static void SampleRule(This *t, ccount iregion)
{
SAMPLERDEFS;
Set *first = samples->rule->first;
Set *last = samples->rule->last;
Set *s;
creal *errcoeff = samples->rule->errcoeff;
count comp, rul, sn;
csize_t setsize = SetSize;
for( s = first; s <= last; NextSet(s) )
if( s->n ) x = ExpandFS(t, b, s->gen, x);
DoSample(t, n, samples->x, f);
for( comp = 0; comp < t->ncomp; ++comp ) {
real sum[nrules];
creal *f1 = f++;
Zap(sum);
for( s = first; s <= last; NextSet(s) )
for( sn = s->n; sn; --sn ) {
creal fun = *f1;
f1 += t->ncomp;
for( rul = 0; rul < nrules; ++rul )
sum[rul] += fun*s->weight[rul];
}
/* Search for the null rule, in the linear space spanned by two
successive null rules in our sequence, which gives the greatest
error estimate among all normalized (1-norm) null rules in this
space. */
for( rul = 1; rul < nrules - 1; ++rul ) {
real maxerr = 0;
for( s = first; s <= last; NextSet(s) )
maxerr = Max(maxerr,
fabsx(sum[rul + 1] + s->scale[rul]*sum[rul])*s->norm[rul]);
sum[rul] = maxerr;
}
res[comp].avg = region->vol*sum[0];
res[comp].err = region->vol*(
(errcoeff[0]*sum[1] <= sum[2] && errcoeff[0]*sum[2] <= sum[3]) ?
errcoeff[1]*sum[1] :
errcoeff[2]*Max(Max(sum[1], sum[2]), sum[3]) );
}
}
static void Rule9Alloc(This *t)
{
static creal w[] = {
RC(-.002361170967785511788400941242259231309691),
RC(.1141539002385732526821323741697655347686),
RC(-.6383392007670238909386026193674701393074),
RC(.7484998850468520800423030047583803945205),
RC(-.001432401703339912514196154599769007103671),
RC(.05747150786448972594860897296200006759892),
RC(-.1422510457143424323449521620935950679394),
RC(-.06287502873828697998942424881040490136987),
RC(.2545911332489590890011611142429070613156),
RC(-1.207328566678236261002219995185143356737),
RC(.8956736576416067650809467826488567200939),
RC(-.3647935698604914666100134551377381205297),
RC(.003541756451678267682601411863388846964536),
RC(-.07260936739589367960492815865074633743652),
RC(.1055749162521899101218622863269817454540),
RC(.002148602555009868771294231899653510655506),
RC(-.03226856389295394999786630399875134318006),
RC(.01063678399023121748083624225818915724455),
RC(.01468910249614349017540783437728097691502),
RC(.5113470834646759143109387357149329909126),
RC(.4597644812080634464633352781605214342691),
RC(.1823967849302457333050067275688690602649),
RC(-.04508628929435784075980562738240804429658),
RC(.2141588352435279340097929526588394300172),
RC(-.02735154652654564472203690086290223507436),
RC(.05494106704871123410060080562462135546101),
RC(.1193759620257077529708962121565290178730),
RC(.6508951939192025059314756320878023215278),
RC(.1474493982943446016775696826942585013243),
RC(.05769338449097348357291272840392627722165),
RC(.03499962660214358382244159694487155861542),
RC(-1.386862771927828143599782668709014266770),
RC(-.2386668732575008878964134721962088068396),
RC(.01553241727660705326386197156586357005224),
RC(.003532809960709087023561817517751309380604),
RC(.09231719987444221619017126187763868745587),
RC(.02254314464717892037990281369120402214829),
RC(.01367577326327282236101845043145111753718),
RC(-.3254475969596012529657378160439011607639),
RC(.001770878225839133841300705931694423482268),
