void RelaxOneHamInt(MessRelaxInpPar &RelaxPar,
double H,double Qs,double Eta,double Is,double Wid,
double *x,double *y)
{
MessRelaxClcPar *RelaxClc=new MessRelaxClcPar[RelaxPar.NumHam+1];
FormIntArr(RelaxClc,RelaxPar,H, Qs, Eta, Is);
my_comp res;
double t0,t1;
int N=my_real(RelaxClc[1].RelInt[0]);
Wid=Wid/2;
for (int i=1;i<=x[0];i++)
{
res=0;
for (int k=1;k<=RelaxPar.NumHam;k++)
{
t1=RelaxClc[k].EndTime;t0=RelaxClc[k-1].EndTime;
for (int k1=1;k1<=N;k1++)
{
my_comp freq=my_comp(-Wid,x[i]-my_real(RelaxClc[k].Freq[k1]));
res=res+
RelaxClc[k].RelInt[k1]
/freq*
( exp(my_comp( -fabs(Wid*t1),my_imag(freq)*(t1-t0)+x[i]*t0 ))-
exp(my_comp(-fabs(Wid*t0),x[i]*t0)) );
}
}
y[i]=my_real(res);
}
delete []RelaxClc;
};
void GenerateInt(CMatrCl &Ham3,CMatrCl &Rot3Rgt,
CMatrCl &Ham1,CMatrCl &Rot1Lft,
double t0,double t1,double MaxNorm,my_comp *&res,double &Tstp,int &Nit)
{
double M=max<double>(MatrNorm(Ham3),MatrNorm(Ham1));
CMatrCl Uni3(4),Uni1(2);Uni3=Uni3*0+1;Uni1=Uni1*0+1;
Nit=int((t1-t0)*M/MaxNorm)+1;
Tstp=(t1-t0)/Nit;
CMatrCl
H3=Uni3+Ham3*my_comp(0,Tstp),
H1=Uni1-Transpon(Ham1)*my_comp(0,Tstp);
delete []res;res=new my_comp[Nit+1];res[0]=Nit;
my_comp d3=my_comp(sqrt(2./(3*8)),0),d2=my_comp(sqrt(4./(3*8)),0),
d1=my_comp(sqrt(6./(3*8)),0);
for (int k=1;k<=Nit;k++)
{
Rot3Rgt=H3*Rot3Rgt;
Rot1Lft=Rot1Lft*H1;
res[k]=
Rot3Rgt(1,1)*d1*d1*Rot1Lft(1,1)+Rot3Rgt(1,2)*d3*d1*Rot1Lft(2,1)+
Rot3Rgt(2,2)*d3*d3*Rot1Lft(2,2)+Rot3Rgt(2,1)*d3*d1*Rot1Lft(1,2)+
Rot3Rgt(3,3)*d3*d3*Rot1Lft(1,1)+Rot3Rgt(3,4)*d3*d1*Rot1Lft(2,1)+
Rot3Rgt(4,4)*d1*d1*Rot1Lft(2,2)+Rot3Rgt(4,3)*d3*d1*Rot1Lft(1,2)+
Rot3Rgt(2,2)*d2*d2*Rot1Lft(1,1)+Rot3Rgt(2,3)*d2*d2*Rot1Lft(2,1)+
Rot3Rgt(3,3)*d2*d2*Rot1Lft(2,2)+Rot3Rgt(3,2)*d2*d2*Rot1Lft(1,2);
}
for (k=1;k<=Nit;k++) res[k]/=M_PI;
};
void FormAmp(CMatrCl &AmpR1,CMatrCl &AmpL1,CMatrCl &AmpR2,CMatrCl &AmpL2,
CMatrCl &AmpR3,CMatrCl &AmpL3)
{
AmpR1.SetMatr(2,4);AmpR1=AmpR1*0;AmpR2=AmpR1;AmpR3=AmpR1;
my_comp d3=my_comp(sqrt(2./(3*8)),0),d2=my_comp(sqrt(4./(3*8)),0),
d1=my_comp(sqrt(6./(3*8)),0);
AmpR1(1,1)=d1;AmpR1(2,2)=d3;
AmpR2(1,3)=d3;AmpR2(2,4)=d1;
AmpR3(1,2)=d2;AmpR3(2,3)=d2;
AmpL1=Transpon(AmpR1);AmpL2=Transpon(AmpR2);AmpL3=Transpon(AmpR3);
};
my_comp URCinnerpod(int l,int s,int u,my_comp c,const CVecCl &a,const CVecCl &b)
{
long double re=my_real(c),im=my_imag(c);
my_comp tmp;
for (int k=l;k<=u;k+=s) { tmp=a[k]*b[k];re+=my_real(tmp);im+=my_imag(tmp);}
