2019-03-19 16:42:47 +02:00
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SUBROUTINE ZUNK1(ZR, ZI, FNU, KODE, MR, N, YR, YI, NZ, TOL, ELIM,
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* ALIM)
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C***BEGIN PROLOGUE ZUNK1
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C***REFER TO ZBESK
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C
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C ZUNK1 COMPUTES K(FNU,Z) AND ITS ANALYTIC CONTINUATION FROM THE
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C RIGHT HALF PLANE TO THE LEFT HALF PLANE BY MEANS OF THE
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C UNIFORM ASYMPTOTIC EXPANSION.
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C MR INDICATES THE DIRECTION OF ROTATION FOR ANALYTIC CONTINUATION.
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C NZ=-1 MEANS AN OVERFLOW WILL OCCUR
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C
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2019-03-20 12:25:42 +02:00
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C***ROUTINES CALLED ZKSCL,ZS1S2,ZUCHK,ZUNIK,D1MACH,AZABS
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2019-03-19 16:42:47 +02:00
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C***END PROLOGUE ZUNK1
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C COMPLEX CFN,CK,CONE,CRSC,CS,CSCL,CSGN,CSPN,CSR,CSS,CWRK,CY,CZERO,
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C *C1,C2,PHI,PHID,RZ,SUM,SUMD,S1,S2,Y,Z,ZETA1,ZETA1D,ZETA2,ZETA2D,ZR
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DOUBLE PRECISION ALIM, ANG, APHI, ASC, ASCLE, BRY, CKI, CKR,
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* CONER, CRSC, CSCL, CSGNI, CSPNI, CSPNR, CSR, CSRR, CSSR,
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* CWRKI, CWRKR, CYI, CYR, C1I, C1R, C2I, C2M, C2R, ELIM, FMR, FN,
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* FNF, FNU, PHIDI, PHIDR, PHII, PHIR, PI, RAST, RAZR, RS1, RZI,
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* RZR, SGN, STI, STR, SUMDI, SUMDR, SUMI, SUMR, S1I, S1R, S2I,
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* S2R, TOL, YI, YR, ZEROI, ZEROR, ZETA1I, ZETA1R, ZETA2I, ZETA2R,
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2019-03-20 12:25:42 +02:00
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* ZET1DI, ZET1DR, ZET2DI, ZET2DR, ZI, ZR, ZRI, ZRR, D1MACH, AZABS
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2019-03-19 16:42:47 +02:00
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INTEGER I, IB, IFLAG, IFN, IL, INIT, INU, IUF, K, KDFLG, KFLAG,
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* KK, KODE, MR, N, NW, NZ, INITD, IC, IPARD, J
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DIMENSION BRY(3), INIT(2), YR(N), YI(N), SUMR(2), SUMI(2),
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* ZETA1R(2), ZETA1I(2), ZETA2R(2), ZETA2I(2), CYR(2), CYI(2),
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* CWRKR(16,3), CWRKI(16,3), CSSR(3), CSRR(3), PHIR(2), PHII(2)
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DATA ZEROR,ZEROI,CONER / 0.0D0, 0.0D0, 1.0D0 /
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DATA PI / 3.14159265358979324D0 /
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C
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KDFLG = 1
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NZ = 0
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C-----------------------------------------------------------------------
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C EXP(-ALIM)=EXP(-ELIM)/TOL=APPROX. ONE PRECISION GREATER THAN
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C THE UNDERFLOW LIMIT
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C-----------------------------------------------------------------------
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CSCL = 1.0D0/TOL
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CRSC = TOL
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CSSR(1) = CSCL
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CSSR(2) = CONER
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CSSR(3) = CRSC
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CSRR(1) = CRSC
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CSRR(2) = CONER
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CSRR(3) = CSCL
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BRY(1) = 1.0D+3*D1MACH(1)/TOL
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BRY(2) = 1.0D0/BRY(1)
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BRY(3) = D1MACH(2)
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ZRR = ZR
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ZRI = ZI
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IF (ZR.GE.0.0D0) GO TO 10
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ZRR = -ZR
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ZRI = -ZI
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10 CONTINUE
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J = 2
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DO 70 I=1,N
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C-----------------------------------------------------------------------
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C J FLIP FLOPS BETWEEN 1 AND 2 IN J = 3 - J
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C-----------------------------------------------------------------------
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J = 3 - J
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FN = FNU + DBLE(FLOAT(I-1))
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INIT(J) = 0
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CALL ZUNIK(ZRR, ZRI, FN, 2, 0, TOL, INIT(J), PHIR(J), PHII(J),
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* ZETA1R(J), ZETA1I(J), ZETA2R(J), ZETA2I(J), SUMR(J), SUMI(J),
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* CWRKR(1,J), CWRKI(1,J))
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IF (KODE.EQ.1) GO TO 20
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STR = ZRR + ZETA2R(J)
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STI = ZRI + ZETA2I(J)
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2019-03-20 12:25:42 +02:00
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RAST = FN/AZABS(STR,STI)
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2019-03-19 16:42:47 +02:00
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STR = STR*RAST*RAST
