int main() {
int n = 2000;
double T = 2000_ns;
double delta_t = T/n;
vector<double> f1_list = { -30_MHz,-25_MHz,-20_MHz,-14.5_MHz,-10_MHz,-5_MHz,0_MHz,5_MHz,10_MHz,14.5_MHz,20_MHz,25_MHz,30_MHz };
for(auto k=f1_list.begin();k!=f1_list.end();k++) {
/* Hamiltonian */
double f1 = *k;
Operator H = 2*pi*(fe*Sz(0)+f1*Sx(0));
for(int i=0;i<N;i++)
H += 2*pi*(fi*Sz(i+1)+Sz(0)*(Azx[i]*Sx(i+1)+Azy[i]*Sy(i+1)+Azz[i]*Sz(i+1)));
auto U = H.U();
/* initial state */
double alpha_e = 7.6216e-4;
double alpha_i = -1.1579e-6;
//Operator rho0 = Op<2>(0,0.5*(1-alpha_e),0,0,0.5*(1+alpha_e));
Operator rho0 = Op<2>(0,0.5,0.5,0.5,0.5);
for(int i=1;i<=N;i++)
rho0 *= Op<2>(i,0.5*(1-alpha_i),0,0,0.5*(1+alpha_i));
/* output stream */
stringstream fnstream;
fnstream << "malonic-DNP_" << f1/1_MHz << "MHz.txt";
string fn = fnstream.str();
ofstream out(fn);
cout << fn << ":" << endl;
/* calculate and output */
for(int i=0;i<=n;i++) {
double t = delta_t*i;
cout << fn << ":\t" << t/T*100 << "%" << endl;
out << t/1_ns << '\t';
Operator rho = U(t)*rho0*U(-t);
Operator rhoe = rho;
for(int j=1;j<=N;j++)
rhoe = rhoe.tr(j);
out << real(tr(rhoe*Sx(0))) << '\t';
out << real(tr(rhoe*Sy(0))) << '\t';
out << real(tr(rhoe*Sz(0))) << '\t';
for(int j=1;j<=N;j++) {
Operator rhoj = rho;
for(int k=0;k<=N;k++) {
if(k==j)
continue;
rhoj = rhoj.tr(k);
}
out << real(tr(rhoj*Sz(j))) << '\t';
}
out << endl;
}
out.close();
}
}
int main() {
int n = 2000;
double T = 2000_ns;
double delta_t = T/n;
vector<double> f1_list = { 5_MHz,10_MHz,14.5_MHz,20_MHz,25_MHz };
for(auto k=f1_list.begin();k!=f1_list.end();k++) {
/* Hamiltonian */
double f1 = *k;
Operator HI;
for(int i=0;i<N;i++)
HI += 2*pi*(fi*Sz(i+1)+Sz(0)*(Azx[i]*Sx(i+1)+Azy[i]*Sy(i+1)+Azz[i]*Sz(i+1)));
auto Ht = [&HI,f1](double t) { return 2*pi*(fe*Sz(0)+2*f1*cos(2*pi*fe*t)*Sx(0))+HI; };
/* initial state */
double alpha_e = 7.6216e-4;
double alpha_i = -1.1579e-6;
//Operator rho0 = Op<2>(0,0.5*(1-alpha_e),0,0,0.5*(1+alpha_e));
Operator rho0 = Op<2>(0,0.5,0.5,0.5,0.5);
for(int i=1;i<=N;i++)
rho0 *= Op<2>(i,0.5*(1-alpha_i),0,0,0.5*(1+alpha_i));
/* output stream */
stringstream fnstream;
fnstream << "malonic-lab-coord-DNP_" << f1/1_MHz << "MHz.txt";
string fn = fnstream.str();
ofstream out(fn);
cout << fn << ":" << endl;
/* calculate and output */
vector<double> time(n+1);
for(int i=0;i<=n;i++) {
time[i] = i*delta_t;
}
vector<Operator> rhot = Operator::SolveLiouvilleEq(Ht,rho0,0.01_ns,time,[fn](double t){ cout << fn << ":" << t/1_ns << endl; });
for(auto &rho: rhot) {
Operator rhoe = rho;
for(int j=1;j<=N;j++)
rhoe = rhoe.tr(j);
out << real(tr(rhoe*Sz(0))) << '\t';
for(int j=1;j<=N;j++) {
Operator rhoj = rho;
for(int k=0;k<=N;k++) {
if(k==j)
continue;
rhoj = rhoj.tr(k);
}
out << real(tr(rhoj*Sz(j))) << '\t';
}
out << endl;
}
out.close();
}
}
RtToken RI_PIXARNOTICE =
"\tThe RenderMan (R) Interface Procedures and Protocol are:\n" \
"\t\tCopyright 1988, 1989, Pixar\n" \
"\t\t\tAll Rights Reserved\n\n" \
"\tRenderman (R) is a registered trademark of Pixar\n";
RtBasis RiBezierBasis = { { -1.0, 3.0, -3.0, 1.0 },
{ 3.0, -6.0, 3.0, 0.0 },
{ -3.0, 3.0, 0.0, 0.0 },
{ 1.0, 0.0, 0.0, 0.0 }
};
/* Define One Sixth of */
#define Sx(a) ((a)/6)
RtBasis RiBSplineBasis = { { Sx(-1.0), Sx( 3.0), Sx(-3.0), Sx( 1.0) },
{ Sx( 3.0), Sx(-6.0), Sx( 3.0), Sx( 0.0) },
{ Sx(-3.0), Sx( 0.0), Sx( 3.0), Sx( 0.0) },
{ Sx( 1.0), Sx( 4.0), Sx( 1.0), Sx( 0.0) }
};
/* Define One Half of */
#define Hf(a) ((a)/2)
RtBasis RiCatmullRomBasis = { { Hf(-1.0), Hf( 3.0), Hf(-3.0), Hf( 1.0) },
