org.apache.commons.math.special.Erf Java Examples

/**
 * For this distribution, {@code X}, this method returns {@code P(X < x)}.
 * If {@code x}is more than 40 standard deviations from the mean, 0 or 1 is returned,
 * as in these cases the actual value is within {@code Double.MIN_VALUE} of 0 or 1.
 *
 * @param x Value at which the CDF is evaluated.
 * @return CDF evaluated at {@code x}.
 * @throws MathException if the algorithm fails to converge
 */
public double cumulativeProbability(double x) throws MathException {
    final double dev = x - mean;
    try {
    return 0.5 * (1.0 + Erf.erf((dev) /
                (standardDeviation * FastMath.sqrt(2.0))));
    } catch (MaxIterationsExceededException ex) {
        if (x < (mean - 20 * standardDeviation)) { // JDK 1.5 blows at 38
            return 0;
        } else if (x > (mean + 20 * standardDeviation)) {
            return 1;
        } else {
            throw ex;
        }
    }
}
 

/**
 * This operation performs the tile updates needed by the generateTile()
 * operation.
 *
 * @param tile
 *            the tile to update
 * @param slabM1
 *            the slab one index less than (so above) the middle slab
 * @param slab
 *            the middle slab
 * @param slabP1
 *            the slab one index greater than (so below) the middle slab
 * @param dist
 *            the step distance
 * @throws MathException
 *             Thrown if the error function cannot be evaluated
 */
private void updateTileByLayer(Tile updateSlab, Slab slabM1, Slab slab,
		Slab slabP1, double dist) throws MathException {

	// Compute the exponentials
	double tExpFac = Erf.erf(cE * dist / slab.interfaceWidth);
	double bExpFac = Erf.erf(cE * (dist - slab.thickness)
			/ (slabP1.interfaceWidth));

	// Update the slab properties
	updateSlab.scatteringLength = getTileValue(slabM1.scatteringLength,
			slab.scatteringLength, slabP1.scatteringLength, tExpFac,
			bExpFac);
	updateSlab.trueAbsLength = getTileValue(slabM1.trueAbsLength,
			slab.trueAbsLength, slabP1.trueAbsLength, tExpFac, bExpFac);
	updateSlab.incAbsLength = getTileValue(slabM1.incAbsLength,
			slab.incAbsLength, slabP1.incAbsLength, tExpFac, bExpFac);

	return;
}
 

/**
 * For this distribution, {@code X}, this method returns {@code P(X < x)}.
 * If {@code x}is more than 40 standard deviations from the mean, 0 or 1 is returned,
 * as in these cases the actual value is within {@code Double.MIN_VALUE} of 0 or 1.
 *
 * @param x Value at which the CDF is evaluated.
 * @return CDF evaluated at {@code x}.
 * @throws MathException if the algorithm fails to converge
 */
public double cumulativeProbability(double x) throws MathException {
    final double dev = x - mean;
    try {
    return 0.5 * (1.0 + Erf.erf((dev) /
                (standardDeviation * FastMath.sqrt(2.0))));
    } catch (MaxIterationsExceededException ex) {
        if (x < (mean - 20 * standardDeviation)) { // JDK 1.5 blows at 38
            return 0;
        } else if (x > (mean + 20 * standardDeviation)) {
            return 1;
        } else {
            throw ex;
        }
    }
}
 

/**
 * For this distribution, X, this method returns P(X &lt; <code>x</code>).
 * @param x the value at which the CDF is evaluated.
 * @return CDF evaluted at <code>x</code>.
 * @throws MathException if the algorithm fails to converge; unless
 * x is more than 20 standard deviations from the mean, in which case the
 * convergence exception is caught and 0 or 1 is returned.
 */
public double cumulativeProbability(double x) throws MathException {
    try {
        return 0.5 * (1.0 + Erf.erf((x - mean) /
                (standardDeviation * Math.sqrt(2.0))));
    } catch (MaxIterationsExceededException ex) {
        if (x < (mean - 20 * standardDeviation)) { // JDK 1.5 blows at 38
            return 0.0d;
        } else if (x > (mean + 20 * standardDeviation)) {
            return 1.0d;
        } else {
            throw ex;
        }
    }
}
 

