LinAlg::Matrix<float> SistemasLineares::GaussJacobi(LinAlg::Matrix<float> MatrizUni, unsigned MaxIterations)
{
//Matriz Resposta
LinAlg::Matrix<float> MatrizRes(MaxIterations, MatrizUni.getNumberOfColumns());
LinAlg::Matrix<float> C (MatrizUni.getNumberOfRows(), MatrizUni.getNumberOfColumns() - 1);
LinAlg::Matrix<float> g (MatrizUni.getNumberOfRows(), 1);
LinAlg::Matrix<float> x0(C.getNumberOfColumns(), 1);
// //Deixa o vetor de chute inicial padronizado como vetor linha
if(this->X0.getNumberOfColumns() < this->X0.getNumberOfRows())
~this->X0;
// //Insere o chute inicial na Matriz resposta
for(unsigned i = 1; i < MatrizRes.getNumberOfColumns() - 1; ++i)
x0(1,i) = this->X0(1,i);
//Laço para contar as linhas da MatrizUni e Matriz C.
for(unsigned i = 1; i <= MatrizUni.getNumberOfRows(); ++i)
{ //Laço para contar as colunas da MAtrizUni e Matriz C.
for(unsigned j = 1; j < MatrizUni.getNumberOfColumns(); ++j)
{
if(i != j)
C(i,j) = - MatrizUni(i,j)/MatrizUni(i,i);//Matriz com a diagonal zerada.
}
g(i,1) = MatrizUni(i,MatrizUni.getNumberOfColumns()) / MatrizUni(i,i);//Matriz dos termos independentes.
}
MatrizRes = ~x0;
for(unsigned k = 1; k < MaxIterations; ++k)
{
x0 = (C * x0) + g;
MatrizRes = MatrizRes || ~x0;
}
return MatrizRes;
}
void CVMath::setupMatrixM1()
{
Line r1 = Points::getInstance().getR1();
Line r2 = Points::getInstance().getR2();
Line r3 = Points::getInstance().getR3();
Line r4 = Points::getInstance().getR4();
l0 << r1.x, r1.y, r1.z;
l1 << r2.x, r2.y, r2.z;
l2 << r3.x, r3.y, r3.z;
l3 << r4.x, r4.y, r4.z;
x0 = l0.cross(l1);
x0 << x0(0)/x0(2), x0(1)/x0(2), 1;
x1 = l2.cross(l3);
x1 << x1(0)/x1(2), x1(1)/x1(2), 1;
l = x0.cross(x1);
Hp = MatrixXd(3, 3);
Hp << 1, 0, 0,
0, 1, 0,
l(0), l(1), l(2);
std::cout << Hp << std::endl;
Vector3d l0;
Vector3d l1;
Hp_INV = MatrixXd(3, 3);
Hp_INV = Hp.inverse().eval();
std::cout << Hp_INV << std::endl;
}
Vector Initialize()
{
Vector x0(3, 0.0);
x0(0) = 10000;
return x0;
}
void MyWidget::process()
{
ui->plainTextEdit->clear();
variant = ui->comboBox->currentIndex();
print(QString("Variant %1").arg(variant));
print(QString("[%1; %2]").arg(x0(), 0, 'g', 5).arg(xFinish(), 0, 'g', 3));
//calc
qreal x = x0(), y = y0(), z = z0();
for (int i = 1; x < xFinish() || qFuzzyCompare(x, xFinish()); ++i)
{
qreal k1 = h() * f(x, y, z);
qreal q1 = h() * g(x, y, z);
qreal k2 = h() * f(x + h() / 2.0, y + k1 / 2.0, z + q1 / 2.0);
qreal q2 = h() * g(x + h() / 2.0, y + k1 / 2.0, z + q1 / 2.0);
qreal k3 = h() * f(x + h() / 2.0, y + k2 / 2.0, z + q2 / 2.0);
qreal q3 = h() * g(x + h() / 2.0, y + k2 / 2.0, z + q2 / 2.0);
qreal k4 = h() * f(x + h(), y + k3, z + q3);
qreal q4 = h() * g(x + h(), y + k3, z + q3);
print(QString("#%1").arg(i));
print(QString("y(%1) = %2").arg(x, 0, 'g', 5).arg(y, 0, 'g', 5));
print(QString("y_ex(%1) = %2").arg(x, 0, 'g',5).arg(yt(x), 0, 'g', 5));
