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Cleanup: whitespace

ridge-regression
Christoph Ruegg 8 years ago
parent
2be8c3a6ee
commit
e0c31b887c
6 changed files with 222 additions and 240 deletions
Whitespace
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  1. 20
      src/Numerics/SpecialFunctions/Airy.cs
  2. 390
      src/Numerics/SpecialFunctions/Amos/AmosHelper.cs
  3. 5
      src/Numerics/SpecialFunctions/Amos/AmosWrapper.cs
  4. 22
      src/Numerics/SpecialFunctions/Bessel.cs
  5. 14
      src/Numerics/SpecialFunctions/Hankel.cs
  6. 11
      src/Numerics/SpecialFunctions/SphericalBessel.cs

20
src/Numerics/SpecialFunctions/Airy.cs
View File

@ -1,8 +1,4 @@
using System; using System.Numerics;
using System.Collections.Generic;
using System.Linq;
using System.Numerics;
using System.Text;
namespace MathNet.Numerics namespace MathNet.Numerics
{ {
@ -31,7 +27,7 @@ namespace MathNet.Numerics
/// If expScaled is true, returns Exp(zta) * Ai(z), where zta = (2/3) * z * Sqrt(z). /// If expScaled is true, returns Exp(zta) * Ai(z), where zta = (2/3) * z * Sqrt(z).
/// </summary> /// </summary>
/// <param name="z">The value to compute the Airy function of.</param> /// <param name="z">The value to compute the Airy function of.</param>
/// <param name="expScaled">If true, returns exponentially-scaled Airy function</param> /// <param name="expScaled">If true, returns exponentially-scaled Airy function</param>
/// <returns></returns> /// <returns></returns>
public static double AiryAi(double z, bool expScaled = false) public static double AiryAi(double z, bool expScaled = false)
{ {
@ -52,7 +48,7 @@ namespace MathNet.Numerics
/// If expScaled is true, returns Exp(zta) * d/dz Ai(z), where zta = (2/3) * z * Sqrt(z). /// If expScaled is true, returns Exp(zta) * d/dz Ai(z), where zta = (2/3) * z * Sqrt(z).
/// </summary> /// </summary>
/// <param name="z">The value to compute the derivative of the Airy function of.</param> /// <param name="z">The value to compute the derivative of the Airy function of.</param>
/// <param name="expScaled">If true, returns exponentially-scaled Airy function</param> /// <param name="expScaled">If true, returns exponentially-scaled Airy function</param>
/// <returns></returns> /// <returns></returns>
public static Complex AiryAiPrime(Complex z, bool expScaled = false) public static Complex AiryAiPrime(Complex z, bool expScaled = false)
{ {
@ -66,7 +62,7 @@ namespace MathNet.Numerics
/// If expScaled is true, returns Exp(zta) * d/dz Ai(z), where zta = (2/3) * z * Sqrt(z). /// If expScaled is true, returns Exp(zta) * d/dz Ai(z), where zta = (2/3) * z * Sqrt(z).
/// </summary> /// </summary>
/// <param name="z">The value to compute the derivative of the Airy function of.</param> /// <param name="z">The value to compute the derivative of the Airy function of.</param>
/// <param name="expScaled">If true, returns exponentially-scaled Airy function</param> /// <param name="expScaled">If true, returns exponentially-scaled Airy function</param>
/// <returns></returns> /// <returns></returns>
public static double AiryAiPrime(double z, bool expScaled = false) public static double AiryAiPrime(double z, bool expScaled = false)
{ {
@ -87,7 +83,7 @@ namespace MathNet.Numerics
/// If expScaled is true, returns Exp(-axzta) * Bi(z) where zta = (2 / 3) * z * Sqrt(z) and axzta = Abs(zta.Real). /// If expScaled is true, returns Exp(-axzta) * Bi(z) where zta = (2 / 3) * z * Sqrt(z) and axzta = Abs(zta.Real).
/// </summary> /// </summary>
/// <param name="z">The value to compute the Airy function of.</param> /// <param name="z">The value to compute the Airy function of.</param>
/// <param name="expScaled">If true, returns exponentially-scaled Airy function</param> /// <param name="expScaled">If true, returns exponentially-scaled Airy function</param>
/// <returns></returns> /// <returns></returns>
public static Complex AiryBi(Complex z, bool expScaled = false) public static Complex AiryBi(Complex z, bool expScaled = false)
{ {
@ -101,7 +97,7 @@ namespace MathNet.Numerics
/// If expScaled is true, returns Exp(-axzta) * Bi(z) where zta = (2 / 3) * z * Sqrt(z) and axzta = Abs(zta.Real). /// If expScaled is true, returns Exp(-axzta) * Bi(z) where zta = (2 / 3) * z * Sqrt(z) and axzta = Abs(zta.Real).
/// </summary> /// </summary>
/// <param name="z">The value to compute the Airy function of.</param> /// <param name="z">The value to compute the Airy function of.</param>
/// <param name="expScaled">If true, returns exponentially-scaled Airy function</param> /// <param name="expScaled">If true, returns exponentially-scaled Airy function</param>
/// <returns></returns> /// <returns></returns>
public static double AiryBi(double z, bool expScaled = false) public static double AiryBi(double z, bool expScaled = false)
{ {
@ -114,7 +110,7 @@ namespace MathNet.Numerics
/// If expScaled is true, returns Exp(-axzta) * d/dz Bi(z) where zta = (2 / 3) * z * Sqrt(z) and axzta = Abs(zta.Real). /// If expScaled is true, returns Exp(-axzta) * d/dz Bi(z) where zta = (2 / 3) * z * Sqrt(z) and axzta = Abs(zta.Real).
/// </summary> /// </summary>
/// <param name="z">The value to compute the derivative of the Airy function of.</param> /// <param name="z">The value to compute the derivative of the Airy function of.</param>
/// <param name="expScaled">If true, returns exponentially-scaled Airy function</param> /// <param name="expScaled">If true, returns exponentially-scaled Airy function</param>
/// <returns></returns> /// <returns></returns>
public static Complex AiryBiPrime(Complex z, bool expScaled = false) public static Complex AiryBiPrime(Complex z, bool expScaled = false)
{ {
@ -128,7 +124,7 @@ namespace MathNet.Numerics
/// If expScaled is true, returns Exp(-axzta) * d/dz Bi(z) where zta = (2 / 3) * z * Sqrt(z) and axzta = Abs(zta.Real). /// If expScaled is true, returns Exp(-axzta) * d/dz Bi(z) where zta = (2 / 3) * z * Sqrt(z) and axzta = Abs(zta.Real).
/// </summary> /// </summary>
/// <param name="z">The value to compute the derivative of the Airy function of.</param> /// <param name="z">The value to compute the derivative of the Airy function of.</param>
/// <param name="expScaled">If true, returns exponentially-scaled Airy function</param> /// <param name="expScaled">If true, returns exponentially-scaled Airy function</param>
/// <returns></returns> /// <returns></returns>
public static double AiryBiPrime(double z, bool expScaled = false) public static double AiryBiPrime(double z, bool expScaled = false)
{ {

390
src/Numerics/SpecialFunctions/Amos/AmosHelper.cs
View File

@ -177,9 +177,9 @@ namespace MathNet.Numerics
tol = Math.Max(d1mach(4), 1.0E-18); tol = Math.Max(d1mach(4), 1.0E-18);
fid = (double)id; fid = (double)id;
if (az > 1.0) goto L70; if (az > 1.0) goto L70;
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
// POWER SERIES FOR ABS(Z).LE.1. // POWER SERIES FOR ABS(Z).LE.1.
