Example usage for org.apache.commons.math3.util MathArrays checkOrder

Introduction

In this page you can find the example usage for org.apache.commons.math3.util MathArrays checkOrder.

Prototype

public static void checkOrder(double[] val) throws NonMonotonicSequenceException 

Source Link

Document

Check that the given array is sorted in strictly increasing order.

Usage

From source file:es.uvigo.ei.sing.laimages.core.operations.BilinearInterpolator.java

@Override
public BilinearInterpolatingFunction interpolate(double[] xval, double[] yval, double[][] fval)
        throws NoDataException, DimensionMismatchException, NonMonotonicSequenceException {
    if (xval.length == 0 || yval.length == 0 || fval.length == 0) {
        throw new NoDataException();
    }/*  w ww  . ja  v a  2 s. co  m*/
    if (xval.length != fval.length) {
        throw new DimensionMismatchException(xval.length, fval.length);
    }
    if (yval.length != fval[0].length) {
        throw new DimensionMismatchException(yval.length, fval[0].length);
    }

    MathArrays.checkOrder(xval);
    MathArrays.checkOrder(yval);

    return new BilinearInterpolatingFunction(xval, yval, fval);
}

---

From source file:de.bund.bfr.math.LinearFunction.java

public LinearFunction(double[] x, double[] y) throws NullArgumentException, NoDataException,
        DimensionMismatchException, NonMonotonicSequenceException {
    if (x == null || y == null) {
        throw new NullArgumentException();
    }/*from  w w  w . j  ava2  s . co m*/
    if (x.length == 0 || y.length == 0) {
        throw new NoDataException();
    }
    if (y.length != x.length) {
        throw new DimensionMismatchException(y.length, x.length);
    }
    MathArrays.checkOrder(x);

    abscissa = MathArrays.copyOf(x);
    ordinate = MathArrays.copyOf(y);
}

---

From source file:es.uvigo.ei.sing.laimages.core.operations.BilinearInterpolatingFunction.java

public BilinearInterpolatingFunction(double[] xval, double[] yval, double[][] fval)
        throws DimensionMismatchException, NoDataException, NonMonotonicSequenceException {
    if (xval.length == 0 || yval.length == 0 || fval.length == 0) {
        throw new NoDataException();
    }// w ww .  j  av a 2  s.  c  o m
    if (xval.length != fval.length) {
        throw new DimensionMismatchException(xval.length, fval.length);
    }
    if (yval.length != fval[0].length) {
        throw new DimensionMismatchException(yval.length, fval[0].length);
    }

    MathArrays.checkOrder(xval);
    MathArrays.checkOrder(yval);

    this.xval = xval;
    this.yval = yval;
    this.fval = fval;
}

---

From source file:au.gov.ga.conn4d.utils.BicubicSplineInterpolator.java

/**
 * {@inheritDoc}//  ww w .j av  a2 s . co m
 */
public BicubicSplineInterpolatingFunction interpolate(final double[] xval, final double[] yval,
        final float[][] 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;

    // Samples (first index is y-coordinate, i.e. subarray variable is x)
    // 0 <= i < xval.length
    // 0 <= j < yval.length
    // fX[j][i] = f(xval[i], yval[j])
    final double[][] fX = new double[yLen][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++) {
            fX[j][i] = fval[i][j];
        }
    }

    final SplineInterpolator spInterpolator = new SplineInterpolator();

    // For each line y[j] (0 <= j < yLen), construct a 1D spline with
    // respect to variable x
    final PolynomialSplineFunction[] ySplineX = new PolynomialSplineFunction[yLen];
    for (int j = 0; j < yLen; j++) {
        ySplineX[j] = spInterpolator.interpolate(xval, fX[j]);
    }

    // For each line x[i] (0 <= i < xLen), construct a 1D spline with
    // respect to variable y generated by array fY_1[i]
    final PolynomialSplineFunction[] xSplineY = new PolynomialSplineFunction[xLen];
    for (int i = 0; i < xLen; i++) {
        xSplineY[i] = spInterpolator.interpolate(yval, fval[i]);
    }