/**
 * For this disbution, X, this method returns P(X &lt; <code>x</code>).
 * @param x the value at which the CDF is evaluated.
 * @return CDF evaluted at <code>x</code>. 
 * @throws MathException if the algorithm fails to converge; unless
 * x is more than 20 standard deviations from the mean, in which case the
 * convergence exception is caught and 0 or 1 is returned.
 */
public double cumulativeProbability(double x) throws MathException {
    try {
        return 0.5 * (1.0 + Erf.erf((x - mean) /
                (standardDeviation * Math.sqrt(2.0))));
    } catch (MaxIterationsExceededException ex) {
        if (x < (mean - 20 * standardDeviation)) { // JDK 1.5 blows at 38
            return 0.0d;
        } else if (x > (mean + 20 * standardDeviation)) {
            return 1.0d;
        } else {
            throw ex;
        }
    }
}
 

/**
 * For this distribution, X, this method returns P(X &lt; <code>x</code>).
 * @param x the value at which the CDF is evaluated.
 * @return CDF evaluted at <code>x</code>.
 * @throws MathException if the algorithm fails to converge; unless
 * x is more than 20 standard deviations from the mean, in which case the
 * convergence exception is caught and 0 or 1 is returned.
 */
public double cumulativeProbability(double x) throws MathException {
    try {
        return 0.5 * (1.0 + Erf.erf((x - mean) /
                (standardDeviation * Math.sqrt(2.0))));
    } catch (MaxIterationsExceededException ex) {
        if (x < (mean - 20 * standardDeviation)) { // JDK 1.5 blows at 38
            return 0.0d;
        } else if (x > (mean + 20 * standardDeviation)) {
            return 1.0d;
        } else {
            throw ex;
        }
    }
}
 

/**
 * For this distribution, X, this method returns P(X &lt; <code>x</code>).
 * @param x the value at which the CDF is evaluated.
 * @return CDF evaluted at <code>x</code>.
 * @throws MathException if the algorithm fails to converge; unless
 * x is more than 20 standard deviations from the mean, in which case the
 * convergence exception is caught and 0 or 1 is returned.
 */
public double cumulativeProbability(double x) throws MathException {
    try {
        return 0.5 * (1.0 + Erf.erf((x - mean) /
                (standardDeviation * Math.sqrt(2.0))));
    } catch (MaxIterationsExceededException ex) {
        if (x < (mean - 20 * standardDeviation)) { // JDK 1.5 blows at 38
            return 0.0d;
        } else if (x > (mean + 20 * standardDeviation)) {
            return 1.0d;
        } else {
            throw ex;
        }
    }
}
 

/**
 * For this distribution, X, this method returns P(X &lt; <code>x</code>).
 * @param x the value at which the CDF is evaluated.
 * @return CDF evaluted at <code>x</code>. 
 * @throws MathException if the algorithm fails to converge; unless
 * x is more than 20 standard deviations from the mean, in which case the
 * convergence exception is caught and 0 or 1 is returned.
 */
public double cumulativeProbability(double x) throws MathException {
    try {
        return 0.5 * (1.0 + Erf.erf((x - mean) /
                (standardDeviation * Math.sqrt(2.0))));
    } catch (MaxIterationsExceededException ex) {
        if (x < (mean - 20 * standardDeviation)) { // JDK 1.5 blows at 38
            return 0.0d;
        } else if (x > (mean + 20 * standardDeviation)) {
            return 1.0d;
        } else {
            throw ex;
        }
    }
}
 

