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76 lines
2.8 KiB
Fortran
76 lines
2.8 KiB
Fortran
*DECK BESK0
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FUNCTION BESK0 (X)
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C***BEGIN PROLOGUE BESK0
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C***PURPOSE Compute the modified (hyperbolic) Bessel function of the
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C third kind of order zero.
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C***LIBRARY SLATEC (FNLIB)
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C***CATEGORY C10B1
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C***TYPE SINGLE PRECISION (BESK0-S, DBESK0-D)
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C***KEYWORDS FNLIB, HYPERBOLIC BESSEL FUNCTION,
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C MODIFIED BESSEL FUNCTION, ORDER ZERO, SPECIAL FUNCTIONS,
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C 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 BESK0(X) calculates the modified (hyperbolic) Bessel function
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C of the third kind of order zero for real argument X .GT. 0.0.
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C
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C Series for BK0 on the interval 0. to 4.00000D+00
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C with weighted error 3.57E-19
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C log weighted error 18.45
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C significant figures required 17.99
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C decimal places required 18.97
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C
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C***REFERENCES (NONE)
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C***ROUTINES CALLED BESI0, BESK0E, CSEVL, INITS, R1MACH, XERMSG
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C***REVISION HISTORY (YYMMDD)
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C 770401 DATE WRITTEN
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C 890531 Changed all specific intrinsics to generic. (WRB)
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C 890531 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 900326 Removed duplicate information from DESCRIPTION section.
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C (WRB)
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C***END PROLOGUE BESK0
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DIMENSION BK0CS(11)
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LOGICAL FIRST
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SAVE BK0CS, NTK0, XSML, XMAX, FIRST
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DATA BK0CS( 1) / -.0353273932 3390276872E0 /
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DATA BK0CS( 2) / .3442898999 246284869E0 /
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DATA BK0CS( 3) / .0359799365 1536150163E0 /
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DATA BK0CS( 4) / .0012646154 1144692592E0 /
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DATA BK0CS( 5) / .0000228621 2103119451E0 /
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DATA BK0CS( 6) / .0000002534 7910790261E0 /
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DATA BK0CS( 7) / .0000000019 0451637722E0 /
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DATA BK0CS( 8) / .0000000000 1034969525E0 /
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DATA BK0CS( 9) / .0000000000 0004259816E0 /
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DATA BK0CS(10) / .0000000000 0000013744E0 /
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DATA BK0CS(11) / .0000000000 0000000035E0 /
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DATA FIRST /.TRUE./
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C***FIRST EXECUTABLE STATEMENT BESK0
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IF (FIRST) THEN
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NTK0 = INITS (BK0CS, 11, 0.1*R1MACH(3))
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XSML = SQRT (4.0*R1MACH(3))
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XMAXT = -LOG(R1MACH(1))
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XMAX = XMAXT - 0.5*XMAXT*LOG(XMAXT)/(XMAXT+0.5) - 0.01
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ENDIF
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FIRST = .FALSE.
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C
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IF (X .LE. 0.) CALL XERMSG ('SLATEC', 'BESK0',
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+ 'X IS ZERO OR NEGATIVE', 2, 2)
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IF (X.GT.2.) GO TO 20
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C
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Y = 0.
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IF (X.GT.XSML) Y = X*X
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BESK0 = -LOG(0.5*X)*BESI0(X) - .25 + CSEVL (.5*Y-1., BK0CS, NTK0)
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RETURN
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C
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20 BESK0 = 0.
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IF (X .GT. XMAX) CALL XERMSG ('SLATEC', 'BESK0',
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+ 'X SO BIG K0 UNDERFLOWS', 1, 1)
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IF (X.GT.XMAX) RETURN
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C
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BESK0 = EXP(-X) * BESK0E(X)
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C
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RETURN
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END
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