*DECK CQCBY SUBROUTINE CQCBY (LUN, KPRINT, IPASS) C***BEGIN PROLOGUE CQCBY C***SUBSIDIARY C***PURPOSE Quick check for SLATEC subroutine C CBESY C***LIBRARY SLATEC C***CATEGORY C10A4 C***TYPE COMPLEX (CQCBY-C, ZQCBY-Z) C***KEYWORDS QUICK CHECK, CBESY C***AUTHOR Amos, Don, (SNL) C Goudy, Sue, (SNL) C Walton, Lee, (SNL) C***DESCRIPTION C C *Usage: C C INTEGER LUN, KPRINT, IPASS C C CALL CQCBY (LUN, KPRINT, IPASS) C C *Arguments: C C LUN :IN is the unit number to which output is to be written. C C KPRINT :IN controls the amount of output, as specified in the C SLATEC Guidelines. C C IPASS :OUT indicates whether the test passed or failed. C A value of one is good, indicating no failures. C C *Description: C C CQCBY is a quick check routine for the complex Y Bessel function C generated by subroutine CBESY. C C CQCBY generates sequences of Y Bessel functions from CBESY C and checks them against the evaluation from the formula C C Y(FNU,Z*ROT) = C(FNU+1)*I(FNU,Z)-(2/PI)*CONJG(C(FNU))*K(FNU,Z) C C where ROT = EXP(PI*I/2) , C(FNU)=EXP(PI*FNU*I/2) , I**2=-1 C C and -PI.LT.ARG(Z).LE.PI/2, in the (Z,FNU) space. C C***REFERENCES Abramowitz, M. and Stegun, I. A., Handbook C of Mathematical Functions, Dover Publications, C New York, 1964. C Amos, D. E., A Subroutine Package for Bessel C Functions of a Complex Argument and Nonnegative C Order, SAND85-1018, May, 1985. C***ROUTINES CALLED CBESI, CBESK, CBESY, I1MACH, R1MACH C***REVISION HISTORY (YYMMDD) C 830501 DATE WRITTEN C 890831 Revised to meet new SLATEC standards C C***END PROLOGUE CQCBY C C*Internal Notes: C Machine constants are defined by functions I1MACH and R1MACH. C C The parameter MQC can have values 1 (the default) for a faster, C less definitive test or 2 for a slower, more definitive test. C C**End C C Set test complexity parameter. C INTEGER MQC PARAMETER (MQC=1) C C Declare arguments. C INTEGER LUN, KPRINT, IPASS C C Declare external functions. C INTEGER I1MACH REAL R1MACH EXTERNAL I1MACH, R1MACH C C Declare local variables. C COMPLEX CI, CIP, COE1, COE2, CSGN, CSPN, CW, CWRK, V, W, Y, Z, ZN REAL AA, AB, AER, ALIM, ARG, ATOL, AV, CC, CT, DIG, ELIM, EPS, * ER, ERTOL, FFNU, FILM, FNU, FNUL, HPI, PI, R, RHPI, RL, RM, * R1M4, R1M5, R2, SLAK, ST, T, TOL, TS, XN, XNU, XX, YN, YY INTEGER I, ICASE, IERR, IFNU, IL, IR, IRB, IT, ITL, I4, K, KDO, * KEPS, KK, KODE, K1, K2, LFLG, MFLG, N, NL, NU, NUL, NZ, NZ1, * NZ2 DIMENSION AER(20), CIP(4), CWRK(20), KDO(20), KEPS(20), T(20), * V(20), W(20), XNU(20), Y(20) DATA CIP(1), CIP(2), CIP(3), CIP(4) / * (1.0E0,0.0E0), (0.0E0,1.0E0), (-1.0E0,0.0E0), (0.0E0,-1.0E0) / C C***FIRST EXECUTABLE STATEMENT CQCBY IF (KPRINT.GE.2) THEN