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119 lines
4 KiB
Fortran
119 lines
4 KiB
Fortran
*DECK DGAMIT
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DOUBLE PRECISION FUNCTION DGAMIT (A, X)
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C***BEGIN PROLOGUE DGAMIT
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C***PURPOSE Calculate Tricomi's form of the incomplete Gamma function.
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C***LIBRARY SLATEC (FNLIB)
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C***CATEGORY C7E
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C***TYPE DOUBLE PRECISION (GAMIT-S, DGAMIT-D)
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C***KEYWORDS COMPLEMENTARY INCOMPLETE GAMMA FUNCTION, FNLIB,
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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 Evaluate Tricomi's incomplete Gamma function defined by
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C
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C DGAMIT = X**(-A)/GAMMA(A) * integral from 0 to X of EXP(-T) *
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C T**(A-1.)
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C
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C for A .GT. 0.0 and by analytic continuation for A .LE. 0.0.
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C GAMMA(X) is the complete gamma function of X.
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C
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C DGAMIT is evaluated for arbitrary real values of A and for non-
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C negative values of X (even though DGAMIT is defined for X .LT.
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C 0.0), except that for X = 0 and A .LE. 0.0, DGAMIT is infinite,
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C which is a fatal error.
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C
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C The function and both arguments are DOUBLE PRECISION.
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C
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C A slight deterioration of 2 or 3 digits accuracy will occur when
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C DGAMIT is very large or very small in absolute value, because log-
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C arithmic variables are used. Also, if the parameter A is very
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C close to a negative integer (but not a negative integer), there is
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C a loss of accuracy, which is reported if the result is less than
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C half machine precision.
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C
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C***REFERENCES W. Gautschi, A computational procedure for incomplete
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C gamma functions, ACM Transactions on Mathematical
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C Software 5, 4 (December 1979), pp. 466-481.
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C W. Gautschi, Incomplete gamma functions, Algorithm 542,
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C ACM Transactions on Mathematical Software 5, 4
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C (December 1979), pp. 482-489.
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C***ROUTINES CALLED D1MACH, D9GMIT, D9LGIC, D9LGIT, DGAMR, DLGAMS,
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C DLNGAM, XERCLR, 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 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 920528 DESCRIPTION and REFERENCES sections revised. (WRB)
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C***END PROLOGUE DGAMIT
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DOUBLE PRECISION A, X, AEPS, AINTA, ALGAP1, ALNEPS, ALNG, ALX,
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1 BOT, H, SGA, SGNGAM, SQEPS, T, D1MACH, DGAMR, D9GMIT, D9LGIT,
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2 DLNGAM, D9LGIC
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LOGICAL FIRST
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SAVE ALNEPS, SQEPS, BOT, FIRST
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DATA FIRST /.TRUE./
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C***FIRST EXECUTABLE STATEMENT DGAMIT
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IF (FIRST) THEN
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ALNEPS = -LOG (D1MACH(3))
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SQEPS = SQRT(D1MACH(4))
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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 .LT. 0.D0) CALL XERMSG ('SLATEC', 'DGAMIT', 'X IS NEGATIVE'
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+ , 2, 2)
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C
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IF (X.NE.0.D0) ALX = LOG (X)
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SGA = 1.0D0
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IF (A.NE.0.D0) SGA = SIGN (1.0D0, A)
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AINTA = AINT (A + 0.5D0*SGA)
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AEPS = A - AINTA
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C
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IF (X.GT.0.D0) GO TO 20
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DGAMIT = 0.0D0
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IF (AINTA.GT.0.D0 .OR. AEPS.NE.0.D0) DGAMIT = DGAMR(A+1.0D0)
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RETURN
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C
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20 IF (X.GT.1.D0) GO TO 30
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IF (A.GE.(-0.5D0) .OR. AEPS.NE.0.D0) CALL DLGAMS (A+1.0D0, ALGAP1,
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1 SGNGAM)
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DGAMIT = D9GMIT (A, X, ALGAP1, SGNGAM, ALX)
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RETURN
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C
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30 IF (A.LT.X) GO TO 40
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T = D9LGIT (A, X, DLNGAM(A+1.0D0))
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IF (T.LT.BOT) CALL XERCLR
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DGAMIT = EXP (T)
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RETURN
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C
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40 ALNG = D9LGIC (A, X, ALX)
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C
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C EVALUATE DGAMIT IN TERMS OF LOG (DGAMIC (A, X))
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C
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H = 1.0D0
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IF (AEPS.EQ.0.D0 .AND. AINTA.LE.0.D0) GO TO 50
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C
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CALL DLGAMS (A+1.0D0, ALGAP1, SGNGAM)
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T = LOG (ABS(A)) + ALNG - ALGAP1
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IF (T.GT.ALNEPS) GO TO 60
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C
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IF (T.GT.(-ALNEPS)) H = 1.0D0 - SGA * SGNGAM * EXP(T)
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IF (ABS(H).GT.SQEPS) GO TO 50
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C
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CALL XERCLR
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CALL XERMSG ('SLATEC', 'DGAMIT', 'RESULT LT HALF PRECISION', 1,
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+ 1)
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C
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50 T = -A*ALX + LOG(ABS(H))
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IF (T.LT.BOT) CALL XERCLR
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DGAMIT = SIGN (EXP(T), H)
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RETURN
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C
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60 T = T - A*ALX
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IF (T.LT.BOT) CALL XERCLR
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DGAMIT = -SGA * SGNGAM * EXP(T)
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RETURN
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C
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END
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