Java Code Examples for org.apache.commons.math3.util.FastMath#log()

/**
 * Test of getN method, of class MillerUpdatingRegression.
 */
@Test
public void testAddObsGetNClear() {
    MillerUpdatingRegression instance = new MillerUpdatingRegression(3, true);
    double[][] xAll = new double[airdata[0].length][];
    double[] y = new double[airdata[0].length];
    for (int i = 0; i < airdata[0].length; i++) {
        xAll[i] = new double[3];
        xAll[i][0] = FastMath.log(airdata[3][i]);
        xAll[i][1] = FastMath.log(airdata[4][i]);
        xAll[i][2] = airdata[5][i];
        y[i] = FastMath.log(airdata[2][i]);
    }
    instance.addObservations(xAll, y);
    if (instance.getN() != xAll.length) {
        Assert.fail("Number of observations not correct in bulk addition");
    }
    instance.clear();
    for (int i = 0; i < xAll.length; i++) {
        instance.addObservation(xAll[i], y[i]);
    }
    if (instance.getN() != xAll.length) {
        Assert.fail("Number of observations not correct in drip addition");
    }
    return;
}
 

/**
 * Creates an instance. It will be such that
 * <ul>
 *  <li>{@code a = initValue}</li>
 *  <li>{@code b = -numCall / ln(valueAtNumCall / initValue)}</li>
 * </ul>
 *
 * @param initValue Initial value, i.e. {@link #value(long) value(0)}.
 * @param valueAtNumCall Value of the function at {@code numCall}.
 * @param numCall Argument for which the function returns
 * {@code valueAtNumCall}.
 * @throws NotStrictlyPositiveException if {@code initValue <= 0}.
 * @throws NotStrictlyPositiveException if {@code valueAtNumCall <= 0}.
 * @throws NumberIsTooLargeException if {@code valueAtNumCall >= initValue}.
 * @throws NotStrictlyPositiveException if {@code numCall <= 0}.
 */
public ExponentialDecayFunction(double initValue,
                                double valueAtNumCall,
                                long numCall) {
    if (initValue <= 0) {
        throw new NotStrictlyPositiveException(initValue);
    }
    if (valueAtNumCall <= 0) {
        throw new NotStrictlyPositiveException(valueAtNumCall);
    }
    if (valueAtNumCall >= initValue) {
        throw new NumberIsTooLargeException(valueAtNumCall, initValue, false);
    }
    if (numCall <= 0) {
        throw new NotStrictlyPositiveException(numCall);
    }

    a = initValue;
    oneOverB = -FastMath.log(valueAtNumCall / initValue) / numCall;
}
 

/**
 * A part of the deviance portion of the saddle point approximation.
 * <p>
 * References:
 * <ol>
 * <li>Catherine Loader (2000). "Fast and Accurate Computation of Binomial
 * Probabilities.". <a target="_blank"
 * href="http://www.herine.net/stat/papers/dbinom.pdf">
 * http://www.herine.net/stat/papers/dbinom.pdf</a></li>
 * </ol>
 * </p>
 *
 * @param x the x value.
 * @param mu the average.
 * @return a part of the deviance.
 */
static double getDeviancePart(double x, double mu) {
    double ret;
    if (FastMath.abs(x - mu) < 0.1 * (x + mu)) {
        double d = x - mu;
        double v = d / (x + mu);
        double s1 = v * d;
        double s = Double.NaN;
        double ej = 2.0 * x * v;
        v = v * v;
        int j = 1;
        while (s1 != s) {
            s = s1;
            ej *= v;
            s1 = s + ej / ((j * 2) + 1);
            ++j;
        }
        ret = s1;
    } else {
        ret = x * FastMath.log(x / mu) + mu - x;
    }
    return ret;
}
 

/** Compute natural logarithm of a derivative structure.
 * @param operand array holding the operand
 * @param operandOffset offset of the operand in its array
 * @param result array where result must be stored (for
 * logarithm the result array <em>cannot</em> be the input
 * array)
 * @param resultOffset offset of the result in its array
 */
public void log(final double[] operand, final int operandOffset,
                final double[] result, final int resultOffset) {

    // create the function value and derivatives
    double[] function = new double[1 + order];
    function[0] = FastMath.log(operand[operandOffset]);
    if (order > 0) {
        double inv = 1.0 / operand[operandOffset];
        double xk  = inv;
        for (int i = 1; i <= order; ++i) {
            function[i] = xk;
            xk *= -i * inv;
        }
    }

    // apply function composition
    compose(operand, operandOffset, function, result, resultOffset);

