@q $Id: korder.cweb 1831 2008-05-18 20:13:42Z kamenik $ @>
@q Copyright 2004, Ondra Kamenik @>

@ Start of {\tt korder.cpp} file.

@c

#include "kord_exception.h"
#include "korder.h"

@<|PLUMatrix| copy constructor@>;
@<|PLUMatrix::calcPLU| code@>;
@<|PLUMatrix::multInv| code@>;
@<|MatrixA| constructor code@>;
@<|MatrixS| constructor code@>;
@<|KOrder| member access method specializations@>;
@<|KOrder::sylvesterSolve| unfolded specialization@>;
@<|KOrder::sylvesterSolve| folded specialization@>;
@<|KOrder::switchToFolded| code@>;
@<|KOrder| constructor code@>;

@ 
@<|PLUMatrix| copy constructor@>=
PLUMatrix::PLUMatrix(const PLUMatrix& plu)
	: TwoDMatrix(plu), inv(plu.inv), ipiv(new lapack_int[nrows()])
{
	memcpy(ipiv, plu.ipiv, nrows()*sizeof(lapack_int));
}


@ Here we set |ipiv| and |inv| members of the |PLUMatrix| depending on
its content. It is assumed that subclasses will call this method at
the end of their constructors.

@<|PLUMatrix::calcPLU| code@>=
void PLUMatrix::calcPLU()
{
	lapack_int info;
	lapack_int rows = nrows();
	inv = (const Vector&)getData();
	dgetrf(&rows, &rows, inv.base(), &rows, ipiv, &info);
}

@ Here we just call the LAPACK machinery to multiply by the inverse.

@<|PLUMatrix::multInv| code@>=
void PLUMatrix::multInv(TwoDMatrix& m) const
{
	KORD_RAISE_IF(m.nrows() != ncols(),
				  "The matrix is not square in PLUMatrix::multInv");
	lapack_int info;
	lapack_int mcols = m.ncols();
	lapack_int mrows = m.nrows();
	double* mbase = m.getData().base();
	dgetrs("N", &mrows, &mcols, inv.base(), &mrows, ipiv,
				  mbase, &mrows, &info);
	KORD_RAISE_IF(info != 0,
				  "Info!=0 in PLUMatrix::multInv");
}

@ Here we construct the matrix $A$. Its dimension is |ny|, and it is
$$A=\left[f_{y}\right]+
\left[0 \left[f_{y^{**}_+}\right]\cdot\left[g^{**}_{y^*}\right] 0\right]$$,
where the first zero spans |nstat| columns, and last zero spans
|nforw| columns.

@<|MatrixA| constructor code@>=
MatrixA::MatrixA(const FSSparseTensor& f, const IntSequence& ss,
				 const TwoDMatrix& gy, const PartitionY& ypart)
	: PLUMatrix(ypart.ny())
{
	zeros();

	IntSequence c(1); c[0] = 1;
	FGSTensor f_y(f, ss, c, TensorDimens(ss, c));
	add(1.0, f_y);

	ConstTwoDMatrix gss_ys(ypart.nstat+ypart.npred, ypart.nyss(), gy);
	c[0] = 0;
	FGSTensor f_yss(f, ss, c, TensorDimens(ss, c));
	TwoDMatrix sub(*this, ypart.nstat, ypart.nys());
	sub.multAndAdd(ConstTwoDMatrix(f_yss), gss_ys);

	calcPLU();
}

@ Here we construct the matrix $S$. Its dimension is |ny|, and it is
$$S=\left[f_{y}\right]+
\left[0\quad\left[f_{y^{**}_+}\right]\cdot\left[g^{**}_{y^*}\right]\quad
0\right]+ \left[0\quad 0\quad\left[f_{y^{**}_+}\right]\right]$$
It is, in fact, the matrix $A$ plus the third summand. The first zero
in the summand spans |nstat| columns, the second zero spans |npred|
columns.

