GitHub-Proxy/eigen
1
0
Fork 0
mirror of https://gitlab.com/libeigen/eigen.git synced 2025-04-23 01:59:38 +08:00
Code Issues Packages Projects Releases Wiki Activity

Initial implementation of igamma and igammac.

Browse Source
This commit is contained in:
Eugene Brevdo 2016-03-03 19:39:41 -08:00
parent ab3dc0b0fe
commit 7ea35bfa1c
10 changed files with 459 additions and 2 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

10
Eigen/src/Core/GenericPacketMath.h
View File

@ -78,6 +78,8 @@ struct default_packet_traits
HasDiGamma = 0,
HasErf = 0,
HasErfc = 0,
HasIGamma = 0,
HasIGammac = 0,
HasRound = 0,
HasFloor = 0,
@ -457,6 +459,14 @@ Packet perf(const Packet& a) { using numext::erf; return erf(a); }
template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
Packet perfc(const Packet& a) { using numext::erfc; return erfc(a); }
/** \internal \returns the incomplete gamma function igamma(\a a, \a x) */
template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
Packet pigamma(const Packet& a, const Packet& x) { using numext::igamma; return igamma(a, x); }
/** \internal \returns the complementary incomplete gamma function igammac(\a a, \a x) */
template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
Packet pigammac(const Packet& a, const Packet& x) { using numext::igammac; return igammac(a, x); }
/***************************************************************************
* The following functions might not have to be overwritten for vectorized types
***************************************************************************/

30
Eigen/src/Core/GlobalFunctions.h
View File

@ -129,6 +129,36 @@ namespace Eigen
);
}
/** \returns an expression of the coefficient-wise igamma(\a a, \a x) to the given arrays.
*
* This function computes the coefficient-wise incomplete gamma function.
*
*/
template<typename Derived,typename ExponentDerived>
inline const Eigen::CwiseBinaryOp<Eigen::internal::scalar_igamma_op<typename Derived::Scalar>, const Derived, const ExponentDerived>
igamma(const Eigen::ArrayBase<Derived>& a, const Eigen::ArrayBase<ExponentDerived>& x)
{
return Eigen::CwiseBinaryOp<Eigen::internal::scalar_igamma_op<typename Derived::Scalar>, const Derived, const ExponentDerived>(
a.derived(),
x.derived()
);
}
/** \returns an expression of the coefficient-wise igammac(\a a, \a x) to the given arrays.
*
* This function computes the coefficient-wise complementary incomplete gamma function.
*
*/
template<typename Derived,typename ExponentDerived>
inline const Eigen::CwiseBinaryOp<Eigen::internal::scalar_igammac_op<typename Derived::Scalar>, const Derived, const ExponentDerived>
igammac(const Eigen::ArrayBase<Derived>& a, const Eigen::ArrayBase<ExponentDerived>& x)
{
return Eigen::CwiseBinaryOp<Eigen::internal::scalar_igammac_op<typename Derived::Scalar>, const Derived, const ExponentDerived>(
a.derived(),
x.derived()
);
}
namespace internal
{
EIGEN_ARRAY_DECLARE_GLOBAL_EIGEN_UNARY(real,scalar_real_op)

5
Eigen/src/Core/NumTraits.h
View File

@ -95,6 +95,11 @@ template<typename T> struct GenericNumTraits
static inline T infinity() {
return numext::numeric_limits<T>::infinity();
}
EIGEN_DEVICE_FUNC
static inline T quiet_NaN() {
return numext::numeric_limits<T>::quiet_NaN();
}
};
template<typename T> struct NumTraits : GenericNumTraits<T>

