public double execute(double in) throws DMLRuntimeException {
switch (bFunc) {
case SIN:
return FASTMATH ? FastMath.sin(in) : Math.sin(in);
case COS:
return FASTMATH ? FastMath.cos(in) : Math.cos(in);
case TAN:
return FASTMATH ? FastMath.tan(in) : Math.tan(in);
case ASIN:
return FASTMATH ? FastMath.asin(in) : Math.asin(in);
case ACOS:
return FASTMATH ? FastMath.acos(in) : Math.acos(in);
case ATAN:
return Math.atan(in); // faster in Math
case CEIL:
return FASTMATH ? FastMath.ceil(in) : Math.ceil(in);
case FLOOR:
return FASTMATH ? FastMath.floor(in) : Math.floor(in);
case LOG:
return FASTMATH ? FastMath.log(in) : Math.log(in);
case LOG_NZ:
return (in == 0) ? 0 : FASTMATH ? FastMath.log(in) : Math.log(in);
case ABS:
return Math.abs(in); // no need for FastMath
case SIGN:
return FASTMATH ? FastMath.signum(in) : Math.signum(in);
case SQRT:
return Math.sqrt(in); // faster in Math
case EXP:
return FASTMATH ? FastMath.exp(in) : Math.exp(in);
case ROUND:
return Math.round(in); // no need for FastMath
case PLOGP:
if (in == 0.0) return 0.0;
else if (in < 0) return Double.NaN;
else return (in * (FASTMATH ? FastMath.log(in) : Math.log(in)));
case SPROP:
// sample proportion: P*(1-P)
return in * (1 - in);
case SIGMOID:
// sigmoid: 1/(1+exp(-x))
return FASTMATH ? 1 / (1 + FastMath.exp(-in)) : 1 / (1 + Math.exp(-in));
case SELP:
// select positive: x*(x>0)
return (in > 0) ? in : 0;
default:
throw new DMLRuntimeException("Builtin.execute(): Unknown operation: " + bFunc);
}
}
/**
* Returns an estimate of the <code>p</code>th percentile of the values in the <code>values</code>
* array, starting with the element in (0-based) position <code>begin</code> in the array and
* including <code>length</code> values.
*
* <p>Calls to this method do not modify the internal <code>quantile</code> state of this
* statistic.
*
* <p>
*
* <ul>
* <li>Returns <code>Double.NaN</code> if <code>length = 0</code>
* <li>Returns (for any value of <code>p</code>) <code>values[begin]</code> if <code>length = 1
* </code>
* <li>Throws <code>IllegalArgumentException</code> if <code>values</code> is null , <code>begin
* </code> or <code>length</code> is invalid, or <code>p</code> is not a valid quantile
* value (p must be greater than 0 and less than or equal to 100)
* </ul>
*
* <p>See {@link Percentile} for a description of the percentile estimation algorithm used.
*
* @param values array of input values
* @param p the percentile to compute
* @param begin the first (0-based) element to include in the computation
* @param length the number of array elements to include
* @return the percentile value
* @throws IllegalArgumentException if the parameters are not valid or the input array is null
*/
public double evaluate(final double[] values, final int begin, final int length, final double p) {
test(values, begin, length);
if ((p > 100) || (p <= 0)) {
throw new OutOfRangeException(LocalizedFormats.OUT_OF_BOUNDS_QUANTILE_VALUE, p, 0, 100);
}
if (length == 0) {
return Double.NaN;
}
if (length == 1) {
return values[begin]; // always return single value for n = 1
}
double n = length;
double pos = p * (n + 1) / 100;
double fpos = FastMath.floor(pos);
int intPos = (int) fpos;
double dif = pos - fpos;
double[] work;
int[] pivotsHeap;
if (values == getDataRef()) {
work = getDataRef();
pivotsHeap = cachedPivots;
} else {
work = new double[length];
System.arraycopy(values, begin, work, 0, length);
pivotsHeap = new int[(0x1 << MAX_CACHED_LEVELS) - 1];
Arrays.fill(pivotsHeap, -1);
}
if (pos < 1) {
return select(work, pivotsHeap, 0);
}
if (pos >= n) {
return select(work, pivotsHeap, length - 1);
}
double lower = select(work, pivotsHeap, intPos - 1);
double upper = select(work, pivotsHeap, intPos);
return lower + dif * (upper - lower);
}
/**
* Compute the error of Stirling's series at the given value.
