Gabriele Cosmo
386 lines
16 KiB
C++
386 lines
16 KiB
C++
// $Id:$
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// -*- C++ -*-
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//
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// -----------------------------------------------------------------------
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// HEP Random
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// --- RandLandau ---
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// class implementation file
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// -----------------------------------------------------------------------
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// =======================================================================
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// M Fischler - Created 1/6/2000.
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//
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// The key transform() method uses the algorithm in CERNLIB.
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// This is because I trust that RANLAN routine more than
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// I trust the Bukin-Grozina inverseLandau, which is not
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// claimed to be better than 1% accurate.
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//
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// M Fischler - put and get to/from streams 12/13/04
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// =======================================================================
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#include "CLHEP/Random/RandLandau.h"
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#include <iostream>
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#include <cmath> // for std::log()
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namespace CLHEP {
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std::string RandLandau::name() const {return "RandLandau";}
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HepRandomEngine & RandLandau::engine() {return *localEngine;}
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RandLandau::~RandLandau() {
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}
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void RandLandau::shootArray( const int size, double* vect )
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{
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for( double* v = vect; v != vect + size; ++v )
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*v = shoot();
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}
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void RandLandau::shootArray( HepRandomEngine* anEngine,
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const int size, double* vect )
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{
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for( double* v = vect; v != vect + size; ++v )
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*v = shoot(anEngine);
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}
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void RandLandau::fireArray( const int size, double* vect)
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{
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for( double* v = vect; v != vect + size; ++v )
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*v = fire();
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}
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//
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// Table of values of inverse Landau, from r = .060 to .982
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//
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// Since all these are this is static to this compilation unit only, the
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// info is establised a priori and not at each invocation.
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static const float TABLE_INTERVAL = .001f;
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static const int TABLE_END = 982;
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static const float TABLE_MULTIPLIER = 1.0f/TABLE_INTERVAL;
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// Here comes the big (4K bytes) table ---
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//
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// inverseLandau[ n ] = the inverse cdf at r = n*TABLE_INTERVAL = n/1000.
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//
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// Credit CERNLIB for these computations.
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//
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// This data is float because the algortihm does not benefit from further
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// data accuracy. The numbers below .006 or above .982 are moot since
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// non-table-based methods are used below r=.007 and above .980.
