Point_3 calculateMove(const Vertex_handle &vertex,
const Vector_3 &tangient)
{
DEBUG_START;
Plane_3 plane = dual(vertex->point());
Vector_3 u(plane.a(), plane.b(), plane.c());
if (plane.d() > 0.)
u = -u;
double value = tangient * u;
Plane_3 planeNew(u.x(), u.y(), u.z(), -value);
Point_3 point = dual(planeNew);
DEBUG_END;
return point;
}
//-----------------------------------------------------------------------------
void MGL_EXPORT mgl_datac_set_ri(HADT d, HCDT re, HCDT im)
{
long nx=d->GetNx(),ny=d->GetNy(),nz=d->GetNz();
d->Create(nx,ny,nz);
#pragma omp parallel for
for(long i=0;i<nx*ny*nz;i++) d->a[i] = dual(re->vthr(i),im->vthr(i));
}
void SlidingTileEnvironment::unrank(uint64_t hashVal, SlidingTileState& s, std::vector<int> pattern)
{
// int numEntriesLeft = 16 - pattern.size() + 1;
std::vector<int> dual(pattern.size());
for (int x = 0; x < pattern.size(); x++)
{
auto t = (factorial(15 - x) / factorial(16 - pattern.size()));
dual[x] = hashVal / t;
hashVal %= t;
// hashVal /= numEntriesLeft;
}
for (int x = pattern.size() - 1; x >= 0; x--)
{
for (int y = x - 1; y >= 0; y--)
{
if (dual[y] <= dual[x])
{
dual[x]++;
}
}
}
for (auto &i : s.board)
i = -1;
for (int x = 0; x < pattern.size(); x++)
{
s.board[dual[x]] = pattern[x];
// if (dual[x] != -1)
if (pattern[x] == 0) {
s.x = dual[x] % 4;
s.y = dual[x] / 4;
}
}
}
uint64_t SlidingTileEnvironment::hash(SlidingTileState &a)
{
std::vector<int> pattern{ 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15 };
uint64_t hashval = 0;
// int size = 0;
int numEntriesLeft = 16;
std::vector<int> dual(pattern.size());
for (int x = 0; x < 16; x++)
{
for (int y = 0; y < pattern.size(); y++)
{
if (a.board[x] == pattern[y])
{
dual[a.board[x]] = x;
break;
}
}
}
for (int x = 0; x < pattern.size(); x++)
{
hashval += dual[x] * factorial(numEntriesLeft - 1) / factorial(16 - pattern.size());
for (unsigned y = x; y < pattern.size(); y++)
{
if (dual[y] > dual[x])
dual[y]--;
}
numEntriesLeft--;
}
return hashval;
}
//-----------------------------------------------------------------------------
dual mgl_str2dual(const char *s)
{
setlocale(LC_NUMERIC, "C");
double re=0,im=0; size_t ll=strlen(s);
while(s[ll]<=' ') ll--;
if(*s=='(') sscanf(s,"(%lg,%lg)",&re,&im);
else if(*s=='i') { re=0; im=atof(s+1); }
else if(*s=='[') sscanf(s,"[%lg,%lg]",&re,&im);
else if(*s=='{') sscanf(s,"{%lg,%lg}",&re,&im);
else if(s[ll]=='i')
{
double a,b;
int s1=sscanf(s,"%lg+%lgi",&re,&im);
int s2=sscanf(s,"%lg-%lgi",&a,&b);
if(s1<2)
{
if(s2==2) { re=a; im=-b; }
else { im=atof(s); re=0; }
}
}
else
{
double a,b;
int s1=sscanf(s,"%lg+i%lg",&re,&im);
int s2=sscanf(s,"%lg-i%lg",&a,&b);
if(s1<2)
{
if(s2==2) { re=a; im=-b; }
else { re=atof(s); im=0; }
}
}
setlocale(LC_NUMERIC, "");
return dual(re,im);
}
static VectorXd runL2Estimation(SupportFunctionEstimationDataPtr SFEData)
{
DEBUG_START;
auto data = SFEData->supportData();
auto planes = data->supportPlanes();
auto directions = data->supportDirections<Vector_3>();
auto values = data->supportValues();
std::vector<DualPolyhedron_3::PointIndexed_3> points;
for (unsigned i = 0; i < planes.size(); ++i)
points.push_back(std::make_pair(dual(planes[i]), i));
DualPolyhedron_3 dualP(directions, values, planes, points.begin(),
points.end());
dualP.initialize();
double startingFunctional = dualP.calculateFunctional();
std::cout << "Starting value of functional: " << startingFunctional
<< std::endl;
std::cout << "And square root of it: " << sqrt(startingFunctional)
<< std::endl;
dualP.makeConsistent();
auto solution = calculateSolution(data, values);
DEBUG_END;
return solution;
}
void EmbedderOptimalFlexDraw::optimizeOverEmbeddings(
StaticPlanarSPQRTree &T,
node parent,
node mu,
int bends,
NodeArray<int> cost[],
NodeArray<long long> embedding[])
{
cost[bends][mu] = numeric_limits<int>::max();
long long embeddingsCount = T.numberOfNodeEmbeddings(mu);
for (long long currentEmbedding = 0; currentEmbedding < embeddingsCount; ++currentEmbedding) {
T.embed(mu, currentEmbedding);
Skeleton &skeleton = T.skeleton(mu);
Graph skeletonGraph = skeleton.getGraph();
ConstCombinatorialEmbedding skeletonEmbedding(skeletonGraph);
NodeArray<node> vertexNode(skeletonGraph);
EdgeArray<node> edgeNode(skeletonGraph);
FaceArray<node> faceNode(skeletonEmbedding);