*
* <p>References:
*
* <ol>
* <li>Eric W. Weisstein. "Stirling's Series." From MathWorld--A Wolfram Web Resource. <a
* target="_blank" href="http://mathworld.wolfram.com/StirlingsSeries.html">
* http://mathworld.wolfram.com/StirlingsSeries.html</a>
* </ol>
*
* @param z the value.
* @return the Striling's series error.
*/
static double getStirlingError(double z) {
double ret;
if (z < 15.0) {
double z2 = 2.0 * z;
if (FastMath.floor(z2) == z2) {
ret = EXACT_STIRLING_ERRORS[(int) z2];
} else {
ret = Gamma.logGamma(z + 1.0) - (z + 0.5) * FastMath.log(z) + z - HALF_LOG_2_PI;
}
} else {
double z2 = z * z;
ret =
(0.083333333333333333333
- (0.00277777777777777777778
- (0.00079365079365079365079365
- (0.000595238095238095238095238
- 0.0008417508417508417508417508 / z2)
/ z2)
/ z2)
/ z2)
/ z;
}
return ret;
}
/**
* Create a fraction given the double value and either the maximum error allowed or the maximum
* number of denominator digits.
*
* <p>NOTE: This constructor is called with EITHER - a valid epsilon value and the maxDenominator
* set to Integer.MAX_VALUE (that way the maxDenominator has no effect). OR - a valid
* maxDenominator value and the epsilon value set to zero (that way epsilon only has effect if
* there is an exact match before the maxDenominator value is reached).
*
* <p>It has been done this way so that the same code can be (re)used for both scenarios. However
* this could be confusing to users if it were part of the public API and this constructor should
* therefore remain PRIVATE. See JIRA issue ticket MATH-181 for more details:
*
* <p>https://issues.apache.org/jira/browse/MATH-181
*
* @param value the double value to convert to a fraction.
* @param epsilon maximum error allowed. The resulting fraction is within {@code epsilon} of
* {@code value}, in absolute terms.
* @param maxDenominator maximum denominator value allowed.
* @param maxIterations maximum number of convergents
* @throws FractionConversionException if the continued fraction failed to converge.
*/
private Fraction(double value, double epsilon, int maxDenominator, int maxIterations)
throws FractionConversionException {
long overflow = Integer.MAX_VALUE;
double r0 = value;
long a0 = (long) FastMath.floor(r0);
if (FastMath.abs(a0) > overflow) {
throw new FractionConversionException(value, a0, 1l);
}
// check for (almost) integer arguments, which should not go
// to iterations.
if (FastMath.abs(a0 - value) < epsilon) {
this.numerator = (int) a0;
this.denominator = 1;
return;
}
long p0 = 1;
long q0 = 0;
long p1 = a0;
long q1 = 1;
long p2 = 0;
long q2 = 1;
int n = 0;
boolean stop = false;
do {
++n;
double r1 = 1.0 / (r0 - a0);
long a1 = (long) FastMath.floor(r1);
p2 = (a1 * p1) + p0;
q2 = (a1 * q1) + q0;
if ((FastMath.abs(p2) > overflow) || (FastMath.abs(q2) > overflow)) {
// in maxDenominator mode, if the last fraction was very close to the actual value
// q2 may overflow in the next iteration; in this case return the last one.
