cuni2.f
225 lines
| 7.1 KiB
| text/x-fortran
|
FortranFixedLexer
| r1601 | *DECK CUNI2 | |||
| SUBROUTINE CUNI2 (Z, FNU, KODE, N, Y, NZ, NLAST, FNUL, TOL, ELIM, | ||||
| + ALIM) | ||||
| C***BEGIN PROLOGUE CUNI2 | ||||
| C***SUBSIDIARY | ||||
| C***PURPOSE Subsidiary to CBESI and CBESK | ||||
| C***LIBRARY SLATEC | ||||
| C***TYPE ALL (CUNI2-A, ZUNI2-A) | ||||
| C***AUTHOR Amos, D. E., (SNL) | ||||
| C***DESCRIPTION | ||||
| C | ||||
| C CUNI2 COMPUTES I(FNU,Z) IN THE RIGHT HALF PLANE BY MEANS OF | ||||
| C UNIFORM ASYMPTOTIC EXPANSION FOR J(FNU,ZN) WHERE ZN IS Z*I | ||||
| C OR -Z*I AND ZN IS IN THE RIGHT HALF PLANE ALSO. | ||||
| C | ||||
| C FNUL IS THE SMALLEST ORDER PERMITTED FOR THE ASYMPTOTIC | ||||
| C EXPANSION. NLAST=0 MEANS ALL OF THE Y VALUES WERE SET. | ||||
| C NLAST.NE.0 IS THE NUMBER LEFT TO BE COMPUTED BY ANOTHER | ||||
| C FORMULA FOR ORDERS FNU TO FNU+NLAST-1 BECAUSE FNU+NLAST-1.LT.FNUL. | ||||
| C Y(I)=CZERO FOR I=NLAST+1,N | ||||
| C | ||||
| C***SEE ALSO CBESI, CBESK | ||||
| C***ROUTINES CALLED CAIRY, CUCHK, CUNHJ, CUOIK, R1MACH | ||||
| C***REVISION HISTORY (YYMMDD) | ||||
| C 830501 DATE WRITTEN | ||||
| C 910415 Prologue converted to Version 4.0 format. (BAB) | ||||
| C***END PROLOGUE CUNI2 | ||||
| COMPLEX AI, ARG, ASUM, BSUM, CFN, CI, CID, CIP, CONE, CRSC, CSCL, | ||||
| * CSR, CSS, CY, CZERO, C1, C2, DAI, PHI, RZ, S1, S2, Y, Z, ZB, | ||||
| * ZETA1, ZETA2, ZN, ZAR | ||||
| REAL AARG, AIC, ALIM, ANG, APHI, ASCLE, AY, BRY, CAR, C2I, C2M, | ||||
| * C2R, ELIM, FN, FNU, FNUL, HPI, RS1, SAR, TOL, YY, R1MACH | ||||
| INTEGER I, IFLAG, IN, INU, J, K, KODE, N, NAI, ND, NDAI, NLAST, | ||||
| * NN, NUF, NW, NZ, IDUM | ||||
| DIMENSION BRY(3), Y(N), CIP(4), CSS(3), CSR(3), CY(2) | ||||
| DATA CZERO,CONE,CI/(0.0E0,0.0E0),(1.0E0,0.0E0),(0.0E0,1.0E0)/ | ||||
| DATA CIP(1),CIP(2),CIP(3),CIP(4)/ | ||||
| 1 (1.0E0,0.0E0), (0.0E0,1.0E0), (-1.0E0,0.0E0), (0.0E0,-1.0E0)/ | ||||
| DATA HPI, AIC / | ||||
| 1 1.57079632679489662E+00, 1.265512123484645396E+00/ | ||||
| C***FIRST EXECUTABLE STATEMENT CUNI2 | ||||
| NZ = 0 | ||||
| ND = N | ||||
| NLAST = 0 | ||||
| C----------------------------------------------------------------------- | ||||
| C COMPUTED VALUES WITH EXPONENTS BETWEEN ALIM AND ELIM IN MAG- | ||||
| C NITUDE ARE SCALED TO KEEP INTERMEDIATE ARITHMETIC ON SCALE, | ||||
| C EXP(ALIM)=EXP(ELIM)*TOL | ||||
| C----------------------------------------------------------------------- | ||||
| CSCL = CMPLX(1.0E0/TOL,0.0E0) | ||||
| CRSC = CMPLX(TOL,0.0E0) | ||||
| CSS(1) = CSCL | ||||
| CSS(2) = CONE | ||||
| CSS(3) = CRSC | ||||
| CSR(1) = CRSC | ||||
| CSR(2) = CONE | ||||
| CSR(3) = CSCL | ||||
| BRY(1) = 1.0E+3*R1MACH(1)/TOL | ||||
| YY = AIMAG(Z) | ||||
