void expM(std::complex<double> U[d3][d3], std::complex<double> A[d3][d3]) {
// U = exp(A)
// U = 1 + sum_i 1/i! * A^i
const int nmax=20;
std::complex<double> Atmp1[d3][d3], Atmp2[d3][d3];
for (int i=0; i<d3; i++) {
for (int j=0; j<d3; j++) {
U[i][j] = 0;
}
}
for (int i=0; i<d3; i++) {
U[i][i] = 1;
Atmp1[i][i] = 1;
}
double fact=1;
int i=0;
for (i=1; i<nmax; i++) {
fact *= i;
axb(Atmp2,Atmp1,A);
aeb(Atmp1,Atmp2);
za(Atmp2, 1.0/(double)fact, Atmp2);
apb(U,Atmp2);
if (IsSmall(Atmp2))
break;
}
}
void CalcZ(std::complex<double> Z[3][3], ConfigData *W, int x, int mu) {
std::complex<double> U[3][3], S[3][3], US[3][3];
W->extract(*U, x, mu);
CalcStapleSum(S, W, x, mu);
axb(US, U, S);
projA(Z,US);
za(Z,-1.0,Z);
}
void model_parameters::initialization(void)
{
NAreaAge.initialize();
CatchAreaAge.initialize();
CatchNatAge.initialize();
Nage(1,1) = So*Bo/(1+beta*Bo);
for(int i=sage+1 ; i <= nage ; i++)
{
Nage(1,i) = Nage(1,i-1) * mfexp(-za(i-1));
}
VulB(1) = elem_prod(elem_prod(Nage(1),va),wa);
SB(1) = elem_prod(Nage(1),fa)*wa/2;
tBo = Nage(1)*wa;
calcmaxpos(tBo);
varPos = maxPos*cvPos;
PosX(1) = minPos + (maxPos - minPos) * (0.5+0.5*sin(indmonth(1)*PI/6 - mo*PI/6));
VBarea(1,sarea) = VulB(1)* (cnorm(areas(sarea)+0.5,PosX(1),varPos));
for(int r=sarea+1 ; r <= narea-1 ; r++)
{
VBarea(1,r) = VulB(1)* (cnorm(areas(r)+0.5,PosX(1),varPos)-cnorm(areas(r)-0.5,PosX(1),varPos));
NAreaAge(1)(r) = elem_prod(Nage(1)(sage,nage),(cnorm(areas(r)+0.5,PosX(1),varPos)-cnorm(areas(r)-0.5,PosX(1),varPos)));
}
//VBarea(1,narea) = VulB(1)* (1.0-cnorm(areas(narea)-0.5,PosX(1),varPos));
NationVulB(1,1) = sum(VBarea(1)(sarea,sarea+nationareas(1)-1));
NationVulB(1,2) = sum(VBarea(1)(sarea+nationareas(1),narea));
dvar_vector tmp1(sarea,narea);
dvar_vector tmp2(sarea,narea);
dvar_vector tmp3(sarea,narea);
for(int rr= sarea; rr<=narea; rr++)
{
tmp1(rr)= VBarea(1)(rr)/ (NationVulB(1)(indnatarea(rr)) + 0.0001);
tmp2(rr) = tmp1(rr)*TotEffyear(indnatarea(rr))(indyr(1));
Effarea(1)(rr) = tmp2(rr)*TotEffmonth(indnatarea(rr))(indmonth(1));
}
for(int a= sage; a<= nage;a++)
{
dvar_vector propVBarea(sarea,narea);
for(int rr =sarea; rr<=narea; rr++)
{
propVBarea(rr) = (cnorm(areas(rr)+0.5,PosX(1),varPos)-cnorm(areas(rr)-0.5,PosX(1),varPos))(a-sage+1);
CatchAreaAge(1)(rr)(a) = q*Effarea(1)(rr)*va(a)/(q*Effarea(1)(rr)*va(a)+m)*(1-mfexp(-(q*Effarea(1)(rr)*va(a)+m)))*NAreaAge(1)(rr)(a);
CatchNatAge(1)(indnatarea(rr))(a) += CatchAreaAge(1)(rr)(a);
EffNatAge(indnatarea(rr))(1)(sage-2) = 1;
EffNatAge(indnatarea(rr))(1)(sage-1) = indnatarea(rr);
EffNatAge(indnatarea(rr))(1)(a) += Effarea(1)(rr)*propVBarea(rr);
}
//cout<<"propVBarea "<<propVBarea<<endl;
//cout<<"Effarea(1) "<<Effarea(1)<<endl;
Effage(1)(a) = Effarea(1)* propVBarea;
}
}
int ZipFile::getFileCount() const
{
int count=0;
std::ifstream inp("c:\\test.zip", std::ios::binary);
if(!inp)
{
throw ValueException::FromString("unable to open file");
}
typedef Poco::Zip::ZipArchive za_t;
za_t za(inp);
for (za_t::FileInfos::const_iterator i = za.fileInfoBegin();
i != za.fileInfoEnd(); ++i)
{
if (!i->second.isDirectory()) ++count;
}
return count;
}
void projA(std::complex<double> A[d3][d3], std::complex<double> U[d3][d3]) {
// A = proj(U), where U is projected on a antihermitian traceless matrix A
// proj(U) = ( U - U^dag)/2 - i*( U - U^dag)/2 )/3
std::complex<double> Udag[d3][d3], UmUdag[d3][d3];
aeb(Udag,U);
adag(Udag);
amb(UmUdag, U,Udag);
za(UmUdag, 0.5, UmUdag);
aeb(A,UmUdag);
std::complex<double> trace;
trace = UmUdag[0][0] + UmUdag[1][1] + UmUdag[2][2];
for (int i=0; i<d3; i++) {
A[i][i] -= trace/(double)3;
}
}
void SmallFlowStep(ConfigData *config) {
// Here we have to implement the RK scheme from 1006.4518 [hep-lat]
// Appendix C
// W_0 = V_t
// W_1 = exp(1/4 Z_0) W_0
// W_2 = exp(8/9 Z_1 - 17/36 Z_0) W_1
// W_t+eps = exp(3/4 Z_2 - 8/9 Z_1 + 17/36 Z_0) W_2
//
// Z_i = eps Z(W_i)
//
// The input configuration 'config' will be overwritten with the
// configuration at flow time t'=t+eps.
