/**
* As described by Bernt Arne Ødegaard in Financial Numerical Recipes in C++.
*
* <p>Returns P(X < a, Y < b) where X, Y are gaussian random variables N(0, 1) of the bivariate
* normal distribution with correlation c in [-1, 1] between X and Y.
*/
public static double cdf(double a, double b, double c) {
if (a == Double.NaN || b == Double.NaN || c == Double.NaN) {
throw new IllegalArgumentException("Arguments must be a number.");
}
if (a == Double.NaN) {
System.out.println("");
}
a = handleInfinity(a);
b = handleInfinity(b);
c = handleInfinity(c);
if (a == Double.NaN) {
System.out.println("");
}
if (a <= 0 && b <= 0 && c <= 0) {
final double aprime = a / FastMath.sqrt(2d * (1d - c * c));
final double bprime = b / FastMath.sqrt(2d * (1d - c * c));
double sum = 0;
for (int i = 0; i < A.length; i++) {
for (int j = 0; j < A.length; j++) {
sum += A[i] * A[j] * f(B[i], B[j], aprime, bprime, c);
}
}
sum *= FastMath.sqrt(1d - c * c) / FastMath.PI;
return sum;
}
// a or b may be too big and their multiplication may result in NaN.
if (c * a * b
<= 0) { // c is smaller (between [-1, 1]) and will help to avoid NaNs. So we multiply c
// first.
if ((a <= 0) && (b >= 0) && (c >= 0)) {
return normal.cumulativeProbability(a) - cdf(a, -b, -c);
} else if ((a >= 0) && (b <= 0) && (c >= 0)) {
return normal.cumulativeProbability(b) - cdf(-a, b, -c);
} else if ((a >= 0) && (b >= 0) && (c <= 0)) {
return normal.cumulativeProbability(a)
+ normal.cumulativeProbability(b)
- 1
+ cdf(-a, -b, c);
}
} else if (c * a * b >= 0) {
final double denum = FastMath.sqrt(a * a - 2d * c * a * b + b * b);
final double rho1 = ((c * a - b) * FastMath.signum(a)) / denum;
final double rho2 = ((c * b - a) * FastMath.signum(b)) / denum;
final double delta = (1d - FastMath.signum(a) * FastMath.signum(b)) / 4d;
return cdf(a, 0, rho1) + cdf(b, 0, rho2) - delta;
}
throw new RuntimeException(
"Should never get here. Values of [a; b ; c] = [" + a + "; " + b + "; " + c + "].");
}
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);
}
}