/*
 * 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 bicubic interpolating
function. 
 Caveat: Because the interpolation scheme requires that derivatives be specified at the sample points, those are approximated with finite differences (using the 2-points symmetric formulae). Since their values are undefined at the borders of the provided interpolation ranges, the interpolated values will be wrong at the edges of the patch. The interpolate method will return a function that overrides BicubicInterpolatingFunction.isValidPoint(double, double) to indicate points where the interpolation will be inaccurate. 
Since:
3.4/**
 * Generates a {@link BicubicInterpolatingFunction bicubic interpolating
 * function}.
 * <p>
 *  Caveat: Because the interpolation scheme requires that derivatives be
 *  specified at the sample points, those are approximated with finite
 *  differences (using the 2-points symmetric formulae).
 *  Since their values are undefined at the borders of the provided
 *  interpolation ranges, the interpolated values will be wrong at the
 *  edges of the patch.
 *  The {@code interpolate} method will return a function that overrides
 *  {@link BicubicInterpolatingFunction#isValidPoint(double,double)} to
 *  indicate points where the interpolation will be inaccurate.
 * </p>
 *
 * @since 3.4
 */
public class BicubicInterpolator
    implements BivariateGridInterpolator {
    
{@inheritDoc}
/**
     * {@inheritDoc}
     */
    public BicubicInterpolatingFunction interpolate(final double[] xval,
                                                    final double[] yval,
                                                    final double[][] fval)
        throws NoDataException, DimensionMismatchException,
               NonMonotonicSequenceException, NumberIsTooSmallException {
        if (xval.length == 0 || yval.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);

        final int xLen = xval.length;
        final int yLen = yval.length;

        // Approximation to the partial derivatives using finite differences.
        final double[][] dFdX = new double[xLen][yLen];
        final double[][] dFdY = new double[xLen][yLen];
        final double[][] d2FdXdY = new double[xLen][yLen];
        for (int i = 1; i < xLen - 1; i++) {
            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++) {
                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;

                dFdX[i][j] = (fval[nI][j] - fval[pI][j]) / deltaX;
                dFdY[i][j] = (fval[i][nJ] - fval[i][pJ]) / deltaY;

                final double deltaXY = deltaX * deltaY;

                d2FdXdY[i][j] = (fval[nI][nJ] - fval[nI][pJ] - fval[pI][nJ] + fval[pI][pJ]) / deltaXY;
            }
        }

        // Create the interpolating function.
        return new BicubicInterpolatingFunction(xval, yval, fval,
                                                dFdX, dFdY, d2FdXdY) {
            
{@inheritDoc} /** {@inheritDoc} */
            @Override
            public boolean isValidPoint(double x, double y) {
                if (x < xval[1] ||
                    x > xval[xval.length - 2] ||
                    y < yval[1] ||
                    y > yval[yval.length - 2]) {
                    return false;
                } else {
                    return true;
                }
            }
        };
    }
}