/usr/include/openturns/SpecFunc.hxx is in libopenturns-dev 0.15-2.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
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/**
* @file SpecFunc.hxx
* @brief OpenTURNS wrapper to a library of special functions
*
* (C) Copyright 2005-2011 EDF-EADS-Phimeca
*
* This library is free software; you can redistribute it and/or
* modify it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation; either
* version 2.1 of the License.
*
* This library is distributed in the hope that it will be useful
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
* Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public
* License along with this library; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
*
* @author: $LastChangedBy: schueller $
* @date: $LastChangedDate: 2011-05-24 19:30:41 +0200 (Tue, 24 May 2011) $
* Id: $Id: SpecFunc.hxx 1910 2011-05-24 17:30:41Z schueller $
*/
#ifndef OPENTURNS_SPECFUNC_HXX
#define OPENTURNS_SPECFUNC_HXX
#include "OTprivate.hxx"
namespace OpenTURNS {
namespace Base {
namespace Func {
class SpecFunc{
public:
static const NumericalScalar Precision;
// 0.39894228040143267 = 1 / sqrt(2.pi)
static const NumericalScalar ISQRT2PI;
// 0.57721566490153286 = Euler constant gamma
static const NumericalScalar EulerConstant;
// 1.64493406684822643 = pi^2 / 6
static const NumericalScalar PI2_6;
// 1.28254983016118640 = pi / sqrt(6)
static const NumericalScalar PI_SQRT6;
// 0.45005320754569466 = gamma * sqrt(6) / pi
static const NumericalScalar EULERSQRT6_PI;
// 3.28986813369645287 = pi^2 / 3
static const NumericalScalar PI2_3;
// 0.55132889542179204 = sqrt(3) / pi
static const NumericalScalar SQRT3_PI;
// 1.81379936423421785 = pi / sqrt(3)
static const NumericalScalar PI_SQRT3;
// 1.20205690315959429 = Zeta(3)
static const NumericalScalar ZETA3;
// Minimum positive real number
static const NumericalScalar MinNumericalScalar;
static const NumericalScalar LogMinNumericalScalar;
// Maximum positive real number
static const NumericalScalar MaxNumericalScalar;
static const NumericalScalar LogMaxNumericalScalar;
// First kind real Airy function: Ai(x) = \frac{1}{\pi}\int_0^{\infty} \cos(xt + t^3/3) dt
static NumericalScalar Ai(const NumericalScalar x);
// First kind complex Airy function: Ai(z) = analytical continuation of Ai(x)
static NumericalComplex Ai(const NumericalComplex & z);
// First kind real Airy function derivative: Ai'(x)
static NumericalScalar AiDerivative(const NumericalScalar x);
// First kind complex Airy function derivative: Ai'(z)
static NumericalComplex AiDerivative(const NumericalComplex & z);
// Second kind real Airy function: Bi(x) = \frac{1}{\pi}\int_0^{\infty} \exp(xt - t^3/3) + \sin(xt + t^3/3) dt
static NumericalScalar Bi(const NumericalScalar x);
// Second kind complex Airy function: Bi(z) = analytical continuation of Bi(x)
static NumericalComplex Bi(const NumericalComplex & z);
// Second kind real Airy function derivative: Bi'(x)
static NumericalScalar BiDerivative(const NumericalScalar x);
// Second kind complex Airy function derivative: Bi'(z)
static NumericalComplex BiDerivative(const NumericalComplex & z);
// Beta function: beta(a, b) = \int_0^1 t^{a-1}.(1-t)^{b-1} dt
static NumericalScalar Beta(const NumericalScalar a,
const NumericalScalar b);
// Incomplete beta function: betaInc(a, b, x) = \int_0^x t^{a-1}.(1-t)^{b-1} dt
static NumericalScalar BetaInc(const NumericalScalar a,
const NumericalScalar b,
const NumericalScalar x);
// Incomplete beta function inverse with respect to x
static NumericalScalar BetaIncInv(const NumericalScalar a,
const NumericalScalar b,
const NumericalScalar x);
// Incomplete beta ratio function: betaRatioInc(a, b, x) = \int_0^x t^{a-1}.(1-t)^{b-1} dt / beta(a, b)
static NumericalScalar BetaRatioInc(const NumericalScalar a,
const NumericalScalar b,
const NumericalScalar x);