print(QString("error(%1) = %2").arg(x, 0, 'g',5).arg(ypo(y, x), 0, 'g', 5));
x += h();
y += (k1 + 2.0 * k2 + 2.0 * k3 + k4) / 6.0;
z += (q1 + 2.0 * q2 + 2.0 * q3 + q4) / 6.0;
}
}
void FoncATrou_OPB_Comp<Type>::calc_buf
(
INT ** output,
INT *** input
)
{
for (INT d= 0; d<dim_out() ; d++)
{
convert
(
output[d]+x0(),
input[std::min(d,dim_in()-1)][0]+x0(),
tx()
);
}
INT a0 = _cpt[ycur()];
INT a1 = _cpt[ycur()+1];
for (INT a=a0 ; a<a1 ; a++)
{
INT x = _tx[a];
for (INT d= 0; d<dim_out() ; d++)
output[d][x] = _v[d][a];
}
}
void xRungeKutta4 :: halfTest (void)
{
gpstk::Matrix<double> x0(2,1), truncError(2,1);
x0(0,0) = 0.001; // Initial angle in radians
x0(1,0) = 0.0; // Initial angular velocity in radians/second
PendulumIntegrator pModel(x0,0.);
double g = 9.81, L = 1.0;
pModel.setPhysics(g,L);
double deltaT = .00001; // Step size in seconds for integrator
double time = 0;
double Nper = 2.5; // number of periods
double addError = 0; //Total Error for angle
double addDotError = 0; //Total Error for rate of change in angle
long count = 0;
while (pModel.getTime() < Nper * (2*3.14159265/sqrt(g/L)))
{
pModel.integrateTo((count++)*deltaT,truncError);
addError += fabs(truncError(0,0));
addDotError += fabs(truncError(1,0));
}
CPPUNIT_ASSERT_DOUBLES_EQUAL(-x0(0,0),pModel.getState()(0,0),addError*2);
CPPUNIT_ASSERT_DOUBLES_EQUAL(x0(1,0),pModel.getState()(1,0),addDotError*2);
}
mat nnls_solver(const mat & H, mat mu, const umat & mask, int max_iter, double rel_tol, int n_threads)
{
/****************************************************************************************************
* Description: sequential Coordinate-wise algorithm for non-negative least square regression problem
* A x = b, s.t. x[!m] >= 0, x[m] == 0
* Arguments:
* H : A^T * A
* mu : -A^T * b
* mask : a mask matrix (m) of same dim of x
* max_iter : maximum number of iterations
* rel_tol : stop criterion, minimum change on x between two successive iteration
* n_threads : number of threads
* Return:
* x : solution to argmin_{x, x>=0} ||Ax - b||_F^2
* Reference:
* http://cmp.felk.cvut.cz/ftp/articles/franc/Franc-TR-2005-06.pdf
* Author:
* Eric Xihui Lin <*****@*****.**>
* Version:
* 2015-11-16
****************************************************************************************************/
mat x(H.n_cols, mu.n_cols, fill::zeros);
if (n_threads < 0) n_threads = 0;
bool is_masked = !mask.empty();
#pragma omp parallel for num_threads(n_threads) schedule(dynamic)
for (int j = 0; j < mu.n_cols; j++)
{
if (is_masked && arma::all(mask.col(j)))
continue;
vec x0(H.n_cols);
// x0.fill(-9999);
double tmp;
int i = 0;
double err1, err2 = 9999;
do {
// break if all entries of col_j are masked
x0 = x.col(j);
err1 = err2;
err2 = 0;
for (int k = 0; k < H.n_cols; k++)
{
if (is_masked && mask(k,j) > 0) continue;