291
Eigen/src/Core/SpecialFunctions.h
View File

@ -283,7 +283,7 @@ struct digamma_impl {
Scalar p, q, nz, s, w, y;
bool negative;
const Scalar maxnum = numext::numeric_limits<Scalar>::infinity();
const Scalar maxnum = NumTraits<Scalar>::infinity();
const Scalar m_pi = 3.14159265358979323846;
negative = 0;
@ -401,6 +401,282 @@ struct erfc_impl<double> {
};
#endif // EIGEN_HAS_C99_MATH
/****************************************************************************
* Implementation of igammac (complemented incomplete gamma integral) *
****************************************************************************/
template <typename Scalar>
struct igammac_retval {
typedef Scalar type;
};
#ifndef EIGEN_HAS_C99_MATH
template <typename Scalar>
struct igammac_impl {
EIGEN_DEVICE_FUNC
static Scalar run(Scalar a, Scalar x) {
EIGEN_STATIC_ASSERT((internal::is_same<Scalar, Scalar>::value == false),
THIS_TYPE_IS_NOT_SUPPORTED);
return Scalar(0);
}
};
#else
template <typename Scalar> struct igamma_impl; // predeclare igamma_impl
template <typename Scalar>
struct igammac_impl {
EIGEN_DEVICE_FUNC
static Scalar run(Scalar a, Scalar x) {
/* igamc()
*
* Incomplete gamma integral (modified for Eigen)
*
*
*
* SYNOPSIS:
*
* double a, x, y, igamc();
*
* y = igamc( a, x );
*
* DESCRIPTION:
*
* The function is defined by
*
*
* igamc(a,x) = 1 - igam(a,x)
*
* inf.
* -
* 1 | | -t a-1
* = ----- | e t dt.
* - | |
* | (a) -
* x
*
*
* In this implementation both arguments must be positive.
* The integral is evaluated by either a power series or
* continued fraction expansion, depending on the relative
* values of a and x.
*
* ACCURACY (float):
*
* Relative error:
* arithmetic domain # trials peak rms
* IEEE 0,30 30000 7.8e-6 5.9e-7
*
*
* ACCURACY (double):
*
* Tested at random a, x.
* a x Relative error:
* arithmetic domain domain # trials peak rms
* IEEE 0.5,100 0,100 200000 1.9e-14 1.7e-15
* IEEE 0.01,0.5 0,100 200000 1.4e-13 1.6e-15
*
*/
/*
Cephes Math Library Release 2.2: June, 1992
Copyright 1985, 1987, 1992 by Stephen L. Moshier
Direct inquiries to 30 Frost Street, Cambridge, MA 02140
*/
const Scalar zero = 0;
const Scalar one = 1;
const Scalar two = 2;
const Scalar machep = NumTraits<Scalar>::epsilon();
const Scalar maxlog = ::log(NumTraits<Scalar>::highest());
const Scalar big = one / machep;
Scalar ans, ax, c, yc, r, t, y, z;
Scalar pk, pkm1, pkm2, qk, qkm1, qkm2;
if ((x <= zero) || ( a <= zero)) {
return one;
}
if ((x < one) || (x < a)) {
return (one - igamma_impl<Scalar>::run(a, x));
}
ax = a * ::log(x) - x - lgamma_impl<Scalar>::run(a);
if( ax < -maxlog ) { // underflow
return zero;
}
ax = ::exp(ax);
// continued fraction
y = one - a;
z = x + y + one;
c = zero;
pkm2 = one;
qkm2 = x;
pkm1 = x + one;
qkm1 = z * x;
ans = pkm1/qkm1;
do {
c += one;
y += one;
z += two;
yc = y * c;
pk = pkm1 * z - pkm2 * yc;
qk = qkm1 * z - qkm2 * yc;
if( qk != zero ) {
r = pk/qk;
t = ::abs( (ans - r)/r );
ans = r;
} else {
t = one;
}
pkm2 = pkm1;
pkm1 = pk;
qkm2 = qkm1;
qkm1 = qk;
if (::abs(pk) > big) {
pkm2 *= machep;
pkm1 *= machep;
qkm2 *= machep;
qkm1 *= machep;
}
} while( t > machep );
return ( ans * ax );
}
};
#endif // EIGEN_HAS_C99_MATH
/****************************************************************************
* Implementation of igamma (incomplete gamma integral) *
****************************************************************************/
template <typename Scalar>
struct igamma_retval {
typedef Scalar type;
};
#ifndef EIGEN_HAS_C99_MATH
template <typename Scalar>
struct igamma_impl {
EIGEN_DEVICE_FUNC
static Scalar run(Scalar a, Scalar x) {
EIGEN_STATIC_ASSERT((internal::is_same<Scalar, Scalar>::value == false),
THIS_TYPE_IS_NOT_SUPPORTED);
return Scalar(0);
}
};
#else
template <typename Scalar>
struct igamma_impl {
EIGEN_DEVICE_FUNC
static Scalar run(Scalar a, Scalar x) {
/* igam()
* Incomplete gamma integral
*
*
*
* SYNOPSIS:
*
* double a, x, y, igam();
*
* y = igam( a, x );
*
* DESCRIPTION:
*
* The function is defined by
*
* x
* -
* 1 | | -t a-1
* igam(a,x) = ----- | e t dt.
* - | |
* | (a) -
* 0
*
*
* In this implementation both arguments must be positive.
* The integral is evaluated by either a power series or
* continued fraction expansion, depending on the relative
* values of a and x.
*
* ACCURACY (double):
*
* Relative error:
* arithmetic domain # trials peak rms
* IEEE 0,30 200000 3.6e-14 2.9e-15
* IEEE 0,100 300000 9.9e-14 1.5e-14
*
*
* ACCURACY (float):
*
* Relative error:
* arithmetic domain # trials peak rms
* IEEE 0,30 20000 7.8e-6 5.9e-7
*
*/
/*
Cephes Math Library Release 2.2: June, 1992
Copyright 1985, 1987, 1992 by Stephen L. Moshier
Direct inquiries to 30 Frost Street, Cambridge, MA 02140
*/
/* left tail of incomplete gamma function:
*
* inf. k
* a -x - x
* x e > ----------
* - -
* k=0 | (a+k+1)
*
*/
const Scalar zero = 0;
const Scalar one = 1;
const Scalar machep = NumTraits<Scalar>::epsilon();
const Scalar maxlog = ::log(NumTraits<Scalar>::highest());
double ans, ax, c, r;
if( (x <= zero) || ( a <= zero) ) {
return zero;
}
if( (x > one) && (x > a ) ) {
return (one - igammac_impl<Scalar>::run(a,x));
}
/* Compute x**a * exp(-x) / gamma(a) */
ax = a * ::log(x) - x - lgamma_impl<Scalar>::run(a);
if( ax < -maxlog ) {
// underflow
return zero;
}
ax = ::exp(ax);
/* power series */
r = a;
c = one;
ans = one;
do {
r += one;
c *= x/r;
ans += c;
} while( c/ans > machep );
return( ans * ax/a );
}
};
#endif // EIGEN_HAS_C99_MATH
} // end namespace internal
namespace numext {
@ -429,8 +705,21 @@ EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(erfc, Scalar)
return EIGEN_MATHFUNC_IMPL(erfc, Scalar)::run(x);
}
template <typename Scalar>
EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(igamma, Scalar)
igamma(const Scalar& a, const Scalar& x) {
return EIGEN_MATHFUNC_IMPL(igamma, Scalar)::run(a, x);
}
template <typename Scalar>
EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(igammac, Scalar)
igammac(const Scalar& a, const Scalar& x) {
return EIGEN_MATHFUNC_IMPL(igammac, Scalar)::run(a, x);
}
} // end namespace numext
} // end namespace Eigen
#endif // EIGEN_SPECIAL_FUNCTIONS_H