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
s1r = coner; s1r = coner;
s1i = conei; s1i = conei;
s2r = coner; s2r = coner;
@ -258,21 +258,21 @@ namespace MathNet.Numerics
aii = str * aii + sti * air; aii = str * aii + sti * air;
air = ptr; air = ptr;
return 0; return 0;
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
// CASE FOR ABS(Z).GT.1.0 // CASE FOR ABS(Z).GT.1.0
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
L70: L70:
fnu = (1.0 + fid) / 3.0; fnu = (1.0 + fid) / 3.0;
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
// SET PARAMETERS RELATED TO MACHINE CONSTANTS. // SET PARAMETERS RELATED TO MACHINE CONSTANTS.
// TOL IS THE APPROXIMATE UNIT ROUNDOFF LIMITED TO 1.0D-18. // TOL IS THE APPROXIMATE UNIT ROUNDOFF LIMITED TO 1.0D-18.
// ELIM IS THE APPROXIMATE EXPONENTIAL OVER- AND UNDERFLOW LIMIT. // ELIM IS THE APPROXIMATE EXPONENTIAL OVER- AND UNDERFLOW LIMIT.
// EXP(-ELIM).LT.EXP(-ALIM)=EXP(-ELIM)/TOL AND // EXP(-ELIM).LT.EXP(-ALIM)=EXP(-ELIM)/TOL AND
// EXP(ELIM).GT.EXP(ALIM)=EXP(ELIM)*TOL ARE INTERVALS NEAR // EXP(ELIM).GT.EXP(ALIM)=EXP(ELIM)*TOL ARE INTERVALS NEAR
// UNDERFLOW AND OVERFLOW LIMITS WHERE SCALED ARITHMETIC IS DONE. // UNDERFLOW AND OVERFLOW LIMITS WHERE SCALED ARITHMETIC IS DONE.
// RL IS THE LOWER BOUNDARY OF THE ASYMPTOTIC EXPANSION FOR LARGE Z. // RL IS THE LOWER BOUNDARY OF THE ASYMPTOTIC EXPANSION FOR LARGE Z.
// DIG = NUMBER OF BASE 10 DIGITS IN TOL = 10**(-DIG). // DIG = NUMBER OF BASE 10 DIGITS IN TOL = 10**(-DIG).
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
k1 = i1mach(15); k1 = i1mach(15);
k2 = i1mach(16); k2 = i1mach(16);
r1m5 = d1mach(5); r1m5 = d1mach(5);
@ -285,9 +285,9 @@ namespace MathNet.Numerics
alim = elim + Math.Max(-aa, -41.45); alim = elim + Math.Max(-aa, -41.45);
rl = 1.2 * dig + 3.0; rl = 1.2 * dig + 3.0;
alaz = Math.Log(az); alaz = Math.Log(az);
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
// TEST FOR PROPER RANGE // TEST FOR PROPER RANGE
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
aa = 0.5 / tol; aa = 0.5 / tol;
bb = i1mach(9) * 0.5; bb = i1mach(9) * 0.5;
aa = Math.Min(aa, bb); aa = Math.Min(aa, bb);
@ -298,9 +298,9 @@ namespace MathNet.Numerics
zsqrt(zr, zi, ref csqr, ref csqi); zsqrt(zr, zi, ref csqr, ref csqi);
ztar = tth * (zr * csqr - zi * csqi); ztar = tth * (zr * csqr - zi * csqi);
ztai = tth * (zr * csqi + zi * csqr); ztai = tth * (zr * csqi + zi * csqr);
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
// RE(ZTA).LE.0 WHEN RE(Z).LT.0, ESPECIALLY WHEN IM(Z) IS SMALL // RE(ZTA).LE.0 WHEN RE(Z).LT.0, ESPECIALLY WHEN IM(Z) IS SMALL
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
iflag = 0; iflag = 0;
sfac = 1.0; sfac = 1.0;
ak = ztai; ak = ztai;
@ -318,18 +318,18 @@ namespace MathNet.Numerics
aa = ztar; aa = ztar;
if (aa >= 0.0 && zr > 0.0) goto L110; if (aa >= 0.0 && zr > 0.0) goto L110;
if (kode == 2) goto L100; if (kode == 2) goto L100;
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
// OVERFLOW TEST // OVERFLOW TEST
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
if (aa > -alim) goto L100; if (aa > -alim) goto L100;
aa = -aa + alaz * 0.25; aa = -aa + alaz * 0.25;
iflag = 1; iflag = 1;
sfac = tol; sfac = tol;
if (aa > elim) goto L270; if (aa > elim) goto L270;
L100: L100:
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
// CBKNU AND CACON RETURN EXP(ZTA)*K(FNU,ZTA) ON KODE=2 // CBKNU AND CACON RETURN EXP(ZTA)*K(FNU,ZTA) ON KODE=2
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
mr = 1; mr = 1;
if (zi < 0.0) mr = -1; if (zi < 0.0) mr = -1;
zacai(ztar, ztai, fnu, kode, mr, 1, cyr, cyi, ref nn, rl, tol, elim, alim); zacai(ztar, ztai, fnu, kode, mr, 1, cyr, cyi, ref nn, rl, tol, elim, alim);
@ -338,9 +338,9 @@ namespace MathNet.Numerics
goto L130; goto L130;
L110: L110:
if (kode == 2) goto L120; if (kode == 2) goto L120;
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
// UNDERFLOW TEST // UNDERFLOW TEST
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
if (aa < alim) goto L120; if (aa < alim) goto L120;
aa = -aa - 0.25 * alaz; aa = -aa - 0.25 * alaz;
iflag = 2; iflag = 2;
@ -419,7 +419,7 @@ namespace MathNet.Numerics
nz = 0; nz = 0;
return 0; return 0;
} }
// The Airy function Bi(z) and derivative // The Airy function Bi(z) and derivative
public int zbiry(double zr, double zi, int id, int kode, ref double bir, ref double bii, ref int nz, ref int ierr) public int zbiry(double zr, double zi, int id, int kode, ref double bir, ref double bii, ref int nz, ref int ierr)
{ {
@ -1762,17 +1762,17 @@ namespace MathNet.Numerics
if (n < 1) ierr = 1; if (n < 1) ierr = 1;
if (ierr != 0) return 0; if (ierr != 0) return 0;
nn = n; nn = n;
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
// SET PARAMETERS RELATED TO MACHINE CONSTANTS. // SET PARAMETERS RELATED TO MACHINE CONSTANTS.
// TOL IS THE APPROXIMATE UNIT ROUNDOFF LIMITED TO 1.0E-18. // TOL IS THE APPROXIMATE UNIT ROUNDOFF LIMITED TO 1.0E-18.
// ELIM IS THE APPROXIMATE EXPONENTIAL OVER- AND UNDERFLOW LIMIT. // ELIM IS THE APPROXIMATE EXPONENTIAL OVER- AND UNDERFLOW LIMIT.
// EXP(-ELIM).LT.EXP(-ALIM)=EXP(-ELIM)/TOL AND // EXP(-ELIM).LT.EXP(-ALIM)=EXP(-ELIM)/TOL AND
// EXP(ELIM).GT.EXP(ALIM)=EXP(ELIM)*TOL ARE INTERVALS NEAR // EXP(ELIM).GT.EXP(ALIM)=EXP(ELIM)*TOL ARE INTERVALS NEAR
// UNDERFLOW AND OVERFLOW LIMITS WHERE SCALED ARITHMETIC IS DONE. // UNDERFLOW AND OVERFLOW LIMITS WHERE SCALED ARITHMETIC IS DONE.