tmp = x(k,j) - mu(k,j) / H(k,k);
if (tmp < 0) tmp = 0;
if (tmp != x(k,j))
{
mu.col(j) += (tmp - x(k,j)) * H.col(k);
}
x(k,j) = tmp;
tmp = std::abs(x(k,j) - x0(k));
if (tmp > err2) err2 = tmp;
}
} while(++i < max_iter && std::abs(err1 - err2) / (err1 + 1e-9) > rel_tol);
}
return x;
}
Vector Initialize()
{
Vector x0(3, 0.0);
x0(0) = 400;
x0(1) = 798;
return x0;
}
void MinimizerThread::run()
{
boost::numeric::ublas::vector< double > x0(2);
x0(0) = x0_;
x0(1) = y0_;
if(!solver_->isExternalSolver())
{
NativeSolver *nativeSolver = dynamic_cast< NativeSolver * >(solver_);
if(C_ != NULL)
solver_->setup(*objFunc_, x0, Solver::DefaultSetup(), *C_);
else
solver_->setup(*objFunc_, x0, Solver::DefaultSetup(), NoConstraints());
results_.iterates.clear();
results_.iterates.push_back(x0);
if(nativeSolver->getM() > 1)
{
results_.iteratePointSets.clear();
results_.iteratePointSets.push_back(nativeSolver->getXArray());
}
unsigned int nIter = 0;
NativeSolver::IterationStatus status = NativeSolver::ITERATION_CONTINUE;
while(status == NativeSolver::ITERATION_CONTINUE &&
(nativeSolver->hasBuiltInStoppingCriterion() ||
!stopCrit_->test(*nativeSolver)) &&
nIter < 10000 && !terminationFlag_)
{
status = nativeSolver->iterate();
results_.iterates.push_back(nativeSolver->getX());
if(nativeSolver->getM() > 1)
results_.iteratePointSets.push_back(nativeSolver->getXArray());
nIter++;
}
results_.xMin = nativeSolver->getX()[0];
results_.yMin = nativeSolver->getX()[1];
results_.fMin = nativeSolver->getFVal();
results_.numIter = nativeSolver->getNumIter();
results_.numFuncEval = nativeSolver->getNumFuncEval();
results_.numGradEval = nativeSolver->getNumGradEval();
}
else
{
// TODO: stopping criterion for LMBM?
boost::shared_ptr< Solver::Results > results =
solver_->solve(*objFunc_, x0, GradNormTest(1e-8));
results_.xMin = results->xMin[0];
results_.yMin = results->xMin[1];
results_.fMin = results->fMin;
results_.numIter = results->numIter;
results_.numFuncEval = results->numFuncEval;
results_.numGradEval = results->numGradEval;
//results_.iterates = results->iterates; // TODO: iterates?
}
}
//..
// Our verification program simply instantiate several 'MyGenericContainer'
// templates with the two test types above, and checks that the allocator
// slot is as expected:
//..
int usageExample()
{
bslma::TestAllocator ta0;
bslma::TestAllocator ta1;
//..
// With 'MyTestTypeWithNoBslmaAllocatorTraits', the slot should never be set.
//..
MyTestTypeWithNoBslmaAllocatorTraits x;
allocSlot = &ta0;
MyGenericContainer<MyTestTypeWithNoBslmaAllocatorTraits> x0(x);
ASSERT(&ta0 == allocSlot);
allocSlot = &ta0;
MyGenericContainer<MyTestTypeWithNoBslmaAllocatorTraits> x1(x, &ta1);
ASSERT(&ta0 == allocSlot);
//..
// With 'MyTestTypeWithBslmaAllocatorTraits', the slot should be set to the
// allocator argument, or to 0 if not specified:
//..
