FLA_Error FLA_Scalr_l_blk_var4( FLA_Obj alpha, FLA_Obj A, fla_scalr_t* cntl ) { FLA_Obj ATL, ATR, A00, A01, A02, ABL, ABR, A10, A11, A12, A20, A21, A22; dim_t b; FLA_Part_2x2( A, &ATL, &ATR, &ABL, &ABR, 0, 0, FLA_BR ); while ( FLA_Obj_min_dim( ATL ) > 0 ){ b = FLA_Determine_blocksize( ATL, FLA_TL, FLA_Cntl_blocksize( cntl ) ); FLA_Repart_2x2_to_3x3( ATL, /**/ ATR, &A00, &A01, /**/ &A02, &A10, &A11, /**/ &A12, /* ************* */ /* ******************** */ ABL, /**/ ABR, &A20, &A21, /**/ &A22, b, b, FLA_TL ); /*------------------------------------------------------------*/ // A11 = alpha * tril( A11 ); FLA_Scalr_internal( FLA_LOWER_TRIANGULAR, alpha, A11, FLA_Cntl_sub_scalr( cntl ) ); // A21 = alpha * A21; FLA_Scal_internal( alpha, A21, FLA_Cntl_sub_scal( cntl ) ); /*------------------------------------------------------------*/ FLA_Cont_with_3x3_to_2x2( &ATL, /**/ &ATR, A00, /**/ A01, A02, /* ************** */ /* ****************** */ A10, /**/ A11, A12, &ABL, /**/ &ABR, A20, /**/ A21, A22, FLA_BR ); } return FLA_SUCCESS; }
FLA_Error FLA_Syrk_ut_blk_var5( FLA_Obj alpha, FLA_Obj A, FLA_Obj beta, FLA_Obj C, fla_syrk_t* cntl ) { FLA_Obj AT, A0, AB, A1, A2; dim_t b; FLA_Scalr_internal( FLA_UPPER_TRIANGULAR, beta, C, FLA_Cntl_sub_scalr( cntl ) ); FLA_Part_2x1( A, &AT, &AB, 0, FLA_TOP ); while ( FLA_Obj_length( AT ) < FLA_Obj_length( A ) ){ b = FLA_Determine_blocksize( AB, FLA_BOTTOM, FLA_Cntl_blocksize( cntl ) ); FLA_Repart_2x1_to_3x1( AT, &A0, /* ** */ /* ** */ &A1, AB, &A2, b, FLA_BOTTOM ); /*------------------------------------------------------------*/ /* C = C + A1' * A1 */ FLA_Syrk_internal( FLA_UPPER_TRIANGULAR, FLA_TRANSPOSE, alpha, A1, FLA_ONE, C, FLA_Cntl_sub_syrk( cntl ) ); /*------------------------------------------------------------*/ FLA_Cont_with_3x1_to_2x1( &AT, A0, A1, /* ** */ /* ** */ &AB, A2, FLA_TOP ); } return FLA_SUCCESS; }
FLA_Error FLA_Hemm_lu_blk_var9( FLA_Obj alpha, FLA_Obj A, FLA_Obj B, FLA_Obj beta, FLA_Obj C, fla_hemm_t* cntl ) { FLA_Obj BL, BR, B0, B1, B2; FLA_Obj CL, CR, C0, C1, C2; dim_t b; FLA_Part_1x2( B, &BL, &BR, 0, FLA_LEFT ); FLA_Part_1x2( C, &CL, &CR, 0, FLA_LEFT ); while ( FLA_Obj_width( BL ) < FLA_Obj_width( B ) ){ b = FLA_Determine_blocksize( BR, FLA_RIGHT, FLA_Cntl_blocksize( cntl ) ); FLA_Repart_1x2_to_1x3( BL, /**/ BR, &B0, /**/ &B1, &B2, b, FLA_RIGHT ); FLA_Repart_1x2_to_1x3( CL, /**/ CR, &C0, /**/ &C1, &C2, b, FLA_RIGHT ); /*------------------------------------------------------------*/ /* C1 = C1 + A * B1 */ FLA_Hemm_internal( FLA_LEFT, FLA_UPPER_TRIANGULAR, alpha, A, B1, beta, C1, FLA_Cntl_sub_hemm( cntl ) ); /*------------------------------------------------------------*/ FLA_Cont_with_1x3_to_1x2( &BL, /**/ &BR, B0, B1, /**/ B2, FLA_LEFT ); FLA_Cont_with_1x3_to_1x2( &CL, /**/ &CR, C0, C1, /**/ C2, FLA_LEFT ); } return FLA_SUCCESS; }
FLA_Error FLA_Gemm_tc_blk_var4( FLA_Obj alpha, FLA_Obj A, FLA_Obj B, FLA_Obj beta, FLA_Obj C, fla_gemm_t* cntl ) { FLA_Obj BL, BR, B0, B1, B2; FLA_Obj CL, CR, C0, C1, C2; dim_t b; FLA_Part_1x2( B, &BL, &BR, 0, FLA_RIGHT ); FLA_Part_1x2( C, &CL, &CR, 0, FLA_RIGHT ); while ( FLA_Obj_width( BR ) < FLA_Obj_width( B ) ){ b = FLA_Determine_blocksize( BL, FLA_LEFT, FLA_Cntl_blocksize( cntl ) ); FLA_Repart_1x2_to_1x3( BL, /**/ BR, &B0, &B1, /**/ &B2, b, FLA_LEFT ); FLA_Repart_1x2_to_1x3( CL, /**/ CR, &C0, &C1, /**/ &C2, b, FLA_LEFT ); /*------------------------------------------------------------*/ /* C1 = alpha * A' * B1 + C1; */ FLA_Gemm_internal( FLA_TRANSPOSE, FLA_CONJ_NO_TRANSPOSE, alpha, A, B1, beta, C1, FLA_Cntl_sub_gemm( cntl ) ); /*------------------------------------------------------------*/ FLA_Cont_with_1x3_to_1x2( &BL, /**/ &BR, B0, /**/ B1, B2, FLA_RIGHT ); FLA_Cont_with_1x3_to_1x2( &CL, /**/ &CR, C0, /**/ C1, C2, FLA_RIGHT ); } return FLA_SUCCESS; }
FLA_Error FLA_Apply_Q_UT_lhfr_blk_var2( FLA_Obj A, FLA_Obj T, FLA_Obj W, FLA_Obj B, fla_apqut_t* cntl ) { FLA_Obj BL, BR, B0, B1, B2; FLA_Obj WL, WR, W0, W1, W2; dim_t b; FLA_Part_1x2( B, &BL, &BR, 0, FLA_LEFT ); FLA_Part_1x2( W, &WL, &WR, 0, FLA_LEFT ); while ( FLA_Obj_width( BL ) < FLA_Obj_width( B ) ){ b = FLA_Determine_blocksize( BR, FLA_RIGHT, FLA_Cntl_blocksize( cntl ) ); FLA_Repart_1x2_to_1x3( BL, /**/ BR, &B0, /**/ &B1, &B2, b, FLA_RIGHT ); FLA_Repart_1x2_to_1x3( WL, /**/ WR, &W0, /**/ &W1, &W2, b, FLA_RIGHT ); /*------------------------------------------------------------*/ // B1 = Q' * B1; FLA_Apply_Q_UT_internal( FLA_LEFT, FLA_CONJ_TRANSPOSE, FLA_FORWARD, FLA_ROWWISE, A, T, W1, B1, FLA_Cntl_sub_apqut( cntl ) ); /*------------------------------------------------------------*/ FLA_Cont_with_1x3_to_1x2( &BL, /**/ &BR, B0, B1, /**/ B2, FLA_LEFT ); FLA_Cont_with_1x3_to_1x2( &WL, /**/ &WR, W0, W1, /**/ W2, FLA_LEFT ); } return FLA_SUCCESS; }
FLA_Error FLA_Transpose_blk_var2( FLA_Obj A, fla_tpose_t* cntl ) { FLA_Obj ATL, ATR, A00, A01, A02, ABL, ABR, A10, A11, A12, A20, A21, A22; dim_t b; FLA_Part_2x2( A, &ATL, &ATR, &ABL, &ABR, 0, 0, FLA_TL ); while ( FLA_Obj_length( ATL ) < FLA_Obj_length( A ) ){ b = FLA_Determine_blocksize( ABR, FLA_BR, FLA_Cntl_blocksize( cntl ) ); FLA_Repart_2x2_to_3x3( ATL, /**/ ATR, &A00, /**/ &A01, &A02, /* ************* */ /* ******************** */ &A10, /**/ &A11, &A12, ABL, /**/ ABR, &A20, /**/ &A21, &A22, b, b, FLA_BR ); /*------------------------------------------------------------*/ FLA_Transpose_unb_var2( A11 ); FLA_Swap_t_blk_var2( A21, A12, FLA_Cntl_sub_swap( cntl ) ); /*------------------------------------------------------------*/ FLA_Cont_with_3x3_to_2x2( &ATL, /**/ &ATR, A00, A01, /**/ A02, A10, A11, /**/ A12, /* ************** */ /* ****************** */ &ABL, /**/ &ABR, A20, A21, /**/ A22, FLA_TL ); } return FLA_SUCCESS; }