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STI = -STI*RAST*RAST
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S1R = ZETA1R(J) - STR
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S1I = ZETA1I(J) - STI
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GO TO 30
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20 CONTINUE
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S1R = ZETA1R(J) - ZETA2R(J)
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S1I = ZETA1I(J) - ZETA2I(J)
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30 CONTINUE
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RS1 = S1R
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C-----------------------------------------------------------------------
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C TEST FOR UNDERFLOW AND OVERFLOW
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C-----------------------------------------------------------------------
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IF (DABS(RS1).GT.ELIM) GO TO 60
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IF (KDFLG.EQ.1) KFLAG = 2
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IF (DABS(RS1).LT.ALIM) GO TO 40
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C-----------------------------------------------------------------------
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C REFINE TEST AND SCALE
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C-----------------------------------------------------------------------
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2019-03-20 12:25:42 +02:00
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APHI = AZABS(PHIR(J),PHII(J))
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2019-03-19 16:42:47 +02:00
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RS1 = RS1 + DLOG(APHI)
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IF (DABS(RS1).GT.ELIM) GO TO 60
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IF (KDFLG.EQ.1) KFLAG = 1
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IF (RS1.LT.0.0D0) GO TO 40
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IF (KDFLG.EQ.1) KFLAG = 3
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40 CONTINUE
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C-----------------------------------------------------------------------
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C SCALE S1 TO KEEP INTERMEDIATE ARITHMETIC ON SCALE NEAR
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C EXPONENT EXTREMES
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C-----------------------------------------------------------------------
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S2R = PHIR(J)*SUMR(J) - PHII(J)*SUMI(J)
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S2I = PHIR(J)*SUMI(J) + PHII(J)*SUMR(J)
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STR = DEXP(S1R)*CSSR(KFLAG)
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S1R = STR*DCOS(S1I)
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S1I = STR*DSIN(S1I)
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STR = S2R*S1R - S2I*S1I
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S2I = S1R*S2I + S2R*S1I
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S2R = STR
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IF (KFLAG.NE.1) GO TO 50
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CALL ZUCHK(S2R, S2I, NW, BRY(1), TOL)
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IF (NW.NE.0) GO TO 60
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50 CONTINUE
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CYR(KDFLG) = S2R
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CYI(KDFLG) = S2I
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YR(I) = S2R*CSRR(KFLAG)
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YI(I) = S2I*CSRR(KFLAG)
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IF (KDFLG.EQ.2) GO TO 75
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KDFLG = 2
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GO TO 70
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60 CONTINUE
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IF (RS1.GT.0.0D0) GO TO 300
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C-----------------------------------------------------------------------
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C FOR ZR.LT.0.0, THE I FUNCTION TO BE ADDED WILL OVERFLOW
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C-----------------------------------------------------------------------
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IF (ZR.LT.0.0D0) GO TO 300
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KDFLG = 1
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YR(I)=ZEROR
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YI(I)=ZEROI
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NZ=NZ+1
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IF (I.EQ.1) GO TO 70
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IF ((YR(I-1).EQ.ZEROR).AND.(YI(I-1).EQ.ZEROI)) GO TO 70
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YR(I-1)=ZEROR
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YI(I-1)=ZEROI
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NZ=NZ+1
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70 CONTINUE
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I = N
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75 CONTINUE
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2019-03-20 12:25:42 +02:00
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RAZR = 1.0D0/AZABS(ZRR,ZRI)
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2019-03-19 16:42:47 +02:00
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STR = ZRR*RAZR
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STI = -ZRI*RAZR
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RZR = (STR+STR)*RAZR
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RZI = (STI+STI)*RAZR
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CKR = FN*RZR
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CKI = FN*RZI
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IB = I + 1
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IF (N.LT.IB) GO TO 160
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C-----------------------------------------------------------------------
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C TEST LAST MEMBER FOR UNDERFLOW AND OVERFLOW. SET SEQUENCE TO ZERO
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C ON UNDERFLOW.
