/// <summary>
/// Returns the modified Struve function of order 0.
/// </summary>
/// <param name="x">The value to compute the function of.</param>
public static double StruveL0(double x)
{
//*********************************************************************72
//
//c STRVL0 calculates the modified Struve function of order 0.
//
// DESCRIPTION:
//
// This function calculates the modified Struve function of
// order 0, denoted L0(x), defined as the solution of the
// second-order equation
//
// x*D(Df) + Df - x*f = 2x/pi
//
// This subroutine is set up to work on IEEE machines.
// For other machines, you should retrieve the code
// from the general MISCFUN archive.
//
//
// ERROR RETURNS:
//
// If the value of |XVALUE| is too large, the result
// would cause an floating-pt overflow. An error message
// is printed and the function returns the value of
// sign(XVALUE)*XMAX where XMAX is the largest possible
// floating-pt argument.
//
//
// MACHINE-DEPENDENT PARAMETERS:
//
// NTERM1 - INTEGER - The no. of terms for the array ARL0.
// The recommended value is such that
// ABS(ARL0(NTERM1)) < EPS/100
//
// NTERM2 - INTEGER - The no. of terms for the array ARL0AS.
// The recommended value is such that
// ABS(ARL0AS(NTERM2)) < EPS/100
//
// NTERM3 - INTEGER - The no. of terms for the array AI0ML0.
// The recommended value is such that
// ABS(AI0ML0(NTERM3)) < EPS/100
//
// XLOW - DOUBLE PRECISION - The value of x below which L0(x) = 2*x/pi
// to machine precision. The recommended value is
// 3*SQRT(EPS)
//
// XHIGH1 - DOUBLE PRECISION - The value beyond which the Chebyshev series
// in the asymptotic expansion of I0 - L0 gives
// 1.0 to machine precision. The recommended value
// is SQRT( 30/EPSNEG )
//
// XHIGH2 - DOUBLE PRECISION - The value beyond which the Chebyshev series
// in the asymptotic expansion of I0 gives 1.0
// to machine precision. The recommended value
// is 28 / EPSNEG
//
// XMAX - DOUBLE PRECISION - The value of XMAX, where XMAX is the
// largest possible floating-pt argument.
// This is used to prevent overflow.
//
// For values of EPS, EPSNEG and XMAX the user should refer
// to the file MACHCON.TXT
//
// The machine-arithmetic constants are given in DATA
// statements.
//
//
// INTRINSIC FUNCTIONS USED:
//
// EXP , LOG , SQRT
//
//
// OTHER MISCFUN SUBROUTINES USED:
//
// CHEVAL , ERRPRN
//
//
// AUTHOR:
// DR. ALLAN J. MACLEOD
// DEPT. OF MATHEMATICS AND STATISTICS
// UNIVERSITY OF PAISLEY
// HIGH ST.
// PAISLEY
// SCOTLAND
// PA1 2BE
//
// (e-mail: [email protected] )
//
//
// LATEST REVISION:
// 12 JANUARY, 1996
//
//
if (x < 0.0)
{
return(-StruveL0(-x));
}
double[] ARL0 = new double[28];
ARL0[0] = 0.42127458349979924863;
ARL0[1] = -0.33859536391220612188;
ARL0[2] = 0.21898994812710716064;
ARL0[3] = -0.12349482820713185712;
ARL0[4] = 0.6214209793866958440e-1;
ARL0[5] = -0.2817806028109547545e-1;
ARL0[6] = 0.1157419676638091209e-1;
ARL0[7] = -0.431658574306921179e-2;
ARL0[8] = 0.146142349907298329e-2;
ARL0[9] = -0.44794211805461478e-3;
ARL0[10] = 0.12364746105943761e-3;
ARL0[11] = -0.3049028334797044e-4;
ARL0[12] = 0.663941401521146e-5;