    // Partial derivatives with respect to x at the grid knots
    final double[][] dFdX = new double[xLen][yLen];
    for (int j = 0; j < yLen; j++) {
        final UnivariateFunction f = ySplineX[j].derivative();
        for (int i = 0; i < xLen; i++) {
            dFdX[i][j] = f.value(xval[i]);
        }
    }

    // Partial derivatives with respect to y at the grid knots
    final double[][] dFdY = new double[xLen][yLen];
    for (int i = 0; i < xLen; i++) {
        final UnivariateFunction f = xSplineY[i].derivative();
        for (int j = 0; j < yLen; j++) {
            dFdY[i][j] = f.value(yval[j]);
        }
    }

    // Cross partial derivatives
    final double[][] d2FdXdY = new double[xLen][yLen];
    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);
            d2FdXdY[i][j] = (fval[nI][nJ] - fval[nI][pJ] - fval[pI][nJ] + fval[pI][pJ])
                    / ((xval[nI] - xval[pI]) * (yval[nJ] - yval[pJ]));
        }
    }

    // Create the interpolating splines
    return new BicubicSplineInterpolatingFunction(xval, yval, fval, dFdX, dFdY, d2FdXdY);
}

---

From source file:au.gov.ga.conn4d.utils.TricubicSplineInterpolator.java

/**
 * {@inheritDoc}//from   w  w w . j  ava  2 s. co  m
 */
public TricubicSplineInterpolatingFunction interpolate(final double[] zval, final double[] yval,
        final double[] xval, final double[][][] fval)
        throws NoDataException, DimensionMismatchException, NonMonotonicSequenceException {
    if (zval.length == 0 || yval.length == 0 || xval.length == 0 || fval.length == 0) {
        throw new NoDataException();
    }
    if (zval.length != fval.length) {
        throw new DimensionMismatchException(zval.length, fval.length);
    }

    MathArrays.checkOrder(zval);
    MathArrays.checkOrder(yval);

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

    final double[] zzval;
    final double[][][] ffval = new double[zLen][][];

    if (zval[0] > zval[zLen - 1]) {
        zzval = VectorMath.selectionSort(zval);
        for (int i = 0; i < zLen; i++) {
            ffval[i] = fval[zLen - 1 - i];
        }
    } else {
        zzval = zval;
    }

    // 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[xLen][zLen][yLen];
    final double[][][] fvalZX = new double[yLen][xLen][zLen];
    for (int i = 0; i < zLen; i++) {
        if (ffval[i].length != yLen) {
            throw new DimensionMismatchException(ffval[i].length, yLen);
        }

        for (int j = 0; j < yLen; j++) {
            if (ffval[i][j].length != xLen) {
                throw new DimensionMismatchException(ffval[i][j].length, xLen);
            }

            for (int k = 0; k < xLen; k++) {
                final double v = ffval[i][j][k];
                fvalXY[k][i][j] = v;
                fvalZX[j][k][i] = v;
            }
        }
    }

    final BicubicSplineInterpolator bsi = new BicubicSplineInterpolator();

    // For each line x[i] (0 <= i < xLen), construct a 2D spline in y and z
    final BicubicSplineInterpolatingFunction[] xSplineYZ = new BicubicSplineInterpolatingFunction[zLen];
    for (int i = 0; i < zLen; i++) {
        xSplineYZ[i] = bsi.interpolate(yval, xval, ffval[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(xval, zzval, fvalZX[j]);
    }

    // For each line z[k] (0 <= k < zLen), construct a 2D spline in x and y
    final BicubicSplineInterpolatingFunction[] zSplineXY = new BicubicSplineInterpolatingFunction[xLen];
    for (int k = 0; k < xLen; k++) {
        zSplineXY[k] = bsi.interpolate(zzval, yval, fvalXY[k]);
    }

