void RSA_TestInstantiations()
{
RSASS<PKCS1v15, SHA1>::Verifier x1(1, 1);
RSASS<PKCS1v15, SHA1>::Signer x2(NullRNG(), 1);
RSASS<PKCS1v15, SHA1>::Verifier x3(x2);
RSASS<PKCS1v15, SHA1>::Verifier x4(x2.GetKey());
RSASS<PSS, SHA1>::Verifier x5(x3);
#ifndef __MWERKS__
RSASS<PSSR, SHA1>::Signer x6 = x2;
x3 = x2;
x6 = x2;
#endif
RSAES<PKCS1v15>::Encryptor x7(x2);
#ifndef __GNUC__
RSAES<PKCS1v15>::Encryptor x8(x3);
#endif
RSAES<OAEP<SHA1> >::Encryptor x9(x2);
x4 = x2.GetKey();
RSASS<PKCS1v15, SHA3_256>::Verifier x10(1, 1);
RSASS<PKCS1v15, SHA3_256>::Signer x11(NullRNG(), 1);
RSASS<PKCS1v15, SHA3_256>::Verifier x12(x11);
RSASS<PKCS1v15, SHA3_256>::Verifier x13(x11.GetKey());
}
int main(void)
{
// 3.4.5 Class member access
// p 2
// if the id-expression in a class member access is an
// unqualified-id, and the type of the object expression is of class
// type C (or pointer to class type C), the unqualified-id is looked
// up in the scope of class C. If the type of the object-expression
// is of pointer to scalar type, the unqualified-id is looked up in
// the context of the complete postfix-expression.
// p 3
// if the unqualitified id is ~type-name, and the type of the object
// expression is of a class type C (or pointer to class type C), the
// type-name is looked up in the context of the entire
// postfix-expression and in the scope of class C. The type-name
// shall refer to a class-name. If type-name is found in both
// contexts, the name shall refer to the same class type. If the
// type of the object expression is of scalar type, the type-name is
// looked up in the complete postfix-expression.
typedef X localtype;
//
// 1 non-templatized, pointer, unqualified
//
X x01 ;
X *px = &x01;
px->~X();
X x02 (66);
px = &x02;
px->~localtype();
X x03 (68);
px = &x03;
px->~classtype(); //-g++ //p3: unqual-id lookup in object and postfix-expr
X x04 (70);
px = &x04;
px->~globaltype();
// p 1
// . . . the id-expression is first looked up in the class of the
// object-expression. If the identifier is not found, itis then
// looked up in the context of the entier postfix-expression and
// shall name a class or function template. If the lookup in the
// class of the object-expression finds a template, the name is also
// looked up in teh context of the entier postfix-expression and
// 1 if the name is not found, use the name from the object-expr
// 2 if the name found in postfix-expr != class template, use object-expr
// 3 if name found is class template, name must match object-expr or error
// p 4
// if the id-expr in a class member acess is a qualified-id, the
// id-expression is looked up in both the context of the entire
// postfix-expr and in the scope of the class of the object-expr. If
// the name is found in both contexts, the id-expr shall refer to
// the same entity.
