2019-03-19 16:42:47 +02:00
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SUBROUTINE ZWRSK(ZRR, ZRI, FNU, KODE, N, YR, YI, NZ, CWR, CWI,
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* TOL, ELIM, ALIM)
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C***BEGIN PROLOGUE ZWRSK
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C***REFER TO ZBESI,ZBESK
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C
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C ZWRSK COMPUTES THE I BESSEL FUNCTION FOR RE(Z).GE.0.0 BY
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C NORMALIZING THE I FUNCTION RATIOS FROM ZRATI BY THE WRONSKIAN
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C
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2019-03-20 12:25:42 +02:00
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C***ROUTINES CALLED D1MACH,ZBKNU,ZRATI,AZABS
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2019-03-19 16:42:47 +02:00
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C***END PROLOGUE ZWRSK
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C COMPLEX CINU,CSCL,CT,CW,C1,C2,RCT,ST,Y,ZR
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DOUBLE PRECISION ACT, ACW, ALIM, ASCLE, CINUI, CINUR, CSCLR, CTI,
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* CTR, CWI, CWR, C1I, C1R, C2I, C2R, ELIM, FNU, PTI, PTR, RACT,
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2019-03-20 12:25:42 +02:00
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* STI, STR, TOL, YI, YR, ZRI, ZRR, AZABS, D1MACH
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2019-03-19 16:42:47 +02:00
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INTEGER I, KODE, N, NW, NZ
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DIMENSION YR(N), YI(N), CWR(2), CWI(2)
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C-----------------------------------------------------------------------
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C I(FNU+I-1,Z) BY BACKWARD RECURRENCE FOR RATIOS
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C Y(I)=I(FNU+I,Z)/I(FNU+I-1,Z) FROM CRATI NORMALIZED BY THE
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C WRONSKIAN WITH K(FNU,Z) AND K(FNU+1,Z) FROM CBKNU.
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C-----------------------------------------------------------------------
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NZ = 0
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CALL ZBKNU(ZRR, ZRI, FNU, KODE, 2, CWR, CWI, NW, TOL, ELIM, ALIM)
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IF (NW.NE.0) GO TO 50
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CALL ZRATI(ZRR, ZRI, FNU, N, YR, YI, TOL)
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C-----------------------------------------------------------------------
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C RECUR FORWARD ON I(FNU+1,Z) = R(FNU,Z)*I(FNU,Z),
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C R(FNU+J-1,Z)=Y(J), J=1,...,N
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C-----------------------------------------------------------------------
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CINUR = 1.0D0
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CINUI = 0.0D0
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IF (KODE.EQ.1) GO TO 10
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CINUR = DCOS(ZRI)
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CINUI = DSIN(ZRI)
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10 CONTINUE
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C-----------------------------------------------------------------------
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C ON LOW EXPONENT MACHINES THE K FUNCTIONS CAN BE CLOSE TO BOTH
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C THE UNDER AND OVERFLOW LIMITS AND THE NORMALIZATION MUST BE
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C SCALED TO PREVENT OVER OR UNDERFLOW. CUOIK HAS DETERMINED THAT
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C THE RESULT IS ON SCALE.
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C-----------------------------------------------------------------------
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2019-03-20 12:25:42 +02:00
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ACW = AZABS(CWR(2),CWI(2))
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2019-03-19 16:42:47 +02:00
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ASCLE = 1.0D+3*D1MACH(1)/TOL
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CSCLR = 1.0D0
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IF (ACW.GT.ASCLE) GO TO 20
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CSCLR = 1.0D0/TOL
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GO TO 30
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20 CONTINUE
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ASCLE = 1.0D0/ASCLE
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IF (ACW.LT.ASCLE) GO TO 30
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CSCLR = TOL
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30 CONTINUE
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C1R = CWR(1)*CSCLR
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C1I = CWI(1)*CSCLR
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C2R = CWR(2)*CSCLR
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C2I = CWI(2)*CSCLR
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STR = YR(1)
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STI = YI(1)
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C-----------------------------------------------------------------------
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C CINU=CINU*(CONJG(CT)/CABS(CT))*(1.0D0/CABS(CT) PREVENTS
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C UNDER- OR OVERFLOW PREMATURELY BY SQUARING CABS(CT)
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C-----------------------------------------------------------------------
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PTR = STR*C1R - STI*C1I
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PTI = STR*C1I + STI*C1R
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PTR = PTR + C2R
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PTI = PTI + C2I
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CTR = ZRR*PTR - ZRI*PTI
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CTI = ZRR*PTI + ZRI*PTR
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2019-03-20 12:25:42 +02:00
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ACT = AZABS(CTR,CTI)
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2019-03-19 16:42:47 +02:00
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RACT = 1.0D0/ACT
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CTR = CTR*RACT
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CTI = -CTI*RACT
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PTR = CINUR*RACT
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PTI = CINUI*RACT
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CINUR = PTR*CTR - PTI*CTI
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CINUI = PTR*CTI + PTI*CTR
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YR(1) = CINUR*CSCLR
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YI(1) = CINUI*CSCLR
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IF (N.EQ.1) RETURN
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DO 40 I=2,N
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PTR = STR*CINUR - STI*CINUI
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CINUI = STR*CINUI + STI*CINUR
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CINUR = PTR
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STR = YR(I)
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STI = YI(I)
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YR(I) = CINUR*CSCLR
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YI(I) = CINUI*CSCLR
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40 CONTINUE
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RETURN
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50 CONTINUE
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NZ = -1
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IF(NW.EQ.(-2)) NZ=-2
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RETURN
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END
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