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static const float inverseLandau [TABLE_END+1] = {
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0.0f, // .000
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0.0f, 0.0f, 0.0f, 0.0f, 0.0f, // .001 - .005
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-2.244733f, -2.204365f, -2.168163f, -2.135219f, -2.104898f, // .006 - .010
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-2.076740f, -2.050397f, -2.025605f, -2.002150f, -1.979866f,
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-1.958612f, -1.938275f, -1.918760f, -1.899984f, -1.881879f, // .020
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-1.864385f, -1.847451f, -1.831030f, -1.815083f, -1.799574f,
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-1.784473f, -1.769751f, -1.755383f, -1.741346f, -1.727620f, // .030
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-1.714187f, -1.701029f, -1.688130f, -1.675477f, -1.663057f,
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-1.650858f, -1.638868f, -1.627078f, -1.615477f, -1.604058f, // .040
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-1.592811f, -1.581729f, -1.570806f, -1.560034f, -1.549407f,
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-1.538919f, -1.528565f, -1.518339f, -1.508237f, -1.498254f, // .050
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-1.488386f, -1.478628f, -1.468976f, -1.459428f, -1.449979f,
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-1.440626f, -1.431365f, -1.422195f, -1.413111f, -1.404112f, // .060
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-1.395194f, -1.386356f, -1.377594f, -1.368906f, -1.360291f,
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-1.351746f, -1.343269f, -1.334859f, -1.326512f, -1.318229f, // .070
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-1.310006f, -1.301843f, -1.293737f, -1.285688f, -1.277693f,
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-1.269752f, -1.261863f, -1.254024f, -1.246235f, -1.238494f, // .080
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-1.230800f, -1.223153f, -1.215550f, -1.207990f, -1.200474f,
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-1.192999f, -1.185566f, -1.178172f, -1.170817f, -1.163500f, // .090
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-1.156220f, -1.148977f, -1.141770f, -1.134598f, -1.127459f,
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-1.120354f, -1.113282f, -1.106242f, -1.099233f, -1.092255f, // .100
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-1.085306f, -1.078388f, -1.071498f, -1.064636f, -1.057802f,
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-1.050996f, -1.044215f, -1.037461f, -1.030733f, -1.024029f,
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-1.017350f, -1.010695f, -1.004064f, -.997456f, -.990871f,
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-.984308f, -.977767f, -.971247f, -.964749f, -.958271f,
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-.951813f, -.945375f, -.938957f, -.932558f, -.926178f,
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-.919816f, -.913472f, -.907146f, -.900838f, -.894547f,
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-.888272f, -.882014f, -.875773f, -.869547f, -.863337f,
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-.857142f, -.850963f, -.844798f, -.838648f, -.832512f,
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-.826390f, -.820282f, -.814187f, -.808106f, -.802038f,
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-.795982f, -.789940f, -.783909f, -.777891f, -.771884f, // .150
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-.765889f, -.759906f, -.753934f, -.747973f, -.742023f,
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-.736084f, -.730155f, -.724237f, -.718328f, -.712429f,
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-.706541f, -.700661f, -.694791f, -.688931f, -.683079f,
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-.677236f, -.671402f, -.665576f, -.659759f, -.653950f,
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-.648149f, -.642356f, -.636570f, -.630793f, -.625022f,
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-.619259f, -.613503f, -.607754f, -.602012f, -.596276f,
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-.590548f, -.584825f, -.579109f, -.573399f, -.567695f,
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-.561997f, -.556305f, -.550618f, -.544937f, -.539262f,
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-.533592f, -.527926f, -.522266f, -.516611f, -.510961f,
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-.505315f, -.499674f, -.494037f, -.488405f, -.482777f, // .200
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-.477153f, -.471533f, -.465917f, -.460305f, -.454697f,
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-.449092f, -.443491f, -.437893f, -.432299f, -.426707f,
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-.421119f, -.415534f, -.409951f, -.404372f, -.398795f,
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-.393221f, -.387649f, -.382080f, -.376513f, -.370949f,
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-.365387f, -.359826f, -.354268f, -.348712f, -.343157f,