//
// 2 non-templatized, pointer, qualified
//
X x05 ;
px = &x05;
px->X::~X();
X x06 (66);
px = &x06;
px->X::~localtype();
X x07 (68);
px = &x07;
px->X::~classtype(); // -edg
X x08 (70);
px = &x08;
px->X::~globaltype();
X x09 (66);
px = &x09;
px->localtype::~localtype();
X x10 (68);
px = &x10;
px->classtype::~classtype();
X x11 (70);
px = &x11;
px->globaltype::~globaltype();
X x12 (66);
px = &x12;
px->classtype::~localtype();
X x13 (68);
px = &x13;
px->globaltype::~localtype();
X x14 (70);
px = &x14;
px->localtype::~globaltype();
X x15 (70);
px = &x15;
px->classtype::~globaltype();
X x16 (70);
px = &x16;
px->localtype::~classtype(); //-edg
X x17 (70);
px = &x17;
px->globaltype::~classtype(); //-edg
#if 0
//
// non-templatized, non-pointer
//
X xo5 ;
xo5.~X(); //unqualified
localtype xo6 (66);
xo6.~localtype();
X xo7 (68);
xo7.~classtype();
X xo8 (70);
xo8.~globaltype();
//
// templatized, pointer
//
X_tem<int> xto1 ;
X_tem<int> *pxt = &xto1;
pxt->~X_tem(); //unqualified
typedef X_tem<int> localtype_tem;
localtype_tem xto2 (66);
pxt = &xto2;
pxt->~localtype_tem();
//paragraph 2: unqualitifed id looked up in scope of post-fix expr if object
X_tem<int> xto3 (68);
pxt = &xto3;
pxt->~classtype_tem();
X_tem<int> xto4 (70);
pxt = &xto4;
pxt->~globaltype_tem();
//
// templatized, non-pointer
//
X_tem<int> xto5 ;
xto5.~X_tem(); //unqualified
localtype_tem xto6 (66);
xto6.~localtype_tem();
X_tem<int> xto7 (68);
xto7.~classtype_tem();
X_tem<int> xto8 (70);
xto8.~globaltype_tem();
#endif
return 0;
}
void Membrane::ensureStiffnessMatrices(const Real& young, const Real& nu, const Real& thickness,bool bending, const Real& bendThickness){
assert(hasRefConf());
// do nothing if both matrices exist already
if(KKcst.size()==36 && (!bending ||
#ifdef MEMBRANE_CONDENSE_DKT
KKdkt.size()==54
#else
KKdkt.size()==81
#endif
)) return;
// check thickness
Real t=(isnan(thickness)?2*this->halfThick:thickness);
if(/*also covers NaN*/!(t>0)) throw std::runtime_error("Membrane::ensureStiffnessMatrices: Facet thickness is not positive!");
// plane stress stiffness matrix
Matrix3r E;
E<<1,nu,0, nu,1,0,0,0,(1-nu)/2;
E*=young/(1-pow(nu,2));
// strain-displacement matrix (CCT element)
Real area=this->getArea();
const Real& x1(refPos[0]); const Real& y1(refPos[1]); const Real& x2(refPos[2]); const Real& y2(refPos[3]); const Real& x3(refPos[4]); const Real& y3(refPos[5]);
// Felippa: Introduction to FEM eq. (15.17), pg. 259
Eigen::Matrix<Real,3,6> B;
B<<
(y2-y3),0 ,(y3-y1),0 ,(y1-y2),0 ,
0 ,(x3-x2),0 ,(x1-x3),0 ,(x2-x1),
(x3-x2),(y2-y3),(x1-x3),(y3-y1),(x2-x1),(y1-y2);
B*=1/(2*area);
KKcst.resize(6,6);
KKcst=t*area*B.transpose()*E*B;
// EBcst=E*B;
if(!bending) return;
// strain-displacement matrix (DKT element)
Real dktT=(isnan(bendThickness)?t:bendThickness);
assert(!isnan(dktT));
// [Batoz,Bathe,Ho: 1980], Appendix A: Expansions for the DKT element
// (using the same notation)
Real x23=(x2-x3), x31(x3-x1), x12(x1-x2);
Real y23=(y2-y3), y31(y3-y1), y12(y1-y2);
Real l23_2=(pow(x23,2)+pow(y23,2)), l31_2=(pow(x31,2)+pow(y31,2)), l12_2=(pow(x12,2)+pow(y12,2));
Real P4=-6*x23/l23_2, P5=-6*x31/l31_2, P6=-6*x12/l12_2;
Real t4=-6*y23/l23_2, t5=-6*y31/l31_2, t6=-6*y12/l12_2;
Real q4=3*x23*y23/l23_2, q5=3*x31*y31/l31_2, q6=3*x12*y12/l12_2;
Real r4=3*pow(y23,2)/l23_2, r5=3*pow(y31,2)/l31_2, r6=3*pow(y12,2)/l12_2;
// even though w1, w2, w3 are always zero due to our definition of triangle plane,
// we need to get the corresponding nodal force, therefore cannot condense those DOFs away.
