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Make igamma and igammac work correctly.

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This required replacing ::abs with std::abs.
Modified some unit tests.
This commit is contained in:
Eugene Brevdo 2016-03-04 21:12:10 -08:00
parent 7ea35bfa1c
commit 0b9e0abc96
2 changed files with 119 additions and 64 deletions
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91
Eigen/src/Core/SpecialFunctions.h
View File

@ -296,7 +296,8 @@ struct digamma_impl {
if (x <= zero) { if (x <= zero) {
negative = one; negative = one;
q = x; q = x;
p = ::floor(q); using std::floor;
p = floor(q);
if (p == q) { if (p == q) {
return maxnum; return maxnum;
} }
@ -309,7 +310,8 @@ struct digamma_impl {
p += one; p += one;
nz = q - p; nz = q - p;
} }
nz = m_pi / ::tan(m_pi * nz); using std::tan;
nz = m_pi / tan(m_pi * nz);
} }
else { else {
nz = zero; nz = zero;
@ -327,7 +329,8 @@ struct digamma_impl {
y = digamma_impl_maybe_poly<Scalar>::run(s); y = digamma_impl_maybe_poly<Scalar>::run(s);
y = ::log(s) - (half / s) - y - w; using std::log;
y = log(s) - (half / s) - y - w;
return (negative) ? y - nz : y; return (negative) ? y - nz : y;
} }
@ -426,6 +429,39 @@ struct igammac_impl {
template <typename Scalar> struct igamma_impl; // predeclare igamma_impl template <typename Scalar> struct igamma_impl; // predeclare igamma_impl
template <typename Scalar>
struct igamma_helper {
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
static Scalar machep() { assert(false && "machep not supported for this type"); return 0.0; }
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
static Scalar big() { assert(false && "big not supported for this type"); return 0.0; }
};
template <>
struct igamma_helper<float> {
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
static float machep() {
return NumTraits<float>::epsilon() / 2; // 1.0 - machep == 1.0
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
static float big() {
// use epsneg (1.0 - epsneg == 1.0)
return 1.0 / (NumTraits<float>::epsilon() / 2);
}
};
template <>
struct igamma_helper<double> {
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
static double machep() {
return NumTraits<double>::epsilon() / 2; // 1.0 - machep == 1.0
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
static double big() {
return 1.0 / NumTraits<double>::epsilon();
}
};
template <typename Scalar> template <typename Scalar>
struct igammac_impl { struct igammac_impl {
EIGEN_DEVICE_FUNC EIGEN_DEVICE_FUNC
@ -487,26 +523,35 @@ struct igammac_impl {
const Scalar zero = 0; const Scalar zero = 0;
const Scalar one = 1; const Scalar one = 1;
const Scalar two = 2; const Scalar two = 2;
const Scalar machep = NumTraits<Scalar>::epsilon(); const Scalar machep = igamma_helper<Scalar>::machep();
const Scalar maxlog = ::log(NumTraits<Scalar>::highest()); const Scalar maxlog = ::log(NumTraits<Scalar>::highest());
const Scalar big = one / machep; const Scalar big = igamma_helper<Scalar>::big();
const Scalar biginv = 1 / big;
const Scalar nan = NumTraits<Scalar>::quiet_NaN();
Scalar ans, ax, c, yc, r, t, y, z; Scalar ans, ax, c, yc, r, t, y, z;
