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127 lines
4 KiB
Fortran
127 lines
4 KiB
Fortran
*DECK GAMIC
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REAL FUNCTION GAMIC (A, X)
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C***BEGIN PROLOGUE GAMIC
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C***PURPOSE Calculate the complementary incomplete Gamma function.
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C***LIBRARY SLATEC (FNLIB)
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C***CATEGORY C7E
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C***TYPE SINGLE PRECISION (GAMIC-S, DGAMIC-D)
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C***KEYWORDS COMPLEMENTARY INCOMPLETE GAMMA 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 Evaluate the complementary incomplete gamma function
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C
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C GAMIC = integral from X to infinity of EXP(-T) * T**(A-1.) .
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C
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C GAMIC is evaluated for arbitrary real values of A and for non-
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C negative values of X (even though GAMIC is defined for X .LT.
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C 0.0), except that for X = 0 and A .LE. 0.0, GAMIC is undefined.
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C
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C GAMIC, A, and X are REAL.
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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 GAMIC 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 close
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C to a negative integer (but not a negative integer), there is a loss
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C of accuracy, which is reported if the result is less than half
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C 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 ALGAMS, ALNGAM, R1MACH, R9GMIC, R9GMIT, R9LGIC,
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C R9LGIT, 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 GAMIC
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LOGICAL FIRST
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SAVE EPS, SQEPS, ALNEPS, BOT, FIRST
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DATA FIRST /.TRUE./
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C***FIRST EXECUTABLE STATEMENT GAMIC
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IF (FIRST) THEN
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EPS = 0.5*R1MACH(3)
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SQEPS = SQRT(R1MACH(4))
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ALNEPS = -LOG(R1MACH(3))
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BOT = LOG(R1MACH(1))
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ENDIF
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FIRST = .FALSE.
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C
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IF (X .LT. 0.0) CALL XERMSG ('SLATEC', 'GAMIC', 'X IS NEGATIVE',
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+ 2, 2)
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C
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IF (X.GT.0.0) GO TO 20
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IF (A .LE. 0.0) CALL XERMSG ('SLATEC', 'GAMIC',
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+ 'X = 0 AND A LE 0 SO GAMIC IS UNDEFINED', 3, 2)
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C
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GAMIC = EXP (ALNGAM(A+1.0) - LOG(A))
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RETURN
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C
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20 ALX = LOG(X)
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SGA = 1.0
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IF (A.NE.0.0) SGA = SIGN (1.0, A)
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MA = A + 0.5*SGA
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AEPS = A - MA
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C
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IZERO = 0
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IF (X.GE.1.0) GO TO 60
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C
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IF (A.GT.0.5 .OR. ABS(AEPS).GT.0.001) GO TO 50
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FM = -MA
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E = 2.0
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IF (FM.GT.1.0) E = 2.0*(FM+2.0)/(FM*FM-1.0)
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E = E - ALX*X**(-0.001)
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IF (E*ABS(AEPS).GT.EPS) GO TO 50
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C
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GAMIC = R9GMIC (A, X, ALX)
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RETURN
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C
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50 CALL ALGAMS (A+1.0, ALGAP1, SGNGAM)
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GSTAR = R9GMIT (A, X, ALGAP1, SGNGAM, ALX)
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IF (GSTAR.EQ.0.0) IZERO = 1
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IF (GSTAR.NE.0.0) ALNGS = LOG (ABS(GSTAR))
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IF (GSTAR.NE.0.0) SGNGS = SIGN (1.0, GSTAR)
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GO TO 70
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C
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60 IF (A.LT.X) GAMIC = EXP (R9LGIC(A, X, ALX))
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IF (A.LT.X) RETURN
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C
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SGNGAM = 1.0
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ALGAP1 = ALNGAM (A+1.0)
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SGNGS = 1.0
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ALNGS = R9LGIT (A, X, ALGAP1)
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C
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C EVALUATION OF GAMIC(A,X) IN TERMS OF TRICOMI-S INCOMPLETE GAMMA FN.
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C
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70 H = 1.0
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IF (IZERO.EQ.1) GO TO 80
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C
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T = A*ALX + ALNGS
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IF (T.GT.ALNEPS) GO TO 90
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IF (T.GT.(-ALNEPS)) H = 1.0 - SGNGS*EXP(T)
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C
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IF (ABS(H).LT.SQEPS) CALL XERCLR
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IF (ABS(H) .LT. SQEPS) CALL XERMSG ('SLATEC', 'GAMIC',
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+ 'RESULT LT HALF PRECISION', 1, 1)
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C
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80 SGNG = SIGN (1.0, H) * SGA * SGNGAM
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T = LOG(ABS(H)) + ALGAP1 - LOG(ABS(A))
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IF (T.LT.BOT) CALL XERCLR
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GAMIC = SGNG * EXP(T)
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RETURN
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C
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90 SGNG = -SGNGS * SGA * SGNGAM
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T = T + ALGAP1 - LOG(ABS(A))
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IF (T.LT.BOT) CALL XERCLR
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GAMIC = SGNG * EXP(T)
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RETURN
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C
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END
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