    // Partial derivatives wrt x and wrt y
    final double[][][] dFdX = new double[zLen][yLen][xLen];
    final double[][][] dFdY = new double[zLen][yLen][xLen];
    final double[][][] d2FdXdY = new double[zLen][yLen][xLen];
    for (int k = 0; k < xLen; k++) {
        final BicubicSplineInterpolatingFunction f = zSplineXY[k];
        for (int i = 0; i < zLen; i++) {
            final double z = zzval[i];
            for (int j = 0; j < yLen; j++) {
                final double y = yval[j];
                dFdX[i][j][k] = f.partialDerivativeX(z, y);
                dFdY[i][j][k] = f.partialDerivativeY(z, y);
                d2FdXdY[i][j][k] = f.partialDerivativeXY(z, y);
            }
        }
    }

    // Partial derivatives wrt y and wrt z
    final double[][][] dFdZ = new double[zLen][yLen][xLen];
    final double[][][] d2FdYdZ = new double[zLen][yLen][xLen];
    for (int i = 0; i < zLen; i++) {
        final BicubicSplineInterpolatingFunction f = xSplineYZ[i];
        for (int j = 0; j < yLen; j++) {
            final double y = yval[j];
            for (int k = 0; k < xLen; k++) {
                final double x = xval[k];
                dFdZ[i][j][k] = f.partialDerivativeY(y, x);
                d2FdYdZ[i][j][k] = f.partialDerivativeXY(y, x);
            }
        }
    }

    // Partial derivatives wrt x and wrt z
    final double[][][] d2FdZdX = new double[zLen][yLen][xLen];
    for (int j = 0; j < yLen; j++) {
        final BicubicSplineInterpolatingFunction f = ySplineZX[j];
        for (int k = 0; k < xLen; k++) {
            final double x = xval[k];
            for (int i = 0; i < zLen; i++) {
                final double z = zzval[i];
                d2FdZdX[i][j][k] = f.partialDerivativeXY(x, z);
            }
        }
    }

    // Third partial cross-derivatives
    final double[][][] d3FdXdYdZ = new double[zLen][yLen][xLen];
    for (int i = 0; i < zLen; i++) {
        final int nI = nextIndex(i, zLen);
        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 < xLen; k++) {
                final int nK = nextIndex(k, xLen);
                final int pK = previousIndex(k);

                // XXX Not sure about this formula
                d3FdXdYdZ[i][j][k] = (ffval[nI][nJ][nK] - ffval[nI][pJ][nK] - ffval[pI][nJ][nK]
                        + ffval[pI][pJ][nK] - ffval[nI][nJ][pK] + ffval[nI][pJ][pK] + ffval[pI][nJ][pK]
                        - ffval[pI][pJ][pK])
                        / ((zzval[nI] - zzval[pI]) * (yval[nJ] - yval[pJ]) * (xval[nK] - xval[pK]));
            }
        }
    }

    // Create the interpolating splines
    return new TricubicSplineInterpolatingFunction(zzval, yval, xval, ffval, dFdX, dFdY, dFdZ, d2FdXdY, d2FdZdX,
            d2FdYdZ, d3FdXdYdZ);
}

---

From source file:au.gov.ga.conn4d.utils.SplineInterpolator.java

/**
 * Computes an interpolating function for the data set.
 * /*from  w w w  .  j ava2 s . co m*/
 * @param x
 *            the arguments for the interpolation points
 * @param y
 *            the values for the interpolation points
 * @return a function which interpolates the data set
 * @throws DimensionMismatchException
 *             if {@code x} and {@code y} have different sizes.
 * @throws NonMonotonicSequenceException
 *             if {@code x} is not sorted in strict increasing order.
 * @throws NumberIsTooSmallException
 *             if the size of {@code x} is smaller than 3.
 */
public PolynomialSplineFunction interpolate(double x[], double y[])
        throws DimensionMismatchException, NumberIsTooSmallException, NonMonotonicSequenceException {
    if (x.length != y.length) {
        throw new DimensionMismatchException(x.length, y.length);
    }

    if (x.length < 3) {
        throw new NumberIsTooSmallException(LocalizedFormats.NUMBER_OF_POINTS, x.length, 3, true);
    }