RC(.001074301277504934385647115949826755327753),
RC(.2515001149531479199576969952416196054795) };
static creal g[] = {
RC(.4779536579022695061928604197171830064732),
RC(.2030285873691198677998034402373279133258),
RC(.4476273546261781288207704806530998539285),
RC(.125),
RC(.3430378987808781457001426145164678603407) };
enum { nsets = 9 };
ccount ndim = t->ndim;
ccount twondim = 1 << ndim;
count dim, n, r;
Set *first, *last, *s, *x;
csize_t setsize = SetSize;
Die(first = calloc(nsets, setsize));
last = first;
n = last->n = 1;
last->weight[0] = ndim*(ndim*(ndim*w[0] + w[1]) + w[2]) + w[3];
last->weight[1] = ndim*(ndim*(ndim*w[4] + w[5]) + w[6]) - w[7];
last->weight[2] = ndim*w[8] - last->weight[1];
last->weight[3] = ndim*(ndim*w[9] + w[10]) - 1 + last->weight[0];
last->weight[4] = ndim*w[11] + 1 - last->weight[0];
NextSet(last);
n += last->n = 2*ndim;
last->weight[0] = ndim*(ndim*w[12] + w[13]) + w[14];
last->weight[1] = ndim*(ndim*w[15] + w[16]) + w[17];
last->weight[2] = w[18] - last->weight[1];
last->weight[3] = ndim*w[19] + w[20] + last->weight[0];
last->weight[4] = w[21] - last->weight[0];
last->gen[0] = g[0];
NextSet(last);
n += last->n = 2*ndim;
last->weight[0] = ndim*w[22] + w[23];
last->weight[1] = ndim*w[24] + w[25];
last->weight[2] = w[26] - last->weight[1];
last->weight[3] = ndim*w[27] + w[28];
last->weight[4] = -last->weight[0];
last->gen[0] = g[1];
NextSet(last);
n += last->n = 2*ndim;
last->weight[0] = w[29];
last->weight[1] = w[30];
last->weight[2] = -w[29];
last->weight[3] = w[31];
last->weight[4] = -w[29];
last->gen[0] = g[2];
NextSet(last);
n += last->n = 2*ndim;
last->weight[2] = w[32];
last->gen[0] = g[3];
NextSet(last);
n += last->n = 2*ndim*(ndim - 1);
last->weight[0] = w[33] - ndim*w[12];
last->weight[1] = w[34] - ndim*w[15];
last->weight[2] = -last->weight[1];
last->weight[3] = w[35] + last->weight[0];
last->weight[4] = -last->weight[0];
last->gen[0] = g[0];
last->gen[1] = g[0];
NextSet(last);
n += last->n = 4*ndim*(ndim - 1);
last->weight[0] = w[36];
last->weight[1] = w[37];
last->weight[2] = -w[37];
last->weight[3] = w[38];
last->weight[4] = -w[36];
last->gen[0] = g[0];
last->gen[1] = g[1];
NextSet(last);
n += last->n = 4*ndim*(ndim - 1)*(ndim - 2)/3;
last->weight[0] = w[39];
last->weight[1] = w[40];
last->weight[2] = -w[40];
last->weight[3] = w[39];
last->weight[4] = -w[39];
last->gen[0] = g[0];
last->gen[1] = g[0];
last->gen[2] = g[0];
NextSet(last);
n += last->n = twondim;
last->weight[0] = w[41]/twondim;
last->weight[1] = w[7]/twondim;
last->weight[2] = -last->weight[1];
last->weight[3] = last->weight[0];
last->weight[4] = -last->weight[0];
for( dim = 0; dim < ndim; ++dim )
last->gen[dim] = g[4];
t->rule9.first = first;
t->rule9.last = last;
t->rule9.errcoeff[0] = 5;
t->rule9.errcoeff[1] = 1;
t->rule9.errcoeff[2] = 5;
t->rule9.n = n;
for( s = first; s <= last; NextSet(s) )
for( r = 1; r < nrules - 1; ++r ) {
creal scale = (s->weight[r] == 0) ? 100 :
-s->weight[r + 1]/s->weight[r];
real sum = 0;
for( x = first; x <= last; NextSet(x) )
sum += x->n*fabsx(x->weight[r + 1] + scale*x->weight[r]);
s->scale[r] = scale;
s->norm[r] = 1/sum;
}
}
static void Rule7Alloc(This *t)
{
static creal w[] = {
RC(.01941786667474838842844534313920462333850),
