org.apache.commons.math3.analysis.BivariateFunction Java Examples

/**
 * Compute all partial derivatives.
 */
private void computePartialDerivatives() {
    final int lastI = xval.length - 1;
    final int lastJ = yval.length - 1;
    partialDerivatives = new BivariateFunction[5][lastI][lastJ];

    for (int i = 0; i < lastI; i++) {
        for (int j = 0; j < lastJ; j++) {
            final BicubicSplineFunction f = splines[i][j];
            partialDerivatives[0][i][j] = f.partialDerivativeX();
            partialDerivatives[1][i][j] = f.partialDerivativeY();
            partialDerivatives[2][i][j] = f.partialDerivativeXX();
            partialDerivatives[3][i][j] = f.partialDerivativeYY();
            partialDerivatives[4][i][j] = f.partialDerivativeXY();
        }
    }
}
 

/**
 * Compute all partial derivatives.
 */
private void computePartialDerivatives() {
    final int lastI = xval.length - 1;
    final int lastJ = yval.length - 1;
    partialDerivatives = new BivariateFunction[5][lastI][lastJ];

    for (int i = 0; i < lastI; i++) {
        for (int j = 0; j < lastJ; j++) {
            final BicubicSplineFunction f = splines[i][j];
            partialDerivatives[0][i][j] = f.partialDerivativeX();
            partialDerivatives[1][i][j] = f.partialDerivativeY();
            partialDerivatives[2][i][j] = f.partialDerivativeXX();
            partialDerivatives[3][i][j] = f.partialDerivativeYY();
            partialDerivatives[4][i][j] = f.partialDerivativeXY();
        }
    }
}
 

/**
 * Compute all partial derivatives.
 */
private void computePartialDerivatives() {
    final int lastI = xval.length - 1;
    final int lastJ = yval.length - 1;
    partialDerivatives = new BivariateFunction[5][lastI][lastJ];

    for (int i = 0; i < lastI; i++) {
        for (int j = 0; j < lastJ; j++) {
            final BicubicSplineFunction f = splines[i][j];
            partialDerivatives[0][i][j] = f.partialDerivativeX();
            partialDerivatives[1][i][j] = f.partialDerivativeY();
            partialDerivatives[2][i][j] = f.partialDerivativeXX();
            partialDerivatives[3][i][j] = f.partialDerivativeYY();
            partialDerivatives[4][i][j] = f.partialDerivativeXY();
        }
    }
}
 

/**
 * Compute all partial derivatives.
 */
private void computePartialDerivatives() {
    final int lastI = xval.length - 1;
    final int lastJ = yval.length - 1;
    partialDerivatives = new BivariateFunction[5][lastI][lastJ];

    for (int i = 0; i < lastI; i++) {
        for (int j = 0; j < lastJ; j++) {
            final BicubicSplineFunction f = splines[i][j];
            partialDerivatives[0][i][j] = f.partialDerivativeX();
            partialDerivatives[1][i][j] = f.partialDerivativeY();
            partialDerivatives[2][i][j] = f.partialDerivativeXX();
            partialDerivatives[3][i][j] = f.partialDerivativeYY();
            partialDerivatives[4][i][j] = f.partialDerivativeXY();
        }
    }
}
 

/**
 * @return the partial derivative wrt {@code y}.
 */
public BivariateFunction partialDerivativeY() {
    if (partialDerivativeY == null) {
        computePartialDerivatives();
    }

    return partialDerivativeY;
}
 

/**
 * Interpolating a paraboloid.
 * <p>
 * z = 2 x<sup>2</sup> - 3 y<sup>2</sup> + 4 x y - 5
 */
@Test
public void testParabaloid() {
    final int numberOfElements = 10;
    final double minimumX = -10;
    final double maximumX = 10;
    final double minimumY = -10;
    final double maximumY = 10;
    final int numberOfSamples = 100;

    final double interpolationTolerance = 2e-14;
    final double maxTolerance = 6e-14;

    // Function values
    BivariateFunction f = new BivariateFunction() {
            public double value(double x, double y) {
                return 2 * x * x - 3 * y * y + 4 * x * y - 5;
            }
        };

    testInterpolation(minimumX,
                      maximumX,
                      minimumY,
                      maximumY,
                      numberOfElements,
                      numberOfSamples,
                      f,
                      interpolationTolerance,
                      maxTolerance);
}
 

/**
 * Interpolating a plane.
 * <p>
 * z = 2 x - 3 y + 5
 */
@Test
public void testPlane() {
    BivariateFunction f = new BivariateFunction() {
            public double value(double x, double y) {
                return 2 * x - 3 * y + 5;
            }
        };

    testInterpolation(3000,
                      1e-13,
                      f,
                      false);
}
 

/**
 * @return the second partial derivative wrt {@code y}.
 */
public BivariateFunction partialDerivativeYY() {
    if (partialDerivativeYY == null) {
        computePartialDerivatives();
    }

    return partialDerivativeYY;
}
 

/**
 * @return the second partial cross-derivative.
 */
public BivariateFunction partialDerivativeXY() {
    if (partialDerivativeXY == null) {
        computePartialDerivatives();
    }

    return partialDerivativeXY;
}
 

/**
 * @return the partial derivative wrt {@code x}.
 */
public BivariateFunction partialDerivativeX() {
    if (partialDerivativeX == null) {
        computePartialDerivatives();
    }

    return partialDerivativeX;
}
 

/**
 * @return the partial derivative wrt {@code x}.
 */
public BivariateFunction partialDerivativeX() {
    if (partialDerivativeX == null) {
        computePartialDerivatives();
    }