FLA_Error FLA_Copyt_c_blk_var3( FLA_Obj A, FLA_Obj B, fla_copyt_t* cntl ) { FLA_Obj AL, AR, A0, A1, A2; FLA_Obj BL, BR, B0, B1, B2; dim_t b; FLA_Part_1x2( A, &AL, &AR, 0, FLA_LEFT ); FLA_Part_1x2( B, &BL, &BR, 0, FLA_LEFT ); while ( FLA_Obj_width( AL ) < FLA_Obj_width( A ) ){ b = FLA_Determine_blocksize( AR, FLA_RIGHT, FLA_Cntl_blocksize( cntl ) ); FLA_Repart_1x2_to_1x3( AL, /**/ AR, &A0, /**/ &A1, &A2, b, FLA_RIGHT ); FLA_Repart_1x2_to_1x3( BL, /**/ BR, &B0, /**/ &B1, &B2, b, FLA_RIGHT ); /*------------------------------------------------------------*/ FLA_Copyt_internal( FLA_CONJ_NO_TRANSPOSE, A1, B1, FLA_Cntl_sub_copyt( cntl ) ); /*------------------------------------------------------------*/ FLA_Cont_with_1x3_to_1x2( &AL, /**/ &AR, A0, A1, /**/ A2, FLA_LEFT ); FLA_Cont_with_1x3_to_1x2( &BL, /**/ &BR, B0, B1, /**/ B2, FLA_LEFT ); } return FLA_SUCCESS; }
FLA_Error FLA_Trsm_ruc_blk_var3( FLA_Diag diagA, FLA_Obj alpha, FLA_Obj A, FLA_Obj B, fla_trsm_t* cntl ) { FLA_Obj BT, B0, BB, B1, B2; dim_t b; FLA_Part_2x1( B, &BT, &BB, 0, FLA_TOP ); while ( FLA_Obj_length( BT ) < FLA_Obj_length( B ) ) { b = FLA_Determine_blocksize( BB, FLA_BOTTOM, FLA_Cntl_blocksize( cntl ) ); FLA_Repart_2x1_to_3x1( BT, &B0, /* ** */ /* ** */ &B1, BB, &B2, b, FLA_BOTTOM ); /*------------------------------------------------------------*/ /* B1 = B1 * triu( A ); */ FLA_Trsm_internal( FLA_RIGHT, FLA_UPPER_TRIANGULAR, FLA_CONJ_NO_TRANSPOSE, diagA, alpha, A, B1, FLA_Cntl_sub_trsm( cntl ) ); /*------------------------------------------------------------*/ FLA_Cont_with_3x1_to_2x1( &BT, B0, B1, /* ** */ /* ** */ &BB, B2, FLA_TOP ); } return FLA_SUCCESS; }
FLA_Error FLA_Apply_CAQ2_UT_lhfc_blk_var2( FLA_Obj D, FLA_Obj T, FLA_Obj W1, FLA_Obj C, FLA_Obj E, fla_apcaq2ut_t* cntl ) { FLA_Obj DT, D0, DB, D1, D2; FLA_Obj TT, T0, TB, T1, T2; FLA_Obj ET, E0, EB, E1, E2; dim_t b; FLA_Part_2x1( D, &DT, &DB, 0, FLA_TOP ); FLA_Part_2x1( T, &TT, &TB, 0, FLA_TOP ); FLA_Part_2x1( E, &ET, &EB, 0, FLA_TOP ); while ( FLA_Obj_length( DT ) < FLA_Obj_length( D ) ){ b = FLA_Determine_blocksize( DB, FLA_BOTTOM, FLA_Cntl_blocksize( cntl ) ); FLA_Repart_2x1_to_3x1( DT, &D0, /* ** */ /* ** */ &D1, DB, &D2, b, FLA_BOTTOM ); FLA_Repart_2x1_to_3x1( TT, &T0, /* ** */ /* ** */ &T1, TB, &T2, b, FLA_BOTTOM ); FLA_Repart_2x1_to_3x1( ET, &E0, /* ** */ /* ** */ &E1, EB, &E2, b, FLA_BOTTOM ); /*------------------------------------------------------------*/ // / C \ = Q' / C \ // \ E1 / \ E1 / // // where Q is formed from D1 and T1. FLA_Apply_CAQ2_UT_internal( FLA_LEFT, FLA_CONJ_TRANSPOSE, FLA_FORWARD, FLA_COLUMNWISE, D1, T1, W1, C, E1, FLA_Cntl_sub_apcaq2ut( cntl ) ); /*------------------------------------------------------------*/ FLA_Cont_with_3x1_to_2x1( &DT, D0, D1, /* ** */ /* ** */ &DB, D2, FLA_TOP ); FLA_Cont_with_3x1_to_2x1( &TT, T0, T1, /* ** */ /* ** */ &TB, T2, FLA_TOP ); FLA_Cont_with_3x1_to_2x1( &ET, E0, E1, /* ** */ /* ** */ &EB, E2, FLA_TOP ); } return FLA_SUCCESS; }
FLA_Error FLA_Her2k_uh_blk_var7( FLA_Obj alpha, FLA_Obj A, FLA_Obj B, FLA_Obj beta, FLA_Obj C, fla_her2k_t* cntl ) { FLA_Obj AL, AR, A0, A1, A2; FLA_Obj BL, BR, B0, B1, B2; FLA_Obj CTL, CTR, C00, C01, C02, CBL, CBR, C10, C11, C12, C20, C21, C22; dim_t b; FLA_Scalr_internal( FLA_UPPER_TRIANGULAR, beta, C, FLA_Cntl_sub_scalr( cntl ) ); FLA_Part_1x2( A, &AL, &AR, 0, FLA_RIGHT ); FLA_Part_1x2( B, &BL, &BR, 0, FLA_RIGHT ); FLA_Part_2x2( C, &CTL, &CTR, &CBL, &CBR, 0, 0, FLA_BR ); while ( FLA_Obj_width( AR ) < FLA_Obj_width( A ) ){ b = FLA_Determine_blocksize( AL, FLA_LEFT, FLA_Cntl_blocksize( cntl ) ); FLA_Repart_1x2_to_1x3( AL, /**/ AR, &A0, &A1, /**/ &A2, b, FLA_LEFT ); FLA_Repart_1x2_to_1x3( BL, /**/ BR, &B0, &B1, /**/ &B2, b, FLA_LEFT ); FLA_Repart_2x2_to_3x3( CTL, /**/ CTR, &C00, &C01, /**/ &C02, &C10, &C11, /**/ &C12, /* ************* */ /* ******************** */ CBL, /**/ CBR, &C20, &C21, /**/ &C22, b, b, FLA_TL ); /*------------------------------------------------------------*/ /* C01 = C01 + B0' * A1 */ FLA_Gemm_internal( FLA_CONJ_TRANSPOSE, FLA_NO_TRANSPOSE, alpha, B0, A1, FLA_ONE, C01, FLA_Cntl_sub_gemm1( cntl ) ); /* C12 = C12 + A1' * B2 */ FLA_Gemm_internal( FLA_CONJ_TRANSPOSE, FLA_NO_TRANSPOSE, alpha, A1, B2, FLA_ONE, C12, FLA_Cntl_sub_gemm2( cntl ) ); /* C11 = C11 + A1' * B1 + B1' * A1 */ FLA_Her2k_internal( FLA_UPPER_TRIANGULAR, FLA_CONJ_TRANSPOSE, alpha, A1, B1, FLA_ONE, C11, FLA_Cntl_sub_her2k( cntl ) ); /*------------------------------------------------------------*/ FLA_Cont_with_1x3_to_1x2( &AL, /**/ &AR, A0, /**/ A1, A2, FLA_RIGHT ); FLA_Cont_with_1x3_to_1x2( &BL, /**/ &BR, B0, /**/ B1, B2, FLA_RIGHT ); FLA_Cont_with_3x3_to_2x2( &CTL, /**/ &CTR, C00, /**/ C01, C02, /* ************** */ /* ****************** */ C10, /**/ C11, C12, &CBL, /**/ &CBR, C20, /**/ C21, C22, FLA_BR ); } return FLA_SUCCESS; }