RC(-.4038525770115018254611834753723880293161),
RC(.6448566876746598222277360730193089551024),
RC(.01177982690775806141012214458820955067854),
RC(-.1804131874073360901182293138710989490609),
RC(-.08878582808133504444306598174517276122439),
RC(.05632864580828594137378124255408286479947),
RC(-.009708933337374194214222671569602311669249),
RC(-.9912917677958235813775106862002319060386),
RC(-.1775716561626700888861319634903455224488),
RC(.1235939803204323357183625846672135876752),
RC(.07497814870203369068087999555157339703666),
RC(.5548914705142355977605994477355651401434),
RC(.08804124152269277122645182458858273865209),
RC(.02111835845551338508329573367808085283304),
RC(-.009930220323965333308685820460105538586058),
RC(-.06410005328501090417895544042025034295870),
RC(.03038172903822100765927778829870429682489),
RC(.005889913453879030705061072294104775339268),
RC(-.004854466668687097107111335784801155834624),
RC(.3551433123253401777722639269806910448976) };
static creal g[] = {
RC(.4779536579022695061928604197171830064732),
RC(.2030285873691198677998034402373279133258),
RC(.375),
RC(.3430378987808781457001426145164678603407) };
enum { nsets = 6 };
ccount ndim = t->ndim;
ccount twondim = 1 << ndim;
count dim, n, r;
Set *first, *last, *s, *x;
csize_t setsize = SetSize;
Die(first = calloc(nsets, setsize));
last = first;
n = last->n = 1;
last->weight[0] = ndim*(ndim*w[0] + w[1]) + w[2];
last->weight[1] = ndim*(ndim*w[3] + w[4]) - w[5];
last->weight[2] = ndim*w[6] - last->weight[1];
last->weight[3] = ndim*(ndim*w[7] + w[8]) - w[9];
last->weight[4] = 1 - last->weight[0];
NextSet(last);
n += last->n = 2*ndim;
last->weight[0] = w[10];
last->weight[1] = w[11];
last->weight[2] = -w[10];
last->weight[3] = w[12];
last->weight[4] = -w[10];
last->gen[0] = g[1];
NextSet(last);
n += last->n = 2*ndim;
last->weight[0] = w[13] - ndim*w[0];
last->weight[1] = w[14] - ndim*w[3];
last->weight[2] = w[15] - last->weight[1];
last->weight[3] = w[16] - ndim*w[7];
last->weight[4] = -last->weight[0];
last->gen[0] = g[0];
NextSet(last);
n += last->n = 2*ndim;
last->weight[2] = w[17];
last->gen[0] = g[2];
NextSet(last);
n += last->n = 2*ndim*(ndim - 1);
last->weight[0] = -w[7];
last->weight[1] = w[18];
last->weight[2] = -w[18];
last->weight[3] = w[19];
last->weight[4] = w[7];
last->gen[0] = g[0];
last->gen[1] = g[0];
NextSet(last);
n += last->n = twondim;
last->weight[0] = w[20]/twondim;
last->weight[1] = w[5]/twondim;
last->weight[2] = -last->weight[1];
last->weight[3] = w[9]/twondim;
last->weight[4] = -last->weight[0];
for( dim = 0; dim < ndim; ++dim )
last->gen[dim] = g[3];
t->rule7.first = first;
t->rule7.last = last;
t->rule7.errcoeff[0] = 5;
t->rule7.errcoeff[1] = 1;
t->rule7.errcoeff[2] = 5;
t->rule7.n = n;
for( s = first; s <= last; NextSet(s) )
for( r = 1; r < nrules - 1; ++r ) {
creal scale = (s->weight[r] == 0) ? 100 :
-s->weight[r + 1]/s->weight[r];
real sum = 0;
for( x = first; x <= last; NextSet(x) )
sum += x->n*fabsx(x->weight[r + 1] + scale*x->weight[r]);
s->scale[r] = scale;
s->norm[r] = 1/sum;
}
}
static void Rule11Alloc(This *t)
{
static creal w[][nrules] = {
{ .0009903847688882167, 1.715006248224684, 1.936014978949526,