MyTestTypeWithBslmaAllocatorTraits y;
allocSlot = &ta0;
MyGenericContainer<MyTestTypeWithBslmaAllocatorTraits> y0(y);
ASSERT(0 == allocSlot);
allocSlot = &ta0;
MyGenericContainer<MyTestTypeWithBslmaAllocatorTraits> y1(y, &ta1);
ASSERT(&ta1 == allocSlot);
return 0;
}
void Bidomain::DoOdeRhs(
const Array<OneD, const Array<OneD, NekDouble> >&inarray,
Array<OneD, Array<OneD, NekDouble> >&outarray,
const NekDouble time)
{
int nq = m_fields[0]->GetNpoints();
m_cell->TimeIntegrate(inarray, outarray, time);
if (m_stimDuration > 0 && time < m_stimDuration)
{
Array<OneD,NekDouble> x0(nq);
Array<OneD,NekDouble> x1(nq);
Array<OneD,NekDouble> x2(nq);
Array<OneD,NekDouble> result(nq);
// get the coordinates
m_fields[0]->GetCoords(x0,x1,x2);
LibUtilities::EquationSharedPtr ifunc
= m_session->GetFunction("Stimulus", "u");
ifunc->Evaluate(x0,x1,x2,time, result);
Vmath::Vadd(nq, outarray[0], 1, result, 1, outarray[0], 1);
}
Vmath::Smul(nq, 1.0/m_capMembrane, outarray[0], 1, outarray[0], 1);
}
void MainWindow::plot3(QCustomPlot *customPlot)
{
QVector<double> x0(pts), y0(pts);
update_w(w,1.0);
double y_inc = 1.0;
for (int i=0; i<pts; ++i) {
x0[i] = (double)0.5*i/pts;
y0[i] = y_inc*(w[i]);
}
customPlot->graph()->setData(x0, y0);
customPlot->graph()->setLineStyle(QCPGraph::lsLine);
customPlot->graph()->setScatterStyle(QCPScatterStyle::ssNone); // (QCP::ScatterStyle)(rand()%9+1));
QPen graphPen;
graphPen.setColor(QColor(Qt::GlobalColor(5+graph_counter)));
graphPen.setWidthF(2);
customPlot->graph()->setPen(graphPen);
customPlot->xAxis->setRange(0,0.5);
customPlot->yAxis->setRange(-90,10);
customPlot->legend->setVisible(true);
// customPlot->setInteraction(QCustomPlot::iSelectPlottables);
customPlot->graph()->setName(QString(shape.c_str()));
customPlot->replot();
}
QgsLineString *QgsMapToolAddRectangle::rectangleToLinestring( const bool isOriented ) const
{
std::unique_ptr<QgsLineString> ext( new QgsLineString() );
if ( mRectangle.isEmpty() )
{
return ext.release();
}
QgsPoint x0( mRectangle.xMinimum(), mRectangle.yMinimum() );
QgsPoint x1, x2, x3;
if ( isOriented )
{
const double perpendicular = 90.0 * mSide;
x1 = x0.project( mDistance1, mAzimuth );
x3 = x0.project( mDistance2, mAzimuth + perpendicular );
x2 = x1.project( mDistance2, mAzimuth + perpendicular );
}
else
{
x1 = QgsPoint( mRectangle.xMinimum(), mRectangle.yMaximum() );
x2 = QgsPoint( mRectangle.xMaximum(), mRectangle.yMaximum() );
x3 = QgsPoint( mRectangle.xMaximum(), mRectangle.yMinimum() );
}
ext->addVertex( x0 );
ext->addVertex( x1 );
ext->addVertex( x2 );
ext->addVertex( x3 );
ext->addVertex( x0 );
return ext.release();
}
RANDOM_HILL_CLIMBING::Parameter RANDOM_HILL_CLIMBING::move(RANDOM_HILL_CLIMBING::Parameter par)
{
boost::variate_generator<RNG&, boost::uniform_real<Float_t> > r(_rng, boost::uniform_real<Float_t>(-1,1));
Parameter result;
Float_t factor=4;
Float_t maxpos=0.1*factor;
Float_t maxang=osg::PI/45*factor;
do
{
result._pos=Vec3_t(r(), r(), r())*maxpos;
} while (result._pos.length()>maxpos);
result._pos=par._pos+result._pos;