Graph N;
EdgeArray<int> upper(N);
EdgeArray<int> perUnitCost(N);
NodeArray<int> supply(N);
createNetwork(
parent,
mu,
bends,
cost,
embedding,
skeleton,
edgeNode,
N,
upper,
perUnitCost,
supply);
EdgeArray<int> lower(N, 0);
EdgeArray<int> flow(N);
NodeArray<int> dual(N);
m_minCostFlowComputer.get().call(N, lower, upper, perUnitCost, supply, flow, dual);
int currentCost = 0;
for (edge e = N.firstEdge(); e != nullptr; e = e->succ())
currentCost += perUnitCost[e] * flow[e];
for (adjEntry adj = mu->firstAdj(); adj != nullptr; adj = adj->succ())
currentCost += cost[0][adj->twinNode()];
if (currentCost < cost[bends][mu]) {
cost[bends][mu] = currentCost;
embedding[bends][mu] = currentEmbedding;
}
}
}
dualquat<value_t> fakelog () const {
assert(isunit());
const auto& lower = real().log();
const auto& upper = dual()*real().C();
return dualquat<value_t>(lower, upper);
}
// TODO: expand this
dualquat<value_t> operator*(const dualquat<value_t>& other) const {
const auto& a = real();
const auto& A = dual();
const auto& b = other.real();
const auto& B = other.dual();
return dualquat<value_t>(a*b, (a*B)+(A*b));
}
//-----------------------------------------------------------------------------
MGL_NO_EXPORT void *mgl_cmodify(void *par)
{
mglThreadC *t=(mglThreadC *)par;
const mglFormulaC *f = (const mglFormulaC *)(t->v);
long nx=t->p[0],ny=t->p[1],nz=t->p[2];
dual *b=t->a;
mreal dx,dy,dz;
const dual *v=t->b, *w=t->c;
dx=nx>1?1/(nx-1.):0; dy=ny>1?1/(ny-1.):0; dz=nz>1?1/(nz-1.):0;
#if !MGL_HAVE_PTHREAD
#pragma omp parallel for
#endif
for(long i0=t->id;i0<t->n;i0+=mglNumThr)
{
register long i=i0%nx, j=((i0/nx)%ny), k=i0/(nx*ny);
b[i0] = f->Calc(i*dx, j*dy, k*dz, b[i0], v?v[i0]:dual(0,0), w?w[i0]:dual(0,0));
}
return 0;
}
std::vector<vsr::cga2D::Vec> Intersect(const LineSegment &segment1, const LineSegment &segment2) {
auto L1 = ToLine(segment1);
auto L2 = ToLine(segment2);
// Intersection as a flat point (Flp)
auto intersection = (L1.dual() ^ L2.dual()).dual();
// Check if the only intersection is the point at infinity
if(std::abs(intersection[2]) <= 1e-6) {
return std::vector<vsr::cga2D::Vec>{};
}
// Check if the intersection point is withint the line segments
auto pt = vsr::cga2D::Vec(intersection[0], intersection[1]) / intersection[2];
auto within1 = LineSegmentContainsPoint(segment1, pt);
auto within2 = LineSegmentContainsPoint(segment2, pt);
if(!within1 || !within2) {
return std::vector<vsr::cga2D::Vec>{};
}
return std::vector<vsr::cga2D::Vec>{pt};
}
TEST(SolverContextTest, feature_in_multilabel_out) {
typedef float Data;
typedef double Result;
sdca::size_type n = 50, m = 3, d = 5, pow_from = 0, pow_to = 1;
std::vector<Data> features;
std::vector<sdca::size_type> labels;
std::vector<sdca::size_type> offsets;
std::vector<Data> primal(d * m);
std::vector<Data> dual(m * n);
primal[2] = 1;
dual[3] = 2;
std::mt19937 gen(1);
test_populate_real(n * d, pow_from, pow_to, 1.0f, gen, features);
test_populate_int<sdca::size_type>(n, 1, m, gen, labels);
offsets.resize(n + 1);
std::iota(offsets.begin(), offsets.end(), 0);
auto ctx = sdca::make_context(
sdca::make_input_feature(d, n, &features[0]),
sdca::make_output_multilabel(labels.begin(), labels.end(),
offsets.begin(), offsets.end()),
sdca::make_objective_l2_multilabel_hinge<Data>(),
&dual[0], &primal[0]);
EXPECT_EQ(d, ctx.train.num_dimensions());
EXPECT_EQ(n, ctx.train.num_examples());
EXPECT_EQ(m, ctx.train.num_classes());
EXPECT_EQ(n, ctx.train.out.labels.size());
EXPECT_EQ(n + 1, ctx.train.out.offsets.size());
EXPECT_EQ(primal[2], ctx.primal_variables[2]);
EXPECT_EQ(dual[3], ctx.dual_variables[3]);
EXPECT_FALSE(ctx.is_dual());
sdca::size_type n_tst = n - 5;
labels.resize(n_tst);
offsets.resize(n_tst + 1);
ctx.add_test(sdca::make_input_feature(d, n_tst, &features[0]),
sdca::make_output_multilabel(labels.begin(), labels.end(),
offsets.begin(), offsets.end()));
EXPECT_EQ(static_cast<std::size_t>(1), ctx.test.size());
EXPECT_EQ(d, ctx.test[0].num_dimensions());
EXPECT_EQ(n_tst, ctx.test[0].num_examples());
EXPECT_EQ(m, ctx.test[0].num_classes());
EXPECT_EQ(n_tst, ctx.test[0].out.labels.size());
EXPECT_EQ(n_tst + 1, ctx.test[0].out.offsets.size());
typedef decltype(ctx)::data_type data_type;
typedef decltype(ctx)::result_type result_type;