.517082819560576, 2.05440450381852 },
{ .0084964717409851, -.3755893815889209, -.3673449403754268,
.01445269144914044, .013777599884901202 },
{ .00013587331735072814, .1488632145140549, .02929778657898176,
-.3601489663995932, -.576806291790441 },
{ .022982920777660364, -.2497046640620823, -.1151883520260315,
.3628307003418485, .03726835047700328 },
{ .004202649722286289, .1792501419135204, .05086658220872218,
.007148802650872729, .0068148789397772195 },
{ .0012671889041675774, .0034461267589738897, .04453911087786469,
-.09222852896022966, .057231697338518496 },
{ .0002109560854981544, -.005140483185555825, -.022878282571259,
.01719339732471725, -.044930187438112855 },
{ .016830857056410086, .006536017839876424, .02908926216345833,
-.102141653746035, .027292365738663484 },
{ .00021876823557504823, -.00065134549392297, -.002898884350669207,
-.007504397861080493, .000354747395055699 },
{ .009690420479796819, -.006304672433547204, -.028059634133074954,
.01648362537726711, .01571366799739551 },
{ .030773311284628138, .01266959399788263, .05638741361145884,
.05234610158469334, .049900992192785674 },
{ .0084974310856038, -.005454241018647931, -.02427469611942451,
.014454323316130661, .0137791555266677 },
{ .0017749535291258914, .004826995274768427, .021483070341828822,
.003019236275367777, .0028782064230998723 }
};
static creal g[] = {
.095, .25,
.375, .4,
.4975, .49936724991757,
.38968518428362114, .49998494965443835,
.3951318612385894, .22016983438253684,
.4774686911397297, .2189239229503431,
.4830546566815374, .2288552938881567 };
enum { nsets = 13, ndim = 3 };
count n, r;
Set *first, *last, *s, *x;
csize_t setsize = SetSize;
Die(first = calloc(nsets, setsize));
last = first;
n = last->n = 1;
Copy(last->weight, w[0], nrules);
NextSet(last);
n += last->n = 2*ndim;
Copy(last->weight, w[1], nrules);
last->gen[0] = g[0];
NextSet(last);
n += last->n = 2*ndim;
Copy(last->weight, w[2], nrules);
last->gen[0] = g[1];
NextSet(last);
n += last->n = 2*ndim;
Copy(last->weight, w[3], nrules);
last->gen[0] = g[2];
NextSet(last);
n += last->n = 2*ndim;
Copy(last->weight, w[4], nrules);
last->gen[0] = g[3];
NextSet(last);
n += last->n = 2*ndim;
Copy(last->weight, w[5], nrules);
last->gen[0] = g[4];
NextSet(last);
n += last->n = 2*ndim*(ndim - 1);
Copy(last->weight, w[6], nrules);
last->gen[0] = g[5];
last->gen[1] = g[5];
NextSet(last);
n += last->n = 2*ndim*(ndim - 1);
Copy(last->weight, w[7], nrules);
last->gen[0] = g[6];
last->gen[1] = g[6];
NextSet(last);
n += last->n = 4*ndim*(ndim - 1)*(ndim - 2)/3;
Copy(last->weight, w[8], nrules);
last->gen[0] = g[7];
last->gen[1] = g[7];
last->gen[2] = g[7];
NextSet(last);
n += last->n = 4*ndim*(ndim - 1)*(ndim - 2)/3;
Copy(last->weight, w[9], nrules);
last->gen[0] = g[8];
last->gen[1] = g[8];
last->gen[2] = g[8];
NextSet(last);
n += last->n = 4*ndim*(ndim - 1)*(ndim - 2)/3;
Copy(last->weight, w[10], nrules);
last->gen[0] = g[9];
last->gen[1] = g[9];
last->gen[2] = g[9];
NextSet(last);
n += last->n = 4*ndim*(ndim - 1)*(ndim - 2);
Copy(last->weight, w[11], nrules);
last->gen[0] = g[10];
last->gen[1] = g[11];
last->gen[2] = g[11];
NextSet(last);
n += last->n = 4*ndim*(ndim - 1)*(ndim - 2);
Copy(last->weight, w[12], nrules);