// RL IS THE LOWER BOUNDARY OF THE ASYMPTOTIC EXPANSION FOR LARGE Z. // RL IS THE LOWER BOUNDARY OF THE ASYMPTOTIC EXPANSION FOR LARGE Z.
// DIG = NUMBER OF BASE 10 DIGITS IN TOL = 10**(-DIG). // DIG = NUMBER OF BASE 10 DIGITS IN TOL = 10**(-DIG).
// FNUL IS THE LOWER BOUNDARY OF THE ASYMPTOTIC SERIES FOR LARGE FNU // FNUL IS THE LOWER BOUNDARY OF THE ASYMPTOTIC SERIES FOR LARGE FNU
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
tol = Math.Max(d1mach(4), 1.0E-18); tol = Math.Max(d1mach(4), 1.0E-18);
k1 = i1mach(15); k1 = i1mach(15);
k2 = i1mach(16); k2 = i1mach(16);
@ -1786,9 +1786,9 @@ namespace MathNet.Numerics
alim = elim + Math.Max(-aa, -41.45); alim = elim + Math.Max(-aa, -41.45);
fnul = (dig - 3.0) * 6.0 + 10.0; fnul = (dig - 3.0) * 6.0 + 10.0;
rl = 1.2 * dig + 3.0; rl = 1.2 * dig + 3.0;
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
// TEST FOR PROPER RANGE // TEST FOR PROPER RANGE
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
az = zabs(zr, zi); az = zabs(zr, zi);
fn = fnu + (nn - 1); fn = fnu + (nn - 1);
aa = 0.5 / tol; aa = 0.5 / tol;
@ -1799,9 +1799,9 @@ namespace MathNet.Numerics
aa = Math.Sqrt(aa); aa = Math.Sqrt(aa);
if (az > aa) ierr = 3; if (az > aa) ierr = 3;
if (fn > aa) ierr = 3; if (fn > aa) ierr = 3;
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
// OVERFLOW TEST ON THE LAST MEMBER OF THE SEQUENCE // OVERFLOW TEST ON THE LAST MEMBER OF THE SEQUENCE
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
// UFL = EXP(-ELIM) // UFL = EXP(-ELIM)
ufl = d1mach(1) * 1.0E3; ufl = d1mach(1) * 1.0E3;
if (az < ufl) goto L180; if (az < ufl) goto L180;
@ -1818,24 +1818,24 @@ namespace MathNet.Numerics
if (nuf < 0) goto L180; if (nuf < 0) goto L180;
nz += nuf; nz += nuf;
nn -= nuf; nn -= nuf;
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
// HERE NN=N OR NN=0 SINCE NUF=0,NN, OR -1 ON RETURN FROM CUOIK // HERE NN=N OR NN=0 SINCE NUF=0,NN, OR -1 ON RETURN FROM CUOIK
// IF NUF=NN, THEN CY(I)=CZERO FOR ALL I // IF NUF=NN, THEN CY(I)=CZERO FOR ALL I
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
if (nn == 0) goto L100; if (nn == 0) goto L100;
L60: L60:
if (zr < 0.0) goto L70; if (zr < 0.0) goto L70;
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
// RIGHT HALF PLANE COMPUTATION, REAL(Z).GE.0. // RIGHT HALF PLANE COMPUTATION, REAL(Z).GE.0.
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
zbknu(zr, zi, fnu, kode, nn, cyr, cyi, ref nw, tol, elim, alim); zbknu(zr, zi, fnu, kode, nn, cyr, cyi, ref nw, tol, elim, alim);
if (nw < 0) goto L200; if (nw < 0) goto L200;
nz = nw; nz = nw;
return 0; return 0;
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
// LEFT HALF PLANE COMPUTATION // LEFT HALF PLANE COMPUTATION
// PI/2.LT.ARG(Z).LE.PI AND -PI.LT.ARG(Z).LT.-PI/2. // PI/2.LT.ARG(Z).LE.PI AND -PI.LT.ARG(Z).LT.-PI/2.
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
L70: L70:
if (nz != 0) goto L180; if (nz != 0) goto L180;
mr = 1; mr = 1;
@ -1844,9 +1844,9 @@ namespace MathNet.Numerics
if (nw < 0) goto L200; if (nw < 0) goto L200;
nz = nw; nz = nw;
return 0; return 0;
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
// UNIFORM ASYMPTOTIC EXPANSIONS FOR FNU.GT.FNUL // UNIFORM ASYMPTOTIC EXPANSIONS FOR FNU.GT.FNUL
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
L80: L80:
mr = 0; mr = 0;
if (zr >= 0.0) goto L90; if (zr >= 0.0) goto L90;
@ -2447,8 +2447,8 @@ namespace MathNet.Numerics
#endregion #endregion
const int FLT_RADIX = 2; // the radix used by the representation of all floating-point types const int FLT_RADIX = 2; // the radix used by the representation of all floating-point types
const double DBL_EPSILON = 2.2204460492503130808E-16; // 2^(1 - 53) const double DBL_EPSILON = 2.2204460492503130808E-16; // 2^(1 - 53)
const double DBL_MAX = double.MaxValue; // 2^1024 * (1 - 2^(-53)) const double DBL_MAX = double.MaxValue; // 2^1024 * (1 - 2^(-53))
const double DBL_MIN = 2.2250738585072013831E-308; // 2^(-1021 - 1) const double DBL_MIN = 2.2250738585072013831E-308; // 2^(-1021 - 1)
@ -2545,7 +2545,7 @@ namespace MathNet.Numerics
switch (i) switch (i)
{ {
case 9: return Int32.MaxValue; // the largest magnitude of integer = 2^31 - 1 = 2147483647 case 9: return Int32.MaxValue; // the largest magnitude of integer = 2^31 - 1 = 2147483647
case 14: return 53; // return Precision.DoubleWidth; // the number of base-2 digits. case 14: return 53; // return Precision.DoubleWidth; // the number of base-2 digits.
case 15: return -1021; // EMIN, the smallest exponent E. case 15: return -1021; // EMIN, the smallest exponent E.
