bug #1232: refactor special functions as a new SpecialFunctions module, currently in unsupported/.
diff --git a/test/array.cpp b/test/array.cpp
index 6347c80..d734e60 100644
--- a/test/array.cpp
+++ b/test/array.cpp
@@ -234,12 +234,7 @@
VERIFY_IS_APPROX(m1.sinh(), sinh(m1));
VERIFY_IS_APPROX(m1.cosh(), cosh(m1));
VERIFY_IS_APPROX(m1.tanh(), tanh(m1));
-#if EIGEN_HAS_C99_MATH
- VERIFY_IS_APPROX(m1.lgamma(), lgamma(m1));
- VERIFY_IS_APPROX(m1.digamma(), digamma(m1));
- VERIFY_IS_APPROX(m1.erf(), erf(m1));
- VERIFY_IS_APPROX(m1.erfc(), erfc(m1));
-#endif // EIGEN_HAS_C99_MATH
+
VERIFY_IS_APPROX(m1.arg(), arg(m1));
VERIFY_IS_APPROX(m1.round(), round(m1));
VERIFY_IS_APPROX(m1.floor(), floor(m1));
@@ -313,88 +308,6 @@
m1 += ArrayType::Constant(rows,cols,Scalar(tiny));
VERIFY_IS_APPROX(s1/m1, s1 * m1.inverse());
-
-
-#if EIGEN_HAS_C99_MATH
- // check special functions (comparing against numpy implementation)
- if (!NumTraits<Scalar>::IsComplex)
- {
-
- {
- // Test various propreties of igamma & igammac. These are normalized
- // gamma integrals where
- // igammac(a, x) = Gamma(a, x) / Gamma(a)
- // igamma(a, x) = gamma(a, x) / Gamma(a)
- // where Gamma and gamma are considered the standard unnormalized
- // upper and lower incomplete gamma functions, respectively.
- ArrayType a = m1.abs() + 2;
- ArrayType x = m2.abs() + 2;
- ArrayType zero = ArrayType::Zero(rows, cols);
- ArrayType one = ArrayType::Constant(rows, cols, Scalar(1.0));
- ArrayType a_m1 = a - one;
- ArrayType Gamma_a_x = Eigen::igammac(a, x) * a.lgamma().exp();
- ArrayType Gamma_a_m1_x = Eigen::igammac(a_m1, x) * a_m1.lgamma().exp();
- ArrayType gamma_a_x = Eigen::igamma(a, x) * a.lgamma().exp();
- ArrayType gamma_a_m1_x = Eigen::igamma(a_m1, x) * a_m1.lgamma().exp();
-
- // Gamma(a, 0) == Gamma(a)
- VERIFY_IS_APPROX(Eigen::igammac(a, zero), one);
-
- // Gamma(a, x) + gamma(a, x) == Gamma(a)
- VERIFY_IS_APPROX(Gamma_a_x + gamma_a_x, a.lgamma().exp());
-
- // Gamma(a, x) == (a - 1) * Gamma(a-1, x) + x^(a-1) * exp(-x)
- VERIFY_IS_APPROX(Gamma_a_x, (a - 1) * Gamma_a_m1_x + x.pow(a-1) * (-x).exp());
-
- // gamma(a, x) == (a - 1) * gamma(a-1, x) - x^(a-1) * exp(-x)
- VERIFY_IS_APPROX(gamma_a_x, (a - 1) * gamma_a_m1_x - x.pow(a-1) * (-x).exp());
- }
-
- // Check exact values of igamma and igammac against a third party calculation.
- Scalar a_s[] = {Scalar(0), Scalar(1), Scalar(1.5), Scalar(4), Scalar(0.0001), Scalar(1000.5)};
- Scalar x_s[] = {Scalar(0), Scalar(1), Scalar(1.5), Scalar(4), Scalar(0.0001), Scalar(1000.5)};
-
- // location i*6+j corresponds to a_s[i], x_s[j].