last->gen[0] = g[12];
last->gen[1] = g[12];
last->gen[2] = g[13];
t->rule11.first = first;
t->rule11.last = last;
t->rule11.errcoeff[0] = 4;
t->rule11.errcoeff[1] = .5;
t->rule11.errcoeff[2] = 3;
t->rule11.n = n;
for( s = first; s <= last; NextSet(s) )
for( r = 1; r < nrules - 1; ++r ) {
creal scale = (s->weight[r] == 0) ? 100 :
-s->weight[r + 1]/s->weight[r];
real sum = 0;
for( x = first; x <= last; NextSet(x) )
sum += x->n*fabsx(x->weight[r + 1] + scale*x->weight[r]);
s->scale[r] = scale;
s->norm[r] = 1/sum;
}
}
static void Rule13Alloc(This *t)
{
static creal w[][nrules] = {
{ .00844923090033615, .3213775489050763, .3372900883288987,
-.8264123822525677, .6539094339575232 },
{ .023771474018994404, -.1767341636743844, -.1644903060344491,
.306583861409436, -.2041614154424632},
{ .02940016170142405, .07347600537466073, .07707849911634623,
.002389292538329435, -.174698151579499 },
{ .006644436465817374, -.03638022004364754, -.03804478358506311,
-.1343024157997222, .03937939671417803 },
{ .0042536044255016, .021252979220987123, .02223559940380806,
.08833366840533902, .006974520545933992 },
{ 0, .1460984204026913, .1480693879765931,
0, 0 },
{ .0040664827465935255, .017476132861520992, 4.467143702185815e-6,
.0009786283074168292, .0066677021717782585 },
{ .03362231646315497, .1444954045641582, .150894476707413,
-.1319227889147519, .05512960621544304 },
{ .033200804136503725, .0001307687976001325, 3.6472001075162155e-5,
.00799001220015063, .05443846381278608 },
{ .014093686924979677, .0005380992313941161, .000577719899901388,
.0033917470797606257, .02310903863953934 },
{ .000977069770327625, .0001042259576889814, .0001041757313688177,
.0022949157182832643, .01506937747477189 },
{ .007531996943580376, -.001401152865045733, -.001452822267047819,
-.01358584986119197, -.060570216489018905 },
{ .02577183086722915, .008041788181514763, .008338339968783704,
.04025866859057809, .04225737654686337},
{ .015625, -.1420416552759383, -.147279632923196,
.003760268580063992, .02561989142123099 }
};
static creal g[] = {
.12585646717265545, .3506966822267133,
.4795480315809981, .4978005239276064,
.25, .07972723291487795,
.1904495567970094, .3291384627633596,
.43807365825146577, .499121592026599,
.4895111329084231, .32461421628226944,
.43637106005656195, .1791307322940614,
.2833333333333333, .1038888888888889 };
enum { nsets = 14, ndim = 2 };
count n, r;
Set *first, *last, *s, *x;
csize_t setsize = SetSize;
Die(first = calloc(nsets, setsize));
last = first;
n = last->n = 1;
Copy(last->weight, w[0], nrules);
NextSet(last);
n += last->n = 2*ndim;
Copy(last->weight, w[1], nrules);
last->gen[0] = g[0];
NextSet(last);
n += last->n = 2*ndim;
Copy(last->weight, w[2], nrules);
last->gen[0] = g[1];
NextSet(last);
n += last->n = 2*ndim;
Copy(last->weight, w[3], nrules);
last->gen[0] = g[2];
NextSet(last);
n += last->n = 2*ndim;
Copy(last->weight, w[4], nrules);
last->gen[0] = g[3];
NextSet(last);
n += last->n = 2*ndim;
Copy(last->weight, w[5], nrules);
last->gen[0] = g[4];
NextSet(last);
n += last->n = 2*ndim*(ndim - 1);
Copy(last->weight, w[6], nrules);
last->gen[0] = g[5];
last->gen[1] = g[5];
NextSet(last);
n += last->n = 2*ndim*(ndim - 1);
Copy(last->weight, w[7], nrules);