{ Hf( 2.0), Hf(-5.0), Hf( 4.0), Hf(-1.0) },
{ Hf(-1.0), Hf( 0.0), Hf( 1.0), Hf( 0.0) },
{ Hf( 0.0), Hf( 2.0), Hf( 0.0), Hf( 0.0) }
};
RtBasis RiHermiteBasis = { { 2.0, 1.0, -2.0, 1.0 },
{ -3.0, -2.0, 3.0, -1.0 },
/* >>> start tutorial code >>> */
int main( ) {
DifferentialState xT; // the trolley position
DifferentialState vT; // the trolley velocity
IntermediateState aT; // the trolley acceleration
DifferentialState xL; // the cable length
DifferentialState vL; // the cable velocity
IntermediateState aL; // the cable acceleration
DifferentialState phi; // the excitation angle
DifferentialState omega; // the angular velocity
DifferentialState uT; // trolley velocity control
DifferentialState uL; // cable velocity control
Control duT;
Control duL;
//
// DEFINE THE PARAMETERS:
//
const double tau1 = 0.012790605943772;
const double a1 = 0.047418203070092;
const double tau2 = 0.024695192379264;
const double a2 = 0.034087337273386;
const double g = 9.81;
const double c = 0.2;
const double m = 1318.0;
//
// DEFINE THE MODEL EQUATIONS:
//
DifferentialEquation f, f2, test_expr;
ExportAcadoFunction fun, fun2;
aT = -1.0 / tau1 * vT + a1 / tau1 * uT;
aL = -1.0 / tau2 * vL + a2 / tau2 * uL;
Expression states;
states << xT;
states << vT;
states << xL;
states << vL;
states << phi;
states << omega;
states << uT;
states << uL;
Expression controls;
controls << duT;
controls << duL;
Expression arg;
arg << states;
arg << controls;
int NX = states.getDim();
int NU = controls.getDim();
IntermediateState expr(2);
expr(0) = - 1.0/xL*(-g*sin(phi)-aT*cos(phi)-2*vL*omega-c*omega/(m*xL)) + log(duT/duL)*pow(xL,2);
expr(1) = - 1.0/xL*(-g*tan(phi)-aT*acos(phi)-2*atan(vL)*omega-c*asin(omega)/exp(xL)) + duT/pow(omega,3);
//~ expr(0) = - 1.0/xL*(-g*sin(phi));
//~ expr(1) = duT/pow(omega,3);
DifferentialState lambda("", expr.getDim(),1);
DifferentialState Sx("", states.getDim(),states.getDim());
DifferentialState Su("", states.getDim(),controls.getDim());
Expression S = Sx;
S.appendCols(Su);
// SYMMETRIC DERIVATIVES
Expression S_tmp = S;
S_tmp.appendRows(zeros<double>(NU,NX).appendCols(eye<double>(NU)));
IntermediateState dfS,dl;
Expression f_tmp = symmetricDerivative( expr, arg, S_tmp, lambda, &dfS, &dl );
f << returnLowerTriangular( f_tmp );
fun.init(f, "symmetricDerivative", NX*(1+NX+NU)+expr.getDim(), 0, 2, 0, 0, 0);
// ALTERNATIVE DERIVATIVES
IntermediateState tmp = backwardDerivative( expr, states, lambda );
IntermediateState tmp2 = forwardDerivative( tmp, states );
Expression tmp3 = backwardDerivative( expr, controls, lambda );
Expression tmp4 = multipleForwardDerivative( tmp3, states, Su );
Expression tmp5 = tmp4 + tmp4.transpose() + forwardDerivative( tmp3, controls );
Expression f2_tmp1;
f2_tmp1 = symmetricDoubleProduct( tmp2, Sx );
f2_tmp1.appendCols( zeros<double>(NX,NU) );
Expression f2_tmp2;
f2_tmp2 = Su.transpose()*tmp2*Sx + multipleForwardDerivative( tmp3, states, Sx );
f2_tmp2.appendCols( symmetricDoubleProduct( tmp2, Su ) + tmp5 );
f2_tmp1.appendRows( f2_tmp2 );
f2 << returnLowerTriangular( f2_tmp1 );
fun2.init(f2, "alternativeSymmetric", NX*(1+NX+NU)+expr.getDim(), 0, 2, 0, 0, 0);
Function f1;
f1 << dfS;
f1 << dl;
std::ofstream stream2( "ADtest/ADsymbolic_output2.c" );
stream2 << f1;
stream2.close();
std::ofstream stream( "ADtest/ADsymbolic_output.c" );
fun.exportCode( stream, "double" );
fun2.exportCode( stream, "double" );
test_expr << expr;
stream << test_expr;
stream.close();
return 0;
}
