void LUNMedium ( const AbstractDistMatrix<F>& UPre, AbstractDistMatrix<F>& XPre, bool checkIfSingular ) { DEBUG_CSE const Int m = XPre.Height(); const Int bsize = Blocksize(); const Grid& g = UPre.Grid(); DistMatrixReadProxy<F,F,MC,MR> UProx( UPre ); DistMatrixReadWriteProxy<F,F,MC,MR> XProx( XPre ); auto& U = UProx.GetLocked(); auto& X = XProx.Get(); DistMatrix<F,MC, STAR> U01_MC_STAR(g); DistMatrix<F,STAR,STAR> U11_STAR_STAR(g); DistMatrix<F,MR, STAR> X1Trans_MR_STAR(g); const Int kLast = LastOffset( m, bsize ); Int k=kLast, kOld=m; while( true ) { const bool in2x2 = ( k>0 && U.Get(k,k-1) != F(0) ); if( in2x2 ) --k; const Int nb = kOld-k; const Range<Int> ind0( 0, k ), ind1( k, k+nb ); auto U01 = U( ind0, ind1 ); auto U11 = U( ind1, ind1 ); auto X0 = X( ind0, ALL ); auto X1 = X( ind1, ALL ); U11_STAR_STAR = U11; // U11[* ,* ] <- U11[MC,MR] X1Trans_MR_STAR.AlignWith( X0 ); Transpose( X1, X1Trans_MR_STAR ); // X1^T[MR,* ] := X1^T[MR,* ] U11^-T[* ,* ] // = (U11^-1[* ,* ] X1[* ,MR])^T LocalQuasiTrsm ( RIGHT, UPPER, TRANSPOSE, F(1), U11_STAR_STAR, X1Trans_MR_STAR, checkIfSingular ); Transpose( X1Trans_MR_STAR, X1 ); U01_MC_STAR.AlignWith( X0 ); U01_MC_STAR = U01; // U01[MC,* ] <- U01[MC,MR] // X0[MC,MR] -= U01[MC,* ] X1[* ,MR] LocalGemm ( NORMAL, TRANSPOSE, F(-1), U01_MC_STAR, X1Trans_MR_STAR, F(1), X0 ); if( k == 0 ) break; kOld = k; k -= Min(bsize,k); } }
void LLNMedium ( const AbstractDistMatrix<F>& LPre, AbstractDistMatrix<F>& XPre, bool checkIfSingular ) { DEBUG_CSE const Int m = XPre.Height(); const Int bsize = Blocksize(); const Grid& g = LPre.Grid(); DistMatrixReadProxy<F,F,MC,MR> LProx( LPre ); DistMatrixReadWriteProxy<F,F,MC,MR> XProx( XPre ); auto& L = LProx.GetLocked(); auto& X = XProx.Get(); DistMatrix<F,STAR,STAR> L11_STAR_STAR(g); DistMatrix<F,MC, STAR> L21_MC_STAR(g); DistMatrix<F,MR, STAR> X1Trans_MR_STAR(g); for( Int k=0; k<m; k+=bsize ) { const Int nbProp = Min(bsize,m-k); const bool in2x2 = ( k+nbProp<m && L.Get(k+nbProp-1,k+nbProp) != F(0) ); const Int nb = ( in2x2 ? nbProp+1 : nbProp ); const Range<Int> ind1( k, k+nb ), ind2( k+nb, m ); auto L11 = L( ind1, ind1 ); auto L21 = L( ind2, ind1 ); auto X1 = X( ind1, ALL ); auto X2 = X( ind2, ALL ); L11_STAR_STAR = L11; // L11[* ,* ] <- L11[MC,MR] X1Trans_MR_STAR.AlignWith( X2 ); Transpose( X1, X1Trans_MR_STAR ); // X1^T[MR,* ] := X1^T[MR,* ] L11^-T[* ,* ] // = (L11^-1[* ,* ] X1[* ,MR])^T LocalQuasiTrsm ( RIGHT, LOWER, TRANSPOSE, F(1), L11_STAR_STAR, X1Trans_MR_STAR, checkIfSingular ); Transpose( X1Trans_MR_STAR, X1 ); L21_MC_STAR.AlignWith( X2 ); L21_MC_STAR = L21; // L21[MC,* ] <- L21[MC,MR] // X2[MC,MR] -= L21[MC,* ] X1[* ,MR] LocalGemm ( NORMAL, TRANSPOSE, F(-1), L21_MC_STAR, X1Trans_MR_STAR, F(1), X2 ); } }
