Var Interpreter::make_Callable( Vec<Var> lst, Var self ) {
// remove doubles
for( int i = 0; i < lst.size(); ++i )
for( int j = i + 1; j < lst.size(); ++j )
if ( lst[ i ].expr() == lst[ j ].expr() )
lst.remove_unordered( j-- );
//
Expr surdef_list_data = cst( SI32( lst.size() ) );
for( int i = 0; i < lst.size(); ++i )
surdef_list_data = concat( surdef_list_data, pointer_on( lst[ i ].expr() ) );
Var surdef_list( &type_SurdefList, surdef_list_data );
//
Var self_type = type_of( self ); // returns void if self is not defined
// -> Callable[ surdef_list, self_type, parm_type ]
Var *parms[ 3 ];
parms[ 0 ] = &surdef_list;
parms[ 1 ] = &self_type;
parms[ 2 ] = &void_var;
Var *callable_type = type_for( class_info( class_Callable ), parms );
return Var( callable_type, self ? pointer_on( self.expr() ) : cst() ).add_ref( 0, self );
}
static inline void assemble(boost::shared_ptr<Mesh<Simplex<Dim>>>& mesh, double* vec) {
boost::timer time;
auto Vh = FunctionSpace<Mesh<Simplex<Dim>>, bases<Lagrange<Order, Type>>>::New(_mesh = mesh);
vec[2] = time.elapsed();
vec[1] = Vh->nDof();
Environment::logMemoryUsage( "Assemble Laplacian Memory Usage: FunctionSpace" );
time.restart();
auto v = Vh->element();
auto f = backend()->newVector(Vh);
auto l = form1(_test = Vh, _vector = f);
l = integrate(_range = elements(mesh), _expr = id(v));
vec[4] = time.elapsed();
Environment::logMemoryUsage( "Assemble Laplacian Memory Usage: Form1" );
time.restart();
auto u = Vh->element();
auto A = backend()->newMatrix(Vh, Vh);
vec[5] = time.elapsed();
Environment::logMemoryUsage( "Assemble Laplacian Memory Usage: Matrix" );
time.restart();
auto a = form2(_trial = Vh, _test = Vh, _matrix = A);
a = integrate(_range = elements(mesh), _expr = inner(gradt(u),grad(v)));
a += on(_range = markedfaces(mesh, "Dirichlet"), _rhs = l, _element = u, _expr = cst(0.0));
vec[3] = time.elapsed();
auto mem = Environment::logMemoryUsage( "Assemble Laplacian Memory Usage: form2" );
v[6] = mem.memory_usage/1e9;
LOG(INFO) << "v[6] = " << v[6];
cleanup();
}
void setCstDensity(double d, std::string const& marker = "" )
{
std::string markerUsed = ( marker.empty() )? self_type::defaultMaterialName() : marker;
M_cstDensity[markerUsed]=d;
this->updateDensity( cst(d),marker);
this->updateCinematicViscosity( marker );
}
Expr Inst::_smp_slice( int nout, int beg, int end ) {
if ( beg == 0 and end == size_in_bits( nout ) )
return Expr( this, nout );
if ( beg == end )
return cst();
return Expr();
}
GlobalVariables::GlobalVariables() {
#define DECL_BT( T ) class_##T = new Class;
#include "DeclBaseClass.h"
#include "DeclParmClass.h"
#undef DECL_BT
#define DECL_BT( T ) type_##T = new Type_<T>( class_##T ); class_##T->types << type_##T; type_##T->aryth = true; type_##T->_len = 8 * sizeof( T ); type_##T->_ali = 8 * sizeof( T ); type_##T->_pod = 1;
#include "DeclArytTypes.h"
#undef DECL_BT
#define DECL_BT( T ) type_##T = new Type( class_##T ); class_##T->types << type_##T;
#define DONT_WANT_DeclArytTypes_h
#include "DeclBaseClass.h"
#undef DONT_WANT_DeclArytTypes_h
#undef DECL_BT
type_Type ->_len = 64; type_Type ->_ali = 32; type_Type ->_pod = 1;
type_Void ->_len = 0; type_Void ->_ali = 1; type_Void ->_pod = 1;
type_Error ->_len = 0; type_Error ->_ali = 1; type_Error ->_pod = 1;
type_Def ->_len = 64; type_Def ->_ali = 32; type_Def ->_pod = 1;
type_Class ->_len = 64; type_Class ->_ali = 32; type_Class ->_pod = 1;
type_SurdefList->_len = 64; type_SurdefList->_ali = 32; type_SurdefList->_pod = 1;
type_Varargs ->_len = 64; type_Varargs ->_ali = 32; type_Varargs ->_pod = 1;
type_Bool ->_len = 1; type_Bool ->_ali = 1;
type_ST = sizeof( void * ) == 8 ? type_SI64 : type_SI32;
ptr_size = 8 * sizeof( void * );
main_parsing_context = 0;
ip_snapshot = 0;
pc = 0;
main_scope[ "void" ] = Variable{ room( cst( type_Void, 0, 0 ) ) };
}
int main() {
Expr tcs[] = { cst( 0 ), cst( 1 ) };
PA( tcs[ 0 ] );
PA( tcs[ 1 ] );
PA( cst( 0 ) );
PA( cst( 1 ) );
PA( slice( cst( SI64( 0x01234567 ) ), 8, 32 ) );
Expr gfe = cst( SI64( 0x656667 ) );
PRINT( gfe );
PRINT( gfe.cst_data() );
PRINT( gfe.cst_data( 8 ) );
Expr pgfe = pointer_on( gfe );
PRINT( pgfe );
PRINT( pgfe.vat_data() );
PRINT( pgfe.vat_data( 8 ) );
PRINT( slice( gfe, 8, 32 ) );
PRINT( slice( gfe, 8, 32 ).cst_data() );
PRINT( slice( gfe, 8, 32 ).cst_data( 8 ) );
PRINT( pointer_on( slice( gfe, 8, 32 ) ) );
PRINT( pointer_on( slice( gfe, 8, 32 ) ).vat_data() );
PRINT( add( arch->bt_ptr(), pointer_on( gfe ), cst( 1l ) ) );
