* f(x) = a + b*exp(-((x - c)^2 / (2*d^2))) *
* The parameters have the following meaning: *
parameters is invalid as
* determined by {@link #validateParameters(double[])}
* @throws ZeroException if parameters values are
* invalid as determined by {@link #validateParameters(double[])}
*/
public double value(double x, double[] parameters) throws ZeroException {
validateParameters(parameters);
final double a = parameters[0];
final double b = parameters[1];
final double c = parameters[2];
final double d = parameters[3];
final double xMc = x - c;
return a + b * Math.exp(-xMc * xMc / (2.0 * (d * d)));
}
/**
* Computes the gradient vector for a four variable version of the function
* where the parameters, a, b, c, and d,
* are considered the variables, not x. That is, instead of
* computing the gradient vector for the function f(x) (which would
* just be the derivative of f(x) with respect to x since
* it's a one-dimensional function), computes the gradient vector for the
* function f(a, b, c, d) = a + b*exp(-((x - c)^2 / (2*d^2)))
* treating the specified x as a constant.
*
* The components of the computed gradient vector are the partial
* derivatives of f(a, b, c, d) with respect to each variable.
* That is, the partial derivative of f(a, b, c, d) with respect to
* a, the partial derivative of f(a, b, c, d) with respect
* to b, the partial derivative of f(a, b, c, d) with
* respect to c, and the partial derivative of f(a, b, c,
* d) with respect to d.
*
* @param x x value to be used as constant in f(a, b, c,
* d)
* @param parameters values of a, b, c, and
* d for computation of gradient vector of f(a, b, c,
* d)
*
* @return gradient vector of f(a, b, c, d)
*
* @throws IllegalArgumentException if parameters is invalid as
* determined by {@link #validateParameters(double[])}
* @throws ZeroException if parameters values are
* invalid as determined by {@link #validateParameters(double[])}
*/
public double[] gradient(double x, double[] parameters) throws ZeroException {
validateParameters(parameters);
final double b = parameters[1];
final double c = parameters[2];
final double d = parameters[3];
final double xMc = x - c;
final double d2 = d * d;
final double exp = Math.exp(-xMc * xMc / (2 * d2));
final double f = b * exp * xMc / d2;
return new double[] { 1.0, exp, f, f * xMc / d };
}
/**
* Validates parameters to ensure they are appropriate for the evaluation of
* the value and gradient methods.
*
* @param parameters values of a, b, c, and
* d
*
* @throws IllegalArgumentException if parameters is
* null or if parameters does not have
* length == 4
* @throws ZeroException if parameters[3]
* (d) is 0
*/
private void validateParameters(double[] parameters) throws ZeroException {
if (parameters == null) {
throw new NullArgumentException(LocalizedFormats.INPUT_ARRAY);
}
if (parameters.length != 4) {
throw new DimensionMismatchException(4, parameters.length);
}
if (parameters[3] == 0.0) {
throw new ZeroException();
}
}
}