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92 lines
2.6 KiB
Fortran
92 lines
2.6 KiB
Fortran
*DECK R9GMIC
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FUNCTION R9GMIC (A, X, ALX)
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C***BEGIN PROLOGUE R9GMIC
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C***SUBSIDIARY
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C***PURPOSE Compute the complementary incomplete Gamma function for A
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C near a negative integer and for small X.
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C***LIBRARY SLATEC (FNLIB)
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C***CATEGORY C7E
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C***TYPE SINGLE PRECISION (R9GMIC-S, D9GMIC-D)
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C***KEYWORDS COMPLEMENTARY INCOMPLETE GAMMA FUNCTION, FNLIB, SMALL X,
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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 Compute the complementary incomplete gamma function for A near
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C a negative integer and for small X.
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C
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C***REFERENCES (NONE)
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C***ROUTINES CALLED ALNGAM, R1MACH, 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 900720 Routine changed from user-callable to subsidiary. (WRB)
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C***END PROLOGUE R9GMIC
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SAVE EULER, EPS, BOT
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DATA EULER / .5772156649 015329 E0 /
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DATA EPS, BOT / 2*0.0 /
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C***FIRST EXECUTABLE STATEMENT R9GMIC
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IF (EPS.EQ.0.0) EPS = 0.5*R1MACH(3)
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IF (BOT.EQ.0.0) BOT = LOG(R1MACH(1))
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C
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IF (A .GT. 0.0) CALL XERMSG ('SLATEC', 'R9GMIC',
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+ 'A MUST BE NEAR A NEGATIVE INTEGER', 2, 2)
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IF (X .LE. 0.0) CALL XERMSG ('SLATEC', 'R9GMIC',
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+ 'X MUST BE GT ZERO', 3, 2)
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C
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MA = A - 0.5
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FM = -MA
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M = -MA
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C
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TE = 1.0
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T = 1.0
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S = T
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DO 20 K=1,200
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FKP1 = K + 1
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TE = -X*TE/(FM+FKP1)
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T = TE/FKP1
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S = S + T
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IF (ABS(T).LT.EPS*S) GO TO 30
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20 CONTINUE
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CALL XERMSG ('SLATEC', 'R9GMIC',
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+ 'NO CONVERGENCE IN 200 TERMS OF CONTINUED FRACTION', 4, 2)
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C
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30 R9GMIC = -ALX - EULER + X*S/(FM+1.0)
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IF (M.EQ.0) RETURN
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C
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IF (M.EQ.1) R9GMIC = -R9GMIC - 1.0 + 1.0/X
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IF (M.EQ.1) RETURN
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C
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TE = FM
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T = 1.0
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S = T
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MM1 = M - 1
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DO 40 K=1,MM1
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FK = K
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TE = -X*TE/FK
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T = TE/(FM-FK)
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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 DO 60 K=1,M
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R9GMIC = R9GMIC + 1.0/K
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60 CONTINUE
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C
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SGNG = 1.0
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IF (MOD(M,2).EQ.1) SGNG = -1.0
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ALNG = LOG(R9GMIC) - ALNGAM(FM+1.0)
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C
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R9GMIC = 0.0
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IF (ALNG.GT.BOT) R9GMIC = SGNG*EXP(ALNG)
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IF (S.NE.0.0) R9GMIC = R9GMIC + SIGN (EXP(-FM*ALX+LOG(ABS(S)/FM))
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1 , S)
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C
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IF (R9GMIC .EQ. 0.0 .AND. S .EQ. 0.0) CALL XERMSG ('SLATEC',
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+ 'R9GMIC', 'RESULT UNDERFLOWS', 1, 1)
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RETURN
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C
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END
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