boost::variate_generator<RNG&, boost::uniform_real<Float_t> > rsimple(_rng, boost::uniform_real<Float_t>(0,1));
Float_t x0(rsimple());
Float_t t1(2*osg::PI*rsimple()), t2(2*osg::PI*rsimple());
Float_t s1(sin(t1)), s2(sin(t2)), c1(cos(t1)), c2(cos(t2));
Float_t r1(sqrt(1-x0)), r2(sqrt(x0));
Quat_t randomori=Quat_t(s1*r1, c1*r1, s2*r2, c2*r2);
result._ori.slerp(maxang, Quat_t(), randomori);
Quat_t temp=par._ori*result._ori;
result._ori=temp;
// bond rotatio
result._bond=vector<Float_t>(_fit->RotCount());
for (unsigned int i=0; i!=_fit->RotCount(); ++i)
{
result._bond[i]=par._bond[i]+r()*maxang;
}
return result;
}
int gauss(dvec& x, dvec& w) {
int n = x.size();
double dist = 1;
double tol = 1e-15;
int iter = 0;
// Use Chebyshev-Gauss nodes and initial guess
initguess(x);
// chebnodes(x);
dvec x0(x);
dvec L(n,0.0);
dvec Lp(n,0.0);
dvec a(n,0.0);
dvec b(n,0.0);
rec_legendre(a,b);
// Iteratively correct nodes with Newton's method
while(dist>tol) {
newton_step(a,b,x,L,Lp);
dist = dist_max(x,x0);
++iter;
x0 = x;
}
// Compute Weights
for(int i=0;i<n;++i){
w[i] = 2.0/((1-x[i]*x[i])*(Lp[i]*Lp[i]));
}
return iter;
}
void MainWindow::plot2(QCustomPlot *customPlot)
{
QVector<double> x0(pts), y0(pts);
update_w(w,1.0);
double y_inc = 1.0;
for (int i=0; i<pts; ++i) {
x0[i] = (double)0.5*i/pts;
y0[i] = y_inc*(w[i]);
}
order = get_order();
ui->order->setText(QApplication::translate("MainWindow", std::to_string(order).c_str(), 0));
ui->ripple->setText(QApplication::translate("MainWindow", std::to_string(ripple()).c_str(), 0));
ui->fc->setText(QApplication::translate("MainWindow", std::to_string(fc()).c_str(), 0));
customPlot->graph()->setData(x0, y0);
customPlot->graph()->setLineStyle(QCPGraph::lsLine); //(QCPGraph::LineStyle)(rand()%5+1));
customPlot->graph()->setScatterStyle(QCPScatterStyle::ssNone); // (QCP::ScatterStyle)(rand()%9+1));
QPen graphPen;
// graphPen.setColor(QColor(rand()%245+10, rand()%245+10, rand()%245+10));
//graphPen.setWidthF(rand()/(double)RAND_MAX*2+1);
graph_counter++;
graph_counter = graph_counter%9;
graphPen.setColor(QColor(Qt::GlobalColor(5+graph_counter)));
graphPen.setWidthF(2);
customPlot->graph()->setPen(graphPen);
customPlot->xAxis->setRange(0,0.5);
customPlot->yAxis->setRange(-90,10);
customPlot->legend->setVisible(true);
// customPlot->setInteraction(QCustomPlot::iSelectPlottables);
customPlot->graph()->setName(QString(shape.c_str()));
customPlot->replot();
}
int main(int argc, char **argv) {
vctr x0(2);
vctr u(1);
x0.at(0)=0.1;
x0.at(1)=0.0;
u.at(0)=0.0;
double dt_max=0.1;
double state_dim=2;
double control_dim=1;
double tspan=2.0*M_PI;
RK4 sys(&flow,dt_max,state_dim,control_dim);
traj sol = sys.sim(tspan,x0,u);
sys.print_traj(sol);
printf("cost: %f\n",cost(sol));
//Plot result
vctr path(sol.time.size());
for(int i=0;i<sol.path.size();i++)
{
path.at(i)=sol.path[i][0];
}
plt::plot(sol.time,path);
plt::xlim(0, (int) ceil(sol.time.back()));
plt::show();
//plt::save("./basic.png");
return 0;
}
/// Implementation of the sparsity structure
