static void SymLDL_Decompose(SymBandMatrixView<T> A)
{
TMVAssert(A.uplo() == Lower);
TMVAssert(A.ct() == NonConj);
TMVAssert(A.issym());
TMVAssert(A.nlo() == 1);
const ptrdiff_t N = A.size();
#ifdef XDEBUG
Matrix<T> A0(A);
//cout<<"SymLDLDecompose:\n";
//cout<<"A = "<<TMV_Text(A)<<" "<<A<<endl;
#endif
T* Dj = A.ptr();
T* Lj = A.diag(-1).ptr();
if (A.isdm()) {
T Ax0 = *Lj;
if (*Dj == T(0)) {
#ifdef NOTHROW
std::cerr<<"Non Posdef HermBandMatrix found\n";
exit(1);
#else
throw NonPosDefSymBandLDL<T>(A);
#endif
}
*Lj /= *Dj;
++Dj;
*Dj -= *Lj * Ax0;
++Lj;
} else {
ptrdiff_t step = A.diagstep();
for(ptrdiff_t j=0;j<N-1;++j) {
T Ax0 = *Lj;
if (*Dj == T(0)) {
#ifdef NOTHROW
std::cerr<<"Non Posdef HermBandMatrix found\n";
exit(1);
#else
throw NonPosDefSymBandLDL<T>(A);
#endif
}
*Lj /= *Dj;
Dj += step;
*Dj -= *Lj * Ax0;
Lj += step;
}
}
if (*Dj == T(0)) {
#ifdef NOTHROW
std::cerr<<"Non Posdef HermBandMatrix found\n";
exit(1);
#else
throw NonPosDefSymBandLDL<T>(A);
#endif
}
#ifdef XDEBUG
//cout<<"Done SymLDLDecom\n";
BandMatrix<T> L = A.lowerBand();
L.diag().SetAllTo(T(1));
DiagMatrix<T> D = DiagMatrixViewOf(A.diag());
BandMatrix<T> A2 = L * D * L.transpose();
TMV_RealType(T) normldl = TMV_SQR(Norm(L))*Norm(D);
//cout<<"L = "<<L<<endl;
//cout<<"D = "<<D<<endl;
//cout<<"A2 = "<<A2<<endl;
//cout<<"cf. A0 = "<<A0<<endl;
if (!(Norm(A2-A0) < 0.001*normldl)) {
cerr<<"SymLDLDecomp: A = "<<TMV_Text(A)<<" "<<A0<<endl;
cerr<<"Done: A = "<<A<<endl;
cerr<<"L = "<<L<<endl;
cerr<<"D = "<<D<<endl;
cerr<<"LT = "<<L.transpose()<<endl;
cerr<<"L*D*LT = "<<A2<<endl;
cerr<<"Norm(diff) = "<<Norm(A2-A0);
cerr<<" Norm(L)^2*Norm(D) = "<<normldl<<endl;
abort();
}
#endif
}
static void NonLapLDL_Decompose(SymBandMatrixView<T> A)
{
// For tridiagonal Hermitian band matrices, the sqrt can
// become a significant fraction of the calculation.
// This is unnecessary if we instead decompose A into L D Lt
// where L is unit diagonal.
//
// In this case, the equations become:
//
// A = L0 D L0t
//
// ( A00 Ax0t ) = ( 1 0 ) ( D0 0 ) ( 1 Lx0t )
// ( Ax0 Axx ) = ( Lx0 1 ) ( 0 Dx ) ( 0 1 )
// = ( 1 0 ) ( D0 D0 Lx0t )
// = ( Lx0 1 ) ( 0 Dx )
//
// The equations from this are:
//
// A00 = D0
// Ax0 = Lx0 D0
// Axx = Lx0 D0 Lx0t + Axx'
//
// where Axx' = Dx is the sub-matrix for the next step.
//
TMVAssert(A.uplo() == Lower);
TMVAssert(A.ct() == NonConj);
TMVAssert(A.isherm());
TMVAssert(A.nlo() == 1);
const ptrdiff_t N = A.size();
#ifdef XDEBUG
Matrix<T> A0(A);
//cout<<"LDLDecompose:\n";
//cout<<"A = "<<TMV_Text(A)<<" "<<A<<endl;
#endif
TMV_RealType(T)* Dj = A.realPart().ptr();
T* Lj = A.diag(-1).ptr();
if (A.isdm()) {
for(ptrdiff_t j=0;j<N-1;++j) {
T Ax0 = *Lj;
if (*Dj == TMV_RealType(T)(0)) {
#ifdef NOTHROW
std::cerr<<"Non Posdef HermBandMatrix found\n";
exit(1);
#else
throw NonPosDefHermBandLDL<T>(A);
#endif
}
*Lj /= *Dj;
if (isReal(T())) ++Dj; else Dj+=2;
*Dj -= TMV_REAL(TMV_CONJ(*Lj) * Ax0);
++Lj;
}
} else {
const ptrdiff_t Dstep = A.diag().realPart().step();
const ptrdiff_t Lstep = A.diag().step();
for(ptrdiff_t j=0;j<N-1;++j) {
T Ax0 = *Lj;
if (*Dj == TMV_RealType(T)(0)) {
#ifdef NOTHROW
std::cerr<<"Non Posdef HermBandMatrix found\n";
exit(1);
#else
throw NonPosDefHermBandLDL<T>(A);
#endif
}
*Lj /= *Dj;
Dj += Dstep;
*Dj -= TMV_REAL(TMV_CONJ(*Lj) * Ax0);
Lj += Lstep;
}
}
if (*Dj == TMV_RealType(T)(0)) {
#ifdef NOTHROW
std::cerr<<"Non Posdef HermBandMatrix found\n";
exit(1);
#else
throw NonPosDefHermBandLDL<T>(A);
#endif
}
#ifdef XDEBUG
//cout<<"Done LDLDecompose\n";
BandMatrix<T> L = A.lowerBand();
L.diag().SetAllTo(T(1));
DiagMatrix<T> D = DiagMatrixViewOf(A.diag());
BandMatrix<T> A2 = L * D * L.adjoint();
TMV_RealType(T) normldl = TMV_SQR(Norm(L))*Norm(D);
//cout<<"Done: A = "<<A<<endl;
//cout<<"L = "<<L<<endl;
//cout<<"D = "<<D<<endl;
//cout<<"A2 = "<<A2<<endl;
//cout<<"cf A0 = "<<A0<<endl;
if (!(Norm(A2-A0) < 0.001*normldl)) {
cerr<<"LDL_Decompose: A = "<<TMV_Text(A)<<" "<<A0<<endl;
cerr<<"Done: A = "<<A<<endl;
cerr<<"L = "<<L<<endl;
cerr<<"D = "<<D<<endl;
cerr<<"Lt = "<<L.adjoint()<<endl;
cerr<<"L*D*Lt = "<<A2<<endl;
cerr<<"Norm(diff) = "<<Norm(A2-A0);
cerr<<" Norm(L)^2*Norm(D) = "<<normldl<<endl;
abort();
}
#endif
}
