general_quadrature.f90 File Reference

Modules
module	general_quadrature_gbl

Functions/Subroutines
subroutine, public	general_quadrature_gbl::gl_expand_A_B (x, w, n, x_AB, w_AB, A, B)
	Takes the Gauss-Legendre rule for the interval [0,1] and expands it for the given interval [A,B]. More...
recursive real(kind=cfp) function, public	general_quadrature_gbl::quad1d (f, A, B, eps, Qest)
	Adaptive 1D quadrature based on Gauss-Legendre rule. More...
recursive real(kind=cfp) function, public	general_quadrature_gbl::quad2d (f, Ax, Bx, Ay, By, eps, Qest)
	Adaptive 2D quadrature on rectangle based on Gauss-Kronrod rule. The algorithm is based on that of Romanowski published in Int. J. Q. Chem. More...
real(kind=cfp) function, public	general_quadrature_gbl::gl2d (f, Ax, Bx, Ay, By)
	2D Quadrature on rectangle using the Gauss-Kronrod rule of order 8. The meaning of the input variables is identical to quad2d input parameters. More...
subroutine, public	general_quadrature_gbl::DQAGS (F, A, B, EPSABS, EPSREL, RESULT, ABSERR, NEVAL, IER, LIMIT, LENW, LAST, IWORK, WORK)
	***BEGIN PROLOGUE DQAGS ***PURPOSE 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 real(kind=cfp) (QAGS-S, DQAGS-D) ***KEYWORDS AUTOMATIC INTEGRATOR, END POINT SINGULARITIES, EXTRAPOLATION, GENERAL-PURPOSE, GLOBALLY ADAPTIVE, QUADPACK, QUADRATURE ***AUTHOR Piessens, Robert Applied Mathematics and Programming Division K. U. Leuven de Doncker, Elise Applied Mathematics and Programming Division K. U. Leuven ***DESCRIPTION More...
subroutine, public	general_quadrature_gbl::DQELG (N, EPSTAB, RESULT, ABSERR, RES3LA, NRES)
	***BEGIN PROLOGUE DQELG ***SUBSIDIARY ***PURPOSE The routine determines the limit of a given sequence of approximations, by means of the Epsilon algorithm of P.Wynn. An estimate of the absolute error is also given. The condensed Epsilon table is computed. Only those elements needed for the computation of the next diagonal are preserved. ***LIBRARY SLATEC ***TYPE real(kind=cfp) (QELG-S, DQELG-D) ***KEYWORDS CONVERGENCE ACCELERATION, EPSILON ALGORITHM, EXTRAPOLATION ***AUTHOR Piessens, Robert Applied Mathematics and Programming Division K. U. Leuven de Doncker, Elise Applied Mathematics and Programming Division K. U. Leuven ***DESCRIPTION More...
subroutine	general_quadrature_gbl::DQK21 (F, A, B, RESULT, ABSERR, RESABS, RESASC)
	***BEGIN PROLOGUE DQK21 ***PURPOSE To compute I = Integral of F over (A,B), with error estimate J = Integral of ABS(F) over (A,B) ***LIBRARY SLATEC (QUADPACK) ***CATEGORY H2A1A2 ***TYPE real(kind=cfp) (QK21-S, DQK21-D) ***KEYWORDS 21-POINT GAUSS-KRONROD RULES, QUADPACK, QUADRATURE ***AUTHOR Piessens, Robert Applied Mathematics and Programming Division K. U. Leuven de Doncker, Elise Applied Mathematics and Programming Division K. U. Leuven ***DESCRIPTION More...

