kronrodintegral.cpp

有很多的函数库

/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */

/*
 Copyright (C) 2006 François du Vignaud

 This file is part of QuantLib, a free-software/open-source library
 for financial quantitative analysts and developers - http://quantlib.org/

 QuantLib is free software: you can redistribute it and/or modify it
 under the terms of the QuantLib license.  You should have received a
 copy of the license along with this program; if not, please email
 <[e-mail]>. The license is also available online at
 <http://quantlib.org/license.shtml>.

 This program is distributed in the hope that it will be useful, but WITHOUT
 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
 FOR A PARTICULAR PURPOSE.  See the license for more details.
*/

#include <ql/math/integrals/kronrodintegral.hpp>
#include <ql/types.hpp>

namespace QuantLib {

    static Real rescaleError(Real err,
                             const Real resultAbs,
                             const Real resultAsc) {
        err = std::fabs(err) ;
        if (resultAsc != 0 && err != 0){
            Real scale = pow((200 * err / resultAsc), 1.5) ;
            if (scale < 1)
                err = resultAsc * scale ;
            else
                err = resultAsc ;
            }
        if (resultAbs > QL_MIN_POSITIVE_REAL / (50 * QL_EPSILON )){
            Real min_err = 50 * QL_EPSILON  * resultAbs ;
            if (min_err > err)
                err = min_err ;
            }
        return err ;
    }

    /* Gauss-Kronrod-Patterson quadrature coefficients for use in
    quadpack routine qng. These coefficients were calculated with
    101 decimal digit arithmetic by L. W. Fullerton, Bell Labs, Nov
    1981. */

    /* x1, abscissae common to the 10-, 21-, 43- and 87-point rule */
    static const Real x1[5] = {
        0.973906528517171720077964012084452,
        0.865063366688984510732096688423493,
        0.679409568299024406234327365114874,
        0.433395394129247190799265943165784,
        0.148874338981631210884826001129720
        } ;

    /* w10, weights of the 10-point formula */
    static const Real w10[5] = {
        0.066671344308688137593568809893332,
        0.149451349150580593145776339657697,
        0.219086362515982043995534934228163,
        0.269266719309996355091226921569469,
        0.295524224714752870173892994651338
        } ;

    /* x2, abscissae common to the 21-, 43- and 87-point rule */
    static const Real x2[5] = {
        0.995657163025808080735527280689003,
        0.930157491355708226001207180059508,
        0.780817726586416897063717578345042,
        0.562757134668604683339000099272694,
        0.294392862701460198131126603103866
        } ;

    /* w21a, weights of the 21-point formula for abscissae x1 */
    static const Real w21a[5] = {
        0.032558162307964727478818972459390,
        0.075039674810919952767043140916190,
        0.109387158802297641899210590325805,
        0.134709217311473325928054001771707,
        0.147739104901338491374841515972068
        } ;

    /* w21b, weights of the 21-point formula for abscissae x2 */
    static const Real w21b[6] = {
        0.011694638867371874278064396062192,
        0.054755896574351996031381300244580,
        0.093125454583697605535065465083366,
        0.123491976262065851077958109831074,
        0.142775938577060080797094273138717,
        0.149445554002916905664936468389821
        } ;

    /* x3, abscissae common to the 43- and 87-point rule */
    static const Real x3[11] = {
        0.999333360901932081394099323919911,
        0.987433402908088869795961478381209,
        0.954807934814266299257919200290473,
        0.900148695748328293625099494069092,
        0.825198314983114150847066732588520,
        0.732148388989304982612354848755461,
        0.622847970537725238641159120344323,
        0.499479574071056499952214885499755,
        0.364901661346580768043989548502644,
        0.222254919776601296498260928066212,
        0.074650617461383322043914435796506
        } ;

    /* w43a, weights of the 43-point formula for abscissae x1, x3 */
    static const Real w43a[10] = {
        0.016296734289666564924281974617663,
        0.037522876120869501461613795898115,
        0.054694902058255442147212685465005,
        0.067355414609478086075553166302174,
        0.073870199632393953432140695251367,
        0.005768556059769796184184327908655,
        0.027371890593248842081276069289151,
        0.046560826910428830743339154433824,
        0.061744995201442564496240336030883,
        0.071387267268693397768559114425516
        } ;