/**
 * For this distribution, X, this method returns P(X &lt; <code>x</code>).
 * @param x the value at which the CDF is evaluated.
 * @return CDF evaluted at <code>x</code>. 
 * @throws MathException if the algorithm fails to converge; unless
 * x is more than 20 standard deviations from the mean, in which case the
 * convergence exception is caught and 0 or 1 is returned.
 */
public double cumulativeProbability(double x) throws MathException {
    try {
        return 0.5 * (1.0 + Erf.erf((x - mean) /
                (standardDeviation * Math.sqrt(2.0))));
    } catch (MaxIterationsExceededException ex) {
        if (x < (mean - 20 * standardDeviation)) { // JDK 1.5 blows at 38
            return 0.0d;
        } else if (x > (mean + 20 * standardDeviation)) {
            return 1.0d;
        } else {
            throw ex;
        }
    }
}
 

/**
 * For this distribution, X, this method returns P(X &lt; <code>x</code>).
 * @param x the value at which the CDF is evaluated.
 * @return CDF evaluted at <code>x</code>. 
 * @throws MathException if the algorithm fails to converge; unless
 * x is more than 20 standard deviations from the mean, in which case the
 * convergence exception is caught and 0 or 1 is returned.
 */
public double cumulativeProbability(double x) throws MathException {
    try {
        return 0.5 * (1.0 + Erf.erf((x - mean) /
                (standardDeviation * Math.sqrt(2.0))));
    } catch (MaxIterationsExceededException ex) {
        if (x < (mean - 20 * standardDeviation)) { // JDK 1.5 blows at 38
            return 0.0d;
        } else if (x > (mean + 20 * standardDeviation)) {
            return 1.0d;
        } else {
            throw ex;
        }
    }
}
 

/**
 * For this distribution, X, this method returns P(X &lt; <code>x</code>).
 * @param x the value at which the CDF is evaluated.
 * @return CDF evaluted at <code>x</code>.
 * @throws MathException if the algorithm fails to converge; unless
 * x is more than 20 standard deviations from the mean, in which case the
 * convergence exception is caught and 0 or 1 is returned.
 */
public double cumulativeProbability(double x) throws MathException {
    try {
        return 0.5 * (1.0 + Erf.erf((x - mean) /
                (standardDeviation * Math.sqrt(2.0))));
    } catch (MaxIterationsExceededException ex) {
        if (x < (mean - 20 * standardDeviation)) { // JDK 1.5 blows at 38
            return 0.0d;
        } else if (x > (mean + 20 * standardDeviation)) {
            return 1.0d;
        } else {
            throw ex;
        }
    }
}
 

/**
 * For this distribution, X, this method returns P(X &lt; <code>x</code>).
 * @param x the value at which the CDF is evaluated.
 * @return CDF evaluted at <code>x</code>.
 * @throws MathException if the algorithm fails to converge; unless
 * x is more than 20 standard deviations from the mean, in which case the
 * convergence exception is caught and 0 or 1 is returned.
 */
public double cumulativeProbability(double x) throws MathException {
    try {
        return 0.5 * (1.0 + Erf.erf((x - mean) /
                (standardDeviation * Math.sqrt(2.0))));
    } catch (MaxIterationsExceededException ex) {
        if (x < (mean - 20 * standardDeviation)) { // JDK 1.5 blows at 38
            return 0.0d;
        } else if (x > (mean + 20 * standardDeviation)) {
            return 1.0d;
        } else {
            throw ex;
        }
    }
}
 

/**
 * For this disbution, X, this method returns P(X &lt; <code>x</code>).
 * @param x the value at which the CDF is evaluated.
 * @return CDF evaluted at <code>x</code>. 
 * @throws MathException if the algorithm fails to converge; unless
 * x is more than 20 standard deviations from the mean, in which case the
 * convergence exception is caught and 0 or 1 is returned.
 */
public double cumulativeProbability(double x) throws MathException {
    try {
        return 0.5 * (1.0 + Erf.erf((x - mean) /
                (standardDeviation * Math.sqrt(2.0))));
    } catch (MaxIterationsExceededException ex) {
        if (x < (mean - 20 * standardDeviation)) { // JDK 1.5 blows at 38
            return 0.0d;
        } else if (x > (mean + 20 * standardDeviation)) {
            return 1.0d;
        } else {
            throw ex;
        }
    }
}
 