    // Number of intervals. The number of data points is n + 1.
    final int n = x.length - 1;

    MathArrays.checkOrder(x);

    // Differences between knot points
    final double h[] = new double[n];
    for (int i = 0; i < n; i++) {
        h[i] = x[i + 1] - x[i];
    }

    final double mu[] = new double[n];
    final double z[] = new double[n + 1];
    mu[0] = 0d;
    z[0] = 0d;
    double g = 0;
    for (int i = 1; i < n; i++) {
        g = 2d * (x[i + 1] - x[i - 1]) - h[i - 1] * mu[i - 1];
        mu[i] = h[i] / g;
        z[i] = (3d * (y[i + 1] * h[i - 1] - y[i] * (x[i + 1] - x[i - 1]) + y[i - 1] * h[i]) / (h[i - 1] * h[i])
                - h[i - 1] * z[i - 1]) / g;
    }

    // cubic spline coefficients -- b is linear, c quadratic, d is cubic
    // (original y's are constants)
    final double b[] = new double[n];
    final double c[] = new double[n + 1];
    final double d[] = new double[n];

    z[n] = 0d;
    c[n] = 0d;

    for (int j = n - 1; j >= 0; j--) {
        c[j] = z[j] - mu[j] * c[j + 1];
        b[j] = (y[j + 1] - y[j]) / h[j] - h[j] * (c[j + 1] + 2d * c[j]) / 3d;
        d[j] = (c[j + 1] - c[j]) / (3d * h[j]);
    }

    final PolynomialFunction polynomials[] = new PolynomialFunction[n];
    final double coefficients[] = new double[4];
    for (int i = 0; i < n; i++) {
        coefficients[0] = y[i];
        coefficients[1] = b[i];
        coefficients[2] = c[i];
        coefficients[3] = d[i];
        polynomials[i] = new PolynomialFunction(coefficients);
    }

    return new PolynomialSplineFunction(x, polynomials);
}

---

From source file:au.gov.ga.conn4d.utils.BicubicSplineInterpolator.java

public BicubicSplineInterpolatingFunction 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();
    }//from   w  w  w  . ja v  a2s. c  om
    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;

    // Samples (first index is y-coordinate, i.e. subarray variable is x)
    // 0 <= i < xval.length
    // 0 <= j < yval.length
    // fX[j][i] = f(xval[i], yval[j])
    final double[][] fX = new double[yLen][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++) {
            fX[j][i] = fval[i][j];
        }
    }

    final SplineInterpolator spInterpolator = new SplineInterpolator();

    // For each line y[j] (0 <= j < yLen), construct a 1D spline with
    // respect to variable x
    final PolynomialSplineFunction[] ySplineX = new PolynomialSplineFunction[yLen];
    for (int j = 0; j < yLen; j++) {
        ySplineX[j] = spInterpolator.interpolate(xval, fX[j]);
    }

    // For each line x[i] (0 <= i < xLen), construct a 1D spline with
    // respect to variable y generated by array fY_1[i]
    final PolynomialSplineFunction[] xSplineY = new PolynomialSplineFunction[xLen];
    for (int i = 0; i < xLen; i++) {
        xSplineY[i] = spInterpolator.interpolate(yval, fval[i]);
    }

    // Partial derivatives with respect to x at the grid knots
    final double[][] dFdX = new double[xLen][yLen];
    for (int j = 0; j < yLen; j++) {
        final UnivariateFunction f = ySplineX[j].derivative();
        for (int i = 0; i < xLen; i++) {
            dFdX[i][j] = f.value(xval[i]);
        }
    }