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C-----------------------------------------------------------------------
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FN = FNU + DBLE(FLOAT(N-1))
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IPARD = 1
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IF (MR.NE.0) IPARD = 0
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INITD = 0
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CALL ZUNIK(ZRR, ZRI, FN, 2, IPARD, TOL, INITD, PHIDR, PHIDI,
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* ZET1DR, ZET1DI, ZET2DR, ZET2DI, SUMDR, SUMDI, CWRKR(1,3),
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* CWRKI(1,3))
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IF (KODE.EQ.1) GO TO 80
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STR = ZRR + ZET2DR
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STI = ZRI + ZET2DI
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2019-03-20 12:25:42 +02:00
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RAST = FN/AZABS(STR,STI)
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2019-03-19 16:42:47 +02:00
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STR = STR*RAST*RAST
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STI = -STI*RAST*RAST
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S1R = ZET1DR - STR
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S1I = ZET1DI - STI
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GO TO 90
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80 CONTINUE
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S1R = ZET1DR - ZET2DR
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S1I = ZET1DI - ZET2DI
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90 CONTINUE
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RS1 = S1R
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IF (DABS(RS1).GT.ELIM) GO TO 95
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IF (DABS(RS1).LT.ALIM) GO TO 100
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C----------------------------------------------------------------------------
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C REFINE ESTIMATE AND TEST
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C-------------------------------------------------------------------------
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2019-03-20 12:25:42 +02:00
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APHI = AZABS(PHIDR,PHIDI)
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2019-03-19 16:42:47 +02:00
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RS1 = RS1+DLOG(APHI)
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IF (DABS(RS1).LT.ELIM) GO TO 100
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95 CONTINUE
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IF (DABS(RS1).GT.0.0D0) GO TO 300
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C-----------------------------------------------------------------------
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C FOR ZR.LT.0.0, THE I FUNCTION TO BE ADDED WILL OVERFLOW
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C-----------------------------------------------------------------------
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IF (ZR.LT.0.0D0) GO TO 300
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NZ = N
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DO 96 I=1,N
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YR(I) = ZEROR
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YI(I) = ZEROI
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96 CONTINUE
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RETURN
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C---------------------------------------------------------------------------
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C FORWARD RECUR FOR REMAINDER OF THE SEQUENCE
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C----------------------------------------------------------------------------
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100 CONTINUE
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S1R = CYR(1)
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S1I = CYI(1)
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S2R = CYR(2)
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S2I = CYI(2)
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C1R = CSRR(KFLAG)
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ASCLE = BRY(KFLAG)
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DO 120 I=IB,N
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C2R = S2R
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C2I = S2I
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S2R = CKR*C2R - CKI*C2I + S1R
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S2I = CKR*C2I + CKI*C2R + S1I
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S1R = C2R
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S1I = C2I
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CKR = CKR + RZR
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CKI = CKI + RZI
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C2R = S2R*C1R
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C2I = S2I*C1R
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YR(I) = C2R
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YI(I) = C2I
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IF (KFLAG.GE.3) GO TO 120
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STR = DABS(C2R)
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STI = DABS(C2I)
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C2M = DMAX1(STR,STI)
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IF (C2M.LE.ASCLE) GO TO 120
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KFLAG = KFLAG + 1
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ASCLE = BRY(KFLAG)
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S1R = S1R*C1R
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S1I = S1I*C1R
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S2R = C2R
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S2I = C2I
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S1R = S1R*CSSR(KFLAG)
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S1I = S1I*CSSR(KFLAG)
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S2R = S2R*CSSR(KFLAG)
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S2I = S2I*CSSR(KFLAG)
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C1R = CSRR(KFLAG)
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120 CONTINUE
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160 CONTINUE
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IF (MR.EQ.0) RETURN
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C-----------------------------------------------------------------------
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C ANALYTIC CONTINUATION FOR RE(Z).LT.0.0D0
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C-----------------------------------------------------------------------
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NZ = 0
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FMR = DBLE(FLOAT(MR))
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SGN = -DSIGN(PI,FMR)
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C-----------------------------------------------------------------------
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C CSPN AND CSGN ARE COEFF OF K AND I FUNCTIONS RESP.
