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/*
* Licensed to the Apache Software Foundation (ASF) under one or more
* contributor license agreements. See the NOTICE file distributed with
* this work for additional information regarding copyright ownership.
* The ASF licenses this file to You 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 org.apache.commons.math3.analysis.interpolation;
import org.apache.commons.math3.exception.DimensionMismatchException;
import org.apache.commons.math3.exception.NoDataException;
import org.apache.commons.math3.exception.NonMonotonicSequenceException;
import org.apache.commons.math3.exception.NumberIsTooSmallException;
import org.apache.commons.math3.util.MathArrays;
/**
* Generates a tricubic interpolating function.
*
* @since 3.4
*/
public class TricubicInterpolator
implements TrivariateGridInterpolator {
/**
* {@inheritDoc}
*/
public TricubicInterpolatingFunction interpolate(final double[] xval,
final double[] yval,
final double[] zval,
final double[][][] fval)
throws NoDataException, NumberIsTooSmallException,
DimensionMismatchException, NonMonotonicSequenceException {
if (xval.length == 0 || yval.length == 0 || zval.length == 0 || fval.length == 0) {
throw new NoDataException();
}
if (xval.length != fval.length) {
throw new DimensionMismatchException(xval.length, fval.length);
}
MathArrays.checkOrder(xval);
MathArrays.checkOrder(yval);
MathArrays.checkOrder(zval);
final int xLen = xval.length;
final int yLen = yval.length;
final int zLen = zval.length;
// Approximation to the partial derivatives using finite differences.
final double[][][] dFdX = new double[xLen][yLen][zLen];
final double[][][] dFdY = new double[xLen][yLen][zLen];
final double[][][] dFdZ = new double[xLen][yLen][zLen];
final double[][][] d2FdXdY = new double[xLen][yLen][zLen];
final double[][][] d2FdXdZ = new double[xLen][yLen][zLen];
final double[][][] d2FdYdZ = new double[xLen][yLen][zLen];
final double[][][] d3FdXdYdZ = new double[xLen][yLen][zLen];
for (int i = 1; i < xLen - 1; i++) {
if (yval.length != fval[i].length) {
throw new DimensionMismatchException(yval.length, fval[i].length);
}
final int nI = i + 1;
final int pI = i - 1;
final double nX = xval[nI];
final double pX = xval[pI];
final double deltaX = nX - pX;
for (int j = 1; j < yLen - 1; j++) {
if (zval.length != fval[i][j].length) {
throw new DimensionMismatchException(zval.length, fval[i][j].length);
}
final int nJ = j + 1;
final int pJ = j - 1;
final double nY = yval[nJ];
final double pY = yval[pJ];
final double deltaY = nY - pY;
final double deltaXY = deltaX * deltaY;
for (int k = 1; k < zLen - 1; k++) {
final int nK = k + 1;
final int pK = k - 1;
final double nZ = zval[nK];
final double pZ = zval[pK];
final double deltaZ = nZ - pZ;
dFdX[i][j][k] = (fval[nI][j][k] - fval[pI][j][k]) / deltaX;
dFdY[i][j][k] = (fval[i][nJ][k] - fval[i][pJ][k]) / deltaY;
dFdZ[i][j][k] = (fval[i][j][nK] - fval[i][j][pK]) / deltaZ;
final double deltaXZ = deltaX * deltaZ;
final double deltaYZ = deltaY * deltaZ;
d2FdXdY[i][j][k] = (fval[nI][nJ][k] - fval[nI][pJ][k] - fval[pI][nJ][k] + fval[pI][pJ][k]) / deltaXY;
d2FdXdZ[i][j][k] = (fval[nI][j][nK] - fval[nI][j][pK] - fval[pI][j][nK] + fval[pI][j][pK]) / deltaXZ;
d2FdYdZ[i][j][k] = (fval[i][nJ][nK] - fval[i][nJ][pK] - fval[i][pJ][nK] + fval[i][pJ][pK]) / deltaYZ;
final double deltaXYZ = deltaXY * deltaZ;
d3FdXdYdZ[i][j][k] = (fval[nI][nJ][nK] - fval[nI][pJ][nK] -
fval[pI][nJ][nK] + fval[pI][pJ][nK] -
fval[nI][nJ][pK] + fval[nI][pJ][pK] +
fval[pI][nJ][pK] - fval[pI][pJ][pK]) / deltaXYZ;
}
}
}
// Create the interpolating function.
return new TricubicInterpolatingFunction(xval, yval, zval, fval,
dFdX, dFdY, dFdZ,
d2FdXdY, d2FdXdZ, d2FdYdZ,
d3FdXdYdZ) {
/** {@inheritDoc} */
@Override
public boolean isValidPoint(double x, double y, double z) {
if (x < xval[1] ||
x > xval[xval.length - 2] ||
y < yval[1] ||
y > yval[yval.length - 2] ||
z < zval[1] ||
z > zval[zval.length - 2]) {
return false;
} else {
return true;
}
}
};
}
}
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