FLA_Error FLA_Eig_gest_nl_blk_var1( FLA_Obj A, FLA_Obj Y, FLA_Obj B, fla_eig_gest_t* cntl ) { FLA_Obj ATL, ATR, A00, A01, A02, ABL, ABR, A10, A11, A12, A20, A21, A22; FLA_Obj BTL, BTR, B00, B01, B02, BBL, BBR, B10, B11, B12, B20, B21, B22; FLA_Obj YT, Y01, YB, Y11, Y21; FLA_Obj Y21_l, Y21_r; dim_t b; FLA_Part_2x2( A, &ATL, &ATR, &ABL, &ABR, 0, 0, FLA_TL ); FLA_Part_2x2( B, &BTL, &BTR, &BBL, &BBR, 0, 0, FLA_TL ); FLA_Part_2x1( Y, &YT, &YB, 0, FLA_TOP ); while ( FLA_Obj_length( ATL ) < FLA_Obj_length( A ) ){ b = FLA_Determine_blocksize( ABR, FLA_BR, FLA_Cntl_blocksize( cntl ) ); FLA_Repart_2x2_to_3x3( ATL, /**/ ATR, &A00, /**/ &A01, &A02, /* ************* */ /* ******************** */ &A10, /**/ &A11, &A12, ABL, /**/ ABR, &A20, /**/ &A21, &A22, b, b, FLA_BR ); FLA_Repart_2x2_to_3x3( BTL, /**/ BTR, &B00, /**/ &B01, &B02, /* ************* */ /* ******************** */ &B10, /**/ &B11, &B12, BBL, /**/ BBR, &B20, /**/ &B21, &B22, b, b, FLA_BR ); FLA_Repart_2x1_to_3x1( YT, &Y01, /* ** */ /* *** */ &Y11, YB, &Y21, b, FLA_BOTTOM ); /*------------------------------------------------------------*/ FLA_Part_1x2( Y21, &Y21_l, &Y21_r, b, FLA_LEFT ); // Y21 = A22 * B21; FLA_Hemm_internal( FLA_LEFT, FLA_LOWER_TRIANGULAR, FLA_ONE, A22, B21, FLA_ZERO, Y21_l, FLA_Cntl_sub_hemm( cntl ) ); // A21 = A21 * tril( B11 ); FLA_Trmm_internal( FLA_RIGHT, FLA_LOWER_TRIANGULAR, FLA_NO_TRANSPOSE, FLA_NONUNIT_DIAG, FLA_ONE, B11, A21, FLA_Cntl_sub_trmm1( cntl ) ); // A21 = A21 + 1/2 * Y21; FLA_Axpy_internal( FLA_ONE_HALF, Y21_l, A21, FLA_Cntl_sub_axpy1( cntl ) ); // A11 = tril( B11 )' * A11 * tril( B11 ); FLA_Eig_gest_internal( FLA_NO_INVERSE, FLA_LOWER_TRIANGULAR, A11, Y11, B11, FLA_Cntl_sub_eig_gest( cntl ) ); // A11 = A11 + A21' * B21 + B21' * A21; FLA_Her2k_internal( FLA_LOWER_TRIANGULAR, FLA_CONJ_TRANSPOSE, FLA_ONE, A21, B21, FLA_ONE, A11, FLA_Cntl_sub_her2k( cntl ) ); // A21 = A21 + 1/2 * Y21; FLA_Axpy_internal( FLA_ONE_HALF, Y21_l, A21, FLA_Cntl_sub_axpy2( cntl ) ); // A21 = tril( B22 )' * A21; FLA_Trmm_internal( FLA_LEFT, FLA_LOWER_TRIANGULAR, FLA_CONJ_TRANSPOSE, FLA_NONUNIT_DIAG, FLA_ONE, B22, A21, FLA_Cntl_sub_trmm2( cntl ) ); /*------------------------------------------------------------*/ FLA_Cont_with_3x3_to_2x2( &ATL, /**/ &ATR, A00, A01, /**/ A02, A10, A11, /**/ A12, /* ************** */ /* ****************** */ &ABL, /**/ &ABR, A20, A21, /**/ A22, FLA_TL ); FLA_Cont_with_3x3_to_2x2( &BTL, /**/ &BTR, B00, B01, /**/ B02, B10, B11, /**/ B12, /* ************** */ /* ****************** */ &BBL, /**/ &BBR, B20, B21, /**/ B22, FLA_TL ); FLA_Cont_with_3x1_to_2x1( &YT, Y01, Y11, /* ** */ /* *** */ &YB, Y21, FLA_TOP ); } return FLA_SUCCESS; }
FLA_Error FLA_Trsv_lc_blk_var1( FLA_Diag diagA, FLA_Obj A, FLA_Obj x, fla_trsv_t* cntl ) { FLA_Obj ATL, ATR, A00, A01, A02, ABL, ABR, A10, A11, A12, A20, A21, A22; FLA_Obj xT, x0, xB, x1, x2; dim_t b; FLA_Part_2x2( A, &ATL, &ATR, &ABL, &ABR, 0, 0, FLA_BR ); FLA_Part_2x1( x, &xT, &xB, 0, FLA_BOTTOM ); while ( FLA_Obj_length( ABR ) < FLA_Obj_length( A ) ){ b = FLA_Determine_blocksize( ATL, FLA_TL, FLA_Cntl_blocksize( cntl ) ); FLA_Repart_2x2_to_3x3( ATL, /**/ ATR, &A00, &A01, /**/ &A02, &A10, &A11, /**/ &A12, /* ************* */ /* ******************** */ ABL, /**/ ABR, &A20, &A21, /**/ &A22, b, b, FLA_TL ); FLA_Repart_2x1_to_3x1( xT, &x0, &x1, /* ** */ /* ** */ xB, &x2, b, FLA_TOP ); /*------------------------------------------------------------*/ /* x1 = x1 - A21' * x2; */ FLA_Gemv_internal( FLA_CONJ_TRANSPOSE, FLA_MINUS_ONE, A21, x2, FLA_ONE, x1, FLA_Cntl_sub_gemv( cntl ) ); /* x1 = tril( A11' ) \ x1; */ FLA_Trsv_internal( FLA_LOWER_TRIANGULAR, FLA_CONJ_TRANSPOSE, diagA, A11, x1, FLA_Cntl_sub_trsv( cntl ) ); /*------------------------------------------------------------*/ FLA_Cont_with_3x3_to_2x2( &ATL, /**/ &ATR, A00, /**/ A01, A02, /* ************** */ /* ****************** */ A10, /**/ A11, A12, &ABL, /**/ &ABR, A20, /**/ A21, A22, FLA_BR ); FLA_Cont_with_3x1_to_2x1( &xT, x0, /* ** */ /* ** */ x1, &xB, x2, FLA_BOTTOM ); } return FLA_SUCCESS; }
FLA_Error FLA_Hemm_lu_blk_var3( FLA_Obj alpha, FLA_Obj A, FLA_Obj B, FLA_Obj beta, FLA_Obj C, fla_hemm_t* cntl ) { FLA_Obj ATL, ATR, A00, A01, A02, ABL, ABR, A10, A11, A12, A20, A21, A22; FLA_Obj BT, B0, BB, B1, B2; FLA_Obj CT, C0, CB, C1, C2; dim_t b; FLA_Scal_internal( beta, C, FLA_Cntl_sub_scal( cntl ) ); FLA_Part_2x2( A, &ATL, &ATR, &ABL, &ABR, 0, 0, FLA_TL ); FLA_Part_2x1( B, &BT, &BB, 0, FLA_TOP ); FLA_Part_2x1( C, &CT, &CB, 0, FLA_TOP ); while ( FLA_Obj_length( ATL ) < FLA_Obj_length( A ) ){ b = FLA_Determine_blocksize( ABR, FLA_BR, FLA_Cntl_blocksize( cntl ) ); FLA_Repart_2x2_to_3x3( ATL, /**/ ATR, &A00, /**/ &A01, &A02, /* ************* */ /* ******************** */ &A10, /**/ &A11, &A12, ABL, /**/ ABR, &A20, /**/ &A21, &A22, b, b, FLA_BR ); FLA_Repart_2x1_to_3x1( BT, &B0, /* ** */ /* ** */ &B1, BB, &B2, b, FLA_BOTTOM ); FLA_Repart_2x1_to_3x1( CT, &C0, /* ** */ /* ** */ &C1, CB, &C2, b, FLA_BOTTOM ); /*------------------------------------------------------------*/ /* C1 = C1 + A11 * B1 */ FLA_Hemm_internal( FLA_LEFT, FLA_UPPER_TRIANGULAR, alpha, A11, B1, FLA_ONE, C1, FLA_Cntl_sub_hemm( cntl ) ); /* C1 = C1 + A12 * B2 */ FLA_Gemm_internal( FLA_NO_TRANSPOSE, FLA_NO_TRANSPOSE, alpha, A12, B2, FLA_ONE, C1, FLA_Cntl_sub_gemm1( cntl ) ); /* C2 = C2 + A12' * B1 */ FLA_Gemm_internal( FLA_CONJ_TRANSPOSE, FLA_NO_TRANSPOSE, alpha, A12, B1, FLA_ONE, C2, FLA_Cntl_sub_gemm2( cntl ) ); /*------------------------------------------------------------*/ FLA_Cont_with_3x3_to_2x2( &ATL, /**/ &ATR, A00, A01, /**/ A02, A10, A11, /**/ A12, /* ************** */ /* ****************** */ &ABL, /**/ &ABR, A20, A21, /**/ A22, FLA_TL ); FLA_Cont_with_3x1_to_2x1( &BT, B0, B1, /* ** */ /* ** */ &BB, B2, FLA_TOP ); FLA_Cont_with_3x1_to_2x1( &CT, C0, C1, /* ** */ /* ** */ &CB, C2, FLA_TOP ); } return FLA_SUCCESS; }
