amos/dgamln.f

   1       DOUBLE PRECISION FUNCTION DGAMLN(Z,IERR)
   2 C***BEGIN PROLOGUE  DGAMLN
   3 C***DATE WRITTEN   830501   (YYMMDD)
   4 C***REVISION DATE  830501   (YYMMDD)
   5 C***CATEGORY NO.  B5F
   6 C***KEYWORDS  GAMMA FUNCTION,LOGARITHM OF GAMMA FUNCTION
   7 C***AUTHOR  AMOS, DONALD E., SANDIA NATIONAL LABORATORIES
   8 C***PURPOSE  TO COMPUTE THE LOGARITHM OF THE GAMMA FUNCTION
   9 C***DESCRIPTION
  10 C
  11 C               **** A DOUBLE PRECISION ROUTINE ****
  12 C         DGAMLN COMPUTES THE NATURAL LOG OF THE GAMMA FUNCTION FOR
  13 C         Z.GT.0.  THE ASYMPTOTIC EXPANSION IS USED TO GENERATE VALUES
  14 C         GREATER THAN ZMIN WHICH ARE ADJUSTED BY THE RECURSION
  15 C         G(Z+1)=Z*G(Z) FOR Z.LE.ZMIN.  THE FUNCTION WAS MADE AS
  16 C         PORTABLE AS POSSIBLE BY COMPUTIMG ZMIN FROM THE NUMBER OF BASE
  17 C         10 DIGITS IN A WORD, RLN=AMAX1(-ALOG10(R1MACH(4)),0.5E-18)
  18 C         LIMITED TO 18 DIGITS OF (RELATIVE) ACCURACY.
  19 C
  20 C         SINCE INTEGER ARGUMENTS ARE COMMON, A TABLE LOOK UP ON 100
  21 C         VALUES IS USED FOR SPEED OF EXECUTION.
  22 C
  23 C     DESCRIPTION OF ARGUMENTS
  24 C
  25 C         INPUT      Z IS D0UBLE PRECISION
  26 C           Z      - ARGUMENT, Z.GT.0.0D0
  27 C
  28 C         OUTPUT      DGAMLN IS DOUBLE PRECISION
  29 C           DGAMLN  - NATURAL LOG OF THE GAMMA FUNCTION AT Z.NE.0.0D0
  30 C           IERR    - ERROR FLAG
  31 C                     IERR=0, NORMAL RETURN, COMPUTATION COMPLETED
  32 C                     IERR=1, Z.LE.0.0D0,    NO COMPUTATION
  33 C
  34 C
  35 C***REFERENCES  COMPUTATION OF BESSEL FUNCTIONS OF COMPLEX ARGUMENT
  36 C                 BY D. E. AMOS, SAND83-0083, MAY, 1983.
  37 C***ROUTINES CALLED  I1MACH,D1MACH
  38 C***END PROLOGUE  DGAMLN
  39       DOUBLE PRECISION CF, CON, FLN, FZ, GLN, RLN, S, TLG, TRM, TST,
  40      * T1, WDTOL, Z, ZDMY, ZINC, ZM, ZMIN, ZP, ZSQ, D1MACH
  41       INTEGER I, IERR, I1M, K, MZ, NZ, I1MACH
  42       DIMENSION CF(22), GLN(100)
  43 C           LNGAMMA(N), N=1,100
  44       DATA GLN(1), GLN(2), GLN(3), GLN(4), GLN(5), GLN(6), GLN(7),
  45      1     GLN(8), GLN(9), GLN(10), GLN(11), GLN(12), GLN(13), GLN(14),
  46      2     GLN(15), GLN(16), GLN(17), GLN(18), GLN(19), GLN(20),
  47      3     GLN(21), GLN(22)/
  48      4     0.00000000000000000D+00,     0.00000000000000000D+00,
  49      5     6.93147180559945309D-01,     1.79175946922805500D+00,
  50      6     3.17805383034794562D+00,     4.78749174278204599D+00,
  51      7     6.57925121201010100D+00,     8.52516136106541430D+00,
  52      8     1.06046029027452502D+01,     1.28018274800814696D+01,
  53      9     1.51044125730755153D+01,     1.75023078458738858D+01,
  54      A     1.99872144956618861D+01,     2.25521638531234229D+01,
  55      B     2.51912211827386815D+01,     2.78992713838408916D+01,
  56      C     3.06718601060806728D+01,     3.35050734501368889D+01,
  57      D     3.63954452080330536D+01,     3.93398841871994940D+01,
  58      E     4.23356164607534850D+01,     4.53801388984769080D+01/
  59       DATA GLN(23), GLN(24), GLN(25), GLN(26), GLN(27), GLN(28),
