/*
* 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 2.2
* @deprecated To be removed in 4.0 (see MATH-1166).
*/
@Deprecated
public class TricubicSplineInterpolator
implements TrivariateGridInterpolator {
/**
* {@inheritDoc}
*/
public TricubicSplineInterpolatingFunction 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;
// Samples, re-ordered as (z, x, y) and (y, z, x) tuplets
// fvalXY[k][i][j] = f(xval[i], yval[j], zval[k])
// fvalZX[j][k][i] = f(xval[i], yval[j], zval[k])
final double[][][] fvalXY = new double[zLen][xLen][yLen];
final double[][][] fvalZX = new double[yLen][zLen][xLen];
for (int i = 0; i < xLen; i++) {
if (fval[i].length != yLen) {
throw new DimensionMismatchException(fval[i].length, yLen);
}
for (int j = 0; j < yLen; j++) {
if (fval[i][j].length != zLen) {
throw new DimensionMismatchException(fval[i][j].length, zLen);
}
for (int k = 0; k < zLen; k++) {
final double v = fval[i][j][k];
fvalXY[k][i][j] = v;
fvalZX[j][k][i] = v;
}
}
}
final BicubicSplineInterpolator bsi = new BicubicSplineInterpolator(true);
// For each line x[i] (0 <= i < xLen), construct a 2D spline in y and z
final BicubicSplineInterpolatingFunction[] xSplineYZ
= new BicubicSplineInterpolatingFunction[xLen];
for (int i = 0; i < xLen; i++) {
xSplineYZ[i] = bsi.interpolate(yval, zval, fval[i]);
}
// For each line y[j] (0 <= j < yLen), construct a 2D spline in z and x
final BicubicSplineInterpolatingFunction[] ySplineZX
= new BicubicSplineInterpolatingFunction[yLen];
for (int j = 0; j < yLen; j++) {
ySplineZX[j] = bsi.interpolate(zval, xval, fvalZX[j]);
}
// For each line z[k] (0 <= k < zLen), construct a 2D spline in x and y
final BicubicSplineInterpolatingFunction[] zSplineXY
= new BicubicSplineInterpolatingFunction[zLen];
for (int k = 0; k < zLen; k++) {
zSplineXY[k] = bsi.interpolate(xval, yval, fvalXY[k]);
}
// Partial derivatives wrt x and wrt y
final double[][][] dFdX = new double[xLen][yLen][zLen];
final double[][][] dFdY = new double[xLen][yLen][zLen];
final double[][][] d2FdXdY = new double[xLen][yLen][zLen];
for (int k = 0; k < zLen; k++) {
final BicubicSplineInterpolatingFunction f = zSplineXY[k];
for (int i = 0; i < xLen; i++) {
final double x = xval[i];
for (int j = 0; j < yLen; j++) {
final double y = yval[j];
dFdX[i][j][k] = f.partialDerivativeX(x, y);
dFdY[i][j][k] = f.partialDerivativeY(x, y);
d2FdXdY[i][j][k] = f.partialDerivativeXY(x, y);
}
}
}
// Partial derivatives wrt y and wrt z
final double[][][] dFdZ = new double[xLen][yLen][zLen];
final double[][][] d2FdYdZ = new double[xLen][yLen][zLen];
for (int i = 0; i < xLen; i++) {
final BicubicSplineInterpolatingFunction f = xSplineYZ[i];
for (int j = 0; j < yLen; j++) {
final double y = yval[j];
for (int k = 0; k < zLen; k++) {
final double z = zval[k];
dFdZ[i][j][k] = f.partialDerivativeY(y, z);
d2FdYdZ[i][j][k] = f.partialDerivativeXY(y, z);
}
}
}
// Partial derivatives wrt x and wrt z
final double[][][] d2FdZdX = new double[xLen][yLen][zLen];
for (int j = 0; j < yLen; j++) {
final BicubicSplineInterpolatingFunction f = ySplineZX[j];
for (int k = 0; k < zLen; k++) {
final double z = zval[k];
for (int i = 0; i < xLen; i++) {
final double x = xval[i];
d2FdZdX[i][j][k] = f.partialDerivativeXY(z, x);
}
}
}
// Third partial cross-derivatives
final double[][][] d3FdXdYdZ = new double[xLen][yLen][zLen];
for (int i = 0; i < xLen ; i++) {
final int nI = nextIndex(i, xLen);
final int pI = previousIndex(i);
for (int j = 0; j < yLen; j++) {
final int nJ = nextIndex(j, yLen);
final int pJ = previousIndex(j);
for (int k = 0; k < zLen; k++) {
final int nK = nextIndex(k, zLen);
final int pK = previousIndex(k);
// XXX Not sure about this formula
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]) /
((xval[nI] - xval[pI]) * (yval[nJ] - yval[pJ]) * (zval[nK] - zval[pK])) ;
}
}
}
// Create the interpolating splines
return new TricubicSplineInterpolatingFunction(xval, yval, zval, fval,
dFdX, dFdY, dFdZ,
d2FdXdY, d2FdZdX, d2FdYdZ,
d3FdXdYdZ);
}
/**
* Compute the next index of an array, clipping if necessary.
* It is assumed (but not checked) that {@code i} is larger than or equal to 0}.
*
* @param i Index
* @param max Upper limit of the array
* @return the next index
*/
private int nextIndex(int i, int max) {
final int index = i + 1;
return index < max ? index : index - 1;
}
/**
* Compute the previous index of an array, clipping if necessary.
* It is assumed (but not checked) that {@code i} is smaller than the size of the array.
*
* @param i Index
* @return the previous index
*/
private int previousIndex(int i) {
final int index = i - 1;
return index >= 0 ? index : 0;
}
}