PRINT( val_at( add( arch->bt_ptr(), pointer_on( gfe ), cst( 1l ) ), 16 ) );
// Expr sa = syscall( cst( 6 ), 2, tcs, 32 ).ret;
// Expr sb = syscall( cst( 6 ), 2, tcs, 32 ).ret;
// PA( sa );
// PA( sb );
// Expr pa = pointer_on( tcs[ 0 ], 64 );
// Expr pb = pointer_on( tcs[ 0 ], 64 );
// PA( pa );
// PA( pb );
// PA( add( bt_SI32, cst( 10 ), cst( 20 ) ) );
// PA( rand( 64 ) );
// PA( slice( cst( SI64( 0x176548 ) ), 8, 32 ) );
// Expr struct_expr = concat( cst( 0x17 ), rand( 32 ) );
// PA( struct_expr );
// PA( slice( struct_expr, 0, 16 ) );
// PA( slice( struct_expr, 0, 32 ) );
// PA( slice( struct_expr, 32, 64 ) );
// PA( slice( struct_expr, 32, 63 ) );
// PA( val_at( pointer_on( cst( 0x32 ), 64 ), 32 ) );
// PA( pointer_on( val_at( cst( 0x32 ), 32 ), 32 ) );
}
std::shared_ptr<nokkhum::Camera> CameraFactory::getCamera(std::shared_ptr<nokkhum::CameraAttribute> cameraAttribute) {
LOG(INFO) << "Build camera name: " << cameraAttribute->getName() << " url: " << cameraAttribute->getVideoUri();
CameraStartTimer cst(100000); //100 s
cst.start();
std::shared_ptr<nokkhum::Camera> camera = std::make_shared<nokkhum::CvIpCamera> (cameraAttribute->getWidth(), cameraAttribute->getHeight(),
cameraAttribute->getFps(), cameraAttribute->getVideoUri(), cameraAttribute->getUsername(),
cameraAttribute->getPassword());
cst.stop();
//LOG(INFO) << "return camera";
return camera;
}
void
PreconditionerBlockMS<space_type>::initAMS( void )
{
M_grad = Grad( _domainSpace=M_Qh, _imageSpace=M_Vh);
// This preconditioner is linked to that backend : the backend will
// automatically use the preconditioner.
auto prec = preconditioner(_pc=pcTypeConvertStrToEnum(soption(M_prefix_11+".pc-type")),
_backend=backend(_name=M_prefix_11),
_prefix=M_prefix_11,
_matrix=M_11
);
prec->setMatrix(M_11);
prec->attachAuxiliarySparseMatrix("G",M_grad.matPtr());
if(boption(M_prefix_11+".useEdge"))
{
LOG(INFO) << "[ AMS ] : using SetConstantEdgeVector \n";
ozz.on(_range=elements(M_Vh->mesh()),_expr=vec(cst(1),cst(0),cst(0)));
zoz.on(_range=elements(M_Vh->mesh()),_expr=vec(cst(0),cst(1),cst(0)));
zzo.on(_range=elements(M_Vh->mesh()),_expr=vec(cst(0),cst(0),cst(1)));
*M_ozz = ozz; M_ozz->close();
*M_zoz = zoz; M_zoz->close();
*M_zzo = zzo; M_zzo->close();
prec->attachAuxiliaryVector("Px",M_ozz);
prec->attachAuxiliaryVector("Py",M_zoz);
prec->attachAuxiliaryVector("Pz",M_zzo);
}
else
{
LOG(INFO) << "[ AMS ] : using SetCoordinates \n";
X.on(_range=elements(M_Vh->mesh()),_expr=Px());
Y.on(_range=elements(M_Vh->mesh()),_expr=Py());
Z.on(_range=elements(M_Vh->mesh()),_expr=Pz());
*M_X = X; M_X->close();
*M_Y = Y; M_Y->close();
*M_Z = Z; M_Z->close();
prec->attachAuxiliaryVector("X",M_X);
prec->attachAuxiliaryVector("Y",M_Y);
prec->attachAuxiliaryVector("Z",M_Z);
}
}
/** Copy contents of another Wflograph.
* @param original is a weighted flograph to be copied to this object
*/
void Wflograph::copyFrom(const Wflograph& original) {
if (N != original.n() || maxEdge < original.m()) {
resize(original.n(), original.m());
} else {
reset();
}
N = original.n();
for (edge e = original.first(); e != 0; e = original.next(e)) {
edge ee = join(original.left(e),original.right(e));
cpy(ee) = original.cpy(e); cst(ee) = original.cst(e);
flo(ee) = original.flo(e);
}
setSrcSnk(original.src(),original.snk());
sortAdjLists();
}
Var *Interpreter::_make_varargs_type( const Vec<Var> &uv_args, const Vec<Var> &nv_args, const Vec<int> &nv_name, int off ) {
// class VarargsItemEnd
if ( off >= uv_args.size() + nv_args.size() )
return &type_VarargsItemEnd;
// class VarargsItemBeg[ data_type, data_name, next_type ]
Var data_type = type_of( off >= uv_args.size() ? nv_args[ off - uv_args.size() ] : uv_args[ off ] );
Var data_name( &type_SI32, cst( off >= uv_args.size() ? nv_name[ off - uv_args.size() ] : -1 ) );
Var *parms[ 3 ];
parms[ 0 ] = &data_type;
parms[ 1 ] = &data_name;
parms[ 2 ] = _make_varargs_type( uv_args, nv_args, nv_name, off + 1 );
return type_for( class_info( class_VarargsItemBeg ), parms );
}
Var Interpreter::make_varargs_var( const Vec<Var> &uv_args, const Vec<Var> &nv_args, const Vec<int> &nv_name ) {
Var *type = _make_varargs_type( uv_args, nv_args, nv_name, 0 );
Expr data = cst();
for( int i = 0; i < uv_args.size(); ++i )
data = concat( data, pointer_on( uv_args[ i ].expr() ) );
for( int i = 0; i < nv_args.size(); ++i )
data = concat( data, pointer_on( nv_args[ i ].expr() ) );
Var res( type, data );