  60      1     GLN(29), GLN(30), GLN(31), GLN(32), GLN(33), GLN(34),
  61      2     GLN(35), GLN(36), GLN(37), GLN(38), GLN(39), GLN(40),
  62      3     GLN(41), GLN(42), GLN(43), GLN(44)/
  63      4     4.84711813518352239D+01,     5.16066755677643736D+01,
  64      5     5.47847293981123192D+01,     5.80036052229805199D+01,
  65      6     6.12617017610020020D+01,     6.45575386270063311D+01,
  66      7     6.78897431371815350D+01,     7.12570389671680090D+01,
  67      8     7.46582363488301644D+01,     7.80922235533153106D+01,
  68      9     8.15579594561150372D+01,     8.50544670175815174D+01,
  69      A     8.85808275421976788D+01,     9.21361756036870925D+01,
  70      B     9.57196945421432025D+01,     9.93306124547874269D+01,
  71      C     1.02968198614513813D+02,     1.06631760260643459D+02,
  72      D     1.10320639714757395D+02,     1.14034211781461703D+02,
  73      E     1.17771881399745072D+02,     1.21533081515438634D+02/
  74       DATA GLN(45), GLN(46), GLN(47), GLN(48), GLN(49), GLN(50),
  75      1     GLN(51), GLN(52), GLN(53), GLN(54), GLN(55), GLN(56),
  76      2     GLN(57), GLN(58), GLN(59), GLN(60), GLN(61), GLN(62),
  77      3     GLN(63), GLN(64), GLN(65), GLN(66)/
  78      4     1.25317271149356895D+02,     1.29123933639127215D+02,
  79      5     1.32952575035616310D+02,     1.36802722637326368D+02,
  80      6     1.40673923648234259D+02,     1.44565743946344886D+02,
  81      7     1.48477766951773032D+02,     1.52409592584497358D+02,
  82      8     1.56360836303078785D+02,     1.60331128216630907D+02,
  83      9     1.64320112263195181D+02,     1.68327445448427652D+02,
  84      A     1.72352797139162802D+02,     1.76395848406997352D+02,
  85      B     1.80456291417543771D+02,     1.84533828861449491D+02,
  86      C     1.88628173423671591D+02,     1.92739047287844902D+02,
  87      D     1.96866181672889994D+02,     2.01009316399281527D+02,
  88      E     2.05168199482641199D+02,     2.09342586752536836D+02/
  89       DATA GLN(67), GLN(68), GLN(69), GLN(70), GLN(71), GLN(72),
  90      1     GLN(73), GLN(74), GLN(75), GLN(76), GLN(77), GLN(78),
  91      2     GLN(79), GLN(80), GLN(81), GLN(82), GLN(83), GLN(84),
  92      3     GLN(85), GLN(86), GLN(87), GLN(88)/
  93      4     2.13532241494563261D+02,     2.17736934113954227D+02,
  94      5     2.21956441819130334D+02,     2.26190548323727593D+02,
  95      6     2.30439043565776952D+02,     2.34701723442818268D+02,
  96      7     2.38978389561834323D+02,     2.43268849002982714D+02,
  97      8     2.47572914096186884D+02,     2.51890402209723194D+02,
  98      9     2.56221135550009525D+02,     2.60564940971863209D+02,
  99      A     2.64921649798552801D+02,     2.69291097651019823D+02,
 100      B     2.73673124285693704D+02,     2.78067573440366143D+02,
 101      C     2.82474292687630396D+02,     2.86893133295426994D+02,
 102      D     2.91323950094270308D+02,     2.95766601350760624D+02,
 103      E     3.00220948647014132D+02,     3.04686856765668715D+02/
 104       DATA GLN(89), GLN(90), GLN(91), GLN(92), GLN(93), GLN(94),
 105      1     GLN(95), GLN(96), GLN(97), GLN(98), GLN(99), GLN(100)/
 106      2     3.09164193580146922D+02,     3.13652829949879062D+02,