Variables
integer, parameter, public	general_quadrature_gbl::n_7 = 7
	Order of the Gauss-Legendre quadrature to which the x_7 and w_7 arrays correspond. More...
real(kind=cfp), dimension(2 *n_7+1), parameter, public	general_quadrature_gbl::w_7 = (/0.015376620998058634177314196788602209_cfp,0.035183023744054062354633708225333669_cfp,0.05357961023358596750593477334293465_cfp,0.06978533896307715722390239725551416_cfp,0.08313460290849696677660043024060441_cfp,0.09308050000778110551340028093321141_cfp,0.09921574266355578822805916322191966_cfp,0.10128912096278063644031009998375966_cfp,0.09921574266355578822805916322191966_cfp,0.09308050000778110551340028093321141_cfp,0.08313460290849696677660043024060441_cfp,0.06978533896307715722390239725551416_cfp,0.05357961023358596750593477334293465_cfp,0.035183023744054062354633708225333669_cfp,0.015376620998058634177314196788602209_cfp/)
	Weights for the Gauss-Legendre quadrature of order 7 on interval [0,1]. More...
real(kind=cfp), dimension(2 *n_7+1), parameter, public	general_quadrature_gbl::x_7 = (/0.0060037409897572857552171407066937094_cfp,0.031363303799647047846120526144895264_cfp,0.075896708294786391899675839612891574_cfp,0.13779113431991497629190697269303100_cfp,0.21451391369573057623138663137304468_cfp,0.30292432646121831505139631450947727_cfp,0.39940295300128273884968584830270190_cfp,0.50000000000000000000000000000000000_cfp,0.60059704699871726115031415169729810_cfp,0.69707567353878168494860368549052273_cfp,0.78548608630426942376861336862695532_cfp,0.86220886568008502370809302730696900_cfp,0.92410329170521360810032416038710843_cfp,0.96863669620035295215387947385510474_cfp,0.99399625901024271424478285929330629_cfp/)
	Abscissas for the Gauss-Legendre quadrature of order 7 on interval [0,1]. More...
integer, parameter, public	general_quadrature_gbl::n_10 = 10
	Order of the Gauss-Legendre quadrature to which the x_10 and w_10 arrays correspond. More...
real(kind=cfp), dimension(2 *n_10+1), parameter, public	general_quadrature_gbl::x_10 = (/0.0031239146898052498698789820310295354_cfp,0.016386580716846852841688892546152419_cfp,0.039950332924799585604906433142515553_cfp,0.073318317708341358176374680706216165_cfp,0.11578001826216104569206107434688598_cfp,0.16643059790129384034701666500483042_cfp,0.22419058205639009647049060163784336_cfp,0.28782893989628060821316555572810597_cfp,0.35598934159879945169960374196769984_cfp,0.42721907291955245453148450883065683_cfp,0.50000000000000000000000000000000000_cfp,0.57278092708044754546851549116934317_cfp,0.64401065840120054830039625803230016_cfp,0.71217106010371939178683444427189403_cfp,0.77580941794360990352950939836215664_cfp,0.83356940209870615965298333499516958_cfp,0.88421998173783895430793892565311402_cfp,0.92668168229165864182362531929378384_cfp,0.96004966707520041439509356685748445_cfp,0.98361341928315314715831110745384758_cfp,0.99687608531019475013012101796897046_cfp/)
	Abscissas for the Gauss-Legendre quadrature of order 10 on interval [0,1]. More...
real(kind=cfp), dimension(2 *n_10+1), parameter, public	general_quadrature_gbl::w_10 = (/0.008008614128887166662112308429235508_cfp,0.018476894885426246899975334149664833_cfp,0.028567212713428604141817913236223979_cfp,0.038050056814189651008525826650091590_cfp,0.046722211728016930776644870556966044_cfp,0.05439864958357418883173728903505282_cfp,0.06091570802686426709768358856286680_cfp,0.06613446931666873089052628724838780_cfp,0.06994369739553657736106671193379156_cfp,0.07226220199498502953191358327687627_cfp,0.07304056682484521359599257384168559_cfp,0.07226220199498502953191358327687627_cfp,0.06994369739553657736106671193379156_cfp,0.06613446931666873089052628724838780_cfp,0.06091570802686426709768358856286680_cfp,0.05439864958357418883173728903505282_cfp,0.046722211728016930776644870556966044_cfp,0.038050056814189651008525826650091590_cfp,0.028567212713428604141817913236223979_cfp,0.018476894885426246899975334149664833_cfp,0.008008614128887166662112308429235508_cfp/)
	Weights for the Gauss-Legendre quadrature of order 10 on interval [0,1]. More...