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133 lines
5.4 KiB
Fortran
133 lines
5.4 KiB
Fortran
*DECK AIE
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FUNCTION AIE (X)
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C***BEGIN PROLOGUE AIE
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C***PURPOSE Calculate the Airy function for a negative argument and an
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C exponentially scaled Airy function for a non-negative
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C argument.
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C***LIBRARY SLATEC (FNLIB)
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C***CATEGORY C10D
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C***TYPE SINGLE PRECISION (AIE-S, DAIE-D)
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C***KEYWORDS EXPONENTIALLY SCALED AIRY FUNCTION, FNLIB,
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C SPECIAL FUNCTIONS
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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 AIE(X) computes the exponentially scaled Airy function for
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C non-negative X. It evaluates AI(X) for X .LE. 0.0 and
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C EXP(ZETA)*AI(X) for X .GE. 0.0 where ZETA = (2.0/3.0)*(X**1.5).
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C
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C Series for AIF on the interval -1.00000D+00 to 1.00000D+00
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C with weighted error 1.09E-19
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C log weighted error 18.96
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C significant figures required 17.76
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C decimal places required 19.44
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C
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C Series for AIG on the interval -1.00000D+00 to 1.00000D+00
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C with weighted error 1.51E-17
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C log weighted error 16.82
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C significant figures required 15.19
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C decimal places required 17.27
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C
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C Series for AIP on the interval 0. to 1.00000D+00
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C with weighted error 5.10E-17
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C log weighted error 16.29
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C significant figures required 14.41
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C decimal places required 17.06
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C
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C***REFERENCES (NONE)
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C***ROUTINES CALLED CSEVL, INITS, R1MACH, R9AIMP
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C***REVISION HISTORY (YYMMDD)
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C 770701 DATE WRITTEN
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C 890206 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 920618 Removed space from variable names. (RWC, WRB)
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C***END PROLOGUE AIE
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DIMENSION AIFCS(9), AIGCS(8), AIPCS(34)
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LOGICAL FIRST
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SAVE AIFCS, AIGCS, AIPCS, NAIF, NAIG,
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1 NAIP, X3SML, X32SML, XBIG, FIRST
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DATA AIFCS( 1) / -.0379713584 9666999750E0 /
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DATA AIFCS( 2) / .0591918885 3726363857E0 /
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DATA AIFCS( 3) / .0009862928 0577279975E0 /
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DATA AIFCS( 4) / .0000068488 4381907656E0 /
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DATA AIFCS( 5) / .0000000259 4202596219E0 /
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DATA AIFCS( 6) / .0000000000 6176612774E0 /
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DATA AIFCS( 7) / .0000000000 0010092454E0 /
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DATA AIFCS( 8) / .0000000000 0000012014E0 /
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DATA AIFCS( 9) / .0000000000 0000000010E0 /
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DATA AIGCS( 1) / .0181523655 8116127E0 /
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DATA AIGCS( 2) / .0215725631 6601076E0 /
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DATA AIGCS( 3) / .0002567835 6987483E0 /
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DATA AIGCS( 4) / .0000014265 2141197E0 /
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DATA AIGCS( 5) / .0000000045 7211492E0 /
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DATA AIGCS( 6) / .0000000000 0952517E0 /
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DATA AIGCS( 7) / .0000000000 0001392E0 /
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DATA AIGCS( 8) / .0000000000 0000001E0 /
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DATA AIPCS( 1) / -.0187519297 793868E0 /
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DATA AIPCS( 2) / -.0091443848 250055E0 /
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DATA AIPCS( 3) / .0009010457 337825E0 /
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DATA AIPCS( 4) / -.0001394184 127221E0 /
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DATA AIPCS( 5) / .0000273815 815785E0 /
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DATA AIPCS( 6) / -.0000062750 421119E0 /
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DATA AIPCS( 7) / .0000016064 844184E0 /
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DATA AIPCS( 8) / -.0000004476 392158E0 /
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DATA AIPCS( 9) / .0000001334 635874E0 /
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DATA AIPCS(10) / -.0000000420 735334E0 /
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DATA AIPCS(11) / .0000000139 021990E0 /
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DATA AIPCS(12) / -.0000000047 831848E0 /
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DATA AIPCS(13) / .0000000017 047897E0 /
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DATA AIPCS(14) / -.0000000006 268389E0 /
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DATA AIPCS(15) / .0000000002 369824E0 /
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DATA AIPCS(16) / -.0000000000 918641E0 /
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DATA AIPCS(17) / .0000000000 364278E0 /
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DATA AIPCS(18) / -.0000000000 147475E0 /
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DATA AIPCS(19) / .0000000000 060851E0 /
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DATA AIPCS(20) / -.0000000000 025552E0 /
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DATA AIPCS(21) / .0000000000 010906E0 /
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DATA AIPCS(22) / -.0000000000 004725E0 /
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DATA AIPCS(23) / .0000000000 002076E0 /
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DATA AIPCS(24) / -.0000000000 000924E0 /
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DATA AIPCS(25) / .0000000000 000417E0 /
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DATA AIPCS(26) / -.0000000000 000190E0 /
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DATA AIPCS(27) / .0000000000 000087E0 /
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DATA AIPCS(28) / -.0000000000 000040E0 /
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DATA AIPCS(29) / .0000000000 000019E0 /
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DATA AIPCS(30) / -.0000000000 000009E0 /
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DATA AIPCS(31) / .0000000000 000004E0 /
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DATA AIPCS(32) / -.0000000000 000002E0 /
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DATA AIPCS(33) / .0000000000 000001E0 /
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DATA AIPCS(34) / -.0000000000 000000E0 /
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DATA FIRST /.TRUE./
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C***FIRST EXECUTABLE STATEMENT AIE
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IF (FIRST) THEN
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ETA = 0.1*R1MACH(3)
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NAIF = INITS (AIFCS, 9, ETA)
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NAIG = INITS (AIGCS, 8, ETA)
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NAIP = INITS (AIPCS, 34, ETA)
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C
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X3SML = ETA**0.3333
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X32SML = 1.3104*X3SML**2
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XBIG = R1MACH(2)**0.6666
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ENDIF
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FIRST = .FALSE.
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C
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IF (X.GE.(-1.0)) GO TO 20
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CALL R9AIMP (X, XM, THETA)
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AIE = XM * COS(THETA)
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RETURN
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C
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20 IF (X.GT.1.0) GO TO 30
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Z = 0.0
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IF (ABS(X).GT.X3SML) Z = X**3
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AIE = 0.375 + (CSEVL (Z, AIFCS, NAIF) - X*(0.25 +
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1 CSEVL (Z, AIGCS, NAIG)) )
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IF (X.GT.X32SML) AIE = AIE * EXP(2.0*X*SQRT(X)/3.0)
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RETURN
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C
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30 SQRTX = SQRT(X)
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Z = -1.0
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IF (X.LT.XBIG) Z = 2.0/(X*SQRTX) - 1.0
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AIE = (.28125 + CSEVL (Z, AIPCS, NAIP))/SQRT(SQRTX)
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RETURN
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C
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END
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