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-.337604f, -.332053f, -.326503f, -.320955f, -.315408f,
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-.309863f, -.304318f, -.298775f, -.293233f, -.287692f,
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-.282152f, -.276613f, -.271074f, -.265536f, -.259999f,
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-.254462f, -.248926f, -.243389f, -.237854f, -.232318f,
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-.226783f, -.221247f, -.215712f, -.210176f, -.204641f, // .250
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-.199105f, -.193568f, -.188032f, -.182495f, -.176957f,
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-.171419f, -.165880f, -.160341f, -.154800f, -.149259f,
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-.143717f, -.138173f, -.132629f, -.127083f, -.121537f,
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-.115989f, -.110439f, -.104889f, -.099336f, -.093782f,
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-.088227f, -.082670f, -.077111f, -.071550f, -.065987f,
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-.060423f, -.054856f, -.049288f, -.043717f, -.038144f,
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-.032569f, -.026991f, -.021411f, -.015828f, -.010243f,
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-.004656f, .000934f, .006527f, .012123f, .017722f,
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.023323f, .028928f, .034535f, .040146f, .045759f,
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.051376f, .056997f, .062620f, .068247f, .073877f, // .300
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.079511f, .085149f, .090790f, .096435f, .102083f,
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.107736f, .113392f, .119052f, .124716f, .130385f,
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.136057f, .141734f, .147414f, .153100f, .158789f,
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.164483f, .170181f, .175884f, .181592f, .187304f,
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.193021f, .198743f, .204469f, .210201f, .215937f,
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.221678f, .227425f, .233177f, .238933f, .244696f,
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.250463f, .256236f, .262014f, .267798f, .273587f,
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.279382f, .285183f, .290989f, .296801f, .302619f,
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.308443f, .314273f, .320109f, .325951f, .331799f,
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.337654f, .343515f, .349382f, .355255f, .361135f, // .350
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.367022f, .372915f, .378815f, .384721f, .390634f,
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.396554f, .402481f, .408415f, .414356f, .420304f,
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.426260f, .432222f, .438192f, .444169f, .450153f,
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.456145f, .462144f, .468151f, .474166f, .480188f,
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.486218f, .492256f, .498302f, .504356f, .510418f,
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.516488f, .522566f, .528653f, .534747f, .540850f,
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.546962f, .553082f, .559210f, .565347f, .571493f,
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.577648f, .583811f, .589983f, .596164f, .602355f,
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.608554f, .614762f, .620980f, .627207f, .633444f,
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.639689f, .645945f, .652210f, .658484f, .664768f, // .400
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.671062f, .677366f, .683680f, .690004f, .696338f,
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.702682f, .709036f, .715400f, .721775f, .728160f,
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.734556f, .740963f, .747379f, .753807f, .760246f,
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.766695f, .773155f, .779627f, .786109f, .792603f,
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.799107f, .805624f, .812151f, .818690f, .825241f,
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.831803f, .838377f, .844962f, .851560f, .858170f,
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.864791f, .871425f, .878071f, .884729f, .891399f,
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.898082f, .904778f, .911486f, .918206f, .924940f,
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.931686f, .938446f, .945218f, .952003f, .958802f,
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.965614f, .972439f, .979278f, .986130f, .992996f, // .450
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.999875f, 1.006769f, 1.013676f, 1.020597f, 1.027533f,
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1.034482f, 1.041446f, 1.048424f, 1.055417f, 1.062424f,
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1.069446f, 1.076482f, 1.083534f, 1.090600f, 1.097681f,
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1.104778f, 1.111889f, 1.119016f, 1.126159f, 1.133316f,
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1.140490f, 1.147679f, 1.154884f, 1.162105f, 1.169342f,
