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;
}