// We allocate a new ConfigData
// W_0 = V_t : W0 = config;
ConfigData *S0 = new ConfigData(opt.ns, opt.ns, opt.ns, opt.nt, 3);
// W_1 = exp(1/4 Z_0) W_0
ConfigData *W1 = new ConfigData(opt.ns, opt.ns, opt.ns, opt.nt, 3);
#pragma omp parallel for
for (int x=0; x<opt.ns*opt.ns*opt.ns*opt.nt; x++) {
std::complex<double> U[3][3], Z0[3][3], A[3][3], expA[3][3], newU[3][3];
for (int mu=0; mu<4; mu++) {
// For link U_x,mu
CalcZ(Z0, config, x, mu);
S0->replace(*Z0, x, mu); // save this into ConfigData for Z0s
za(A, 1.0/4.0*opt.eps, Z0);
expM(expA, A);
config->extract(*U, x, mu);
axb(newU, expA, U);
#ifdef DEBUG
if (testUnitarity(newU) > 1e-5) {
std::cout << "WARNING: New link in SmallFlowStep() not unitary anymore!" << std::endl;
}
#endif
W1->replace(*newU, x, mu);
}
}
// W_2 = exp(8/9 Z_1 - 17/36 Z_0) W_1
ConfigData *W2 = new ConfigData(opt.ns, opt.ns, opt.ns, opt.nt, 3);
#pragma omp parallel for
for (int x=0; x<opt.ns*opt.ns*opt.ns*opt.nt; x++) {
std::complex<double> U[3][3], Z0[3][3], Z1[3][3], A[3][3], A2[3][3], expA[3][3], newU[3][3];
for (int mu=0; mu<4; mu++) {
// First part with Z0
S0->extract(*Z0, x, mu); // get this from ConfigData for Z0s
za(A, -17.0/36.0*opt.eps, Z0);
// Add second part with Z1
CalcZ(Z1, W1, x, mu);
za(A2, 8.0/9.0*opt.eps, Z1);
// Add both parts
apb(A,A2);
S0->replace(*A, x, mu); // save this into ConfigData S0 (A=-17/36*Z0 + 8/9*Z1)
expM(expA, A);
W1->extract(*U, x, mu);
axb(newU, expA, U);
#ifdef DEBUG
if (testUnitarity(newU) > 1e-5) {
std::cout << "WARNING: New link in SmallFlowStep() not unitary anymore!" << std::endl;
}
#endif
W2->replace(*newU, x, mu);
}
}
delete W1; W1 = 0;
// W_t+eps = exp(3/4 Z_2 - 8/9 Z_1 + 17/36 Z_0) W_2
#pragma omp parallel for
for (int x=0; x<opt.ns*opt.ns*opt.ns*opt.nt; x++) {
std::complex<double> U[3][3], Z0[3][3], Z2[3][3], A[3][3], A2[3][3], expA[3][3], newU[3][3];
for (int mu=0; mu<4; mu++) {
// For link U_x,mu
// First part with Z0 and Z1
S0->extract(*Z0, x, mu); // load -17/36*Z0 + 8/9*Z1
za(A, -1.0, Z0); // switch the sign
// Add third part with Z2
CalcZ(Z2, W2, x, mu);
za(A2, 3.0/4.0*opt.eps, Z2);
// Add both parts
apb(A,A2);
expM(expA, A);
W2->extract(*U, x, mu);
axb(newU, expA, U);
#ifdef DEBUG
if (testUnitarity(newU) > 1e-5) {
std::cout << "WARNING: New link in SmallFlowStep() not unitary anymore!" << std::endl;
}
#endif
config->replace(*newU, x, mu);
}
}
// Cleaning up
delete W2; W2 = 0;
delete S0; S0 = 0;
}