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1.176595f, 1.183864f, 1.191149f, 1.198451f, 1.205770f,
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1.213105f, 1.220457f, 1.227826f, 1.235211f, 1.242614f,
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1.250034f, 1.257471f, 1.264926f, 1.272398f, 1.279888f,
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1.287395f, 1.294921f, 1.302464f, 1.310026f, 1.317605f,
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1.325203f, 1.332819f, 1.340454f, 1.348108f, 1.355780f, // .500
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1.363472f, 1.371182f, 1.378912f, 1.386660f, 1.394429f,
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1.402216f, 1.410024f, 1.417851f, 1.425698f, 1.433565f,
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1.441453f, 1.449360f, 1.457288f, 1.465237f, 1.473206f,
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1.481196f, 1.489208f, 1.497240f, 1.505293f, 1.513368f,
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1.521465f, 1.529583f, 1.537723f, 1.545885f, 1.554068f,
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1.562275f, 1.570503f, 1.578754f, 1.587028f, 1.595325f,
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1.603644f, 1.611987f, 1.620353f, 1.628743f, 1.637156f,
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1.645593f, 1.654053f, 1.662538f, 1.671047f, 1.679581f,
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1.688139f, 1.696721f, 1.705329f, 1.713961f, 1.722619f,
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1.731303f, 1.740011f, 1.748746f, 1.757506f, 1.766293f, // .550
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1.775106f, 1.783945f, 1.792810f, 1.801703f, 1.810623f,
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1.819569f, 1.828543f, 1.837545f, 1.846574f, 1.855631f,
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1.864717f, 1.873830f, 1.882972f, 1.892143f, 1.901343f,
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1.910572f, 1.919830f, 1.929117f, 1.938434f, 1.947781f,
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1.957158f, 1.966566f, 1.976004f, 1.985473f, 1.994972f,
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2.004503f, 2.014065f, 2.023659f, 2.033285f, 2.042943f,
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2.052633f, 2.062355f, 2.072110f, 2.081899f, 2.091720f,
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2.101575f, 2.111464f, 2.121386f, 2.131343f, 2.141334f,
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2.151360f, 2.161421f, 2.171517f, 2.181648f, 2.191815f,
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2.202018f, 2.212257f, 2.222533f, 2.232845f, 2.243195f, // .600
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2.253582f, 2.264006f, 2.274468f, 2.284968f, 2.295507f,
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2.306084f, 2.316701f, 2.327356f, 2.338051f, 2.348786f,
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2.359562f, 2.370377f, 2.381234f, 2.392131f, 2.403070f,
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2.414051f, 2.425073f, 2.436138f, 2.447246f, 2.458397f,
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2.469591f, 2.480828f, 2.492110f, 2.503436f, 2.514807f,
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2.526222f, 2.537684f, 2.549190f, 2.560743f, 2.572343f,
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2.583989f, 2.595682f, 2.607423f, 2.619212f, 2.631050f,
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2.642936f, 2.654871f, 2.666855f, 2.678890f, 2.690975f,
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2.703110f, 2.715297f, 2.727535f, 2.739825f, 2.752168f,
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2.764563f, 2.777012f, 2.789514f, 2.802070f, 2.814681f, // .650
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2.827347f, 2.840069f, 2.852846f, 2.865680f, 2.878570f,
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2.891518f, 2.904524f, 2.917588f, 2.930712f, 2.943894f,
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2.957136f, 2.970439f, 2.983802f, 2.997227f, 3.010714f,
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3.024263f, 3.037875f, 3.051551f, 3.065290f, 3.079095f,
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3.092965f, 3.106900f, 3.120902f, 3.134971f, 3.149107f,
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3.163312f, 3.177585f, 3.191928f, 3.206340f, 3.220824f,
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3.235378f, 3.250005f, 3.264704f, 3.279477f, 3.294323f,
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3.309244f, 3.324240f, 3.339312f, 3.354461f, 3.369687f,
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3.384992f, 3.400375f, 3.415838f, 3.431381f, 3.447005f,
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3.462711f, 3.478500f, 3.494372f, 3.510328f, 3.526370f, // .700
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3.542497f, 3.558711f, 3.575012f, 3.591402f, 3.607881f,
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3.624450f, 3.641111f, 3.657863f, 3.674708f, 3.691646f,
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3.708680f, 3.725809f, 3.743034f, 3.760357f, 3.777779f,
