Add randomized properties tests for betainc special function.
diff --git a/test/array.cpp b/test/array.cpp
index 8ed1269..4cd4f26 100644
--- a/test/array.cpp
+++ b/test/array.cpp
@@ -708,6 +708,61 @@
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
}