EXPECT_TRUE((std::is_same<Data, data_type>::value));
EXPECT_TRUE((std::is_same<Result, result_type>::value));
}
//-----------------------------------------------------------------------------
void MGL_EXPORT mgl_datac_set_ap(HADT d, HCDT a, HCDT p)
{
long nx=d->GetNx(),ny=d->GetNy(),nz=d->GetNz();
d->Create(nx,ny,nz);
#pragma omp parallel for
for(long i=0;i<nx*ny*nz;i++)
{
register mreal aa=a->vthr(i), pp=p->vthr(i);
d->a[i] = dual(aa*cos(pp), aa*sin(pp));
}
}
//-----------------------------------------------------------------------------
// evaluate formula for 'x'='r', 'y'='n'='v', 't'='z', 'u'='a' variables
dual mglFormulaC::Calc(dual x,dual y,dual t,dual u) const
{
Error=0;
dual a1[MGL_VS]; memset(a1,0,MGL_VS*sizeof(dual));
a1['a'-'a'] = a1['u'-'a'] = u;
a1['x'-'a'] = a1['r'-'a'] = x;
a1['y'-'a'] = a1['n'-'a'] = a1['v'-'a'] = y;
a1['z'-'a'] = a1['t'-'a'] = t;
a1['i'-'a'] = dual(0,1);
dual b = CalcIn(a1);
return mgl_isfin(b) ? b : NAN;
}
double EvtDecayPlaneNormalAngle(const EvtVector4R& p,const EvtVector4R& q,
const EvtVector4R& d1,const EvtVector4R& d2){
EvtVector4C lc=dual(EvtGenFunctions::directProd(d1,d2)).cont2(q);
EvtVector4R l(real(lc.get(0)),real(lc.get(1)),
real(lc.get(2)),real(lc.get(3)));
double pq=p*q;
return q.mass()*(p*l)/sqrt(-(pq*pq-p.mass2()*q.mass2())*l.mass2());
}
TEST(SolverContextTest, kernel_in_multilabel_out) {
typedef double Data;
typedef double Result;
sdca::size_type n = 50, m = 3, pow_from = 0, pow_to = 1;
std::vector<Data> kernel;
std::vector<sdca::size_type> labels;
std::vector<sdca::size_type> offsets;
std::vector<Data> dual(m * n);
dual[3] = 2;
std::mt19937 gen(1);
test_populate_real(n * n, pow_from, pow_to, 1.0, gen, kernel);
test_populate_int<sdca::size_type>(n, 1, m, gen, labels);
offsets.resize(n + 1);
std::iota(offsets.begin(), offsets.end(), 0);
auto ctx = sdca::make_context(
sdca::make_input_kernel(n, &kernel[0]),
sdca::make_output_multilabel(labels.begin(), labels.end(),
offsets.begin(), offsets.end()),
sdca::make_objective_l2_multilabel_hinge_smooth<Data>(),
&dual[0]);
EXPECT_EQ(n, ctx.train.num_examples());
EXPECT_EQ(m, ctx.train.num_classes());
EXPECT_EQ(n, ctx.train.out.labels.size());
EXPECT_EQ(n + 1, ctx.train.out.offsets.size());
EXPECT_EQ(dual[3], ctx.dual_variables[3]);
EXPECT_TRUE(ctx.is_dual());
sdca::size_type n_tst = n - 5;
labels.resize(n_tst);
offsets.resize(n_tst + 1);
ctx.add_test(sdca::make_input_kernel(n, n_tst, &kernel[0]),
sdca::make_output_multilabel(labels.begin(), labels.end(),
offsets.begin(), offsets.end()));
EXPECT_EQ(n_tst, ctx.test[0].num_examples());
EXPECT_EQ(m, ctx.test[0].num_classes());
EXPECT_EQ(n_tst, ctx.test[0].out.labels.size());
EXPECT_EQ(n_tst + 1, ctx.test[0].out.offsets.size());
typedef decltype(ctx)::data_type data_type;
typedef decltype(ctx)::result_type result_type;
EXPECT_TRUE((std::is_same<Data, data_type>::value));
EXPECT_TRUE((std::is_same<Result, result_type>::value));
}
int main()
{
em::mv<7>::type Ie = {1.0};
em::mv<1,2,4>::type a = {1.0,2.0,3.0};
std::cout << "a: " << a << ", *a: " << dual(a) << ", **a: " << dual(dual(a)) << std::endl;
std::cout << "a*~I: " << a*(~Ie) << ", a*~I*I: " << a*(~Ie)*Ie << std::endl;
std::cout << "a*~I: " << a*(~Ie) << ", a*~I*~I: " << a*(~Ie)*(~Ie) << std::endl;
static const sa::mv<1>::type e1={1.0};
static const sa::mv<2>::type e2={1.0};
static const sa::mv<4>::type e3={1.0};
static const sa::mv<0x40>::type e0={1.0};
std::cout << "dual(e1*e2): " << dual(e1*e2) << std::endl;
std::cout << "dual(e3*e0): " << dual(e3*e0) << std::endl;
std::cout << "*(*(e1*e2) ^ *(e3*e0)): " << dual(dual(e1*e2) ^ dual(e3*e0)) << std::endl;
}
//-----------------------------------------------------------------------------
void mglFromStr(HADT d,char *buf,long NX,long NY,long NZ) // TODO: add multithreading read
{
if(NX<1 || NY <1 || NZ<1) return;
mgl_datac_create(d, NX,NY,NZ);
long nb = strlen(buf);
register long i=0, j=0;
setlocale(LC_NUMERIC, "C");
while(j<nb)
{
while(buf[j]<=' ' && j<nb) j++;
while(buf[j]=='#') // skip comment
{
if(i>0 || buf[j+1]!='#') // this is columns id
while(!isn(buf[j]) && j<nb) j++;
else
{
while(!isn(buf[j]) && j<nb)
{
if(buf[j]>='a' && buf[j]<='z')
d->id.push_back(buf[j]);
j++;
}
}
while(buf[j]<=' ' && j<nb) j++;