ARL0[13] = -0.125538357703889e-5;
ARL0[14] = 0.20073446451228e-6;
ARL0[15] = -0.2588260170637e-7;
ARL0[16] = 0.241143742758e-8;
ARL0[17] = -0.10159674352e-9;
ARL0[18] = -0.1202430736e-10;
ARL0[19] = 0.262906137e-11;
ARL0[20] = -0.15313190e-12;
ARL0[21] = -0.1574760e-13;
ARL0[22] = 0.315635e-14;
ARL0[23] = -0.4096e-16;
ARL0[24] = -0.3620e-16;
ARL0[25] = 0.239e-17;
ARL0[26] = 0.36e-18;
ARL0[27] = -0.4e-19;
double[] ARL0AS = new double[16];
ARL0AS[0] = 2.00861308235605888600;
ARL0AS[1] = 0.403737966500438470e-2;
ARL0AS[2] = -0.25199480286580267e-3;
ARL0AS[3] = 0.1605736682811176e-4;
ARL0AS[4] = -0.103692182473444e-5;
ARL0AS[5] = 0.6765578876305e-7;
ARL0AS[6] = -0.444999906756e-8;
ARL0AS[7] = 0.29468889228e-9;
ARL0AS[8] = -0.1962180522e-10;
ARL0AS[9] = 0.131330306e-11;
ARL0AS[10] = -0.8819190e-13;
ARL0AS[11] = 0.595376e-14;
ARL0AS[12] = -0.40389e-15;
ARL0AS[13] = 0.2651e-16;
ARL0AS[14] = -0.208e-17;
ARL0AS[15] = 0.11e-18;
double[] AI0ML0 = new double[24];
AI0ML0[0] = 2.00326510241160643125;
AI0ML0[1] = 0.195206851576492081e-2;
AI0ML0[2] = 0.38239523569908328e-3;
AI0ML0[3] = 0.7534280817054436e-4;
AI0ML0[4] = 0.1495957655897078e-4;
AI0ML0[5] = 0.299940531210557e-5;
AI0ML0[6] = 0.60769604822459e-6;
AI0ML0[7] = 0.12399495544506e-6;
AI0ML0[8] = 0.2523262552649e-7;
AI0ML0[9] = 0.504634857332e-8;
AI0ML0[10] = 0.97913236230e-9;
AI0ML0[11] = 0.18389115241e-9;
AI0ML0[12] = 0.3376309278e-10;
AI0ML0[13] = 0.611179703e-11;
AI0ML0[14] = 0.108472972e-11;
AI0ML0[15] = 0.18861271e-12;
AI0ML0[16] = 0.3280345e-13;
AI0ML0[17] = 0.565647e-14;
AI0ML0[18] = 0.93300e-15;
AI0ML0[19] = 0.15881e-15;
AI0ML0[20] = 0.2791e-16;
AI0ML0[21] = 0.389e-17;
AI0ML0[22] = 0.70e-18;
AI0ML0[23] = 0.16e-18;
// MACHINE-DEPENDENT VALUES (Suitable for IEEE-arithmetic machines)
const int nterm1 = 25;
const int nterm2 = 14;
const int nterm3 = 21;
const double xlow = 4.4703484e-8;
const double xmax = 1.797693e308;
const double xhigh1 = 5.1982303e8;
const double xhigh2 = 2.5220158e17;
// Code for |xvalue| <= 16
if (x <= 16.0)
{
if (x < xlow)
{
return(Constants.TwoInvPi * x);
}
double T = (4.0 * x - 24.0) / (x + 24.0);
return(Constants.TwoInvPi * x * Evaluate.ChebyshevSum(nterm1, ARL0, T) * Math.Exp(x));
}
// Code for |xvalue| > 16
double ch1;
if (x > xhigh2)
{
ch1 = 1.0;
}
else
{
double T = (x - 28.0) / (4.0 - x);
ch1 = Evaluate.ChebyshevSum(nterm2, ARL0AS, T);
}
double ch2;
if (x > xhigh1)
{
ch2 = 1.0;
}
else
{
double xsq = x * x;
double T = (800.0 - xsq) / (288.0 + xsq);
ch2 = Evaluate.ChebyshevSum(nterm3, AI0ML0, T);
}
double test = Math.Log(ch1) - Constants.LogSqrt2Pi - Math.Log(x) / 2.0 + x;
if (test > Math.Log(xmax))
{
throw new ArithmeticException("ERROR IN MISCFUN FUNCTION STRVL0: ARGUMENT CAUSES OVERFLOW");
}
return(Math.Exp(test) - Constants.TwoInvPi * ch2 / x);
}
/// <summary>
/// Returns the modified Struve function of order 1.
/// </summary>
/// <param name="x">The value to compute the function of.</param>
public static double StruveL1(double x)
{
//*********************************************************************72
//
//c STRVL1 calculates the modified Struve function of order 1.