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C-----------------------------------------------------------------------
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CSGNI = SGN
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INU = INT(SNGL(FNU))
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FNF = FNU - DBLE(FLOAT(INU))
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IFN = INU + N - 1
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ANG = FNF*SGN
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CSPNR = DCOS(ANG)
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CSPNI = DSIN(ANG)
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IF (MOD(IFN,2).EQ.0) GO TO 170
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CSPNR = -CSPNR
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CSPNI = -CSPNI
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170 CONTINUE
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ASC = BRY(1)
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IUF = 0
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KK = N
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KDFLG = 1
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IB = IB - 1
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IC = IB - 1
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DO 270 K=1,N
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FN = FNU + DBLE(FLOAT(KK-1))
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C-----------------------------------------------------------------------
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C LOGIC TO SORT OUT CASES WHOSE PARAMETERS WERE SET FOR THE K
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C FUNCTION ABOVE
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C-----------------------------------------------------------------------
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M=3
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IF (N.GT.2) GO TO 175
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172 CONTINUE
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INITD = INIT(J)
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PHIDR = PHIR(J)
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PHIDI = PHII(J)
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ZET1DR = ZETA1R(J)
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ZET1DI = ZETA1I(J)
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ZET2DR = ZETA2R(J)
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ZET2DI = ZETA2I(J)
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SUMDR = SUMR(J)
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SUMDI = SUMI(J)
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M = J
|
|
|
|
|
J = 3 - J
|
|
|
|
|
GO TO 180
|
|
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|
|
175 CONTINUE
|
|
|
|
|
IF ((KK.EQ.N).AND.(IB.LT.N)) GO TO 180
|
|
|
|
|
IF ((KK.EQ.IB).OR.(KK.EQ.IC)) GO TO 172
|
|
|
|
|
INITD = 0
|
|
|
|
|
180 CONTINUE
|
|
|
|
|
CALL ZUNIK(ZRR, ZRI, FN, 1, 0, TOL, INITD, PHIDR, PHIDI,
|
|
|
|
|
* ZET1DR, ZET1DI, ZET2DR, ZET2DI, SUMDR, SUMDI,
|
|
|
|
|
* CWRKR(1,M), CWRKI(1,M))
|
|
|
|
|
IF (KODE.EQ.1) GO TO 200
|
|
