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Merged in tillahoffmann/eigen (pull request PR-173)

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Added zeta function of two arguments and polygamma function
This commit is contained in:
Benoit Steiner
2016-04-06 09:40:17 -07:00
parent 7781f865cb 726bd5f077
commit 10bdd8e378
10 changed files with 539 additions and 0 deletions
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26
test/array.cpp
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@@ -322,6 +322,32 @@ template<typename ArrayType> void array_real(const ArrayType& m)
std::numeric_limits<RealScalar>::infinity());
VERIFY_IS_EQUAL(numext::digamma(Scalar(-1)),
std::numeric_limits<RealScalar>::infinity());
// Check the zeta function against scipy.special.zeta
VERIFY_IS_APPROX(numext::zeta(Scalar(1.5), Scalar(2)), RealScalar(1.61237534869));
VERIFY_IS_APPROX(numext::zeta(Scalar(4), Scalar(1.5)), RealScalar(0.234848505667));
VERIFY_IS_APPROX(numext::zeta(Scalar(10.5), Scalar(3)), RealScalar(1.03086757337e-5));
VERIFY_IS_APPROX(numext::zeta(Scalar(10000.5), Scalar(1.0001)), RealScalar(0.367879440865));
VERIFY_IS_APPROX(numext::zeta(Scalar(3), Scalar(-2.5)), RealScalar(0.054102025820864097));
VERIFY_IS_EQUAL(numext::zeta(Scalar(1), Scalar(1.2345)), // The second scalar does not matter
std::numeric_limits<RealScalar>::infinity());
// Check the polygamma against scipy.special.polygamma examples
VERIFY_IS_APPROX(numext::polygamma(Scalar(1), Scalar(2)), RealScalar(0.644934066848));
VERIFY_IS_APPROX(numext::polygamma(Scalar(1), Scalar(3)), RealScalar(0.394934066848));
VERIFY_IS_APPROX(numext::polygamma(Scalar(1), Scalar(25.5)), RealScalar(0.0399946696496));
// Check the polygamma function over a larger range of values
VERIFY_IS_APPROX(numext::polygamma(Scalar(17), Scalar(4.7)), RealScalar(293.334565435));
VERIFY_IS_APPROX(numext::polygamma(Scalar(31), Scalar(11.8)), RealScalar(0.445487887616));
VERIFY_IS_APPROX(numext::polygamma(Scalar(28), Scalar(17.7)), RealScalar(-2.47810300902e-07));
VERIFY_IS_APPROX(numext::polygamma(Scalar(8), Scalar(30.2)), RealScalar(-8.29668781082e-09));
/* The following tests only pass for doubles because floats cannot handle the large values of
the gamma function.
VERIFY_IS_APPROX(numext::polygamma(Scalar(42), Scalar(15.8)), RealScalar(-0.434562276666));
VERIFY_IS_APPROX(numext::polygamma(Scalar(147), Scalar(54.1)), RealScalar(0.567742190178));
VERIFY_IS_APPROX(numext::polygamma(Scalar(170), Scalar(64)), RealScalar(-0.0108615497927));
*/
{
// Test various propreties of igamma & igammac. These are normalized