for( int i = 0, off = 0; i < uv_args.size(); off += bt_ST->size_in_bits(), ++i )
res.add_ref( off, uv_args[ i ] );
for( int i = 0, off = 0; i < nv_args.size(); off += bt_ST->size_in_bits(), ++i )
res.add_ref( off, nv_args[ i ] );
return res;
}
TEST(ChangeSalariedTransactionTest, PayrollTest) {
int empid = 10;
AddHourlyEmployee ht(empid, "Test11", "Home10", 50.00);
ht.Execute();
ChangeSalariedTransaction cst(empid, 1000.00);
cst.Execute();
Employee *e = ((DatabaseProxy *)getInstance())->GetEmployee(empid);
EXPECT_TRUE(e != 0);
SalariedClassification* ms = dynamic_cast<SalariedClassification*>(e->GetPaymentClassification());
EXPECT_TRUE(ms != 0);
EXPECT_TRUE(ms->GetSalary() == 1000.00);
}
Expr Ast_Def::_parse_in( ParsingContext &context ) const {
std::set<String> res;
if ( context.parent ) {
std::set<String> avail;
avail.insert( name );
get_potentially_needed_ext_vars( res, avail );
}
//
Def *c = new Def( this );
//
SI64 ptr = SI64( ST( c ) );
Expr out = room( cst( ip->type_Def, 64, &ptr ) );
out->flags |= Inst::SURDEF;
if ( stat )
out->flags |= Inst::STATIC;
return context.reg_var( name, out, true );
}
void Interpreter::import( String filename ) {
if ( already_imported( filename ) )
return;
// -> source data
ReadFile r( filename.c_str() );
if ( not r )
return disp_error( "Impossible to open " + filename );
// -> lexical data
Lexer l( error_list );
l.parse( r.data, filename.c_str() );
if ( error_list )
return;
// -> binary stream
IrWriter t( error_list );
t.parse( l.root() );
if ( error_list )
return;
// -> make a new SourceFile
ST bin_size = t.size_of_binary_data();
Vec<PI8> data( Size(), sizeof( SI32 ) + bin_size + sizeof( SI32 ) + filename.size() + 1 );
reinterpret_cast<SI32 &>( data[ 0 ] ) = bin_size;
t.copy_binary_data_to( data.ptr() + sizeof( SI32 ) );
reinterpret_cast<SI32 &>( data[ sizeof( int ) + bin_size ] ) = filename.size();
memcpy( data.ptr() + sizeof( SI32 ) + bin_size + sizeof( SI32 ), filename.c_str(), filename.size() + 1 );
const Expr &sf = *sourcefiles.push_back( pointer_on( cst( data.ptr(), 0, 8 * data.size() ) ) );
// -> virtual machine
if ( not main_scope )
main_scope = new Scope( 0 );
main_scope->parse( sf, sf_info( sf )->tok_data );
}
Expr Ast_Class::_parse_in( ParsingContext &context ) const {
std::set<String> res;
if ( context.parent ) {
std::set<String> avail;
avail.insert( name );
get_potentially_needed_ext_vars( res, avail );
}
//
Class *c = 0;
#define DECL_BT( T ) if ( name == #T ) { c = ip->class_##T; c->ast_item = this; }
#include "../Ssa/DeclBaseClass.h"
#include "../Ssa/DeclParmClass.h"
#undef DECL_BT
if ( not c )
c = new Class( this );
//
SI64 ptr = SI64( ST( c ) );
Expr val = cst( ip->type_Class, 64, &ptr );
Expr out = room( val );
out->flags |= Inst::SURDEF;
return context.reg_var( name, out, true );
}
void initFromMesh( mesh_ptrtype const& mesh, bool useExtendedDofTable )
{
super_type::initFromMesh(mesh,useExtendedDofTable);
M_fieldDensity = this->dynamicViscositySpace()->elementPtr( cst( this->cstDensity() ) );
M_fieldCinematicViscosity = this->dynamicViscositySpace()->elementPtr( cst( this->cstCinematicViscosity() ) );
}
int
PreconditionerAS<space_type,coef_space_type>::applyInverse ( const vector_type& X /*R*/, vector_type& Y /*W*/) const
{
/*
* We solve Here P_v w = r
* With P_v^-1 = diag(P_m)^-1 (=A)
* + P (\bar L + g \bar Q) P^t (=B)
* + C (L^-1) C^T (=C)
*/
U = X;
U.close();
// solve equ (12)
if ( this->type() == AS )
{
tic();
*M_r = U;
M_r->close();
// step A : diag(Pm)^-1*r
A->pointwiseDivide(*M_r,*M_diagPm);
A->close();
// s = P^t r
M_Pt->multVector(M_r,M_s);
// Impose boundary conditions on M_s
#if 1
M_qh3_elt = *M_s;
M_qh3_elt.close();
#if FEELPP_DIM == 3
M_qh3_elt.on( _range=boundaryfaces( M_Qh3->mesh() ), _expr=vec(cst(0.), cst(0.), cst(0.)) );
#else
M_qh3_elt.on( _range=boundaryfaces( M_Qh3->mesh() ), _expr=vec(cst(0.), cst(0.)) );
#endif
*M_s = M_qh3_elt;
M_s->close();
#endif
#if 1
// Subvectors for M_s (per component) need to be updated
M_s1 = M_s->createSubVector(M_Qh3_indices[0], true);
M_s2 = M_s->createSubVector(M_Qh3_indices[1], true);
#if FEELPP_DIM == 3
M_s3 = M_s->createSubVector(M_Qh3_indices[2], true);
#endif
#else
// s = [ s1, s2, s3 ]
M_s->updateSubVector(M_s1, M_Qh3_indices[0]);
M_s->updateSubVector(M_s2, M_Qh3_indices[1]);
#if FEELPP_DIM == 3
M_s->updateSubVector(M_s3, M_Qh3_indices[2]);
#endif
#endif
M_s->close();
/*
* hat(L) + g Q is a (Qh,Qh) matrix
* [[ hat(L) + g Q, 0 , 0 ], [ y1 ] [ s1 ]
