*DECK ALBETA FUNCTION ALBETA (A, B) C***BEGIN PROLOGUE ALBETA C***PURPOSE Compute the natural logarithm of the complete Beta C function. C***LIBRARY SLATEC (FNLIB) C***CATEGORY C7B C***TYPE SINGLE PRECISION (ALBETA-S, DLBETA-D, CLBETA-C) C***KEYWORDS FNLIB, LOGARITHM OF THE COMPLETE BETA FUNCTION, C SPECIAL FUNCTIONS C***AUTHOR Fullerton, W., (LANL) C***DESCRIPTION C C ALBETA computes the natural log of the complete beta function. C C Input Parameters: C A real and positive C B real and positive C C***REFERENCES (NONE) C***ROUTINES CALLED ALNGAM, ALNREL, GAMMA, R9LGMC, XERMSG C***REVISION HISTORY (YYMMDD) C 770701 DATE WRITTEN C 890531 Changed all specific intrinsics to generic. (WRB) C 890531 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 900326 Removed duplicate information from DESCRIPTION section. C (WRB) C 900727 Added EXTERNAL statement. (WRB) C***END PROLOGUE ALBETA EXTERNAL GAMMA SAVE SQ2PIL DATA SQ2PIL / 0.9189385332 0467274 E0 / C***FIRST EXECUTABLE STATEMENT ALBETA P = MIN (A, B) Q = MAX (A, B) C IF (P .LE. 0.0) CALL XERMSG ('SLATEC', 'ALBETA', + 'BOTH ARGUMENTS MUST BE GT ZERO', 1, 2) IF (P.GE.10.0) GO TO 30 IF (Q.GE.10.0) GO TO 20 C C P AND Q ARE SMALL. C ALBETA = LOG(GAMMA(P) * (GAMMA(Q)/GAMMA(P+Q)) ) RETURN C C P IS SMALL, BUT Q IS BIG. C 20 CORR = R9LGMC(Q) - R9LGMC(P+Q) ALBETA = ALNGAM(P) + CORR + P - P*LOG(P+Q) + 1 (Q-0.5)*ALNREL(-P/(P+Q)) RETURN C C P AND Q ARE BIG. C 30 CORR = R9LGMC(P) + R9LGMC(Q) - R9LGMC(P+Q) ALBETA = -0.5*LOG(Q) + SQ2PIL + CORR + (P-0.5)*LOG(P/(P+Q)) 1 + Q*ALNREL(-P/(P+Q)) RETURN C END