/**
* Since the algorithm to calculate the CDF of a bivariate gaussian distribution fails with
* infinity, we change infinity to the maximum value a Double can be. This allows the mentioned
* algorithm to provide the appropriate answer.
*/
private static double handleInfinity(double n) {
if (Double.isInfinite(n)) {
n = FastMath.copySign(Double.MAX_VALUE, n);
}
return n;
}
/**
* Compute the <a href="http://mathworld.wolfram.com/SquareRoot.html" TARGET="_top"> square
* root</a> of this complex number. Implements the following algorithm to compute {@code sqrt(a +
* bi)}:
*
* <ol>
* <li>Let {@code t = sqrt((|a| + |a + bi|) / 2)}
* <li>
* <pre>if {@code a ≥ 0} return {@code t + (b/2t)i}
* else return {@code |b|/2t + sign(b)t i }</pre>
* </ol>
*
* where
*
* <ul>
* <li>{@code |a| = }{@link Math#abs}(a)
* <li>{@code |a + bi| = }{@link Complex#abs}(a + bi)
* <li>{@code sign(b) = }{@link FastMath#copySign(double,double) copySign(1d, b)}
* </ul>
*
* <br>
* Returns {@link Complex#NaN} if either real or imaginary part of the input argument is {@code
* NaN}. <br>
* Infinite values in real or imaginary parts of the input may result in infinite or NaN values
* returned in parts of the result.
*
* <pre>
* Examples:
* <code>
* sqrt(1 ± INFINITY i) = INFINITY + NaN i
* sqrt(INFINITY + i) = INFINITY + 0i
* sqrt(-INFINITY + i) = 0 + INFINITY i
* sqrt(INFINITY ± INFINITY i) = INFINITY + NaN i
* sqrt(-INFINITY ± INFINITY i) = NaN ± INFINITY i
* </code>
* </pre>
*
* @return the square root of {@code this}.
* @since 1.2
*/
public Complex sqrt() {
if (isNaN) {
return NaN;
}
if (real == 0.0 && imaginary == 0.0) {
return createComplex(0.0, 0.0);
}
double t = FastMath.sqrt((FastMath.abs(real) + abs()) / 2.0);
if (real >= 0.0) {
return createComplex(t, imaginary / (2.0 * t));
} else {
return createComplex(
FastMath.abs(imaginary) / (2.0 * t), FastMath.copySign(1d, imaginary) * t);
}
}