 107      3     3.18152639620209327D+02,     3.22663499126726177D+02,
 108      4     3.27185287703775217D+02,     3.31717887196928473D+02,
 109      5     3.36261181979198477D+02,     3.40815058870799018D+02,
 110      6     3.45379407062266854D+02,     3.49954118040770237D+02,
 111      7     3.54539085519440809D+02,     3.59134205369575399D+02/
 112 C             COEFFICIENTS OF ASYMPTOTIC EXPANSION
 113       DATA CF(1), CF(2), CF(3), CF(4), CF(5), CF(6), CF(7), CF(8),
 114      1     CF(9), CF(10), CF(11), CF(12), CF(13), CF(14), CF(15),
 115      2     CF(16), CF(17), CF(18), CF(19), CF(20), CF(21), CF(22)/
 116      3     8.33333333333333333D-02,    -2.77777777777777778D-03,
 117      4     7.93650793650793651D-04,    -5.95238095238095238D-04,
 118      5     8.41750841750841751D-04,    -1.91752691752691753D-03,
 119      6     6.41025641025641026D-03,    -2.95506535947712418D-02,
 120      7     1.79644372368830573D-01,    -1.39243221690590112D+00,
 121      8     1.34028640441683920D+01,    -1.56848284626002017D+02,
 122      9     2.19310333333333333D+03,    -3.61087712537249894D+04,
 123      A     6.91472268851313067D+05,    -1.52382215394074162D+07,
 124      B     3.82900751391414141D+08,    -1.08822660357843911D+10,
 125      C     3.47320283765002252D+11,    -1.23696021422692745D+13,
 126      D     4.88788064793079335D+14,    -2.13203339609193739D+16/
 127 C
 128 C             LN(2*PI)
 129       DATA CON                    /     1.83787706640934548D+00/
 130 C
 131 C***FIRST EXECUTABLE STATEMENT  DGAMLN
 132       IERR=0
 133       IF (Z.LE.0.0D0) GO TO 70
 134       IF (Z.GT.101.0D0) GO TO 10
 135       NZ = INT(SNGL(Z))
 136       FZ = Z - FLOAT(NZ)
 137       IF (FZ.GT.0.0D0) GO TO 10
 138       IF (NZ.GT.100) GO TO 10
 139       DGAMLN = GLN(NZ)
 140       RETURN
 141    10 CONTINUE
 142       WDTOL = D1MACH(4)
 143       WDTOL = DMAX1(WDTOL,0.5D-18)
 144       I1M = I1MACH(14)
 145       RLN = D1MACH(5)*FLOAT(I1M)
 146       FLN = DMIN1(RLN,20.0D0)
 147       FLN = DMAX1(FLN,3.0D0)
 148       FLN = FLN - 3.0D0
 149       ZM = 1.8000D0 + 0.3875D0*FLN
 150       MZ = INT(SNGL(ZM)) + 1
 151       ZMIN = FLOAT(MZ)
 152       ZDMY = Z
 153       ZINC = 0.0D0
 154       IF (Z.GE.ZMIN) GO TO 20
 155       ZINC = ZMIN - FLOAT(NZ)
 156       ZDMY = Z + ZINC
 157    20 CONTINUE
 158       ZP = 1.0D0/ZDMY
 159       T1 = CF(1)*ZP
 160       S = T1
 161       IF (ZP.LT.WDTOL) GO TO 40
 162       ZSQ = ZP*ZP
 163       TST = T1*WDTOL
 164       DO 30 K=2,22
 165         ZP = ZP*ZSQ
 166         TRM = CF(K)*ZP
 167         IF (DABS(TRM).LT.TST) GO TO 40
 168         S = S + TRM
 169    30 CONTINUE
 170    40 CONTINUE
 171       IF (ZINC.NE.0.0D0) GO TO 50
 172       TLG = DLOG(Z)
 173       DGAMLN = Z*(TLG-1.0D0) + 0.5D0*(CON-TLG) + S
 174       RETURN
 175    50 CONTINUE
 176       ZP = 1.0D0
 177       NZ = INT(SNGL(ZINC))
 178       DO 60 I=1,NZ
 179         ZP = ZP*(Z+FLOAT(I-1))
 180    60 CONTINUE
 181       TLG = DLOG(ZDMY)
 182       DGAMLN = ZDMY*(TLG-1.0D0) - DLOG(ZP) + 0.5D0*(CON-TLG) + S
 183       RETURN
 184 C
 185 C
 186    70 CONTINUE
 187       IERR=1
 188       RETURN
 189       END