edu.mines.jtk.interp

Class CubicInterpolator

java.lang.Object

edu.mines.jtk.interp.CubicInterpolator

public class CubicInterpolator
extends java.lang.Object

Piecewise cubic interpolation of a function y(x).

Piecewise cubic interpolators differ in the method they use to compute slopes y'(x) at specified x (knots). The classic cubic spline computes the slopes to obtain a continuous second derivative at the knots. These splines often yield unacceptable wiggliness (overshoot) between the knots. A linear spline yields no overshoot, but has discontinuous first (and higher) derivatives. A monotonic spline has continuous first derivatives and yields monotonic interpolation (with no overshoot) where function values at the knots are monotonically increasing or decreasing.

For x outside the range of values specified when an interpolator was constructed, the interpolator extrapolates using the cubic polynomial corresponding to the knot nearest to x.

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
static class	CubicInterpolator.Method The method used to compute 1st derivatives y'(x).

Constructor Summary

Constructors

Constructor and Description
CubicInterpolator(CubicInterpolator.Method method, float[] x, float[] y) Constructs an interpolator.
CubicInterpolator(CubicInterpolator.Method method, int n, float[] x, float[] y) Constructs an interpolator.
CubicInterpolator(float[] x, float[] y) Constructs an interpolator with default method monotonic.
CubicInterpolator(float[] x, float[] y, float[] y1) Constructs an interpolator with specified 1st derivatives y'(x).

Method Summary

Methods

Modifier and Type	Method and Description
float	interpolate(float x) Interpolates a function value y(x).
float[]	interpolate(float[] x) Returns an array of interpolated function values y(x).
void	interpolate(float[] x, float[] y) Interpolates an array of function values y(x).
void	interpolate(int n, float[] x, float[] y) Interpolates an array of function values y(x).
float	interpolate0(float x) Interpolates a function value y(x).
float[]	interpolate0(float[] x) Returns an array of interpolated function values y(x).
void	interpolate0(float[] x, float[] y) Interpolates an array of function values y(x).
void	interpolate0(int n, float[] x, float[] y) Interpolates an array of function values y(x).
float	interpolate1(float x) Interpolates the first derivative y'(x).
float[]	interpolate1(float[] x) Returns an array of interpolated first derivatives y'(x).
void	interpolate1(float[] x, float[] y) Interpolates an array of first derivatives y'(x).
void	interpolate1(int n, float[] x, float[] y) Interpolates an array of first derivatives y'(x).
float	interpolate2(float x) Interpolates the second derivative y''(x).
float[]	interpolate2(float[] x) Returns an array of interpolated second derivatives y''(x).
void	interpolate2(float[] x, float[] y) Interpolates an array of second derivatives y''(x).
void	interpolate2(int n, float[] x, float[] y) Interpolates an array of second derivatives y''(x).
float	interpolate3(float x) Interpolates the third derivative y'''(x).
float[]	interpolate3(float[] x) Returns an array of interpolated third derivatives y'''(x).
void	interpolate3(float[] x, float[] y) Interpolates an array of third derivatives y'''(x).
void	interpolate3(int n, float[] x, float[] y) Interpolates an array of third derivatives y'''(x).

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

CubicInterpolator

public CubicInterpolator(float[] x,
                 float[] y,
                 float[] y1)

Constructs an interpolator with specified 1st derivatives y'(x).

Parameters:

x - array of values at which y(x) are specified. These values must be monotonically increasing or decreasing, with no equal values. (In other words, the array must be monotonic-definite.)

y - array of function values y(x).

y1 - array of 1st derivatives y'(x).

CubicInterpolator

public CubicInterpolator(float[] x,
                 float[] y)

Constructs an interpolator with default method monotonic.

Parameters:

x - array of values at which y(x) are specified. These values must be monotonically increasing or decreasing, with no equal values. (In other words, the array must be monotonic-definite.)

y - array of function values y(x).

CubicInterpolator

public CubicInterpolator(CubicInterpolator.Method method,
                 float[] x,
                 float[] y)

Constructs an interpolator.

Parameters:

method - interpolation method: LINEAR, MONOTONIC, or SPLINE.

x - array of values at which y(x) are specified. These values must be monotonically increasing or decreasing, with no equal values. (In other words, the array must be monotonic-definite.)

y - array of function values y(x).

CubicInterpolator

public CubicInterpolator(CubicInterpolator.Method method,
                 int n,
                 float[] x,
                 float[] y)

Constructs an interpolator.

