gamln.f
198 lines
| 8.4 KiB
| text/x-fortran
|
FortranFixedLexer
| r1601 | *DECK GAMLN | |||
| REAL FUNCTION GAMLN (Z, IERR) | ||||
| C***BEGIN PROLOGUE GAMLN | ||||
| C***SUBSIDIARY | ||||
| C***PURPOSE Compute the logarithm of the Gamma function | ||||
| C***LIBRARY SLATEC | ||||
| C***CATEGORY C7A | ||||
| C***TYPE SINGLE PRECISION (GAMLN-S, DGAMLN-D) | ||||
| C***KEYWORDS LOGARITHM OF GAMMA FUNCTION | ||||
| C***AUTHOR Amos, D. E., (SNL) | ||||
| C***DESCRIPTION | ||||
| C | ||||
| C GAMLN COMPUTES THE NATURAL LOG OF THE GAMMA FUNCTION FOR | ||||
| C Z.GT.0. THE ASYMPTOTIC EXPANSION IS USED TO GENERATE VALUES | ||||
| C GREATER THAN ZMIN WHICH ARE ADJUSTED BY THE RECURSION | ||||
| C G(Z+1)=Z*G(Z) FOR Z.LE.ZMIN. THE FUNCTION WAS MADE AS | ||||
| C PORTABLE AS POSSIBLE BY COMPUTING ZMIN FROM THE NUMBER OF BASE | ||||
| C 10 DIGITS IN A WORD, RLN=MAX(-ALOG10(R1MACH(4)),0.5E-18) | ||||
| C LIMITED TO 18 DIGITS OF (RELATIVE) ACCURACY. | ||||
| C | ||||
| C SINCE INTEGER ARGUMENTS ARE COMMON, A TABLE LOOK UP ON 100 | ||||
| C VALUES IS USED FOR SPEED OF EXECUTION. | ||||
| C | ||||
| C DESCRIPTION OF ARGUMENTS | ||||
| C | ||||
| C INPUT | ||||
| C Z - REAL ARGUMENT, Z.GT.0.0E0 | ||||
| C | ||||
| C OUTPUT | ||||
| C GAMLN - NATURAL LOG OF THE GAMMA FUNCTION AT Z | ||||
| C IERR - ERROR FLAG | ||||
| C IERR=0, NORMAL RETURN, COMPUTATION COMPLETED | ||||
| C IERR=1, Z.LE.0.0E0, NO COMPUTATION | ||||
| C | ||||
| C***REFERENCES COMPUTATION OF BESSEL FUNCTIONS OF COMPLEX ARGUMENT | ||||
| C BY D. E. AMOS, SAND83-0083, MAY, 1983. | ||||
| C***ROUTINES CALLED I1MACH, R1MACH | ||||
| C***REVISION HISTORY (YYMMDD) | ||||
| C 830501 DATE WRITTEN | ||||
| C 830501 REVISION DATE from Version 3.2 | ||||
| C 910415 Prologue converted to Version 4.0 format. (BAB) | ||||
| C 920128 Category corrected. (WRB) | ||||
| C 921215 GAMLN defined for Z negative. (WRB) | ||||
| C***END PROLOGUE GAMLN | ||||
| C | ||||
| INTEGER I, I1M, K, MZ, NZ, IERR, I1MACH | ||||
| REAL CF, CON, FLN, FZ, GLN, RLN, S, TLG, TRM, TST, T1, WDTOL, Z, | ||||
| * ZDMY, ZINC, ZM, ZMIN, ZP, ZSQ | ||||
| REAL R1MACH | ||||
| DIMENSION CF(22), GLN(100) | ||||
| C LNGAMMA(N), N=1,100 | ||||
| DATA GLN(1), GLN(2), GLN(3), GLN(4), GLN(5), GLN(6), GLN(7), | ||||
| 1 GLN(8), GLN(9), GLN(10), GLN(11), GLN(12), GLN(13), GLN(14), | ||||
| 2 GLN(15), GLN(16), GLN(17), GLN(18), GLN(19), GLN(20), | ||||
| 3 GLN(21), GLN(22)/ | ||||
| 4 0.00000000000000000E+00, 0.00000000000000000E+00, | ||||
| 5 6.93147180559945309E-01, 1.79175946922805500E+00, | ||||
| 6 3.17805383034794562E+00, 4.78749174278204599E+00, | ||||
| 7 6.57925121201010100E+00, 8.52516136106541430E+00, | ||||
| 8 1.06046029027452502E+01, 1.28018274800814696E+01, | ||||
| 9 1.51044125730755153E+01, 1.75023078458738858E+01, | ||||
| A 1.99872144956618861E+01, 2.25521638531234229E+01, | ||||
| B 2.51912211827386815E+01, 2.78992713838408916E+01, | ||||
| C 3.06718601060806728E+01, 3.35050734501368889E+01, | ||||