FLA_Error FLA_Trmm_llt_blk_var1( FLA_Diag diagA, FLA_Obj alpha, FLA_Obj A, FLA_Obj B, fla_trmm_t* cntl ) { FLA_Obj ATL, ATR, A00, A01, A02, ABL, ABR, A10, A11, A12, A20, A21, A22; FLA_Obj BT, B0, BB, B1, B2; dim_t b; FLA_Part_2x2( A, &ATL, &ATR, &ABL, &ABR, 0, 0, FLA_TL ); FLA_Part_2x1( B, &BT, &BB, 0, FLA_TOP ); while ( FLA_Obj_length( ATL ) < FLA_Obj_length( A ) ){ b = FLA_Determine_blocksize( ABR, FLA_BR, FLA_Cntl_blocksize( cntl ) ); FLA_Repart_2x2_to_3x3( ATL, /**/ ATR, &A00, /**/ &A01, &A02, /* ************* */ /* ******************** */ &A10, /**/ &A11, &A12, ABL, /**/ ABR, &A20, /**/ &A21, &A22, b, b, FLA_BR ); FLA_Repart_2x1_to_3x1( BT, &B0, /* ** */ /* ** */ &B1, BB, &B2, b, FLA_BOTTOM ); /*------------------------------------------------------------*/ /* B1 = tril( A11 )' * B1; */ FLA_Trmm_internal( FLA_LEFT, FLA_LOWER_TRIANGULAR, FLA_TRANSPOSE, diagA, alpha, A11, B1, FLA_Cntl_sub_trmm( cntl ) ); /* B1 = B1 + A21' * B2; */ FLA_Gemm_internal( FLA_TRANSPOSE, FLA_NO_TRANSPOSE, alpha, A21, B2, FLA_ONE, B1, FLA_Cntl_sub_gemm( cntl ) ); /*------------------------------------------------------------*/ FLA_Cont_with_3x3_to_2x2( &ATL, /**/ &ATR, A00, A01, /**/ A02, A10, A11, /**/ A12, /* ************** */ /* ****************** */ &ABL, /**/ &ABR, A20, A21, /**/ A22, FLA_TL ); FLA_Cont_with_3x1_to_2x1( &BT, B0, B1, /* ** */ /* ** */ &BB, B2, FLA_TOP ); } return FLA_SUCCESS; }
FLA_Error FLA_Gemm_nn_omp_var5( FLA_Obj alpha, FLA_Obj A, FLA_Obj B, FLA_Obj C, fla_gemm_t* cntl ) { FLA_Obj AL, AR, A0, A1, A2; FLA_Obj BT, B0, BB, B1, B2; FLA_Obj C_local; int b; FLA_Part_1x2( A, &AL, &AR, 0, FLA_LEFT ); FLA_Part_2x1( B, &BT, &BB, 0, FLA_TOP ); #pragma intel omp parallel taskq { while ( FLA_Obj_width( AL ) < FLA_Obj_width( A ) ){ b = FLA_Determine_blocksize( A, AL, FLA_LEFT, FLA_Cntl_blocksize( cntl ) ); //b = min( FLA_Obj_width( AR ), nb_alg ); FLA_Repart_1x2_to_1x3( AL, /**/ AR, &A0, /**/ &A1, &A2, b, FLA_RIGHT ); FLA_Repart_2x1_to_3x1( BT, &B0, /* ** */ /* ** */ &B1, BB, &B2, b, FLA_BOTTOM ); /*------------------------------------------------------------*/ #pragma intel omp task captureprivate(A1,B1) private(C_local) { FLA_Obj_create_conf_to( FLA_NO_TRANSPOSE, C, &C_local ); FLA_Obj_set_to_zero( C_local ); /* C = alpha * A1 * B1 + C; */ FLA_Gemm_external( FLA_NO_TRANSPOSE, FLA_NO_TRANSPOSE, alpha, A1, B1, FLA_ONE, C_local ); REF_Axpy_sync_circular( FLA_ONE, C_local, C ); FLA_Obj_free( &C_local ); } /*------------------------------------------------------------*/ FLA_Cont_with_1x3_to_1x2( &AL, /**/ &AR, A0, A1, /**/ A2, FLA_LEFT ); FLA_Cont_with_3x1_to_2x1( &BT, B0, B1, /* ** */ /* ** */ &BB, B2, FLA_TOP ); } } return FLA_SUCCESS; }
FLA_Error FLA_Sylv_nn_blk_var8( FLA_Obj isgn, FLA_Obj A, FLA_Obj B, FLA_Obj C, FLA_Obj scale, fla_sylv_t* cntl ) { FLA_Obj ATL, ATR, A00, A01, A02, ABL, ABR, A10, A11, A12, A20, A21, A22; FLA_Obj BTL, BTR, B00, B01, B02, BBL, BBR, B10, B11, B12, B20, B21, B22; FLA_Obj CTL, CTR, C00, C01, C02, CBL, CBR, C10, C11, C12, C20, C21, C22; dim_t b; FLA_Part_2x2( A, &ATL, &ATR, &ABL, &ABR, 0, 0, FLA_BR ); FLA_Part_2x2( B, &BTL, &BTR, &BBL, &BBR, 0, 0, FLA_TL ); FLA_Part_2x2( C, &CTL, &CTR, &CBL, &CBR, 0, 0, FLA_BL ); while ( FLA_Obj_length( ABR ) < FLA_Obj_length( A ) ){ b = FLA_Determine_blocksize( CTR, FLA_TR, FLA_Cntl_blocksize( cntl ) ); FLA_Repart_2x2_to_3x3( ATL, /**/ ATR, &A00, &A01, /**/ &A02, &A10, &A11, /**/ &A12, /* ************* */ /* ******************** */ ABL, /**/ ABR, &A20, &A21, /**/ &A22, b, b, FLA_TL ); FLA_Repart_2x2_to_3x3( BTL, /**/ BTR, &B00, /**/ &B01, &B02, /* ************* */ /* ******************** */ &B10, /**/ &B11, &B12, BBL, /**/ BBR, &B20, /**/ &B21, &B22, b, b, FLA_BR ); FLA_Repart_2x2_to_3x3( CTL, /**/ CTR, &C00, /**/ &C01, &C02, &C10, /**/ &C11, &C12, /* ************* */ /* ******************** */ CBL, /**/ CBR, &C20, /**/ &C21, &C22, b, b, FLA_TR ); // Loop Invariant: // CTL = CTL - ATR * sylv( ABR, BTL, CBL ) // CTR = CTR // CBL = sylv( ABR, BTL, CBL ) // CBR = sylv( ABR, BBR, CBR - sylv( ABR, BTL, CBL ) * BTR ) /*------------------------------------------------------------*/ // C10 = sylv( A11, B00, C10 ); FLA_Sylv_internal( FLA_NO_TRANSPOSE, FLA_NO_TRANSPOSE, isgn, A11, B00, C10, scale, FLA_Cntl_sub_sylv1( cntl ) ); // C00 = C00 - A01 * C10; FLA_Gemm_internal( FLA_NO_TRANSPOSE, FLA_NO_TRANSPOSE, FLA_MINUS_ONE, A01, C10, FLA_ONE, C00, FLA_Cntl_sub_gemm1( cntl ) ); // C11 = sylv( A11, B11, C11 - A12 * C21 -/+ C10 * B01 ); FLA_Gemm_internal( FLA_NO_TRANSPOSE, FLA_NO_TRANSPOSE, FLA_NEGATE( isgn ), C10, B01, FLA_ONE, C11, FLA_Cntl_sub_gemm2( cntl ) ); FLA_Gemm_internal( FLA_NO_TRANSPOSE, FLA_NO_TRANSPOSE, FLA_MINUS_ONE, A12, C21, FLA_ONE, C11, FLA_Cntl_sub_gemm3( cntl ) ); FLA_Sylv_internal( FLA_NO_TRANSPOSE, FLA_NO_TRANSPOSE, isgn, A11, B11, C11, scale, FLA_Cntl_sub_sylv2( cntl ) ); // C01 = C01 - A01 * C11 - A02 * C21; FLA_Gemm_internal( FLA_NO_TRANSPOSE, FLA_NO_TRANSPOSE, FLA_MINUS_ONE, A02, C21, FLA_ONE, C01, FLA_Cntl_sub_gemm4( cntl ) ); FLA_Gemm_internal( FLA_NO_TRANSPOSE, FLA_NO_TRANSPOSE, FLA_MINUS_ONE, A01, C11, FLA_ONE, C01, FLA_Cntl_sub_gemm5( cntl ) ); // C12 = sylv( A11, B22, C12 - A12 * C22 -/+ C10 * B02 -/+ C11 * B12 ); FLA_Gemm_internal( FLA_NO_TRANSPOSE, FLA_NO_TRANSPOSE, FLA_NEGATE( isgn ), C11, B12, FLA_ONE, C12, FLA_Cntl_sub_gemm6( cntl ) ); FLA_Gemm_internal( FLA_NO_TRANSPOSE, FLA_NO_TRANSPOSE, FLA_NEGATE( isgn ), C10, B02, FLA_ONE, C12, FLA_Cntl_sub_gemm7( cntl ) ); FLA_Gemm_internal( FLA_NO_TRANSPOSE, FLA_NO_TRANSPOSE, FLA_MINUS_ONE, A12, C22, FLA_ONE, C12, FLA_Cntl_sub_gemm8( cntl ) ); FLA_Sylv_internal( FLA_NO_TRANSPOSE, FLA_NO_TRANSPOSE, isgn, A11, B22, C12, scale, FLA_Cntl_sub_sylv3( cntl ) ); /*------------------------------------------------------------*/ FLA_Cont_with_3x3_to_2x2( &ATL, /**/ &ATR, A00, /**/ A01, A02, /* ************** */ /* ****************** */ A10, /**/ A11, A12, &ABL, /**/ &ABR, A20, /**/ A21, A22, FLA_BR ); FLA_Cont_with_3x3_to_2x2( &BTL, /**/ &BTR, B00, B01, /**/ B02, B10, B11, /**/ B12, /* ************** */ /* ****************** */ &BBL, /**/ &BBR, B20, B21, /**/ B22, FLA_TL ); FLA_Cont_with_3x3_to_2x2( &CTL, /**/ &CTR, C00, C01, /**/ C02, /* ************** */ /* ****************** */ C10, C11, /**/ C12, &CBL, /**/ &CBR, C20, C21, /**/ C22, FLA_BL ); } return FLA_SUCCESS; }
FLA_Error FLA_Copyr_u_blk_var4( FLA_Obj A, FLA_Obj B, fla_copyr_t* cntl ) { FLA_Obj ATL, ATR, A00, A01, A02, ABL, ABR, A10, A11, A12, A20, A21, A22; FLA_Obj BTL, BTR, B00, B01, B02, BBL, BBR, B10, B11, B12, B20, B21, B22; dim_t b; FLA_Part_2x2( A, &ATL, &ATR, &ABL, &ABR, 0, 0, FLA_BR ); FLA_Part_2x2( B, &BTL, &BTR, &BBL, &BBR, 0, 0, FLA_BR ); while ( FLA_Obj_min_dim( ATL ) > 0 ){ b = FLA_Determine_blocksize( ATL, FLA_TL, FLA_Cntl_blocksize( cntl ) ); FLA_Repart_2x2_to_3x3( ATL, /**/ ATR, &A00, &A01, /**/ &A02, &A10, &A11, /**/ &A12, /* ************* */ /* ******************** */ ABL, /**/ ABR, &A20, &A21, /**/ &A22, b, b, FLA_TL ); FLA_Repart_2x2_to_3x3( BTL, /**/ BTR, &B00, &B01, /**/ &B02, &B10, &B11, /**/ &B12, /* ************* */ /* ******************** */ BBL, /**/ BBR, &B20, &B21, /**/ &B22, b, b, FLA_TL ); /*------------------------------------------------------------*/ // B11 = triu( A11 ); FLA_Copyr_internal( FLA_UPPER_TRIANGULAR, A11, B11, FLA_Cntl_sub_copyr( cntl ) ); // B01 = A01; FLA_Copy_internal( A01, B01, FLA_Cntl_sub_copy( cntl ) ); /*------------------------------------------------------------*/ FLA_Cont_with_3x3_to_2x2( &ATL, /**/ &ATR, A00, /**/ A01, A02, /* ************** */ /* ****************** */ A10, /**/ A11, A12, &ABL, /**/ &ABR, A20, /**/ A21, A22, FLA_BR ); FLA_Cont_with_3x3_to_2x2( &BTL, /**/ &BTR, B00, /**/ B01, B02, /* ************** */ /* ****************** */ B10, /**/ B11, B12, &BBL, /**/ &BBR, B20, /**/ B21, B22, FLA_BR ); } return FLA_SUCCESS; }
FLA_Error FLA_Sylv_nh_blk_var16( FLA_Obj isgn, FLA_Obj A, FLA_Obj B, FLA_Obj C, FLA_Obj scale, fla_sylv_t* cntl ) { FLA_Obj ATL, ATR, A00, A01, A02, ABL, ABR, A10, A11, A12, A20, A21, A22; FLA_Obj CT, C0, CB, C1, C2; dim_t b; FLA_Part_2x2( A, &ATL, &ATR, &ABL, &ABR, 0, 0, FLA_BR ); FLA_Part_2x1( C, &CT, &CB, 0, FLA_BOTTOM ); while ( FLA_Obj_length( ABR ) < FLA_Obj_length( A ) ){ b = FLA_Determine_blocksize( CT, FLA_TOP, FLA_Cntl_blocksize( cntl ) ); FLA_Repart_2x2_to_3x3( ATL, /**/ ATR, &A00, &A01, /**/ &A02, &A10, &A11, /**/ &A12, /* ************* */ /* ******************** */ ABL, /**/ ABR, &A20, &A21, /**/ &A22, b, b, FLA_TL ); FLA_Repart_2x1_to_3x1( CT, &C0, &C1, /* ** */ /* ** */ CB, &C2, b, FLA_TOP ); // Loop Invariant: // CT = CT - ATR * sylv( ABR, B', CB ) // CB = sylv( ABR, B', CB ) /*------------------------------------------------------------*/ // C1 = sylv( A11, B', C1 ); FLA_Sylv_internal( FLA_NO_TRANSPOSE, FLA_CONJ_TRANSPOSE, isgn, A11, B, C1, scale, FLA_Cntl_sub_sylv1( cntl ) ); // C0 = C0 - A01 * C1; FLA_Gemm_internal( FLA_NO_TRANSPOSE, FLA_NO_TRANSPOSE, FLA_MINUS_ONE, A01, C1, FLA_ONE, C0, FLA_Cntl_sub_gemm1( cntl ) ); /*------------------------------------------------------------*/ FLA_Cont_with_3x3_to_2x2( &ATL, /**/ &ATR, A00, /**/ A01, A02, /* ************** */ /* ****************** */ A10, /**/ A11, A12, &ABL, /**/ &ABR, A20, /**/ A21, A22, FLA_BR ); FLA_Cont_with_3x1_to_2x1( &CT, C0, /* ** */ /* ** */ C1, &CB, C2, FLA_BOTTOM ); } return FLA_SUCCESS; }
FLA_Error FLA_Her2k_un_blk_var6( FLA_Obj alpha, FLA_Obj A, FLA_Obj B, FLA_Obj beta, FLA_Obj C, fla_her2k_t* cntl ) { FLA_Obj AT, A0, AB, A1, A2; FLA_Obj BT, B0, BB, B1, B2; FLA_Obj CTL, CTR, C00, C01, C02, CBL, CBR, C10, C11, C12, C20, C21, C22; dim_t b; FLA_Scalr_internal( FLA_UPPER_TRIANGULAR, beta, C, FLA_Cntl_sub_scalr( cntl ) ); FLA_Part_2x1( A, &AT, &AB, 0, FLA_BOTTOM ); FLA_Part_2x1( B, &BT, &BB, 0, FLA_BOTTOM ); FLA_Part_2x2( C, &CTL, &CTR, &CBL, &CBR, 0, 0, FLA_BR ); while ( FLA_Obj_length( AB ) < FLA_Obj_length( A ) ){ b = FLA_Determine_blocksize( AT, FLA_TOP, FLA_Cntl_blocksize( cntl ) ); FLA_Repart_2x1_to_3x1( AT, &A0, &A1, /* ** */ /* ** */ AB, &A2, b, FLA_TOP ); FLA_Repart_2x1_to_3x1( BT, &B0, &B1, /* ** */ /* ** */ BB, &B2, b, FLA_TOP ); FLA_Repart_2x2_to_3x3( CTL, /**/ CTR, &C00, &C01, /**/ &C02, &C10, &C11, /**/ &C12, /* ************* */ /* ******************** */ CBL, /**/ CBR, &C20, &C21, /**/ &C22, b, b, FLA_TL ); /*------------------------------------------------------------*/ /* C01 = C01 + A0 * B1' */ FLA_Gemm_internal( FLA_NO_TRANSPOSE, FLA_CONJ_TRANSPOSE, alpha, A0, B1, FLA_ONE, C01, FLA_Cntl_sub_gemm1( cntl ) ); /* C12 = C12 + B1 * A2' */ FLA_Gemm_internal( FLA_NO_TRANSPOSE, FLA_CONJ_TRANSPOSE, alpha, B1, A2, FLA_ONE, C12, FLA_Cntl_sub_gemm2( cntl ) ); /* C11 = C11 + A1 * B1' + B1 * A1' */ FLA_Her2k_internal( FLA_UPPER_TRIANGULAR, FLA_NO_TRANSPOSE, alpha, A1, B1, FLA_ONE, C11, FLA_Cntl_sub_her2k( cntl ) ); /*------------------------------------------------------------*/ FLA_Cont_with_3x1_to_2x1( &AT, A0, /* ** */ /* ** */ A1, &AB, A2, FLA_BOTTOM ); FLA_Cont_with_3x1_to_2x1( &BT, B0, /* ** */ /* ** */ B1, &BB, B2, FLA_BOTTOM ); FLA_Cont_with_3x3_to_2x2( &CTL, /**/ &CTR, C00, /**/ C01, C02, /* ************** */ /* ****************** */ C10, /**/ C11, C12, &CBL, /**/ &CBR, C20, /**/ C21, C22, FLA_BR ); } return FLA_SUCCESS; }
