Java FastMath.abs方法代碼示例

import org.apache.commons.math3.util.FastMath; //導入方法依賴的package包/類
private double updateP (double duration, double[] p, double[] pDot, double[] pDotDot, double[] pDotDotDot){
	double max_dotdotdot = 0.0;
	for (int i = 0; i < (p.length-1); i++){
		if (FastMath.abs(pDotDotDot[i]) > max_dotdotdot)
			max_dotdotdot = FastMath.abs(pDotDotDot[i]);
	}
			
	double timeStep = FastMath.min(FastMath.pow((epsilon*6/max_dotdotdot), 1.0/3), FastMath.min(duration, max_step));

	double timeStepSquare = timeStep*timeStep*0.5;
	for (int i = 0; i < (p.length-1); i++){
		double new_val = p[i] + pDot[i]*timeStep + pDotDot[i]*timeStepSquare;
		double diff = FastMath.abs(new_val - p[i]);
		while (new_val > 1 || new_val < 0 || diff>0.2){
			timeStep *= 0.9;
			timeStepSquare = timeStep*timeStep*0.5;
			new_val = p[i] + pDot[i]*timeStep + pDotDot[i]*timeStepSquare;
			diff = FastMath.abs(new_val - p[i]);
		}			
	}
	doUpdating(timeStep, timeStepSquare, p, pDot, pDotDot);
	duration -= timeStep;
	return duration;
	
	
}
 

import org.apache.commons.math3.util.FastMath; //導入方法依賴的package包/類
public ValueType nthRoot(CalculatedValue g, int n)
{
    try
    {
        final List<Complex> roots = g.getComplex().nthRoot(n);
        for (Complex root : roots)
        {
            if (FastMath.abs(root.getImaginary()) < 1E-15)
            {
                return setValue(root.getReal());
            }
        }
        if (!roots.isEmpty())
        {
            return setComplexValue(roots.get(0));
        }
    }
    catch (Exception ex)
    {
        // nothing to do
    }
    return invalidate(ErrorType.NOT_A_NUMBER);
}
 

import org.apache.commons.math3.util.FastMath; //導入方法依賴的package包/類
/**Solve  a  system of composed of a Lower Triangular Matrix
 * {@link RealMatrix}.
 * <p>
 * This method is called to solve systems of equations which are
 * of the lower triangular form. The matrix {@link RealMatrix}
 * is assumed, though not checked, to be in lower triangular form.
 * The vector {@link RealVector} is overwritten with the solution.
 * The matrix is checked that it is square and its dimensions match
 * the length of the vector.
 * </p>
 * @param rm RealMatrix which is lower triangular
 * @param b  RealVector this is overwritten
 * @throws DimensionMismatchException if the matrix and vector are not
 * conformable
 * @throws NonSquareMatrixException if the matrix {@code rm} is not square
 * @throws MathArithmeticException if the absolute value of one of the diagonal
 * coefficient of {@code rm} is lower than {@link Precision#SAFE_MIN}
 */
public static void solveLowerTriangularSystem(RealMatrix rm, RealVector b)
    throws DimensionMismatchException, MathArithmeticException,
    NonSquareMatrixException {
    if ((rm == null) || (b == null) || ( rm.getRowDimension() != b.getDimension())) {
        throw new DimensionMismatchException(
                (rm == null) ? 0 : rm.getRowDimension(),
                (b == null) ? 0 : b.getDimension());
    }
    if( rm.getColumnDimension() != rm.getRowDimension() ){
        throw new NonSquareMatrixException(rm.getRowDimension(),
                                           rm.getColumnDimension());
    }
    int rows = rm.getRowDimension();
    for( int i = 0 ; i < rows ; i++ ){
        double diag = rm.getEntry(i, i);
        if( FastMath.abs(diag) < Precision.SAFE_MIN ){
            throw new MathArithmeticException(LocalizedFormats.ZERO_DENOMINATOR);
        }
        double bi = b.getEntry(i)/diag;
        b.setEntry(i,  bi );
        for( int j = i+1; j< rows; j++ ){
            b.setEntry(j, b.getEntry(j)-bi*rm.getEntry(j,i)  );
        }
    }
}
 

import org.apache.commons.math3.util.FastMath; //導入方法依賴的package包/類
/** Get the cell to which a point belongs.
 * <p>If the returned cell is a leaf node the points belongs to the
 * interior of the node, if the cell is an internal node the points
 * belongs to the node cut sub-hyperplane.</p>
 * @param point point to check
 * @param tolerance tolerance below which points close to a cut hyperplane
 * are considered to belong to the hyperplane itself
 * @return the tree cell to which the point belongs
 */
public BSPTree<S> getCell(final Point<S> point, final double tolerance) {

    if (cut == null) {
        return this;
    }

    // position of the point with respect to the cut hyperplane
    final double offset = cut.getHyperplane().getOffset(point);

    if (FastMath.abs(offset) < tolerance) {
        return this;
    } else if (offset <= 0) {
        // point is on the minus side of the cut hyperplane
        return minus.getCell(point, tolerance);
    } else {
        // point is on the plus side of the cut hyperplane
        return plus.getCell(point, tolerance);
    }