last->gen[0] = g[6];
last->gen[1] = g[6];
NextSet(last);
n += last->n = 2*ndim*(ndim - 1);
Copy(last->weight, w[8], nrules);
last->gen[0] = g[7];
last->gen[1] = g[7];
NextSet(last);
n += last->n = 2*ndim*(ndim - 1);
Copy(last->weight, w[9], nrules);
last->gen[0] = g[8];
last->gen[1] = g[8];
NextSet(last);
n += last->n = 2*ndim*(ndim - 1);
Copy(last->weight, w[10], nrules);
last->gen[0] = g[9];
last->gen[1] = g[9];
NextSet(last);
n += last->n = 4*ndim*(ndim - 1);
Copy(last->weight, w[11], nrules);
last->gen[0] = g[10];
last->gen[1] = g[11];
NextSet(last);
n += last->n = 4*ndim*(ndim - 1);
Copy(last->weight, w[12], nrules);
last->gen[0] = g[12];
last->gen[1] = g[13];
NextSet(last);
n += last->n = 4*ndim*(ndim - 1);
Copy(last->weight, w[13], nrules);
last->gen[0] = g[14];
last->gen[1] = g[15];
t->rule13.first = first;
t->rule13.last = last;
t->rule13.errcoeff[0] = 10;
t->rule13.errcoeff[1] = 1;
t->rule13.errcoeff[2] = 5;
t->rule13.n = n;
for( s = first; s <= last; NextSet(s) )
for( r = 1; r < nrules - 1; ++r ) {
creal scale = (s->weight[r] == 0) ? 100 :
-s->weight[r + 1]/s->weight[r];
real sum = 0;
for( x = first; x <= last; NextSet(x) )
sum += x->n*fabsx(x->weight[r + 1] + scale*x->weight[r]);
s->scale[r] = scale;
s->norm[r] = 1/sum;
}
}
static void Sample(This *t, Region *region)
{
csize_t setsize = SetSize;
creal vol = ldexp(1., -region->div);
real *x = t->frame, *f = x + t->rule.n*t->ndim;
Set *first = t->rule.first, *last = t->rule.last, *s;
Bounds *b, *B = region->bounds + t->ndim;
Result *result = RegionResult(region), *res, *Res = result + t->ncomp;
creal *errcoeff = t->rule.errcoeff;
creal ratio = Sq(IndexSet(first,2)->gen[0]/
IndexSet(first,1)->gen[0]);
ccount offset = 2*t->ndim*t->ncomp;
count dim, rul, n, maxdim = 0;
real maxrange = 0;
for( b = region->bounds, dim = 0; b < B; ++b, ++dim ) {
creal range = b->upper - b->lower;
if( range > maxrange ) {
maxrange = range;
maxdim = dim;
}
}
for( s = first; s <= last; NextSet(s) )
if( s->n ) x = ExpandFS(t, region->bounds, s->gen, x);
DoSample(t, t->rule.n, t->frame, f);
for( res = result; res < Res; ++res ) {
real sum[nrules];
creal *f1 = f;
creal base = *f1*2*(1 - ratio);
real maxdiff = 0;
count bisectdim = maxdim;
for( dim = 0; dim < t->ndim; ++dim ) {
creal *fp = f1 + t->ncomp;
creal *fm = fp + t->ncomp;
creal fourthdiff = fabs(base +
ratio*(fp[0] + fm[0]) - (fp[offset] + fm[offset]));
f1 = fm;
if( fourthdiff > maxdiff ) {
maxdiff = fourthdiff;
bisectdim = dim;
}
}
res->bisectdim = bisectdim;
f1 = f++;
Zap(sum);
for( s = first; s <= last; NextSet(s) )
for( n = s->n; n; --n ) {
creal fun = *f1;
f1 += t->ncomp;
for( rul = 0; rul < nrules; ++rul )
sum[rul] += fun*s->weight[rul];
}
/* Search for the null rule, in the linear space spanned by two
successive null rules in our sequence, which gives the greatest
error estimate among all normalized (1-norm) null rules in this
space. */
for( rul = 1; rul < nrules - 1; ++rul ) {
real maxerr = 0;
for( s = first; s <= last; NextSet(s) )
maxerr = Max(maxerr,
fabs(sum[rul + 1] + s->scale[rul]*sum[rul])*s->norm[rul]);
sum[rul] = maxerr;
}
res->avg = vol*sum[0];
res->err = vol*(
(errcoeff[0]*sum[1] <= sum[2] && errcoeff[0]*sum[2] <= sum[3]) ?
