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- *DECK AIE
- FUNCTION AIE (X)
- C***BEGIN PROLOGUE AIE
- C***PURPOSE Calculate the Airy function for a negative argument and an
- C exponentially scaled Airy function for a non-negative
- C argument.
- C***LIBRARY SLATEC (FNLIB)
- C***CATEGORY C10D
- C***TYPE SINGLE PRECISION (AIE-S, DAIE-D)
- C***KEYWORDS EXPONENTIALLY SCALED AIRY FUNCTION, FNLIB,
- C SPECIAL FUNCTIONS
- C***AUTHOR Fullerton, W., (LANL)
- C***DESCRIPTION
- C
- C AIE(X) computes the exponentially scaled Airy function for
- C non-negative X. It evaluates AI(X) for X .LE. 0.0 and
- C EXP(ZETA)*AI(X) for X .GE. 0.0 where ZETA = (2.0/3.0)*(X**1.5).
- C
- C Series for AIF on the interval -1.00000D+00 to 1.00000D+00
- C with weighted error 1.09E-19
- C log weighted error 18.96
- C significant figures required 17.76
- C decimal places required 19.44
- C
- C Series for AIG on the interval -1.00000D+00 to 1.00000D+00
- C with weighted error 1.51E-17
- C log weighted error 16.82
- C significant figures required 15.19
- C decimal places required 17.27
- C
- C Series for AIP on the interval 0. to 1.00000D+00
- C with weighted error 5.10E-17
- C log weighted error 16.29
- C significant figures required 14.41
- C decimal places required 17.06
- C
- C***REFERENCES (NONE)
- C***ROUTINES CALLED CSEVL, INITS, R1MACH, R9AIMP
- C***REVISION HISTORY (YYMMDD)
- C 770701 DATE WRITTEN
- C 890206 REVISION DATE from Version 3.2
- C 891214 Prologue converted to Version 4.0 format. (BAB)
- C 920618 Removed space from variable names. (RWC, WRB)
- C***END PROLOGUE AIE
- DIMENSION AIFCS(9), AIGCS(8), AIPCS(34)
- LOGICAL FIRST
- SAVE AIFCS, AIGCS, AIPCS, NAIF, NAIG,
- 1 NAIP, X3SML, X32SML, XBIG, FIRST
- DATA AIFCS( 1) / -.0379713584 9666999750E0 /
- DATA AIFCS( 2) / .0591918885 3726363857E0 /
- DATA AIFCS( 3) / .0009862928 0577279975E0 /
- DATA AIFCS( 4) / .0000068488 4381907656E0 /
- DATA AIFCS( 5) / .0000000259 4202596219E0 /
- DATA AIFCS( 6) / .0000000000 6176612774E0 /
- DATA AIFCS( 7) / .0000000000 0010092454E0 /
- DATA AIFCS( 8) / .0000000000 0000012014E0 /
- DATA AIFCS( 9) / .0000000000 0000000010E0 /
- DATA AIGCS( 1) / .0181523655 8116127E0 /
- DATA AIGCS( 2) / .0215725631 6601076E0 /
- DATA AIGCS( 3) / .0002567835 6987483E0 /
- DATA AIGCS( 4) / .0000014265 2141197E0 /
- DATA AIGCS( 5) / .0000000045 7211492E0 /
- DATA AIGCS( 6) / .0000000000 0952517E0 /
- DATA AIGCS( 7) / .0000000000 0001392E0 /
- DATA AIGCS( 8) / .0000000000 0000001E0 /
- DATA AIPCS( 1) / -.0187519297 793868E0 /
- DATA AIPCS( 2) / -.0091443848 250055E0 /
- DATA AIPCS( 3) / .0009010457 337825E0 /
- DATA AIPCS( 4) / -.0001394184 127221E0 /
- DATA AIPCS( 5) / .0000273815 815785E0 /
- DATA AIPCS( 6) / -.0000062750 421119E0 /
- DATA AIPCS( 7) / .0000016064 844184E0 /
- DATA AIPCS( 8) / -.0000004476 392158E0 /
- DATA AIPCS( 9) / .0000001334 635874E0 /
- DATA AIPCS(10) / -.0000000420 735334E0 /
- DATA AIPCS(11) / .0000000139 021990E0 /
- DATA AIPCS(12) / -.0000000047 831848E0 /
- DATA AIPCS(13) / .0000000017 047897E0 /
- DATA AIPCS(14) / -.0000000006 268389E0 /
- DATA AIPCS(15) / .0000000002 369824E0 /
- DATA AIPCS(16) / -.0000000000 918641E0 /
- DATA AIPCS(17) / .0000000000 364278E0 /
- DATA AIPCS(18) / -.0000000000 147475E0 /
- DATA AIPCS(19) / .0000000000 060851E0 /
- DATA AIPCS(20) / -.0000000000 025552E0 /
- DATA AIPCS(21) / .0000000000 010906E0 /
- DATA AIPCS(22) / -.0000000000 004725E0 /
- DATA AIPCS(23) / .0000000000 002076E0 /
- DATA AIPCS(24) / -.0000000000 000924E0 /
- DATA AIPCS(25) / .0000000000 000417E0 /
- DATA AIPCS(26) / -.0000000000 000190E0 /
- DATA AIPCS(27) / .0000000000 000087E0 /
- DATA AIPCS(28) / -.0000000000 000040E0 /
- DATA AIPCS(29) / .0000000000 000019E0 /
- DATA AIPCS(30) / -.0000000000 000009E0 /
- DATA AIPCS(31) / .0000000000 000004E0 /
- DATA AIPCS(32) / -.0000000000 000002E0 /
- DATA AIPCS(33) / .0000000000 000001E0 /
- DATA AIPCS(34) / -.0000000000 000000E0 /
- DATA FIRST /.TRUE./
- C***FIRST EXECUTABLE STATEMENT AIE
- IF (FIRST) THEN
- ETA = 0.1*R1MACH(3)
- NAIF = INITS (AIFCS, 9, ETA)
- NAIG = INITS (AIGCS, 8, ETA)
- NAIP = INITS (AIPCS, 34, ETA)
- C
- X3SML = ETA**0.3333
- X32SML = 1.3104*X3SML**2
- XBIG = R1MACH(2)**0.6666
- ENDIF
- FIRST = .FALSE.
- C
- IF (X.GE.(-1.0)) GO TO 20
- CALL R9AIMP (X, XM, THETA)
- AIE = XM * COS(THETA)
- RETURN
- C
- 20 IF (X.GT.1.0) GO TO 30
- Z = 0.0
- IF (ABS(X).GT.X3SML) Z = X**3
- AIE = 0.375 + (CSEVL (Z, AIFCS, NAIF) - X*(0.25 +
- 1 CSEVL (Z, AIGCS, NAIG)) )
- IF (X.GT.X32SML) AIE = AIE * EXP(2.0*X*SQRT(X)/3.0)
- RETURN
- C
- 30 SQRTX = SQRT(X)
- Z = -1.0
- IF (X.LT.XBIG) Z = 2.0/(X*SQRTX) - 1.0
- AIE = (.28125 + CSEVL (Z, AIPCS, NAIP))/SQRT(SQRTX)
- RETURN
- C
- END
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