smile.interpolation.AbstractInterpolation Maven / Gradle / Ivy
/*
* Copyright (c) 2010-2021 Haifeng Li. All rights reserved.
*
* Smile is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* Smile is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with Smile. If not, see interpolate to
* decide if to use locate or hunt
* on the next call, which is invisible to the user.
*/
private boolean cor;
/**
* The number of control points.
*/
int n;
/**
* The tabulated control points.
*/
double[] xx;
/**
* The function values at control points.
*/
double[] yy;
/**
* Constructor. Setup for interpolation on a table of x and y.
* The value in x must be monotonic, either increasing or decreasing.
*
* @param x the tabulated points.
* @param y the function values at x.
*/
public AbstractInterpolation(double[] x, double[] y) {
if (x.length != y.length) {
throw new IllegalArgumentException("x and y have different length");
}
this.n = x.length;
if (n < 2) {
throw new IllegalArgumentException("locate size error");
}
this.xx = x;
this.yy = y;
jsav = 0;
cor = false;
dj = Math.min(1, (int) Math.pow(n, 0.25));
}
@Override
public double interpolate(double x) {
int jlo = search(x);
return rawinterp(jlo, x);
}
/**
* Given a value x, return a value j such that x is (insofar as possible)
* centered in the subrange xx[j..j+m-1], where xx is the stored data. The
* returned value is not less than 0, nor greater than n-1, where n is the
* length of xx.
*
* @param x a real number.
* @return the index {@code j} of x in the tabulated points.
*/
protected int search(double x) {
return cor ? hunt(x) : locate(x);
}
/**
* Given a value x, return a value j such that x is (insofar as possible)
* centered in the subrange xx[j..j+m-1], where xx is the stored data. The
* returned value is not less than 0, nor greater than n-1, where n is the
* length of xx. This method employs the bisection algorithm.
*
* @param x a real number.
* @return the index {@code j} of x in the tabulated points.
*/
private int locate(double x) {
int ju, jm, jl;
boolean ascnd = (xx[n - 1] >= xx[0]);
jl = 0;
ju = n - 1;
while (ju - jl > 1) {
jm = (ju + jl) >> 1;
if (x >= xx[jm] == ascnd) {
jl = jm;
} else {
ju = jm;
}
}
cor = Math.abs(jl - jsav) <= dj;
jsav = jl;
return Math.max(0, Math.min(n - 2, jl));
}
/**
* Searches with correlated values. If two calls that
* are close, instead of a full bisection, it anticipates
* that the next call will also be.
*
* Given a value x, return a value j such that x is (insofar as possible)
* centered in the subrange xx[j..j+m-1], where xx is the stored data. The
* returned value is not less than 0, nor greater than n-1, where n is the
* length of xx.
*
* @param x a real number.
* @return the index {@code j} of x in the tabulated points.
*/
private int hunt(double x) {
int jl = jsav, jm, ju, inc = 1;
boolean ascnd = (xx[n - 1] >= xx[0]);
if (jl < 0 || jl > n - 1) {
jl = 0;
ju = n - 1;
} else {
if (x >= xx[jl] == ascnd) {
for (;;) {
ju = jl + inc;
if (ju >= n - 1) {
ju = n - 1;
break;
} else if (x < xx[ju] == ascnd) {
break;
} else {
jl = ju;
inc += inc;
}
}
} else {
ju = jl;
for (;;) {
jl = jl - inc;
if (jl <= 0) {
jl = 0;
break;
} else if (x >= xx[jl] == ascnd) {
break;
} else {
ju = jl;
inc += inc;
}
}
}
}
while (ju - jl > 1) {
jm = (ju + jl) >> 1;
if (x >= xx[jm] == ascnd) {
jl = jm;
} else {
ju = jm;
}
}
cor = Math.abs(jl - jsav) <= dj;
jsav = jl;
return Math.max(0, Math.min(n - 2, jl));
}
/**
* Subclasses provide this as the actual interpolation method.
*
* @param jlo the value jlo is such that x is (insofar as possible)
* centered in the subrange xx[j..j+m-1], where xx is the stored data.
* @param x interpolate at this value
* @return the raw interpolated value.
*/
public abstract double rawinterp(int jlo, double x);
}