|
|
|
STR = ZRR + ZET2DR
|
|
|
|
|
STI = ZRI + ZET2DI
|
2019-03-20 12:25:42 +02:00
|
|
|
RAST = FN/AZABS(STR,STI)
|
2019-03-19 16:42:47 +02:00
|
|
|
STR = STR*RAST*RAST
|
|
|
|
|
STI = -STI*RAST*RAST
|
|
|
|
|
S1R = -ZET1DR + STR
|
|
|
|
|
S1I = -ZET1DI + STI
|
|
|
|
|
GO TO 210
|
|
|
|
|
200 CONTINUE
|
|
|
|
|
S1R = -ZET1DR + ZET2DR
|
|
|
|
|
S1I = -ZET1DI + ZET2DI
|
|
|
|
|
210 CONTINUE
|
|
|
|
|
C-----------------------------------------------------------------------
|
|
|
|
|
C TEST FOR UNDERFLOW AND OVERFLOW
|
|
|
|
|
C-----------------------------------------------------------------------
|
|
|
|
|
RS1 = S1R
|
|
|
|
|
IF (DABS(RS1).GT.ELIM) GO TO 260
|
|
|
|
|
IF (KDFLG.EQ.1) IFLAG = 2
|
|
|
|
|
IF (DABS(RS1).LT.ALIM) GO TO 220
|
|
|
|
|
C-----------------------------------------------------------------------
|
|
|
|
|
C REFINE TEST AND SCALE
|
|
|
|
|
C-----------------------------------------------------------------------
|
2019-03-20 12:25:42 +02:00
|
|
|
APHI = AZABS(PHIDR,PHIDI)
|
2019-03-19 16:42:47 +02:00
|
|
|
RS1 = RS1 + DLOG(APHI)
|
|
|
|
|
IF (DABS(RS1).GT.ELIM) GO TO 260
|
|
|
|
|
IF (KDFLG.EQ.1) IFLAG = 1
|
|
|
|
|
IF (RS1.LT.0.0D0) GO TO 220
|
|
|
|
|
IF (KDFLG.EQ.1) IFLAG = 3
|
|
|
|
|
220 CONTINUE
|
|
|
|
|
STR = PHIDR*SUMDR - PHIDI*SUMDI
|
|
|
|
|
STI = PHIDR*SUMDI + PHIDI*SUMDR
|
|
|
|
|
S2R = -CSGNI*STI
|
|
|
|
|
S2I = CSGNI*STR
|
|
|
|
|
STR = DEXP(S1R)*CSSR(IFLAG)
|
|
|
|
|
S1R = STR*DCOS(S1I)
|
|
|
|
|
S1I = STR*DSIN(S1I)
|
|
|
|
|
STR = S2R*S1R - S2I*S1I
|
|
|
|
|
S2I = S2R*S1I + S2I*S1R
|
|
|
|
|
S2R = STR
|
|
|
|
|
IF (IFLAG.NE.1) GO TO 230
|
|
|
|
|
CALL ZUCHK(S2R, S2I, NW, BRY(1), TOL)
|
|
|
|
|
IF (NW.EQ.0) GO TO 230
|
|
|
|
|
S2R = ZEROR
|
|
|
|
|
S2I = ZEROI
|
|
|
|
|
230 CONTINUE
|
|
|
|
|
CYR(KDFLG) = S2R
|
|
|
|
|
CYI(KDFLG) = S2I
|
|
|
|
|
C2R = S2R
|
|
|
|
|
C2I = S2I
|
|
|
|
|
S2R = S2R*CSRR(IFLAG)
|
|
|
|
|
S2I = S2I*CSRR(IFLAG)
|
|
|
|
|
C-----------------------------------------------------------------------
|
|
|
|
|
C ADD I AND K FUNCTIONS, K SEQUENCE IN Y(I), I=1,N
|
|
|
|
|
C-----------------------------------------------------------------------
|
|
|
|
|
S1R = YR(KK)
|
|
|
|
|
S1I = YI(KK)
|
|
|
|
|
IF (KODE.EQ.1) GO TO 250
|
|
|
|
|
CALL ZS1S2(ZRR, ZRI, S1R, S1I, S2R, S2I, NW, ASC, ALIM, IUF)
|
|
|
|
|
NZ = NZ + NW
|
|
|
|
|
250 CONTINUE
|
|
|
|
|
YR(KK) = S1R*CSPNR - S1I*CSPNI + S2R
|
|
|
|
|
YI(KK) = CSPNR*S1I + CSPNI*S1R + S2I
|
|
|
|
|
KK = KK - 1
|
|
|
|
|
CSPNR = -CSPNR
|
|
|
|
|
CSPNI = -CSPNI
|
|
|
|
|
IF (C2R.NE.0.0D0 .OR. C2I.NE.0.0D0) GO TO 255
|
|
|
|
|
KDFLG = 1
|
|
|
|
|
GO TO 270
|
|
|
|
|
255 CONTINUE
|
|
|
|
|
IF (KDFLG.EQ.2) GO TO 275
|
|
|
|
|
KDFLG = 2
|
|
|
|
|
GO TO 270
|
|
|
|
|
260 CONTINUE
|
|
|
|
|
IF (RS1.GT.0.0D0) GO TO 300
|
|
|
|
|
S2R = ZEROR
|
|
|
|
|
S2I = ZEROI
|
|
|
|
|
GO TO 230
|
|
|
|
|
270 CONTINUE
|
|
|
|
|
K = N
|
|
|
|
|
275 CONTINUE
|
|
|
|
|
IL = N - K
|
|
|
|
|
IF (IL.EQ.0) RETURN
|
|
|
|
|
C-----------------------------------------------------------------------
|
|
|
|
|
C RECUR BACKWARD FOR REMAINDER OF I SEQUENCE AND ADD IN THE
|
|
|
|
|
C K FUNCTIONS, SCALING THE I SEQUENCE DURING RECURRENCE TO KEEP
|
|
|
|
|
C INTERMEDIATE ARITHMETIC ON SCALE NEAR EXPONENT EXTREMES.