case 16: return 1024; // EMAX, the largest exponent E = 2^10 case 16: return 1024; // EMAX, the largest exponent E = 2^10
} }
@ -2823,29 +2823,29 @@ namespace MathNet.Numerics
if (az <= 2.0) goto L10; if (az <= 2.0) goto L10;
if (az * az * 0.25 > dfnu + 1.0) goto L20; if (az * az * 0.25 > dfnu + 1.0) goto L20;
L10: L10:
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
// POWER SERIES FOR THE I FUNCTION // POWER SERIES FOR THE I FUNCTION
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
zseri(znr, zni, fnu, kode, nn, yr, yi, ref nw, tol, elim, alim); zseri(znr, zni, fnu, kode, nn, yr, yi, ref nw, tol, elim, alim);
goto L40; goto L40;
L20: L20:
if (az < rl) goto L30; if (az < rl) goto L30;
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
// ASYMPTOTIC EXPANSION FOR LARGE Z FOR THE I FUNCTION // ASYMPTOTIC EXPANSION FOR LARGE Z FOR THE I FUNCTION
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
zasyi(znr, zni, fnu, kode, nn, yr, yi, ref nw, rl, tol, elim, alim); zasyi(znr, zni, fnu, kode, nn, yr, yi, ref nw, rl, tol, elim, alim);
if (nw < 0) goto L80; if (nw < 0) goto L80;
goto L40; goto L40;
L30: L30:
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
// MILLER ALGORITHM NORMALIZED BY THE SERIES FOR THE I FUNCTION // MILLER ALGORITHM NORMALIZED BY THE SERIES FOR THE I FUNCTION
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
zmlri(znr, zni, fnu, kode, nn, yr, yi, ref nw, tol); zmlri(znr, zni, fnu, kode, nn, yr, yi, ref nw, tol);
if (nw < 0) goto L80; if (nw < 0) goto L80;
L40: L40:
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
// ANALYTIC CONTINUATION TO THE LEFT HALF PLANE FOR THE K FUNCTION // ANALYTIC CONTINUATION TO THE LEFT HALF PLANE FOR THE K FUNCTION
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
zbknu(znr, zni, fnu, kode, 1, cyr, cyi, ref nw, tol, elim, alim); zbknu(znr, zni, fnu, kode, 1, cyr, cyi, ref nw, tol, elim, alim);
if (nw != 0) goto L80; if (nw != 0) goto L80;
fmr = (double)mr; fmr = (double)mr;
@ -2857,10 +2857,10 @@ namespace MathNet.Numerics
csgnr = -csgni * Math.Sin(yy); csgnr = -csgni * Math.Sin(yy);
csgni = csgni * Math.Cos(yy); csgni = csgni * Math.Cos(yy);
L50: L50:
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
// CALCULATE CSPN=EXP(FNU*PI*I) TO MINIMIZE LOSSES OF SIGNIFICANCE // CALCULATE CSPN=EXP(FNU*PI*I) TO MINIMIZE LOSSES OF SIGNIFICANCE
// WHEN FNU IS LARGE // WHEN FNU IS LARGE
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
inu = (int)fnu; inu = (int)fnu;
arg = (fnu - (double)inu) * sgn; arg = (fnu - (double)inu) * sgn;
cspnr = Math.Cos(arg); cspnr = Math.Cos(arg);
@ -2932,9 +2932,9 @@ namespace MathNet.Numerics
nn = n; nn = n;
zbinu(znr, zni, fnu, kode, nn, yr, yi, ref nw, rl, fnul, tol, elim, alim); zbinu(znr, zni, fnu, kode, nn, yr, yi, ref nw, rl, fnul, tol, elim, alim);
if (nw < 0) goto L90; if (nw < 0) goto L90;
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
// ANALYTIC CONTINUATION TO THE LEFT HALF PLANE FOR THE K FUNCTION // ANALYTIC CONTINUATION TO THE LEFT HALF PLANE FOR THE K FUNCTION
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
nn = Math.Min(2, n); nn = Math.Min(2, n);
zbknu(znr, zni, fnu, kode, nn, cyr, cyi, ref nw, tol, elim, alim); zbknu(znr, zni, fnu, kode, nn, cyr, cyi, ref nw, tol, elim, alim);
if (nw != 0) goto L90; if (nw != 0) goto L90;
@ -2950,10 +2950,10 @@ namespace MathNet.Numerics
spn = Math.Sin(yy); spn = Math.Sin(yy);
zmlt(csgnr, csgni, cpn, spn, ref csgnr, ref csgni); zmlt(csgnr, csgni, cpn, spn, ref csgnr, ref csgni);
L10: L10:
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
// CALCULATE CSPN=EXP(FNU*PI*I) TO MINIMIZE LOSSES OF SIGNIFICANCE // CALCULATE CSPN=EXP(FNU*PI*I) TO MINIMIZE LOSSES OF SIGNIFICANCE
// WHEN FNU IS LARGE // WHEN FNU IS LARGE
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
inu = (int)fnu; inu = (int)fnu;
arg = (fnu - (double)inu) * sgn; arg = (fnu - (double)inu) * sgn;
cpn = Math.Cos(arg); cpn = Math.Cos(arg);
@ -3011,9 +3011,9 @@ namespace MathNet.Numerics
fn = fnu + 1.0; fn = fnu + 1.0;
ckr = fn * rzr; ckr = fn * rzr;
cki = fn * rzi; cki = fn * rzi;
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
// SCALE NEAR EXPONENT EXTREMES DURING RECURRENCE ON K FUNCTIONS // SCALE NEAR EXPONENT EXTREMES DURING RECURRENCE ON K FUNCTIONS
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
cscl = 1.0 / tol; cscl = 1.0 / tol;
cscr = tol; cscr = tol;
cssr[0] = cscl; cssr[0] = cscl;
@ -3142,9 +3142,9 @@ namespace MathNet.Numerics
rtr1 = Math.Sqrt(arm); rtr1 = Math.Sqrt(arm);
il = Math.Min(2, n); il = Math.Min(2, n);
dfnu = fnu + (n - il); dfnu = fnu + (n - il);
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
// OVERFLOW TEST // OVERFLOW TEST
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
raz = 1.0 / az; raz = 1.0 / az;
str = zr * raz; str = zr * raz;
sti = -zi * raz; sti = -zi * raz;
@ -3169,21 +3169,21 @@ namespace MathNet.Numerics
if (dnu2 > rtr1) fdn = dnu2 * dnu2; if (dnu2 > rtr1) fdn = dnu2 * dnu2;
ezr = zr * 8.0; ezr = zr * 8.0;
ezi = zi * 8.0; ezi = zi * 8.0;
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
// WHEN Z IS IMAGINARY, THE ERROR TEST MUST BE MADE RELATIVE TO THE // WHEN Z IS IMAGINARY, THE ERROR TEST MUST BE MADE RELATIVE TO THE
// FIRST RECIPROCAL POWER SINCE THIS IS THE LEADING TERM OF THE // FIRST RECIPROCAL POWER SINCE THIS IS THE LEADING TERM OF THE
// EXPANSION FOR THE IMAGINARY PART. // EXPANSION FOR THE IMAGINARY PART.