WRITE (LUN,99999) 99999 FORMAT (' QUICK CHECK ROUTINE FOR THE Y BESSEL FUNCTION FROM ', * 'CBESY'/) ENDIF C----------------------------------------------------------------------- C Set parameters related to machine constants. C TOL is the approximate unit roundoff limited to 1.0E-18. C ELIM is the approximate exponential over- and underflow limit. C exp(-ELIM).lt.exp(-ALIM)=exp(-ELIM)/TOL and C exp(ELIM).gt.exp(ALIM)=exp(ELIM)*TOL are intervals near C underflow and overflow limits where scaled arithmetic is done. C RL is the lower boundary of the asymptotic expansion for large Z. C DIG = number of base 10 digits in TOL = 10**(-DIG). C FNUL is the lower boundary of the asymptotic series for large FNU. C----------------------------------------------------------------------- R1M4 = R1MACH(4) TOL = MAX(R1M4,1.0E-18) ATOL = 100.0E0*TOL AA = -LOG10(R1M4) K1 = I1MACH(12) K2 = I1MACH(13) R1M5 = R1MACH(5) K = MIN(ABS(K1),ABS(K2)) ELIM = 2.303E0*(K*R1M5-3.0E0) AB = AA*2.303E0 ALIM = ELIM + MAX(-AB,-41.45E0) DIG = MIN(AA,18.0E0) FNUL = 10.0E0 + 6.0E0*(DIG-3.0E0) RL = 1.2E0*DIG + 3.0E0 SLAK = 3.0E0+4.0E0*(-LOG10(TOL)-7.0E0)/11.0E0 SLAK = MAX(SLAK,3.0E0) ERTOL = TOL*10.0E0**SLAK RM = 0.5E0*(ALIM + ELIM) RM = MIN(RM,200.0E0) RM = MAX(RM,RL+10.0E0) R2 = MIN(RM,FNUL) IF (KPRINT.GE.2) THEN WRITE (LUN,99998) 99998 FORMAT (' PARAMETERS'/ * 5X,'TOL ',8X,'ELIM',8X,'ALIM',8X,'RL ',8X,'FNUL',8X,'DIG') WRITE (LUN,99997) TOL, ELIM, ALIM, RL, FNUL, DIG 99997 FORMAT (1X,6E12.4/) ENDIF C----------------------------------------------------------------------- C Set other constants needed in the tests. C----------------------------------------------------------------------- CI = (0.0E0,1.0E0) HPI = 2.0E0*ATAN(1.0E0) RHPI = 1.0E0/HPI PI = HPI + HPI C----------------------------------------------------------------------- C Generate angles for construction of complex Z to be used in tests. C----------------------------------------------------------------------- C KDO(K), K = 1,IL determines which of the IL angles in -PI to PI C are used to compute values of Z. C KDO(K) = 0 means that the index K will be used for one or two C values of Z, depending on the choice of KEPS(K) C = 1 means that the index K and the corresponding angle C will be skipped C KEPS(K), K = 1,IL determines which of the angles get incremented C up and down to put values of Z in regions where different C formulae are used. C KEPS(K) = 0 means that the angle will be used without change C = 1 means that the angle will be incremented up and C down by EPS C The angles to be used are stored in the T(I) array, I = 1,ITL. C----------------------------------------------------------------------- IF (MQC.NE.2) THEN NL = 2 IL = 5 DO 5 I = 1,IL KEPS(I) = 0 KDO(I) = 0 5 CONTINUE KDO(5) = 1 NUL = 5 XNU(1) = 0.0E0 XNU(2) = 1.0E0 XNU(3) = 2.0E0 XNU(4) = 0.5E0*FNUL XNU(5) = FNUL + 1.2E0 ELSE NL = 4 IL = 13 DO 6 I = 1,IL KDO(I) = 0 KEPS(I) = 0 6 CONTINUE KDO(2) = 1 KDO(6) = 1 KDO(8) = 1 KDO(11) = 1 KDO(12) = 1 KDO(13) = 1 KEPS(3) = 1 KEPS(4) = 1 KEPS(5) = 1 KEPS(9) = 1 NUL = 6 XNU(1) = 0.0E0 XNU(2) = 0.6E0 XNU(3) = 1.3E0 XNU(4) = 2.0E0 XNU(5) = 0.5E0*FNUL XNU(6) = FNUL + 1.2E0 ENDIF I = 2 EPS = 0.01E0 FILM = IL - 1 T(1) = -PI + EPS DO 30 K = 2,IL IF (KDO(K).EQ.0) THEN T(I) = PI*(-IL+2*K-1)/FILM IF (KEPS(K).NE.0) THEN TS = T(I) T(I) = TS - EPS I = I + 1 T(I) = TS + EPS ELSE I = I + 1 ENDIF ENDIF 30 CONTINUE ITL = I - 1 C----------------------------------------------------------------------- C Test values of Z in -PI/2.lt.arg(Z).le.PI C----------------------------------------------------------------------- IF (KPRINT.GE.2) THEN WRITE (LUN,99996) 99996 FORMAT (' CHECKS IN THE (Z,FNU) SPACE') ENDIF LFLG = 0 DO 190 KODE = 1,2 DO 180 N = 1,NL DO 170 NU = 1,NUL C----------------------------------------------------------------------- C Construct values which will be used to set C COE1 = exp(i*(FNU+1)*PI/2) and C COE2 = (2/pi)*exp(-i*FNU*PI/2). C----------------------------------------------------------------------- FNU = XNU(NU) IFNU = INT(FNU) FFNU = FNU - IFNU ARG = HPI*FFNU CSGN = CMPLX(COS(ARG),SIN(ARG)) I4 = MOD(IFNU,4) + 1 CSGN = CSGN*CIP(I4) CSPN = CONJG(CSGN)*CMPLX(RHPI,0.0E0) CSGN = CSGN*CI DO 160 ICASE = 1,3 IRB = MIN(2,ICASE) DO 150 IR = IRB,4 C-------------- switch (icase) GO TO (50, 60, 70), ICASE 50 CONTINUE R = (EPS*(4-IR)+2.0E0*(IR-1))/3.0E0 GO TO 80 60 CONTINUE R = (2.0E0*(4-IR)+R2*(IR-1))/3.0E0 GO TO 80 70 CONTINUE IF (R2.GE.RM) GO TO 160 R = (R2*(4-IR)+RM*(IR-1))/3.0E0 80 CONTINUE C-------------- end switch DO 140 IT = 1,ITL CT = COS(T(IT)) ST = SIN(T(IT)) IF (ABS(CT).LT.ATOL) CT = 0.0E0 IF (ABS(ST).LT.ATOL) ST = 0.0E0 Z = CMPLX(R*CT,R*ST) XX = REAL(Z) YY = AIMAG(Z) CALL CBESI(Z, FNU, KODE, N, W, NZ2, IERR) C---------------- Underflow in CBESI - skip test for this case. IF (NZ2.NE.0) GO TO 140 CALL CBESK(Z, FNU, KODE, N, Y, NZ1, IERR) C---------------- Underflow in CBESK - skip test for this case. IF (NZ1.NE.0) GO TO 140 ZN = Z*CI XN = -YY YN = XX CALL CBESY(ZN, FNU, KODE, N, V, NZ, CWRK, IERR) C---------------- Underflow in CBESY - skip test for this case. IF (NZ.NE.0) GO TO 140 COE1 = CSGN COE2 = CSPN IF (KODE.EQ.2) THEN C------------------ Adjust scale for I and K functions. CC = -XX - ABS(XX) IF (CC.GT.