| D 3.63954452080330536E+01, 3.93398841871994940E+01, | ||||
| E 4.23356164607534850E+01, 4.53801388984769080E+01/ | ||||
| DATA GLN(23), GLN(24), GLN(25), GLN(26), GLN(27), GLN(28), | ||||
| 1 GLN(29), GLN(30), GLN(31), GLN(32), GLN(33), GLN(34), | ||||
| 2 GLN(35), GLN(36), GLN(37), GLN(38), GLN(39), GLN(40), | ||||
| 3 GLN(41), GLN(42), GLN(43), GLN(44)/ | ||||
| 4 4.84711813518352239E+01, 5.16066755677643736E+01, | ||||
| 5 5.47847293981123192E+01, 5.80036052229805199E+01, | ||||
| 6 6.12617017610020020E+01, 6.45575386270063311E+01, | ||||
| 7 6.78897431371815350E+01, 7.12570389671680090E+01, | ||||
| 8 7.46582363488301644E+01, 7.80922235533153106E+01, | ||||
| 9 8.15579594561150372E+01, 8.50544670175815174E+01, | ||||
| A 8.85808275421976788E+01, 9.21361756036870925E+01, | ||||
| B 9.57196945421432025E+01, 9.93306124547874269E+01, | ||||
| C 1.02968198614513813E+02, 1.06631760260643459E+02, | ||||
| D 1.10320639714757395E+02, 1.14034211781461703E+02, | ||||
| E 1.17771881399745072E+02, 1.21533081515438634E+02/ | ||||
| DATA GLN(45), GLN(46), GLN(47), GLN(48), GLN(49), GLN(50), | ||||
| 1 GLN(51), GLN(52), GLN(53), GLN(54), GLN(55), GLN(56), | ||||
| 2 GLN(57), GLN(58), GLN(59), GLN(60), GLN(61), GLN(62), | ||||
| 3 GLN(63), GLN(64), GLN(65), GLN(66)/ | ||||
| 4 1.25317271149356895E+02, 1.29123933639127215E+02, | ||||
| 5 1.32952575035616310E+02, 1.36802722637326368E+02, | ||||
| 6 1.40673923648234259E+02, 1.44565743946344886E+02, | ||||
| 7 1.48477766951773032E+02, 1.52409592584497358E+02, | ||||
| 8 1.56360836303078785E+02, 1.60331128216630907E+02, | ||||
| 9 1.64320112263195181E+02, 1.68327445448427652E+02, | ||||
| A 1.72352797139162802E+02, 1.76395848406997352E+02, | ||||
| B 1.80456291417543771E+02, 1.84533828861449491E+02, | ||||
| C 1.88628173423671591E+02, 1.92739047287844902E+02, | ||||
| D 1.96866181672889994E+02, 2.01009316399281527E+02, | ||||
| E 2.05168199482641199E+02, 2.09342586752536836E+02/ | ||||
| DATA GLN(67), GLN(68), GLN(69), GLN(70), GLN(71), GLN(72), | ||||
| 1 GLN(73), GLN(74), GLN(75), GLN(76), GLN(77), GLN(78), | ||||
| 2 GLN(79), GLN(80), GLN(81), GLN(82), GLN(83), GLN(84), | ||||
| 3 GLN(85), GLN(86), GLN(87), GLN(88)/ | ||||
| 4 2.13532241494563261E+02, 2.17736934113954227E+02, | ||||
| 5 2.21956441819130334E+02, 2.26190548323727593E+02, | ||||
| 6 2.30439043565776952E+02, 2.34701723442818268E+02, | ||||
| 7 2.38978389561834323E+02, 2.43268849002982714E+02, | ||||
| 8 2.47572914096186884E+02, 2.51890402209723194E+02, | ||||
| 9 2.56221135550009525E+02, 2.60564940971863209E+02, | ||||
| A 2.64921649798552801E+02, 2.69291097651019823E+02, | ||||
| B 2.73673124285693704E+02, 2.78067573440366143E+02, | ||||
| C 2.82474292687630396E+02, 2.86893133295426994E+02, | ||||
| D 2.91323950094270308E+02, 2.95766601350760624E+02, | ||||
| E 3.00220948647014132E+02, 3.04686856765668715E+02/ | ||||
| DATA GLN(89), GLN(90), GLN(91), GLN(92), GLN(93), GLN(94), | ||||