}
char *s=buf+j;
while(buf[j]>=' ' && buf[j]!=';' && j<nb) j++;
buf[j]=0;
double re=0,im=0; size_t ll=strlen(s);
if(*s=='(') sscanf(s,"(%lg,%lg)",&re,&im);
else if(*s=='[') sscanf(s,"[%lg,%lg]",&re,&im);
else if(*s=='{') sscanf(s,"{%lg,%lg}",&re,&im);
else if(s[ll]=='i') { s[ll] = 0; sscanf(s,"%lg+%lg)",&re,&im); }
else sscanf(s,"%lg+i%lg",&re,&im);
d->a[i] = dual(re,im);
i++; if(i>=NX*NY*NZ) break;
}
setlocale(LC_NUMERIC, "");
}
/**
merging a prismatic (oox) and cylindrical (oof) constraint may result in:
<ul>
<li> fixed : all other cases
</ul>
An outer product of the orientation will be zero when they are parallel.
When they define a fixed joint, the locating point is on the
axis of the prismatic joint.
*/
Joint meld_oox_oof(const Joint& slider, const Joint& axis, const bool flip = false) {
//log4cpp::CategoryStream& log = slider.log_cf.infoStream();
//log << (flip ? "meld_oof_oox" : "meld_oox_oof");
//
isis_LOG(lg, isis_FILE, isis_INFO) << (flip ? "meld_oof_oox" : "meld_oox_oof");
e3ga::vector u = e3ga::unit(slider.orientation);
e3ga::vector v = e3ga::unit(axis.orientation);
e3ga::bivector uv = u ^ v;
if (e3ga::zero(uv, DEFAULT_TOLERANCE)) {
return slider;
}
e3ga::vector w = dual(uv);
e3ga::bivector vw = v ^ w;
e3ga::bivector wu = w ^ u;
double uvw = norm(u ^ v ^ w);
e3ga::vector p = axis.location;
e3ga::vector q = slider.location;
e3ga::vector r = q;
double pvw = norm(p ^ v ^ w);
double quw = norm(q ^ u ^ w);
double ruv = norm(r ^ u ^ v);
e3ga::vector location =
(pvw / uvw)*u + (quw / uvw) * v + (ruv / uvw) * w;
Joint result(FIXED,
location, slider.orientation, slider.rotation,
slider, axis);
return result;
}
/*
Synopsis: like the previous one, but for the _dual_ real forms.
*/
Interface::Interface(const ComplexReductiveGroup& G,
const lietype::Layout& lo, tags::DualTag)
: d_in(G.numDualRealForms())
, d_out(G.numDualRealForms())
, d_name(G.numDualRealForms())
{
const size_t ndrf = G.numDualRealForms();
const RootSystem& drs = G.dualRootSystem();
const Fiber& dfundf = G.dualFundamental();
const lietype::Layout dlo = dual(lo);
std::vector<RealFormData> rf_data; rf_data.reserve(ndrf);
for (RealFormNbr drf = 0; drf<ndrf; ++drf)
{
RootNbrSet so = cartanclass::toMostSplit(dfundf,drf,drs);
Grading gr = cartanclass::specialGrading(dfundf,drf,drs);
rf_data.push_back(RealFormData(drf,gr,so));
}
std::sort(rf_data.begin(),rf_data.end());
for (size_t i=0; i<ndrf; ++i)
{
d_in[i] = rf_data[i].realForm();
d_out[d_in[i]] = i;
}
// write names
std::ostringstream os;
for (size_t i=0; i<ndrf; ++i)
{
os.str("");
printType(os,rf_data[i].grading(),dlo);
d_name[i] = os.str();
}
}
static unsigned getNearestOuterItemID(const Cell_handle &cell,
const std::vector<SupportItem> &items,
const Vertex_handle &infinity)
{
DEBUG_START;
Plane_3 plane = getOppositeFacetPlane(cell, infinity);
Point_3 point = dual(plane);
cell->info().point = point;
double distanceMin = MINIMIZATION_STARTING_VALUE;
unsigned iNearest = 0;
const auto &associations = cell->info().associations;
unsigned numUnresolved = 0;
for (unsigned iPlane : associations)
{
SupportItem item = items[iPlane];
Vector_3 u = item.direction;
double value = item.value;
double distance = value - u * (point - CGAL::Origin());
if (!item.resolved)
{
ASSERT(distance > 0. && "Incorrect resolved flag");
if (distance < distanceMin)
{
iNearest = iPlane;
distanceMin = distance;
}
++numUnresolved;
}
}
if (numUnresolved > 0)
ASSERT(distanceMin < MINIMIZATION_STARTING_VALUE
&& "Failed to find");
cell->info().distance = distanceMin;
DEBUG_END;
return iNearest;
}
void OptimalRanking::doCall(
const Graph& G,
NodeArray<int> &rank,
EdgeArray<bool> &reversed,
const EdgeArray<int> &length,
const EdgeArray<int> &costOrig)
{
MinCostFlowReinelt<int> mcf;
// construct min-cost flow problem
GraphCopy GC;
GC.createEmpty(G);
// compute connected component of G
NodeArray<int> component(G);
int numCC = connectedComponents(G,component);
// intialize the array of lists of nodes contained in a CC
Array<List<node> > nodesInCC(numCC);
for(node v : G.nodes)
nodesInCC[component[v]].pushBack(v);
EdgeArray<edge> auxCopy(G);
rank.init(G);
for(int i = 0; i < numCC; ++i)
{
GC.initByNodes(nodesInCC[i], auxCopy);
makeLoopFree(GC);
for(edge e : GC.edges)