    // Partial derivatives with respect to y at the grid knots
    final double[][] dFdY = new double[xLen][yLen];
    for (int i = 0; i < xLen; i++) {
        final UnivariateFunction f = xSplineY[i].derivative();
        for (int j = 0; j < yLen; j++) {
            dFdY[i][j] = f.value(yval[j]);
        }
    }

    // Cross partial derivatives
    final double[][] d2FdXdY = new double[xLen][yLen];
    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);
            d2FdXdY[i][j] = (fval[nI][nJ] - fval[nI][pJ] - fval[pI][nJ] + fval[pI][pJ])
                    / ((xval[nI] - xval[pI]) * (yval[nJ] - yval[pJ]));
        }
    }

    // Create the interpolating splines
    return new BicubicSplineInterpolatingFunction(xval, yval, fval, dFdX, dFdY, d2FdXdY);
}

---

From source file:au.gov.ga.conn4d.utils.BicubicSplineInterpolatingFunction.java

/**
 * @param x Sample values of the x-coordinate, in increasing order.
 * @param y Sample values of the y-coordinate, in increasing order.
 * @param f Values of the function on every grid point.
 * @param dFdX Values of the partial derivative of function with respect
 * to x on every grid point.//from   w w w.j av a 2 s . co m
 * @param dFdY Values of the partial derivative of function with respect
 * to y on every grid point.
 * @param d2FdXdY Values of the cross partial derivative of function on
 * every grid point.
 * @throws DimensionMismatchException if the various arrays do not contain
 * the expected number of elements.
 * @throws NonMonotonicSequenceException if {@code x} or {@code y} are
 * not strictly increasing.
 * @throws NoDataException if any of the arrays has zero length.
 */
public BicubicSplineInterpolatingFunction(double[] x, double[] y, float[][] f, double[][] dFdX, double[][] dFdY,
        double[][] d2FdXdY) throws DimensionMismatchException, NoDataException, NonMonotonicSequenceException {
    final int xLen = x.length;
    final int yLen = y.length;

    if (xLen == 0 || yLen == 0 || f.length == 0 || f[0].length == 0) {
        throw new NoDataException();
    }
    if (xLen != f.length) {
        throw new DimensionMismatchException(xLen, f.length);
    }
    if (xLen != dFdX.length) {
        throw new DimensionMismatchException(xLen, dFdX.length);
    }
    if (xLen != dFdY.length) {
        throw new DimensionMismatchException(xLen, dFdY.length);
    }
    if (xLen != d2FdXdY.length) {
        throw new DimensionMismatchException(xLen, d2FdXdY.length);
    }

    MathArrays.checkOrder(x);
    MathArrays.checkOrder(y);

    xval = x.clone();
    yval = y.clone();

    final int lastI = xLen - 1;
    final int lastJ = yLen - 1;
    splines = new BicubicSplineFunction[lastI][lastJ];

    for (int i = 0; i < lastI; i++) {
        if (f[i].length != yLen) {
            throw new DimensionMismatchException(f[i].length, yLen);
        }
        if (dFdX[i].length != yLen) {
            throw new DimensionMismatchException(dFdX[i].length, yLen);
        }
        if (dFdY[i].length != yLen) {
            throw new DimensionMismatchException(dFdY[i].length, yLen);
        }
        if (d2FdXdY[i].length != yLen) {
            throw new DimensionMismatchException(d2FdXdY[i].length, yLen);
        }
        final int ip1 = i + 1;
        for (int j = 0; j < lastJ; j++) {
            final int jp1 = j + 1;
            final double[] beta = new double[] { f[i][j], f[ip1][j], f[i][jp1], f[ip1][jp1], dFdX[i][j],
                    dFdX[ip1][j], dFdX[i][jp1], dFdX[ip1][jp1], dFdY[i][j], dFdY[ip1][j], dFdY[i][jp1],
                    dFdY[ip1][jp1], d2FdXdY[i][j], d2FdXdY[ip1][j], d2FdXdY[i][jp1], d2FdXdY[ip1][jp1] };

            splines[i][j] = new BicubicSplineFunction(computeSplineCoefficients(beta));
        }
    }
}