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
aez = 8.0 * az; aez = 8.0 * az;
s = tol / aez; s = tol / aez;
jl = (int)(rl + rl) + 2; jl = (int)(rl + rl) + 2;
p1r = zeror; p1r = zeror;
p1i = zeroi; p1i = zeroi;
if (zi == 0.0) goto L30; if (zi == 0.0) goto L30;
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
// CALCULATE EXP(PI*(0.5+FNU+N-IL)*I) TO MINIMIZE LOSSES OF // CALCULATE EXP(PI*(0.5+FNU+N-IL)*I) TO MINIMIZE LOSSES OF
// SIGNIFICANCE WHEN FNU OR N IS LARGE // SIGNIFICANCE WHEN FNU OR N IS LARGE
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
inu = (int)fnu; inu = (int)fnu;
arg = (fnu - (double)inu) * pi; arg = (fnu - (double)inu) * pi;
inu = inu + n - il; inu = inu + n - il;
@ -3313,9 +3313,9 @@ namespace MathNet.Numerics
if (az <= 2.0) goto L10; if (az <= 2.0) goto L10;
if (az * az * 0.25 > dfnu + 1.0) goto L20; if (az * az * 0.25 > dfnu + 1.0) goto L20;
L10: L10:
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
// POWER SERIES // POWER SERIES
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
zseri(zr, zi, fnu, kode, nn, cyr, cyi, ref nw, tol, elim, alim); zseri(zr, zi, fnu, kode, nn, cyr, cyi, ref nw, tol, elim, alim);
inw = Math.Abs(nw); inw = Math.Abs(nw);
nz = nz + inw; nz = nz + inw;
@ -3327,9 +3327,9 @@ namespace MathNet.Numerics
if (az < rl) goto L40; if (az < rl) goto L40;
if (dfnu <= 1.0) goto L30; if (dfnu <= 1.0) goto L30;
if (az + az < dfnu * dfnu) goto L50; if (az + az < dfnu * dfnu) goto L50;
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
// ASYMPTOTIC EXPANSION FOR LARGE Z // ASYMPTOTIC EXPANSION FOR LARGE Z
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
L30: L30:
zasyi(zr, zi, fnu, kode, nn, cyr, cyi, ref nw, rl, tol, elim, alim); zasyi(zr, zi, fnu, kode, nn, cyr, cyi, ref nw, rl, tol, elim, alim);
if (nw < 0) goto L130; if (nw < 0) goto L130;
@ -3337,9 +3337,9 @@ namespace MathNet.Numerics
L40: L40:
if (dfnu <= 1.0) goto L70; if (dfnu <= 1.0) goto L70;
L50: L50:
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
// OVERFLOW AND UNDERFLOW TEST ON I SEQUENCE FOR MILLER ALGORITHM // OVERFLOW AND UNDERFLOW TEST ON I SEQUENCE FOR MILLER ALGORITHM
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
zuoik(zr, zi, fnu, kode, 1, nn, cyr, cyi, ref nw, tol, elim, alim); zuoik(zr, zi, fnu, kode, 1, nn, cyr, cyi, ref nw, tol, elim, alim);
if (nw < 0) goto L130; if (nw < 0) goto L130;
nz = nz + nw; nz = nz + nw;
@ -3351,19 +3351,19 @@ namespace MathNet.Numerics
L60: L60:
if (az > rl) goto L80; if (az > rl) goto L80;
L70: L70:
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
// MILLER ALGORITHM NORMALIZED BY THE SERIES // MILLER ALGORITHM NORMALIZED BY THE SERIES
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
zmlri(zr, zi, fnu, kode, nn, cyr, cyi, ref nw, tol); zmlri(zr, zi, fnu, kode, nn, cyr, cyi, ref nw, tol);
if (nw < 0) goto L130; if (nw < 0) goto L130;
goto L120; goto L120;
L80: L80:
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
// MILLER ALGORITHM NORMALIZED BY THE WRONSKIAN // MILLER ALGORITHM NORMALIZED BY THE WRONSKIAN
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
// OVERFLOW TEST ON K FUNCTIONS USED IN WRONSKIAN // OVERFLOW TEST ON K FUNCTIONS USED IN WRONSKIAN
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
zuoik(zr, zi, fnu, kode, 2, 2, cwr, cwi, ref nw, tol, elim, alim); zuoik(zr, zi, fnu, kode, 2, 2, cwr, cwi, ref nw, tol, elim, alim);
if (nw >= 0) goto L100; if (nw >= 0) goto L100;
nz = nn; nz = nn;
@ -3379,9 +3379,9 @@ namespace MathNet.Numerics
if (nw < 0) goto L130; if (nw < 0) goto L130;
goto L120; goto L120;
L110: L110:
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
// INCREMENT FNU+NN-1 UP TO FNUL, COMPUTE AND RECUR BACKWARD // INCREMENT FNU+NN-1 UP TO FNUL, COMPUTE AND RECUR BACKWARD
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
nui = (int)(fnul - dfnu) + 1; nui = (int)(fnul - dfnu) + 1;
nui = Math.Max(nui, 0); nui = Math.Max(nui, 0);
zbuni(zr, zi, fnu, kode, nn, cyr, cyi, ref nw, nui, ref nlast, fnul, tol, elim, alim); zbuni(zr, zi, fnu, kode, nn, cyr, cyi, ref nw, nui, ref nlast, fnul, tol, elim, alim);
@ -4031,26 +4031,26 @@ namespace MathNet.Numerics
dfnu = fnu + (double)(n - 1); dfnu = fnu + (double)(n - 1);
gnu = dfnu + fnui; gnu = dfnu + fnui;
if (iform == 2) goto L10; if (iform == 2) goto L10;
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
// ASYMPTOTIC EXPANSION FOR I(FNU,Z) FOR LARGE FNU APPLIED IN // ASYMPTOTIC EXPANSION FOR I(FNU,Z) FOR LARGE FNU APPLIED IN
// -PI/3.LE.ARG(Z).LE.PI/3 // -PI/3.LE.ARG(Z).LE.PI/3
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
zuni1(zr, zi, gnu, kode, 2, cyr, cyi, ref nw, ref nlast, fnul, tol, elim, alim); zuni1(zr, zi, gnu, kode, 2, cyr, cyi, ref nw, ref nlast, fnul, tol, elim, alim);
goto L20; goto L20;
L10: L10:
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
// ASYMPTOTIC EXPANSION FOR J(FNU,Z*EXP(M*HPI)) FOR LARGE FNU // ASYMPTOTIC EXPANSION FOR J(FNU,Z*EXP(M*HPI)) FOR LARGE FNU
// APPLIED IN PI/3.LT.ABS(ARG(Z)).LE.PI/2 WHERE M=+I OR -I // APPLIED IN PI/3.LT.ABS(ARG(Z)).LE.PI/2 WHERE M=+I OR -I
// AND HPI=PI/2 // AND HPI=PI/2
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
zuni2(zr, zi, gnu, kode, 2, cyr, cyi, ref nw, ref nlast, fnul, tol, elim, alim); zuni2(zr, zi, gnu, kode, 2, cyr, cyi, ref nw, ref nlast, fnul, tol, elim, alim);
L20: L20:
if (nw < 0) goto L50; if (nw < 0) goto L50;
if (nw != 0) goto L90; if (nw != 0) goto L90;
str = zabs(cyr[0], cyi[0]); str = zabs(cyr[0], cyi[0]);
// ---------------------------------------------------------------------- // ----------------------------------------------------------------------
// SCALE BACKWARD RECURRENCE, BRY(3) IS DEFINED BUT NEVER USED // SCALE BACKWARD RECURRENCE, BRY(3) IS DEFINED BUT NEVER USED
// ---------------------------------------------------------------------- // ----------------------------------------------------------------------
bry[0] = d1mach(1) * 1.0E3 / tol; bry[0] = d1mach(1) * 1.0E3 / tol;
bry[1] = 1.0 / bry[0]; bry[1] = 1.0 / bry[0];
bry[2] = bry[1]; bry[2] = bry[1];
@ -4156,18 +4156,18 @@ namespace MathNet.Numerics
return 0; return 0;
L60: L60:
if (iform == 2) goto L70; if (iform == 2) goto L70;
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
// ASYMPTOTIC EXPANSION FOR I(FNU,Z) FOR LARGE FNU APPLIED IN // ASYMPTOTIC EXPANSION FOR I(FNU,Z) FOR LARGE FNU APPLIED IN
// -PI/3.LE.ARG(Z).LE.PI/3 // -PI/3.LE.ARG(Z).LE.PI/3
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
zuni1(zr, zi, fnu, kode, n, yr, yi, ref nw, ref nlast, fnul, tol, elim, alim); zuni1(zr, zi, fnu, kode, n, yr, yi, ref nw, ref nlast, fnul, tol, elim, alim);
goto L80; goto L80;
L70: L70:
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
