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91 lines
2.5 KiB
Fortran
91 lines
2.5 KiB
Fortran
*DECK D9GMIT
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DOUBLE PRECISION FUNCTION D9GMIT (A, X, ALGAP1, SGNGAM, ALX)
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C***BEGIN PROLOGUE D9GMIT
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C***SUBSIDIARY
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C***PURPOSE Compute Tricomi's incomplete Gamma function for small
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C arguments.
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C***LIBRARY SLATEC (FNLIB)
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C***CATEGORY C7E
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C***TYPE DOUBLE PRECISION (R9GMIT-S, D9GMIT-D)
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C***KEYWORDS COMPLEMENTARY INCOMPLETE GAMMA FUNCTION, FNLIB, SMALL X,
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C SPECIAL FUNCTIONS, TRICOMI
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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 Compute Tricomi's incomplete gamma function for small X.
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C
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C***REFERENCES (NONE)
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C***ROUTINES CALLED D1MACH, DLNGAM, XERMSG
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C***REVISION HISTORY (YYMMDD)
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C 770701 DATE WRITTEN
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C 890531 Changed all specific intrinsics to generic. (WRB)
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C 890911 Removed unnecessary intrinsics. (WRB)
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C 890911 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 900720 Routine changed from user-callable to subsidiary. (WRB)
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C***END PROLOGUE D9GMIT
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DOUBLE PRECISION A, X, ALGAP1, SGNGAM, ALX, AE, AEPS, ALGS, ALG2,
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1 BOT, EPS, FK, S, SGNG2, T, TE, D1MACH, DLNGAM
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LOGICAL FIRST
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SAVE EPS, BOT, FIRST
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DATA FIRST /.TRUE./
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C***FIRST EXECUTABLE STATEMENT D9GMIT
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IF (FIRST) THEN
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EPS = 0.5D0*D1MACH(3)
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BOT = LOG (D1MACH(1))
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ENDIF
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FIRST = .FALSE.
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C
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IF (X .LE. 0.D0) CALL XERMSG ('SLATEC', 'D9GMIT',
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+ 'X SHOULD BE GT 0', 1, 2)
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C
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MA = A + 0.5D0
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IF (A.LT.0.D0) MA = A - 0.5D0
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AEPS = A - MA
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C
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AE = A
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IF (A.LT.(-0.5D0)) AE = AEPS
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C
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T = 1.D0
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TE = AE
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S = T
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DO 20 K=1,200
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FK = K
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TE = -X*TE/FK
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T = TE/(AE+FK)
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S = S + T
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IF (ABS(T).LT.EPS*ABS(S)) GO TO 30
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20 CONTINUE
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CALL XERMSG ('SLATEC', 'D9GMIT',
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+ 'NO CONVERGENCE IN 200 TERMS OF TAYLOR-S SERIES', 2, 2)
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C
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30 IF (A.GE.(-0.5D0)) ALGS = -ALGAP1 + LOG(S)
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IF (A.GE.(-0.5D0)) GO TO 60
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C
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ALGS = -DLNGAM(1.D0+AEPS) + LOG(S)
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S = 1.0D0
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M = -MA - 1
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IF (M.EQ.0) GO TO 50
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T = 1.0D0
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DO 40 K=1,M
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T = X*T/(AEPS-(M+1-K))
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S = S + T
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IF (ABS(T).LT.EPS*ABS(S)) GO TO 50
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40 CONTINUE
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C
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50 D9GMIT = 0.0D0
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ALGS = -MA*LOG(X) + ALGS
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IF (S.EQ.0.D0 .OR. AEPS.EQ.0.D0) GO TO 60
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C
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SGNG2 = SGNGAM * SIGN (1.0D0, S)
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ALG2 = -X - ALGAP1 + LOG(ABS(S))
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C
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IF (ALG2.GT.BOT) D9GMIT = SGNG2 * EXP(ALG2)
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IF (ALGS.GT.BOT) D9GMIT = D9GMIT + EXP(ALGS)
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RETURN
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C
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60 D9GMIT = EXP (ALGS)
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RETURN
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C
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END
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