18
Eigen/src/Core/arch/CUDA/MathFunctions.h
View File

@ -116,6 +116,24 @@ double2 perfc<double2>(const double2& a)
return make_double2(erfc(a.x), erfc(a.y));
}
template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
float4 pigamma<float4>(const float4& a, const float4& x)
{
using numext::pigamma;
return make_float4(
pigamma(a.x, x.x),
pigamma(a.y, x.y),
pigamma(a.z, x.z),
pigamma(a.w, x.w));
}
template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
double2 pigammac<double2>(const double2& a, const double& x)
{
using numext::pigammac;
return make_double2(pigammac(a.x, x.x), pigammac(a.y, x.y));
}
#endif

4
Eigen/src/Core/arch/CUDA/PacketMath.h
View File

@ -43,6 +43,8 @@ template<> struct packet_traits<float> : default_packet_traits
HasDiGamma = 1,
HasErf = 1,
HasErfc = 1,
HasIgamma = 1,
HasIGammac = 1,
HasBlend = 0,
};
@ -67,6 +69,8 @@ template<> struct packet_traits<double> : default_packet_traits
HasDiGamma = 1,
HasErf = 1,
HasErfc = 1,
HasIGamma = 1,
HasIGammac = 1,
HasBlend = 0,
};

49
Eigen/src/Core/functors/BinaryFunctors.h
View File

@ -337,6 +337,55 @@ template<> struct functor_traits<scalar_boolean_or_op> {
};
};
/** \internal
* \brief Template functor to compute the incomplete gamma function igamma(a, x)
*
* \sa class CwiseBinaryOp, Cwise::igamma
*/
template<typename Scalar> struct scalar_igamma_op {
EIGEN_EMPTY_STRUCT_CTOR(scalar_igamma_op)
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& a, const Scalar& x) const {
using numext::igamma; return igamma(a, x);
}
template<typename Packet>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a, const Packet& x) const {
return internal::pigammac(a, x);
}
};
template<typename Scalar>
struct functor_traits<scalar_igamma_op<Scalar> > {
enum {
// Guesstimate
Cost = 20 * NumTraits<Scalar>::MulCost + 10 * NumTraits<Scalar>::AddCost,
PacketAccess = packet_traits<Scalar>::HasIGamma
};
};
/** \internal
* \brief Template functor to compute the complementary incomplete gamma function igammac(a, x)
*
* \sa class CwiseBinaryOp, Cwise::igammac
*/
template<typename Scalar> struct scalar_igammac_op {
EIGEN_EMPTY_STRUCT_CTOR(scalar_igammac_op)
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& a, const Scalar& x) const {
using numext::igammac; return igammac(a, x);
}
template<typename Packet>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a, const Packet& x) const
{
return internal::pigammac(a, x);
}
};
template<typename Scalar>
struct functor_traits<scalar_igammac_op<Scalar> > {
enum {
// Guesstimate
Cost = 20 * NumTraits<Scalar>::MulCost + 10 * NumTraits<Scalar>::AddCost,
PacketAccess = packet_traits<Scalar>::HasIGammac
};
};
//---------- binary functors bound to a constant, thus appearing as a unary functor ----------