(-ALIM)) THEN CW = CMPLX(CC,-YY) COE2 = COE2*EXP(CW) ELSE C-------------------- Scaling problem - skip test for this case COE2 = CMPLX(0.0E0,0.0E0) GO TO 140 ENDIF ENDIF DO 110 KK = 1,N Y(KK) = Y(KK)*COE2 W(KK) = W(KK)*COE1 COE1 = COE1*CI COE2 = -COE2*CI 110 CONTINUE C----------------------------------------------------------------------- C Compare Y(ZN,FNU) with COE1*I(Z,FNU)-COE2*K(Z,FNU). C----------------------------------------------------------------------- MFLG = 0 DO 120 I = 1,N AB = FNU + I - 1 AA = MAX(0.5E0,AB) CW = W(I) - Y(I) AV = CABS(V(I)) ER = CABS(CW-V(I)) IF (AV.NE.0.0E0) THEN IF (YN.EQ.0.0E0) THEN IF (XN.GT.0.0E0) THEN IF (ABS(XN).LT.AA) ER = ER/AV ELSE IF (ABS(FFNU-0.5E0).LT.0.125E0) THEN IF (ABS(XN).LT.AA) ER = ER/AV ELSE ER = ER/AV ENDIF ENDIF ELSE ER = ER/AV ENDIF ENDIF AER(I) = ER IF (ER.GT.ERTOL) MFLG = 1 120 CONTINUE IF (MFLG.NE.0) THEN IF (LFLG.EQ.0) THEN IF (KPRINT.GE.2) THEN WRITE (LUN,99995) ERTOL 99995 FORMAT (/' CASES WHICH VIOLATE THE RELATIVE ', * 'ERROR TEST WITH ERTOL = ',E12.4/) WRITE (LUN,99994) 99994 FORMAT (' INPUT TO CBESY ZN, FNU, KODE, N') ENDIF IF (KPRINT.GE.3) THEN WRITE (LUN,99993) 99993 FORMAT (' COMPARE Y(ZN,FNU) WITH COE1*I(Z,FNU)', * '-COE2*K(Z,FNU)') WRITE (LUN,99992) 99992 FORMAT (' Z = ZN*EXP(-i*PI/2)'/ * ' COE1 = EXP(i*(FNU+1)*PI/2) ', * ' COE2 = (2/PI)*EXP(-i*FNU*PI/2)') WRITE (LUN,99991) 99991 FORMAT (' RESULTS FROM CBESY V(KK)'/ * 9X,'FROM CBESI W(KK)'/ * 9X,'FROM CBESK Y(KK)') WRITE (LUN,99990) 99990 FORMAT (' TEST CASE INDICES IR, IT, ICASE'/) ENDIF ENDIF LFLG = LFLG + 1 IF (KPRINT.GE.2) THEN WRITE (LUN,99989) ZN, FNU, KODE, N 99989 FORMAT (' INPUT: ZN=',2E12.4,3X,'FNU=',E12.4, * 3X,'KODE=',I3,3X,'N=',I3) ENDIF IF (KPRINT.GE.3) THEN WRITE (LUN,99988) (AER(K),K=1,N) 99988 FORMAT (' ERROR: AER(K)=',4E12.4) WRITE (LUN,99987) Z, COE1, COE2 99987 FORMAT (12X,'Z=',2E12.4/12X,'COE1=',2E12.4,3X, * 'COE2=',2E12.4) KK = MAX(NZ1,NZ2) + 1 KK = MIN(N,KK) WRITE (LUN,99986) V(KK), W(KK), Y(KK) 99986 FORMAT (' RESULTS: V(KK)=',2E12.4/ * 12X,'W(KK)=',2E12.4/12X,'Y(KK)=',2E12.4) WRITE (LUN,99985) IR, IT, ICASE 99985 FORMAT (' CASE: IR=',I3,3X,'IT=',I3,3X, * 'ICASE=',I3/) ENDIF ENDIF 140 CONTINUE 150 CONTINUE 160 CONTINUE 170 CONTINUE 180 CONTINUE 190 CONTINUE IF (KPRINT.GE.2) THEN IF (LFLG.EQ.0) THEN WRITE (LUN,99984) 99984 FORMAT (' QUICK CHECKS OK') ELSE WRITE (LUN,99983) LFLG 99983 FORMAT (' ***',I5,' FAILURE(S) FOR CBESY IN THE (Z,FNU) ', * 'PLANE') ENDIF ENDIF IPASS = 0 IF (LFLG.EQ.0) THEN IPASS = 1 ENDIF IF (IPASS.EQ.1.AND.KPRINT.GE.2) THEN WRITE (LUN,99982) 99982 FORMAT (/' ****** CBESY PASSED ALL TESTS ******'/) ENDIF IF (IPASS.EQ.0.AND.KPRINT.GE.1) THEN WRITE (LUN,99981) 99981 FORMAT (/' ****** CBESY FAILED SOME TESTS ******'/) ENDIF RETURN END