FLA_Error FLA_Hemm_ru_blk_var10( FLA_Obj alpha, FLA_Obj A, FLA_Obj B, FLA_Obj beta, FLA_Obj C, fla_hemm_t* cntl )
{
FLA_Obj BT, B0,
BB, B1,
B2;
FLA_Obj CT, C0,
CB, C1,
C2;
dim_t b;
FLA_Part_2x1( B, &BT,
&BB, 0, FLA_BOTTOM );
FLA_Part_2x1( C, &CT,
&CB, 0, FLA_BOTTOM );
while ( FLA_Obj_length( BB ) < FLA_Obj_length( B ) ){
b = FLA_Determine_blocksize( BT, FLA_TOP, FLA_Cntl_blocksize( cntl ) );
FLA_Repart_2x1_to_3x1( BT, &B0,
&B1,
/* ** */ /* ** */
BB, &B2, b, FLA_TOP );
FLA_Repart_2x1_to_3x1( CT, &C0,
&C1,
/* ** */ /* ** */
CB, &C2, b, FLA_TOP );
/*------------------------------------------------------------*/
/* C1 = C1 + B1 * A */
FLA_Hemm_internal( FLA_RIGHT, FLA_UPPER_TRIANGULAR,
alpha, A, B1, beta, C1,
FLA_Cntl_sub_hemm( cntl ) );
/*------------------------------------------------------------*/
FLA_Cont_with_3x1_to_2x1( &BT, B0,
/* ** */ /* ** */
B1,
&BB, B2, FLA_BOTTOM );
FLA_Cont_with_3x1_to_2x1( &CT, C0,
/* ** */ /* ** */
C1,
&CB, C2, FLA_BOTTOM );
}
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_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_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_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_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_Hemm_rl_blk_var6( 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 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_BR );
FLA_Part_1x2( B, &BL, &BR, 0, FLA_RIGHT );
FLA_Part_1x2( C, &CL, &CR, 0, FLA_RIGHT );
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_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 = C1 + B0 * A10' */
FLA_Gemm_internal( FLA_NO_TRANSPOSE, FLA_CONJ_TRANSPOSE,
alpha, B0, A10, FLA_ONE, C1,
FLA_Cntl_sub_gemm1( cntl ) );
/* C1 = C1 + B1 * A11 */
FLA_Hemm_internal( FLA_RIGHT, FLA_LOWER_TRIANGULAR,
alpha, A11, B1, FLA_ONE, C1,
FLA_Cntl_sub_hemm( cntl ) );
/* C1 = C1 + B2 * A21 */
FLA_Gemm_internal( FLA_NO_TRANSPOSE, FLA_NO_TRANSPOSE,
alpha, B2, A21, FLA_ONE, C1,
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_BR );
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;
}