}
 

/** {@inheritDoc} */
@Override
public double probability(double x0,
                          double x1)
    throws NumberIsTooLargeException {
    if (x0 > x1) {
        throw new NumberIsTooLargeException(LocalizedFormats.LOWER_ENDPOINT_ABOVE_UPPER_ENDPOINT,
                                            x0, x1, true);
    }
    if (x0 <= 0 || x1 <= 0) {
        return super.probability(x0, x1);
    }
    final double denom = shape * SQRT2;
    final double v0 = (FastMath.log(x0) - scale) / denom;
    final double v1 = (FastMath.log(x1) - scale) / denom;
    return 0.5 * Erf.erf(v0, v1);
}
 

/** Computes base 10 logarithm of a derivative structure.
 * @param operand array holding the operand
 * @param operandOffset offset of the operand in its array
 * @param result array where result must be stored (for
 * base 10 logarithm the result array <em>cannot</em> be the input array)
 * @param resultOffset offset of the result in its array
 */
public void log10(final double[] operand, final int operandOffset,
                  final double[] result, final int resultOffset) {

    // create the function value and derivatives
    double[] function = new double[1 + order];
    function[0] = FastMath.log10(operand[operandOffset]);
    if (order > 0) {
        double inv = 1.0 / operand[operandOffset];
        double xk  = inv / FastMath.log(10.0);
        for (int i = 1; i <= order; ++i) {
            function[i] = xk;
            xk *= -i * inv;
        }
    }

    // apply function composition
    compose(operand, operandOffset, function, result, resultOffset);

}
 

/**
 * <p>
 * Returns the value of log&nbsp;&Gamma;(x) for x&nbsp;&gt;&nbsp;0.
 * </p>
 * <p>
 * For x &le; 8, the implementation is based on the double precision
 * implementation in the <em>NSWC Library of Mathematics Subroutines</em>,
 * {@code DGAMLN}. For x &gt; 8, the implementation is based on
 * </p>
 * <ul>
 * <li><a href="http://mathworld.wolfram.com/GammaFunction.html">Gamma
 *     Function</a>, equation (28).</li>
 * <li><a href="http://mathworld.wolfram.com/LanczosApproximation.html">
 *     Lanczos Approximation</a>, equations (1) through (5).</li>
 * <li><a href="http://my.fit.edu/~gabdo/gamma.txt">Paul Godfrey, A note on
 *     the computation of the convergent Lanczos complex Gamma
 *     approximation</a></li>
 * </ul>
 *
 * @param x Argument.
 * @return the value of {@code log(Gamma(x))}, {@code Double.NaN} if
 * {@code x <= 0.0}.
 */
public static double logGamma(double x) {
    double ret;

    if (Double.isNaN(x) || (x <= 0.0)) {
        ret = Double.NaN;
    } else if (x < 0.5) {
        return logGamma1p(x) - FastMath.log(x);
    } else if (x <= 2.5) {
        return logGamma1p((x - 0.5) - 0.5);
    } else if (x <= 8.0) {
        final int n = (int) FastMath.floor(x - 1.5);
        double prod = 1.0;
        for (int i = 1; i <= n; i++) {
            prod *= x - i;
        }
        return logGamma1p(x - (n + 1)) + FastMath.log(prod);
    } else {
        double sum = lanczos(x);
        double tmp = x + LANCZOS_G + .5;
        ret = ((x + .5) * FastMath.log(tmp)) - tmp +
            HALF_LOG_2_PI + FastMath.log(sum / x);
    }

    return ret;
}
 

/**
 * A part of the deviance portion of the saddle point approximation.
 * <p>
 * References:
 * <ol>
 * <li>Catherine Loader (2000). "Fast and Accurate Computation of Binomial
 * Probabilities.". <a target="_blank"
 * href="http://www.herine.net/stat/papers/dbinom.pdf">
 * http://www.herine.net/stat/papers/dbinom.pdf</a></li>
 * </ol>
 * </p>
 *
 * @param x the x value.
 * @param mu the average.
 * @return a part of the deviance.
 */
static double getDeviancePart(double x, double mu) {
    double ret;
    if (FastMath.abs(x - mu) < 0.1 * (x + mu)) {
        double d = x - mu;
        double v = d / (x + mu);
        double s1 = v * d;
        double s = Double.NaN;
        double ej = 2.0 * x * v;
        v = v * v;
        int j = 1;
        while (s1 != s) {
            s = s1;
            ej *= v;
            s1 = s + ej / ((j * 2) + 1);
            ++j;
        }
        ret = s1;
    } else {
        ret = x * FastMath.log(x / mu) + mu - x;
    }
    return ret;
}
 