    /* w43b, weights of the 43-point formula for abscissae x3 */
    static const Real w43b[12] = {
        0.001844477640212414100389106552965,
        0.010798689585891651740465406741293,
        0.021895363867795428102523123075149,
        0.032597463975345689443882222526137,
        0.042163137935191811847627924327955,
        0.050741939600184577780189020092084,
        0.058379395542619248375475369330206,
        0.064746404951445885544689259517511,
        0.069566197912356484528633315038405,
        0.072824441471833208150939535192842,
        0.074507751014175118273571813842889,
        0.074722147517403005594425168280423
        } ;

    /* x4, abscissae of the 87-point rule */
    static const Real x4[22] = {
        0.999902977262729234490529830591582,
        0.997989895986678745427496322365960,
        0.992175497860687222808523352251425,
        0.981358163572712773571916941623894,
        0.965057623858384619128284110607926,
        0.943167613133670596816416634507426,
        0.915806414685507209591826430720050,
        0.883221657771316501372117548744163,
        0.845710748462415666605902011504855,
        0.803557658035230982788739474980964,
        0.757005730685495558328942793432020,
        0.706273209787321819824094274740840,
        0.651589466501177922534422205016736,
        0.593223374057961088875273770349144,
        0.531493605970831932285268948562671,
        0.466763623042022844871966781659270,
        0.399424847859218804732101665817923,
        0.329874877106188288265053371824597,
        0.258503559202161551802280975429025,
        0.185695396568346652015917141167606,
        0.111842213179907468172398359241362,
        0.037352123394619870814998165437704
        } ;

    /* w87a, weights of the 87-point formula for abscissae x1, x2, x3 */
    static const Real w87a[21] = {
        0.008148377384149172900002878448190,
        0.018761438201562822243935059003794,
        0.027347451050052286161582829741283,
        0.033677707311637930046581056957588,
        0.036935099820427907614589586742499,
        0.002884872430211530501334156248695,
        0.013685946022712701888950035273128,
        0.023280413502888311123409291030404,
        0.030872497611713358675466394126442,
        0.035693633639418770719351355457044,
        0.000915283345202241360843392549948,
        0.005399280219300471367738743391053,
        0.010947679601118931134327826856808,
        0.016298731696787335262665703223280,
        0.021081568889203835112433060188190,
        0.025370969769253827243467999831710,
        0.029189697756475752501446154084920,
        0.032373202467202789685788194889595,
        0.034783098950365142750781997949596,
        0.036412220731351787562801163687577,
        0.037253875503047708539592001191226
        } ;

    /* w87b, weights of the 87-point formula for abscissae x4    */
    static const Real w87b[23] = {
        0.000274145563762072350016527092881,
        0.001807124155057942948341311753254,
        0.004096869282759164864458070683480,
        0.006758290051847378699816577897424,
        0.009549957672201646536053581325377,
        0.012329447652244853694626639963780,
        0.015010447346388952376697286041943,
        0.017548967986243191099665352925900,
        0.019938037786440888202278192730714,
        0.022194935961012286796332102959499,
        0.024339147126000805470360647041454,
        0.026374505414839207241503786552615,
        0.028286910788771200659968002987960,
        0.030052581128092695322521110347341,
        0.031646751371439929404586051078883,
        0.033050413419978503290785944862689,
        0.034255099704226061787082821046821,
        0.035262412660156681033782717998428,
        0.036076989622888701185500318003895,
        0.036698604498456094498018047441094,
        0.037120549269832576114119958413599,
        0.037334228751935040321235449094698,
        0.037361073762679023410321241766599
        } ;

    Real GaussKronrodNonAdaptive::relativeAccuracy() const {
        return relativeAccuracy_;
    }

    GaussKronrodNonAdaptive::GaussKronrodNonAdaptive(Real absoluteAccuracy,
                                                     Size maxEvaluations,