auto Hx_xi=[&](const Real& xi, const Real& eta) -> Vector9r { Vector9r ret; ret<<
P6*(1-2*xi)+(P5-P6)*eta,
q6*(1-2*xi)-(q5+q6)*eta,
-4+6*(xi+eta)+r6*(1-2*xi)-eta*(r5+r6),
-P6*(1-2*xi)+eta*(P4+P6),
q6*(1-2*xi)-eta*(q6-q4),
-2+6*xi+r6*(1-2*xi)+eta*(r4-r6),
-eta*(P5+P4),
eta*(q4-q5),
-eta*(r5-r4);
return ret;
};
auto Hy_xi=[&](const Real& xi, const Real &eta) -> Vector9r { Vector9r ret; ret<<
t6*(1-2*xi)+eta*(t5-t6),
1+r6*(1-2*xi)-eta*(r5+r6),
-q6*(1-2*xi)+eta*(q5+q6),
-t6*(1-2*xi)+eta*(t4+t6),
-1+r6*(1-2*xi)+eta*(r4-r6),
-q6*(1-2*xi)-eta*(q4-q6),
-eta*(t4+t5),
eta*(r4-r5),
-eta*(q4-q5);
return ret;
};
auto Hx_eta=[&](const Real& xi, const Real& eta) -> Vector9r { Vector9r ret; ret<<
-P5*(1-2*eta)-xi*(P6-P5),
q5*(1-2*eta)-xi*(q5+q6),
-4+6*(xi+eta)+r5*(1-2*eta)-xi*(r5+r6),
xi*(P4+P6),
xi*(q4-q6),
-xi*(r6-r4),
P5*(1-2*eta)-xi*(P4+P5),
q5*(1-2*eta)+xi*(q4-q5),
-2+6*eta+r5*(1-2*eta)+xi*(r4-r5);
return ret;
};
auto Hy_eta=[&](const Real& xi, const Real& eta) -> Vector9r { Vector9r ret; ret<<
-t5*(1-2*eta)-xi*(t6-t5),
1+r5*(1-2*eta)-xi*(r5+r6),
-q5*(1-2*eta)+xi*(q5+q6),
xi*(t4+t6),
xi*(r4-r6),
-xi*(q4-q6),
t5*(1-2*eta)-xi*(t4+t5),
-1+r5*(1-2*eta)+xi*(r4-r5),
-q5*(1-2*eta)-xi*(q4-q5);
return ret;
};
// return B(xi,eta) [Batoz,Bathe,Ho,1980], (30)
auto Bphi=[&](const Real& xi, const Real& eta) -> Eigen::Matrix<Real,3,9> {
Eigen::Matrix<Real,3,9> ret;
ret<<
(y31*Hx_xi(xi,eta)+y12*Hx_eta(xi,eta)).transpose(),
(-x31*Hy_xi(xi,eta)-x12*Hy_eta(xi,eta)).transpose(),
(-x31*Hx_xi(xi,eta)-x12*Hx_eta(xi,eta)+y31*Hy_xi(xi,eta)+y12*Hy_eta(xi,eta)).transpose()
;
return ret/(2*area);
};
// bending elasticity matrix (the same as (t^3/12)*E, E being the plane stress matrix above)
Matrix3r Db;
Db<<1,nu,0, nu,1,0, 0,0,(1-nu)/2;
Db*=young*pow(dktT,3)/(12*(1-pow(nu,2)));
// assemble the matrix here
// KKdkt0 is 9x9, then w_i dofs are condensed away, and KKdkt is only 9x6
#ifdef MEMBRANE_CONDENSE_DKT
MatrixXr KKdkt0(9,9); KKdkt0.setZero();
// MatrixXr EBdkt0(9,6); EBdkt0.setZero();
#else
KKdkt.setZero(9,9);
// EBdkt.setZero(9,6);
#endif
// gauss integration points and their weights
Vector3r xxi(.5,.5,0), eeta(0,.5,.5);
Real ww[]={1/3.,1/3.,1/3.};
for(int i:{0,1,2}){
for(int j:{0,1,2}){
auto b=Bphi(xxi[i],eeta[j]); // evaluate B at the gauss point
#ifdef MEMBRANE_CONDENSE_DKT
KKdkt0
#else
KKdkt
#endif
+=(2*area*ww[j]*ww[i])*b.transpose()*Db*b;
#if 0
#ifdef MEMBRANE_CONDENSE_DKT
EBdkt0
#else
EBdkt
#endif
+=(2*area*ww[j]*ww[i])*Db*b;
#endif
}
}
#ifdef MEMBRANE_CONDENSE_DKT