/**
 * For this distribution, X, this method returns P(X &lt; <code>x</code>).
 * @param x the value at which the CDF is evaluated.
 * @return CDF evaluted at <code>x</code>.
 * @throws MathException if the algorithm fails to converge; unless
 * x is more than 20 standard deviations from the mean, in which case the
 * convergence exception is caught and 0 or 1 is returned.
 */
public double cumulativeProbability(double x) throws MathException {
    try {
        return 0.5 * (1.0 + Erf.erf((x - mean) /
                (standardDeviation * Math.sqrt(2.0))));
    } catch (MaxIterationsExceededException ex) {
        if (x < (mean - 20 * standardDeviation)) { // JDK 1.5 blows at 38
            return 0.0d;
        } else if (x > (mean + 20 * standardDeviation)) {
            return 1.0d;
        } else {
            throw ex;
        }
    }
}
 

/**
 * For this distribution, X, this method returns P(X &lt; <code>x</code>).
 * @param x the value at which the CDF is evaluated.
 * @return CDF evaluted at <code>x</code>.
 * @throws MathException if the algorithm fails to converge; unless
 * x is more than 20 standard deviations from the mean, in which case the
 * convergence exception is caught and 0 or 1 is returned.
 */
public double cumulativeProbability(double x) throws MathException {
    try {
        return 0.5 * (1.0 + Erf.erf((x - mean) /
                (standardDeviation * Math.sqrt(2.0))));
    } catch (MaxIterationsExceededException ex) {
        if (x < (mean - 20 * standardDeviation)) { // JDK 1.5 blows at 38
            return 0.0d;
        } else if (x > (mean + 20 * standardDeviation)) {
            return 1.0d;
        } else {
            throw ex;
        }
    }
}
 

/**
 * For this distribution, X, this method returns P(X &lt; <code>x</code>).
 * @param x the value at which the CDF is evaluated.
 * @return CDF evaluted at <code>x</code>.
 * @throws MathException if the algorithm fails to converge; unless
 * x is more than 20 standard deviations from the mean, in which case the
 * convergence exception is caught and 0 or 1 is returned.
 */
public double cumulativeProbability(double x) throws MathException {
    try {
        return 0.5 * (1.0 + Erf.erf((x - mean) /
                (standardDeviation * Math.sqrt(2.0))));
    } catch (MaxIterationsExceededException ex) {
        if (x < (mean - 20 * standardDeviation)) { // JDK 1.5 blows at 38
            return 0.0d;
        } else if (x > (mean + 20 * standardDeviation)) {
            return 1.0d;
        } else {
            throw ex;
        }
    }
}
 

/**
 * For this distribution, X, this method returns P(X &lt; <code>x</code>).
 * @param x the value at which the CDF is evaluated.
 * @return CDF evaluted at <code>x</code>.
 * @throws MathException if the algorithm fails to converge; unless
 * x is more than 20 standard deviations from the mean, in which case the
 * convergence exception is caught and 0 or 1 is returned.
 */
public double cumulativeProbability(double x) throws MathException {
    try {
        return 0.5 * (1.0 + Erf.erf((x - mean) /
                (standardDeviation * FastMath.sqrt(2.0))));
    } catch (MaxIterationsExceededException ex) {
        if (x < (mean - 20 * standardDeviation)) { // JDK 1.5 blows at 38
            return 0.0d;
        } else if (x > (mean + 20 * standardDeviation)) {
            return 1.0d;
        } else {
            throw ex;
        }
    }
}
 

/**
 * For this distribution, X, this method returns P(X &lt; <code>x</code>).
 * @param x the value at which the CDF is evaluated.
 * @return CDF evaluted at <code>x</code>.
 * @throws MathException if the algorithm fails to converge; unless
 * x is more than 20 standard deviations from the mean, in which case the
 * convergence exception is caught and 0 or 1 is returned.
 */
public double cumulativeProbability(double x) throws MathException {
    try {
        return 0.5 * (1.0 + Erf.erf((x - mean) /
                (standardDeviation * Math.sqrt(2.0))));
    } catch (MaxIterationsExceededException ex) {
        if (x < (mean - 20 * standardDeviation)) { // JDK 1.5 blows at 38
            return 0.0d;
        } else if (x > (mean + 20 * standardDeviation)) {
            return 1.0d;
        } else {
            throw ex;
        }
    }
}
 