// ASYMPTOTIC EXPANSION FOR J(FNU,Z*EXP(M*HPI)) FOR LARGE FNU // ASYMPTOTIC EXPANSION FOR J(FNU,Z*EXP(M*HPI)) FOR LARGE FNU
// APPLIED IN PI/3.LT.ABS(ARG(Z)).LE.PI/2 WHERE M=+I OR -I // APPLIED IN PI/3.LT.ABS(ARG(Z)).LE.PI/2 WHERE M=+I OR -I
// AND HPI=PI/2 // AND HPI=PI/2
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
zuni2(zr, zi, fnu, kode, n, yr, yi, ref nw, ref nlast, fnul, tol, elim, alim); zuni2(zr, zi, fnu, kode, n, yr, yi, ref nw, ref nlast, fnul, tol, elim, alim);
L80: L80:
if (nw < 0) goto L50; if (nw < 0) goto L50;
@ -4831,9 +4831,9 @@ namespace MathNet.Numerics
L20: L20:
dfnu = fnu + (double)(nn - 1); dfnu = fnu + (double)(nn - 1);
fnup = dfnu + 1.0; fnup = dfnu + 1.0;
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
// UNDERFLOW TEST // UNDERFLOW TEST
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
ak1r = ckr * dfnu; ak1r = ckr * dfnu;
ak1i = cki * dfnu; ak1i = cki * dfnu;
ak = dgamln(fnup, ref idum); ak = dgamln(fnup, ref idum);
@ -4923,14 +4923,14 @@ namespace MathNet.Numerics
k--; k--;
} }
return 0; return 0;
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
// RECUR BACKWARD WITH SCALED VALUES // RECUR BACKWARD WITH SCALED VALUES
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
L120: L120:
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
// EXP(-ALIM)=EXP(-ELIM)/TOL=APPROX. ONE PRECISION ABOVE THE // EXP(-ALIM)=EXP(-ELIM)/TOL=APPROX. ONE PRECISION ABOVE THE
// UNDERFLOW LIMIT = ASCLE = D1MACH(1)*SS*1.0D+3 // UNDERFLOW LIMIT = ASCLE = D1MACH(1)*SS*1.0D+3
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
s1r = wr[0]; s1r = wr[0];
s1i = wi[0]; s1i = wi[0];
s2r = wr[1]; s2r = wr[1];
@ -4973,10 +4973,10 @@ namespace MathNet.Numerics
yi[i - 1] = zeroi; yi[i - 1] = zeroi;
} }
return 0; return 0;
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
// RETURN WITH NZ.LT.0 IF ABS(Z*Z/4).GT.FNU+N-NZ-1 COMPLETE // RETURN WITH NZ.LT.0 IF ABS(Z*Z/4).GT.FNU+N-NZ-1 COMPLETE
// THE CALCULATION IN CBINU WITH N=N-ABS(NZ) // THE CALCULATION IN CBINU WITH N=N-ABS(NZ)
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
L190: L190:
nz = -nz; nz = -nz;
return 0; return 0;
@ -5942,11 +5942,11 @@ namespace MathNet.Numerics
nz = 0; nz = 0;
nd = n; nd = n;
nlast = 0; nlast = 0;
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
// COMPUTED VALUES WITH EXPONENTS BETWEEN ALIM AND ELIM IN MAG- // COMPUTED VALUES WITH EXPONENTS BETWEEN ALIM AND ELIM IN MAG-
// NITUDE ARE SCALED TO KEEP INTERMEDIATE ARITHMETIC ON SCALE, // NITUDE ARE SCALED TO KEEP INTERMEDIATE ARITHMETIC ON SCALE,
// EXP(ALIM)=EXP(ELIM)*TOL // EXP(ALIM)=EXP(ELIM)*TOL
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
cscl = 1.0 / tol; cscl = 1.0 / tol;
crsc = tol; crsc = tol;
cssr[0] = cscl; cssr[0] = cscl;
@ -5956,9 +5956,9 @@ namespace MathNet.Numerics
csrr[1] = coner; csrr[1] = coner;
csrr[2] = cscl; csrr[2] = cscl;
bry[0] = d1mach(1) * 1.0E3 / tol; bry[0] = d1mach(1) * 1.0E3 / tol;
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
// ZN IS IN THE RIGHT HALF PLANE AFTER ROTATION BY CI OR -CI // ZN IS IN THE RIGHT HALF PLANE AFTER ROTATION BY CI OR -CI
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
znr = zi; znr = zi;
zni = -zr; zni = -zr;
zbr = zr; zbr = zr;
@ -5981,9 +5981,9 @@ namespace MathNet.Numerics
cidi = -cidi; cidi = -cidi;
c2i = -c2i; c2i = -c2i;
L10: L10:
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
// CHECK FOR UNDERFLOW AND OVERFLOW ON FIRST MEMBER // CHECK FOR UNDERFLOW AND OVERFLOW ON FIRST MEMBER
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
fn = Math.Max(fnu, 1.0); fn = Math.Max(fnu, 1.0);
zunhj(znr, zni, fn, 1, tol, ref phir, ref phii, ref argr, ref argi, ref zeta1r, ref zeta1i, ref zeta2r, ref zeta2i, ref asumr, ref asumi, ref bsumr, ref bsumi); zunhj(znr, zni, fn, 1, tol, ref phir, ref phii, ref argr, ref argi, ref zeta1r, ref zeta1i, ref zeta2r, ref zeta2i, ref asumr, ref asumi, ref bsumr, ref bsumi);
if (kode == 1) goto L20; if (kode == 1) goto L20;
@ -6020,17 +6020,17 @@ namespace MathNet.Numerics
s1r = -zeta1r + zeta2r; s1r = -zeta1r + zeta2r;
s1i = -zeta1i + zeta2i; s1i = -zeta1i + zeta2i;
L60: L60:
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
// TEST FOR UNDERFLOW AND OVERFLOW // TEST FOR UNDERFLOW AND OVERFLOW
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
rs1 = s1r; rs1 = s1r;
if (Math.Abs(rs1) > elim) goto L120; if (Math.Abs(rs1) > elim) goto L120;
if (i == 1) iflag = 2; if (i == 1) iflag = 2;
if (Math.Abs(rs1) < alim) goto L70; if (Math.Abs(rs1) < alim) goto L70;
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
// REFINE TEST AND SCALE // REFINE TEST AND SCALE
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
aphi = zabs(phir, phii); aphi = zabs(phir, phii);
aarg = zabs(argr, argi); aarg = zabs(argr, argi);
rs1 = rs1 + Math.Log(aphi) - Math.Log(aarg) * 0.25 - aic; rs1 = rs1 + Math.Log(aphi) - Math.Log(aarg) * 0.25 - aic;
@ -6039,10 +6039,10 @@ namespace MathNet.Numerics
if (rs1 < 0.0) goto L70; if (rs1 < 0.0) goto L70;
if (i == 1) iflag = 3; if (i == 1) iflag = 3;
L70: L70:
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
// SCALE S1 TO KEEP INTERMEDIATE ARITHMETIC ON SCALE NEAR // SCALE S1 TO KEEP INTERMEDIATE ARITHMETIC ON SCALE NEAR
// EXPONENT EXTREMES // EXPONENT EXTREMES
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
zairy(argr, argi, 0, 2, ref air, ref aii, ref nai, ref idum); zairy(argr, argi, 0, 2, ref air, ref aii, ref nai, ref idum);
zairy(argr, argi, 1, 2, ref dair, ref daii, ref ndai, ref idum); zairy(argr, argi, 1, 2, ref dair, ref daii, ref ndai, ref idum);
str = dair * bsumr - daii * bsumi; str = dair * bsumr - daii * bsumi;
@ -6127,9 +6127,9 @@ namespace MathNet.Numerics
return 0; return 0;
L120: L120:
if (rs1 > 0.0) goto L140; if (rs1 > 0.0) goto L140;
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
// SET UNDERFLOW AND UPDATE PARAMETERS // SET UNDERFLOW AND UPDATE PARAMETERS
// ----------------------------------------------------------------------- // -----------------------------------------------------------------------
yr[nd - 1] = zeror; yr[nd - 1] = zeror;
yi[nd - 1] = zeroi; yi[nd - 1] = zeroi;
nz++; nz++;
@ -6142,15 +6142,15 @@ namespace MathNet.Numerics
if (nd == 0) goto L110; if (nd == 0) goto L110;
fn = fnu + (nd - 1); fn = fnu + (nd - 1);
if (fn < fnul) goto L130; if (fn < fnul) goto L130;
// FN = CIDI // FN = CIDI
// J = NUF + 1 // J = NUF + 1
// K = MOD(J,4) + 1 // K = MOD(J,4) + 1
// S1R = CIPR(K) // S1R = CIPR(K)
// S1I = CIPI(K) // S1I = CIPI(K)
// IF (FN.LT.0.0D0) S1I = -S1I // IF (FN.LT.0.0D0) S1I = -S1I
// STR = C2R*S1R - C2I*S1I // STR = C2R*S1R - C2I*S1I
// C2I = C2R*S1I + C2I*S1R // C2I = C2R*S1I + C2I*S1R
// C2R = STR // C2R = STR
ink = inu + nd - 1; ink = inu + nd - 1;
ink = (ink % 4) + 1; ink = (ink % 4) + 1;