2
Eigen/src/Core/util/ForwardDeclarations.h
View File

@ -206,6 +206,8 @@ template<typename Scalar> struct scalar_add_op;
template<typename Scalar> struct scalar_constant_op;
template<typename Scalar> struct scalar_identity_op;
template<typename Scalar,bool iscpx> struct scalar_sign_op;
template<typename Scalar> struct scalar_igamma_op;
template<typename Scalar> struct scalar_igammac_op;
template<typename LhsScalar,typename RhsScalar=LhsScalar> struct scalar_product_op;
template<typename LhsScalar,typename RhsScalar> struct scalar_multiple2_op;

5
Eigen/src/Core/util/Meta.h
View File

@ -148,6 +148,7 @@ template<typename T> struct numeric_limits
static T (max)() { assert(false && "Highest not supported for this type"); }
static T (min)() { assert(false && "Lowest not supported for this type"); }
static T infinity() { assert(false && "Infinity not supported for this type"); }
static T quiet_NaN() { assert(false && "quiet_NaN not supported for this type"); }
};
template<> struct numeric_limits<float>
{
@ -159,6 +160,8 @@ template<> struct numeric_limits<float>
static float (min)() { return FLT_MIN; }
EIGEN_DEVICE_FUNC
static float infinity() { return CUDART_INF_F; }
EIGEN_DEVICE_FUNC
static float quiet_NaN() { return CUDART_NAN_F; }
};
template<> struct numeric_limits<double>
{
@ -170,6 +173,8 @@ template<> struct numeric_limits<double>
static double (min)() { return DBL_MIN; }
EIGEN_DEVICE_FUNC
static double infinity() { return CUDART_INF; }
EIGEN_DEVICE_FUNC
static double quiet_NaN() { return CUDART_NAN; }
};
template<> struct numeric_limits<int>
{

47
test/array.cpp
View File

@ -296,7 +296,6 @@ template<typename ArrayType> void array_real(const ArrayType& m)
VERIFY_IS_APPROX(m1.pow(2*exponents), m1.square().square());
VERIFY_IS_APPROX(pow(m1(0,0), exponents), ArrayType::Constant(rows,cols,m1(0,0)*m1(0,0)));
VERIFY_IS_APPROX(m3.pow(RealScalar(0.5)), m3.sqrt());
VERIFY_IS_APPROX(pow(m3,RealScalar(0.5)), m3.sqrt());
@ -305,6 +304,14 @@ template<typename ArrayType> void array_real(const ArrayType& m)
VERIFY_IS_APPROX(log10(m3), log(m3)/log(10));
// Smoke test to check any compilation issues
ArrayType m1_abs_p1 = m1.abs() + 1;
ArrayType m2_abs_p1 = m2.abs() + 1;
VERIFY_IS_APPROX(Eigen::igamma(m1_abs_p1, m2_abs_p1), Eigen::igamma(m1_abs_p1, m2_abs_p1));
VERIFY_IS_APPROX(Eigen::igammac(m1_abs_p1, m2_abs_p1), Eigen::igammac(m1_abs_p1, m2_abs_p1));
VERIFY_IS_APPROX(Eigen::igamma(m2_abs_p1, m1_abs_p1), Eigen::igamma(m2_abs_p1, m1_abs_p1));
VERIFY_IS_APPROX(Eigen::igammac(m2_abs_p1, m1_abs_p1), Eigen::igammac(m2_abs_p1, m1_abs_p1));
// scalar by array division
const RealScalar tiny = sqrt(std::numeric_limits<RealScalar>::epsilon());
s1 += Scalar(tiny);
@ -323,6 +330,44 @@ 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());
Scalar a_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(10000.5)};
// 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, 0.0, 0.0, 0.0, 0.0, 0.0},
{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, 0.5013297751014064}};
Scalar igammac_s[][6] = {
{1.0, 1.0, 1.0, 1.0, 1.0, 1.0},
{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, 0.49867022490946517}};
for (int i = 0; i < 6; ++i) {
for (int j = 0; j < 6; ++j) {
//std::cout << numext::igamma(a_s[i], x_s[j]) << " vs. " << igamma_s[i][j] << std::endl;
//std::cout << numext::igammac(a_s[i], x_s[j]) << " c.vs. " <<
//igammac_s[i][j] << std::endl;
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::igammac(a_s[i], x_s[j]), igammac_s[i][j]);
}
}
}
#endif // EIGEN_HAS_C99_MATH