- Scalar nan = std::numeric_limits<Scalar>::quiet_NaN();
- Scalar igamma_s[][6] = {{0.0, nan, nan, nan, nan, nan},
- {0.0, 0.6321205588285578, 0.7768698398515702,
- 0.9816843611112658, 9.999500016666262e-05, 1.0},
- {0.0, 0.4275932955291202, 0.608374823728911,
- 0.9539882943107686, 7.522076445089201e-07, 1.0},
- {0.0, 0.01898815687615381, 0.06564245437845008,
- 0.5665298796332909, 4.166333347221828e-18, 1.0},
- {0.0, 0.9999780593618628, 0.9999899967080838,
- 0.9999996219837988, 0.9991370418689945, 1.0},
- {0.0, 0.0, 0.0, 0.0, 0.0, 0.5042041932513908}};
- Scalar igammac_s[][6] = {{nan, nan, nan, nan, nan, nan},
- {1.0, 0.36787944117144233, 0.22313016014842982,
- 0.018315638888734182, 0.9999000049998333, 0.0},
- {1.0, 0.5724067044708798, 0.3916251762710878,
- 0.04601170568923136, 0.9999992477923555, 0.0},
- {1.0, 0.9810118431238462, 0.9343575456215499,
- 0.4334701203667089, 1.0, 0.0},
- {1.0, 2.1940638138146658e-05, 1.0003291916285e-05,
- 3.7801620118431334e-07, 0.0008629581310054535,
- 0.0},
- {1.0, 1.0, 1.0, 1.0, 1.0, 0.49579580674813944}};
- for (int i = 0; i < 6; ++i) {
- for (int j = 0; j < 6; ++j) {
- if ((std::isnan)(igamma_s[i][j])) {
- VERIFY((std::isnan)(numext::igamma(a_s[i], x_s[j])));
- } else {
- VERIFY_IS_APPROX(numext::igamma(a_s[i], x_s[j]), igamma_s[i][j]);
- }
-
- if ((std::isnan)(igammac_s[i][j])) {
- VERIFY((std::isnan)(numext::igammac(a_s[i], x_s[j])));
- } else {
- VERIFY_IS_APPROX(numext::igammac(a_s[i], x_s[j]), igammac_s[i][j]);
- }
- }
- }
- }
-#endif // EIGEN_HAS_C99_MATH
-
// check inplace transpose
m3 = m1;
m3.transposeInPlace();
@@ -537,242 +450,8 @@
}
-template<typename X, typename Y>
-void verify_component_wise(const X& x, const Y& y)
-{
- for(Index i=0; i<x.size(); ++i)
- {
- if((numext::isfinite)(y(i)))
- VERIFY_IS_APPROX( x(i), y(i) );
- else if((numext::isnan)(y(i)))
- VERIFY((numext::isnan)(x(i)));
- else
- VERIFY_IS_EQUAL( x(i), y(i) );
- }
-}
-
-// check special functions (comparing against numpy implementation)
-template<typename ArrayType> void array_special_functions()
-{
- using std::abs;
- using std::sqrt;
- typedef typename ArrayType::Scalar Scalar;
- typedef typename NumTraits<Scalar>::Real RealScalar;
-
- Scalar plusinf = std::numeric_limits<Scalar>::infinity();
- Scalar nan = std::numeric_limits<Scalar>::quiet_NaN();
-
- // Check the zeta function against scipy.special.zeta
- {
- ArrayType x(7), q(7), res(7), ref(7);
- x << 1.5, 4, 10.5, 10000.5, 3, 1, 0.9;
- q << 2, 1.5, 3, 1.0001, -2.5, 1.2345, 1.2345;
- ref << 1.61237534869, 0.234848505667, 1.03086757337e-5, 0.367879440865, 0.054102025820864097, plusinf, nan;
- CALL_SUBTEST( verify_component_wise(ref, ref); );
- CALL_SUBTEST( res = x.zeta(q); verify_component_wise(res, ref); );
- CALL_SUBTEST( res = zeta(x,q); verify_component_wise(res, ref); );
- }
-
- // digamma
- {
- ArrayType x(7), res(7), ref(7);
- x << 1, 1.5, 4, -10.5, 10000.5, 0, -1;
- ref << -0.5772156649015329, 0.03648997397857645, 1.2561176684318, 2.398239129535781, 9.210340372392849, plusinf, plusinf;
- CALL_SUBTEST( verify_component_wise(ref, ref); );
-
- CALL_SUBTEST( res = x.digamma(); verify_component_wise(res, ref); );
- CALL_SUBTEST( res = digamma(x); verify_component_wise(res, ref); );
- }
-
-
-#if EIGEN_HAS_C99_MATH
- {
- ArrayType n(11), x(11), res(11), ref(11);
- n << 1, 1, 1, 1.5, 17, 31, 28, 8, 42, 147, 170;
- x << 2, 3, 25.5, 1.5, 4.7, 11.8, 17.7, 30.2, 15.8, 54.1, 64;