Scalar pk, pkm1, pkm2, qk, qkm1, qkm2; Scalar pk, pkm1, pkm2, qk, qkm1, qkm2;
if ((x <= zero) || ( a <= zero)) { if ((x < zero) || ( a <= zero)) {
return one; // domain error
return nan;
} }
if ((x < one) || (x < a)) { if ((x < one) || (x < a)) {
return (one - igamma_impl<Scalar>::run(a, x)); return (one - igamma_impl<Scalar>::run(a, x));
} }
ax = a * ::log(x) - x - lgamma_impl<Scalar>::run(a); using std::isinf;
if ((isinf)(x)) return zero;
/* Compute x**a * exp(-x) / gamma(a) */
using std::log;
ax = a * log(x) - x - lgamma_impl<Scalar>::run(a);
if (ax < -maxlog) { // underflow if (ax < -maxlog) { // underflow
return zero; return zero;
} }
ax = ::exp(ax); using std::exp;
ax = exp(ax);
// continued fraction // continued fraction
y = one - a; y = one - a;
@ -518,6 +563,7 @@ struct igammac_impl {
qkm1 = z * x; qkm1 = z * x;
ans = pkm1 / qkm1; ans = pkm1 / qkm1;
using std::abs;
do { do {
c += one; c += one;
y += one; y += one;
@ -527,7 +573,7 @@ struct igammac_impl {
qk = qkm1 * z - qkm2 * yc; qk = qkm1 * z - qkm2 * yc;
if (qk != zero) { if (qk != zero) {
r = pk / qk; r = pk / qk;
t = ::abs( (ans - r)/r ); t = abs((ans - r) / r);
ans = r; ans = r;
} else { } else {
t = one; t = one;
@ -536,11 +582,11 @@ struct igammac_impl {
pkm1 = pk; pkm1 = pk;
qkm2 = qkm1; qkm2 = qkm1;
qkm1 = qk; qkm1 = qk;
if (::abs(pk) > big) { if (abs(pk) > big) {
pkm2 *= machep; pkm2 *= biginv;
pkm1 *= machep; pkm1 *= biginv;
qkm2 *= machep; qkm2 *= biginv;
qkm1 *= machep; qkm1 *= biginv;
} }
} while (t > machep); } while (t > machep);
@ -639,13 +685,16 @@ struct igamma_impl {
*/ */
const Scalar zero = 0; const Scalar zero = 0;
const Scalar one = 1; const Scalar one = 1;
const Scalar machep = NumTraits<Scalar>::epsilon(); const Scalar machep = igamma_helper<Scalar>::machep();
const Scalar maxlog = ::log(NumTraits<Scalar>::highest()); const Scalar maxlog = ::log(NumTraits<Scalar>::highest());
const Scalar nan = NumTraits<Scalar>::quiet_NaN();
double ans, ax, c, r; double ans, ax, c, r;
if( (x <= zero) || ( a <= zero) ) { if (x == zero) return zero;
return zero;
if ((x < zero) || ( a <= zero)) { // domain error
return nan;
} }
if ((x > one) && (x > a)) { if ((x > one) && (x > a)) {
@ -653,12 +702,14 @@ struct igamma_impl {
} }
/* Compute x**a * exp(-x) / gamma(a) */ /* Compute x**a * exp(-x) / gamma(a) */
ax = a * ::log(x) - x - lgamma_impl<Scalar>::run(a); using std::log;
ax = a * log(x) - x - lgamma_impl<Scalar>::run(a);
if (ax < -maxlog) { if (ax < -maxlog) {
// underflow // underflow
return zero; return zero;
} }
ax = ::exp(ax); using std::exp;
ax = exp(ax);
/* power series */ /* power series */
r = a; r = a;

46
test/array.cpp
View File

@ -331,24 +331,22 @@ template<typename ArrayType> void array_real(const ArrayType& m)
VERIFY_IS_EQUAL(numext::digamma(Scalar(-1)), VERIFY_IS_EQUAL(numext::digamma(Scalar(-1)),
std::numeric_limits<RealScalar>::infinity()); std::numeric_limits<RealScalar>::infinity());
Scalar a_s[] = {Scalar(0), Scalar(1), Scalar(1.5), Scalar(4), Scalar(0.0001), Scalar(10000.5)}; 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(10000.5)}; 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]. // location i*6+j corresponds to a_s[i], x_s[j].
