two slices. It panics if len(xs) < 2, elements of xs are not strictly increasing or len(xs) != len(ys). Always returns nil.

func (*AkimaSpline) Predict

func (as *AkimaSpline) Predict(x float64) float64

Predict returns the interpolation value at x.

func (*AkimaSpline) PredictDerivative

func (as *AkimaSpline) PredictDerivative(x float64) float64

PredictDerivative returns the predicted derivative at x.

type ClampedCubic

type ClampedCubic struct {
	// contains filtered or unexported fields
}

ClampedCubic is a piecewise cubic 1-dimensional interpolator with continuous value, first and second derivatives, which can be fitted to (X, Y) value pairs without providing derivatives. It uses the boundary conditions Y′(left end ) = Y′(right end) = 0.

func (*ClampedCubic) Fit

func (cc *ClampedCubic) Fit(xs, ys []float64) error

Fit fits a predictor to (X, Y) value pairs provided as two slices. It panics if len(xs) < 2, elements of xs are not strictly increasing or len(xs) != len(ys). It returns an error if solving the required system of linear equations fails.

func (*ClampedCubic) Predict

func (cc *ClampedCubic) Predict(x float64) float64

Predict returns the interpolation value at x.

func (*ClampedCubic) PredictDerivative

func (cc *ClampedCubic) PredictDerivative(x float64) float64

PredictDerivative returns the predicted derivative at x.

type Constant

type Constant float64

Constant predicts a constant value.

func (Constant) Predict

func (c Constant) Predict(x float64) float64

Predict returns the predicted value at x.

type DerivativePredictor

type DerivativePredictor interface {
	Predictor

	// PredictDerivative returns the predicted derivative at x.
	PredictDerivative(x float64) float64
}

DerivativePredictor predicts both the value and the derivative of a function. It handles both interpolation and extrapolation.

type FittablePredictor

type FittablePredictor interface {
	Fitter
	Predictor
}

FittablePredictor is a Predictor which can fit itself to data.

type Fitter

type Fitter interface {
	// Fit fits a predictor to (X, Y) value pairs provided as two slices.
	// It panics if len(xs) < 2, elements of xs are not strictly increasing
	// or len(xs) != len(ys). Returns an error if fitting fails.
	Fit(xs, ys []float64) error
}

Fitter fits a predictor to data.

type FritschButland

type FritschButland struct {
	// contains filtered or unexported fields
}

FritschButland is a piecewise cubic 1-dimensional interpolator with continuous value and first derivative, which can be fitted to (X, Y) value pairs without providing derivatives. It is monotone, local and produces a C^1 curve. Its downside is that exhibits high tension, flattening out unnaturally the interpolated curve between the nodes. See Fritsch, F. N. and Butland, J., "A method for constructing local monotone piecewise cubic interpolants" (1984), SIAM J. Sci. Statist. Comput., 5(2), pp. 300-304.

func (*FritschButland) Fit

func (fb *FritschButland) Fit(xs, ys []float64) error

Fit fits a predictor to (X, Y) value pairs provided as two slices. It panics if len(xs) < 2, elements of xs are not strictly increasing or len(xs) != len(ys). Always returns nil.

func (*FritschButland) Predict

func (fb *FritschButland) Predict(x float64) float64

Predict returns the interpolation value at x.

func (*FritschButland) PredictDerivative

func (fb *FritschButland) PredictDerivative(x float64) float64

PredictDerivative returns the predicted derivative at x.

type Function

type Function func(float64) float64

Function predicts by evaluating itself.

func (Function) Predict

func (fn Function) Predict(x float64) float64

Predict returns the predicted value at x by evaluating fn(x).

type NaturalCubic

type NaturalCubic struct {
	// contains filtered or unexported fields
}

NaturalCubic is a piecewise cubic 1-dimensional interpolator with continuous value, first and second derivatives, which can be fitted to (X, Y) value pairs without providing derivatives. It uses the boundary conditions Y′′(left end ) = Y′′(right end) = 0. See e.g. https://www.math.drexel.edu/~tolya/cubicspline.pdf for details.

func (*NaturalCubic) Fit

func (nc *NaturalCubic) Fit(xs, ys []float64) error

Fit fits a predictor to (X, Y) value pairs provided as two slices. It panics if len(xs) < 2, elements of xs are not strictly increasing or len(xs) != len(ys). It returns an error if solving the required system of linear equations fails.