void luksan_vlcek_3::set_sparsity(int &lenG, std::vector<int> &iGfun, std::vector<int> &jGvar) const
{
//Initial point
decision_vector x0(get_dimension(),1);
//Numerical procedure
estimate_sparsity(x0, lenG, iGfun, jGvar);
}
ApproximateES(size_t _N, double _lambda_min, double _lambda_max, EnergyMinimizer* _m , float* _x0 = NULL, size_t _max_iter = 10000, int _verbosity = 0, float* _x1 = NULL):
kmc(_lambda_min, _lambda_max),
lambda_min(_lambda_min),
lambda_max(_lambda_max),
N(_N),
minimizer(_m),
max_iter(_max_iter),
verbosity(_verbosity)
{
e1 = e2 = e3 = 0;
short_array x0( new float[N] );
short_array x1( new float[N] );
for(size_t i = 0; i < N; i++) // copy
{
if(_x0 != NULL )
x0[i] = _x0[i];
else x0[i] = 0;
if(_x1 != NULL )
x1[i] = _x1[i];
else x1[i] = x0[i];
}
Undefined u1(lambda_min, x0, x0);
Undefined u2(lambda_max, x1, x1);
Lambda.push(u1);
Lambda.push(u2);
labelings.push_back( x0 );
labelings.push_back( x1 );
}
Matrix dixon(Parser parser, const Matrix& x)
{
Matrix x0(x);
Matrix x1(x);
Matrix p(x);
unsigned k = 0;
do
{
k++;
x0 = x1;
if (k == 1)
{
p = -1*grad(parser, x0);
}
else
{
double beta = -pow(grad(parser,x0).norm(),2)/getScalarPr(p,-p);
p = -1*grad(parser, x0) + beta*p;
}
double alpha = powell(parser,x0,p,swenn_1(parser, x0,p,1));
x1 = x0 + p*alpha;
} while(k < 100 && grad(parser,x0).norm() > myEPS && myEPS && fabs(parser.f(x0)-parser.f(x1))>myEPS);
qDebug() << "iteration = " << k;
return x1;
}
RANDOM_HILL_CLIMBING::Parameter RANDOM_HILL_CLIMBING::init_new_Parameter()
{
boost::variate_generator<RNG&, boost::uniform_real<Float_t> > r(_rng, boost::uniform_real<Float_t>(-1,1));
Parameter result;
// position
do
{
result._pos=_center+Vec3_t(r() ,r(), r())*_radius;
} while ((_center-result._pos).length()>_radius);
// orientation
// random quaternion
// Ken Shoemake
// UNIFORM RANDOM ROTATIONS
// In D. Kirk, editor, Graphics Gems III, pages 124-132. Academic, New York, 1992.
boost::variate_generator<RNG&, boost::uniform_real<Float_t> >
rsimple(_rng, boost::uniform_real<Float_t>(0,1));
Float_t x0(rsimple());
Float_t t1(2*osg::PI*rsimple()), t2(2*osg::PI*rsimple());
Float_t s1(sin(t1)), s2(sin(t2)), c1(cos(t1)), c2(cos(t2));
Float_t r1(sqrt(1-x0)), r2(sqrt(x0));
result._ori=Quat_t(s1*r1, c1*r1, s2*r2, c2*r2);
// bond rotation
result._bond=vector<Float_t>(_fit->RotCount());
for (unsigned int i=0; i!=_fit->RotCount(); ++i)
{
result._bond[i]=r()*osg::PI;
}
return result;
}
PSO::Particle PSO::init_new_Particle()
{
Float_t max_v=_radius/4;
Float_t max_a=osg::PI/4;
boost::variate_generator<RNG&, boost::uniform_real<Float_t> > r(_rng, boost::uniform_real<Float_t>(-1,1));
Particle result;
// position
do
{
result._pos=_center+Vec3_t(r() ,r(), r())*_radius;
} while ((_center-result._pos).length()>_radius);
result._pb=result._pos;
// position velocity
do
{
result._pv=Vec3_t(r(), r(), r())*max_v;
} while (result._pv.length()>max_v);
// orientation
// random quaternion
// Ken Shoemake
// UNIFORM RANDOM ROTATIONS
// In D. Kirk, editor, Graphics Gems III, pages 124-132. Academic, New York, 1992.
