dc/d2f/d9gmit_8f_source.html

 *DECK D9GMIT

       DOUBLE PRECISION FUNCTION d9gmit (A, X, ALGAP1, SGNGAM, ALX)

 C***BEGIN PROLOGUE  D9GMIT

 C***SUBSIDIARY

 C***PURPOSE  Compute Tricomi's incomplete Gamma function for small

 C            arguments.

 C***LIBRARY   SLATEC (FNLIB)

 C***CATEGORY  C7E

 C***TYPE      DOUBLE PRECISION (R9GMIT-S, D9GMIT-D)

 C***KEYWORDS  COMPLEMENTARY INCOMPLETE GAMMA FUNCTION, FNLIB, SMALL X,

 C             SPECIAL FUNCTIONS, TRICOMI

 C***AUTHOR  Fullerton, W., (LANL)

 C***DESCRIPTION

 C

 C Compute Tricomi's incomplete gamma function for small X.

 C

 C***REFERENCES  (NONE)

 C***ROUTINES CALLED  D1MACH, DLNGAM, XERMSG

 C***REVISION HISTORY  (YYMMDD)

 C   770701  DATE WRITTEN

 C   890531  Changed all specific intrinsics to generic.  (WRB)

 C   890911  Removed unnecessary intrinsics.  (WRB)

 C   890911  REVISION DATE from Version 3.2

 C   891214  Prologue converted to Version 4.0 format.  (BAB)

 C   900315  CALLs to XERROR changed to CALLs to XERMSG.  (THJ)

 C   900720  Routine changed from user-callable to subsidiary.  (WRB)

 C***END PROLOGUE  D9GMIT

       DOUBLE PRECISION A, X, ALGAP1, SGNGAM, ALX, AE, AEPS, ALGS, ALG2,

      1  bot, eps, fk, s, sgng2, t, te, d1mach, dlngam

       LOGICAL FIRST

       SAVE eps, bot, first

       DATA first /.true./

 C***FIRST EXECUTABLE STATEMENT  D9GMIT

       IF (first) THEN

          eps = 0.5d0*d1mach(3)

          bot = log(d1mach(1))

       ENDIF

       first = .false.

 C

       IF (x .LE. 0.d0) CALL xermsg('SLATEC', 'D9GMIT',

      +   'X SHOULD BE GT 0', 1, 2)

 C

       ma = a + 0.5d0

       IF (a.LT.0.d0) ma = a - 0.5d0

       aeps = a - ma

 C

       ae = a

       IF (a.LT.(-0.5d0)) ae = aeps

 C

       t = 1.d0

       te = ae

       s = t

       DO 20 k=1,200

         fk = k

         te = -x*te/fk

         t = te/(ae+fk)

         s = s + t

         IF (abs(t).LT.eps*abs(s)) go to 30

  20   CONTINUE

       CALL xermsg('SLATEC', 'D9GMIT',

      +   'NO CONVERGENCE IN 200 TERMS OF TAYLOR-S SERIES', 2, 2)

 C

  30   IF (a.GE.(-0.5d0)) algs = -algap1 + log(s)

       IF (a.GE.(-0.5d0)) go to 60

 C

       algs = -dlngam(1.d0+aeps) + log(s)

       s = 1.0d0

       m = -ma - 1

       IF (m.EQ.0) go to 50

       t = 1.0d0

       DO 40 k=1,m

         t = x*t/(aeps-(m+1-k))

         s = s + t

         IF (abs(t).LT.eps*abs(s)) go to 50

  40   CONTINUE

 C

  50   d9gmit = 0.0d0

       algs = -ma*log(x) + algs

       IF (s.EQ.0.d0 .OR. aeps.EQ.0.d0) go to 60

 C

       sgng2 = sgngam * sign(1.0d0, s)

       alg2 = -x - algap1 + log(abs(s))

 C

       IF (alg2.GT.bot) d9gmit = sgng2 * exp(alg2)

       IF (algs.GT.bot) d9gmit = d9gmit + exp(algs)

       RETURN

 C

  60   d9gmit = exp(algs)

       RETURN

 C

       END

log
OCTAVE_EXPORT octave_value_list or N dimensional array whose elements are all equal to the base of natural logarithms The constant ex $e satisfies the equation log(e)

dlngam
double precision function dlngam(X)
Definition: dlngam.f:2

d9gmit
double precision function d9gmit(A, X, ALGAP1, SGNGAM, ALX)
Definition: d9gmit.f:2

base_det::exp
int exp(void) const
Definition: DET.h:66

false
is false
Definition: cellfun.cc:398

to
may be zero for pure relative error test tem the relative tolerance must be greater than or equal to
Definition: Quad-opts.cc:233

xermsg
subroutine xermsg(LIBRAR, SUBROU, MESSG, NERR, LEVEL)
Definition: xermsg.f:2

abs
OCTAVE_EXPORT octave_value_list return the value of the option it must match the dimension of the state and the relative tolerance must also be a vector of the same length tem it must match the dimension of the state and the absolute tolerance must also be a vector of the same length The local error test applied at each integration step is xample roup abs(local error in x(i))<