func (*NaturalCubic) Predict

func (nc *NaturalCubic) Predict(x float64) float64

Predict returns the interpolation value at x.

func (*NaturalCubic) PredictDerivative

func (nc *NaturalCubic) PredictDerivative(x float64) float64

PredictDerivative returns the predicted derivative at x.

type NotAKnotCubic

type NotAKnotCubic struct {
	// contains filtered or unexported fields
}

NotAKnotCubic is a piecewise cubic 1-dimensional interpolator with continuous value, first and second derivatives, which can be fitted to (X, Y) value pairs without providing derivatives. It imposes the condition that the third derivative of the interpolant is continuous in the first and last interior node. See http://www.cs.tau.ac.il/~turkel/notes/numeng/spline_note.pdf for details.

func (*NotAKnotCubic) Fit

func (nak *NotAKnotCubic) Fit(xs, ys []float64) error

Fit fits a predictor to (X, Y) value pairs provided as two slices. It panics if len(xs) < 3 (because at least one interior node is required), elements of xs are not strictly increasing or len(xs) != len(ys). It returns an error if solving the required system of linear equations fails.

func (*NotAKnotCubic) Predict

func (nak *NotAKnotCubic) Predict(x float64) float64

Predict returns the interpolation value at x.

func (*NotAKnotCubic) PredictDerivative

func (nak *NotAKnotCubic) PredictDerivative(x float64) float64

PredictDerivative returns the predicted derivative at x.

type PiecewiseConstant

type PiecewiseConstant struct {
	// contains filtered or unexported fields
}

PiecewiseConstant is a left-continuous, piecewise constant 1-dimensional interpolator.

func (*PiecewiseConstant) Fit

func (pc *PiecewiseConstant) Fit(xs, ys []float64) error

Fit fits a predictor to (X, Y) value pairs provided as two slices. It panics if len(xs) < 2, elements of xs are not strictly increasing or len(xs) != len(ys). Always returns nil.

func (PiecewiseConstant) Predict

func (pc PiecewiseConstant) Predict(x float64) float64

Predict returns the interpolation value at x.

type PiecewiseCubic

type PiecewiseCubic struct {
	// contains filtered or unexported fields
}

PiecewiseCubic is a piecewise cubic 1-dimensional interpolator with continuous value and first derivative.

func (*PiecewiseCubic) FitWithDerivatives

func (pc *PiecewiseCubic) FitWithDerivatives(xs, ys, dydxs []float64)

FitWithDerivatives fits a piecewise cubic predictor to (X, Y, dY/dX) value triples provided as three slices. It panics if len(xs) < 2, elements of xs are not strictly increasing, len(xs) != len(ys) or len(xs) != len(dydxs).

func (*PiecewiseCubic) Predict

func (pc *PiecewiseCubic) Predict(x float64) float64

Predict returns the interpolation value at x.

func (*PiecewiseCubic) PredictDerivative

func (pc *PiecewiseCubic) PredictDerivative(x float64) float64

PredictDerivative returns the predicted derivative at x.

type PiecewiseLinear

type PiecewiseLinear struct {
	// contains filtered or unexported fields
}

PiecewiseLinear is a piecewise linear 1-dimensional interpolator.

func (*PiecewiseLinear) Fit

func (pl *PiecewiseLinear) Fit(xs, ys []float64) error

Fit fits a predictor to (X, Y) value pairs provided as two slices. It panics if len(xs) < 2, elements of xs are not strictly increasing or len(xs) != len(ys). Always returns nil.

func (PiecewiseLinear) Predict

func (pl PiecewiseLinear) Predict(x float64) float64

Predict returns the interpolation value at x.

type Predictor

type Predictor interface {
	// Predict returns the predicted value at x.
	Predict(x float64) float64
}

Predictor predicts the value of a function. It handles both interpolation and extrapolation.