    return partialDerivativeX;
}
 

/**
 * @return the partial derivative wrt {@code y}.
 */
public BivariateFunction partialDerivativeY() {
    if (partialDerivativeY == null) {
        computePartialDerivatives();
    }

    return partialDerivativeY;
}
 

/**
 * Make interpolation function for grid data
 *
 * @param x X data
 * @param y Y data
 * @param z Z data
 * @return Interpolation function
 */
public static BivariateFunction getBiInterpFunc(Array x, Array y, Array z) {
    double[] xd = (double[]) ArrayUtil.copyToNDJavaArray_Double(x);
    double[] yd = (double[]) ArrayUtil.copyToNDJavaArray_Double(y);
    double[][] zd = (double[][]) ArrayUtil.copyToNDJavaArray_Double(z);
    BivariateGridInterpolator li = new BicubicInterpolator();
    BivariateFunction func = li.interpolate(xd, yd, zd);

    return func;
}
 

/**
 * @return the second partial derivative wrt {@code y}.
 */
public BivariateFunction partialDerivativeYY() {
    if (partialDerivativeYY == null) {
        computePartialDerivatives();
    }

    return partialDerivativeYY;
}
 

/**
 * @return the second partial cross-derivative.
 */
public BivariateFunction partialDerivativeXY() {
    if (partialDerivativeXY == null) {
        computePartialDerivatives();
    }

    return partialDerivativeXY;
}
 

/**
 * @return the partial derivative wrt {@code x}.
 */
public BivariateFunction partialDerivativeX() {
    if (partialDerivativeX == null) {
        computePartialDerivatives();
    }

    return partialDerivativeX;
}
 

/**
 * @return the second partial derivative wrt {@code x}.
 */
public BivariateFunction partialDerivativeXX() {
    if (partialDerivativeXX == null) {
        computePartialDerivatives();
    }

    return partialDerivativeXX;
}
 

/**
 * @return the second partial derivative wrt {@code y}.
 */
public BivariateFunction partialDerivativeYY() {
    if (partialDerivativeYY == null) {
        computePartialDerivatives();
    }

    return partialDerivativeYY;
}
 

/**
 * @return the second partial cross-derivative.
 */
public BivariateFunction partialDerivativeXY() {
    if (partialDerivativeXY == null) {
        computePartialDerivatives();
    }

    return partialDerivativeXY;
}
 

/**
 * @return the partial derivative wrt {@code y}.
 */
public BivariateFunction partialDerivativeY() {
    if (partialDerivativeY == null) {
        computePartialDerivatives();
    }

    return partialDerivativeY;
}
 

/**
 * @return the partial derivative wrt {@code x}.
 */
public BivariateFunction partialDerivativeX() {
    if (partialDerivativeX == null) {
        computePartialDerivatives();
    }

    return partialDerivativeX;
}
 

/**
 * @return the partial derivative wrt {@code y}.
 */
public BivariateFunction partialDerivativeY() {
    if (partialDerivativeY == null) {
        computePartialDerivatives();
    }

    return partialDerivativeY;
}
 

/**
 * @return the second partial derivative wrt {@code x}.
 */
public BivariateFunction partialDerivativeXX() {
    if (partialDerivativeXX == null) {
        computePartialDerivatives();
    }

    return partialDerivativeXX;
}
 

/**
 * @return the second partial derivative wrt {@code y}.
 */
public BivariateFunction partialDerivativeYY() {
    if (partialDerivativeYY == null) {
        computePartialDerivatives();
    }

    return partialDerivativeYY;
}
 

/**
 * @return the second partial cross-derivative.
 */
public BivariateFunction partialDerivativeXY() {
    if (partialDerivativeXY == null) {
        computePartialDerivatives();
    }

    return partialDerivativeXY;
}
 

/**
 * Interpolating a paraboloid.
 * <p>
 * z = 2 x<sup>2</sup> - 3 y<sup>2</sup> + 4 x y - 5
 */
@Test
public void testParabaloid() {
    final int numberOfElements = 10;
    final double minimumX = -10;
    final double maximumX = 10;
    final double minimumY = -10;
    final double maximumY = 10;
    final int numberOfSamples = 100;

    final double interpolationTolerance = 2e-14;
    final double maxTolerance = 6e-14;

    // Function values
    BivariateFunction f = new BivariateFunction() {
            public double value(double x, double y) {
                return 2 * x * x - 3 * y * y + 4 * x * y - 5;
            }
        };

    testInterpolation(minimumX,
                      maximumX,
                      minimumY,
                      maximumY,
                      numberOfElements,
                      numberOfSamples,
                      f,
                      interpolationTolerance,
                      maxTolerance);
}
 

/**
 * @return the partial derivative wrt {@code y}.
 */
public BivariateFunction partialDerivativeY() {
    if (partialDerivativeY == null) {
        computePartialDerivatives();
    }

    return partialDerivativeY;
}
 

/**
 * @return the second partial derivative wrt {@code x}.
 */
public BivariateFunction partialDerivativeXX() {
    if (partialDerivativeXX == null) {
        computePartialDerivatives();
    }

    return partialDerivativeXX;
}
 

/**
 * @return the second partial derivative wrt {@code y}.
 */
public BivariateFunction partialDerivativeYY() {
    if (partialDerivativeYY == null) {
        computePartialDerivatives();
    }

    return partialDerivativeYY;
}
 

/**
 * @return the second partial cross-derivative.
 */
public BivariateFunction partialDerivativeXY() {
    if (partialDerivativeXY == null) {
        computePartialDerivatives();
    }

    return partialDerivativeXY;
}