/**
 * This operation generates the interfacial profile using an error function
 * of numRough ordinate steps based on those of the hyperbolic tangent.
 *
 * @param numRough
 *            the number of ordinate steps
 * @param zInt
 *            FIXME! This array must be preallocated with a size n =
 *            maxRoughSize.
 * @param rufInt
 *            FIXME! This array must be preallocated with a size n =
 *            maxRoughSize.
 * @throws MathException
 *             Thrown if the error function cannot be calculated
 */
public void getInterfacialProfile(int numRough, double[] zInt,
		double[] rufInt) throws MathException {

	// cE ensures Gaussian = 0.5 when z = zhwhm
	final double cE = 1.665;
	double dist = 0.0, step = 0.0, oHalfstep = 0.0, zTemp = 0.0;
	int j;

	// Check nRough to make sure it is legitimate
	if (numRough < 1) {
		numRough = 1;
	}
	// Set the step size
	step = 2.0 / (numRough + 1);

	// Evaluate the lower half of the interface
	dist = -step / 2.0;
	// Steps calculated from inverse tanh. Note that all of the indices are
	// shifted by -1 from the VB code because this version is zero indexed!
	zInt[numRough / 2] = Math.log((1.0 + dist) / (1.0 - dist)) / (2.0 * cE);
	rufInt[numRough / 2] = Erf.erf(cE * zInt[numRough / 2]);
	for (j = numRough / 2 - 1; j >= 0; j--) {
		dist = dist - step;
		zInt[j] = Math.log((1.0 + dist) / (1.0 - dist)) / (2.0 * cE);
		rufInt[j] = Erf.erf(cE * zInt[j]);
	}

	// Evaluate the upper half of the interface
	dist = step / 2.0;
	// Steps calculated from inverse tanh. Note that all of the indices are
	// shifted by -1 from the VB code because this version is zero indexed!
	zInt[numRough / 2 + 1] = Math.log((1.0 + dist) / (1.0 - dist))
			/ (2.0 * cE);
	rufInt[numRough / 2 + 1] = Erf.erf(cE * zInt[numRough / 2 + 1]);
	for (j = numRough / 2 + 2; j <= numRough; j++) {
		dist = dist + step;
		zInt[j] = Math.log((1.0 + dist) / (1.0 - dist)) / (2.0 * cE);
		rufInt[j] = Erf.erf(cE * zInt[j]);
	}

	// Calculate step widths
	oHalfstep = 0.5 * (zInt[1] - zInt[0]);
	for (j = 0; j <= numRough / 2; j++) {
		zTemp = zInt[j];
		// The zInt values are symmetric, so this loop only computes the
		// bottom half and sets the upper half without doing the
		// calculation.
		zInt[j] = oHalfstep + 0.5 * (zInt[j + 1] - zInt[j]);
		zInt[numRough - j] = zInt[j];
		oHalfstep = 0.5 * (zInt[j + 1] - zTemp);
	}

	return;
}
 

/**
 * For this distribution, {@code X}, this method returns {@code P(X < x)}.
 * If {@code x}is more than 40 standard deviations from the mean, 0 or 1 is returned,
 * as in these cases the actual value is within {@code Double.MIN_VALUE} of 0 or 1.
 *
 * @param x Value at which the CDF is evaluated.
 * @return CDF evaluated at {@code x}.
 * @throws MathException if the algorithm fails to converge
 */
public double cumulativeProbability(double x) throws MathException {
    final double dev = x - mean;
    if (FastMath.abs(dev) > 40 * standardDeviation) {
        return dev < 0 ? 0.0d : 1.0d;
    }
    return 0.5 * (1 + Erf.erf(dev / (standardDeviation * FastMath.sqrt(2))));
}
 