Example

Code:play 

package main

import (
	"fmt"
	"math"
	"os"
	"text/tabwriter"

	"gonum.org/v1/gonum/interp"
)

func main() {
	// An example of fitting different interpolation
	// algorithms to (X, Y) data with widely varying slope.
	//
	// Cubic interpolators have to balance the smoothness
	// of the generated curve with suppressing ugly wiggles
	// (compare the output of AkimaSpline with that of
	// FritschButland).
	xs := []float64{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}
	ys := []float64{0, 0.001, 0.002, 0.1, 1, 2, 2.5, -10, -10.01, 2.49, 2.53, 2.55}

	var pc interp.PiecewiseConstant
	var pl interp.PiecewiseLinear
	var as interp.AkimaSpline
	var fb interp.FritschButland

	predictors := []interp.FittablePredictor{&pc, &pl, &as, &fb}
	for i, p := range predictors {
		err := p.Fit(xs, ys)
		if err != nil {
			panic(fmt.Sprintf("Error fitting %d-th predictor: %v", i, err))
		}
	}

	n := len(xs)
	dx := 0.25
	nPts := int(math.Round(float64(n-1)/dx)) + 1

	w := tabwriter.NewWriter(os.Stdout, 8, 0, 1, ' ', tabwriter.AlignRight)
	fmt.Fprintln(w, "x\tPC\tPL\tAS\tFB\t")
	for i := 0; i < nPts; i++ {
		x := xs[0] + float64(i)*dx
		fmt.Fprintf(w, "%.2f", x)
		for _, predictor := range predictors {
			y := predictor.Predict(x)
			fmt.Fprintf(w, "\t%.2f", y)
		}
		fmt.Fprintln(w, "\t")
	}
	fmt.Fprintln(w)
	w.Flush()
}

Output:

       x      PC      PL      AS      FB
    0.00    0.00    0.00    0.00    0.00
    0.25    0.00    0.00    0.00    0.00
    0.50    0.00    0.00    0.00    0.00
    0.75    0.00    0.00    0.00    0.00
    1.00    0.00    0.00    0.00    0.00
    1.25    0.00    0.00    0.00    0.00
    1.50    0.00    0.00    0.00    0.00
    1.75    0.00    0.00    0.00    0.00
    2.00    0.00    0.00    0.00    0.00
    2.25    0.10    0.03   -0.01    0.01
    2.50    0.10    0.05   -0.01    0.03
    2.75    0.10    0.08    0.02    0.06
    3.00    0.10    0.10    0.10    0.10
    3.25    1.00    0.33    0.26    0.22
    3.50    1.00    0.55    0.49    0.45
    3.75    1.00    0.78    0.75    0.73
    4.00    1.00    1.00    1.00    1.00
    4.25    2.00    1.25    1.24    1.26
    4.50    2.00    1.50    1.50    1.54
    4.75    2.00    1.75    1.75    1.79
    5.00    2.00    2.00    2.00    2.00
    5.25    2.50    2.12    2.22    2.17
    5.50    2.50    2.25    2.37    2.33
    5.75    2.50    2.38    2.47    2.45
    6.00    2.50    2.50    2.50    2.50
    6.25  -10.00   -0.62    0.83    0.55
    6.50  -10.00   -3.75   -2.98   -3.75
    6.75  -10.00   -6.88   -7.18   -8.04
    7.00  -10.00  -10.00  -10.00  -10.00
    7.25  -10.01  -10.00  -11.16  -10.00
    7.50  -10.01  -10.00  -11.55  -10.01
    7.75  -10.01  -10.01  -11.18  -10.01
    8.00  -10.01  -10.01  -10.01  -10.01
    8.25    2.49   -6.88   -7.18   -8.06
    8.50    2.49   -3.76   -2.99   -3.77
    8.75    2.49   -0.63    0.82    0.53
    9.00    2.49    2.49    2.49    2.49
    9.25    2.53    2.50    2.50    2.51
    9.50    2.53    2.51    2.51    2.52
    9.75    2.53    2.52    2.52    2.52
   10.00    2.53    2.53    2.53    2.53
   10.25    2.55    2.53    2.54    2.54
   10.50    2.55    2.54    2.54    2.54
   10.75    2.55    2.54    2.55    2.55
   11.00    2.55    2.55    2.55    2.55

Source Files

cubic.go doc.go interp.go

Version
v0.14.0 (latest)
Published
Aug 19, 2023
Platform
linux/amd64
Imports
3 packages
Last checked
6 hours ago

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