FLA_Error FLA_Syrk_ln_blk_var1( FLA_Obj alpha, FLA_Obj A, FLA_Obj beta, FLA_Obj C, fla_syrk_t* cntl ) { FLA_Obj AT, A0, AB, A1, A2; FLA_Obj CTL, CTR, C00, C01, C02, CBL, CBR, C10, C11, C12, C20, C21, C22; dim_t b; FLA_Part_2x1( A, &AT, &AB, 0, FLA_TOP ); FLA_Part_2x2( C, &CTL, &CTR, &CBL, &CBR, 0, 0, FLA_TL ); while ( FLA_Obj_length( AT ) < FLA_Obj_length( A ) ){ b = FLA_Determine_blocksize( AB, FLA_BOTTOM, FLA_Cntl_blocksize( cntl ) ); FLA_Repart_2x1_to_3x1( AT, &A0, /* ** */ /* ** */ &A1, AB, &A2, b, FLA_BOTTOM ); FLA_Repart_2x2_to_3x3( CTL, /**/ CTR, &C00, /**/ &C01, &C02, /* ************* */ /* ******************** */ &C10, /**/ &C11, &C12, CBL, /**/ CBR, &C20, /**/ &C21, &C22, b, b, FLA_BR ); /*------------------------------------------------------------*/ /* C10 = C10 + A1 * A0' */ FLA_Gemm_internal( FLA_NO_TRANSPOSE, FLA_TRANSPOSE, alpha, A1, A0, beta, C10, FLA_Cntl_sub_gemm( cntl ) ); /* C11 = C11 + A1 * A1' */ FLA_Syrk_internal( FLA_LOWER_TRIANGULAR, FLA_NO_TRANSPOSE, alpha, A1, beta, C11, FLA_Cntl_sub_syrk( cntl ) ); /*------------------------------------------------------------*/ FLA_Cont_with_3x1_to_2x1( &AT, A0, A1, /* ** */ /* ** */ &AB, A2, FLA_TOP ); FLA_Cont_with_3x3_to_2x2( &CTL, /**/ &CTR, C00, C01, /**/ C02, C10, C11, /**/ C12, /* ************** */ /* ****************** */ &CBL, /**/ &CBR, C20, C21, /**/ C22, FLA_TL ); } return FLA_SUCCESS; }
FLA_Error FLA_Lyap_n_blk_var1( FLA_Obj isgn, FLA_Obj A, FLA_Obj C, FLA_Obj scale, fla_lyap_t* cntl ) { FLA_Obj ATL, ATR, A00, A01, A02, ABL, ABR, A10, A11, A12, A20, A21, A22; FLA_Obj CTL, CTR, C00, C01, C02, CBL, CBR, C10, C11, C12, C20, C21, C22; dim_t b; FLA_Part_2x2( A, &ATL, &ATR, &ABL, &ABR, 0, 0, FLA_BR ); FLA_Part_2x2( C, &CTL, &CTR, &CBL, &CBR, 0, 0, FLA_BR ); while ( FLA_Obj_length( CTL ) > 0 ){ b = FLA_Determine_blocksize( CTL, FLA_TL, FLA_Cntl_blocksize( cntl ) ); FLA_Repart_2x2_to_3x3( ATL, /**/ ATR, &A00, &A01, /**/ &A02, &A10, &A11, /**/ &A12, /* ************* */ /* ******************** */ ABL, /**/ ABR, &A20, &A21, /**/ &A22, b, b, FLA_TL ); FLA_Repart_2x2_to_3x3( CTL, /**/ CTR, &C00, &C01, /**/ &C02, &C10, &C11, /**/ &C12, /* ************* */ /* ******************** */ CBL, /**/ CBR, &C20, &C21, /**/ &C22, b, b, FLA_TL ); /*------------------------------------------------------------*/ // C12 = isgn * C12 - A12 * C22; // C12 = sylv( A11, A22', C12 ); FLA_Hemm_internal( FLA_RIGHT, FLA_UPPER_TRIANGULAR, FLA_MINUS_ONE, C22, A12, isgn, C12, FLA_Cntl_sub_hemm( cntl ) ); FLA_Sylv_internal( FLA_NO_TRANSPOSE, FLA_CONJ_TRANSPOSE, FLA_ONE, A11, A22, C12, scale, FLA_Cntl_sub_sylv( cntl ) ); // C11 = isgn * C11 - A12 * C12' - C12 * A12'; FLA_Her2k_internal( FLA_UPPER_TRIANGULAR, FLA_NO_TRANSPOSE, FLA_MINUS_ONE, A12, C12, isgn, C11, FLA_Cntl_sub_her2k( cntl ) ); // C11 = lyap_n( A11, C11 ); FLA_Lyap_internal( FLA_NO_TRANSPOSE, FLA_ONE, A11, C11, scale, FLA_Cntl_sub_lyap( cntl ) ); /*------------------------------------------------------------*/ FLA_Cont_with_3x3_to_2x2( &ATL, /**/ &ATR, A00, /**/ A01, A02, /* ************** */ /* ****************** */ A10, /**/ A11, A12, &ABL, /**/ &ABR, A20, /**/ A21, A22, FLA_BR ); FLA_Cont_with_3x3_to_2x2( &CTL, /**/ &CTR, C00, /**/ C01, C02, /* ************** */ /* ****************** */ C10, /**/ C11, C12, &CBL, /**/ &CBR, C20, /**/ C21, C22, FLA_BR ); } return FLA_SUCCESS; }
FLA_Error FLA_UDdate_UT_blk_var2( FLA_Obj R, FLA_Obj C, FLA_Obj D, FLA_Obj T, fla_uddateut_t* cntl ) { FLA_Obj CT, C0, CB, C1, C2; FLA_Obj DT, D0, DB, D1, D2; FLA_Obj TT, T0, TB, T1, T2; dim_t b_C, b_D, b_T; FLA_Part_2x1( C, &CT, &CB, 0, FLA_TOP ); FLA_Part_2x1( D, &DT, &DB, 0, FLA_TOP ); FLA_Part_2x1( T, &TT, &TB, 0, FLA_TOP ); while ( FLA_Obj_length( CT ) < FLA_Obj_length( C ) && FLA_Obj_length( DT ) < FLA_Obj_length( D ) ) { b_C = FLA_Determine_blocksize( CB, FLA_BOTTOM, FLA_Cntl_blocksize( cntl ) ); b_D = FLA_Determine_blocksize( DB, FLA_BOTTOM, FLA_Cntl_blocksize( cntl ) ); b_T = FLA_Determine_blocksize( TB, FLA_BOTTOM, FLA_Cntl_blocksize( cntl ) ); FLA_Repart_2x1_to_3x1( CT, &C0, /* ** */ /* ****** */ &C1, CB, &C2, b_C, FLA_BOTTOM ); FLA_Repart_2x1_to_3x1( DT, &D0, /* ** */ /* ****** */ &D1, DB, &D2, b_D, FLA_BOTTOM ); FLA_Repart_2x1_to_3x1( TT, &T0, /* ** */ /* ****** */ &T1, TB, &T2, b_T, FLA_BOTTOM ); /*------------------------------------------------------------*/ /* Perform an up/downdate of the upper triangular Cholesky factor R via "UD" UT Householder transformations: [ R, ... C1, ... D1, T1 ] = FLA_UDdate_UT( R, ... C1, ... D1, T1 ); by updating R in such a way that removes the contributions of the rows in D1 while simultaneously adding new contributions to the factorization from the rows of C1. Note that C1 and D1 are also updated in the process. Also note that either C1 or D1 may become empty at any iteration. */ FLA_UDdate_UT_internal( R, C1, D1, T1, FLA_Cntl_sub_uddateut( cntl ) ); /*------------------------------------------------------------*/ FLA_Cont_with_3x1_to_2x1( &CT, C0, C1, /* ** */ /* ****** */ &CB, C2, FLA_TOP ); FLA_Cont_with_3x1_to_2x1( &DT, D0, D1, /* ** */ /* ****** */ &DB, D2, FLA_TOP ); FLA_Cont_with_3x1_to_2x1( &TT, T0, T1, /* ** */ /* ****** */ &TB, T2, FLA_TOP ); } return FLA_SUCCESS; }