@<|MatrixS| constructor code@>=
MatrixS::MatrixS(const FSSparseTensor& f, const IntSequence& ss,
				 const TwoDMatrix& gy, const PartitionY& ypart)
	: PLUMatrix(ypart.ny())
{
	zeros();

	IntSequence c(1); c[0] = 1;
	FGSTensor f_y(f, ss, c, TensorDimens(ss, c));
	add(1.0, f_y);

	ConstTwoDMatrix gss_ys(ypart.nstat+ypart.npred, ypart.nyss(), gy);
	c[0] = 0;
	FGSTensor f_yss(f, ss, c, TensorDimens(ss, c));
	TwoDMatrix sub(*this, ypart.nstat, ypart.nys());
	sub.multAndAdd(ConstTwoDMatrix(f_yss), gss_ys);

	TwoDMatrix sub2(*this, ypart.nstat+ypart.npred, ypart.nyss());
	sub2.add(1.0, f_yss);

	calcPLU();
}


@ Here is the constructor of the |KOrder| class. We pass what we have
to. The partitioning of the $y$ vector, a sparse container with model
derivatives, then the first order approximation, these are $g_y$ and
$g_u$ matrices, and covariance matrix of exogenous shocks |v|.

We build the members, it is nothing difficult. Note that we do not make
a physical copy of sparse tensors, so during running the class, the
outer world must not change them.

In the body, we have to set |nvs| array, and initialize $g$ and $G$
containers to comply to preconditions of |performStep|.

@<|KOrder| constructor code@>=
KOrder::KOrder(int num_stat, int num_pred, int num_both, int num_forw,
			   const TensorContainer<FSSparseTensor>& fcont,
			   const TwoDMatrix& gy, const TwoDMatrix& gu, const TwoDMatrix& v,
			   Journal& jr)
	: ypart(num_stat, num_pred, num_both, num_forw),@/
	  ny(ypart.ny()), nu(gu.ncols()), maxk(fcont.getMaxDim()),@/
	  nvs(4),@/
	  _ug(4), _fg(4), _ugs(4), _fgs(4), _ugss(4), _fgss(4), @/
	  _uG(4), _fG(4),@/
	  _uZstack(&_uG, ypart.nyss(), &_ug, ny, ypart.nys(), nu),@/
	  _fZstack(&_fG, ypart.nyss(), &_fg, ny, ypart.nys(), nu),@/
	  _uGstack(&_ugs, ypart.nys(), nu),@/
	  _fGstack(&_fgs, ypart.nys(), nu),@/
	  _um(maxk, v), _fm(_um), f(fcont),@/
	  matA(*(f.get(Symmetry(1))), _uZstack.getStackSizes(), gy, ypart),@/
	  matS(*(f.get(Symmetry(1))), _uZstack.getStackSizes(), gy, ypart),@/
	  matB(*(f.get(Symmetry(1))), _uZstack.getStackSizes()),@/
	  journal(jr)@/
{
	KORD_RAISE_IF(gy.ncols() != ypart.nys(),
				  "Wrong number of columns in gy in KOrder constructor");
	KORD_RAISE_IF(v.ncols() != nu,
				  "Wrong number of columns of Vcov in KOrder constructor");
	KORD_RAISE_IF(nu != v.nrows(),
				  "Wrong number of rows of Vcov in KOrder constructor");
	KORD_RAISE_IF(maxk < 2,
				  "Order of approximation must be at least 2 in KOrder constructor");
	KORD_RAISE_IF(gy.nrows() != ypart.ny(),
				  "Wrong number of rows in gy in KOrder constructor");
	KORD_RAISE_IF(gu.nrows() != ypart.ny(),
				  "Wrong number of rows in gu in KOrder constructor");
	KORD_RAISE_IF(gu.ncols() != nu,
				  "Wrong number of columns in gu in KOrder constructor");

	// set nvs:
	nvs[0] = ypart.nys(); nvs[1] = nu; nvs[2] = nu; nvs[3] = 1;

	@<put $g_y$ and $g_u$ to the container@>;
	@<put $G_y$, $G_u$ and $G_{u'}$ to the container@>;@q'@>
}

@ Note that $g_\sigma$ is zero by the nature and we do not insert it to
the container. We insert a new physical copies.