- ref << 0.644934066848, 0.394934066848, 0.0399946696496, nan, 293.334565435, 0.445487887616, -2.47810300902e-07, -8.29668781082e-09, -0.434562276666, 0.567742190178, -0.0108615497927;
- CALL_SUBTEST( verify_component_wise(ref, ref); );
-
- if(sizeof(RealScalar)>=8) { // double
- // Reason for commented line: http://eigen.tuxfamily.org/bz/show_bug.cgi?id=1232
- // CALL_SUBTEST( res = x.polygamma(n); verify_component_wise(res, ref); );
- CALL_SUBTEST( res = polygamma(n,x); verify_component_wise(res, ref); );
- }
- else {
- // CALL_SUBTEST( res = x.polygamma(n); verify_component_wise(res.head(8), ref.head(8)); );
- CALL_SUBTEST( res = polygamma(n,x); verify_component_wise(res.head(8), ref.head(8)); );
- }
- }
-#endif
-
-#if EIGEN_HAS_C99_MATH
- {
- // Inputs and ground truth generated with scipy via:
- // a = np.logspace(-3, 3, 5) - 1e-3
- // b = np.logspace(-3, 3, 5) - 1e-3
- // x = np.linspace(-0.1, 1.1, 5)
- // (full_a, full_b, full_x) = np.vectorize(lambda a, b, x: (a, b, x))(*np.ix_(a, b, x))
- // full_a = full_a.flatten().tolist() # same for full_b, full_x
- // v = scipy.special.betainc(full_a, full_b, full_x).flatten().tolist()
- //
- // Note in Eigen, we call betainc with arguments in the order (x, a, b).
- ArrayType a(125);
- ArrayType b(125);
- ArrayType x(125);
- ArrayType v(125);
- ArrayType res(125);
-
- a << 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
- 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
- 0.03062277660168379, 0.03062277660168379, 0.03062277660168379,
- 0.03062277660168379, 0.03062277660168379, 0.03062277660168379,
- 0.03062277660168379, 0.03062277660168379, 0.03062277660168379,
- 0.03062277660168379, 0.03062277660168379, 0.03062277660168379,
- 0.03062277660168379, 0.03062277660168379, 0.03062277660168379,
- 0.03062277660168379, 0.03062277660168379, 0.03062277660168379,
- 0.03062277660168379, 0.03062277660168379, 0.03062277660168379,
- 0.03062277660168379, 0.03062277660168379, 0.03062277660168379,
- 0.03062277660168379, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999,
- 0.999, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999,
- 0.999, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999,
- 31.62177660168379, 31.62177660168379, 31.62177660168379,
- 31.62177660168379, 31.62177660168379, 31.62177660168379,
- 31.62177660168379, 31.62177660168379, 31.62177660168379,
- 31.62177660168379, 31.62177660168379, 31.62177660168379,
- 31.62177660168379, 31.62177660168379, 31.62177660168379,
- 31.62177660168379, 31.62177660168379, 31.62177660168379,
- 31.62177660168379, 31.62177660168379, 31.62177660168379,
- 31.62177660168379, 31.62177660168379, 31.62177660168379,
- 31.62177660168379, 999.999, 999.999, 999.999, 999.999, 999.999, 999.999,
- 999.999, 999.999, 999.999, 999.999, 999.999, 999.999, 999.999, 999.999,
- 999.999, 999.999, 999.999, 999.999, 999.999, 999.999, 999.999, 999.999,
- 999.999, 999.999, 999.999;
-
- b << 0.0, 0.0, 0.0, 0.0, 0.0, 0.03062277660168379, 0.03062277660168379,
- 0.03062277660168379, 0.03062277660168379, 0.03062277660168379, 0.999,
- 0.999, 0.999, 0.999, 0.999, 31.62177660168379, 31.62177660168379,
- 31.62177660168379, 31.62177660168379, 31.62177660168379, 999.999,
- 999.999, 999.999, 999.999, 999.999, 0.0, 0.0, 0.0, 0.0, 0.0,
- 0.03062277660168379, 0.03062277660168379, 0.03062277660168379,
- 0.03062277660168379, 0.03062277660168379, 0.999, 0.999, 0.999, 0.999,
- 0.999, 31.62177660168379, 31.62177660168379, 31.62177660168379,
- 31.62177660168379, 31.62177660168379, 999.999, 999.999, 999.999,
