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119 lines
5.1 KiB
Fortran
119 lines
5.1 KiB
Fortran
*DECK BESK0E
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FUNCTION BESK0E (X)
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C***BEGIN PROLOGUE BESK0E
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C***PURPOSE Compute the exponentially scaled modified (hyperbolic)
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C Bessel function of the 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 (BESK0E-S, DBSK0E-D)
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C***KEYWORDS EXPONENTIALLY SCALED, 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 BESK0E(X) computes the exponentially scaled modified (hyperbolic)
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C Bessel function of third kind of order zero for real argument
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C X .GT. 0.0, i.e., EXP(X)*K0(X).
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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 Series for AK0 on the interval 1.25000D-01 to 5.00000D-01
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C with weighted error 5.34E-17
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C log weighted error 16.27
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C significant figures required 14.92
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C decimal places required 16.89
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C
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C Series for AK02 on the interval 0. to 1.25000D-01
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C with weighted error 2.34E-17
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C log weighted error 16.63
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C significant figures required 14.67
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C decimal places required 17.20
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C
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C***REFERENCES (NONE)
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C***ROUTINES CALLED BESI0, 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 BESK0E
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DIMENSION BK0CS(11), AK0CS(17), AK02CS(14)
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LOGICAL FIRST
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SAVE BK0CS, AK0CS, AK02CS, NTK0, NTAK0, NTAK02, XSML, 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 AK0CS( 1) / -.0764394790 3327941E0 /
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DATA AK0CS( 2) / -.0223565260 5699819E0 /
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DATA AK0CS( 3) / .0007734181 1546938E0 /
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DATA AK0CS( 4) / -.0000428100 6688886E0 /
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DATA AK0CS( 5) / .0000030817 0017386E0 /
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DATA AK0CS( 6) / -.0000002639 3672220E0 /
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DATA AK0CS( 7) / .0000000256 3713036E0 /
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DATA AK0CS( 8) / -.0000000027 4270554E0 /
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DATA AK0CS( 9) / .0000000003 1694296E0 /
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DATA AK0CS(10) / -.0000000000 3902353E0 /
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DATA AK0CS(11) / .0000000000 0506804E0 /
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DATA AK0CS(12) / -.0000000000 0068895E0 /
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DATA AK0CS(13) / .0000000000 0009744E0 /
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DATA AK0CS(14) / -.0000000000 0001427E0 /
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DATA AK0CS(15) / .0000000000 0000215E0 /
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DATA AK0CS(16) / -.0000000000 0000033E0 /
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DATA AK0CS(17) / .0000000000 0000005E0 /
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DATA AK02CS( 1) / -.0120186982 6307592E0 /
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DATA AK02CS( 2) / -.0091748526 9102569E0 /
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DATA AK02CS( 3) / .0001444550 9317750E0 /
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DATA AK02CS( 4) / -.0000040136 1417543E0 /
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DATA AK02CS( 5) / .0000001567 8318108E0 /
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DATA AK02CS( 6) / -.0000000077 7011043E0 /
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DATA AK02CS( 7) / .0000000004 6111825E0 /
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DATA AK02CS( 8) / -.0000000000 3158592E0 /
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DATA AK02CS( 9) / .0000000000 0243501E0 /
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DATA AK02CS(10) / -.0000000000 0020743E0 /
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DATA AK02CS(11) / .0000000000 0001925E0 /
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DATA AK02CS(12) / -.0000000000 0000192E0 /
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DATA AK02CS(13) / .0000000000 0000020E0 /
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DATA AK02CS(14) / -.0000000000 0000002E0 /
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DATA FIRST /.TRUE./
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C***FIRST EXECUTABLE STATEMENT BESK0E
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IF (FIRST) THEN
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NTK0 = INITS (BK0CS, 11, 0.1*R1MACH(3))
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NTAK0 = INITS (AK0CS, 17, 0.1*R1MACH(3))
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NTAK02 = INITS (AK02CS, 14, 0.1*R1MACH(3))
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XSML = SQRT (4.0*R1MACH(3))
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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', 'BESK0E',
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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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BESK0E = EXP(X) * (-LOG(0.5*X)*BESI0(X)
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1 - .25 + CSEVL (.5*Y-1., BK0CS, NTK0) )
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RETURN
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C
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20 IF (X.LE.8.) BESK0E = (1.25 + CSEVL ((16./X-5.)/3., AK0CS, NTAK0))
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1 / SQRT(X)
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IF (X.GT.8.) BESK0E = (1.25 + CSEVL (16./X-1., AK02CS, NTAK02))
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1 / SQRT(X)
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C
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RETURN
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END
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