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124 lines
5.3 KiB
Fortran
124 lines
5.3 KiB
Fortran
*DECK BESK1E
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FUNCTION BESK1E (X)
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C***BEGIN PROLOGUE BESK1E
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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 one.
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C***LIBRARY SLATEC (FNLIB)
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C***CATEGORY C10B1
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C***TYPE SINGLE PRECISION (BESK1E-S, DBSK1E-D)
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C***KEYWORDS EXPONENTIALLY SCALED, FNLIB, HYPERBOLIC BESSEL FUNCTION,
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C MODIFIED BESSEL FUNCTION, ORDER ONE, 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 BESK1E(X) computes the exponentially scaled modified (hyperbolic)
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C Bessel function of third kind of order one for real argument
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C X .GT. 0.0, i.e., EXP(X)*K1(X).
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C
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C Series for BK1 on the interval 0. to 4.00000D+00
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C with weighted error 7.02E-18
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C log weighted error 17.15
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C significant figures required 16.73
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C decimal places required 17.67
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C
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C Series for AK1 on the interval 1.25000D-01 to 5.00000D-01
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C with weighted error 6.06E-17
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C log weighted error 16.22
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C significant figures required 15.41
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C decimal places required 16.83
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C
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C Series for AK12 on the interval 0. to 1.25000D-01
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C with weighted error 2.58E-17
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C log weighted error 16.59
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C significant figures required 15.22
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C decimal places required 17.16
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C
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C***REFERENCES (NONE)
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C***ROUTINES CALLED BESI1, 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 BESK1E
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DIMENSION BK1CS(11), AK1CS(17), AK12CS(14)
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LOGICAL FIRST
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SAVE BK1CS, AK1CS, AK12CS, NTK1, NTAK1, NTAK12, XMIN, XSML,
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1 FIRST
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DATA BK1CS( 1) / .0253002273 389477705E0 /
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DATA BK1CS( 2) / -.3531559607 76544876E0 /
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DATA BK1CS( 3) / -.1226111808 22657148E0 /
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DATA BK1CS( 4) / -.0069757238 596398643E0 /
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DATA BK1CS( 5) / -.0001730288 957513052E0 /
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DATA BK1CS( 6) / -.0000024334 061415659E0 /
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DATA BK1CS( 7) / -.0000000221 338763073E0 /
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DATA BK1CS( 8) / -.0000000001 411488392E0 /
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DATA BK1CS( 9) / -.0000000000 006666901E0 /
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DATA BK1CS(10) / -.0000000000 000024274E0 /
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DATA BK1CS(11) / -.0000000000 000000070E0 /
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DATA AK1CS( 1) / .2744313406 973883E0 /
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DATA AK1CS( 2) / .0757198995 3199368E0 /
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DATA AK1CS( 3) / -.0014410515 5647540E0 /
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DATA AK1CS( 4) / .0000665011 6955125E0 /
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DATA AK1CS( 5) / -.0000043699 8470952E0 /
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DATA AK1CS( 6) / .0000003540 2774997E0 /
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DATA AK1CS( 7) / -.0000000331 1163779E0 /
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DATA AK1CS( 8) / .0000000034 4597758E0 /
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DATA AK1CS( 9) / -.0000000003 8989323E0 /
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DATA AK1CS(10) / .0000000000 4720819E0 /
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DATA AK1CS(11) / -.0000000000 0604783E0 /
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DATA AK1CS(12) / .0000000000 0081284E0 /
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DATA AK1CS(13) / -.0000000000 0011386E0 /
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DATA AK1CS(14) / .0000000000 0001654E0 /
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DATA AK1CS(15) / -.0000000000 0000248E0 /
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DATA AK1CS(16) / .0000000000 0000038E0 /
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DATA AK1CS(17) / -.0000000000 0000006E0 /
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DATA AK12CS( 1) / .0637930834 3739001E0 /
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DATA AK12CS( 2) / .0283288781 3049721E0 /
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DATA AK12CS( 3) / -.0002475370 6739052E0 /
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DATA AK12CS( 4) / .0000057719 7245160E0 /
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DATA AK12CS( 5) / -.0000002068 9392195E0 /
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DATA AK12CS( 6) / .0000000097 3998344E0 /
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DATA AK12CS( 7) / -.0000000005 5853361E0 /
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DATA AK12CS( 8) / .0000000000 3732996E0 /
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DATA AK12CS( 9) / -.0000000000 0282505E0 /
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DATA AK12CS(10) / .0000000000 0023720E0 /
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DATA AK12CS(11) / -.0000000000 0002176E0 /
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DATA AK12CS(12) / .0000000000 0000215E0 /
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DATA AK12CS(13) / -.0000000000 0000022E0 /
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DATA AK12CS(14) / .0000000000 0000002E0 /
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DATA FIRST /.TRUE./
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C***FIRST EXECUTABLE STATEMENT BESK1E
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IF (FIRST) THEN
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NTK1 = INITS (BK1CS, 11, 0.1*R1MACH(3))
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NTAK1 = INITS (AK1CS, 17, 0.1*R1MACH(3))
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NTAK12 = INITS (AK12CS, 14, 0.1*R1MACH(3))
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C
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XMIN = EXP (MAX(LOG(R1MACH(1)), -LOG(R1MACH(2))) + .01)
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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', 'BESK1E',
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+ 'X IS ZERO OR NEGATIVE', 2, 2)
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IF (X.GT.2.0) GO TO 20
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C
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IF (X .LT. XMIN) CALL XERMSG ('SLATEC', 'BESK1E',
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+ 'X SO SMALL K1 OVERFLOWS', 3, 2)
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Y = 0.
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IF (X.GT.XSML) Y = X*X
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BESK1E = EXP(X) * (LOG(0.5*X)*BESI1(X) +
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1 (0.75 + CSEVL (.5*Y-1., BK1CS, NTK1))/X )
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RETURN
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C
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20 IF (X.LE.8.) BESK1E = (1.25 + CSEVL ((16./X-5.)/3., AK1CS, NTAK1))
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1 / SQRT(X)
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IF (X.GT.8.) BESK1E = (1.25 + CSEVL (16./X-1., AK12CS, NTAK12))
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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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