if (epsilon == 0.0 && FastMath.abs(q1) < maxDenominator) {
break;
}
throw new FractionConversionException(value, p2, q2);
}
double convergent = (double) p2 / (double) q2;
if (n < maxIterations && FastMath.abs(convergent - value) > epsilon && q2 < maxDenominator) {
p0 = p1;
p1 = p2;
q0 = q1;
q1 = q2;
a0 = a1;
r0 = r1;
} else {
stop = true;
}
} while (!stop);
if (n >= maxIterations) {
throw new FractionConversionException(value, maxIterations);
}
if (q2 < maxDenominator) {
this.numerator = (int) p2;
this.denominator = (int) q2;
} else {
this.numerator = (int) p1;
this.denominator = (int) q1;
}
}
/**
* Returns the value of log B(p, q) for 0 ≤ x ≤ 1 and p, q > 0. Based on the <em>NSWC Library of
* Mathematics Subroutines</em> implementation, {@code DBETLN}.
*
* @param p First argument.
* @param q Second argument.
* @return the value of {@code log(Beta(p, q))}, {@code NaN} if {@code p <= 0} or {@code q <= 0}.
*/
public static double logBeta(final double p, final double q) {
if (Double.isNaN(p) || Double.isNaN(q) || (p <= 0.0) || (q <= 0.0)) {
return Double.NaN;
}
final double a = FastMath.min(p, q);
final double b = FastMath.max(p, q);
if (a >= 10.0) {
final double w = sumDeltaMinusDeltaSum(a, b);
final double h = a / b;
final double c = h / (1.0 + h);
final double u = -(a - 0.5) * FastMath.log(c);
final double v = b * FastMath.log1p(h);
if (u <= v) {
return (((-0.5 * FastMath.log(b) + HALF_LOG_TWO_PI) + w) - u) - v;
} else {
return (((-0.5 * FastMath.log(b) + HALF_LOG_TWO_PI) + w) - v) - u;
}
} else if (a > 2.0) {
if (b > 1000.0) {
final int n = (int) FastMath.floor(a - 1.0);
double prod = 1.0;
double ared = a;
for (int i = 0; i < n; i++) {
ared -= 1.0;
prod *= ared / (1.0 + ared / b);
}
return (FastMath.log(prod) - n * FastMath.log(b))
+ (Gamma.logGamma(ared) + logGammaMinusLogGammaSum(ared, b));
} else {
double prod1 = 1.0;
double ared = a;
while (ared > 2.0) {
ared -= 1.0;
final double h = ared / b;
prod1 *= h / (1.0 + h);
}
if (b < 10.0) {
double prod2 = 1.0;
double bred = b;
while (bred > 2.0) {
bred -= 1.0;
prod2 *= bred / (ared + bred);
}
return FastMath.log(prod1)
+ FastMath.log(prod2)
+ (Gamma.logGamma(ared) + (Gamma.logGamma(bred) - logGammaSum(ared, bred)));
} else {
return FastMath.log(prod1) + Gamma.logGamma(ared) + logGammaMinusLogGammaSum(ared, b);
}
}
} else if (a >= 1.0) {
if (b > 2.0) {
if (b < 10.0) {
double prod = 1.0;
double bred = b;
while (bred > 2.0) {
bred -= 1.0;
prod *= bred / (a + bred);
}
return FastMath.log(prod)
+ (Gamma.logGamma(a) + (Gamma.logGamma(bred) - logGammaSum(a, bred)));
} else {
return Gamma.logGamma(a) + logGammaMinusLogGammaSum(a, b);
}
} else {
return Gamma.logGamma(a) + Gamma.logGamma(b) - logGammaSum(a, b);
}
} else {
if (b >= 10.0) {
return Gamma.logGamma(a) + logGammaMinusLogGammaSum(a, b);
} else {
// The following command is the original NSWC implementation.
// return Gamma.logGamma(a) +
// (Gamma.logGamma(b) - Gamma.logGamma(a + b));
// The following command turns out to be more accurate.
return FastMath.log(Gamma.gamma(a) * Gamma.gamma(b) / Gamma.gamma(a + b));
}
}
}
