/**
* Calculates the Nth generalized harmonic number. See <a
* href="http://mathworld.wolfram.com/HarmonicSeries.html">Harmonic Series</a>.
*
* @param n the term in the series to calculate (must be ≥ 1)
* @param m the exponent; special case m == 1.0 is the harmonic series
* @return the nth generalized harmonic number
*/
private double generalizedHarmonic(final int n, final double m) {
double value = 0;
for (int k = n; k > 0; --k) {
value += 1.0 / FastMath.pow(k, m);
}
return value;
}
/**
* The probability mass function P(X = x) for a Zipf distribution.
*
* @param x the value at which the probability density function is evaluated.
* @return the value of the probability mass function at x
*/
public double probability(final int x) {
if (x <= 0 || x > numberOfElements) {
return 0.0;
}
return (1.0 / FastMath.pow(x, exponent)) / generalizedHarmonic(numberOfElements, exponent);
}
private void calculateBlbSum(
double[] sample,
double samplingRate,
double bagExp,
final int numberOfBags,
final int numberOfBootstraps,
Mean perbootstrapTime,
Mean perbagTime) {
bagSums = new double[numberOfBags];
int bag_size = (int) FastMath.ceil(FastMath.pow(sample.length, bagExp));
int[] index = new int[sample.length];
for (int ii = 0; ii < sample.length; ii++) {
index[ii] = ii;
}
int[] origIndex = index.clone();
long bootstrapTime = 0;
Mean actualSum = new Mean();
for (int ii = 0; ii < numberOfBags; ii++) {
SamplingUtilities.KnuthShuffle(index);
double[] sampleBag = new double[bag_size];
for (int jj = 0; jj < bag_size; jj++) {
sampleBag[jj] = sample[index[jj]];
}
BootstrapSum sum =
new BootstrapSum(sampleBag, samplingRate, numberOfBootstraps, sample.length);
bagSums[ii] = sum.Sum();
actualSum.increment(bagSums[ii]);
perbootstrapTime.increment(sum.getMeanTime());
bootstrapTime += sum.getTimes()[sum.getTimes().length - 1];
perbagTime.increment(sum.getTimes()[sum.getTimes().length - 1]);
index = origIndex.clone();
}
meanSum = actualSum.getResult();
totalTime = bootstrapTime;
}
/** {@inheritDoc} */
@Override
public void integrate(final ExpandableStatefulODE equations, final double t)
throws MathIllegalStateException, MathIllegalArgumentException {
sanityChecks(equations, t);
setEquations(equations);
final boolean forward = t > equations.getTime();
// create some internal working arrays
final double[] y0 = equations.getCompleteState();
final double[] y = y0.clone();
final int stages = c.length + 1;
final double[][] yDotK = new double[stages][y.length];
final double[] yTmp = y0.clone();
final double[] yDotTmp = new double[y.length];
// set up an interpolator sharing the integrator arrays
final RungeKuttaStepInterpolator interpolator = (RungeKuttaStepInterpolator) prototype.copy();
interpolator.reinitialize(
this, yTmp, yDotK, forward, equations.getPrimaryMapper(), equations.getSecondaryMappers());
interpolator.storeTime(equations.getTime());
// set up integration control objects
stepStart = equations.getTime();
double hNew = 0;
boolean firstTime = true;
initIntegration(equations.getTime(), y0, t);
// main integration loop
isLastStep = false;
do {
interpolator.shift();
// iterate over step size, ensuring local normalized error is smaller than 1
double error = 10;
while (error >= 1.0) {
if (firstTime || !fsal) {
// first stage
computeDerivatives(stepStart, y, yDotK[0]);
}
if (firstTime) {
final double[] scale = new double[mainSetDimension];
if (vecAbsoluteTolerance == null) {
for (int i = 0; i < scale.length; ++i) {
scale[i] = scalAbsoluteTolerance + scalRelativeTolerance * FastMath.abs(y[i]);
}
} else {
for (int i = 0; i < scale.length; ++i) {
scale[i] = vecAbsoluteTolerance[i] + vecRelativeTolerance[i] * FastMath.abs(y[i]);
}
}
hNew = initializeStep(forward, getOrder(), scale, stepStart, y, yDotK[0], yTmp, yDotK[1]);
firstTime = false;
}
stepSize = hNew;
if (forward) {
if (stepStart + stepSize >= t) {
stepSize = t - stepStart;
}
} else {
if (stepStart + stepSize <= t) {
stepSize = t - stepStart;
}
}
// next stages
for (int k = 1; k < stages; ++k) {
for (int j = 0; j < y0.length; ++j) {
double sum = a[k - 1][0] * yDotK[0][j];
for (int l = 1; l < k; ++l) {
sum += a[k - 1][l] * yDotK[l][j];
}
yTmp[j] = y[j] + stepSize * sum;
}
computeDerivatives(stepStart + c[k - 1] * stepSize, yTmp, yDotK[k]);
}
// estimate the state at the end of the step
for (int j = 0; j < y0.length; ++j) {
double sum = b[0] * yDotK[0][j];
for (int l = 1; l < stages; ++l) {
sum += b[l] * yDotK[l][j];
}
yTmp[j] = y[j] + stepSize * sum;
}
// estimate the error at the end of the step
error = estimateError(yDotK, y, yTmp, stepSize);
if (error >= 1.0) {
// reject the step and attempt to reduce error by stepsize control
final double factor =
FastMath.min(
maxGrowth, FastMath.max(minReduction, safety * FastMath.pow(error, exp)));
hNew = filterStep(stepSize * factor, forward, false);
}
}
// local error is small enough: accept the step, trigger events and step handlers
interpolator.storeTime(stepStart + stepSize);
System.arraycopy(yTmp, 0, y, 0, y0.length);
System.arraycopy(yDotK[stages - 1], 0, yDotTmp, 0, y0.length);
stepStart = acceptStep(interpolator, y, yDotTmp, t);
System.arraycopy(y, 0, yTmp, 0, y.length);
if (!isLastStep) {
// prepare next step
interpolator.storeTime(stepStart);
if (fsal) {
// save the last evaluation for the next step
System.arraycopy(yDotTmp, 0, yDotK[0], 0, y0.length);
}
// stepsize control for next step
final double factor =
FastMath.min(maxGrowth, FastMath.max(minReduction, safety * FastMath.pow(error, exp)));
final double scaledH = stepSize * factor;
final double nextT = stepStart + scaledH;
final boolean nextIsLast = forward ? (nextT >= t) : (nextT <= t);
hNew = filterStep(scaledH, forward, nextIsLast);
final double filteredNextT = stepStart + hNew;
final boolean filteredNextIsLast = forward ? (filteredNextT >= t) : (filteredNextT <= t);
if (filteredNextIsLast) {
hNew = t - stepStart;
}
}
} while (!isLastStep);
// dispatch results
equations.setTime(stepStart);
equations.setCompleteState(y);
resetInternalState();
}
/**
* Returns a <code>double</code> whose value is <tt>(this<sup>exponent</sup>)</tt>, returning the
* result in reduced form.
*
* @param exponent exponent to which this <code>BigFraction</code> is to be raised.
* @return <tt>this<sup>exponent</sup></tt>.
*/
public double pow(final double exponent) {
return FastMath.pow(numerator.doubleValue(), exponent)
/ FastMath.pow(denominator.doubleValue(), exponent);
}