* [ 0, hat(L) + g Q, 0 ], * [ y2 ] = [ s2 ]
* [ 0, 0 , hat(L) + g Q ]] [ y3 ] [ s3 ]
*/
M_lgqOp->applyInverse(M_s1,M_y1);
M_lgqOp->applyInverse(M_s2,M_y2);
#if FEELPP_DIM == 3
M_lgqOp->applyInverse(M_s3,M_y3);
#endif
// y = [ y1, y2, y3 ]
M_y->updateSubVector(M_y1, M_Qh3_indices[0]);
M_y->updateSubVector(M_y2, M_Qh3_indices[1]);
#if FEELPP_DIM == 3
M_y->updateSubVector(M_y3, M_Qh3_indices[2]);
#endif
M_y->close();
// step B : P*y
M_P->multVector(M_y,B);
// Impose boundary conditions on B = Py
#if 1
M_vh_elt = *B;
M_vh_elt.close();
#if FEELPP_DIM == 3
M_vh_elt.on( _range=boundaryfaces( M_Qh3->mesh() ), _expr=vec(cst(0.), cst(0.), cst(0.)) );
#else
M_vh_elt.on( _range=boundaryfaces( M_Qh3->mesh() ), _expr=vec(cst(0.), cst(0.)) );
#endif
*B = M_vh_elt;
B->close();
#endif
// t = C^t r
M_Ct->multVector(M_r,M_t);
// Impose boundary conditions on M_t
#if 1
M_qh_elt = *M_t;
M_qh_elt.close();
M_qh_elt.on( _range=boundaryfaces( M_Qh3->mesh() ), _expr=cst(0.) );
*M_t = M_qh_elt;
M_t->close();
#endif
// 14.b : hat(L) z = t
M_lOp->applyInverse(M_t,M_z);
M_z->close();
// step C : M_C z
M_C->multVector(M_z,C);
C->scale(1./M_g);
// Impose boundary conditions on C = Cz
#if 1
M_vh_elt = *C;
M_vh_elt.close();
#if FEELPP_DIM == 3
M_vh_elt.on( _range=boundaryfaces( M_Qh3->mesh() ), _expr=vec(cst(0.), cst(0.), cst(0.)) );
#else
M_vh_elt.on( _range=boundaryfaces( M_Qh3->mesh() ), _expr=vec(cst(0.), cst(0.)) );
#endif
*C = M_vh_elt;
C->close();
#endif
//if(M_g != 1.0)
A->add(*C);
A->add(*B);
C->close();
B->close();
A->close();
toc("assemble preconditioner AS",FLAGS_v>0);
*M_uout = *A; // 15 : w = A + B + C
}
else if( this->type() == SIMPLE )
{
SimpleOp->applyInverse(X, Y);
*M_uout = Y;
}
else
{
Y=U;
*M_uout = Y;
}
M_uout->close();
tic();
Y=*M_uout;
Y.close();
toc("PreconditionerAS::applyInverse", FLAGS_v>0 );
return 0;
}
void assembleDivergence();
void assembleGradient();
void assembleSchurApp( double mu, double rho, double alpha = 0 );
#if 0
BOOST_PARAMETER_MEMBER_FUNCTION( ( sparse_matrix_ptrtype ),
update,
tag,
( required
( matrix,*( boost::is_convertible<mpl::_,boost::shared_ptr<MatrixSparse> > ) )
( bc, *) )
( optional
( diffusion,*( boost::is_convertible<mpl::_,ExprBase> ), cst(M_mu) )
( density,*( boost::is_convertible<mpl::_,ExprBase> ), cst(M_rho) )
( convection,*( boost::is_convertible<mpl::_,ExprBase> ), zero<Dim>() )
( tn, *( std::is_arithmetic<mpl::_> ), 0. )
( tn1, *( std::is_arithmetic<mpl::_> ), 0. )
) )
{
this->setDiffusion( diffusion );
this->setDensity( diffusion );
this->setConvection( convection);
this->setBC( bc );
this->setTimes( std::pair<double,double>( tn1, tn) )
this->update( matrix );
}
#endif
CSonTime& CSonTime::operator =(LPCTSTR mstr)
{
CSonTime cst(mstr);
operator=(cst);
return *this;
}
void run()
{
Environment::changeRepository( boost::format( "/testsuite/feeldiscr/%1%/P%2%/" )
% Environment::about().appName()
% OrderPoly );
/* change parameters below */
const int nDim = 2;
const int nOrderPoly = OrderPoly;
const int nOrderGeo = 1;
//------------------------------------------------------------------------------//
typedef Mesh< Simplex<nDim, 1,nDim> > mesh_type;
typedef Mesh< Simplex<nDim, 1,nDim> > mesh_bis_type;
double meshSize = option("hsize").as<double>();
double meshSizeBis = option("hsize-bis").as<double>();
// mesh
GeoTool::Node x1( 0,0 );
GeoTool::Node x2( 4,1 );
GeoTool::Rectangle Omega( meshSize,"Omega",x1,x2 );
Omega.setMarker( _type="line",_name="Entree",_marker4=true );
Omega.setMarker( _type="line",_name="Sortie",_marker2=true );
Omega.setMarker( _type="line",_name="Paroi",_marker1=true,_marker3=true );
Omega.setMarker( _type="surface",_name="Fluid",_markerAll=true );
auto mesh = Omega.createMesh(_mesh=new mesh_type,_name="omega_"+ mesh_type::shape_type::name() );
LOG(INFO) << "created mesh\n";
GeoTool::Rectangle OmegaBis( meshSizeBis,"Omega",x1,x2 );
OmegaBis.setMarker( _type="line",_name="Entree",_marker4=true );
OmegaBis.setMarker( _type="line",_name="Sortie",_marker2=true );
OmegaBis.setMarker( _type="line",_name="Paroi",_marker1=true,_marker3=true );
OmegaBis.setMarker( _type="surface",_name="Fluid",_markerAll=true );
auto meshBis = OmegaBis.createMesh(_mesh=new mesh_bis_type,_name="omegaBis_"+ mesh_type::shape_type::name() );
//auto meshBis= mesh->createP1mesh();
LOG(INFO) << "created meshBis\n";
typedef Lagrange<nOrderPoly,Scalar,Continuous,PointSetFekete> basis_type;
typedef FunctionSpace<mesh_type, bases<basis_type> > space_type;
