Java Code Examples for org.apache.commons.math.util.FastMath#scalb()

The following examples show how to use org.apache.commons.math.util.FastMath#scalb() . You can vote up the ones you like or vote down the ones you don't like, and go to the original project or source file by following the links above each example. You may check out the related API usage on the sidebar.
Example 1
Source File: Math_55_Vector3D_t.java    From coming with MIT License 5 votes vote down vote up 
/** Compute the cross-product of two vectors.
 * @param v1 first vector
 * @param v2 second vector
 * @return the cross product v1 ^ v2 as a new Vector
 */
public static Vector3D crossProduct(final Vector3D v1, final Vector3D v2) {

    final double n1 = v1.getNormSq();
    final double n2 = v2.getNormSq();
    if ((n1 * n2) < MathUtils.SAFE_MIN) {
        return ZERO;
    }

    // rescale both vectors without losing precision,
    // to ensure their norm are the same order of magnitude
    final int deltaExp = (FastMath.getExponent(n1) - FastMath.getExponent(n2)) / 4;
    final double x1    = FastMath.scalb(v1.x, -deltaExp);
    final double y1    = FastMath.scalb(v1.y, -deltaExp);
    final double z1    = FastMath.scalb(v1.z, -deltaExp);
    final double x2    = FastMath.scalb(v2.x,  deltaExp);
    final double y2    = FastMath.scalb(v2.y,  deltaExp);
    final double z2    = FastMath.scalb(v2.z,  deltaExp);

    // we reduce cancellation errors by preconditioning,
    // we replace v1 by v3 = v1 - rho v2 with rho chosen in order to compute
    // v3 without loss of precision. See Kahan lecture
    // "Computing Cross-Products and Rotations in 2- and 3-Dimensional Euclidean Spaces"
    // available at http://www.cs.berkeley.edu/~wkahan/MathH110/Cross.pdf

    // compute rho as an 8 bits approximation of v1.v2 / v2.v2
    final double ratio = (x1 * x2 + y1 * y2 + z1 * z2) / FastMath.scalb(n2, 2 * deltaExp);
    final double rho   = FastMath.rint(256 * ratio) / 256;

    final double x3 = x1 - rho * x2;
    final double y3 = y1 - rho * y2;
    final double z3 = z1 - rho * z2;

    // compute cross product from v3 and v2 instead of v1 and v2
    return new Vector3D(y3 * z2 - z3 * y2, z3 * x2 - x3 * z2, x3 * y2 - y3 * x2);

}
Example 2
Source File: Vector3D_t.java    From coming with MIT License 5 votes vote down vote up 
/** Compute the cross-product of two vectors.
 * @param v1 first vector
 * @param v2 second vector
 * @return the cross product v1 ^ v2 as a new Vector
 */
public static Vector3D crossProduct(final Vector3D v1, final Vector3D v2) {

    final double n1 = v1.getNormSq();
    final double n2 = v2.getNormSq();
    if ((n1 * n2) < MathUtils.SAFE_MIN) {
        return ZERO;
    }

    // rescale both vectors without losing precision,
    // to ensure their norm are the same order of magnitude
    final int deltaExp = (FastMath.getExponent(n1) - FastMath.getExponent(n2)) / 4;
    final double x1    = FastMath.scalb(v1.x, -deltaExp);
    final double y1    = FastMath.scalb(v1.y, -deltaExp);
    final double z1    = FastMath.scalb(v1.z, -deltaExp);
    final double x2    = FastMath.scalb(v2.x,  deltaExp);
    final double y2    = FastMath.scalb(v2.y,  deltaExp);
    final double z2    = FastMath.scalb(v2.z,  deltaExp);

    // we reduce cancellation errors by preconditioning,
    // we replace v1 by v3 = v1 - rho v2 with rho chosen in order to compute
    // v3 without loss of precision. See Kahan lecture
    // "Computing Cross-Products and Rotations in 2- and 3-Dimensional Euclidean Spaces"
    // available at http://www.cs.berkeley.edu/~wkahan/MathH110/Cross.pdf

    // compute rho as an 8 bits approximation of v1.v2 / v2.v2
    final double ratio = (x1 * x2 + y1 * y2 + z1 * z2) / FastMath.scalb(n2, 2 * deltaExp);
    final double rho   = FastMath.rint(256 * ratio) / 256;

    final double x3 = x1 - rho * x2;
    final double y3 = y1 - rho * y2;
    final double z3 = z1 - rho * z2;

    // compute cross product from v3 and v2 instead of v1 and v2
    return new Vector3D(y3 * z2 - z3 * y2, z3 * x2 - x3 * z2, x3 * y2 - y3 * x2);

}
Example 3
Source File: Vector3DTest.java    From astor with GNU General Public License v2.0 5 votes vote down vote up 
@Test
public void testCrossProductCancellation() {
    Vector3D v1 = new Vector3D(9070467121.0, 4535233560.0, 1);
    Vector3D v2 = new Vector3D(9070467123.0, 4535233561.0, 1);
    checkVector(Vector3D.crossProduct(v1, v2), -1, 2, 1);

    double scale    = FastMath.scalb(1.0, 100);
    Vector3D big1   = new Vector3D(scale, v1);
    Vector3D small2 = new Vector3D(1 / scale, v2);
    checkVector(Vector3D.crossProduct(big1, small2), -1, 2, 1);

}
Example 4
Source File: Vector3DTest.java    From astor with GNU General Public License v2.0 5 votes vote down vote up 
@Test
public void testCrossProductCancellation() {
    Vector3D v1 = new Vector3D(9070467121.0, 4535233560.0, 1);
    Vector3D v2 = new Vector3D(9070467123.0, 4535233561.0, 1);
    checkVector(Vector3D.crossProduct(v1, v2), -1, 2, 1);

    double scale    = FastMath.scalb(1.0, 100);
    Vector3D big1   = new Vector3D(scale, v1);
    Vector3D small2 = new Vector3D(1 / scale, v2);
    checkVector(Vector3D.crossProduct(big1, small2), -1, 2, 1);

}