//
// DESCRIPTION:
//
// This function calculates the modified Struve function of
// order 1, denoted L1(x), defined as the solution of
//
// x*x*D(Df) + x*Df - (x*x+1)f = 2*x*x/pi
//
// This subroutine is set up to work on IEEE machines.
// For other machines, you should retrieve the code
// from the general MISCFUN archive.
//
//
// ERROR RETURNS:
//
// If the value of |XVALUE| is too large, the result
// would cause an floating-pt overflow. An error message
// is printed and the function returns the value of
// sign(XVALUE)*XMAX where XMAX is the largest possible
// floating-pt argument.
//
//
// MACHINE-DEPENDENT PARAMETERS:
//
// NTERM1 - INTEGER - The no. of terms for the array ARL1.
// The recommended value is such that
// ABS(ARL1(NTERM1)) < EPS/100
//
// NTERM2 - INTEGER - The no. of terms for the array ARL1AS.
// The recommended value is such that
// ABS(ARL1AS(NTERM2)) < EPS/100
//
// NTERM3 - INTEGER - The no. of terms for the array AI1ML1.
// The recommended value is such that
// ABS(AI1ML1(NTERM3)) < EPS/100
//
// XLOW1 - DOUBLE PRECISION - The value of x below which
// L1(x) = 2*x*x/(3*pi)
// to machine precision. The recommended
// value is SQRT(15*EPS)
//
// XLOW2 - DOUBLE PRECISION - The value of x below which L1(x) set to 0.0.
// This is used to prevent underflow. The
// recommended value is
// SQRT(5*XMIN)
//
// XHIGH1 - DOUBLE PRECISION - The value of |x| above which the Chebyshev
// series in the asymptotic expansion of I1
// equals 1.0 to machine precision. The
// recommended value is SQRT( 30 / EPSNEG ).
//
// XHIGH2 - DOUBLE PRECISION - The value of |x| above which the Chebyshev
// series in the asymptotic expansion of I1 - L1
// equals 1.0 to machine precision. The recommended
// value is 30 / EPSNEG.
//
// XMAX - DOUBLE PRECISION - The value of XMAX, where XMAX is the
// largest possible floating-pt argument.
// This is used to prevent overflow.
//
// For values of EPS, EPSNEG, XMIN, and XMAX the user should refer
// to the file MACHCON.TXT
//
// The machine-arithmetic constants are given in DATA
// statements.
//
//
// INTRINSIC FUNCTIONS USED:
//
// EXP , LOG , SQRT
//
//
// OTHER MISCFUN SUBROUTINES USED:
//
// CHEVAL , ERRPRN
//
//
// AUTHOR:
// DR. ALLAN J. MACLEOD
// DEPT. OF MATHEMATICS AND STATISTICS
// UNIVERSITY OF PAISLEY
// HIGH ST.
// PAISLEY
// SCOTLAND
// PA1 2BE
//
// (e-mail: [email protected] )
//
//
// LATEST UPDATE:
// 12 JANUARY, 1996
//
//
if (x < 0.0)
{
return(StruveL1(-x));
}
double[] ARL1 = new double[27];
ARL1[0] = 0.38996027351229538208;
ARL1[1] = -0.33658096101975749366;
ARL1[2] = 0.23012467912501645616;
ARL1[3] = -0.13121594007960832327;
ARL1[4] = 0.6425922289912846518e-1;
ARL1[5] = -0.2750032950616635833e-1;
ARL1[6] = 0.1040234148637208871e-1;
ARL1[7] = -0.350532294936388080e-2;
ARL1[8] = 0.105748498421439717e-2;
ARL1[9] = -0.28609426403666558e-3;
ARL1[10] = 0.6925708785942208e-4;
ARL1[11] = -0.1489693951122717e-4;