Scalar nan = std::numeric_limits<Scalar>::quiet_NaN(); Scalar nan = std::numeric_limits<Scalar>::quiet_NaN();
Scalar igamma_s[][6] = { Scalar igamma_s[][6] = {{0.0, nan, nan, nan, nan, nan},
{0.0, 0.0, 0.0, 0.0, 0.0, 0.0}, {0.0, 0.6321205588285578, 0.7768698398515702,
{0.0, 0.6321205588285578, 0.7768698398515702, 0.9816843611112658, 0.9816843611112658, 9.999500016666262e-05, 1.0},
9.999500016666262e-05, 1.0}, {0.0, 0.4275932955291202, 0.608374823728911,
{0.0, 0.4275932955291202, 0.608374823728911, 0.9539882943107686, 0.9539882943107686, 7.522076445089201e-07, 1.0},
7.522076445089201e-07, 1.0}, {0.0, 0.01898815687615381, 0.06564245437845008,
{0.0, 0.01898815687615381, 0.06564245437845008, 0.5665298796332909, 0.5665298796332909, 4.166333347221828e-18, 1.0},
4.166333347221828e-18, 1.0}, {0.0, 0.9999780593618628, 0.9999899967080838,
{0.0, 0.9999780593618628, 0.9999899967080838, 0.9999996219837988, 0.9999996219837988, 0.9991370418689945, 1.0},
0.9991370418689945, 1.0}, {0.0, 0.0, 0.0, 0.0, 0.0, 0.5042041932513908}};
{0.0, 0.0, 0.0, 0.0, 0.0, 0.5013297751014064}}; Scalar igammac_s[][6] = {{nan, nan, nan, nan, nan, nan},
Scalar igammac_s[][6] = {
{1.0, 1.0, 1.0, 1.0, 1.0, 1.0},
{1.0, 0.36787944117144233, 0.22313016014842982, {1.0, 0.36787944117144233, 0.22313016014842982,
0.018315638888734182, 0.9999000049998333, 0.0}, 0.018315638888734182, 0.9999000049998333, 0.0},
{1.0, 0.5724067044708798, 0.3916251762710878, {1.0, 0.5724067044708798, 0.3916251762710878,
@ -356,19 +354,25 @@ template<typename ArrayType> void array_real(const ArrayType& m)
{1.0, 0.9810118431238462, 0.9343575456215499, {1.0, 0.9810118431238462, 0.9343575456215499,
0.4334701203667089, 1.0, 0.0}, 0.4334701203667089, 1.0, 0.0},
{1.0, 2.1940638138146658e-05, 1.0003291916285e-05, {1.0, 2.1940638138146658e-05, 1.0003291916285e-05,
3.7801620118431334e-07, 0.0008629581310054535, 0.0}, 3.7801620118431334e-07, 0.0008629581310054535,
{1.0, 1.0, 1.0, 1.0, 1.0, 0.49867022490946517}}; 0.0},
{1.0, 1.0, 1.0, 1.0, 1.0, 0.49579580674813944}};
for (int i = 0; i < 6; ++i) { for (int i = 0; i < 6; ++i) {
for (int j = 0; j < 6; ++j) { for (int j = 0; j < 6; ++j) {
//std::cout << numext::igamma(a_s[i], x_s[j]) << " vs. " << igamma_s[i][j] << std::endl; if ((std::isnan)(igamma_s[i][j])) {
//std::cout << numext::igammac(a_s[i], x_s[j]) << " c.vs. " << VERIFY((std::isnan)(numext::igamma(a_s[i], x_s[j])));
//igammac_s[i][j] << std::endl; } else {
std::cout << a_s[i] << ", " << x_s[j] << std::endl;
VERIFY_IS_APPROX(numext::igamma(a_s[i], x_s[j]), igamma_s[i][j]); 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]); VERIFY_IS_APPROX(numext::igammac(a_s[i], x_s[j]), igammac_s[i][j]);
} }
} }
} }
}
#endif // EIGEN_HAS_C99_MATH #endif // EIGEN_HAS_C99_MATH
// check inplace transpose // check inplace transpose