/** {@inheritDoc} */
public double density(double x) {
    recomputeZ();
    if (x < 0 || x > 1) {
        return 0;
    } else if (x == 0) {
        if (alpha < 1) {
            throw new NumberIsTooSmallException(LocalizedFormats.CANNOT_COMPUTE_BETA_DENSITY_AT_0_FOR_SOME_ALPHA, alpha, 1, false);
        }
        return 0;
    } else if (x == 1) {
        if (beta < 1) {
            throw new NumberIsTooSmallException(LocalizedFormats.CANNOT_COMPUTE_BETA_DENSITY_AT_1_FOR_SOME_BETA, beta, 1, false);
        }
        return 0;
    } else {
        double logX = FastMath.log(x);
        double log1mX = FastMath.log1p(-x);
        return FastMath.exp((alpha - 1) * logX + (beta - 1) * log1mX - z);
    }
}
 

/**
 * {@inheritDoc}
 *
 * @since 2.1
 */
public double density(double x) {
    final double nhalf = numeratorDegreesOfFreedom / 2;
    final double mhalf = denominatorDegreesOfFreedom / 2;
    final double logx = FastMath.log(x);
    final double logn = FastMath.log(numeratorDegreesOfFreedom);
    final double logm = FastMath.log(denominatorDegreesOfFreedom);
    final double lognxm = FastMath.log(numeratorDegreesOfFreedom * x +
                                       denominatorDegreesOfFreedom);
    return FastMath.exp(nhalf * logn + nhalf * logx - logx +
                        mhalf * logm - nhalf * lognxm - mhalf * lognxm -
                        Beta.logBeta(nhalf, mhalf));
}
 

/**
 * Creates a Gamma distribution.
 *
 * @param rng Random number generator.
 * @param shape the shape parameter
 * @param scale the scale parameter
 * @param inverseCumAccuracy the maximum absolute error in inverse
 * cumulative probability estimates (defaults to
 * {@link #DEFAULT_INVERSE_ABSOLUTE_ACCURACY}).
 * @throws NotStrictlyPositiveException if {@code shape <= 0} or
 * {@code scale <= 0}.
 * @since 3.1
 */
public GammaDistribution(RandomGenerator rng,
                         double shape,
                         double scale,
                         double inverseCumAccuracy)
    throws NotStrictlyPositiveException {
    super(rng);

    if (shape <= 0) {
        throw new NotStrictlyPositiveException(LocalizedFormats.SHAPE, shape);
    }
    if (scale <= 0) {
        throw new NotStrictlyPositiveException(LocalizedFormats.SCALE, scale);
    }

    this.shape = shape;
    this.scale = scale;
    this.solverAbsoluteAccuracy = inverseCumAccuracy;
    this.shiftedShape = shape + Gamma.LANCZOS_G + 0.5;
    final double aux = FastMath.E / (2.0 * FastMath.PI * shiftedShape);
    this.densityPrefactor2 = shape * FastMath.sqrt(aux) / Gamma.lanczos(shape);
    this.densityPrefactor1 = this.densityPrefactor2 / scale *
            FastMath.pow(shiftedShape, -shape) *
            FastMath.exp(shape + Gamma.LANCZOS_G);
    this.minY = shape + Gamma.LANCZOS_G - FastMath.log(Double.MAX_VALUE);
    this.maxLogY = FastMath.log(Double.MAX_VALUE) / (shape - 1.0);
}
 

@Override
public double inverseCumulativeProbability(double p) throws OutOfRangeException {
    if (p < 0.0 || p > 1.0) {
        throw new OutOfRangeException(p, 0.0, 1.0);
    } else if (p == 0) {
        return Double.NEGATIVE_INFINITY;
    } else if (p == 1) {
        return Double.POSITIVE_INFINITY;
    }
    return mu - FastMath.log(-FastMath.log(p)) * beta;
}
 

/** {@inheritDoc} */
@Override
public double logDensity(double x) {
    final double n = degreesOfFreedom;
    final double nPlus1Over2 = (n + 1) / 2;
    return factor - nPlus1Over2 * FastMath.log(1 + x * x / n);
}
 

/** Creates the default logarithmic probability density test expected values.
 *
 * The default implementation simply computes the logarithm of all the values in
 * {@link #makeDensityTestValues()}.
 *
 * @return double[] the default logarithmic probability density test expected values.
 */
public double[] makeLogDensityTestValues() {
    final double[] densityTestValues = makeDensityTestValues();
    final double[] logDensityTestValues = new double[densityTestValues.length];
    for (int i = 0; i < densityTestValues.length; i++) {
        logDensityTestValues[i] = FastMath.log(densityTestValues[i]);
    }
    return logDensityTestValues;
}
 

