amos

func Zacai ¶

func Zacai(ZR, ZI, FNU float64, KODE, MR, N int, YR, YI []float64, RL, TOL, ELIM, ALIM float64) (
	ZRout, ZIout, FNUout float64, KODEout, MRout, Nout int, YRout, YIout []float64, NZ int, RLout, TOLout, ELIMout, ALIMout float64)

ZACAI APPLIES THE ANALYTIC CONTINUATION FORMULA

K(FNU,ZN*EXP(MP))=K(FNU,ZN)*EXP(-MP*FNU) - MP*I(FNU,ZN)
      MP=PI*MR*CMPLX(0.0,1.0)

TO CONTINUE THE K FUNCTION FROM THE RIGHT HALF TO THE LEFT HALF Z PLANE FOR USE WITH ZAIRY WHERE FNU=1/3 OR 2/3 AND N=1. ZACAI IS THE SAME AS ZACON WITH THE PARTS FOR LARGER ORDERS AND RECURRENCE REMOVED. A RECURSIVE CALL TO ZACON CAN RESULT if ZACON IS CALLED FROM ZAIRY.

func Zairy ¶

func Zairy(ZR, ZI float64, ID, KODE int) (AIR, AII float64, NZ, IERR int)

func Zasyi ¶

func Zasyi(ZR, ZI, FNU float64, KODE, N int, YR, YI []float64, RL, TOL, ELIM, ALIM float64) (
	ZRout, ZIout, FNUout float64, KODEout, Nout int, YRout, YIout []float64, NZ int, RLout, TOLout, ELIMout, ALIMout float64)

ZASYI COMPUTES THE I BESSEL FUNCTION FOR REAL(Z)>=0.0 BY MEANS OF THE ASYMPTOTIC EXPANSION FOR LARGE CABS(Z) IN THE REGION CABS(Z)>MAX(RL,FNU*FNU/2). NZ=0 IS A NORMAL return. NZ<0 INDICATES AN OVERFLOW ON KODE=1.

func Zbknu ¶

func Zbknu(ZR, ZI, FNU float64, KODE, N int, YR, YI []float64, TOL, ELIM, ALIM float64) (ZRout, ZIout, FNUout float64, KODEout, Nout int, YRout, YIout []float64, NZ int, TOLout, ELIMout, ALIMout float64)

sbknu computes the k bessel function in the right half z plane.

func Zkscl ¶

func Zkscl(ZRR, ZRI, FNU float64, N int, YR, YI []float64, RZR, RZI, ASCLE, TOL, ELIM float64) (
	ZRRout, ZRIout, FNUout float64, Nout int, YRout, YIout []float64, NZ int, RZRout, RZIout, ASCLEout, TOLout, ELIMout float64)

SET K FUNCTIONS TO ZERO ON UNDERFLOW, CONTINUE RECURRENCE ON SCALED FUNCTIONS UNTIL TWO MEMBERS COME ON SCALE, THEN return WITH MIN(NZ+2,N) VALUES SCALED BY 1/TOL.

func Zmlri ¶

func Zmlri(ZR, ZI, FNU float64, KODE, N int, YR, YI []float64, TOL float64) (
	ZRout, ZIout, FNUout float64, KODEout, Nout int, YRout, YIout []float64, NZ int, TOLout float64)

ZMLRI COMPUTES THE I BESSEL FUNCTION FOR RE(Z)>=0.0 BY THE MILLER ALGORITHM NORMALIZED BY A NEUMANN SERIES.

func Zs1s2 ¶

func Zs1s2(zr, s1, s2 complex128, scale, lim float64, iuf int) (s1o, s2o complex128, nz, iufo int)

Zs1s2 tests for a possible underflow resulting from the addition of the I and K functions in the analytic continuation formula where s1 == K function and s2 == I function.

When kode == 1, the I and K functions are different orders of magnitude.

When kode == 2, they may both be of the same order of magnitude, but the maximum must be at least one precision above the underflow limit.

func Zseri ¶

func Zseri(z complex128, fnu float64, kode, n int, y []complex128, tol, elim, alim float64) (nz int)

Zseri computes the I bessel function for real(z) >= 0 by means of the power series for large |z| in the region |z| <= 2*sqrt(fnu+1).

nz = 0 is a normal return. nz > 0 means that the last nz components were set to zero due to underflow. nz < 0 means that underflow occurred, but the condition |z| <= 2*sqrt(fnu+1) was violated and the computation must be completed in another routine with n -= abs(nz).

func Zuchk ¶

func Zuchk(y complex128, scale, tol float64) int

Zuchk tests whether the magnitude of the real or imaginary part would underflow when y is scaled by tol.

y enters as a scaled quantity whose magnitude is greater than

1e3 + 3*dmach(1)/tol

y is accepted if the underflow is at least one precision below the magnitude of the largest component. Otherwise an underflow is assumed as the phase angle does not have sufficient accuracy.