boost::variate_generator<RNG&, boost::uniform_real<Float_t> >
rsimple(_rng, boost::uniform_real<Float_t>(0,1));
Float_t x0(rsimple());
Float_t t1(2*osg::PI*rsimple()), t2(2*osg::PI*rsimple());
Float_t s1(sin(t1)), s2(sin(t2)), c1(cos(t1)), c2(cos(t2));
Float_t r1(sqrt(1-x0)), r2(sqrt(x0));
result._ori=Quat_t(s1*r1, c1*r1, s2*r2, c2*r2);
result._ob=result._ori;
// orientation velocity
x0=rsimple();
t1=2*osg::PI*rsimple();
t2=2*osg::PI*rsimple();
s1=sin(t1);
s2=sin(t2);
c1=cos(t1);
c2=cos(t2);
r1=sqrt(1-x0);
r2=sqrt(x0);
Quat_t randomori=Quat_t(s1*r1, c1*r1, s2*r2, c2*r2);
// max possible orientation velocity is pi(180)
// but we allow only initanglevel orientation velocity
result._ov.slerp(max_a/osg::PI, Quat_t(), randomori);
// bond rotation
result._bond=vector<Float_t>(_fit->RotCount());
result._bv=vector<Float_t>(_fit->RotCount());
for (unsigned int i=0; i!=_fit->RotCount(); ++i)
{
result._bond[i]=r()*osg::PI;
// scale by maximum angle step width
result._bv[i]=r()*max_a;
}
result._bb=result._bond;
return result;
}
void CrankNicolsonSorUpdater::update( const std::vector<double> & uOld,
std::vector<double>* uNew,
const std::vector<double> & prem ) const
{
int N = uOld.size()-1;
double c = getAlpha();
// uOld restricted in the interior region
Eigen::VectorXd u = Eigen::VectorXd::Zero(N-1);
for (int i=0; i<N-1; i++) { u(i) = uOld[i+1]; }
// Construct b-vector
Eigen::VectorXd b = d_B*u;
b(0) += 0.5*c*((*uNew)[0]+uOld[0]);
b(N-2) += 0.5*c*((*uNew)[N]+uOld[N]);
// Use the state vector at the previous time step as initial estimate
Eigen::VectorXd x0 = Eigen::VectorXd::Zero(N-1);
for (int i=0; i<N-1; i++) { x0(i) = uOld[i+1]; }
// Construct early exercise premium vector
Eigen::VectorXd p = Eigen::VectorXd::Zero(0);
if ( prem.size()>0 ) {
p = Eigen::VectorXd::Zero(N-1);
for (int i=0; i<N-1; i++) {
p(i) = prem[i+1];
// If early exercise premium is given, the initial
// estimate x0 is set to early exercise premium.
// This is a reasonable choice because:
// (1) At the 1st time step, i.e., m=0,
// early_exercise_premium = K*exp(ax)*max(1-exp(x),0),
// which is exactly the same as the terminal condition;
// (2) At the successive time steps, i.e., m>0,
// early_exercise_premium serves as a good approximation
// of the value of state vectors.
x0(i) = prem[i+1];
}
}
// update
std::tuple<Eigen::VectorXd, int> res = sor(d_omega, d_A, b, d_tol, x0, p);
Eigen::VectorXd x = std::get<0>(res);
for (int i=0; i<N-1; i++) { (*uNew)[i+1] = x(i); }
}
/// Implementation of the sparsity structure
void snopt_toyprob::set_sparsity(int& lenG, std::vector<int>& iGfun, std::vector<int>& jGvar) const
{
//Initial point
decision_vector x0(2);
x0[0] = 1; x0[1] = 1;
//Numerical procedure
this->estimate_sparsity(x0, lenG, iGfun, jGvar);
}
int main(int argc, char *argv[])
{
// A decorated affine form
yalaa::aff_e_d_dec x0(iv_t(-1.0, 2.0));
// A new affine form has the best decoration, as long as its original interval
// is not empty or invalid.
std::cout << "Decoration of x0: " << get_special(x0) << std::endl;
// Square x0 is D5 (= 6), the best decoration
std::cout << x0 << "^2 = " << sqr(x0) << " Deco: " << get_special(sqr(x0))
<< " Valid: " << is_valid(sqr(x0)) << std::endl;
// The natural domain of sqrt is R+. Thus the resulting decoration of sqrt(x0)
// is D2 (=3) (possibly defined)
std::cout << "sqrt(" << x0 << ") = " << sqrt(x0) << " Deco: " << get_special(sqrt(x0))
<< " Valid: " << is_valid(sqrt(x0)) << std::endl;
// The natural domain of log is R+, Thus the decoration is D2, as for lim x->0 log(x) is unbounded
// the computation overflows for the natural domain resulting in Infinity as central value
// Note the changed value of valid. Even if the decoration quality is the some as for sqrt(x0),
// is_valid returns now false, as the form has no numerical meaningful value anymore.
std::cout << "log(" << x0 << ") = " << log(x0) << " Deco: " << get_special(log(x0))
<< " Valid: " << is_valid(log(x0)) << std::endl;
// A form for an empty interval is created. The decoration is D0 (=1).