if(reversed[GC.original(e)])
GC.reverseEdge(e);
// special cases:
if(GC.numberOfNodes() == 1) {
rank[GC.original(GC.firstNode())] = 0;
continue;
} else if(GC.numberOfEdges() == 1) {
edge e = GC.original(GC.firstEdge());
rank[e->source()] = 0;
rank[e->target()] = length[e];
continue;
}
EdgeArray<int> lowerBound(GC,0);
EdgeArray<int> upperBound(GC,mcf.infinity());
EdgeArray<int> cost(GC);
NodeArray<int> supply(GC);
for(edge e : GC.edges)
cost[e] = -length[GC.original(e)];
for(node v : GC.nodes) {
int s = 0;
edge e;
forall_adj_edges(e,v) {
if(v == e->source())
s += costOrig[GC.original(e)];
else
s -= costOrig[GC.original(e)];
}
supply[v] = s;
}
OGDF_ASSERT(isAcyclic(GC) == true);
// find min-cost flow
EdgeArray<int> flow(GC);
NodeArray<int> dual(GC);
#ifdef OGDF_DEBUG
bool feasible =
#endif
mcf.call(GC, lowerBound, upperBound, cost, supply, flow, dual);
OGDF_ASSERT(feasible);
for(node v : GC.nodes)
rank[GC.original(v)] = dual[v];
}
}
//-----------------------------------------------------------------------------
// Formula constructor (automatically parse and "compile" formula)
mglFormulaC::mglFormulaC(const char *string)
{
Error=0;
Left=Right=0;
Res=0; Kod=0;
if(!string) { Kod = EQ_NUM; Res = 0; return; }
char *str = new char[strlen(string)+1];
strcpy(str,string);
long n,len;
mgl_strtrim(str);
mgl_strlwr(str);
len=strlen(str);
if(str[0]==0) { delete []str; return; }
if(str[0]=='(' && mglCheck(&(str[1]),len-2)) // remove braces
{
memmove(str,str+1,len);
len-=2; str[len]=0;
}
len=strlen(str);
n=mglFindInText(str,"<>="); // low priority -- conditions
if(n>=0)
{
if(str[n]=='<') Kod=EQ_LT;
else if(str[n]=='>') Kod=EQ_GT;
else Kod=EQ_EQ;
str[n]=0;
Left=new mglFormulaC(str);
Right=new mglFormulaC(str+n+1);
delete []str; return;
}
n=mglFindInText(str,"+-"); // normal priority -- additions
if(n>=0 && (n<2 || str[n-1]!='e' || (str[n-2]!='.' && !isdigit(str[n-2]))))
{
if(str[n]=='+') Kod=EQ_ADD; else Kod=EQ_SUB;
str[n]=0;
Left=new mglFormulaC(str);
Right=new mglFormulaC(str+n+1);
delete []str; return;
}
n=mglFindInText(str,"*/"); // high priority -- multiplications
if(n>=0)
{
if(str[n]=='*') Kod=EQ_MUL; else Kod=EQ_DIV;
str[n]=0;
Left=new mglFormulaC(str);
Right=new mglFormulaC(str+n+1);
delete []str; return;
}
n=mglFindInText(str,"^"); // highest priority -- power
if(n>=0)
{
Kod=EQ_IPOW; str[n]=0;
Left=new mglFormulaC(str);
Right=new mglFormulaC(str+n+1);
delete []str; return;
}
for(n=0;n<len;n++) if(str[n]=='(') break;
if(n>=len) // this is number or variable
{
Kod = EQ_NUM;
// Left = Right = 0;
if(str[1]==0 && str[0]>='a' && str[0]<='z') // available variables
{ Kod=EQ_A; Res = str[0]-'a'; }
else if(!strcmp(str,"rnd")) Kod=EQ_RND;
else if(!strcmp(str,"pi")) Res=M_PI;
else if(!strcmp(str,"inf")) Res=INFINITY;
else if(str[0]=='i') Res = dual(0,atof(str+1));
else Res = (str[len-1]=='i') ? dual(0,atof(str)) : atof(str);
}
else
{
char name[128];
mgl_strncpy(name,str,128); name[127]=name[n]=0;
memmove(str,str+n+1,len-n);
len=strlen(str); str[--len]=0;
if(!strcmp(name,"sin")) Kod=EQ_SIN;
else if(!strcmp(name,"cos")) Kod=EQ_COS;
else if(!strcmp(name,"tg")) Kod=EQ_TAN;
else if(!strcmp(name,"tan")) Kod=EQ_TAN;
else if(!strcmp(name,"asin")) Kod=EQ_ASIN;
else if(!strcmp(name,"acos")) Kod=EQ_ACOS;
else if(!strcmp(name,"atan")) Kod=EQ_ATAN;
else if(!strcmp(name,"sinh")) Kod=EQ_SINH;
else if(!strcmp(name,"cosh")) Kod=EQ_COSH;
else if(!strcmp(name,"tanh")) Kod=EQ_TANH;
else if(!strcmp(name,"sh")) Kod=EQ_SINH;
else if(!strcmp(name,"ch")) Kod=EQ_COSH;
else if(!strcmp(name,"th")) Kod=EQ_TANH;
else if(!strcmp(name,"sqrt")) Kod=EQ_SQRT;
else if(!strcmp(name,"log")) Kod=EQ_LOG;
else if(!strcmp(name,"pow")) Kod=EQ_POW;
else if(!strcmp(name,"exp")) Kod=EQ_EXP;
else if(!strcmp(name,"lg")) Kod=EQ_LG;
else if(!strcmp(name,"ln")) Kod=EQ_LN;
else if(!strcmp(name,"abs")) Kod=EQ_ABS;
else if(!strcmp(name,"arg")) Kod=EQ_ARG;
else if(!strcmp(name,"conj")) Kod=EQ_CONJ;
else if(!strcmp(name,"real")) Kod=EQ_REAL;
else if(!strcmp(name,"imag")) Kod=EQ_IMAG;
else if(!strcmp(name,"norm")) Kod=EQ_NORM;
else if(!strcmp(name,"cmplx")) Kod=EQ_CMPLX;
else if(!strcmp(name,"hypot")) Kod=EQ_HYPOT;
else { delete []str; return; } // unknown function
n=mglFindInText(str,",");
if(n>=0)
{
str[n]=0;
Left=new mglFormulaC(str);