}
 

import org.apache.commons.math3.util.FastMath; //導入方法依賴的package包/類
private double updateP (double duration, double[] p, double[] pDot, double[] pDotDot, double[] pDotDotDot) throws Exception{
	double max_dotdotdot = 0.0;
	for (int i = 0; i < p.length; i++){
		if (FastMath.abs(pDotDotDot[i]) > max_dotdotdot)
			max_dotdotdot = FastMath.abs(pDotDotDot[i]);
	}
	
	double timeStep = FastMath.min(FastMath.pow((epsilon*6/max_dotdotdot), 1.0/3), FastMath.min(duration, max_step));

	double timeStepSquare = timeStep*timeStep*0.5;
	for (int i = 0; i < p.length; i++){
		double new_val = p[i] + pDot[i]*timeStep + pDotDot[i]*timeStepSquare;
		double diff = FastMath.abs(new_val - p[i]);
		while (new_val > 1 || new_val < 0 || diff>0.2){
			timeStep *= 0.9;
			if (timeStep<1e-32){
				System.out.println("values are " + p[i] + " " + pDot[i]  + " " + pDotDot[i] + " " + pDotDotDot[i]);
				System.out.println("index is " + i + " of " + p.length + " " + lineages*states);
				System.out.println("minimum step size of 1e-32 reached");
				throw new Exception("error in the calculation of transition probabilities");
			}
			timeStepSquare = timeStep*timeStep*0.5;
			new_val = p[i] + pDot[i]*timeStep + pDotDot[i]*timeStepSquare;
			diff = FastMath.abs(new_val - p[i]);
		}			
	}
	doUpdating(timeStep, timeStepSquare, p, pDot, pDotDot);
	duration -= timeStep;
	return duration;		
}
 

import org.apache.commons.math3.util.FastMath; //導入方法依賴的package包/類
/** Get the intersection point of three planes.
 * @param plane1 first plane1
 * @param plane2 second plane2
 * @param plane3 third plane2
 * @return intersection point of three planes, null if some planes are parallel
 */
public static Vector3D intersection(final Plane plane1, final Plane plane2, final Plane plane3) {

    // coefficients of the three planes linear equations
    final double a1 = plane1.w.getX();
    final double b1 = plane1.w.getY();
    final double c1 = plane1.w.getZ();
    final double d1 = plane1.originOffset;

    final double a2 = plane2.w.getX();
    final double b2 = plane2.w.getY();
    final double c2 = plane2.w.getZ();
    final double d2 = plane2.originOffset;

    final double a3 = plane3.w.getX();
    final double b3 = plane3.w.getY();
    final double c3 = plane3.w.getZ();
    final double d3 = plane3.originOffset;

    // direct Cramer resolution of the linear system
    // (this is still feasible for a 3x3 system)
    final double a23         = b2 * c3 - b3 * c2;
    final double b23         = c2 * a3 - c3 * a2;
    final double c23         = a2 * b3 - a3 * b2;
    final double determinant = a1 * a23 + b1 * b23 + c1 * c23;
    if (FastMath.abs(determinant) < 1.0e-10) {
        return null;
    }

    final double r = 1.0 / determinant;
    return new Vector3D(
                        (-a23 * d1 - (c1 * b3 - c3 * b1) * d2 - (c2 * b1 - c1 * b2) * d3) * r,
                        (-b23 * d1 - (c3 * a1 - c1 * a3) * d2 - (c1 * a2 - c2 * a1) * d3) * r,
                        (-c23 * d1 - (b1 * a3 - b3 * a1) * d2 - (b2 * a1 - b1 * a2) * d3) * r);