@<put $g_y$ and $g_u$ to the container@>=
	UGSTensor* tgy = new UGSTensor(ny, TensorDimens(Symmetry(1,0,0,0), nvs));
	tgy->getData() = gy.getData();
	insertDerivative<unfold>(tgy);
	UGSTensor* tgu = new UGSTensor(ny, TensorDimens(Symmetry(0,1,0,0), nvs));
	tgu->getData() = gu.getData();
	insertDerivative<unfold>(tgu);

@ Also note that since $g_\sigma$ is zero, so $G_\sigma$.
@<put $G_y$, $G_u$ and $G_{u'}$ to the container@>=
	UGSTensor* tGy = faaDiBrunoG<unfold>(Symmetry(1,0,0,0));
	G<unfold>().insert(tGy);
	UGSTensor* tGu = faaDiBrunoG<unfold>(Symmetry(0,1,0,0));
	G<unfold>().insert(tGu);
	UGSTensor* tGup = faaDiBrunoG<unfold>(Symmetry(0,0,1,0));
	G<unfold>().insert(tGup);



@ Here we have an unfolded specialization of |sylvesterSolve|. We
simply create the sylvester object and solve it. Note that the $g^*_y$
is not continuous in memory as assumed by the sylvester code, so we
make a temporary copy and pass it as matrix $C$.

If the $B$ matrix is empty, in other words there are now forward
looking variables, then the system becomes $AX=D$ which is solved by
simple |matA.multInv()|.

If one wants to display the diagnostic messages from the Sylvester
module, then after the |sylv.solve()| one needs to call
|sylv.getParams().print("")|.


@<|KOrder::sylvesterSolve| unfolded specialization@>=
template<>@/
void KOrder::sylvesterSolve<KOrder::unfold>(ctraits<unfold>::Ttensor& der) const
{
	JournalRecordPair pa(journal);
	pa << "Sylvester equation for dimension = " << der.getSym()[0] << endrec;
	if (ypart.nys() > 0 && ypart.nyss() > 0) {
		KORD_RAISE_IF(! der.isFinite(),
					  "RHS of Sylverster is not finite");
		TwoDMatrix gs_y(*(gs<unfold>().get(Symmetry(1,0,0,0))));
		GeneralSylvester sylv(der.getSym()[0], ny, ypart.nys(),
							  ypart.nstat+ypart.npred,
							  matA.getData().base(), matB.getData().base(),
							  gs_y.getData().base(), der.getData().base());
		sylv.solve();
	} else if (ypart.nys() > 0 && ypart.nyss() == 0) {
		matA.multInv(der);
	}
}

@ Here is the folded specialization of sylvester. We unfold the right
hand side. Then we solve it by the unfolded version of
|sylvesterSolve|, and fold it back and copy to output vector.

@<|KOrder::sylvesterSolve| folded specialization@>=
template<>@/
void KOrder::sylvesterSolve<KOrder::fold>(ctraits<fold>::Ttensor& der) const
{
	ctraits<unfold>::Ttensor tmp(der);
	sylvesterSolve<unfold>(tmp);
	ctraits<fold>::Ttensor ftmp(tmp);
	der.getData() = (const Vector&)(ftmp.getData());
}

@ 
@<|KOrder::switchToFolded| code@>=
void KOrder::switchToFolded()
{
	JournalRecordPair pa(journal);
	pa << "Switching from unfolded to folded" << endrec;

	int maxdim = g<unfold>().getMaxDim();
	for (int dim = 1; dim <= maxdim; dim++) {
		SymmetrySet ss(dim, 4);
		for (symiterator si(ss); !si.isEnd(); ++si) {
			if ((*si)[2] == 0 && g<unfold>().check(*si)) {
				FGSTensor* ft = new FGSTensor(*(g<unfold>().get(*si)));
				insertDerivative<fold>(ft);
				if (dim > 1) {
					gss<unfold>().remove(*si);
					gs<unfold>().remove(*si);
					g<unfold>().remove(*si);
				}
			}
			if (G<unfold>().check(*si)) {
				FGSTensor* ft = new FGSTensor(*(G<unfold>().get(*si)));
				G<fold>().insert(ft);
				if (dim > 1) {
					G<fold>().remove(*si);
				}
			}
		}
	}
}



@ These are the specializations of container access methods. Nothing
interesting here.