Right=new mglFormulaC(str+n+1);
}
else
Left=new mglFormulaC(str);
}
delete []str;
}
void work()
{
read();
dual();
scan();
}
/**
Convert a joint marker into a c3ga plane.
*/
c3ga::plane c3gaPlane( const Joint joint ) {
c3ga::normalizedPoint locate_pnt = c3ga_point( joint.location );
c3ga::normalizedPoint orient_vec = c3ga_point( joint.orientation );
return c3ga::plane
(locate_pnt ^ dual(orient_vec), 0);
}
//######################################################################
/// this is the Volume Algorithm
int
VOL_problem::solve(VOL_user_hooks& hooks, const bool use_preset_dual)
{
if (initialize(use_preset_dual) < 0) // initialize several parameters
return -1;
double best_ub = parm.ubinit; // upper bound
int retval = 0;
VOL_dvector rc(psize); // reduced costs
VOL_dual dual(dsize); // dual vector
dual.u = dsol;
VOL_primal primal(psize, dsize); // primal vector
retval = hooks.compute_rc(dual.u, rc); // compute reduced costs
if (retval < 0) return -1;
// solve relaxed problem
retval = hooks.solve_subproblem(dual.u, rc, dual.lcost,
primal.x, primal.v, primal.value);
if (retval < 0) return -1;
// set target for the lagrangian value
double target = readjust_target(-COIN_DBL_MAX/2, dual.lcost);
// find primal violation
primal.find_max_viol(dual_lb, dual_ub); // this may be left out for speed
VOL_primal pstar(primal); // set pstar=primal
pstar.find_max_viol(dual_lb, dual_ub); // set violation of pstar
dual.compute_xrc(pstar.x, primal.x, rc); // compute xrc
//
VOL_dual dstar(dual); // dstar is the best dual solution so far
VOL_dual dlast(dual); // set dlast=dual
iter_ = 0;
if (parm.printflag)
print_info(iter_, primal, pstar, dual);
VOL_swing swing;
VOL_alpha_factor alpha_factor;
double * lcost_sequence = new double[parm.ascent_check_invl];
const int ascent_first_check = VolMax(parm.ascent_first_check,
parm.ascent_check_invl);
for (iter_ = 1; iter_ <= parm.maxsgriters; ++iter_) { // main iteration
dlast = dual;
// take a dual step
dual.step(target, lambda_, dual_lb, dual_ub, pstar.v);
// compute reduced costs
retval = hooks.compute_rc(dual.u, rc);
if (retval < 0) break;
// solve relaxed problem
retval = hooks.solve_subproblem(dual.u, rc, dual.lcost,
primal.x, primal.v, primal.value);
if (retval < 0) break;
// set the violation of primal
primal.find_max_viol(dual_lb, dual_ub); // this may be left out for speed
dual.compute_xrc(pstar.x, primal.x, rc); // compute xrc
if (dual.lcost > dstar.lcost) {
dstar = dual; // update dstar
}
// check if target should be updated
target = readjust_target(target, dstar.lcost);
// compute inner product between the new subgradient and the
// last direction. This to decide among green, yellow, red
const double ascent = dual.ascent(primal.v, dlast.u);
// green, yellow, red
swing.cond(dlast, dual.lcost, ascent, iter_);
// change lambda if needed
lambda_ *= swing.lfactor(parm, lambda_, iter_);
if (iter_ % parm.alphaint == 0) { // change alpha if needed
const double fact = alpha_factor.factor(parm, dstar.lcost, alpha_);
if (fact != 1.0 && (parm.printflag & 2)) {
printf(" ------------decreasing alpha to %f\n", alpha_*fact);
}
alpha_ *= fact;
}
// convex combination with new primal vector
pstar.cc(power_heur(primal, pstar, dual), primal);
pstar.find_max_viol(dual_lb, dual_ub); // find maximum violation of pstar
if (swing.rd)
dual = dstar; // if there is no improvement reset dual=dstar
if ((iter_ % parm.printinvl == 0) && parm.printflag) { // printing iteration information
print_info(iter_, primal, pstar, dual);
swing.print();
}
if (iter_ % parm.heurinvl == 0) { // run primal heuristic
double ub = COIN_DBL_MAX;
retval = hooks.heuristics(*this, pstar.x, ub);
if (retval < 0) break;
if (ub < best_ub)
best_ub = ub;
}
// save dual solution every 500 iterations
if (iter_ % 500 == 0 && parm.temp_dualfile != 0) {
FILE* outfile = fopen(parm.temp_dualfile, "w");
const VOL_dvector& u = dstar.u;
const int m = u.size();
for (int i = 0; i < m; ++i) {
fprintf(outfile, "%i %f\n", i+1, u[i]);
}
fclose(outfile);
}
// test terminating criteria
const bool primal_feas =
(pstar.viol < parm.primal_abs_precision);
//const double gap = VolAbs(pstar.value - dstar.lcost);
const double gap = pstar.value - dstar.lcost;
const bool small_gap = VolAbs(dstar.lcost) < 0.0001 ?