---

From source file:au.gov.ga.conn4d.utils.SplineInterpolator.java

public PolynomialSplineFunction interpolate(double x[], float y[])
        throws DimensionMismatchException, NumberIsTooSmallException, NonMonotonicSequenceException {
    if (x.length != y.length) {
        throw new DimensionMismatchException(x.length, y.length);
    }//from   ww w. j a  v a  2 s.c  om

    if (x.length < 3) {
        throw new NumberIsTooSmallException(LocalizedFormats.NUMBER_OF_POINTS, x.length, 3, true);
    }

    // Number of intervals. The number of data points is n + 1.
    final int n = x.length - 1;

    MathArrays.checkOrder(x);

    // Differences between knot points
    final double h[] = new double[n];
    for (int i = 0; i < n; i++) {
        h[i] = x[i + 1] - x[i];
    }

    final double mu[] = new double[n];
    final double z[] = new double[n + 1];
    mu[0] = 0d;
    z[0] = 0d;
    double g = 0;
    for (int i = 1; i < n; i++) {
        g = 2d * (x[i + 1] - x[i - 1]) - h[i - 1] * mu[i - 1];
        mu[i] = h[i] / g;
        z[i] = (3d * (y[i + 1] * h[i - 1] - y[i] * (x[i + 1] - x[i - 1]) + y[i - 1] * h[i]) / (h[i - 1] * h[i])
                - h[i - 1] * z[i - 1]) / g;
    }

    // cubic spline coefficients -- b is linear, c quadratic, d is cubic
    // (original y's are constants)
    final double b[] = new double[n];
    final double c[] = new double[n + 1];
    final double d[] = new double[n];

    z[n] = 0d;
    c[n] = 0d;

    for (int j = n - 1; j >= 0; j--) {
        c[j] = z[j] - mu[j] * c[j + 1];
        b[j] = (y[j + 1] - y[j]) / h[j] - h[j] * (c[j + 1] + 2d * c[j]) / 3d;
        d[j] = (c[j + 1] - c[j]) / (3d * h[j]);
    }

    final PolynomialFunction polynomials[] = new PolynomialFunction[n];
    final double coefficients[] = new double[4];
    for (int i = 0; i < n; i++) {
        coefficients[0] = y[i];
        coefficients[1] = b[i];
        coefficients[2] = c[i];
        coefficients[3] = d[i];
        polynomials[i] = new PolynomialFunction(coefficients);
    }

    return new PolynomialSplineFunction(x, polynomials);
}

---

From source file:au.gov.ga.conn4d.utils.TricubicSplineInterpolator.java

public TricubicSplineInterpolatingFunction interpolate(final double[] zval, final double[] yval,
        final double[] xval, final float[][][] fval)
        throws NoDataException, DimensionMismatchException, NonMonotonicSequenceException {
    if (zval.length == 0 || yval.length == 0 || xval.length == 0 || fval.length == 0) {
        throw new NoDataException();
    }// w  w w .  j a va  2 s .c o  m
    if (zval.length != fval.length) {
        throw new DimensionMismatchException(zval.length, fval.length);
    }

    MathArrays.checkOrder(yval);
    MathArrays.checkOrder(xval);

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

    final double[] zzval;
    float[][][] ffval = new float[zLen][][];

    if (zval[0] > zval[zLen - 1]) {
        zzval = VectorMath.selectionSort(zval);
        for (int i = 0; i < zLen; i++) {
            ffval[i] = fval[zLen - 1 - i];
        }
    } else {
        zzval = zval;
        ffval = fval;
    }