errcoeff[1]*sum[1] :
errcoeff[2]*Max(Max(sum[1], sum[2]), sum[3]) );
}
if( VERBOSE > 2 ) {
Vector(char, out, 64*NDIM + 128*NCOMP);
char *oe = out;
count comp;
cchar *msg = "\nRegion (" REALF ") - (" REALF ")";
for( b = region->bounds; b < B; ++b ) {
oe += sprintf(oe, msg, b->lower, b->upper);
msg = "\n (" REALF ") - (" REALF ")";
}
for( res = result, comp = 0; res < Res; ++res )
oe += sprintf(oe, "\n[" COUNT "] "
REAL " +- " REAL, ++comp, res->avg, res->err);
Print(out);
}
static void Rule7Alloc(This *t)
{
static creal w[] = {
.019417866674748388428, -.40385257701150182546,
.64485668767465982223, .01177982690775806141,
-.18041318740733609012, -.088785828081335044443,
.056328645808285941374, -.0097089333373741942142,
-.99129176779582358138, -.17757165616267008889,
.12359398032043233572, .074978148702033690681,
.55489147051423559776, .088041241522692771226,
.021118358455513385083, -.0099302203239653333087,
-.064100053285010904179, .030381729038221007659,
.0058899134538790307051, -.0048544666686870971071,
.35514331232534017777 };
static creal g[] = {
.47795365790226950619, .20302858736911986780,
.375, .34303789878087814570 };
enum { nsets = 6 };
ccount ndim = t->ndim;
ccount twondim = 1 << ndim;
count dim, n, r;
Set *first, *last, *s, *x;
csize_t setsize = SetSize;
Die(first = calloc(nsets, setsize));
last = first;
n = last->n = 1;
last->weight[0] = ndim*(ndim*w[0] + w[1]) + w[2];
last->weight[1] = ndim*(ndim*w[3] + w[4]) - w[5];
last->weight[2] = ndim*w[6] - last->weight[1];
last->weight[3] = ndim*(ndim*w[7] + w[8]) - w[9];
last->weight[4] = 1 - last->weight[0];
NextSet(last);
n += last->n = 2*ndim;
last->weight[0] = w[10];
last->weight[1] = w[11];
last->weight[2] = -w[10];
last->weight[3] = w[12];
last->weight[4] = -w[10];
last->gen[0] = g[1];
NextSet(last);
n += last->n = 2*ndim;
last->weight[0] = w[13] - ndim*w[0];
last->weight[1] = w[14] - ndim*w[3];
last->weight[2] = w[15] - last->weight[1];
last->weight[3] = w[16] - ndim*w[7];
last->weight[4] = -last->weight[0];
last->gen[0] = g[0];
NextSet(last);
n += last->n = 2*ndim;
last->weight[2] = w[17];
last->gen[0] = g[2];
NextSet(last);
n += last->n = 2*ndim*(ndim - 1);
last->weight[0] = -w[7];
last->weight[1] = w[18];
last->weight[2] = -w[18];
last->weight[3] = w[19];
last->weight[4] = w[7];
last->gen[0] = g[0];
last->gen[1] = g[0];
NextSet(last);
n += last->n = twondim;
last->weight[0] = w[20]/twondim;
last->weight[1] = w[5]/twondim;
last->weight[2] = -last->weight[1];
last->weight[3] = w[9]/twondim;
last->weight[4] = -last->weight[0];
for( dim = 0; dim < ndim; ++dim )
last->gen[dim] = g[3];
t->rule.first = first;
t->rule.last = last;
t->rule.errcoeff[0] = 5;
t->rule.errcoeff[1] = 1;
t->rule.errcoeff[2] = 5;
t->rule.n = n;
for( s = first; s <= last; NextSet(s) )
for( r = 1; r < nrules - 1; ++r ) {
creal scale = (s->weight[r] == 0) ? 100 :
-s->weight[r + 1]/s->weight[r];
real sum = 0;
for( x = first; x <= last; NextSet(x) )
sum += x->n*fabs(x->weight[r + 1] + scale*x->weight[r]);
s->scale[r] = scale;
s->norm[r] = 1/sum;
}
}
static void Rule9Alloc(This *t)
{
static creal w[] = {
-.0023611709677855117884, .11415390023857325268,
-.63833920076702389094, .74849988504685208004,
-.0014324017033399125142, .057471507864489725949,
-.14225104571434243234, -.062875028738286979989,
.254591133248959089, -1.207328566678236261,
.89567365764160676508, -.36479356986049146661,
.0035417564516782676826, -.072609367395893679605,
.10557491625218991012, .0021486025550098687713,
-.032268563892953949998, .010636783990231217481,