|
|
|
|
|
C-----------------------------------------------------------------------
|
|
|
|
|
S1R = CYR(1)
|
|
|
|
|
S1I = CYI(1)
|
|
|
|
|
S2R = CYR(2)
|
|
|
|
|
S2I = CYI(2)
|
|
|
|
|
CSR = CSRR(IFLAG)
|
|
|
|
|
ASCLE = BRY(IFLAG)
|
|
|
|
|
FN = DBLE(FLOAT(INU+IL))
|
|
|
|
|
DO 290 I=1,IL
|
|
|
|
|
C2R = S2R
|
|
|
|
|
C2I = S2I
|
|
|
|
|
S2R = S1R + (FN+FNF)*(RZR*C2R-RZI*C2I)
|
|
|
|
|
S2I = S1I + (FN+FNF)*(RZR*C2I+RZI*C2R)
|
|
|
|
|
S1R = C2R
|
|
|
|
|
S1I = C2I
|
|
|
|
|
FN = FN - 1.0D0
|
|
|
|
|
C2R = S2R*CSR
|
|
|
|
|
C2I = S2I*CSR
|
|
|
|
|
CKR = C2R
|
|
|
|
|
CKI = C2I
|
|
|
|
|
C1R = YR(KK)
|
|
|
|
|
C1I = YI(KK)
|
|
|
|
|
IF (KODE.EQ.1) GO TO 280
|
|
|
|
|
CALL ZS1S2(ZRR, ZRI, C1R, C1I, C2R, C2I, NW, ASC, ALIM, IUF)
|
|
|
|
|
NZ = NZ + NW
|
|
|
|
|
280 CONTINUE
|
|
|
|
|
YR(KK) = C1R*CSPNR - C1I*CSPNI + C2R
|
|
|
|
|
YI(KK) = C1R*CSPNI + C1I*CSPNR + C2I
|
|
|
|
|
KK = KK - 1
|
|
|
|
|
CSPNR = -CSPNR
|
|
|
|
|
CSPNI = -CSPNI
|
|
|
|
|
IF (IFLAG.GE.3) GO TO 290
|
|
|
|
|
C2R = DABS(CKR)
|
|
|
|
|
C2I = DABS(CKI)
|
|
|
|
|
C2M = DMAX1(C2R,C2I)
|
|
|
|
|
IF (C2M.LE.ASCLE) GO TO 290
|
|
|
|
|
IFLAG = IFLAG + 1
|
|
|
|
|
ASCLE = BRY(IFLAG)
|
|
|
|
|
S1R = S1R*CSR
|
|
|
|
|
S1I = S1I*CSR
|
|
|
|
|
S2R = CKR
|
|
|
|
|
S2I = CKI
|
|
|
|
|
S1R = S1R*CSSR(IFLAG)
|
|
|
|
|
S1I = S1I*CSSR(IFLAG)
|
|
|
|
|
S2R = S2R*CSSR(IFLAG)
|
|
|
|
|
S2I = S2I*CSSR(IFLAG)
|
|
|
|
|
CSR = CSRR(IFLAG)
|
|
|
|
|
290 CONTINUE
|
|
|
|
|
RETURN
|
|
|
|
|
300 CONTINUE
|
|
|
|
|
NZ = -1
|
|
|
|
|
RETURN
|
|
|
|
|
END
|