    // 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[xLen][zLen][yLen];
    final double[][][] fvalZX = new double[yLen][xLen][zLen];
    for (int i = 0; i < zLen; i++) {
        if (ffval[i].length != yLen) {
            throw new DimensionMismatchException(ffval[i].length, yLen);
        }

        for (int j = 0; j < yLen; j++) {
            if (ffval[i][j].length != xLen) {
                throw new DimensionMismatchException(ffval[i][j].length, xLen);
            }

            for (int k = 0; k < xLen; k++) {
                final double v = ffval[i][j][k];
                fvalXY[k][i][j] = v;
                fvalZX[j][k][i] = v;
            }
        }
    }

    final BicubicSplineInterpolator bsi = new BicubicSplineInterpolator();

    // For each line x[i] (0 <= i < xLen), construct a 2D spline in y and z
    final BicubicSplineInterpolatingFunction[] xSplineYZ = new BicubicSplineInterpolatingFunction[zLen];
    for (int i = 0; i < zLen; i++) {
        xSplineYZ[i] = bsi.interpolate(yval, xval, ffval[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(xval, zzval, fvalZX[j]);
    }

    // For each line z[k] (0 <= k < zLen), construct a 2D spline in x and y
    final BicubicSplineInterpolatingFunction[] zSplineXY = new BicubicSplineInterpolatingFunction[xLen];
    for (int k = 0; k < xLen; k++) {
        zSplineXY[k] = bsi.interpolate(zzval, yval, fvalXY[k]);
    }

    // Partial derivatives wrt x and wrt y
    final double[][][] dFdX = new double[zLen][yLen][xLen];
    final double[][][] dFdY = new double[zLen][yLen][xLen];
    final double[][][] d2FdXdY = new double[zLen][yLen][xLen];
    for (int k = 0; k < xLen; k++) {
        final BicubicSplineInterpolatingFunction f = zSplineXY[k];
        for (int i = 0; i < zLen; i++) {
            final double x = zzval[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[zLen][yLen][xLen];
    final double[][][] d2FdYdZ = new double[zLen][yLen][xLen];
    for (int i = 0; i < zLen; i++) {
        final BicubicSplineInterpolatingFunction f = xSplineYZ[i];
        for (int j = 0; j < yLen; j++) {
            final double y = yval[j];
            for (int k = 0; k < xLen; k++) {
                final double z = xval[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[zLen][yLen][xLen];
    for (int j = 0; j < yLen; j++) {
        final BicubicSplineInterpolatingFunction f = ySplineZX[j];
        for (int k = 0; k < xLen; k++) {
            final double z = xval[k];
            for (int i = 0; i < zLen; i++) {
                final double x = zzval[i];
                d2FdZdX[i][j][k] = f.partialDerivativeXY(z, x);
            }
        }
    }

    // Third partial cross-derivatives
    final double[][][] d3FdXdYdZ = new double[zLen][yLen][xLen];
    for (int i = 0; i < zLen; i++) {
        final int nI = nextIndex(i, zLen);
        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 < xLen; k++) {
                final int nK = nextIndex(k, xLen);
                final int pK = previousIndex(k);

                // XXX Not sure about this formula
                d3FdXdYdZ[i][j][k] = (ffval[nI][nJ][nK] - ffval[nI][pJ][nK] - ffval[pI][nJ][nK]
                        + ffval[pI][pJ][nK] - ffval[nI][nJ][pK] + ffval[nI][pJ][pK] + ffval[pI][nJ][pK]
                        - ffval[pI][pJ][pK])
                        / ((zzval[nI] - zzval[pI]) * (yval[nJ] - yval[pJ]) * (xval[nK] - xval[pK]));
            }
        }
    }

    // Create the interpolating splines
    return new TricubicSplineInterpolatingFunction(zzval, yval, xval, ffval, dFdX, dFdY, dFdZ, d2FdXdY, d2FdZdX,
            d2FdYdZ, d3FdXdYdZ);
}

---

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