return my_comp(re,im);
};
CVecCl operator/(const CVecCl &vec,const my_comp coef)
{ CVecCl ret=vec;
if (fabs(coef)>MathZer)
{for (int k=1;k<=my_real(ret.Ptr[0]);k++) ret.Ptr[k]/=coef;}
else
{ for (int k=1;k<=my_real(ret.Ptr[0]);k++) ret.Ptr[k]=my_comp(MathInf,MathInf);
cout<<"Error......... Zero Division in CVecCl/n";}
return ret; };
void FormIntArr(MessRelaxClcPar *RelaxClc,MessRelaxInpPar &RelaxPar,
double H,double Qs,double Eta,double Is)
{
int N=8;//Mat.Dim();
CMatrCl Mat(N),TimeShiftLeft,TimeShiftRight;
CMatrCl Mat3,Mat3Eig,Mat3L,Mat3R, Mat1,Mat1Eig,Mat1L,Mat1R;
CMatrCl Uni3(4),Uni1(2);Uni3=Uni3*0+1;Uni1=Uni1*0+1;
TimeShiftLeft=Uni3;TimeShiftRight=Uni1;
CVecCl Int(N),Pos(N);
RelaxPar.Times[0]=0;
RelaxClc[0].EndTime=0;
for (int k=1;k<=RelaxPar.NumHam;k++)
{
QsHMat(Mat,RelaxPar.Teta[k],RelaxPar.Phi[k],H, -Qs, Eta, -Is,&Mat3,&Mat1);
RelaxClc[k].EndTime=RelaxPar.Times[k];
// CMatrCl AmpL,AmpR;
// AmpL=R0HQsAmpVec_();
// AmpR=TimeShiftRight*AmpL;AmpL=Conj(Transpon(Conj(Transpon(AmpL))*TimeShiftLeft));
CMatrCl Eig,Lft,Rgt;
Mat1=Transpon(Mat1);
GetVecIntTurn_(Int,Pos,Mat3,Mat1,TimeShiftLeft,TimeShiftRight,
&Mat3Eig,&Mat3L,&Mat3R,&Mat1Eig,&Mat1L,&Mat1R);
RelaxClc[k].RelInt=Int;
RelaxClc[k].Freq=Pos;
Eig=Mat3Eig;
for (int i=1;i<=Mat3.Dim();i++)
Eig(i,i)=exp(my_comp(0,-my_real(Mat3Eig(i,i))*
(RelaxPar.Times[k]-RelaxPar.Times[k-1])));
Mat3=Mat3L*Eig*Mat3R;
TimeShiftLeft= Mat3*TimeShiftLeft;
Eig=Mat1Eig;
for ( i=1;i<=Mat1.Dim();i++)
Eig(i,i)=exp(my_comp(0,my_real(Mat1Eig(i,i))*
(RelaxPar.Times[k]-RelaxPar.Times[k-1])));
Mat1=Mat1L*Eig*Mat1R;
TimeShiftRight=TimeShiftRight*Mat1;
}
};
///
// ======================= Mul Var ============================
//
//int MaxNit;
void GenerateIntVar(CMatrCl &Ham3,CMatrCl &Rot3Rgt,
CMatrCl &Ham1,CMatrCl &Rot1Lft,
double t0,double t1,double MaxNorm,my_comp *&res,double &Tstp,int &Nit)
{
double M=max<double>(MatrNorm(Ham3),MatrNorm(Ham1));
CMatrCl Uni3(4),Uni1(2);Uni3=Uni3*0+1;Uni1=Uni1*0+1;
Nit=int((t1-t0)*M/MaxNorm)+1;
//Nit=1;
Tstp=(t1-t0)/Nit;
//if (Nit>MaxNit) MaxNit=Nit;
// CMatrCl AmpR,AmpL;
// AmpR=R0HQsAmpVec_();AmpL=Conj(Transpon(AmpR));
CMatrCl AmpR1,AmpL1,AmpR2,AmpL2,AmpR3,AmpL3;
FormAmp(AmpR1,AmpL1,AmpR2,AmpL2,AmpR3,AmpL3);
CMatrCl
H3=Uni3+Ham3*my_comp(0,Tstp),
H1=Uni1-Transpon(Ham1)*my_comp(0,Tstp);
// H3=Uni3+Transpon(Ham3*my_comp(0,Tstp)),
