void UUnb
( AbstractDistMatrix<F>& APre,
AbstractDistMatrix<F>& householderScalarsPre )
{
DEBUG_CSE
DistMatrixReadWriteProxy<F,F,MC,MR> AProx( APre );
DistMatrixWriteProxy<F,F,STAR,STAR>
householderScalarsProx( householderScalarsPre );
auto& A = AProx.Get();
auto& householderScalars = householderScalarsProx.Get();
const Grid& g = A.Grid();
const Int n = A.Height();
const Int householderScalarsHeight = Max(n-1,0);
householderScalars.SetGrid( g );
householderScalars.Resize( householderScalarsHeight, 1 );
DistMatrix<F,MC,STAR> a21_MC(g);
DistMatrix<F,MR,STAR> a21_MR(g);
DistMatrix<F,MC,STAR> x1_MC(g);
DistMatrix<F,MR,STAR> x12Adj_MR(g);
for( Int k=0; k<n-1; ++k )
{
const Range<Int> ind1( k, k+1 ),
ind2( k+1, n );
auto a21 = A( ind2, ind1 );
auto A22 = A( ind2, ind2 );
auto A2 = A( IR(0,n), ind2 );
auto alpha21T = A( IR(k+1,k+2), ind1 );
auto a21B = A( IR(k+2,n), ind1 );
// Find tau and v such that
// / I - tau | 1 | | 1, v^H | \ | alpha21T | = | beta |
// \ | v | / | a21B | | 0 |
const F tau = LeftReflector( alpha21T, a21B );
householderScalars.Set(k,0,tau);
// Temporarily set a21 := | 1 |
// | v |
F beta=0;
if( alpha21T.IsLocal(0,0) )
beta = alpha21T.GetLocal(0,0);
alpha21T.Set(0,0,F(1));
// A2 := A2 Hous(a21,tau)^H
// = A2 (I - conj(tau) a21 a21^H)
// = A2 - conj(tau) (A2 a21) a21^H
// -----------------------------------
// x1 := A2 a21
a21_MR.AlignWith( A2 );
a21_MR = a21;
x1_MC.AlignWith( A2 );
Zeros( x1_MC, n, 1 );
LocalGemv( NORMAL, F(1), A2, a21_MR, F(0), x1_MC );
El::AllReduce( x1_MC, A2.RowComm() );
// A2 := A2 - conj(tau) x1 a21^H
LocalGer( -Conj(tau), x1_MC, a21_MR, A2 );
// A22 := Hous(a21,tau) A22
// = (I - tau a21 a21^H) A22
// = A22 - tau a21 (A22^H a21)^H
// ----------------------------------
// x12^H := (a21^H A22)^H = A22^H a21
a21_MC.AlignWith( A22 );
a21_MC = a21;
x12Adj_MR.AlignWith( A22 );
Zeros( x12Adj_MR, A22.Width(), 1 );
LocalGemv( ADJOINT, F(1), A22, a21_MC, F(0), x12Adj_MR );
El::AllReduce( x12Adj_MR, A22.ColComm() );
// A22 := A22 - tau a21 x12
LocalGer( -tau, a21_MC, x12Adj_MR, A22 );
// Put beta back
if( alpha21T.IsLocal(0,0) )
alpha21T.SetLocal(0,0,beta);
}
}
void LowerBlocked
( AbstractDistMatrix<F>& APre,
AbstractDistMatrix<F>& householderScalarsPre )
{
DEBUG_CSE
DEBUG_ONLY(AssertSameGrids( APre, householderScalarsPre ))
DistMatrixReadWriteProxy<F,F,MC,MR> AProx( APre );
DistMatrixWriteProxy<F,F,STAR,STAR>
householderScalarsProx( householderScalarsPre );
auto& A = AProx.Get();
auto& householderScalars = householderScalarsProx.Get();
const Grid& g = A.Grid();
const Int n = A.Height();
householderScalars.Resize( Max(n-1,0), 1 );
DistMatrix<F,MC,STAR> UB1_MC_STAR(g), V21_MC_STAR(g);
DistMatrix<F,MR,STAR> V01_MR_STAR(g), VB1_MR_STAR(g), UB1_MR_STAR(g);
DistMatrix<F,STAR,STAR> G11_STAR_STAR(g);
const Int bsize = Blocksize();
for( Int k=0; k<n-1; k+=bsize )
{
const Int nb = Min(bsize,n-1-k);
const Range<Int> ind0( 0, k ),
ind1( k, k+nb ),
indB( k, n ), indR( k, n ),
ind2( k+nb, n );
auto ABR = A( indB, indR );
auto A22 = A( ind2, ind2 );
auto householderScalars1 = householderScalars( ind1, ALL );
UB1_MC_STAR.AlignWith( ABR );
UB1_MR_STAR.AlignWith( ABR );
VB1_MR_STAR.AlignWith( ABR );
UB1_MC_STAR.Resize( n-k, nb );
UB1_MR_STAR.Resize( n-k, nb );
VB1_MR_STAR.Resize( n-k, nb );
G11_STAR_STAR.Resize( nb, nb );
hessenberg::LowerPanel
( ABR, householderScalars1, UB1_MC_STAR, UB1_MR_STAR, VB1_MR_STAR,
G11_STAR_STAR );
auto AB0 = A( indB, ind0 );
auto A2R = A( ind2, indR );
auto U21_MC_STAR = UB1_MC_STAR( IR(nb,END), ALL );
// AB0 := AB0 - (UB1 inv(G11)^H UB1^H AB0)
// = AB0 - (UB1 ((AB0^H UB1) inv(G11))^H)
// -------------------------------------------
V01_MR_STAR.AlignWith( AB0 );
Zeros( V01_MR_STAR, k, nb );
LocalGemm( ADJOINT, NORMAL, F(1), AB0, UB1_MC_STAR, F(0), V01_MR_STAR );
El::AllReduce( V01_MR_STAR, AB0.ColComm() );
LocalTrsm
( RIGHT, UPPER, NORMAL, NON_UNIT, F(1), G11_STAR_STAR, V01_MR_STAR );
LocalGemm
( NORMAL, ADJOINT, F(-1), UB1_MC_STAR, V01_MR_STAR, F(1), AB0 );
// A2R := (A2R - U21 inv(G11)^H VB1^H)(I - UB1 inv(G11) UB1^H)
// -----------------------------------------------------------
// A2R := A2R - U21 inv(G11)^H VB1^H
// (note: VB1 is overwritten)
LocalTrsm
( RIGHT, UPPER, NORMAL, NON_UNIT, F(1), G11_STAR_STAR, VB1_MR_STAR );
LocalGemm
( NORMAL, ADJOINT, F(-1), U21_MC_STAR, VB1_MR_STAR, F(1), A2R );
// A2R := A2R - ((A2R UB1) inv(G11)) UB1^H
V21_MC_STAR.AlignWith( A2R );
Zeros( V21_MC_STAR, A2R.Height(), nb );
LocalGemm( NORMAL, NORMAL, F(1), A2R, UB1_MR_STAR, F(0), V21_MC_STAR );
El::AllReduce( V21_MC_STAR, A2R.RowComm() );
LocalTrsm
( RIGHT, UPPER, NORMAL, NON_UNIT, F(1), G11_STAR_STAR, V21_MC_STAR );
LocalGemm
( NORMAL, ADJOINT, F(-1), V21_MC_STAR, UB1_MR_STAR, F(1), A2R );
}
}