void LLNLarge ( const AbstractDistMatrix<F>& LPre, AbstractDistMatrix<F>& XPre, bool checkIfSingular ) { DEBUG_CSE const Int m = XPre.Height(); const Int bsize = Blocksize(); const Grid& g = LPre.Grid(); DistMatrixReadProxy<F,F,MC,MR> LProx( LPre ); DistMatrixReadWriteProxy<F,F,MC,MR> XProx( XPre ); auto& L = LProx.GetLocked(); auto& X = XProx.Get(); DistMatrix<F,STAR,STAR> L11_STAR_STAR(g); DistMatrix<F,MC, STAR> L21_MC_STAR(g); DistMatrix<F,STAR,MR > X1_STAR_MR(g); DistMatrix<F,STAR,VR > X1_STAR_VR(g); for( Int k=0; k<m; k+=bsize ) { const Int nbProp = Min(bsize,m-k); const bool in2x2 = ( k+nbProp<m && L.Get(k+nbProp-1,k+nbProp) != F(0) ); const Int nb = ( in2x2 ? nbProp+1 : nbProp ); const Range<Int> ind1( k, k+nb ), ind2( k+nb, m ); auto L11 = L( ind1, ind1 ); auto L21 = L( ind2, ind1 ); auto X1 = X( ind1, ALL ); auto X2 = X( ind2, ALL ); // X1[* ,VR] := L11^-1[* ,* ] X1[* ,VR] L11_STAR_STAR = L11; X1_STAR_VR = X1; LocalQuasiTrsm ( LEFT, LOWER, NORMAL, F(1), L11_STAR_STAR, X1_STAR_VR, checkIfSingular ); X1_STAR_MR.AlignWith( X2 ); X1_STAR_MR = X1_STAR_VR; // X1[* ,MR] <- X1[* ,VR] X1 = X1_STAR_MR; // X1[MC,MR] <- X1[* ,MR] L21_MC_STAR.AlignWith( X2 ); L21_MC_STAR = L21; // L21[MC,* ] <- L21[MC,MR] // X2[MC,MR] -= L21[MC,* ] X1[* ,MR] LocalGemm( NORMAL, NORMAL, F(-1), L21_MC_STAR, X1_STAR_MR, F(1), X2 ); } }
void LUNLarge ( const ElementalMatrix<F>& UPre, ElementalMatrix<F>& XPre, bool checkIfSingular ) { DEBUG_CSE const Int m = XPre.Height(); const Int bsize = Blocksize(); const Grid& g = UPre.Grid(); DistMatrixReadProxy<F,F,MC,MR> UProx( UPre ); DistMatrixReadWriteProxy<F,F,MC,MR> XProx( XPre ); auto& U = UProx.GetLocked(); auto& X = XProx.Get(); DistMatrix<F,MC, STAR> U01_MC_STAR(g); DistMatrix<F,STAR,STAR> U11_STAR_STAR(g); DistMatrix<F,STAR,MR > X1_STAR_MR(g); DistMatrix<F,STAR,VR > X1_STAR_VR(g); const Int kLast = LastOffset( m, bsize ); Int k=kLast, kOld=m; while( true ) { const bool in2x2 = ( k>0 && U.Get(k,k-1) != F(0) ); if( in2x2 ) --k; const Int nb = kOld-k; const Range<Int> ind0( 0, k ), ind1( k, k+nb ); auto U01 = U( ind0, ind1 ); auto U11 = U( ind1, ind1 ); auto X0 = X( ind0, ALL ); auto X1 = X( ind1, ALL ); U11_STAR_STAR = U11; // U11[* ,* ] <- U11[MC,MR] X1_STAR_VR = X1; // X1[* ,VR] <- X1[MC,MR] // X1[* ,VR] := U11^-1[* ,* ] X1[* ,VR] LocalQuasiTrsm ( LEFT, UPPER, NORMAL, F(1), U11_STAR_STAR, X1_STAR_VR, checkIfSingular ); X1_STAR_MR.AlignWith( X0 ); X1_STAR_MR = X1_STAR_VR; // X1[* ,MR] <- X1[* ,VR] X1 = X1_STAR_MR; // X1[MC,MR] <- X1[* ,MR] U01_MC_STAR.AlignWith( X0 ); U01_MC_STAR = U01; // U01[MC,* ] <- U01[MC,MR] // X0[MC,MR] -= U01[MC,* ] X1[* ,MR] LocalGemm( NORMAL, NORMAL, F(-1), U01_MC_STAR, X1_STAR_MR, F(1), X0 ); if( k == 0 ) break; kOld = k; k -= Min(bsize,k); } }