| C----------------------------------------------------------------------- | ||||
| C ZN IS IN THE RIGHT HALF PLANE AFTER ROTATION BY CI OR -CI | ||||
| C----------------------------------------------------------------------- | ||||
| ZN = -Z*CI | ||||
| ZB = Z | ||||
| CID = -CI | ||||
| INU = FNU | ||||
| ANG = HPI*(FNU-INU) | ||||
| CAR = COS(ANG) | ||||
| SAR = SIN(ANG) | ||||
| C2 = CMPLX(CAR,SAR) | ||||
| ZAR = C2 | ||||
| IN = INU + N - 1 | ||||
| IN = MOD(IN,4) | ||||
| C2 = C2*CIP(IN+1) | ||||
| IF (YY.GT.0.0E0) GO TO 10 | ||||
| ZN = CONJG(-ZN) | ||||
| ZB = CONJG(ZB) | ||||
| CID = -CID | ||||
| C2 = CONJG(C2) | ||||
| 10 CONTINUE | ||||
| C----------------------------------------------------------------------- | ||||
| C CHECK FOR UNDERFLOW AND OVERFLOW ON FIRST MEMBER | ||||
| C----------------------------------------------------------------------- | ||||
| FN = MAX(FNU,1.0E0) | ||||
| CALL CUNHJ(ZN, FN, 1, TOL, PHI, ARG, ZETA1, ZETA2, ASUM, BSUM) | ||||
| IF (KODE.EQ.1) GO TO 20 | ||||
| CFN = CMPLX(FNU,0.0E0) | ||||
| S1 = -ZETA1 + CFN*(CFN/(ZB+ZETA2)) | ||||
| GO TO 30 | ||||
| 20 CONTINUE | ||||
| S1 = -ZETA1 + ZETA2 | ||||
| 30 CONTINUE | ||||
| RS1 = REAL(S1) | ||||
| IF (ABS(RS1).GT.ELIM) GO TO 150 | ||||
| 40 CONTINUE | ||||
| NN = MIN(2,ND) | ||||
| DO 90 I=1,NN | ||||
| FN = FNU + (ND-I) | ||||
| CALL CUNHJ(ZN, FN, 0, TOL, PHI, ARG, ZETA1, ZETA2, ASUM, BSUM) | ||||
| IF (KODE.EQ.1) GO TO 50 | ||||
| CFN = CMPLX(FN,0.0E0) | ||||
| AY = ABS(YY) | ||||
| S1 = -ZETA1 + CFN*(CFN/(ZB+ZETA2)) + CMPLX(0.0E0,AY) | ||||
| GO TO 60 | ||||
| 50 CONTINUE | ||||
| S1 = -ZETA1 + ZETA2 | ||||
| 60 CONTINUE | ||||
| C----------------------------------------------------------------------- | ||||
| C TEST FOR UNDERFLOW AND OVERFLOW | ||||
| C----------------------------------------------------------------------- | ||||
| RS1 = REAL(S1) | ||||
| IF (ABS(RS1).GT.ELIM) GO TO 120 | ||||
| IF (I.EQ.1) IFLAG = 2 | ||||
| IF (ABS(RS1).LT.ALIM) GO TO 70 | ||||
| C----------------------------------------------------------------------- | ||||
| C REFINE TEST AND SCALE | ||||
| C----------------------------------------------------------------------- | ||||
| C----------------------------------------------------------------------- | ||||
| APHI = ABS(PHI) | ||||
| AARG = ABS(ARG) | ||||
| RS1 = RS1 + ALOG(APHI) - 0.25E0*ALOG(AARG) - AIC | ||||
| IF (ABS(RS1).GT.ELIM) GO TO 120 | ||||
| IF (I.EQ.1) IFLAG = 1 | ||||
| IF (RS1.LT.0.0E0) GO TO 70 | ||||
| IF (I.EQ.1) IFLAG = 3 | ||||
| 70 CONTINUE | ||||
| C----------------------------------------------------------------------- | ||||
| C SCALE S1 TO KEEP INTERMEDIATE ARITHMETIC ON SCALE NEAR | ||||
| C EXPONENT EXTREMES | ||||