}
 

import org.apache.commons.math3.util.FastMath; //導入方法依賴的package包/類
/** {@inheritDoc} */
public boolean isNonSingular() {
    for (double diag : rDiag) {
        if (FastMath.abs(diag) <= threshold) {
            return false;
        }
    }
    return true;
}
 

import org.apache.commons.math3.util.FastMath; //導入方法依賴的package包/類
/** {@inheritDoc} */
public double distance1(Vector<Euclidean2D> p) {
    Vector2D p3 = (Vector2D) p;
    final double dx = FastMath.abs(p3.x - x);
    final double dy = FastMath.abs(p3.y - y);
    return dx + dy;
}
 

import org.apache.commons.math3.util.FastMath; //導入方法依賴的package包/類
/** {@inheritDoc} */
public double distance1(Vector<Euclidean3D> v) {
    final Vector3D v3 = (Vector3D) v;
    final double dx = FastMath.abs(v3.x - x);
    final double dy = FastMath.abs(v3.y - y);
    final double dz = FastMath.abs(v3.z - z);
    return dx + dy + dz;
}
 

import org.apache.commons.math3.util.FastMath; //導入方法依賴的package包/類
/**
 * Computes the L1 norm of the (quasi-)triangular matrix T.
 *
 * @return the L1 norm of matrix T
 */
private double getNorm() {
    double norm = 0.0;
    for (int i = 0; i < matrixT.length; i++) {
        // as matrix T is (quasi-)triangular, also take the sub-diagonal element into account
        for (int j = FastMath.max(i - 1, 0); j < matrixT.length; j++) {
            norm += FastMath.abs(matrixT[i][j]);
        }
    }
    return norm;
}
 

import org.apache.commons.math3.util.FastMath; //導入方法依賴的package包/類
public String getFormat() {
    if (FastMath.abs(sig) < 0.001) {
        return "%.3g";
    } else {
        return "%.2g";
    }
}
 

import org.apache.commons.math3.util.FastMath; //導入方法依賴的package包/類
/**
 * Find the first small sub-diagonal element and returns its index.
 *
 * @param startIdx the starting index for the search
 * @param norm the L1 norm of the matrix
 * @return the index of the first small sub-diagonal element
 */
private int findSmallSubDiagonalElement(final int startIdx, final double norm) {
    int l = startIdx;
    while (l > 0) {
        double s = FastMath.abs(matrixT[l - 1][l - 1]) + FastMath.abs(matrixT[l][l]);
        if (s == 0.0) {
            s = norm;
        }
        if (FastMath.abs(matrixT[l][l - 1]) < epsilon * s) {
            break;
        }
        l--;
    }
    return l;
}
 

import org.apache.commons.math3.util.FastMath; //導入方法依賴的package包/類
/**
 * Gcd between two positive numbers.
 * <p>
 * Gets the greatest common divisor of two numbers, using the "binary gcd" method,
 * which avoids division and modulo operations. See Knuth 4.5.2 algorithm B.
 * This algorithm is due to Josef Stein (1961).
 * </p>
 * Special cases:
 * <ul>
 * <li>The result of {@code gcd(x, x)}, {@code gcd(0, x)} and {@code gcd(x, 0)} is the value of {@code x}.</li>
 * <li>The invocation {@code gcd(0, 0)} is the only one which returns {@code 0}.</li>
 * </ul>
 *
 * @param a first number, must be &ge; 0
 * @param b second number, must be &ge; 0
 * @return gcd(a,b)
 */
static int gcdPositive(int a, int b){
    // both a and b must be positive, it is not checked here
    // gdc(a,0) = a
    if (a == 0) {
        return b;
    } else if (b == 0) {
        return a;
    }

    // make a and b odd, keep in mind the common power of twos
    final int aTwos = Integer.numberOfTrailingZeros(a);
    a >>= aTwos;
    final int bTwos = Integer.numberOfTrailingZeros(b);
    b >>= bTwos;
    final int shift = FastMath.min(aTwos, bTwos);

    // a and b >0
    // if a > b then gdc(a,b) = gcd(a-b,b)
    // if a < b then gcd(a,b) = gcd(b-a,a)
    // so next a is the absolute difference and next b is the minimum of current values
    while (a != b) {
        final int delta = a - b;
        b = FastMath.min(a, b);
        a = FastMath.abs(delta);
        // for speed optimization:
        // remove any power of two in a as b is guaranteed to be odd throughout all iterations
        a >>= Integer.numberOfTrailingZeros(a);
    }