@Test
public void testPCorr() {
    MillerUpdatingRegression instance = new MillerUpdatingRegression(4, false);
    double[][] x = new double[airdata[0].length][];
    double[] y = new double[airdata[0].length];
    double[] cp = new double[10];
    double[] yxcorr = new double[4];
    double[] diag = new double[4];
    double sumysq = 0.0;
    int off = 0;
    for (int i = 0; i < airdata[0].length; i++) {
        x[i] = new double[4];
        x[i][0] = 1.0;
        x[i][1] = FastMath.log(airdata[3][i]);
        x[i][2] = FastMath.log(airdata[4][i]);
        x[i][3] = airdata[5][i];
        y[i] = FastMath.log(airdata[2][i]);
        off = 0;
        for (int j = 0; j < 4; j++) {
            double tmp = x[i][j];
            for (int k = 0; k <= j; k++, off++) {
                cp[off] += tmp * x[i][k];
            }
            yxcorr[j] += tmp * y[i];
        }
        sumysq += y[i] * y[i];
    }
    PearsonsCorrelation pearson = new PearsonsCorrelation(x);
    RealMatrix corr = pearson.getCorrelationMatrix();
    off = 0;
    for (int i = 0; i < 4; i++, off += (i + 1)) {
        diag[i] = FastMath.sqrt(cp[off]);
    }

    instance.addObservations(x, y);
    double[] pc = instance.getPartialCorrelations(0);
    int idx = 0;
    off = 0;
    int off2 = 6;
    for (int i = 0; i < 4; i++) {
        for (int j = 0; j < i; j++) {
            if (FastMath.abs(pc[idx] - cp[off] / (diag[i] * diag[j])) > 1.0e-8) {
                Assert.fail("Failed cross products... i = " + i + " j = " + j);
            }
            ++idx;
            ++off;
        }
        ++off;
        if (FastMath.abs(pc[i+off2] - yxcorr[ i] / (FastMath.sqrt(sumysq) * diag[i])) > 1.0e-8) {
            Assert.fail("Assert.failed cross product i = " + i + " y");
        }
    }
    double[] pc2 = instance.getPartialCorrelations(1);

    idx = 0;

    for (int i = 1; i < 4; i++) {
        for (int j = 1; j < i; j++) {
            if (FastMath.abs(pc2[idx] - corr.getEntry(j, i)) > 1.0e-8) {
                Assert.fail("Failed cross products... i = " + i + " j = " + j);
            }
            ++idx;
        }
    }
    double[] pc3 = instance.getPartialCorrelations(2);
    if (pc3 == null) {
        Assert.fail("Should not be null");
    }
    return;
}
 

@Override
public double getDensity(double dist, double h) {
	return dist < h ? FastMath.log(FastMath.cos(0.5 * Math.PI * dist / h)) : Double.NEGATIVE_INFINITY;
}
 

/**
 * {@inheritDoc}
 */
@Override
public void increment(final double d) {
    value += FastMath.log(d);
    n++;
}
 

private void addValue(double val) {
    this.value += FastMath.log(val);
    n++;
}
 

/** {@inheritDoc}
 * @since 3.1
 * @exception OutOfRangeException if parameter is outside of function domain
 */
public DerivativeStructure value(final DerivativeStructure t)
    throws OutOfRangeException {
    final double x = t.getValue();
    if (x < lo || x > hi) {
        throw new OutOfRangeException(x, lo, hi);
    }
    double[] f = new double[t.getOrder() + 1];

    // function value
    f[0] = FastMath.log((x - lo) / (hi - x));

    if (Double.isInfinite(f[0])) {

        if (f.length > 1) {
            f[1] = Double.POSITIVE_INFINITY;
        }
        // fill the array with infinities
        // (for x close to lo the signs will flip between -inf and +inf,
        //  for x close to hi the signs will always be +inf)
        // this is probably overkill, since the call to compose at the end
        // of the method will transform most infinities into NaN ...
        for (int i = 2; i < f.length; ++i) {
            f[i] = f[i - 2];
        }

    } else {

        // function derivatives
        final double invL = 1.0 / (x - lo);
        double xL = invL;
        final double invH = 1.0 / (hi - x);
        double xH = invH;
        for (int i = 1; i < f.length; ++i) {
            f[i] = xL + xH;
            xL  *= -i * invL;
            xH  *=  i * invH;
        }
    }

    return t.compose(f);
}
 

/**
 * {@inheritDoc}
 *
 * For scale {@code m}, and shape {@code s} of this distribution, the PDF
 * is given by
 * <ul>
 * <li>{@code 0} if {@code x <= 0},</li>
 * <li>{@code exp(-0.5 * ((ln(x) - m) / s)^2) / (s * sqrt(2 * pi) * x)}
 * otherwise.</li>
 * </ul>
 */
public double density(double x) {
    if (x <= 0) {
        return 0;
    }
    final double x0 = FastMath.log(x) - scale;
    final double x1 = x0 / shape;
    return FastMath.exp(-0.5 * x1 * x1) / (shape * SQRT2PI * x);
}