auto Xh = space_type::New( mesh );
auto u = Xh->element();
auto v = Xh->element();
auto u2 = Xh->element();
LOG(INFO) << "created space and elements\n";
auto mybackend = backend();
//--------------------------------------------------------------//
auto A = mybackend->newMatrix( Xh, Xh );
auto F = mybackend->newVector( Xh );
auto pi = cst( M_PI );
auto u_exact = cos( pi*Px() )*sin( pi*Py() );
auto dudx = -pi*sin( pi*Px() )*sin( pi*Py() );
auto dudy = pi*cos( pi*Px() )*cos( pi*Py() );
auto grad_u_uexact = vec( dudx,dudy );
auto lap = -2*pi*pi*cos( pi*Px() )*sin( pi*Py() );
//auto lap = -pi*pi*cos(pi*Px())*sin(pi*Py())
// -pi*pi*cos(pi*Px())*sin(pi*Py());
LOG(INFO) << "created exact data and matrix/vector\n";
auto f = -lap;//cst(1.);
double gammabc=10;
// assemblage
form2( Xh, Xh, A, _init=true ) =
integrate( elements( mesh ), //_Q<15>(),
+ gradt( u )*trans( grad( v ) ) );
form2( Xh, Xh, A ) +=
integrate( boundaryfaces( mesh ),
- gradt( u )*N()*id( v )
+ gammabc*idt( u )*id( v )/hFace() );
form1( Xh, F, _init=true ) =
integrate( elements( mesh ), // _Q<10>(),
trans( f )*id( v ) );
form1( Xh, F ) +=
integrate( boundaryfaces( mesh ),
+ gammabc*u_exact*id( v )/hFace() );
LOG(INFO) << "A,F assembled\n";
//form2( Xh, Xh, A ) +=
// on( boundaryfaces(mesh) , u, F, u_exact );
// solve system
mybackend->solve( A,u,F );
LOG(INFO) << "A u = F solved\n";
//--------------------------------------------------------------//
auto a2 = form2( _test=Xh, _trial=Xh );
auto f2 = form1( _test=Xh );
LOG(INFO) << "created form2 a2 and form1 F2\n";
// assemblage
a2 = integrate( elements( meshBis ),
+ gradt( u2 )*trans( grad( v ) ),
_Q<10>() );
LOG(INFO) << "a2 grad.grad term\n";
a2 += integrate( boundaryfaces( meshBis ),
- gradt( u2 )*N()*id( v )
+ gammabc*idt( u2 )*id( v )/hFace(),
_Q<10>() );
LOG(INFO) << "a2 weak dirichlet terms\n";
f2 = integrate( elements( meshBis ),
trans( f )*id( v ),
_Q<10>() );
LOG(INFO) << "f2 source term\n";
f2 += integrate( boundaryfaces( meshBis ),
+ gammabc*u_exact*id( v )/hFace(),
_Q<10>() );
LOG(INFO) << "f2 dirichlet terms\n";
LOG(INFO) << "a2,f2 assembled\n";
//form2( Xh, Xh, A2 ) +=
// on( boundaryfaces(mesh) , u2, F2, u_exact );
#if 0
for ( size_type i = 0 ; i< F->size() ; ++i )
{
auto errOnF = std::abs( ( *F )( i )-( *F2 )( i ) );
if ( errOnF > 1e-8 )
std::cout << "\nerrOnF : " << errOnF;
}
std::cout << "\nFin errOnF !!!!\n";
#endif
// solve system
a2.solve( _rhs=f2, _solution=u2 );
auto diff = std::sqrt( integrate( elements( mesh ), ( idv( u )-idv( u2 ) )*( idv( u )-idv( u2 ) ) ).evaluate()( 0,0 ) );
#if 0
auto int1 = integrate( elements( mesh ), abs( idv( u ) ) ).evaluate()( 0,0 );
auto int2 = integrate( elements( mesh ), abs( idv( u2 ) ) ).evaluate()( 0,0 );
std::cout << "\nThe diff : " << diff
<< " int1 :" << int1
<< " int2 :" << int2
<< "\n";
#endif
#if USE_BOOST_TEST
BOOST_CHECK_SMALL( diff,1e-2 );
#endif
//--------------------------------------------------------------//
if ( option("exporter.export").as<bool>() )
{
// export
auto ex = exporter( _mesh=mesh );
ex->add( "u", u );
ex->add( "ubis", u2 );
ex->save();
}
}
Expr GlobalVariables::void_var() {
return room( cst( type_Void, 0, 0 ) );
}
( optional
( quad, *, typename vf::detail::integrate_type<Args>::_quad_type() )
( geomap, *, GeomapStrategyType::GEOMAP_OPT )
( quad1, *, typename vf::detail::integrate_type<Args>::_quad1_type() )
( use_tbb, ( bool ), false )
( use_harts, ( bool ), false )
( grainsize, ( int ), 100 )
( partitioner, *, "auto" )
( verbose, ( bool ), false )
( parallel, *( boost::is_integral<mpl::_> ), 1 )
( worldcomm, (WorldComm), Environment::worldComm() )
)
)
{
double meas = integrate( _range=range, _expr=cst(1.0), _quad=quad, _quad1=quad1, _geomap=geomap,
_use_tbb=use_tbb, _use_harts=use_harts, _grainsize=grainsize,
_partitioner=partitioner, _verbose=verbose ).evaluate( parallel,worldcomm )( 0, 0 );
DLOG(INFO) << "[mean] nelements = " << nelements(range) << "\n";
DLOG(INFO) << "[mean] measure = " << meas << "\n";
CHECK( math::abs(meas) > 1e-13 ) << "Invalid domain measure : " << meas << ", domain range: " << nelements( range ) << "\n";
auto eint = integrate( _range=range, _expr=expr, _quad=quad, _geomap=geomap,
_quad1=quad1, _use_tbb=use_tbb, _use_harts=use_harts, _grainsize=grainsize,
_partitioner=partitioner, _verbose=verbose ).evaluate( parallel,worldcomm );
DLOG(INFO) << "[mean] integral = " << eint << "\n";