(gap < parm.gap_abs_precision) :
( (gap < parm.gap_abs_precision) ||
(gap/VolAbs(dstar.lcost) < parm.gap_rel_precision) );
// test optimality
if (primal_feas && small_gap){
if (parm.printflag) printf(" small lp gap \n");
break;
}
// test proving integer optimality
if (best_ub - dstar.lcost < parm.granularity){
if (parm.printflag) printf(" small ip gap \n");
break;
}
// test for non-improvement
const int k = iter_ % parm.ascent_check_invl;
if (iter_ > ascent_first_check) {
if (dstar.lcost - lcost_sequence[k] <
VolAbs(lcost_sequence[k]) * parm.minimum_rel_ascent){
if (parm.printflag) printf(" small improvement \n");
break;
}
}
lcost_sequence[k] = dstar.lcost;
}
delete[] lcost_sequence;
if (parm.printflag)
print_info(iter_, primal, pstar, dual);
// set solution to return
value = dstar.lcost;
psol = pstar.x;
dsol = dstar.u;
viol = pstar.v;
return retval;
}
void EmbedderOptimalFlexDraw::call(Graph &G, adjEntry &adjExternal)
{
StaticPlanarSPQRTree T(G);
NodeArray<int> cost[4];
NodeArray<long long> embedding[4];
for (int bends = 0; bends < 4; ++bends) {
cost[bends].init(T.tree());
embedding[bends].init(T.tree());
}
int minCost = numeric_limits<int>::max();
node minCostRoot;
long long minCostEmbedding;
for (node root = T.tree().firstNode(); root != nullptr; root = root->succ()) {
T.rootTreeAt(root);
for (adjEntry adj = root->firstAdj(); adj != nullptr; adj = adj->succ())
computePrincipalSplitComponentCost(T, cost, embedding, root, adj->twinNode());
optimizeOverEmbeddings(T, nullptr, root, 0, cost, embedding);
if (cost[0][root] < minCost) {
minCost = cost[0][root];
minCostEmbedding = embedding[0][root];
minCostRoot = root;
}
}
T.rootTreeAt(minCostRoot);
T.embed(minCostRoot, minCostEmbedding);
for (adjEntry adj = minCostRoot->firstAdj(); adj != nullptr; adj = adj->succ())
computePrincipalSplitComponentCost(T, cost, embedding, minCostRoot, adj->twinNode());
Skeleton &skeleton = T.skeleton(minCostRoot);
Graph skeletonGraph = skeleton.getGraph();
ConstCombinatorialEmbedding skeletonEmbedding(skeletonGraph);
EdgeArray<node> edgeNode(skeletonGraph);
Graph N;
EdgeArray<int> upper(N);
EdgeArray<int> perUnitCost(N);
NodeArray<int> supply(N);
createNetwork(
nullptr,
minCostRoot,
0,
cost,
embedding,
skeleton,
edgeNode,
N,
upper,
perUnitCost,
supply);
EdgeArray<int> lower(N, 0);
EdgeArray<int> flow(N);
NodeArray<int> dual(N);
m_minCostFlowComputer.get().call(N, lower, upper, perUnitCost, supply, flow, dual);
for (node mu = T.tree().firstNode(); mu != nullptr; mu = mu->succ()) {
if (mu == minCostRoot)
continue;
int bends = 0;
for (adjEntry adj = edgeNode[T.skeleton(mu).referenceEdge()]->firstAdj(); adj != nullptr; adj = adj->succ())
bends += abs(flow[adj->theEdge()]);
T.embed(mu, embedding[bends][mu]);
}
T.embed(G);
ConstCombinatorialEmbedding graphEmbedding(G);
adjExternal = graphEmbedding.externalFace()->firstAdj();
}
// JOIN operation; higher in lattice. Done by finding the dual of the
// meet of the dual of the 2 inputs.