// H1=Uni1-Ham1*my_comp(0,Tstp);
delete []res;res=new my_comp[Nit+1];res[0]=Nit;
for (int k=1;k<=Nit;k++)
{
Rot3Rgt=H3*Rot3Rgt;
Rot1Lft=Rot1Lft*H1;
// Rot3Rgt=Rot3Rgt*H3;
// Rot1Lft=H1*Rot1Lft;
res[k]=Trace(AmpR1*Rot3Rgt*AmpL1*Rot1Lft)/M_PI+
Trace(AmpR2*Rot3Rgt*AmpL2*Rot1Lft)/M_PI+
Trace(AmpR3*Rot3Rgt*AmpL3*Rot1Lft)/M_PI;
// Rot1Lft=H1*Rot1Lft;
// res[k]=Trace(AmpL*DirectMultiplyOfMat(Rot3Rgt,Rot1Lft)*AmpR)/M_PI;
// The same as trace, but we have not to transpon(Ham1)
// and multiply Rot3,Rot1 from the same side
//cout<<t0<<" "<<my_real(res[k])<<" "<<my_imag(res[k])<<"\n";t0+=Tstp;
}
};
main()
{
unsigned char ret;
unsigned char buf[8];
unsigned char i=0;
unsigned char l1=strlen(pass);
unsigned char l2;
lcd_init();
lcd_cmd(0x80);
lcd_string("password:"******"Invalid");
delay_ms(5000);
}
else
{
//ret=strcmp(pass,buf);
ret=my_comp(pass,buf,l2);
if(ret==0)
{
lcd_cmd(0x01);
lcd_string("Valid");
delay_ms(5000);
}
else
{
lcd_cmd(0x01);
lcd_string("Invalid");
delay_ms(5000);
}
}
}
int URCunsymdet(CMatrCl &a,double eps,my_comp &d1,int &d2,int *rear)
{
int i,j,k,l,N=a.Dim();
my_comp x,y;
double *tmp=new double[N+1];tmp[0]=N;
double xd,yd;
for (i=1;i<=N;i++)
tmp[i]=1/sqrt(fabs(URCinnerpod(1,1,N,0,CMatrCl::GetRow(a,i),CMatrCl::GetRow(a,i))));
d1=my_comp(1,0);d2=0;
// d1=0;d2=1;
for (k=1;k<=N;k++)
{
//cout<<" k= "<<k<<"\n";
l=k;xd=0;
for (i=k;i<=N;i++)
{
y=URCinnerpod(1,1,k-1,-a(i,k),CMatrCl::GetRow(a,i),CMatrCl::GetCol(a,k));
//cout<<" i= "<<i<<"\n";
a(i,k)=-y;yd=fabs(y*tmp[i]);
if (yd>xd) {xd=yd;l=i;}
}
if (l!=k)
{
d1=-d1;
for (j=1;j<=N;j++) { y=a(k,j); a(k,j)=a(l,j); a(l,j)=y; }
tmp[l]=tmp[k];
}
rear[k]=l;
d1*=a(k,k);
if (xd<8*eps)
{delete []tmp;cout<<"Det=0. Cannot complete LU decomposion\n";return 0;}
l1:
//cout<<" d1= "<<d1<<"\n";
if (fabs(d1)>=1) { d1*=0.0625;d2+=4;goto l1; }
l2:
//cout<<"d1= "<<d1<<"\n";
if (fabs(d1)<0.0625) { d1*=16;d2-=4;goto l2; }
x=-1/a(k,k);
for (j=k+1;j<=N;j++)
a(k,j)=x*URCinnerpod(1,1,k-1,-a(k,j),CMatrCl::GetRow(a,k),CMatrCl::GetCol(a,j));
}
delete []tmp;
return 1;
};
void RelaxOneHamIntMul(MessRelaxInpPar &RelaxPar,
double H,double Qs,double Eta,double Is,double Wid,
double *x,double *y)
{
CMatrCl Rot3Rgt(4),Rot1Lft(2),Ham(8),Ham3(4),Ham1(2),tmp3(4),tmp1(2);
Rot1Lft=Rot1Lft*0+1;Rot3Rgt=Rot3Rgt*0+1;
my_comp *res=NULL;
double Tstp;
Wid=Wid/2;
int Nit;
//MaxNit=0;
double CurT,CurItT,t0,t1;
for (int xi=1;xi<=x[0];xi++) y[xi]=0;