yalaa::aff_e_d_dec empty(iv_t(1, -1));
std::cout << "Decoration of an empty affine form: " << get_special(empty)
<< " Valid: " << is_valid(empty) << std::endl;
// If the empty is used as input argument of an operation, the result is again D0
std::cout << "cos(" << empty << ") = " << cos(empty) << " Deco: " << get_special(cos(empty))
<< " Valid: " << is_valid(cos(empty)) << std::endl;
// Combination of an affine form with a scalar
// Normally scalars are treated like affine forms with a D5 decoration. However, if they have a
// special value like NaN or infinity, the combination results in D-1 (=0) with indicates some
// error.
std::cout << "3.0*" << x0 << ") = " << 3*x0 << " Deco: " << get_special(3*x0)
<< " Valid: " << is_valid(3*x0) << std::endl;
std::cout << "infinity*" << x0 << ") = " << std::numeric_limits<double>::infinity()*x0
<< " Deco: " << get_special(std::numeric_limits<double>::infinity()*x0)
<< " Valid: " << is_valid(std::numeric_limits<double>::infinity()*x0) << std::endl;
// Decoations are propagated through inductively defined functions
// Thus f = sqrt(x0) + x0
// has the decoration D2, as sqrt(x0) is D2.
yalaa::aff_e_d_dec sqrtx0(sqrt(x0));
std::cout << "sqrt(" << x0 << ") + " << x0 << " = " << sqrt(x0) + x0
<< " Deco: " << get_special(sqrt(x0) + x0)
<< " Valid: " << is_valid(sqrt(x0) + x0) << std::endl;
// The natural domain of exp is not violated, but the computation overflows resulting in D4
// (defined and continuous). No statement is made about the boundness!
// Commented out, as some libraries like C-XSC abort the program in case of an overflow.
// yalaa::aff_e_d_dec x1(1000.0);
// std::cout << "exp(" << x1 << ") = " << exp(x1) << " Deco: " << get_special(exp(x1)) << std::endl;
return 0;
}
void Skel_OPB_Comp::calc_buf(INT ** output,U_INT1 *** input)
{
if (first_line_in_pack())
{
for (INT d =0; d < dim_in() ; d++)
{
U_INT1 ** l = input[d];
for (int y = y0Buf() ; y < y1Buf() ; y++)
convert
(
_im_init[y-y0Buf()],
l[y]+x0Buf(),
x1Buf()-x0Buf()
);
Skeleton
(
_skel[d],
_im_init,
_sz.x,
_sz.y,
_larg
);
}
}
for (INT d =0; d < dim_in() ; d++)
convert
(
output[d]+x0(),
_skel[d][y_in_pack()-dy0()]-dx0(),
tx()
);
if (_AvecDist)
convert
(
output[1]+x0(),
_im_init[y_in_pack()-dy0()]-dx0(),
tx()
);
}
Vector Initialize()
{
Vector x0(8, 0.0);
x0(0) = 11;
x0(1) = 11;
x0(2) = 0;
x0(3) = 4.5165e12;
x0(4) = 0;
x0(5) = 4.5165e12;
x0(6) = 0;
x0(7) = 0;
return x0;
}
int main() {
char user[3];
read(0, user, 3);
if (x0(user) || x1(user) || x2(user) || x3(user) || x4(user)) {
failure();
}
else {
success();
}
}
// calculate distance line-point
double distance2(double x,double y,double z, const double *p) {
// distance line point is D= | (xp-x0) cross ux |
// where ux is direction of line and x0 is a point in the line (like t = 0)
ROOT::Math::XYZVector xp(x,y,z);
ROOT::Math::XYZVector x0(p[0], p[2], 0. );
ROOT::Math::XYZVector x1(p[0] + p[1], p[2] + p[3], 1. );
ROOT::Math::XYZVector u = (x1-x0).Unit();
double d2 = ((xp-x0).Cross(u)) .Mag2();
return d2;
}
/// Implementation of the sparsity structure: automated detection
void earth_planet::set_sparsity(int &lenG, std::vector<int> &iGfun, std::vector<int> &jGvar) const
{
//Initial point
decision_vector x0(get_dimension());
for (pagmo::decision_vector::size_type i = 0; i<x0.size(); ++i)
{
x0[i] = get_lb()[i] + (get_ub()[i] - get_lb()[i]) / 3.12345;
}
//Numerical procedure
estimate_sparsity(x0, lenG, iGfun, jGvar);
}