void AugmentedKKT
( const ElementalMatrix<Real>& A,
const ElementalMatrix<Real>& x,
const ElementalMatrix<Real>& z,
ElementalMatrix<Real>& JPre,
bool onlyLower )
{
EL_DEBUG_CSE
const Int m = A.Height();
const Int n = A.Width();
DistMatrixWriteProxy<Real,Real,MC,MR> JProx( JPre );
auto& J = JProx.Get();
Zeros( J, m+n, m+n );
const IR xInd(0,n), yInd(n,n+m);
auto Jxx = J(xInd,xInd); auto Jxy = J(xInd,yInd);
auto Jyx = J(yInd,xInd); auto Jyy = J(yInd,yInd);
DistMatrix<Real,MC,STAR> d( z );
DiagonalSolve( LEFT, NORMAL, x, d );
Diagonal( Jxx, d );
Jyx = A;
if( !onlyLower )
Transpose( A, Jxy );
}
void KKT
( const ElementalMatrix<Real>& A,
const ElementalMatrix<Real>& x,
const ElementalMatrix<Real>& z,
ElementalMatrix<Real>& JPre, bool onlyLower )
{
EL_DEBUG_CSE
const Int m = A.Height();
const Int n = A.Width();
DistMatrixWriteProxy<Real,Real,MC,MR> JProx( JPre );
auto& J = JProx.Get();
Zeros( J, 2*n+m, 2*n+m );
const IR xInd(0,n), yInd(n,n+m), zInd(n+m,2*n+m);
auto Jxx = J(xInd,xInd); auto Jxy = J(xInd,yInd); auto Jxz = J(xInd,zInd);
auto Jyx = J(yInd,xInd); auto Jyy = J(yInd,yInd); auto Jyz = J(yInd,zInd);
auto Jzx = J(zInd,xInd); auto Jzy = J(zInd,yInd); auto Jzz = J(zInd,zInd);
// Jyx := A
// ========
Jyx = A;
// Jzx := -I
// =========
Identity( Jzx, n, n );
Jzx *= -1;
// Jzz := - z <> x
// ===============
DistMatrix<Real,MC,STAR> t(x);
DiagonalSolve( LEFT, NORMAL, z, t );
t *= -1;
Diagonal( Jzz, t );
if( !onlyLower )
{
// Jxy := A^T
// ==========
Transpose( A, Jxy );
// Jxz := -I
// =========
Identity( Jxz, n, n );
Jxz *= -1;
}
}