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3.795300f, 3.812921f, 3.830645f, 3.848470f, 3.866400f,
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3.884434f, 3.902574f, 3.920821f, 3.939176f, 3.957640f,
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3.976215f, 3.994901f, 4.013699f, 4.032612f, 4.051639f,
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4.070783f, 4.090045f, 4.109425f, 4.128925f, 4.148547f,
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4.168292f, 4.188160f, 4.208154f, 4.228275f, 4.248524f,
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4.268903f, 4.289413f, 4.310056f, 4.330832f, 4.351745f,
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4.372794f, 4.393982f, 4.415310f, 4.436781f, 4.458395f,
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4.480154f, 4.502060f, 4.524114f, 4.546319f, 4.568676f, // .750
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4.591187f, 4.613854f, 4.636678f, 4.659662f, 4.682807f,
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4.706116f, 4.729590f, 4.753231f, 4.777041f, 4.801024f,
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4.825179f, 4.849511f, 4.874020f, 4.898710f, 4.923582f,
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4.948639f, 4.973883f, 4.999316f, 5.024942f, 5.050761f,
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5.076778f, 5.102993f, 5.129411f, 5.156034f, 5.182864f,
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5.209903f, 5.237156f, 5.264625f, 5.292312f, 5.320220f,
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5.348354f, 5.376714f, 5.405306f, 5.434131f, 5.463193f,
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5.492496f, 5.522042f, 5.551836f, 5.581880f, 5.612178f,
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5.642734f, 5.673552f, 5.704634f, 5.735986f, 5.767610f, // .800
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5.799512f, 5.831694f, 5.864161f, 5.896918f, 5.929968f,
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5.963316f, 5.996967f, 6.030925f, 6.065194f, 6.099780f,
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6.134687f, 6.169921f, 6.205486f, 6.241387f, 6.277630f,
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6.314220f, 6.351163f, 6.388465f, 6.426130f, 6.464166f,
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6.502578f, 6.541371f, 6.580553f, 6.620130f, 6.660109f,
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6.700495f, 6.741297f, 6.782520f, 6.824173f, 6.866262f,
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6.908795f, 6.951780f, 6.995225f, 7.039137f, 7.083525f,
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7.128398f, 7.173764f, 7.219632f, 7.266011f, 7.312910f,
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7.360339f, 7.408308f, 7.456827f, 7.505905f, 7.555554f,
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7.605785f, 7.656608f, 7.708035f, 7.760077f, 7.812747f, // .850
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7.866057f, 7.920019f, 7.974647f, 8.029953f, 8.085952f,
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8.142657f, 8.200083f, 8.258245f, 8.317158f, 8.376837f,
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8.437300f, 8.498562f, 8.560641f, 8.623554f, 8.687319f,
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8.751955f, 8.817481f, 8.883916f, 8.951282f, 9.019600f,
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9.088889f, 9.159174f, 9.230477f, 9.302822f, 9.376233f,
|
|
9.450735f, 9.526355f, 9.603118f, 9.681054f, 9.760191f,
|
|
9.840558f, 9.922186f, 10.005107f, 10.089353f, 10.174959f,
|
|
10.261958f, 10.350389f, 10.440287f, 10.531693f, 10.624646f,
|
|
10.719188f, 10.815362f, 10.913214f, 11.012789f, 11.114137f,
|
|
11.217307f, 11.322352f, 11.429325f, 11.538283f, 11.649285f, // .900
|
|
|
|
11.762390f, 11.877664f, 11.995170f, 12.114979f, 12.237161f,
|
|
12.361791f, 12.488946f, 12.618708f, 12.751161f, 12.886394f,
|
|
13.024498f, 13.165570f, 13.309711f, 13.457026f, 13.607625f,
|
|
13.761625f, 13.919145f, 14.080314f, 14.245263f, 14.414134f,
|
|
14.587072f, 14.764233f, 14.945778f, 15.131877f, 15.322712f,
|
|
15.518470f, 15.719353f, 15.925570f, 16.137345f, 16.354912f,
|
|
16.578520f, 16.808433f, 17.044929f, 17.288305f, 17.538873f,
|
|
17.796967f, 18.062943f, 18.337176f, 18.620068f, 18.912049f,
|
|
19.213574f, 19.525133f, 19.847249f, 20.180480f, 20.525429f,
|
|
20.882738f, 21.253102f, 21.637266f, 22.036036f, 22.450278f, // .950
|
|
22.880933f, 23.329017f, 23.795634f, 24.281981f, 24.789364f,
|
|
25.319207f, 25.873062f, 26.452634f, 27.059789f, 27.696581f, // .960
|
|
28.365274f, 29.068370f, 29.808638f, 30.589157f, 31.413354f,
|
|
32.285060f, 33.208568f, 34.188705f, 35.230920f, 36.341388f, // .970
|
|
37.527131f, 38.796172f, 40.157721f, 41.622399f, 43.202525f,
|
|
44.912465f, 46.769077f, 48.792279f, 51.005773f, 53.437996f, // .980
|
|
56.123356f, 59.103894f, // .982
|
|
|
|
}; // End of the inverseLandau table
|
|
|
|
double RandLandau::transform (double r) {
|
|
|
|
double u = r * TABLE_MULTIPLIER;
|
|
int index = int(u);
|
|
double du = u - index;
|
|
|
|
// du is scaled such that the we dont have to multiply by TABLE_INTERVAL
|
|
// when interpolating.