.014689102496143490175, .51134708346467591431,
.45976448120806344646, .18239678493024573331,
-.04508628929435784076, .21415883524352793401,
-.027351546526545644722, .054941067048711234101,
.11937596202570775297, .65089519391920250593,
.14744939829434460168, .057693384490973483573,
.034999626602143583822, -1.3868627719278281436,
-.2386668732575008879, .015532417276607053264,
.0035328099607090870236, .09231719987444221619,
.02254314464717892038, .013675773263272822361,
-.32544759695960125297, .0017708782258391338413,
.0010743012775049343856, .25150011495314791996 };
static creal g[] = {
.47795365790226950619, .20302858736911986780,
.44762735462617812882, .125,
.34303789878087814570 };
enum { nsets = 9 };
ccount ndim = t->ndim;
ccount twondim = 1 << ndim;
count dim, n, r;
Set *first, *last, *s, *x;
csize_t setsize = SetSize;
Die(first = calloc(nsets, setsize));
last = first;
n = last->n = 1;
last->weight[0] = ndim*(ndim*(ndim*w[0] + w[1]) + w[2]) + w[3];
last->weight[1] = ndim*(ndim*(ndim*w[4] + w[5]) + w[6]) - w[7];
last->weight[2] = ndim*w[8] - last->weight[1];
last->weight[3] = ndim*(ndim*w[9] + w[10]) - 1 + last->weight[0];
last->weight[4] = ndim*w[11] + 1 - last->weight[0];
NextSet(last);
n += last->n = 2*ndim;
last->weight[0] = ndim*(ndim*w[12] + w[13]) + w[14];
last->weight[1] = ndim*(ndim*w[15] + w[16]) + w[17];
last->weight[2] = w[18] - last->weight[1];
last->weight[3] = ndim*w[19] + w[20] + last->weight[0];
last->weight[4] = w[21] - last->weight[0];
last->gen[0] = g[0];
NextSet(last);
n += last->n = 2*ndim;
last->weight[0] = ndim*w[22] + w[23];
last->weight[1] = ndim*w[24] + w[25];
last->weight[2] = w[26] - last->weight[1];
last->weight[3] = ndim*w[27] + w[28];
last->weight[4] = -last->weight[0];
last->gen[0] = g[1];
NextSet(last);
n += last->n = 2*ndim;
last->weight[0] = w[29];
last->weight[1] = w[30];
last->weight[2] = -w[29];
last->weight[3] = w[31];
last->weight[4] = -w[29];
last->gen[0] = g[2];
NextSet(last);
n += last->n = 2*ndim;
last->weight[2] = w[32];
last->gen[0] = g[3];
NextSet(last);
n += last->n = 2*ndim*(ndim - 1);
last->weight[0] = w[33] - ndim*w[12];
last->weight[1] = w[34] - ndim*w[15];
last->weight[2] = -last->weight[1];
last->weight[3] = w[35] + last->weight[0];
last->weight[4] = -last->weight[0];
last->gen[0] = g[0];
last->gen[1] = g[0];
NextSet(last);
n += last->n = 4*ndim*(ndim - 1);
last->weight[0] = w[36];
last->weight[1] = w[37];
last->weight[2] = -w[37];
last->weight[3] = w[38];
last->weight[4] = -w[36];
last->gen[0] = g[0];
last->gen[1] = g[1];
NextSet(last);
n += last->n = 4*ndim*(ndim - 1)*(ndim - 2)/3;
last->weight[0] = w[39];
last->weight[1] = w[40];
last->weight[2] = -w[40];
last->weight[3] = w[39];
last->weight[4] = -w[39];
last->gen[0] = g[0];
last->gen[1] = g[0];
last->gen[2] = g[0];
NextSet(last);
n += last->n = twondim;
last->weight[0] = w[41]/twondim;
last->weight[1] = w[7]/twondim;
last->weight[2] = -last->weight[1];
last->weight[3] = last->weight[0];
last->weight[4] = -last->weight[0];
for( dim = 0; dim < ndim; ++dim )
last->gen[dim] = g[4];
t->rule.first = first;
t->rule.last = last;
t->rule.errcoeff[0] = 5;
t->rule.errcoeff[1] = 1;
t->rule.errcoeff[2] = 5;
t->rule.n = n;
for( s = first; s <= last; NextSet(s) )
for( r = 1; r < nrules - 1; ++r ) {
creal scale = (s->weight[r] == 0) ? 100 :
-s->weight[r + 1]/s->weight[r];
real sum = 0;
for( x = first; x <= last; NextSet(x) )
sum += x->n*fabs(x->weight[r + 1] + scale*x->weight[r]);
s->scale[r] = scale;
s->norm[r] = 1/sum;
}
}