FLA_Error FLA_Gemm_nn_omp_var15( FLA_Obj alpha, FLA_Obj A, FLA_Obj B, FLA_Obj C, fla_gemm_t* cntl ) { FLA_Obj AT, A0, AB, A1, A2; FLA_Obj CT, C0, CB, C1, C2; FLA_Obj AL, AR, A10, A11, A12; FLA_Obj BT, B0, BB, B1, B2; FLA_Obj C1_local; int i, j, lock_ldim, lock_i; int b_m, b_k; FLA_Part_2x1( A, &AT, &AB, 0, FLA_TOP ); FLA_Part_2x1( C, &CT, &CB, 0, FLA_TOP ); #pragma intel omp parallel taskq { while ( FLA_Obj_length( AT ) < FLA_Obj_length( A ) ) { b_m = FLA_Determine_blocksize( A, AT, FLA_TOP, FLA_Cntl_blocksize( cntl ) ); FLA_Repart_2x1_to_3x1( AT, &A0, /* ** */ /* ** */ &A1, AB, &A2, b_m, FLA_BOTTOM ); FLA_Repart_2x1_to_3x1( CT, &C0, /* ** */ /* ** */ &C1, CB, &C2, b_m, FLA_BOTTOM ); /*------------------------------------------------------------*/ /* C1 = alpha * A1 * B + C1; */ FLA_Part_1x2( A1, &AL, &AR, 0, FLA_LEFT ); FLA_Part_2x1( B, &BT, &BB, 0, FLA_TOP ); while ( FLA_Obj_width( AL ) < FLA_Obj_width( A ) ) { b_k = FLA_Determine_blocksize( A, AL, FLA_LEFT, FLA_Cntl_blocksize( cntl ) ); // Get the index of the current partition. // FIX THIS: need + b_m - 1 or something like this //j = FLA_Obj_length( CT ) / b_m; //i = FLA_Obj_width( AL ) / b_k; //lock_ldim = FLA_get_num_threads_in_m_dim(omp_get_num_threads()); lock_i = FLA_Obj_length( CT ) / b_m; FLA_Repart_1x2_to_1x3( AL, /**/ AR, &A10, /**/ &A11, &A12, b_k, FLA_RIGHT ); FLA_Repart_2x1_to_3x1( BT, &B0, /* ** */ /* ** */ &B1, BB, &B2, b_k, FLA_BOTTOM ); /*------------------------------------------------------------*/ /* C1 = alpha * A11 * B1 + C1; */ //// FLA_Gemm( FLA_NO_TRANSPOSE, FLA_NO_TRANSPOSE, //// alpha, A11, B1, FLA_ONE, C1 ); #pragma intel omp task captureprivate( lock_i, A11, B1, C1 ), private( C1_local ) { FLA_Obj_create_conf_to( FLA_NO_TRANSPOSE, C1, &C1_local ); FLA_Obj_set_to_zero( C1_local ); /* C1_local = alpha * A1 * B11 + C1_local; */ FLA_Gemm_external( FLA_NO_TRANSPOSE, FLA_NO_TRANSPOSE, alpha, A11, B1, FLA_ONE, C1_local ); // Acquire lock[i] (the lock for C1). omp_set_lock( &fla_omp_lock[lock_i] ); /* C1 += C1_local */ FLA_Axpy_external( FLA_ONE, C1_local, C1 ); //FLA_Axpy_sync_pipeline2( j*lock_ldim, FLA_ONE, C1_local, C1 ); //FLA_Axpy_sync_circular2( j*lock_ldim, i, FLA_ONE, C1_local, C1 ); //REF_Axpy_sync_circular2( j*lock_ldim, i, FLA_ONE, C1_local, C1 ); // Release lock[i] (the lock for C1). omp_unset_lock( &fla_omp_lock[lock_i] ); FLA_Obj_free( &C1_local ); } /*------------------------------------------------------------*/ FLA_Cont_with_1x3_to_1x2( &AL, /**/ &AR, A10, A11, /**/ A12, FLA_LEFT ); FLA_Cont_with_3x1_to_2x1( &BT, B0, B1, /* ** */ /* ** */ &BB, B2, FLA_TOP ); } /*------------------------------------------------------------*/ FLA_Cont_with_3x1_to_2x1( &AT, A0, A1, /* ** */ /* ** */ &AB, A2, FLA_TOP ); FLA_Cont_with_3x1_to_2x1( &CT, C0, C1, /* ** */ /* ** */ &CB, C2, FLA_TOP ); } } return FLA_SUCCESS; }
FLA_Error FLA_Eig_gest_il_blk_var2( FLA_Obj A, FLA_Obj Y, FLA_Obj B, fla_eig_gest_t* cntl ) { FLA_Obj ATL, ATR, A00, A01, A02, ABL, ABR, A10, A11, A12, A20, A21, A22; FLA_Obj BTL, BTR, B00, B01, B02, BBL, BBR, B10, B11, B12, B20, B21, B22; FLA_Obj YL, YR, Y10, Y11, Y12; FLA_Obj Y10_t, Y10_b; dim_t b; FLA_Part_2x2( A, &ATL, &ATR, &ABL, &ABR, 0, 0, FLA_TL ); FLA_Part_2x2( B, &BTL, &BTR, &BBL, &BBR, 0, 0, FLA_TL ); FLA_Part_1x2( Y, &YL, &YR, 0, FLA_LEFT ); while ( FLA_Obj_length( ATL ) < FLA_Obj_length( A ) ){ b = FLA_Determine_blocksize( ABR, FLA_BR, FLA_Cntl_blocksize( cntl ) ); FLA_Repart_2x2_to_3x3( ATL, /**/ ATR, &A00, /**/ &A01, &A02, /* ************* */ /* ******************** */ &A10, /**/ &A11, &A12, ABL, /**/ ABR, &A20, /**/ &A21, &A22, b, b, FLA_BR ); FLA_Repart_2x2_to_3x3( BTL, /**/ BTR, &B00, /**/ &B01, &B02, /* ************* */ /* ******************** */ &B10, /**/ &B11, &B12, BBL, /**/ BBR, &B20, /**/ &B21, &B22, b, b, FLA_BR ); FLA_Repart_1x2_to_1x3( YL, /**/ YR, &Y10, /**/ &Y11, &Y12, b, FLA_RIGHT ); /*------------------------------------------------------------*/ FLA_Part_2x1( Y10, &Y10_t, &Y10_b, b, FLA_TOP ); // Y10 = 1/2 * B10 * A00; FLA_Hemm_internal( FLA_RIGHT, FLA_LOWER_TRIANGULAR, FLA_ONE_HALF, A00, B10, FLA_ZERO, Y10_t, FLA_Cntl_sub_hemm( cntl ) ); // A10 = A10 - Y10; FLA_Axpy_internal( FLA_MINUS_ONE, Y10_t, A10, FLA_Cntl_sub_axpy1( cntl ) ); // A11 = A11 - A10 * B10' - B10 * A10'; FLA_Her2k_internal( FLA_LOWER_TRIANGULAR, FLA_NO_TRANSPOSE, FLA_MINUS_ONE, A10, B10, FLA_ONE, A11, FLA_Cntl_sub_her2k( cntl ) ); // A11 = inv( tril( B11 ) ) * A11 * inv( tril( B11 )' ); FLA_Eig_gest_internal( FLA_INVERSE, FLA_LOWER_TRIANGULAR, A11, Y11, B11, FLA_Cntl_sub_eig_gest( cntl ) ); // A21 = A21 - A20 * B10'; FLA_Gemm_internal( FLA_NO_TRANSPOSE, FLA_CONJ_TRANSPOSE, FLA_MINUS_ONE, A20, B10, FLA_ONE, A21, FLA_Cntl_sub_gemm1( cntl ) ); // A21 = A21 * inv( tril( B11 )' ); FLA_Trsm_internal( FLA_RIGHT, FLA_LOWER_TRIANGULAR, FLA_CONJ_TRANSPOSE, FLA_NONUNIT_DIAG, FLA_ONE, B11, A21, FLA_Cntl_sub_trsm1( cntl ) ); // A10 = A10 - Y10; FLA_Axpy_internal( FLA_MINUS_ONE, Y10_t, A10, FLA_Cntl_sub_axpy2( cntl ) ); // A10 = inv( tril( B11 ) ) * A10; FLA_Trsm_internal( FLA_LEFT, FLA_LOWER_TRIANGULAR, FLA_NO_TRANSPOSE, FLA_NONUNIT_DIAG, FLA_ONE, B11, A10, FLA_Cntl_sub_trsm2( cntl ) ); /*------------------------------------------------------------*/ FLA_Cont_with_3x3_to_2x2( &ATL, /**/ &ATR, A00, A01, /**/ A02, A10, A11, /**/ A12, /* ************** */ /* ****************** */ &ABL, /**/ &ABR, A20, A21, /**/ A22, FLA_TL ); FLA_Cont_with_3x3_to_2x2( &BTL, /**/ &BTR, B00, B01, /**/ B02, B10, B11, /**/ B12, /* ************** */ /* ****************** */ &BBL, /**/ &BBR, B20, B21, /**/ B22, FLA_TL ); FLA_Cont_with_1x3_to_1x2( &YL, /**/ &YR, Y10, Y11, /**/ Y12, FLA_LEFT ); } return FLA_SUCCESS; }