|
|
|
|
// Five cases:
|
|
// A) Between .070 and .800 the function is so smooth, straight
|
|
// linear interpolation is adequate.
|
|
// B) Between .007 and .070, and between .800 and .980, quadratic
|
|
// interpolation is used. This requires the same 4 points as
|
|
// a cubic spline (thus we need .006 and .981 and .982) but
|
|
// the quadratic interpolation is accurate enough and quicker.
|
|
// C) Below .007 an asymptotic expansion for low negative lambda
|
|
// (involving two logs) is used; there is a pade-style correction
|
|
// factor.
|
|
// D) Above .980, a simple pade approximation is made (asymptotic to
|
|
// 1/(1-r)), but...
|
|
// E) the coefficients in that pade are different above r=.999.
|
|
|
|
if ( index >= 70 && index <= 800 ) { // (A)
|
|
|
|
double f0 = inverseLandau [index];
|
|
double f1 = inverseLandau [index+1];
|
|
return f0 + du * (f1 - f0);
|
|
|
|
} else if ( index >= 7 && index <= 980 ) { // (B)
|
|
|
|
double f_1 = inverseLandau [index-1];
|
|
double f0 = inverseLandau [index];
|
|
double f1 = inverseLandau [index+1];
|
|
double f2 = inverseLandau [index+2];
|
|
|
|
return f0 + du * (f1 - f0 - .25*(1-du)* (f2 -f1 - f0 + f_1) );
|
|
|
|
} else if ( index < 7 ) { // (C)
|
|
|
|
const double n0 = 0.99858950;
|
|
const double n1 = 34.5213058; const double d1 = 34.1760202;
|
|
const double n2 = 17.0854528; const double d2 = 4.01244582;
|
|
|
|
double logr = std::log(r);
|
|
double x = 1/logr;
|
|
double x2 = x*x;
|
|
|
|
double pade = (n0 + n1*x + n2*x2) / (1.0 + d1*x + d2*x2);
|
|
|
|
return ( - std::log ( -.91893853 - logr ) -1 ) * pade;
|
|
|
|
} else if ( index <= 999 ) { // (D)
|
|
|
|
const double n0 = 1.00060006;
|
|
const double n1 = 263.991156; const double d1 = 257.368075;
|
|
const double n2 = 4373.20068; const double d2 = 3414.48018;
|
|
|
|
double x = 1-r;
|
|
double x2 = x*x;
|
|
|
|
return (n0 + n1*x + n2*x2) / (x * (1.0 + d1*x + d2*x2));
|
|
|
|
} else { // (E)
|
|
|
|
const double n0 = 1.00001538;
|
|
const double n1 = 6075.14119; const double d1 = 6065.11919;
|
|
const double n2 = 734266.409; const double d2 = 694021.044;
|
|
|
|
double x = 1-r;
|
|
double x2 = x*x;
|
|
|
|
return (n0 + n1*x + n2*x2) / (x * (1.0 + d1*x + d2*x2));
|
|
|
|
}
|
|
|
|
} // transform()
|
|
|
|
std::ostream & RandLandau::put ( std::ostream & os ) const {
|
|
int pr=os.precision(20);
|
|
os << " " << name() << "\n";
|
|
os.precision(pr);
|
|
return os;
|
|
}
|
|
|
|
std::istream & RandLandau::get ( std::istream & is ) {
|
|
std::string inName;
|
|
is >> inName;
|
|
if (inName != name()) {
|
|
is.clear(std::ios::badbit | is.rdstate());
|
|
std::cerr << "Mismatch when expecting to read state of a "
|
|
<< name() << " distribution\n"
|
|
<< "Name found was " << inName
|
|
<< "\nistream is left in the badbit state\n";
|
|
return is;
|
|
}
|
|
return is;
|
|
}
|
|
|
|
} // namespace CLHEP
|