| C----------------------------------------------------------------------- | ||||
| CALL CAIRY(ARG, 0, 2, AI, NAI, IDUM) | ||||
| CALL CAIRY(ARG, 1, 2, DAI, NDAI, IDUM) | ||||
| S2 = PHI*(AI*ASUM+DAI*BSUM) | ||||
| C2R = REAL(S1) | ||||
| C2I = AIMAG(S1) | ||||
| C2M = EXP(C2R)*REAL(CSS(IFLAG)) | ||||
| S1 = CMPLX(C2M,0.0E0)*CMPLX(COS(C2I),SIN(C2I)) | ||||
| S2 = S2*S1 | ||||
| IF (IFLAG.NE.1) GO TO 80 | ||||
| CALL CUCHK(S2, NW, BRY(1), TOL) | ||||
| IF (NW.NE.0) GO TO 120 | ||||
| 80 CONTINUE | ||||
| IF (YY.LE.0.0E0) S2 = CONJG(S2) | ||||
| J = ND - I + 1 | ||||
| S2 = S2*C2 | ||||
| CY(I) = S2 | ||||
| Y(J) = S2*CSR(IFLAG) | ||||
| C2 = C2*CID | ||||
| 90 CONTINUE | ||||
| IF (ND.LE.2) GO TO 110 | ||||
| RZ = CMPLX(2.0E0,0.0E0)/Z | ||||
| BRY(2) = 1.0E0/BRY(1) | ||||
| BRY(3) = R1MACH(2) | ||||
| S1 = CY(1) | ||||
| S2 = CY(2) | ||||
| C1 = CSR(IFLAG) | ||||
| ASCLE = BRY(IFLAG) | ||||
| K = ND - 2 | ||||
| FN = K | ||||
| DO 100 I=3,ND | ||||
| C2 = S2 | ||||
| S2 = S1 + CMPLX(FNU+FN,0.0E0)*RZ*S2 | ||||
| S1 = C2 | ||||
| C2 = S2*C1 | ||||
| Y(K) = C2 | ||||
| K = K - 1 | ||||
| FN = FN - 1.0E0 | ||||
| IF (IFLAG.GE.3) GO TO 100 | ||||
| C2R = REAL(C2) | ||||
| C2I = AIMAG(C2) | ||||
| C2R = ABS(C2R) | ||||
| C2I = ABS(C2I) | ||||
| C2M = MAX(C2R,C2I) | ||||
| IF (C2M.LE.ASCLE) GO TO 100 | ||||
| IFLAG = IFLAG + 1 | ||||
| ASCLE = BRY(IFLAG) | ||||
| S1 = S1*C1 | ||||
| S2 = C2 | ||||
| S1 = S1*CSS(IFLAG) | ||||
| S2 = S2*CSS(IFLAG) | ||||
| C1 = CSR(IFLAG) | ||||
| 100 CONTINUE | ||||
| 110 CONTINUE | ||||
| RETURN | ||||
| 120 CONTINUE | ||||
| IF (RS1.GT.0.0E0) GO TO 140 | ||||
| C----------------------------------------------------------------------- | ||||
| C SET UNDERFLOW AND UPDATE PARAMETERS | ||||
| C----------------------------------------------------------------------- | ||||
| Y(ND) = CZERO | ||||
| NZ = NZ + 1 | ||||
| ND = ND - 1 | ||||
| IF (ND.EQ.0) GO TO 110 | ||||
| CALL CUOIK(Z, FNU, KODE, 1, ND, Y, NUF, TOL, ELIM, ALIM) | ||||
| IF (NUF.LT.0) GO TO 140 | ||||
| ND = ND - NUF | ||||
| NZ = NZ + NUF | ||||
| IF (ND.EQ.0) GO TO 110 | ||||
| FN = FNU + (ND-1) | ||||
| IF (FN.LT.FNUL) GO TO 130 | ||||
| C FN = AIMAG(CID) | ||||
| C J = NUF + 1 | ||||
| C K = MOD(J,4) + 1 | ||||
| C S1 = CIP(K) | ||||
| C IF (FN.LT.0.0E0) S1 = CONJG(S1) | ||||
| C C2 = C2*S1 | ||||
| IN = INU + ND - 1 | ||||
| IN = MOD(IN,4) + 1 | ||||
| C2 = ZAR*CIP(IN) | ||||
| IF (YY.LE.0.0E0)C2=CONJG(C2) | ||||
| GO TO 40 | ||||
| 130 CONTINUE | ||||
| NLAST = ND | ||||
| RETURN | ||||
| 140 CONTINUE | ||||
| NZ = -1 | ||||
| RETURN | ||||
| 150 CONTINUE | ||||
| IF (RS1.GT.0.0E0) GO TO 140 | ||||
| NZ = N | ||||
| DO 160 I=1,N | ||||
| Y(I) = CZERO | ||||
| 160 CONTINUE | ||||
| RETURN | ||||
| END | ||||