FLA_Error FLA_Symm_ru_blk_var4( FLA_Obj alpha, FLA_Obj A, FLA_Obj B, FLA_Obj beta, FLA_Obj C, fla_symm_t* cntl ) { FLA_Obj ATL, ATR, A00, A01, A02, ABL, ABR, A10, A11, A12, A20, A21, A22; FLA_Obj BL, BR, B0, B1, B2; FLA_Obj CL, CR, C0, C1, C2; dim_t b; FLA_Scal_internal( beta, C, FLA_Cntl_sub_scal( cntl ) ); FLA_Part_2x2( A, &ATL, &ATR, &ABL, &ABR, 0, 0, FLA_TL ); FLA_Part_1x2( B, &BL, &BR, 0, FLA_LEFT ); FLA_Part_1x2( C, &CL, &CR, 0, FLA_LEFT ); while ( FLA_Obj_length( ATL ) < FLA_Obj_length( A ) ){ b = FLA_Determine_blocksize( ABR, FLA_BR, FLA_Cntl_blocksize( cntl ) ); FLA_Repart_2x2_to_3x3( ATL, /**/ ATR, &A00, /**/ &A01, &A02, /* ************* */ /* ******************** */ &A10, /**/ &A11, &A12, ABL, /**/ ABR, &A20, /**/ &A21, &A22, b, b, FLA_BR ); FLA_Repart_1x2_to_1x3( BL, /**/ BR, &B0, /**/ &B1, &B2, b, FLA_RIGHT ); FLA_Repart_1x2_to_1x3( CL, /**/ CR, &C0, /**/ &C1, &C2, b, FLA_RIGHT ); /*------------------------------------------------------------*/ /* C0 = C0 + B1 * A01' */ FLA_Gemm_internal( FLA_NO_TRANSPOSE, FLA_TRANSPOSE, alpha, B1, A01, FLA_ONE, C0, FLA_Cntl_sub_gemm1( cntl ) ); /* C1 = C1 + B1 * A11 */ FLA_Symm_internal( FLA_RIGHT, FLA_UPPER_TRIANGULAR, alpha, A11, B1, FLA_ONE, C1, FLA_Cntl_sub_symm( cntl ) ); /* C2 = C2 + B1 * A12 */ FLA_Gemm_internal( FLA_NO_TRANSPOSE, FLA_NO_TRANSPOSE, alpha, B1, A12, FLA_ONE, C2, FLA_Cntl_sub_gemm2( cntl ) ); /*------------------------------------------------------------*/ FLA_Cont_with_3x3_to_2x2( &ATL, /**/ &ATR, A00, A01, /**/ A02, A10, A11, /**/ A12, /* ************** */ /* ****************** */ &ABL, /**/ &ABR, A20, A21, /**/ A22, FLA_TL ); FLA_Cont_with_1x3_to_1x2( &BL, /**/ &BR, B0, B1, /**/ B2, FLA_LEFT ); FLA_Cont_with_1x3_to_1x2( &CL, /**/ &CR, C0, C1, /**/ C2, FLA_LEFT ); } return FLA_SUCCESS; }
FLA_Error FLA_Apply_Q_UT_rnfr_blk_var3( FLA_Obj A, FLA_Obj TW, FLA_Obj W, FLA_Obj B, fla_apqut_t* cntl ) { FLA_Obj ATL, ATR, A00, A01, A02, ABL, ABR, A10, A11, A12, A20, A21, A22; FLA_Obj TWTL, TWTR, TW00, TW01, TW02, TWBL, TWBR, TW10, T11, W12, TW20, TW21, TW22; FLA_Obj WTL, WTR, WBL, WBR; FLA_Obj BL, BR, B0, B1, B2; dim_t b; FLA_Part_2x2( A, &ATL, &ATR, &ABL, &ABR, 0, 0, FLA_TL ); FLA_Part_2x2( TW, &TWTL, &TWTR, &TWBL, &TWBR, 0, 0, FLA_TL ); FLA_Part_1x2( B, &BL, &BR, 0, FLA_LEFT ); while ( FLA_Obj_min_dim( ABR ) > 0 ){ b = FLA_Determine_blocksize( ABR, FLA_BR, FLA_Cntl_blocksize( cntl ) ); FLA_Repart_2x2_to_3x3( ATL, /**/ ATR, &A00, /**/ &A01, &A02, /* ************* */ /* ******************** */ &A10, /**/ &A11, &A12, ABL, /**/ ABR, &A20, /**/ &A21, &A22, b, b, FLA_BR ); FLA_Repart_2x2_to_3x3( TWTL, /**/ TWTR, &TW00, /**/ &TW01, &TW02, /* *************** */ /* *********************** */ &TW10, /**/ &T11, &W12, TWBL, /**/ TWBR, &TW20, /**/ &TW21, &TW22, b, b, FLA_BR ); FLA_Repart_1x2_to_1x3( BL, /**/ BR, &B0, /**/ &B1, &B2, b, FLA_RIGHT ); /*------------------------------------------------------------*/ FLA_Part_2x2( W, &WTL, &WTR, &WBL, &WBR, b, FLA_Obj_length( B1 ), FLA_TL ); // WTL = B1; FLA_Copyt_internal( FLA_TRANSPOSE, B1, WTL, FLA_Cntl_sub_copyt( cntl ) ); // U11 = trilu( A11 ); // U12 = A12; // Let WTL^T be conformal to B1. // // WTL^T = ( B1 * U11^T + B2 * U12^T ) * inv( triu(T11) ); // WTL = inv( triu(T11) )^T * ( U11 * B1^T + U12 * B2^T ); FLA_Trmm_internal( FLA_LEFT, FLA_UPPER_TRIANGULAR, FLA_NO_TRANSPOSE, FLA_UNIT_DIAG, FLA_ONE, A11, WTL, FLA_Cntl_sub_trmm1( cntl ) ); FLA_Gemm_internal( FLA_NO_TRANSPOSE, FLA_TRANSPOSE, FLA_ONE, A12, B2, FLA_ONE, WTL, FLA_Cntl_sub_gemm1( cntl ) ); FLA_Trsm_internal( FLA_LEFT, FLA_UPPER_TRIANGULAR, FLA_TRANSPOSE, FLA_NONUNIT_DIAG, FLA_ONE, T11, WTL, FLA_Cntl_sub_trsm( cntl ) ); // B2 = B2 - WTL^T * conj(U12); // B1 = B1 - WTL^T * conj(U11); // = B1 - ( U11' * WTL )^T; FLA_Gemm_internal( FLA_TRANSPOSE, FLA_CONJ_NO_TRANSPOSE, FLA_MINUS_ONE, WTL, A12, FLA_ONE, B2, FLA_Cntl_sub_gemm2( cntl ) ); FLA_Trmm_internal( FLA_LEFT, FLA_UPPER_TRIANGULAR, FLA_CONJ_TRANSPOSE, FLA_UNIT_DIAG, FLA_MINUS_ONE, A11, WTL, FLA_Cntl_sub_trmm2( cntl ) ); FLA_Axpyt_internal( FLA_TRANSPOSE, FLA_ONE, WTL, B1, FLA_Cntl_sub_axpyt( cntl ) ); /*------------------------------------------------------------*/ FLA_Cont_with_3x3_to_2x2( &ATL, /**/ &ATR, A00, A01, /**/ A02, A10, A11, /**/ A12, /* ************** */ /* ****************** */ &ABL, /**/ &ABR, A20, A21, /**/ A22, FLA_TL ); FLA_Cont_with_3x3_to_2x2( &TWTL, /**/ &TWTR, TW00, TW01, /**/ TW02, TW10, T11, /**/ W12, /* **************** */ /* ********************* */ &TWBL, /**/ &TWBR, TW20, TW21, /**/ TW22, FLA_TL ); FLA_Cont_with_1x3_to_1x2( &BL, /**/ &BR, B0, B1, /**/ B2, FLA_LEFT ); } return FLA_SUCCESS; }