DQNG(3)

SYNOPSIS
SUBROUTINE DQNG (F, A, B, EPSABS, EPSREL, RESULT, ABSERR, NEVAL, + IER)

NAME
dqng - The routine calculates an approximation result to a given definite integral I = integral of F over (A,B), hopefully satisfying following claim for accuracy ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

LIBRARY
SLATEC (QUADPACK)

CATEGORY
H2A1A1

TYPE
DOUBLE PRECISION (QNG-S, DQNG-D)

KEYWORDS
AUTOMATIC INTEGRATOR, GAUSS-KRONROD(PATTERSON) RULES, NONADAPTIVE, QUADPACK, QUADRATURE, SMOOTH INTEGRAND

AUTHOR
Piessens, Robert Applied Mathematics and Programming Division K. U. Leuven de Doncker, Elise Applied Mathematics and Programming Division K. U. Leuven

DESCRIPTION
NON-ADAPTIVE INTEGRATION STANDARD FORTRAN SUBROUTINE DOUBLE PRECISION VERSION F - Double precision Function subprogram defining the integrand function F(X). The actual name for F needs to be declared E X T E R N A L in the driver program. A - Double precision Lower limit of integration B - Double precision Upper limit of integration EPSABS - Double precision Absolute accuracy requested EPSREL - Double precision Relative accuracy requested If EPSABS.LE.0 And EPSREL.LT.MAX(50*REL.MACH.ACC.,0.5D-28), The routine will end with IER = 6. ON RETURN RESULT - Double precision Approximation to the integral I Result is obtained by applying the 21-POINT GAUSS-KRONROD RULE (RES21) obtained by optimal addition of abscissae to the 10-POINT GAUSS RULE (RES10), or by applying the 43-POINT RULE (RES43) obtained by optimal addition of abscissae to the 21-POINT GAUSS-KRONROD RULE, or by applying the 87-POINT RULE (RES87) obtained by optimal addition of abscissae to the 43-POINT RULE. ABSERR - Double precision Estimate of the modulus of the absolute error, which should EQUAL or EXCEED ABS(I-RESULT) NEVAL - Integer Number of integrand evaluations IER - IER = 0 normal and reliable termination of the routine. It is assumed that the requested accuracy has been achieved. IER.GT.0 Abnormal termination of the routine. It is assumed that the requested accuracy has not been achieved. ERROR MESSAGES IER = 1 The maximum number of steps has been executed. The integral is probably too difficult to be calculated by DQNG. = 6 The input is invalid, because EPSABS.LE.0 AND EPSREL.LT.MAX(50*REL.MACH.ACC.,0.5D-28). RESULT, ABSERR and NEVAL are set to zero.

REFERENCES
(NONE)

ROUTINES CALLED
D1MACH, XERMSG

REVISION HISTORY (YYMMDD)
800101 DATE WRITTEN
890531 Changed all specific intrinsics to generic. (WRB)
890531 REVISION DATE from Version 3.2
891214 Prologue converted to Version 4.0 format. (BAB)
900315 CALLs to XERROR changed to CALLs to XERMSG. (THJ)