GNU Octave: libcruft/amos/dgamln.f Source File

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00001       DOUBLE PRECISION FUNCTION DGAMLN(Z,IERR)
00002 C***BEGIN PROLOGUE  DGAMLN
00003 C***DATE WRITTEN   830501   (YYMMDD)
00004 C***REVISION DATE  830501   (YYMMDD)
00005 C***CATEGORY NO.  B5F
00006 C***KEYWORDS  GAMMA FUNCTION,LOGARITHM OF GAMMA FUNCTION
00007 C***AUTHOR  AMOS, DONALD E., SANDIA NATIONAL LABORATORIES
00008 C***PURPOSE  TO COMPUTE THE LOGARITHM OF THE GAMMA FUNCTION
00009 C***DESCRIPTION
00010 C
00011 C               **** A DOUBLE PRECISION ROUTINE ****
00012 C         DGAMLN COMPUTES THE NATURAL LOG OF THE GAMMA FUNCTION FOR
00013 C         Z.GT.0.  THE ASYMPTOTIC EXPANSION IS USED TO GENERATE VALUES
00014 C         GREATER THAN ZMIN WHICH ARE ADJUSTED BY THE RECURSION
00015 C         G(Z+1)=Z*G(Z) FOR Z.LE.ZMIN.  THE FUNCTION WAS MADE AS
00016 C         PORTABLE AS POSSIBLE BY COMPUTIMG ZMIN FROM THE NUMBER OF BASE
00017 C         10 DIGITS IN A WORD, RLN=AMAX1(-ALOG10(R1MACH(4)),0.5E-18)
00018 C         LIMITED TO 18 DIGITS OF (RELATIVE) ACCURACY.
00019 C
00020 C         SINCE INTEGER ARGUMENTS ARE COMMON, A TABLE LOOK UP ON 100
00021 C         VALUES IS USED FOR SPEED OF EXECUTION.
00022 C
00023 C     DESCRIPTION OF ARGUMENTS
00024 C
00025 C         INPUT      Z IS D0UBLE PRECISION
00026 C           Z      - ARGUMENT, Z.GT.0.0D0
00027 C
00028 C         OUTPUT      DGAMLN IS DOUBLE PRECISION
00029 C           DGAMLN  - NATURAL LOG OF THE GAMMA FUNCTION AT Z.NE.0.0D0
00030 C           IERR    - ERROR FLAG
00031 C                     IERR=0, NORMAL RETURN, COMPUTATION COMPLETED
00032 C                     IERR=1, Z.LE.0.0D0,    NO COMPUTATION
00033 C
00034 C
00035 C***REFERENCES  COMPUTATION OF BESSEL FUNCTIONS OF COMPLEX ARGUMENT
00036 C                 BY D. E. AMOS, SAND83-0083, MAY, 1983.
00037 C***ROUTINES CALLED  I1MACH,D1MACH
00038 C***END PROLOGUE  DGAMLN
00039       DOUBLE PRECISION CF, CON, FLN, FZ, GLN, RLN, S, TLG, TRM, TST,
00040      * T1, WDTOL, Z, ZDMY, ZINC, ZM, ZMIN, ZP, ZSQ, D1MACH
00041       INTEGER I, IERR, I1M, K, MZ, NZ, I1MACH
00042       DIMENSION CF(22), GLN(100)
00043 C           LNGAMMA(N), N=1,100
00044       DATA GLN(1), GLN(2), GLN(3), GLN(4), GLN(5), GLN(6), GLN(7),
00045      1     GLN(8), GLN(9), GLN(10), GLN(11), GLN(12), GLN(13), GLN(14),
00046      2     GLN(15), GLN(16), GLN(17), GLN(18), GLN(19), GLN(20),
00047      3     GLN(21), GLN(22)/
00048      4     0.00000000000000000D+00,     0.00000000000000000D+00,
00049      5     6.93147180559945309D-01,     1.79175946922805500D+00,
00050      6     3.17805383034794562D+00,     4.78749174278204599D+00,
00051      7     6.57925121201010100D+00,     8.52516136106541430D+00,
00052      8     1.06046029027452502D+01,     1.28018274800814696D+01,
00053      9     1.51044125730755153D+01,     1.75023078458738858D+01,
00054      A     1.99872144956618861D+01,     2.25521638531234229D+01,
00055      B     2.51912211827386815D+01,     2.78992713838408916D+01,
00056      C     3.06718601060806728D+01,     3.35050734501368889D+01,
00057      D     3.63954452080330536D+01,     3.93398841871994940D+01,
00058      E     4.23356164607534850D+01,     4.53801388984769080D+01/
00059       DATA GLN(23), GLN(24), GLN(25), GLN(26), GLN(27), GLN(28),