c2r = car * cipr[ink - 1] - sar * cipi[ink - 1]; c2r = car * cipr[ink - 1] - sar * cipi[ink - 1];
@ -7669,7 +7669,7 @@ namespace MathNet.Numerics
if (nw == -2) nz = -2; if (nw == -2) nz = -2;
return 0; return 0;
} }
#endregion #endregion
} }
} }

5
src/Numerics/SpecialFunctions/Amos/AmosWrapper.cs
View File

@ -1,8 +1,5 @@
using System; using System;
using System.Collections.Generic;
using System.Linq;
using System.Numerics; using System.Numerics;
using System.Text;
namespace MathNet.Numerics namespace MathNet.Numerics
{ {
@ -264,7 +261,7 @@ namespace MathNet.Numerics
return double.NaN; return double.NaN;
} }
return Cbesj(v, new Complex(z, 0)).Real; return Cbesj(v, new Complex(z, 0)).Real;
} }
// Return Exp(-Abs(y)) * J(v, z) where y = z.Imaginary // Return Exp(-Abs(y)) * J(v, z) where y = z.Imaginary

22
src/Numerics/SpecialFunctions/Bessel.cs
View File

@ -1,8 +1,4 @@
using System; using System.Numerics;
using System.Collections.Generic;
using System.Linq;
using System.Numerics;
using System.Text;
namespace MathNet.Numerics namespace MathNet.Numerics
{ {
@ -18,7 +14,7 @@ namespace MathNet.Numerics
/// </summary> /// </summary>
/// <param name="v">The order of the Bessel function</param> /// <param name="v">The order of the Bessel function</param>
/// <param name="z">The value to compute the Bessel function of.</param> /// <param name="z">The value to compute the Bessel function of.</param>
/// <param name="expScaled">If true, returns exponentially-scaled Bessel function</param> /// <param name="expScaled">If true, returns exponentially-scaled Bessel function</param>
/// <returns></returns> /// <returns></returns>
public static Complex BesselJ(double v, Complex z, bool expScaled = false) public static Complex BesselJ(double v, Complex z, bool expScaled = false)
{ {
@ -33,7 +29,7 @@ namespace MathNet.Numerics
/// </summary> /// </summary>
/// <param name="v">The order of the Bessel function</param> /// <param name="v">The order of the Bessel function</param>
/// <param name="z">The value to compute the Bessel function of.</param> /// <param name="z">The value to compute the Bessel function of.</param>
/// <param name="expScaled">If true, returns exponentially-scaled Bessel function</param> /// <param name="expScaled">If true, returns exponentially-scaled Bessel function</param>
/// <returns></returns> /// <returns></returns>
public static double BesselJ(double v, double z, bool expScaled = false) public static double BesselJ(double v, double z, bool expScaled = false)
{ {
@ -48,7 +44,7 @@ namespace MathNet.Numerics
/// </summary> /// </summary>
/// <param name="v">The order of the Bessel function</param> /// <param name="v">The order of the Bessel function</param>
/// <param name="z">The value to compute the Bessel function of.</param> /// <param name="z">The value to compute the Bessel function of.</param>
/// <param name="expScaled">If true, returns exponentially-scaled Bessel function</param> /// <param name="expScaled">If true, returns exponentially-scaled Bessel function</param>
/// <returns></returns> /// <returns></returns>
public static Complex BesselY(double v, Complex z, bool expScaled = false) public static Complex BesselY(double v, Complex z, bool expScaled = false)
{ {
@ -63,7 +59,7 @@ namespace MathNet.Numerics
/// </summary> /// </summary>
/// <param name="v">The order of the Bessel function</param> /// <param name="v">The order of the Bessel function</param>
/// <param name="z">The value to compute the Bessel function of.</param> /// <param name="z">The value to compute the Bessel function of.</param>
/// <param name="expScaled">If true, returns exponentially-scaled Bessel function</param> /// <param name="expScaled">If true, returns exponentially-scaled Bessel function</param>
/// <returns></returns> /// <returns></returns>
public static double BesselY(double v, double z, bool expScaled = false) public static double BesselY(double v, double z, bool expScaled = false)
{ {
@ -78,7 +74,7 @@ namespace MathNet.Numerics
/// </summary> /// </summary>
/// <param name="v">The order of the Bessel function</param> /// <param name="v">The order of the Bessel function</param>
/// <param name="z">The value to compute the Bessel function of.</param> /// <param name="z">The value to compute the Bessel function of.</param>
/// <param name="expScaled">If true, returns exponentially-scaled Bessel function</param> /// <param name="expScaled">If true, returns exponentially-scaled Bessel function</param>
/// <returns></returns> /// <returns></returns>
public static Complex BesselI(double v, Complex z, bool expScaled = false) public static Complex BesselI(double v, Complex z, bool expScaled = false)
{ {
@ -93,7 +89,7 @@ namespace MathNet.Numerics
/// </summary> /// </summary>
/// <param name="v">The order of the Bessel function</param> /// <param name="v">The order of the Bessel function</param>
/// <param name="z">The value to compute the Bessel function of.</param> /// <param name="z">The value to compute the Bessel function of.</param>
/// <param name="expScaled">If true, returns exponentially-scaled Bessel function</param> /// <param name="expScaled">If true, returns exponentially-scaled Bessel function</param>
/// <returns></returns> /// <returns></returns>
public static double BesselI(double v, double z, bool expScaled = false) public static double BesselI(double v, double z, bool expScaled = false)
{ {
@ -115,7 +111,7 @@ namespace MathNet.Numerics
/// </summary> /// </summary>
/// <param name="v">The order of the Bessel function</param> /// <param name="v">The order of the Bessel function</param>
/// <param name="z">The value to compute the Bessel function of.</param> /// <param name="z">The value to compute the Bessel function of.</param>
/// <param name="expScaled">If true, returns exponentially-scaled Bessel function</param> /// <param name="expScaled">If true, returns exponentially-scaled Bessel function</param>
/// <returns></returns> /// <returns></returns>
public static Complex BesselK(double v, Complex z, bool expScaled = false) public static Complex BesselK(double v, Complex z, bool expScaled = false)
{ {
@ -130,7 +126,7 @@ namespace MathNet.Numerics
/// </summary> /// </summary>
/// <param name="v">The order of the Bessel function</param> /// <param name="v">The order of the Bessel function</param>
/// <param name="z">The value to compute the Bessel function of.</param> /// <param name="z">The value to compute the Bessel function of.</param>
/// <param name="expScaled">If true, returns exponentially-scaled Bessel function</param> /// <param name="expScaled">If true, returns exponentially-scaled Bessel function</param>
/// <returns></returns> /// <returns></returns>
public static double BesselK(double v, double z, bool expScaled = false) public static double BesselK(double v, double z, bool expScaled = false)