for (int t=1;t<=RelaxPar.NumHam;t++)
{
t1=RelaxPar.Times[t];t0=RelaxPar.Times[t-1];
QsHMat(Ham,RelaxPar.Teta[t],RelaxPar.Phi[t],H, -Qs, Eta, -Is,&Ham3,&Ham1);
// GenerateIntVar(Ham3,Rot3Rgt,Ham1,Rot1Lft,t0,t1,0.01,res,Tstp,Nit);
GenerateInt(Ham3,Rot3Rgt,Ham1,Rot1Lft,t0,t1,0.01,res,Tstp,Nit);
CurT=t0;
for (xi=1;xi<=x[0];xi++)
{
my_comp freq=my_comp(-Wid,x[xi]);
CurItT=CurT;
for (int ti=1;ti<=Nit;ti++)
{
y[xi]+=my_real(res[ti]*exp(freq*CurItT))*Tstp;
CurItT+=Tstp;
}
}
}
delete []res;
//cout<<MaxNit<<"\n";
//cout<<Ham3<<Ham1<<"\n";
};
my_comp operator*(const CVecCl &vec,const CVecCl &vec1)
{ my_comp s=my_comp(0,0);
for (int k=1;k<=my_real(vec.Ptr[0]);k++) s+=vec.Ptr[k]*vec1.Ptr[k];
return s; };
CVecCl operator*(const CVecCl &vec,const my_comp coef)
{ CVecCl ret=vec;
if (fabs(coef)>MathZer)
{for (int k=1;k<=my_real(ret.Ptr[0]);k++) ret.Ptr[k]*=coef;}
else { for (int k=1;k<=my_real(ret.Ptr[0]);k++) ret.Ptr[k]=my_comp(0,0);}
return ret; };
CVecCl operator*(const CVecCl &vec, double coef) {return vec*my_comp(coef);}
int URComeig(CMatrCl &a,CMatrCl &Lft,CMatrCl &Rgt)
{
my_comp ctmp,c1,c2,s1,s2,ch,cg,ce,cb,cd,cki,cmi;
double tem,tau,g,hj,te,tee,max,s,c,isw,de,d,root1,root2,sa,ca,cotx,cot2x;
double sig,sx,cx,e,b,nd,eta,tse,cos2a,sin2a,tep,root,sh,cb1;//chsb,hr,hi,
double sb,nc,tanh,ch1;
int i,j,k,m,it,mark=0,N=a.Dim();
double *en=new double[N+1];
double eps=1e-14;
Lft=a*0;Lft=Lft+1;Rgt=Lft;
//CMatrCl Contr=a;
// проверка числа выполненных операций
for (it=1;it<=35;it++)
{
if (mark) goto done;
// критерий сходимости
tau=0;
for (k=1;k<=N;k++)
{
tem=0;
for (i=1;i<=N;i++)
if (i!=k) tem+=fabs(my_real(a(i,k)))+fabs(my_imag(a(i,k)));
tau+=tem;
en[k]=tem+fabs(my_real(a(k,k)))+fabs(my_imag(a(k,k)));
}
// перестановка строк и столбцов
for (k=1;k<N;k++)
{
max=en[k];i=k;
for (j=k+1;j<=N;j++)
if (en[j]>max) {max=en[j];i=j;}
if (i!=k)
{
en[i]=en[k];
for (j=1;j<=N;j++)
{
ctmp=a(k,j);a(k,j)=a(i,j);a(i,j)=ctmp;
ctmp=Rgt(k,j);Rgt(k,j)=Rgt(i,j);Rgt(i,j)=ctmp;
}
for (j=1;j<=N;j++)
{
ctmp=a(j,k);a(j,k)=a(j,i);a(j,i)=ctmp;
ctmp=Lft(j,k);Lft(j,k)=Lft(j,i);Lft(j,i)=ctmp;
}
}
}
if (tau<100*eps) goto done;
// перебор элементов матрицы
mark=1;
for (k=1;k<N;k++)
{
for (m=k+1;m<=N;m++)
{
ch=my_comp(0);g=0;hj=0;
for (i=1;i<=N;i++)
if ((i!=k) && (i!=m))
{
ch+=a(k,i)*conj(a(m,i))-a(i,k)*conj(a(i,m));
te=norm(a(i,k))+norm(a(m,i));
tee=norm(a(k,i))+norm(a(i,m));