00060      1     GLN(29), GLN(30), GLN(31), GLN(32), GLN(33), GLN(34),
00061      2     GLN(35), GLN(36), GLN(37), GLN(38), GLN(39), GLN(40),
00062      3     GLN(41), GLN(42), GLN(43), GLN(44)/
00063      4     4.84711813518352239D+01,     5.16066755677643736D+01,
00064      5     5.47847293981123192D+01,     5.80036052229805199D+01,
00065      6     6.12617017610020020D+01,     6.45575386270063311D+01,
00066      7     6.78897431371815350D+01,     7.12570389671680090D+01,
00067      8     7.46582363488301644D+01,     7.80922235533153106D+01,
00068      9     8.15579594561150372D+01,     8.50544670175815174D+01,
00069      A     8.85808275421976788D+01,     9.21361756036870925D+01,
00070      B     9.57196945421432025D+01,     9.93306124547874269D+01,
00071      C     1.02968198614513813D+02,     1.06631760260643459D+02,
00072      D     1.10320639714757395D+02,     1.14034211781461703D+02,
00073      E     1.17771881399745072D+02,     1.21533081515438634D+02/
00074       DATA GLN(45), GLN(46), GLN(47), GLN(48), GLN(49), GLN(50),
00075      1     GLN(51), GLN(52), GLN(53), GLN(54), GLN(55), GLN(56),
00076      2     GLN(57), GLN(58), GLN(59), GLN(60), GLN(61), GLN(62),
00077      3     GLN(63), GLN(64), GLN(65), GLN(66)/
00078      4     1.25317271149356895D+02,     1.29123933639127215D+02,
00079      5     1.32952575035616310D+02,     1.36802722637326368D+02,
00080      6     1.40673923648234259D+02,     1.44565743946344886D+02,
00081      7     1.48477766951773032D+02,     1.52409592584497358D+02,
00082      8     1.56360836303078785D+02,     1.60331128216630907D+02,
00083      9     1.64320112263195181D+02,     1.68327445448427652D+02,
00084      A     1.72352797139162802D+02,     1.76395848406997352D+02,
00085      B     1.80456291417543771D+02,     1.84533828861449491D+02,
00086      C     1.88628173423671591D+02,     1.92739047287844902D+02,
00087      D     1.96866181672889994D+02,     2.01009316399281527D+02,
00088      E     2.05168199482641199D+02,     2.09342586752536836D+02/
00089       DATA GLN(67), GLN(68), GLN(69), GLN(70), GLN(71), GLN(72),
00090      1     GLN(73), GLN(74), GLN(75), GLN(76), GLN(77), GLN(78),
00091      2     GLN(79), GLN(80), GLN(81), GLN(82), GLN(83), GLN(84),
00092      3     GLN(85), GLN(86), GLN(87), GLN(88)/
00093      4     2.13532241494563261D+02,     2.17736934113954227D+02,
00094      5     2.21956441819130334D+02,     2.26190548323727593D+02,
00095      6     2.30439043565776952D+02,     2.34701723442818268D+02,
00096      7     2.38978389561834323D+02,     2.43268849002982714D+02,
00097      8     2.47572914096186884D+02,     2.51890402209723194D+02,
00098      9     2.56221135550009525D+02,     2.60564940971863209D+02,
00099      A     2.64921649798552801D+02,     2.69291097651019823D+02,
00100      B     2.73673124285693704D+02,     2.78067573440366143D+02,
00101      C     2.82474292687630396D+02,     2.86893133295426994D+02,
00102      D     2.91323950094270308D+02,     2.95766601350760624D+02,
00103      E     3.00220948647014132D+02,     3.04686856765668715D+02/
00104       DATA GLN(89), GLN(90), GLN(91), GLN(92), GLN(93), GLN(94),
00105      1     GLN(95), GLN(96), GLN(97), GLN(98), GLN(99), GLN(100)/
00106      2     3.09164193580146922D+02,     3.13652829949879062D+02,