const Type *join( const Type *t ) const {
return dual()->meet(t->dual())->dual(); }
void EvtKstarnunu::decay(EvtParticle *p){
static EvtId NUE=EvtPDL::getId("nu_e");
static EvtId NUM=EvtPDL::getId("nu_mu");
static EvtId NUT=EvtPDL::getId("nu_tau");
static EvtId NUEB=EvtPDL::getId("anti-nu_e");
static EvtId NUMB=EvtPDL::getId("anti-nu_mu");
static EvtId NUTB=EvtPDL::getId("anti-nu_tau");
p->initializePhaseSpace(getNDaug(),getDaugs());
double m_b = p->mass();
EvtParticle *meson, *neutrino1, *neutrino2;
meson = p->getDaug(0);
neutrino1 = p->getDaug(1);
neutrino2 = p->getDaug(2);
EvtVector4R momnu1 = neutrino1->getP4();
EvtVector4R momnu2 = neutrino2->getP4();
EvtVector4R momkstar = meson->getP4();
double v0_0, a1_0, a2_0;
double m2v0, a1_b, a2_b;
v0_0 = 0.47;
a1_0 = 0.37;
a2_0 = 0.40;
m2v0 = 5.*5.;
a1_b = -0.023;
a2_b = 0.034;
EvtVector4R q = momnu1+momnu2;
double q2 = q.mass2();
double v0, a1, a2;
v0 = v0_0/(1-q2/m2v0);
a1 = a1_0*(1+a1_b*q2);
a2 = a2_0*(1+a2_b*q2);
EvtVector4R p4b; p4b.set(m_b,0.,0.,0.); // Do calcs in mother rest frame
double m_k = meson->mass();
EvtTensor4C tds=(-2*v0/(m_b+m_k))*dual(EvtGenFunctions::directProd(p4b,momkstar))
- EvtComplex(0.0,1.0)*
( (m_b+m_k)*a1*EvtTensor4C::g()
- (a2/(m_b+m_k))*EvtGenFunctions::directProd(p4b-momkstar,p4b+momkstar));
EvtVector4C l;
if (getDaug(1)==NUE||getDaug(1)==NUM||getDaug(1)==NUT) {
l=EvtLeptonVACurrent(neutrino1->spParentNeutrino(),
neutrino2->spParentNeutrino());
}
if (getDaug(1)==NUEB||getDaug(1)==NUMB||getDaug(1)==NUTB) {
l=EvtLeptonVACurrent(neutrino2->spParentNeutrino(),
neutrino1->spParentNeutrino());
}
EvtVector4C et0,et1,et2;
et0 = tds.cont1( meson->epsParent(0).conj() );
et1 = tds.cont1( meson->epsParent(1).conj() );
et2 = tds.cont1( meson->epsParent(2).conj() );
vertex(0,l*et0);
vertex(1,l*et1);
vertex(2,l*et2);
return;
}
//======================================================
void EvtBcVNpi::decay( EvtParticle *root_particle ) {
++nCall;
// cout<<"BcVNpi::decay()"<<endl;
root_particle->initializePhaseSpace(getNDaug(),getDaugs());
EvtVector4R
p4b(root_particle->mass(), 0., 0., 0.), // Bc momentum
p4meson=root_particle->getDaug(0)->getP4(), // J/psi momenta
Q=p4b-p4meson;
double Q2=Q.mass2();
// check pi-mesons and calculate hadronic current
EvtVector4C hardCur;
// bool foundHadCurr=false;
if( getNDaug() == 2) {
hardCur = wcurr->WCurrent( root_particle->getDaug(1)->getP4() );
// foundHadCurr=true;
}
else if( getNDaug() == 3) {
hardCur = wcurr->WCurrent( root_particle->getDaug(1)->getP4() ,
root_particle->getDaug(2)->getP4()
);
// foundHadCurr=true;
}
else if( getNDaug() == 4) {
hardCur = wcurr->WCurrent( root_particle->getDaug(1)->getP4() ,
root_particle->getDaug(2)->getP4(),
root_particle->getDaug(3)->getP4()
);
// foundHadCurr=true;
}
else if( getNDaug() == 6) // Bc -> psi pi+ pi+ pi- pi- pi+ from [Kuhn, Was, hep-ph/0602162
{
hardCur = wcurr->WCurrent(root_particle->getDaug(1)->getP4(),
root_particle->getDaug(2)->getP4(),
root_particle->getDaug(3)->getP4(),
root_particle->getDaug(4)->getP4(),
root_particle->getDaug(5)->getP4()
);
// foundHadCurr=true;
}
else {
report(Severity::Error,"EvtGen") << "Have not yet implemented this final state in BCNPI model" << endl;
report(Severity::Error,"EvtGen") << "Ndaug="<<getNDaug() << endl;
int id;
for ( id=0; id<(getNDaug()-1); id++ )
report(Severity::Error,"EvtGen") << "Daug " << id << " "<<EvtPDL::name(getDaug(id)).c_str() << endl;
::abort();
};
// calculate Bc -> V W form-factors
double a1f, a2f, vf, a0f;
double m_meson = root_particle->getDaug(0)->mass();
double m_b = root_particle->mass();
ffmodel->getvectorff(root_particle->getId(),
root_particle->getDaug(0)->getId(),
Q2,
m_meson,
&a1f,
&a2f,
&vf,
&a0f);
double a3f = ((m_b+m_meson)/(2.0*m_meson))*a1f -
((m_b-m_meson)/(2.0*m_meson))*a2f;
// calculate Bc -> V W current
EvtTensor4C H;
H = a1f*(m_b+m_meson)*EvtTensor4C::g();
H.addDirProd((-a2f/(m_b+m_meson))*p4b,p4b+p4meson);
H+=EvtComplex(0.0,vf/(m_b+m_meson))*dual(EvtGenFunctions::directProd(p4meson+p4b,p4b-p4meson));
H.addDirProd((a0f-a3f)*2.0*(m_meson/Q2)*p4b,p4b-p4meson);
EvtVector4C Heps=H.cont2(hardCur);
for(int i=0; i<4; i++) {
EvtVector4C eps=root_particle->getDaug(0)->epsParent(i).conj(); // psi-meson polarization vector
EvtComplex amp=eps*Heps;
vertex(i,amp);
};
}