| 1 GLN(95), GLN(96), GLN(97), GLN(98), GLN(99), GLN(100)/ | ||||
| 2 3.09164193580146922E+02, 3.13652829949879062E+02, | ||||
| 3 3.18152639620209327E+02, 3.22663499126726177E+02, | ||||
| 4 3.27185287703775217E+02, 3.31717887196928473E+02, | ||||
| 5 3.36261181979198477E+02, 3.40815058870799018E+02, | ||||
| 6 3.45379407062266854E+02, 3.49954118040770237E+02, | ||||
| 7 3.54539085519440809E+02, 3.59134205369575399E+02/ | ||||
| C COEFFICIENTS OF ASYMPTOTIC EXPANSION | ||||
| DATA CF(1), CF(2), CF(3), CF(4), CF(5), CF(6), CF(7), CF(8), | ||||
| 1 CF(9), CF(10), CF(11), CF(12), CF(13), CF(14), CF(15), | ||||
| 2 CF(16), CF(17), CF(18), CF(19), CF(20), CF(21), CF(22)/ | ||||
| 3 8.33333333333333333E-02, -2.77777777777777778E-03, | ||||
| 4 7.93650793650793651E-04, -5.95238095238095238E-04, | ||||
| 5 8.41750841750841751E-04, -1.91752691752691753E-03, | ||||
| 6 6.41025641025641026E-03, -2.95506535947712418E-02, | ||||
| 7 1.79644372368830573E-01, -1.39243221690590112E+00, | ||||
| 8 1.34028640441683920E+01, -1.56848284626002017E+02, | ||||
| 9 2.19310333333333333E+03, -3.61087712537249894E+04, | ||||
| A 6.91472268851313067E+05, -1.52382215394074162E+07, | ||||
| B 3.82900751391414141E+08, -1.08822660357843911E+10, | ||||
| C 3.47320283765002252E+11, -1.23696021422692745E+13, | ||||
| D 4.88788064793079335E+14, -2.13203339609193739E+16/ | ||||
| C | ||||
| C LN(2*PI) | ||||
| DATA CON / 1.83787706640934548E+00/ | ||||
| C | ||||
| C***FIRST EXECUTABLE STATEMENT GAMLN | ||||
| IERR=0 | ||||
| IF (Z.LE.0.0E0) GO TO 70 | ||||
| IF (Z.GT.101.0E0) GO TO 10 | ||||
| NZ = Z | ||||
| FZ = Z - NZ | ||||
| IF (FZ.GT.0.0E0) GO TO 10 | ||||
| IF (NZ.GT.100) GO TO 10 | ||||
| GAMLN = GLN(NZ) | ||||
| RETURN | ||||
| 10 CONTINUE | ||||
| WDTOL = R1MACH(4) | ||||
| WDTOL = MAX(WDTOL,0.5E-18) | ||||
| I1M = I1MACH(11) | ||||
| RLN = R1MACH(5)*I1M | ||||
| FLN = MIN(RLN,20.0E0) | ||||
| FLN = MAX(FLN,3.0E0) | ||||
| FLN = FLN - 3.0E0 | ||||
| ZM = 1.8000E0 + 0.3875E0*FLN | ||||
| MZ = ZM + 1 | ||||
| ZMIN = MZ | ||||
| ZDMY = Z | ||||
| ZINC = 0.0E0 | ||||
| IF (Z.GE.ZMIN) GO TO 20 | ||||
| ZINC = ZMIN - NZ | ||||
| ZDMY = Z + ZINC | ||||
| 20 CONTINUE | ||||
| ZP = 1.0E0/ZDMY | ||||
| T1 = CF(1)*ZP | ||||
| S = T1 | ||||
| IF (ZP.LT.WDTOL) GO TO 40 | ||||
| ZSQ = ZP*ZP | ||||
| TST = T1*WDTOL | ||||
| DO 30 K=2,22 | ||||
| ZP = ZP*ZSQ | ||||
| TRM = CF(K)*ZP | ||||
| IF (ABS(TRM).LT.TST) GO TO 40 | ||||
| S = S + TRM | ||||
| 30 CONTINUE | ||||
| 40 CONTINUE | ||||
| IF (ZINC.NE.0.0E0) GO TO 50 | ||||
| TLG = ALOG(Z) | ||||
| GAMLN = Z*(TLG-1.0E0) + 0.5E0*(CON-TLG) + S | ||||
| RETURN | ||||
| 50 CONTINUE | ||||
| ZP = 1.0E0 | ||||
| NZ = ZINC | ||||
| DO 60 I=1,NZ | ||||
| ZP = ZP*(Z+(I-1)) | ||||
| 60 CONTINUE | ||||
| TLG = ALOG(ZDMY) | ||||
| GAMLN = ZDMY*(TLG-1.0E0) - ALOG(ZP) + 0.5E0*(CON-TLG) + S | ||||
| RETURN | ||||
| C | ||||
| C | ||||
| 70 CONTINUE | ||||
| GAMLN = R1MACH(2) | ||||
| IERR=1 | ||||
| RETURN | ||||
| END | ||||