DLOG(INFO) << "[mean] mean = " << eint/meas << "\n";
return eint/meas;
}
}
#endif // FEELPP_VF_MEAN_HPP
void
NavierStokes::run()
{
this->init();
auto U = Xh->element( "(u,p)" );
auto V = Xh->element( "(u,q)" );
auto u = U.element<0>( "u" );
auto v = V.element<0>( "u" );
auto p = U.element<1>( "p" );
auto q = V.element<1>( "p" );
#if defined( FEELPP_USE_LM )
auto lambda = U.element<2>();
auto nu = V.element<2>();
#endif
//# endmarker4 #
LOG(INFO) << "[dof] number of dof: " << Xh->nDof() << "\n";
LOG(INFO) << "[dof] number of dof/proc: " << Xh->nLocalDof() << "\n";
LOG(INFO) << "[dof] number of dof(U): " << Xh->functionSpace<0>()->nDof() << "\n";
LOG(INFO) << "[dof] number of dof/proc(U): " << Xh->functionSpace<0>()->nLocalDof() << "\n";
LOG(INFO) << "[dof] number of dof(P): " << Xh->functionSpace<1>()->nDof() << "\n";
LOG(INFO) << "[dof] number of dof/proc(P): " << Xh->functionSpace<1>()->nLocalDof() << "\n";
LOG(INFO) << "Data Summary:\n";
LOG(INFO) << " hsize = " << meshSize << "\n";
LOG(INFO) << " export = " << this->vm().count( "export" ) << "\n";
LOG(INFO) << " mu = " << mu << "\n";
LOG(INFO) << " bccoeff = " << penalbc << "\n";
//# marker5 #
auto deft = gradt( u )+trans(gradt(u));
auto def = grad( v )+trans(grad(v));
//# endmarker5 #
//# marker6 #
// total stress tensor (trial)
auto SigmaNt = -idt( p )*N()+mu*deft*N();
// total stress tensor (test)
auto SigmaN = -id( p )*N()+mu*def*N();
//# endmarker6 #
auto F = M_backend->newVector( Xh );
auto D = M_backend->newMatrix( Xh, Xh );
// right hand side
auto ns_rhs = form1( _test=Xh, _vector=F );
LOG(INFO) << "[navier-stokes] vector local assembly done\n";
// construction of the BDF
auto bdfns=bdf(_space=Xh);
/*
* Construction of the left hand side
*/
auto navierstokes = form2( _test=Xh, _trial=Xh, _matrix=D );
mpi::timer chrono;
navierstokes += integrate( elements( mesh ), mu*inner( deft,def )+ trans(idt( u ))*id( v )*bdfns->polyDerivCoefficient( 0 ) );
LOG(INFO) << "mu*inner(deft,def)+(bdf(u),v): " << chrono.elapsed() << "\n";
chrono.restart();
navierstokes +=integrate( elements( mesh ), - div( v )*idt( p ) + divt( u )*id( q ) );
LOG(INFO) << "(u,p): " << chrono.elapsed() << "\n";
chrono.restart();
#if defined( FEELPP_USE_LM )
navierstokes +=integrate( elements( mesh ), id( q )*idt( lambda ) + idt( p )*id( nu ) );
LOG(INFO) << "(lambda,p): " << chrono.elapsed() << "\n";
chrono.restart();
#endif
std::for_each( inflow_conditions.begin(), inflow_conditions.end(),
[&]( BoundaryCondition const& bc )
{
// right hand side
ns_rhs += integrate( markedfaces( mesh, bc.marker() ), inner( idf(&bc,BoundaryCondition::operator()),-SigmaN+penalbc*id( v )/hFace() ) );
navierstokes +=integrate( boundaryfaces( mesh ), -inner( SigmaNt,id( v ) ) );
navierstokes +=integrate( boundaryfaces( mesh ), -inner( SigmaN,idt( u ) ) );
navierstokes +=integrate( boundaryfaces( mesh ), +penalbc*inner( idt( u ),id( v ) )/hFace() );
});
std::for_each( wall_conditions.begin(), wall_conditions.end(),
[&]( BoundaryCondition const& bc )
{
navierstokes +=integrate( boundaryfaces( mesh ), -inner( SigmaNt,id( v ) ) );
navierstokes +=integrate( boundaryfaces( mesh ), -inner( SigmaN,idt( u ) ) );
navierstokes +=integrate( boundaryfaces( mesh ), +penalbc*inner( idt( u ),id( v ) )/hFace() );
});
std::for_each( outflow_conditions.begin(), outflow_conditions.end(),
[&]( BoundaryCondition const& bc )
{
ns_rhs += integrate( markedfaces( mesh, bc.marker() ), inner( idf(&bc,BoundaryCondition::operator()),N() ) );
});
LOG(INFO) << "bc: " << chrono.elapsed() << "\n";
chrono.restart();
u = vf::project( _space=Xh->functionSpace<0>(), _expr=cst(0.) );
p = vf::project( _space=Xh->functionSpace<1>(), _expr=cst(0.) );
M_bdf->initialize( U );
for( bdfns->start(); bdfns->isFinished(); bdfns->next() )
{
// add time dependent terms
auto bdf_poly = bdfns->polyDeriv();
form1( _test=Xh, _vector=Ft ) =
integrate( _range=elements(mesh), _expr=trans(idv( bdf_poly ))*id( v ) );
// add convective terms
form1( _test=Xh, _vector=Ft ) +=
integrate( _range=elements(mesh), _expr=trans(gradv(u)*idv( u ))*id(v) );
// add contrib from time independent terms
Ft->add( 1., F );
// add time stepping terms from BDF to right hand side
backend()->solve( _matrix=D, _solution=U, _rhs=Ft );
this->exportResults( bdfns->time(), U );
}
} // NavierNavierstokes::run
Expr phi( Expr cond, Expr ok, Expr ko ) {
// known value ?
bool v;
if ( cond.get_val( v ) )
return v ? ok : ko;
// the same value in all the cases ?
