void UUnb( UnitOrNonUnit diag, Matrix<F>& A, const Matrix<F>& U )
{
EL_DEBUG_CSE
// Use the Variant 4 algorithm
// (which annoyingly requires conjugations for the Her2)
const Int n = A.Height();
const Int lda = A.LDim();
const Int ldu = U.LDim();
F* ABuffer = A.Buffer();
const F* UBuffer = U.LockedBuffer();
vector<F> a12Conj( n ), u12Conj( n );
for( Int j=0; j<n; ++j )
{
const Int a21Height = n - (j+1);
// Extract and store the diagonal value of U
const F upsilon11 = ( diag==UNIT ? 1 : UBuffer[j+j*ldu] );
// a01 := a01 / upsilon11
F* a01 = &ABuffer[j*lda];
if( diag != UNIT )
for( Int k=0; k<j; ++k )
a01[k] /= upsilon11;
// A02 := A02 - a01 u12
F* A02 = &ABuffer[(j+1)*lda];
const F* u12 = &UBuffer[j+(j+1)*ldu];
blas::Geru( j, a21Height, F(-1), a01, 1, u12, ldu, A02, lda );
// alpha11 := alpha11 / |upsilon11|^2
ABuffer[j+j*lda] /= upsilon11*Conj(upsilon11);
const F alpha11 = ABuffer[j+j*lda];
// a12 := a12 / conj(upsilon11)
F* a12 = &ABuffer[j+(j+1)*lda];
if( diag != UNIT )
for( Int k=0; k<a21Height; ++k )
a12[k*lda] /= Conj(upsilon11);
// a12 := a12 - (alpha11/2)u12
for( Int k=0; k<a21Height; ++k )
a12[k*lda] -= (alpha11/F(2))*u12[k*ldu];
// A22 := A22 - (a12' u12 + u12' a12)
F* A22 = &ABuffer[(j+1)+(j+1)*lda];
for( Int k=0; k<a21Height; ++k )
a12Conj[k] = Conj(a12[k*lda]);
for( Int k=0; k<a21Height; ++k )
u12Conj[k] = Conj(u12[k*ldu]);
blas::Her2
( 'U', a21Height,
F(-1), u12Conj.data(), 1, a12Conj.data(), 1, A22, lda );
// a12 := a12 - (alpha11/2)u12
for( Int k=0; k<a21Height; ++k )
a12[k*lda] -= (alpha11/F(2))*u12[k*ldu];
}
}
inline void
TwoSidedTrsmUUnb( UnitOrNonUnit diag, Matrix<F>& A, const Matrix<F>& U )
{
#ifndef RELEASE
PushCallStack("internal::TwoSidedTrsmUUnb");
#endif
// Use the Variant 4 algorithm
// (which annoyingly requires conjugations for the Her2)
const int n = A.Height();
const int lda = A.LDim();
const int ldu = U.LDim();
F* ABuffer = A.Buffer();
const F* UBuffer = U.LockedBuffer();
std::vector<F> a12Conj( n ), u12Conj( n );
for( int j=0; j<n; ++j )
{
const int a21Height = n - (j+1);
// Extract and store the diagonal value of U
const F upsilon11 = ( diag==UNIT ? 1 : UBuffer[j+j*ldu] );
// a01 := a01 / upsilon11
F* a01 = &ABuffer[j*lda];
if( diag != UNIT )
for( int k=0; k<j; ++k )
a01[k] /= upsilon11;
// A02 := A02 - a01 u12
F* A02 = &ABuffer[(j+1)*lda];
const F* u12 = &UBuffer[j+(j+1)*ldu];
blas::Geru( j, a21Height, F(-1), a01, 1, u12, ldu, A02, lda );
// alpha11 := alpha11 / |upsilon11|^2
ABuffer[j+j*lda] /= upsilon11*Conj(upsilon11);
const F alpha11 = ABuffer[j+j*lda];
// a12 := a12 / conj(upsilon11)
F* a12 = &ABuffer[j+(j+1)*lda];
if( diag != UNIT )
for( int k=0; k<a21Height; ++k )
a12[k*lda] /= Conj(upsilon11);
// a12 := a12 - (alpha11/2)u12
for( int k=0; k<a21Height; ++k )
a12[k*lda] -= (alpha11/2)*u12[k*ldu];
// A22 := A22 - (a12' u12 + u12' a12)
F* A22 = &ABuffer[(j+1)+(j+1)*lda];
for( int k=0; k<a21Height; ++k )
a12Conj[k] = Conj(a12[k*lda]);
for( int k=0; k<a21Height; ++k )
u12Conj[k] = Conj(u12[k*ldu]);
blas::Her2
( 'U', a21Height, F(-1), &u12Conj[0], 1, &a12Conj[0], 1, A22, lda );
// a12 := a12 - (alpha11/2)u12
for( int k=0; k<a21Height; ++k )
a12[k*lda] -= (alpha11/2)*u12[k*ldu];
}
#ifndef RELEASE
PopCallStack();
#endif
}