00107      3     3.18152639620209327D+02,     3.22663499126726177D+02,
00108      4     3.27185287703775217D+02,     3.31717887196928473D+02,
00109      5     3.36261181979198477D+02,     3.40815058870799018D+02,
00110      6     3.45379407062266854D+02,     3.49954118040770237D+02,
00111      7     3.54539085519440809D+02,     3.59134205369575399D+02/
00112 C             COEFFICIENTS OF ASYMPTOTIC EXPANSION
00113       DATA CF(1), CF(2), CF(3), CF(4), CF(5), CF(6), CF(7), CF(8),
00114      1     CF(9), CF(10), CF(11), CF(12), CF(13), CF(14), CF(15),
00115      2     CF(16), CF(17), CF(18), CF(19), CF(20), CF(21), CF(22)/
00116      3     8.33333333333333333D-02,    -2.77777777777777778D-03,
00117      4     7.93650793650793651D-04,    -5.95238095238095238D-04,
00118      5     8.41750841750841751D-04,    -1.91752691752691753D-03,
00119      6     6.41025641025641026D-03,    -2.95506535947712418D-02,
00120      7     1.79644372368830573D-01,    -1.39243221690590112D+00,
00121      8     1.34028640441683920D+01,    -1.56848284626002017D+02,
00122      9     2.19310333333333333D+03,    -3.61087712537249894D+04,
00123      A     6.91472268851313067D+05,    -1.52382215394074162D+07,
00124      B     3.82900751391414141D+08,    -1.08822660357843911D+10,
00125      C     3.47320283765002252D+11,    -1.23696021422692745D+13,
00126      D     4.88788064793079335D+14,    -2.13203339609193739D+16/
00127 C
00128 C             LN(2*PI)
00129       DATA CON                    /     1.83787706640934548D+00/
00130 C
00131 C***FIRST EXECUTABLE STATEMENT  DGAMLN
00132       IERR=0
00133       IF (Z.LE.0.0D0) GO TO 70
00134       IF (Z.GT.101.0D0) GO TO 10
00135       NZ = INT(SNGL(Z))
00136       FZ = Z - FLOAT(NZ)
00137       IF (FZ.GT.0.0D0) GO TO 10
00138       IF (NZ.GT.100) GO TO 10
00139       DGAMLN = GLN(NZ)
00140       RETURN
00141    10 CONTINUE
00142       WDTOL = D1MACH(4)
00143       WDTOL = DMAX1(WDTOL,0.5D-18)
00144       I1M = I1MACH(14)
00145       RLN = D1MACH(5)*FLOAT(I1M)
00146       FLN = DMIN1(RLN,20.0D0)
00147       FLN = DMAX1(FLN,3.0D0)
00148       FLN = FLN - 3.0D0
00149       ZM = 1.8000D0 + 0.3875D0*FLN
00150       MZ = INT(SNGL(ZM)) + 1
00151       ZMIN = FLOAT(MZ)
00152       ZDMY = Z
00153       ZINC = 0.0D0
00154       IF (Z.GE.ZMIN) GO TO 20
00155       ZINC = ZMIN - FLOAT(NZ)
00156       ZDMY = Z + ZINC
00157    20 CONTINUE
00158       ZP = 1.0D0/ZDMY
00159       T1 = CF(1)*ZP
00160       S = T1
00161       IF (ZP.LT.WDTOL) GO TO 40
00162       ZSQ = ZP*ZP
00163       TST = T1*WDTOL
00164       DO 30 K=2,22
00165         ZP = ZP*ZSQ
00166         TRM = CF(K)*ZP
00167         IF (DABS(TRM).LT.TST) GO TO 40
00168         S = S + TRM
00169    30 CONTINUE
00170    40 CONTINUE
00171       IF (ZINC.NE.0.0D0) GO TO 50
00172       TLG = DLOG(Z)
00173       DGAMLN = Z*(TLG-1.0D0) + 0.5D0*(CON-TLG) + S
00174       RETURN
00175    50 CONTINUE
00176       ZP = 1.0D0
00177       NZ = INT(SNGL(ZINC))
00178       DO 60 I=1,NZ
00179         ZP = ZP*(Z+FLOAT(I-1))
00180    60 CONTINUE
00181       TLG = DLOG(ZDMY)
00182       DGAMLN = ZDMY*(TLG-1.0D0) - DLOG(ZP) + 0.5D0*(CON-TLG) + S
00183       RETURN
00184 C
00185 C
00186    70 CONTINUE
00187       IERR=1
00188       RETURN
00189       END