if ( ok == ko )
return ok;
// if ok or ko are undefined
// if ( ok.inst->undefined() ) return ko;
// if ( ko.inst->undefined() ) return ok;
// phi( not c, a, b ) -> phi( c, b, a )
if ( cond.inst->inst_id() == Inst::Id_Op_not )
return phi( cond.inst->inp_expr( 0 ), ko, ok );
// phi( c, true, false ) -> c
// phi( c, false, true ) -> not c
if ( ok.size_in_bits() == 1 and ko.size_in_bits() == 1 ) {
bool va, vb;
if ( ok.get_val( va ) and ko.get_val( vb ) ) {
if ( va and not vb )
return cond;
if ( vb and not va )
return op_not( bt_Bool, cond );
}
}
// phi( c, b, c )
if ( cond == ko )
return phi( cond, ok, cst( false ) );
// phi( c, c, b )
if ( cond == ok )
return phi( cond, cst( true ), ko );
// if ok is a phi node tree which contain cond in the conditions
if ( Expr nok = phi_with_cond( cond, 1, ok ) )
return phi( cond, nok, ko );
// if ko is a phi node tree which contain cond in the conditions
if ( Expr nko = phi_with_cond( cond, 0, ko ) )
return phi( cond, ok, nko );
// phi( cond, a, phi( cond, ) )
// cond = bool( ... )
//if ( cond.inst->inst_id() == Inst::Id_Conv and cond.inst->out_bt( 0 ) == bt_Bool )
// cond = cond.inst->inp_expr( 0 );
// else, create a new inst
Phi *res = new Phi;
res->inp_repl( 0, cond );
res->inp_repl( 1, ok );
res->inp_repl( 2, ko );
return Expr( Inst::factorized( res ), 0 );
}
void
TestInterpolationHCurl3D::testInterpolation( std::string one_element_mesh )
{
//auto myexpr = unitX() + unitY() + unitZ() ; //(1,1,1)
auto myexpr = vec( cst(1.), cst(1.), cst(1.));
// one element mesh
auto mesh_name = one_element_mesh + ".msh"; //create the mesh and load it
fs::path mesh_path( mesh_name );
mesh_ptrtype oneelement_mesh = loadMesh( _mesh=new mesh_type,
_filename=mesh_name);
// refined mesh (export)
auto refine_level = std::floor(1 - math::log( 0.1 )); //Deduce refine level from meshSize (option)
mesh_ptrtype mesh = loadMesh( _mesh=new mesh_type,
_filename=mesh_name,
_refine=( int )refine_level);
space_ptrtype Xh = space_type::New( oneelement_mesh );
std::vector<std::string> faces = {"yzFace","xyzFace","xyFace"};
std::vector<std::string> edges = {"zAxis","yAxis","yzAxis","xyAxis","xzAxis","xAxis"};
element_type U_h_int = Xh->element();
element_type U_h_on = Xh->element();
element_type U_h_on_boundary = Xh->element();
submesh1d_ptrtype edgeMesh( new submesh1d_type );
edgeMesh = createSubmesh(oneelement_mesh, boundaryedges(oneelement_mesh) ); //submesh of edges
// Tangents on ref element
auto t0 = vec(cst(0.),cst(0.),cst(-2.));
auto t1 = vec(cst(0.),cst(2.),cst(0.));
auto t2 = vec(cst(0.),cst(-2.),cst(2.));
auto t3 = vec(cst(2.),cst(-2.),cst(0.));
auto t4 = vec(cst(2.),cst(0.),cst(-2.));
auto t5 = vec(cst(2.),cst(0.),cst(0.));
// Jacobian of geometrical transforms
std::string jac;
if(mesh_path.stem().string() == "one-elt-ref-3d" || mesh_path.stem().string() == "one-elt-real-h**o-3d" )
jac = "{1,0,0,0,1,0,0,0,1}:x:y:z";
else if(mesh_path.stem().string() == "one-elt-real-rotx" )
jac = "{1,0,0,0,0,-1,0,1,0}:x:y:z";
else if(mesh_path.stem().string() == "one-elt-real-roty" )
jac = "{0,0,1,0,1,0,-1,0,0}:x:y:z";
else if(mesh_path.stem().string() == "one-elt-real-rotz" )
jac = "{0,-1,0,1,0,0,0,0,1}:x:y:z";
U_h_int(0) = integrate( markedelements(edgeMesh, edges[0]), trans(expr<3,3>(jac)*t0)*myexpr ).evaluate()(0,0);
U_h_int(1) = integrate( markedelements(edgeMesh, edges[1]), trans(expr<3,3>(jac)*t1)*myexpr ).evaluate()(0,0);
U_h_int(2) = integrate( markedelements(edgeMesh, edges[2]), trans(expr<3,3>(jac)*t2)*myexpr ).evaluate()(0,0);
U_h_int(3) = integrate( markedelements(edgeMesh, edges[3]), trans(expr<3,3>(jac)*t3)*myexpr ).evaluate()(0,0);
U_h_int(4) = integrate( markedelements(edgeMesh, edges[4]), trans(expr<3,3>(jac)*t4)*myexpr ).evaluate()(0,0);
U_h_int(5) = integrate( markedelements(edgeMesh, edges[5]), trans(expr<3,3>(jac)*t5)*myexpr ).evaluate()(0,0);
for(int i=0; i<edges.size(); i++)
{
double edgeLength = integrate( markedelements(edgeMesh, edges[i]), cst(1.) ).evaluate()(0,0);
U_h_int(i) /= edgeLength;
}
#if 0 //Doesn't work for now
for(int i=0; i<Xh->nLocalDof(); i++)
{
CHECK( edgeMesh->hasMarkers( {edges[i]} ) );
U_h_int(i) = integrate( markedelements(edgeMesh, edges[i]), trans( print(T(),"T=") )*myexpr ).evaluate()(0,0);
std::cout << "U_h_int(" << i << ")= " << U_h_int(i) << std::endl;
}
#endif
// nedelec interpolant using on keyword
// interpolate on element
U_h_on.zero();
U_h_on.on(_range=elements(oneelement_mesh), _expr=myexpr);
U_h_on_boundary.on(_range=boundaryfaces(oneelement_mesh), _expr=myexpr);
auto exporter_proj = exporter( _mesh=mesh, _name=( boost::format( "%1%" ) % this->about().appName() ).str() );
exporter_proj->step( 0 )->add( "U_interpolation_handly_"+mesh_path.stem().string(), U_h_int );
exporter_proj->step( 0 )->add( "U_interpolation_on_"+mesh_path.stem().string(), U_h_on );
exporter_proj->save();
// print coefficient only for reference element
U_h_int.printMatlab( "U_h_int_" + mesh_path.stem().string() + ".m" );
U_h_on.printMatlab( "U_h_on_" + mesh_path.stem().string() + ".m" );
U_h_on_boundary.printMatlab( "U_h_on_boundary_" + mesh_path.stem().string() + ".m" );
//L2 norm of error
auto error = vf::project(_space=Xh, _range=elements(oneelement_mesh), _expr=idv(U_h_int) - idv(U_h_on) );
double L2error = error.l2Norm();
std::cout << "L2 error (elements) = " << L2error << std::endl;
auto error_boundary = vf::project(_space=Xh, _range=elements(oneelement_mesh), _expr=idv(U_h_int) - idv(U_h_on_boundary) );