- 999.999, 999.999, 0.0, 0.0, 0.0, 0.0, 0.0, 0.03062277660168379,
- 0.03062277660168379, 0.03062277660168379, 0.03062277660168379,
- 0.03062277660168379, 0.999, 0.999, 0.999, 0.999, 0.999,
- 31.62177660168379, 31.62177660168379, 31.62177660168379,
- 31.62177660168379, 31.62177660168379, 999.999, 999.999, 999.999,
- 999.999, 999.999, 0.0, 0.0, 0.0, 0.0, 0.0, 0.03062277660168379,
- 0.03062277660168379, 0.03062277660168379, 0.03062277660168379,
- 0.03062277660168379, 0.999, 0.999, 0.999, 0.999, 0.999,
- 31.62177660168379, 31.62177660168379, 31.62177660168379,
- 31.62177660168379, 31.62177660168379, 999.999, 999.999, 999.999,
- 999.999, 999.999, 0.0, 0.0, 0.0, 0.0, 0.0, 0.03062277660168379,
- 0.03062277660168379, 0.03062277660168379, 0.03062277660168379,
- 0.03062277660168379, 0.999, 0.999, 0.999, 0.999, 0.999,
- 31.62177660168379, 31.62177660168379, 31.62177660168379,
- 31.62177660168379, 31.62177660168379, 999.999, 999.999, 999.999,
- 999.999, 999.999;
-
- x << -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5,
- 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2,
- 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1,
- 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1,
- -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8,
- 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5,
- 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2,
- 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1,
- 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5,
- 0.8, 1.1;
-
- v << nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,
- nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,
- nan, nan, nan, 0.47972119876364683, 0.5, 0.5202788012363533, nan, nan,
- 0.9518683957740043, 0.9789663010413743, 0.9931729188073435, nan, nan,
- 0.999995949033062, 0.9999999999993698, 0.9999999999999999, nan, nan,
- 0.9999999999999999, 0.9999999999999999, 0.9999999999999999, nan, nan,
- nan, nan, nan, nan, nan, 0.006827081192655869, 0.0210336989586256,
- 0.04813160422599567, nan, nan, 0.20014344256217678, 0.5000000000000001,
- 0.7998565574378232, nan, nan, 0.9991401428435834, 0.999999999698403,
- 0.9999999999999999, nan, nan, 0.9999999999999999, 0.9999999999999999,
- 0.9999999999999999, nan, nan, nan, nan, nan, nan, nan,
- 1.0646600232370887e-25, 6.301722877826246e-13, 4.050966937974938e-06,
- nan, nan, 7.864342668429763e-23, 3.015969667594166e-10,
- 0.0008598571564165444, nan, nan, 6.031987710123844e-08,
- 0.5000000000000007, 0.9999999396801229, nan, nan, 0.9999999999999999,
- 0.9999999999999999, 0.9999999999999999, nan, nan, nan, nan, nan, nan,
- nan, 0.0, 7.029920380986636e-306, 2.2450728208591345e-101, nan, nan,
- 0.0, 9.275871147869727e-302, 1.2232913026152827e-97, nan, nan, 0.0,
- 3.0891393081932924e-252, 2.9303043666183996e-60, nan, nan,
- 2.248913486879199e-196, 0.5000000000004947, 0.9999999999999999, nan;
-
- 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
-}
-
void test_array()
{
-#ifndef EIGEN_HAS_C99_MATH
- std::cerr << "WARNING: testing of special math functions disabled" << std::endl;
-#endif
-
for(int i = 0; i < g_repeat; i++) {
CALL_SUBTEST_1( array(Array<float, 1, 1>()) );
CALL_SUBTEST_2( array(Array22f()) );
@@ -812,7 +491,4 @@
VERIFY((internal::is_same< internal::global_math_functions_filtering_base<Xpr>::type,
ArrayBase<Xpr>
>::value));
-
- CALL_SUBTEST_7(array_special_functions<ArrayXf>());
- CALL_SUBTEST_7(array_special_functions<ArrayXd>());
}