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/*
* Copyright (c) 2021, Peter Abeles. All Rights Reserved.
*
* This file is part of BoofCV (http://boofcv.org).
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package boofcv.alg.interpolate.array;
/**
*
* Neville's algorithm for polynomial interpolation and extrapolation. Neville's algorithm improves upon
* Lagrange's formula by avoiding repetitive calculations.
*
*
* See Numerical Recipes Third Edition page 118.
*
*
* @author Peter Abeles
*/
public class PolynomialNeville_F32 extends Interpolate1D_F32 {
private final float[] c;
private final float[] d;
public PolynomialNeville_F32( int maxDegree ) {
super(maxDegree);
c = new float[M];
d = new float[M];
}
public PolynomialNeville_F32( int maxDegree, float x[], float y[], int size ) {
super(maxDegree, x, y, size);
c = new float[M];
d = new float[M];
}
@Override
protected float compute( float sample ) {
int i0 = index0;
// find the index with the smallest difference and set c and b arrays
// to their initial values
int closestIndex = 0;
float smallestDiff = Math.abs(sample - x[i0]);
for (int i = i0; i < i0 + M; i++) {
float diff = Math.abs(sample - x[i]);
if (diff < smallestDiff) {
closestIndex = i - i0;
smallestDiff = diff;
}
c[i - i0] = y[i];
d[i - i0] = y[i];
}
float estimate = y[i0 + closestIndex--];
for (int m = 1; m < M; m++) {
for (int i = 0; i < M - m; i++) {
float ho = x[i0 + i] - sample;
float hp = x[i0 + i + m] - sample;
float w = c[i + 1] - d[i];
float den = ho - hp;
if (den == 0.0) {
throw new RuntimeException("Two x's are identical");
}
den = w/den;
d[i] = hp*den;
c[i] = ho*den;
}
if (2*(closestIndex + 1) < M - m) {
estimate += c[closestIndex + 1];
} else {
estimate += d[closestIndex];
closestIndex--;
}
}
return estimate;
}
}
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