vie2_timestep_sin()

template<typename T >

void cntr::vie2_timestep_sin	(	int	n,
		herm_matrix< T > &	G,
		function< T > &	Gsin,
		herm_matrix< T > &	F,
		herm_matrix< T > &	Fcc,
		function< T > &	Fsin,
		herm_matrix< T > &	Q,
		function< T > &	Qsin,
		T	beta,
		T	h,
		int	SolveOrder
	)

One step VIE solver \((1+F)*G=Q\) for Green's function with instantaneous contributions for given integration order.

Purpose

One solvs the linear equation \((1+F)*G=Q\) for \(G(t, t^\prime)\) with the given input kernel \(F(t, t^\prime)\), its hermitian conjugate \(F^\ddagger(t, t^\prime)\), and the source term \(Q(t, t^\prime)\) for the given integration order 'kt' at a given timestep. The Green's functions \(G(t, t^\prime)\) and \(Q(t, t^\prime)\) have instantaneous contributions.

Parameters

n	[int] time step
&G	[herm_matrix<T>] solution
&Gsin	[function<T>] singular component fo G
&F	[herm_matrix<T>] green's function on left-hand side
&Fcc	[herm_matrix<T>] Complex conjugate of F
&Fsin	[function<T>] singular component fo F
&Q	[herm_matrix<T>] green's function on right-hand side
&Qsin	[function<T>] singular component of Q
beta	[double] inverse temperature
h	[double] time interval
SolveOrder	[int] integration order

Definition at line 1779 of file cntr_vie2_impl.hpp.

References cntr::function< T >::get_value(), cntr::herm_matrix< T >::incr_timestep(), cntr::herm_matrix< T >::nt(), cntr::herm_matrix< T >::ntau(), cntr::function< T >::set_value(), cntr::herm_matrix< T >::sig(), cntr::herm_matrix< T >::size1(), and cntr::herm_matrix< T >::size2().

                                                                                                                                                                                         {

    int n1=(n<=SolveOrder && n>=0 ? 0 : n);
    int n2=(n<=SolveOrder && n>=0 ? SolveOrder : n);
    int nt=F.nt(),ntau=F.ntau(),size1=F.size1(),sig=F.sig();

    assert(n >= -1);
    assert(ntau > 0);
    assert(SolveOrder > 0 && SolveOrder <= 5);
    assert(SolveOrder <= 2 * ntau + 2);
    assert(ntau == Fcc.ntau());
    assert(ntau == F.ntau());
    assert(ntau == Q.ntau());
    assert(F.sig()== G.sig());
    assert(Fcc.sig()== G.sig());
    assert(Q.sig()== G.sig());
    assert(F.size1()== size1);
    assert(F.size2()== size1);
    assert(Fcc.size1()== size1);
    assert(Fcc.size2()== size1);
    assert(Q.size1()== size1);
    assert(Q.size2()== size1);
    assert(n1 <= F.nt());
    assert(n1 <= Fcc.nt());
    assert(n1 <= G.nt());
    assert(n1 <= Q.nt());

    function<T> funFinv(n2,size1);

    cntr::herm_matrix<T> tmpF(nt,ntau,size1,sig),tmpFcc(nt,ntau,size1,sig),tmpF1(nt,ntau,size1,sig),tmpQ(nt,ntau,size1,sig);
    cdmatrix cdF,cdFinv,cdQ,cdG;
    //Check consistency
    assert(G.sig()==F.sig());
    assert(G.nt()==F.nt());
    assert(G.nt()==Q.nt());

    for(int n=-1;n<=n2;n++){
      Fsin.get_value(n,cdF);
      Qsin.get_value(n,cdQ);
      cdF=cdF+cdmatrix::Identity(size1,size1);
      cdFinv=cdF.inverse();  //Expected  that these matrices are small
      cdG=cdFinv*cdQ;
      funFinv.set_value(n,cdFinv);
      Gsin.set_value(n,cdG);
    }

    tmpF=F;
    tmpFcc=Fcc;
    tmpQ=Q;

    //Set new F and Q
    for(int n=-1;n<=n2;n++){
      tmpF.left_multiply(n,funFinv,1.0);
      tmpFcc.right_multiply(n,funFinv,1.0);
      tmpQ.left_multiply(n,funFinv,1.0);
    }
    tmpF1=tmpF;

    for(int n=-1;n<=n2;n++){
      tmpF1.right_multiply(n,Gsin,1.0);
    }
    for(int i=-1;i<=n2;i++){
      tmpQ.incr_timestep(i,tmpF1,-1.0);
    }
    vie2_timestep(n,G,tmpF,tmpFcc,tmpQ,integration::I<T>(SolveOrder),beta,h);
  }

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