double L2error_boundary = error_boundary.l2Norm();
std::cout << "L2 error (boundary) = " << L2error_boundary << std::endl;
BOOST_CHECK_SMALL( L2error_boundary - L2error, 1e-13 );
}
Expr Interpreter::cst_ptr( SI64 val ) {
if ( arch->ptr_size == 32 )
return cst( SI32( val ) );
return cst( val );
}
void initFromSpace( space_ptrtype const& space )
{
super_type::initFromSpace(space);
M_fieldDensity = this->dynamicViscositySpace()->elementPtr( cst( this->cstDensity() ) );
M_fieldCinematicViscosity = this->dynamicViscositySpace()->elementPtr( cst( this->cstCinematicViscosity() ) );
}
Expr Var::expr() const {
return data and data->ptr ? data->ptr->expr() : cst( Vec<PI8>() );
}
//#include <cplex.h>
//
void CliquePartitionProblem::cps(std::string const &fileName,
ILpSolver & solver) const {
int const n(nV());
//
char const binary(solver.binary());
char const continuous(solver.continuous());
char const leq(solver.leq());
char const eq(solver.eq());
char const geq(solver.geq());
//
ColumnBuffer columnBuffer(continuous);
DoubleVector denseCost(n * (n - 1), 0);
for (auto const & e : _costs) {
int const u(e._i);
int const v(e._j);
int const id(ijtok(n, u, v));
denseCost[id] = e._v;
}
//cpCost(denseCost);
//IntVector index(n * (n - 1));
int nCols(0);
for (int u(0); u < nV(); ++u) {
for (int v(u + 1); v < nV(); ++v, ++nCols) {
int const id(ijtok(n, u, v));
columnBuffer.add(denseCost[id], binary, 0, 1, GetStr("x_", u, "_", v));
if (id != nCols) {
std::cout << "wrong numbering" << std::endl;
std::exit(-1);
}
}
}
columnBuffer.add(cst(), continuous, 1, 1, "CST");
solver.add(columnBuffer);
RowBuffer rowBuffer;
double const eps(1e-20);
for (int u(0); u < nV(); ++u) {
for (int v(u + 1); v < nV(); ++v) {
int const uv(ijtok(n, u, v));
for (int w(v + 1); w < nV(); ++w) {
int const uw(ijtok(n, u, w));
int const vw(ijtok(n, v, w));
if (denseCost[uv] > -eps || denseCost[vw] > -eps) {
rowBuffer.add(1, leq, GetStr("T_", u, "_", v, "_", w));
rowBuffer.add(uv, 1);
rowBuffer.add(vw, 1);
rowBuffer.add(uw, -1);
}
if (denseCost[vw] > -eps || denseCost[uw] > -eps) {
rowBuffer.add(1, leq, GetStr("T_", v, "_", w, "_", u));
rowBuffer.add(vw, 1);
rowBuffer.add(uw, 1);
rowBuffer.add(uv, -1);
}
if (denseCost[uw] > -eps || denseCost[uv] > -eps) {
rowBuffer.add(1, leq, GetStr("T_", w, "_", u, "_", v));
rowBuffer.add(uw, 1);
rowBuffer.add(uv, 1);
rowBuffer.add(vw, -1);
}
}
}
}
solver.add(rowBuffer);
solver.maximize();
solver.write(fileName + ".lp");
solver.run();
double objval = solver.objValue();
std::cout << "optimal solution value : " << std::setprecision(20) << objval << std::endl;
}
// <int Order_s, int Order_p, int Order_t>
void Convection ::initLinearOperator2( sparse_matrix_ptrtype& L )
{
boost::timer ti;
LOG(INFO) << "[initLinearOperator2] start\n";
mesh_ptrtype mesh = Xh->mesh();
element_type U( Xh, "u" );
element_type Un( Xh, "un" );
element_type V( Xh, "v" );
element_0_type u = U. element<0>(); // fonction vitesse
element_0_type un = Un. element<0>(); // fonction vitesse
element_0_type v = V. element<0>(); // fonction test vitesse
element_1_type p = U. element<1>(); // fonction pression
element_1_type pn = Un. element<1>(); // fonction pression
element_1_type q = V. element<1>(); // fonction test pression
element_2_type t = U. element<2>(); // fonction temperature
element_2_type tn = Un. element<2>(); // fonction temperature
element_2_type s = V. element<2>(); // fonction test temperature
#if defined( FEELPP_USE_LM )
element_3_type xi = U. element<3>(); // fonction multipliers
element_3_type eta = V. element<3>(); // fonction test multipliers
#endif
double gr= M_current_Grashofs;
double sqgr( 1/math::sqrt( gr ) );
double pr = M_current_Prandtl;
double sqgrpr( 1/( pr*math::sqrt( gr ) ) );
double gamma( this->vm()["penalbc"]. as<double>() );
double k=this->vm()["k"]. as<double>();
double nu=this->vm()["nu"]. as<double>();
double rho=this->vm()["rho"]. as<double>();
//double dt=this->vm()["dt"]. as<double>();
int adim=this->vm()["adim"]. as<int>();
int weakdir=this->vm()["weakdir"]. as<int>();
//choix de la valeur des paramètres dimensionnés ou adimensionnés
double a=0.0,b=0.0,c=0.0;
double pC=1;
if ( adim == 0 ) pC = this->vm()["pC"]. as<double>();
if ( adim==1 )
{
a=1;
b=sqgr;
c=sqgrpr;
}
else
{
a=rho;
b=nu;
c=k;
}
double expansion = 1;
if ( adim == 0 ) expansion=3.7e-3;
auto bf = form2( _test=Xh, _trial=Xh, _matrix=L );
// Temperature
#if CONVECTION_DIM==2
// buyoancy forces c(theta,v)
bf +=integrate( _range=elements( mesh ),
_expr=-expansion*idt( t )*( trans( vec( constant( 0. ),constant( 1.0 ) ) )*id( v ) ) );
#else
bf +=integrate( _range=elements( mesh ),
_expr=-expansion*idt( t )*( trans( vec( cst(0.), constant( 0. ),constant( 1.0 ) ) )*id( v ) ) );
#endif
LOG(INFO) << "[initLinearOperator] temperature Force terms done\n";
// heat conduction/diffusion: e(beta1,theta,chi)+f(theta,chi)
bf += integrate( _range=elements( mesh ),
_expr=cst( c )*gradt( t )*trans( grad( s ) ) );
LOG(INFO) << "[initLinearOperator] Temperature Diffusion terms done\n";
if ( weakdir == 1 )
{
// weak Dirichlet on temperature (T=0|left wall)
bf += integrate ( markedfaces( mesh, "Tfixed" ),
- gradt( t )*N()*id( s )*cst_ref( sqgrpr ) );
bf += integrate ( markedfaces( mesh, "Tfixed" ),
- grad( s )*N()*idt( t )*cst_ref( sqgrpr ) );
bf += integrate ( markedfaces( mesh, "Tfixed" ),
gamma*idt( t )*id( s )/hFace() );
}
LOG(INFO) << "[initLinearOperator2] done in " << ti.elapsed() << "s\n";
}