@<|KOrder| member access method specializations@>=
	template<> ctraits<KOrder::unfold>::Tg& KOrder::g<KOrder::unfold>()
		{@+ return _ug;@+}
	template<>@; const ctraits<KOrder::unfold>::Tg& KOrder::g<KOrder::unfold>()@+const@;
		{@+ return _ug;@+}
	template<> ctraits<KOrder::fold>::Tg& KOrder::g<KOrder::fold>()
		{@+ return _fg;@+}
	template<> const ctraits<KOrder::fold>::Tg& KOrder::g<KOrder::fold>()@+const@;
		{@+ return _fg;@+}
	template<> ctraits<KOrder::unfold>::Tgs& KOrder::gs<KOrder::unfold>()
		{@+ return _ugs;@+}
	template<> const ctraits<KOrder::unfold>::Tgs& KOrder::gs<KOrder::unfold>()@+const@;
		{@+ return _ugs;@+}
	template<> ctraits<KOrder::fold>::Tgs& KOrder::gs<KOrder::fold>()
		{@+ return _fgs;@+}
	template<> const ctraits<KOrder::fold>::Tgs& KOrder::gs<KOrder::fold>()@+const@;
		{@+ return _fgs;@+}
	template<> ctraits<KOrder::unfold>::Tgss& KOrder::gss<KOrder::unfold>()
		{@+ return _ugss;@+}
	template<> const ctraits<KOrder::unfold>::Tgss& KOrder::gss<KOrder::unfold>()@+const@;
		{@+ return _ugss;@+}
	template<> ctraits<KOrder::fold>::Tgss& KOrder::gss<KOrder::fold>()
		{@+ return _fgss;@+}
	template<> const ctraits<KOrder::fold>::Tgss& KOrder::gss<KOrder::fold>()@+const@;
		{@+ return _fgss;@+}
	template<> ctraits<KOrder::unfold>::TG& KOrder::G<KOrder::unfold>()
		{@+ return _uG;@+}
	template<> const ctraits<KOrder::unfold>::TG& KOrder::G<KOrder::unfold>()@+const@;
		{@+ return _uG;@+}
	template<> ctraits<KOrder::fold>::TG& KOrder::G<KOrder::fold>()
		{@+ return _fG;@+}
	template<> const ctraits<KOrder::fold>::TG& KOrder::G<KOrder::fold>()@+const@;
		{@+ return _fG;@+}
	template<> ctraits<KOrder::unfold>::TZstack& KOrder::Zstack<KOrder::unfold>()
		{@+ return _uZstack;@+}
	template<> const ctraits<KOrder::unfold>::TZstack& KOrder::Zstack<KOrder::unfold>()@+const@;
		{@+ return _uZstack;@+}
	template<> ctraits<KOrder::fold>::TZstack& KOrder::Zstack<KOrder::fold>()
		{@+ return _fZstack;@+}
	template<> const ctraits<KOrder::fold>::TZstack& KOrder::Zstack<KOrder::fold>()@+const@;
		{@+ return _fZstack;@+}
	template<> ctraits<KOrder::unfold>::TGstack& KOrder::Gstack<KOrder::unfold>()
		{@+ return _uGstack;@+}
	template<> const ctraits<KOrder::unfold>::TGstack& KOrder::Gstack<KOrder::unfold>()@+const@;
		{@+ return _uGstack;@+}
	template<> ctraits<KOrder::fold>::TGstack& KOrder::Gstack<KOrder::fold>()
		{@+ return _fGstack;@+}
	template<> const ctraits<KOrder::fold>::TGstack& KOrder::Gstack<KOrder::fold>()@+const@;
		{@+ return _fGstack;@+}
	template<> ctraits<KOrder::unfold>::Tm& KOrder::m<KOrder::unfold>()
		{@+ return _um;@+}
	template<> const ctraits<KOrder::unfold>::Tm& KOrder::m<KOrder::unfold>()@+const@;
		{@+ return _um;@+}
	template<> ctraits<KOrder::fold>::Tm& KOrder::m<KOrder::fold>()
		{@+ return _fm;@+}
	template<> const ctraits<KOrder::fold>::Tm& KOrder::m<KOrder::fold>()@+const@;
		{@+ return _fm;@+}


@ End of {\tt korder.cpp} file.