{ {

14
src/Numerics/SpecialFunctions/Hankel.cs
View File

@ -1,8 +1,4 @@
using System; using System.Numerics;
using System.Collections.Generic;
using System.Linq;
using System.Numerics;
using System.Text;
namespace MathNet.Numerics namespace MathNet.Numerics
{ {
@ -18,7 +14,7 @@ namespace MathNet.Numerics
/// </summary> /// </summary>
/// <param name="n">The order of the Bessel function</param> /// <param name="n">The order of the Bessel function</param>
/// <param name="z">The value to compute the Bessel function of.</param> /// <param name="z">The value to compute the Bessel function of.</param>
/// <param name="expScaled">If true, returns exponentially-scaled Hankel function</param> /// <param name="expScaled">If true, returns exponentially-scaled Hankel function</param>
/// <returns></returns> /// <returns></returns>
public static Complex HankelH1(double n, Complex z, bool expScaled = false) public static Complex HankelH1(double n, Complex z, bool expScaled = false)
{ {
@ -33,7 +29,7 @@ namespace MathNet.Numerics
/// </summary> /// </summary>
/// <param name="n">The order of the Bessel function</param> /// <param name="n">The order of the Bessel function</param>
/// <param name="z">The value to compute the Bessel function of.</param> /// <param name="z">The value to compute the Bessel function of.</param>
/// <param name="expScaled">If true, returns exponentially-scaled Hankel function</param> /// <param name="expScaled">If true, returns exponentially-scaled Hankel function</param>
/// <returns></returns> /// <returns></returns>
public static double HankelH1(double n, double z, bool expScaled = false) public static double HankelH1(double n, double z, bool expScaled = false)
{ {
@ -47,7 +43,7 @@ namespace MathNet.Numerics
/// </summary> /// </summary>
/// <param name="n">The order of the Hankel function</param> /// <param name="n">The order of the Hankel function</param>
/// <param name="z">The value to compute the Bessel function of.</param> /// <param name="z">The value to compute the Bessel function of.</param>
/// <param name="expScaled">If true, returns exponentially-scaled Hankel function</param> /// <param name="expScaled">If true, returns exponentially-scaled Hankel function</param>
/// <returns></returns> /// <returns></returns>
public static Complex HankelH2(double n, Complex z, bool expScaled = false) public static Complex HankelH2(double n, Complex z, bool expScaled = false)
{ {
@ -62,7 +58,7 @@ namespace MathNet.Numerics
/// </summary> /// </summary>
/// <param name="n">The order of the Bessel function</param> /// <param name="n">The order of the Bessel function</param>
/// <param name="z">The value to compute the Bessel function of.</param> /// <param name="z">The value to compute the Bessel function of.</param>
/// <param name="expScaled">If true, returns exponentially-scaled Hankel function</param> /// <param name="expScaled">If true, returns exponentially-scaled Hankel function</param>
/// <returns></returns> /// <returns></returns>
public static double HankelH2(double n, double z, bool expScaled = false) public static double HankelH2(double n, double z, bool expScaled = false)
{ {

11
src/Numerics/SpecialFunctions/SphericalBessel.cs
View File

@ -1,8 +1,5 @@
using System; using System;
using System.Collections.Generic;
using System.Linq;
using System.Numerics; using System.Numerics;
using System.Text;
namespace MathNet.Numerics namespace MathNet.Numerics
{ {
@ -18,7 +15,7 @@ namespace MathNet.Numerics
/// </summary> /// </summary>
/// <param name="v">The order of the spherical Bessel function</param> /// <param name="v">The order of the spherical Bessel function</param>
/// <param name="z">The value to compute the spherical Bessel function of.</param> /// <param name="z">The value to compute the spherical Bessel function of.</param>
/// <param name="expScaled">If true, returns exponentially-scaled spherical Bessel function</param> /// <param name="expScaled">If true, returns exponentially-scaled spherical Bessel function</param>
/// <returns></returns> /// <returns></returns>
public static Complex SphericalBesselJ(double v, Complex z, bool expScaled = false) public static Complex SphericalBesselJ(double v, Complex z, bool expScaled = false)
{ {
@ -34,7 +31,7 @@ namespace MathNet.Numerics
/// </summary> /// </summary>
/// <param name="v">The order of the spherical Bessel function</param> /// <param name="v">The order of the spherical Bessel function</param>
/// <param name="z">The value to compute the spherical Bessel function of.</param> /// <param name="z">The value to compute the spherical Bessel function of.</param>
/// <param name="expScaled">If true, returns exponentially-scaled spherical Bessel function</param> /// <param name="expScaled">If true, returns exponentially-scaled spherical Bessel function</param>
/// <returns></returns> /// <returns></returns>
public static double SphericalBesselJ(double v, double z, bool expScaled = false) public static double SphericalBesselJ(double v, double z, bool expScaled = false)
{ {
@ -50,7 +47,7 @@ namespace MathNet.Numerics
/// </summary> /// </summary>
/// <param name="v">The order of the spherical Bessel function</param> /// <param name="v">The order of the spherical Bessel function</param>
/// <param name="z">The value to compute the spherical Bessel function of.</param> /// <param name="z">The value to compute the spherical Bessel function of.</param>
/// <param name="expScaled">If true, returns exponentially-scaled spherical Bessel function</param> /// <param name="expScaled">If true, returns exponentially-scaled spherical Bessel function</param>
/// <returns></returns> /// <returns></returns>
public static Complex SphericalBesselY(double v, Complex z, bool expScaled = false) public static Complex SphericalBesselY(double v, Complex z, bool expScaled = false)
{ {
@ -66,7 +63,7 @@ namespace MathNet.Numerics
/// </summary> /// </summary>
/// <param name="v">The order of the spherical Bessel function</param> /// <param name="v">The order of the spherical Bessel function</param>
/// <param name="z">The value to compute the spherical Bessel function of.</param> /// <param name="z">The value to compute the spherical Bessel function of.</param>
/// <param name="expScaled">If true, returns exponentially-scaled spherical Bessel function</param> /// <param name="expScaled">If true, returns exponentially-scaled spherical Bessel function</param>
/// <returns></returns> /// <returns></returns>
public static double SphericalBesselY(double v, double z, bool expScaled = false) public static double SphericalBesselY(double v, double z, bool expScaled = false)
{ {

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