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77 lines
2.8 KiB
Fortran
77 lines
2.8 KiB
Fortran
*DECK DBSKES
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SUBROUTINE DBSKES (XNU, X, NIN, BKE)
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C***BEGIN PROLOGUE DBSKES
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C***PURPOSE Compute a sequence of exponentially scaled modified Bessel
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C functions of the third kind of fractional order.
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C***LIBRARY SLATEC (FNLIB)
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C***CATEGORY C10B3
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C***TYPE DOUBLE PRECISION (BESKES-S, DBSKES-D)
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C***KEYWORDS EXPONENTIALLY SCALED, FNLIB, FRACTIONAL ORDER,
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C MODIFIED BESSEL FUNCTION, SEQUENCE OF BESSEL FUNCTIONS,
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C SPECIAL FUNCTIONS, THIRD KIND
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C***AUTHOR Fullerton, W., (LANL)
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C***DESCRIPTION
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C
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C DBSKES(XNU,X,NIN,BKE) computes a double precision sequence
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C of exponentially scaled modified Bessel functions
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C of the third kind of order XNU + I at X, where X .GT. 0,
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C XNU lies in (-1,1), and I = 0, 1, ... , NIN - 1, if NIN is positive
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C and I = 0, -1, ... , NIN + 1, if NIN is negative. On return, the
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C vector BKE(.) contains the results at X for order starting at XNU.
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C XNU, X, and BKE are double precision. NIN is integer.
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C
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C***REFERENCES (NONE)
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C***ROUTINES CALLED D1MACH, D9KNUS, XERMSG
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C***REVISION HISTORY (YYMMDD)
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C 770601 DATE WRITTEN
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C 890531 Changed all specific intrinsics to generic. (WRB)
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C 890911 Removed unnecessary intrinsics. (WRB)
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C 890911 REVISION DATE from Version 3.2
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C 891214 Prologue converted to Version 4.0 format. (BAB)
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C 900315 CALLs to XERROR changed to CALLs to XERMSG. (THJ)
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C***END PROLOGUE DBSKES
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DOUBLE PRECISION XNU, X, BKE(*), BKNU1, V, VINCR, VEND, ALNBIG,
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1 D1MACH, DIRECT
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SAVE ALNBIG
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DATA ALNBIG / 0.D0 /
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C***FIRST EXECUTABLE STATEMENT DBSKES
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IF (ALNBIG.EQ.0.D0) ALNBIG = LOG (D1MACH(2))
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C
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V = ABS(XNU)
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N = ABS(NIN)
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C
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IF (V .GE. 1.D0) CALL XERMSG ('SLATEC', 'DBSKES',
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+ 'ABS(XNU) MUST BE LT 1', 2, 2)
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IF (X .LE. 0.D0) CALL XERMSG ('SLATEC', 'DBSKES', 'X IS LE 0', 3,
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+ 2)
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IF (N .EQ. 0) CALL XERMSG ('SLATEC', 'DBSKES',
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+ 'N THE NUMBER IN THE SEQUENCE IS 0', 4, 2)
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C
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CALL D9KNUS (V, X, BKE(1), BKNU1, ISWTCH)
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IF (N.EQ.1) RETURN
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C
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VINCR = SIGN (1.0, REAL(NIN))
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DIRECT = VINCR
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IF (XNU.NE.0.D0) DIRECT = VINCR*SIGN(1.D0, XNU)
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IF (ISWTCH .EQ. 1 .AND. DIRECT .GT. 0.) CALL XERMSG ('SLATEC',
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+ 'DBSKES', 'X SO SMALL BESSEL K-SUB-XNU+1 OVERFLOWS', 5, 2)
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BKE(2) = BKNU1
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C
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IF (DIRECT.LT.0.) CALL D9KNUS (ABS(XNU+VINCR), X, BKE(2), BKNU1,
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1 ISWTCH)
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IF (N.EQ.2) RETURN
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C
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VEND = ABS (XNU+NIN) - 1.0D0
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IF ((VEND-.5D0)*LOG(VEND)+0.27D0-VEND*(LOG(X)-.694D0) .GT.
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+ ALNBIG) CALL XERMSG ('SLATEC', 'DBSKES',
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+ 'X SO SMALL OR ABS(NU) SO BIG THAT BESSEL K-SUB-NU ' //
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+ 'OVERFLOWS', 5, 2)
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C
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V = XNU
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DO 10 I=3,N
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V = V + VINCR
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BKE(I) = 2.0D0*V*BKE(I-1)/X + BKE(I-2)
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10 CONTINUE
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C
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RETURN
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END
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