Parameters:

method - interpolation method: LINEAR, MONOTONIC, or SPLINE.

n - number of x and y(x) values specified.

x - array[n] of values at which y(x) are specified. These values must be monotonically increasing or decreasing, with no equal values. (In other words, the array must be monotonic-definite.)

y - array[n] of function values y(x).

Method Detail

interpolate

public float interpolate(float x)

Interpolates a function value y(x). Same as interpolate0(float).

Parameters:

x - value at which to interpolate.

Returns:

interpolated function value y(x).

interpolate0

public float interpolate0(float x)

Interpolates a function value y(x).

Parameters:

x - value at which to interpolate.

Returns:

interpolated function value y(x).

interpolate1

public float interpolate1(float x)

Interpolates the first derivative y'(x).

Parameters:

x - value at which to interpolate.

Returns:

interpolated first derivative y'(x).

interpolate2

public float interpolate2(float x)

Interpolates the second derivative y''(x).

Parameters:

x - value at which to interpolate.

Returns:

interpolated second derivative y''(x).

interpolate3

public float interpolate3(float x)

Interpolates the third derivative y'''(x).

Parameters:

x - value at which to interpolate.

Returns:

interpolated third derivative y'''(x).

interpolate

public float[] interpolate(float[] x)

Returns an array of interpolated function values y(x). Same as interpolate0(float[]).

Parameters:

x - array of values at which to interpolate.

Returns:

array of interpolated function values.

interpolate0

public float[] interpolate0(float[] x)

Returns an array of interpolated function values y(x).

Parameters:

x - array of values at which to interpolate.

Returns:

array of interpolated function values.

interpolate

public void interpolate(float[] x,
               float[] y)

Interpolates an array of function values y(x). Same as interpolate0(float[],float[]).

Parameters:

x - array of values at which to interpolate.

y - array of interpolated function values.

interpolate0

public void interpolate0(float[] x,
                float[] y)

Interpolates an array of function values y(x).

Parameters:

x - array of values at which to interpolate.

y - array of interpolated function values.

interpolate1

public float[] interpolate1(float[] x)

Returns an array of interpolated first derivatives y'(x).

Parameters:

x - array of values at which to interpolate.

Returns:

array of interpolated first derivatives y'(x).

interpolate1

public void interpolate1(float[] x,
                float[] y)

Interpolates an array of first derivatives y'(x).

Parameters:

x - array of values at which to interpolate.

y - array of interpolated first derivatives y'(x).

interpolate2

public float[] interpolate2(float[] x)

Returns an array of interpolated second derivatives y''(x).

Parameters:

x - array of values at which to interpolate.

Returns:

array of interpolated second derivatives y''(x).

interpolate2

public void interpolate2(float[] x,
                float[] y)

Interpolates an array of second derivatives y''(x).

Parameters:

x - array of values at which to interpolate.

y - array of interpolated second derivatives y''(x).

interpolate3

public float[] interpolate3(float[] x)

Returns an array of interpolated third derivatives y'''(x).

Parameters:

x - array of values at which to interpolate.

Returns:

array of interpolated third derivatives y'''(x).

interpolate3

public void interpolate3(float[] x,
                float[] y)

Interpolates an array of third derivatives y'''(x).

Parameters:

x - array of values at which to interpolate.

y - array of interpolated third derivatives y'''(x).

interpolate

public void interpolate(int n,
               float[] x,
               float[] y)

Interpolates an array of function values y(x). Same as interpolate0(int,float[],float[]).

Parameters:

n - number of values to interpolate.

x - array of values at which to interpolate.

y - array of interpolated function values.

interpolate0

public void interpolate0(int n,
                float[] x,
                float[] y)

Interpolates an array of function values y(x).

Parameters:

n - number of values to interpolate.

x - array of values at which to interpolate.

y - array of interpolated function values.

interpolate1

public void interpolate1(int n,
                float[] x,
                float[] y)

Interpolates an array of first derivatives y'(x).

Parameters:

n - number of derivatives to interpolate.

x - array of values at which to interpolate.

y - array of interpolated first derivatives y'(x).

interpolate2

public void interpolate2(int n,
                float[] x,
                float[] y)

Interpolates an array of second derivatives y''(x).

Parameters:

n - number of derivatives to interpolate.

x - array of values at which to interpolate.

y - array of interpolated second derivatives y''(x).

interpolate3

public void interpolate3(int n,
                float[] x,
                float[] y)

Interpolates an array of third derivatives y'''(x).

Parameters:

n - number of derivatives to interpolate.

x - array of values at which to interpolate.

y - array of interpolated third derivatives y'''(x).