// Incomplete beta ratio function inverse with respect to x
static NumericalScalar BetaRatioIncInv(const NumericalScalar a,
const NumericalScalar b,
const NumericalScalar x);
// Natural logarithm of the beta function
static NumericalScalar LnBeta(const NumericalScalar a,
const NumericalScalar b);
static NumericalScalar LogBeta(const NumericalScalar a,
const NumericalScalar b);
// Dawson function: Dawson(x) = \exp(-x^2) * \int_0^x \exp(t^2) dt
static NumericalScalar Dawson(const NumericalScalar x);
// Debye function of order n: DebyeN(x, n) = n / x^n \int_0^x t^n/(\exp(t)-1) dt
static NumericalScalar Debye(const NumericalScalar x,
const UnsignedLong n);
// Real Faddeeva function: faddeeva(z) = exp(-z^2).erfc(-I*z)
// static NumericalComplex Faddeeva(const NumericalScalar x);
// Complex Faddeeva function: faddeeva(z) = exp(-z^2)\erfc(-I*z)
static NumericalComplex Faddeeva(const NumericalComplex & z);
// Gamma function: gamma(a) = \int_0^{\infty} t^{a-1}\exp(-t) dt
static NumericalScalar Gamma(const NumericalScalar a);
// Complex gamma function: gamma(a) = \int_0^{\infty} t^{a-1}\exp(-t) dt
static NumericalComplex Gamma(const NumericalComplex & a);
// Natural logarithm of the gamma function
static NumericalScalar LnGamma(const NumericalScalar a);
static NumericalScalar LogGamma(const NumericalScalar a);
// Incomplete gamma function: gamma(a, x) = \int_0^x t^{a-1}\exp(-t) dt
static NumericalScalar GammaInc(const NumericalScalar a,
const NumericalScalar x);
// Incomplete gamma function inverse with respect to x
static NumericalScalar GammaIncInv(const NumericalScalar a,
const NumericalScalar x);
// Digamma function: psi(x) = ((dgamma/dx) / gamma)(x)
static NumericalScalar DiGamma(const NumericalScalar x);
static NumericalScalar Psi(const NumericalScalar x);
// Inverse of the DiGamma function
static NumericalScalar DiGammaInv(const NumericalScalar a);
// Trigamma function: TriGamma(x) = ((d^2gamma/dx^2) / gamma)(x)
static NumericalScalar TriGamma(const NumericalScalar x);
// Hypergeometric function of type (1,1): hyperGeom_1_1(p1, q1, x) = \sum_{n=0}^{\infty} [\prod_{k=0}^{n-1} (p1 + k) / (q1 + k)] * x^n / n!
static NumericalScalar HyperGeom_1_1(const NumericalScalar p1,
const NumericalScalar q1,
const NumericalScalar x);
// Complex hypergeometric function of type (1,1): hyperGeom_1_1(p1, q1, x) = \sum_{n=0}^{\infty} [\prod_{k=0}^{n-1} (p1 + k) / (q1 + k)] * x^n / n!
static NumericalComplex HyperGeom_1_1(const NumericalScalar p1,
const NumericalScalar q1,
const NumericalComplex & x);
// Hypergeometric function of type (2,1): hyperGeom_2_1(p1, p2, q1, x) = \sum_{n=0}^{\infty} [\prod_{k=0}^{n-1} (p1 + k) . (p2 + k) / (q1 + k)] * x^n / n!
static NumericalScalar HyperGeom_2_1(const NumericalScalar p1,
const NumericalScalar p2,
const NumericalScalar q1,
const NumericalScalar x);
// Hypergeometric function of type (2,2): hyperGeom_2_1(p1, p2, q1, q2, x) = \sum_{n=0}^{\infty} [\prod_{k=0}^{n-1} (p1 + k) . (p2 + k) / (q1 + k) / (q2 + k)] * x^n / n!
static NumericalScalar HyperGeom_2_2(const NumericalScalar p1,
const NumericalScalar p2,
const NumericalScalar q1,
const NumericalScalar q2,
const NumericalScalar x);
// Erf function erf(x) = 2 / \sqrt(\pi) . \int_0^x \exp(-t^2) dt
static NumericalScalar Erf(const NumericalScalar x);
// Erf function erfc(x) = 1 - erf(x)
static NumericalScalar ErfC(const NumericalScalar x);
// Inverse of the erf function
static NumericalScalar ErfInv(const NumericalScalar x);
// Real branch of Lambert W function (principal or secndary)
static NumericalScalar LambertW(const NumericalScalar x,
const Bool principal = true);
// MarcumQ- function
// static NumericalScalar MarcumQFunction(const NumericalScalar a,const NumericalScalar b);
}; /* class SpecFunc */
} /* namespace Func */
} /* namespace Base */
} /* namespace OpenTURNS */
#endif /* OPENTURNS_SPECFUNC_HXX */
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