/**
 * For this distribution, {@code X}, this method returns {@code P(X < x)}.
 * If {@code x}is more than 40 standard deviations from the mean, 0 or 1 is returned,
 * as in these cases the actual value is within {@code Double.MIN_VALUE} of 0 or 1.
 *
 * @param x Value at which the CDF is evaluated.
 * @return CDF evaluated at {@code x}.
 * @throws MathException if the algorithm fails to converge
 */
public double cumulativeProbability(double x) throws MathException {
    final double dev = x - mean;
    if (FastMath.abs(dev) > 40 * standardDeviation) {
        return dev < 0 ? 0.0d : 1.0d;
    }
    return 0.5 * (1 + Erf.erf(dev / (standardDeviation * FastMath.sqrt(2))));
}
 

/**
 * For this distribution, {@code X}, this method returns {@code P(X < x)}.
 * If {@code x}is more than 40 standard deviations from the mean, 0 or 1 is returned,
 * as in these cases the actual value is within {@code Double.MIN_VALUE} of 0 or 1.
 *
 * @param x Value at which the CDF is evaluated.
 * @return CDF evaluated at {@code x}.
 * @throws MathException if the algorithm fails to converge
 */
public double cumulativeProbability(double x) throws MathException {
    final double dev = x - mean;
    if (FastMath.abs(dev) > 40 * standardDeviation) {
        return dev < 0 ? 0.0d : 1.0d;
    }
    return 0.5 * (1 + Erf.erf(dev / (standardDeviation * FastMath.sqrt(2))));
}
 

/**
 * For this distribution, {@code X}, this method returns {@code P(X < x)}. If
 * {@code x}is more than 40 standard deviations from the mean, 0 or 1 is
 * returned, as in these cases the actual value is within
 * {@code Double.MIN_VALUE} of 0 or 1.
 *
 * @param x Value at which the CDF is evaluated.
 * @return CDF evaluated at {@code x}.
 * @throws MathException if the algorithm fails to converge
 */
public double cumulativeProbability(double x) throws MathException {
	final double dev = x - mean;
	if (FastMath.abs(dev) > 40 * standardDeviation) {// Math-60
		return dev < 0 ? 0.0d : 1.0d;
	}

	return 0.5 * (1.0 + Erf.erf((dev) / (standardDeviation * FastMath.sqrt(2.0))));

}
 

/**
 * For this distribution, {@code X}, this method returns {@code P(X < x)}.
 * If {@code x}is more than 40 standard deviations from the mean, 0 or 1 is returned,
 * as in these cases the actual value is within {@code Double.MIN_VALUE} of 0 or 1.
 *
 * @param x Value at which the CDF is evaluated.
 * @return CDF evaluated at {@code x}.
 * @throws MathException if the algorithm fails to converge
 */
public double cumulativeProbability(double x) throws MathException {
    final double dev = x - mean;
    if (FastMath.abs(dev) > 40 * standardDeviation) { 
        return dev < 0 ? 0.0d : 1.0d;
    }
    return 0.5 * (1.0 + Erf.erf((dev) /
                (standardDeviation * FastMath.sqrt(2.0))));
}
 

/**
 * For this disbution, X, this method returns P(X &lt; <code>x</code>).
 * @param x the value at which the CDF is evaluated.
 * @return CDF evaluted at <code>x</code>. 
 * @throws MathException if the algorithm fails to converge.
 */
public double cumulativeProbability(double x) throws MathException {
    return 0.5 * (1.0 + Erf.erf((x - mean) /
            (standardDeviation * Math.sqrt(2.0))));
}
 

/**
 * For this disbution, X, this method returns P(X &lt; <code>x</code>).
 * @param x the value at which the CDF is evaluated.
 * @return CDF evaluted at <code>x</code>. 
 * @throws MathException if the algorithm fails to converge; unless
 * x is more than 20 standard deviations from the mean, in which case the
 * convergence exception is caught and 0 or 1 is returned.
 */
public double cumulativeProbability(double x) throws MathException {
        return 0.5 * (1.0 + Erf.erf((x - mean) /
                (standardDeviation * Math.sqrt(2.0))));
}