g+=te+tee;hj+=tee-te;
}
cb=a(k,m)+a(m,k);
ce=a(k,m)-a(m,k);
cd=a(k,k)-a(m,m);
te= sqr(my_real(cb))+sqr(my_imag(ce))+sqr(my_real(cd));
tee=sqr(my_imag(cb))+sqr(my_real(ce))+sqr(my_imag(cd));
if (te>=tee)
{
isw=1;c=my_real(cb);s=my_imag(ce);d=my_real(cd);de=my_imag(cd);
root2=sqrt(te);
}
else
{
isw=-1;c=my_imag(cb);s=-my_real(ce);d=my_imag(cd);de=my_real(cd);
root2=sqrt(tee);
}
root1=sqrt(s*s+c*c);
sig=-1;if (d>=0) sig=1;
sa=0;ca=-1;if (c>=0) ca=1;
if (root1<eps)
{
sx=0;sa=0;cx=1;ca=1;
if (isw>0) e=my_real(ce);else e=my_imag(ce);
if (isw>0) b=my_imag(cb);else b=-my_real(cb);
nd=sqr(d)+sqr(de);
goto enter1;
}
if (fabs(s)>eps) {ca=c/root1;sa=s/root1;}
cot2x=d/root1;
cotx=cot2x+(sig*sqrt(1+sqr(cot2x)));
sx=sig/sqrt(1+sqr(cotx));cx=sx*cotx;
// определение параметров вращения
eta=(my_real(ce)*my_real(cb)+my_imag(ce)*my_imag(cb))/root1;
tse=(my_real(cb)*my_imag(cb)-my_real(ce)*my_imag(ce))/root1;
te =sig*(-root1*de+tse*d)/root2;
tee=(d*de+root1*tse)/root2;
nd =sqr(root2)+sqr(tee);
tee=hj*cx*sx;cos2a=sqr(ca)-sqr(sa);
sin2a=2*ca*sa;tem=my_real(ch)*cos2a+my_imag(ch)*sin2a;
tep=my_imag(ch)*cos2a-my_real(ch)*sin2a;
ch =sqr(cx)*ch+my_comp(-sqr(sx)*tem-ca*tee,sqr(sx)*tep-sa*tee);
b=isw*te*ca+eta*sa;
e=ca*eta-isw*te*sa;
enter1:
s=my_real(ch)-sig*root2*e;
c=my_imag(ch)-sig*root2*b;
root=sqrt(sqr(c)+sqr(s));
if (root<eps) {cb1=1;ch1=1;sb=0;sh=0;goto trans;}
cb1=-c/root;sb=s/root;
tee=cb1*b-e*sb;nc=sqr(tee);
tanh=root/(g+2*(nc+nd));
ch1=1/sqrt(1-sqr(tanh));
sh=ch1*tanh;
// подготовка к преобразованию
trans:
tem=sx*sh*(sa*cb1-sb*ca);
c1=my_comp(cx*ch1-tem,-sx*sh*(ca*cb1+sa*sb));
c2=my_comp(cx*ch1+tem,my_imag(c1));
tep=sx*ch1*ca;tem=cx*sh*sb;
s1=my_comp(tep-tem,0);s2=my_comp(-tep-tem,0);
tep=sx*ch1*sa;tem=cx*sh*cb1;
s1=my_comp(my_real(s1),tep+tem);s2=my_comp(my_real(s2),tep-tem);
// проверка выполнять преобразование или нет
tem=fabs(s1);tep=fabs(s2);
if ( (tem>eps) || (tep>eps) )
{
mark=0;
// левое преобразование
for (i=1;i<=N;i++)
{
cki=a(k,i);cmi=a(m,i);
a(k,i)=c1*cki+s1*cmi;
a(m,i)=s2*cki+c2*cmi;
cki=Rgt(k,i);cmi=Rgt(m,i);
Rgt(k,i)=c1*cki+s1*cmi;
Rgt(m,i)=s2*cki+c2*cmi;
}
// правое преобразование
for (i=1;i<=N;i++)
{
cki=a(i,k);cmi=a(i,m);
a(i,k)=c2*cki-s2*cmi;
a(i,m)=-s1*cki+c1*cmi;
cki=Lft(i,k);cmi=Lft(i,m);
Lft(i,k)=c2*cki-s2*cmi;
Lft(i,m)=-s1*cki+c1*cmi;
}
}
}
}
}
done:
//cout<<Contr-Lft*a*Rgt;
delete []en;
return 1;
}
