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Add randomized properties tests for betainc special function.

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This commit is contained in:
Eugene Brevdo 2016-06-05 11:10:30 -07:00
parent 39baff850c
commit c53687dd14
1 changed files with 55 additions and 0 deletions
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55
test/array.cpp
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@ -708,6 +708,61 @@ template<typename ArrayType> void array_special_functions()
CALL_SUBTEST(res = betainc(a, b, x);
verify_component_wise(res, v););
}
// Test various properties of betainc
{
ArrayType m1 = ArrayType::Random(32);
ArrayType m2 = ArrayType::Random(32);
ArrayType m3 = ArrayType::Random(32);
ArrayType one = ArrayType::Constant(32, Scalar(1.0));
const Scalar eps = std::numeric_limits<Scalar>::epsilon();
ArrayType a = (m1 * 4.0).exp();
ArrayType b = (m2 * 4.0).exp();
ArrayType x = m3.abs();
// betainc(a, 1, x) == x**a
CALL_SUBTEST(
ArrayType test = betainc(a, one, x);
ArrayType expected = x.pow(a);
verify_component_wise(test, expected););
// betainc(1, b, x) == 1 - (1 - x)**b
CALL_SUBTEST(
ArrayType test = betainc(one, b, x);
ArrayType expected = one - (one - x).pow(b);
verify_component_wise(test, expected););
// betainc(a, b, x) == 1 - betainc(b, a, 1-x)
CALL_SUBTEST(
ArrayType test = betainc(a, b, x) + betainc(b, a, one - x);
ArrayType expected = one;
verify_component_wise(test, expected););
// betainc(a+1, b, x) = betainc(a, b, x) - x**a * (1 - x)**b / (a * beta(a, b))
CALL_SUBTEST(
ArrayType num = x.pow(a) * (one - x).pow(b);
ArrayType denom = a * (a.lgamma() + b.lgamma() - (a + b).lgamma()).exp();
// Add eps to rhs and lhs so that component-wise test doesn't result in
// nans when both outputs are zeros.
ArrayType expected = betainc(a, b, x) - num / denom + eps;
ArrayType test = betainc(a + one, b, x) + eps;
if (sizeof(Scalar) >= 8) { // double
verify_component_wise(test, expected);
} else {
// Reason for limited test: http://eigen.tuxfamily.org/bz/show_bug.cgi?id=1232
verify_component_wise(test.head(8), expected.head(8));
});
// betainc(a, b+1, x) = betainc(a, b, x) + x**a * (1 - x)**b / (b * beta(a, b))
CALL_SUBTEST(
// Add eps to rhs and lhs so that component-wise test doesn't result in
// nans when both outputs are zeros.
ArrayType num = x.pow(a) * (one - x).pow(b);
ArrayType denom = b * (a.lgamma() + b.lgamma() - (a + b).lgamma()).exp();
ArrayType expected = betainc(a, b, x) + num / denom + eps;
ArrayType test = betainc(a, b + one, x) + eps;
verify_component_wise(test, expected););
}
#endif
}