ARL1[12] = 0.281035582597128e-5;
ARL1[13] = -0.45503879297776e-6;
ARL1[14] = 0.6090171561770e-7;
ARL1[15] = -0.623543724808e-8;
ARL1[16] = 0.38430012067e-9;
ARL1[17] = 0.790543916e-11;
ARL1[18] = -0.489824083e-11;
ARL1[19] = 0.46356884e-12;
ARL1[20] = 0.684205e-14;
ARL1[21] = -0.569748e-14;
ARL1[22] = 0.35324e-15;
ARL1[23] = 0.4244e-16;
ARL1[24] = -0.644e-17;
ARL1[25] = -0.21e-18;
ARL1[26] = 0.9e-19;
double[] ARL1AS = new double[17];
ARL1AS[0] = 1.97540378441652356868;
ARL1AS[1] = -0.1195130555088294181e-1;
ARL1AS[2] = 0.33639485269196046e-3;
ARL1AS[3] = -0.1009115655481549e-4;
ARL1AS[4] = 0.30638951321998e-6;
ARL1AS[5] = -0.953704370396e-8;
ARL1AS[6] = 0.29524735558e-9;
ARL1AS[7] = -0.951078318e-11;
ARL1AS[8] = 0.28203667e-12;
ARL1AS[9] = -0.1134175e-13;
ARL1AS[10] = 0.147e-17;
ARL1AS[11] = -0.6232e-16;
ARL1AS[12] = -0.751e-17;
ARL1AS[13] = -0.17e-18;
ARL1AS[14] = 0.51e-18;
ARL1AS[15] = 0.23e-18;
ARL1AS[16] = 0.5e-19;
double[] AI1ML1 = new double[26];
AI1ML1[0] = 1.99679361896789136501;
AI1ML1[1] = -0.190663261409686132e-2;
AI1ML1[2] = -0.36094622410174481e-3;
AI1ML1[3] = -0.6841847304599820e-4;
AI1ML1[4] = -0.1299008228509426e-4;
AI1ML1[5] = -0.247152188705765e-5;
AI1ML1[6] = -0.47147839691972e-6;
AI1ML1[7] = -0.9020819982592e-7;
AI1ML1[8] = -0.1730458637504e-7;
AI1ML1[9] = -0.332323670159e-8;
AI1ML1[10] = -0.63736421735e-9;
AI1ML1[11] = -0.12180239756e-9;
AI1ML1[12] = -0.2317346832e-10;
AI1ML1[13] = -0.439068833e-11;
AI1ML1[14] = -0.82847110e-12;
AI1ML1[15] = -0.15562249e-12;
AI1ML1[16] = -0.2913112e-13;
AI1ML1[17] = -0.543965e-14;
AI1ML1[18] = -0.101177e-14;
AI1ML1[19] = -0.18767e-15;
AI1ML1[20] = -0.3484e-16;
AI1ML1[21] = -0.643e-17;
AI1ML1[22] = -0.118e-17;
AI1ML1[23] = -0.22e-18;
AI1ML1[24] = -0.4e-19;
AI1ML1[25] = -0.1e-19;
// MACHINE-DEPENDENT VALUES (Suitable for IEEE-arithmetic machines)
const int nterm1 = 24;
const int nterm2 = 13;
const int nterm3 = 22;
const double xlow1 = 5.7711949e-8;
const double xlow2 = 3.3354714e-154;
const double xmax = 1.797693e308;
const double xhigh1 = 5.19823025e8;
const double xhigh2 = 2.7021597e17;
// CODE FOR |x| <= 16
if (x <= 16.0)
{
if (x <= xlow2)
{
return(0.0);
}
double xsq = x * x;
if (x < xlow1)
{
return(xsq / Constants.Pi3Over2);
}
double t = (4.0 * x - 24.0) / (x + 24.0);
return(xsq * Evaluate.ChebyshevSum(nterm1, ARL1, t) * Math.Exp(x) / Constants.Pi3Over2);
}
// CODE FOR |x| > 16
double ch1;
if (x > xhigh2)
{
ch1 = 1.0;
}
else
{
double t = (x - 30.0) / (2.0 - x);
ch1 = Evaluate.ChebyshevSum(nterm2, ARL1AS, t);
}
double ch2;
if (x > xhigh1)
{
ch2 = 1.0;
}
else
{
double xsq = x * x;
double t = (800.0 - xsq) / (288.0 + xsq);
ch2 = Evaluate.ChebyshevSum(nterm3, AI1ML1, t);
}
double test = Math.Log(ch1) - Constants.LogSqrt2Pi - Math.Log(x) / 2.0 + x;
if (test > Math.Log(xmax))
{
throw new ArithmeticException("ERROR IN MISCFUN FUNCTION STRVL1: ARGUMENT CAUSES OVERFLOW");
}
return(Math.Exp(test) - Constants.TwoInvPi * ch2);
}