// extract columns [_ 1 2 _ 4 5 _ 7 8]
KKdkt.setZero(9,6);
for(int i:{0,1,2}){
KKdkt.col(2*i)=KKdkt0.col(3*i+1);
KKdkt.col(2*i+1)=KKdkt0.col(3*i+2);
}
#endif
};
// Test the DynSysModel class
void test_DynSysModel()
{
// Make a 4 variable model
GAParams::SetNumVars( 4 );
DynSysModel m;
// Create monomial x1, x2, x3, x4, x1*x2, x3*x4, x1*x2*x3*x4
Monomial c0( "0000" ); c0.mCoeff = false;
Monomial c1( "0000" ); c1.mCoeff = true;
Monomial x4( "0001" );
Monomial x3( "0010" );
Monomial x2( "0100" );
Monomial x1( "1000" );
Monomial x34( "0011" );
Monomial x12( "1100" );
Monomial x14( "1001" );
Monomial x1234("1111" );
Polynomial f;
f.AddTerm( c0 );
std::cout << "f = " << f.ToString( true ) << std::endl;
Polynomial g;
g.AddTerm( c1 );
std::cout << "g = " << g.ToString( true ) << std::endl;
// f1(x) = x1 + x2 + x4;
Polynomial f1;
f1.AddTerm( x1 ); f1.AddTerm( x2 ); f1.AddTerm( x4 );
std::cout << "f1 = " << f1.ToString( true ) << std::endl;
Polynomial::mMaxSupport = 2;
m.SetFunction( 1, f );
m.SetFunction( 2, g );
m.SetFunction( 3, f );
m.SetFunction( 4, f1 );
ComplexityMatrix cmplx_mat;
ComplexityMatrixRow row;
cmplx_mat.assign( 4, row );
m.SetPolyComplexities( );
double s;
s = m[1].mComplexityScore;
s = m[2].mComplexityScore;
s = m[3].mComplexityScore;
s = m[4].mComplexityScore;
/*
// f2(x) = x1*x2*x3*x4;
Polynomial f2;
f2.AddTerm( x1234 );
std::cout << "f2 = " << f2.ToString( true ) << std::endl;
// f3(x) = x1*x2 + x3*x4;
Polynomial f3;
f3.AddTerm( x12 );
f3.AddTerm( x34 );
std::cout << "f3 = " << f3.ToString( true ) << std::endl;
// f3'(x) = x1*x4;
Polynomial f3p;
f3p.AddTerm( x14 );
std::cout << "f3p = " << f3p.ToString( true ) << std::endl;
// f4(x) = x3 + x4;
Polynomial f4;
f4.AddTerm( x3 ); f4.AddTerm( x4 );
std::cout << "f4 = " << f4.ToString( true ) << std::endl;
// Assign the functions to the model
m.SetFunction( 1, f1 ); m.SetFunction( 2, f2 );
m.SetFunction( 3, f3p ); m.SetFunction( 4, f4 );
*/
TimeSeries t2;
// t2.push_back( NTuple("1101" ) );
// t2.push_back( NTuple("1011" ) );
t2.push_back( NTuple("1100" ) );
t2.push_back( NTuple("0010" ) );
t2.push_back( NTuple("0001" ) );
t2.push_back( NTuple("1001" ) );
t2.push_back( NTuple("0001" ) );
// Better to pass a reference to the time series for the result
// TimeSeries t3 = m.Iterate( NTuple( "1111" ), 6 );
// Test iteration for only the k'th variable
size_t k = 3;
TimeSeries t4;
size_t h = m.Iterate( t2, k, t4 );
TimeSeriesIter iter = t4.begin();
while( iter != t4.end() )
{
std::cout << *iter++ << std::endl;
}
}