    // gcd(a,a) = a, just "add" the common power of twos
    return a << shift;
}
 

import org.apache.commons.math3.util.FastMath; //導入方法依賴的package包/類
/**
 * Computes the <a href="http://en.wikipedia.org/wiki/G-test">G statistic
 * for Goodness of Fit</a> comparing {@code observed} and {@code expected}
 * frequency counts.
 *
 * <p>This statistic can be used to perform a G test (Log-Likelihood Ratio
 * Test) evaluating the null hypothesis that the observed counts follow the
 * expected distribution.</p>
 *
 * <p><strong>Preconditions</strong>: <ul>
 * <li>Expected counts must all be positive. </li>
 * <li>Observed counts must all be &ge; 0. </li>
 * <li>The observed and expected arrays must have the same length and their
 * common length must be at least 2. </li></ul></p>
 *
 * <p>If any of the preconditions are not met, a
 * {@code MathIllegalArgumentException} is thrown.</p>
 *
 * <p><strong>Note:</strong>This implementation rescales the
 * {@code expected} array if necessary to ensure that the sum of the
 * expected and observed counts are equal.</p>
 *
 * @param observed array of observed frequency counts
 * @param expected array of expected frequency counts
 * @return G-Test statistic
 * @throws NotPositiveException if {@code observed} has negative entries
 * @throws NotStrictlyPositiveException if {@code expected} has entries that
 * are not strictly positive
 * @throws DimensionMismatchException if the array lengths do not match or
 * are less than 2.
 */
public double g(final double[] expected, final long[] observed)
        throws NotPositiveException, NotStrictlyPositiveException,
        DimensionMismatchException {

    if (expected.length < 2) {
        throw new DimensionMismatchException(expected.length, 2);
    }
    if (expected.length != observed.length) {
        throw new DimensionMismatchException(expected.length, observed.length);
    }
    MathArrays.checkPositive(expected);
    MathArrays.checkNonNegative(observed);

    double sumExpected = 0d;
    double sumObserved = 0d;
    for (int i = 0; i < observed.length; i++) {
        sumExpected += expected[i];
        sumObserved += observed[i];
    }
    double ratio = 1d;
    boolean rescale = false;
    if (FastMath.abs(sumExpected - sumObserved) > 10E-6) {
        ratio = sumObserved / sumExpected;
        rescale = true;
    }
    double sum = 0d;
    for (int i = 0; i < observed.length; i++) {
        final double dev = rescale ?
                FastMath.log((double) observed[i] / (ratio * expected[i])) :
                    FastMath.log((double) observed[i] / expected[i]);
        sum += ((double) observed[i]) * dev;
    }
    return 2d * sum;
}
 

import org.apache.commons.math3.util.FastMath; //導入方法依賴的package包/類
/**
 * Calculates the Cholesky decomposition of the given matrix.
 * @param matrix the matrix to decompose
 * @param relativeSymmetryThreshold threshold above which off-diagonal
 * elements are considered too different and matrix not symmetric
 * @param absolutePositivityThreshold threshold below which diagonal
 * elements are considered null and matrix not positive definite
 * @throws NonSquareMatrixException if the matrix is not square.
 * @throws NonSymmetricMatrixException if the matrix is not symmetric.
 * @throws NonPositiveDefiniteMatrixException if the matrix is not
 * strictly positive definite.
 * @see #Cholesky(RealMatrix)
 * @see #DEFAULT_RELATIVE_SYMMETRY_THRESHOLD
 * @see #DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD
 */
public Cholesky(final RealMatrix matrix,
                                 final double relativeSymmetryThreshold,
                                 final double absolutePositivityThreshold) {
    if (!matrix.isSquare()) {
        throw new NonSquareMatrixException(matrix.getRowDimension(),
                                           matrix.getColumnDimension());
    }

    final int order = matrix.getRowDimension();
    lTData   = matrix.getData();
    cachedL  = null;
    cachedLT = null;

    // check the matrix before transformation
    for (int i = 0; i < order; ++i) {
        final double[] lI = lTData[i];

        // check off-diagonal elements (and reset them to 0)
        for (int j = i + 1; j < order; ++j) {
            final double[] lJ = lTData[j];
            final double lIJ = lI[j];
            final double lJI = lJ[i];
            final double maxDelta =
                relativeSymmetryThreshold * FastMath.max(FastMath.abs(lIJ), FastMath.abs(lJI));
            if (FastMath.abs(lIJ - lJI) > maxDelta) {
              //double mean = .5*(lIJ+lJI);
              //lTData[j][i] = lTData[i][j] = mean;
              System.out.print("entries: "+lIJ+" "+lJI);
                throw new NonSymmetricMatrixException(i, j, relativeSymmetryThreshold);
            }
            lJ[i] = 0;
       }
    }

    // transform the matrix
    for (int i = 0; i < order; ++i) {

        final double[] ltI = lTData[i];

        // check diagonal element
        if (ltI[i] <= absolutePositivityThreshold) {
            throw new NonPositiveDefiniteMatrixException(ltI[i], i, absolutePositivityThreshold);
        }

        ltI[i] = FastMath.sqrt(ltI[i]);
        final double inverse = 1.0 / ltI[i];

        for (int q = order - 1; q > i; --q) {
            ltI[q] *= inverse;
            final double[] ltQ = lTData[q];
            for (int p = q; p < order; ++p) {
                ltQ[p] -= ltI[q] * ltI[p];
            }
        }
    }
}