@Test
public void testConvergenceOnFunctionAccuracy() {
BracketingNthOrderBrentSolverDFP solver =
new BracketingNthOrderBrentSolverDFP(
relativeAccuracy, absoluteAccuracy, field.newDfp(1.0e-20), 20);
UnivariateDfpFunction f =
new UnivariateDfpFunction() {
public Dfp value(Dfp x) {
Dfp one = field.getOne();
Dfp oneHalf = one.divide(2);
Dfp xMo = x.subtract(one);
Dfp xMh = x.subtract(oneHalf);
Dfp xPh = x.add(oneHalf);
Dfp xPo = x.add(one);
return xMo.multiply(xMh).multiply(x).multiply(xPh).multiply(xPo);
}
};
Dfp result =
solver.solve(
20,
f,
field.newDfp(0.2),
field.newDfp(0.9),
field.newDfp(0.4),
AllowedSolution.BELOW_SIDE);
Assert.assertTrue(f.value(result).abs().lessThan(solver.getFunctionValueAccuracy()));
Assert.assertTrue(f.value(result).negativeOrNull());
Assert.assertTrue(
result.subtract(field.newDfp(0.5)).subtract(solver.getAbsoluteAccuracy()).positiveOrNull());
result =
solver.solve(
20,
f,
field.newDfp(-0.9),
field.newDfp(-0.2),
field.newDfp(-0.4),
AllowedSolution.ABOVE_SIDE);
Assert.assertTrue(f.value(result).abs().lessThan(solver.getFunctionValueAccuracy()));
Assert.assertTrue(f.value(result).positiveOrNull());
Assert.assertTrue(
result.add(field.newDfp(0.5)).subtract(solver.getAbsoluteAccuracy()).negativeOrNull());
}
private void check(
UnivariateDfpFunction f,
int maxEval,
double min,
double max,
AllowedSolution allowedSolution) {
BracketingNthOrderBrentSolverDFP solver =
new BracketingNthOrderBrentSolverDFP(
relativeAccuracy, absoluteAccuracy, functionValueAccuracy, 20);
Dfp xResult = solver.solve(maxEval, f, field.newDfp(min), field.newDfp(max), allowedSolution);
Dfp yResult = f.value(xResult);
switch (allowedSolution) {
case ANY_SIDE:
Assert.assertTrue(yResult.abs().lessThan(functionValueAccuracy.multiply(2)));
break;
case LEFT_SIDE:
{
boolean increasing = f.value(xResult).add(absoluteAccuracy).greaterThan(yResult);
Assert.assertTrue(increasing ? yResult.negativeOrNull() : yResult.positiveOrNull());
break;
}
case RIGHT_SIDE:
{
boolean increasing = f.value(xResult).add(absoluteAccuracy).greaterThan(yResult);
Assert.assertTrue(increasing ? yResult.positiveOrNull() : yResult.negativeOrNull());
break;
}
case BELOW_SIDE:
Assert.assertTrue(yResult.negativeOrNull());
break;
case ABOVE_SIDE:
Assert.assertTrue(yResult.positiveOrNull());
break;
default:
// this should never happen
throw new MathInternalError(null);
}
}