FLA_Error FLA_Gemm_hn_unb_var2( FLA_Obj alpha, FLA_Obj A, FLA_Obj B, FLA_Obj beta, FLA_Obj C )
{
FLA_Obj AL, AR, A0, a1, A2;
FLA_Obj CT, C0,
CB, c1t,
C2;
FLA_Scal_external( beta, C );
FLA_Part_1x2( A, &AL, &AR, 0, FLA_RIGHT );
FLA_Part_2x1( C, &CT,
&CB, 0, FLA_BOTTOM );
while ( FLA_Obj_width( AR ) < FLA_Obj_width( A ) ){
FLA_Repart_1x2_to_1x3( AL, /**/ AR, &A0, &a1, /**/ &A2,
1, FLA_LEFT );
FLA_Repart_2x1_to_3x1( CT, &C0,
&c1t,
/* ** */ /* *** */
CB, &C2, 1, FLA_TOP );
/*------------------------------------------------------------*/
/* c1t = a1' * B + c1t */
/* c1t' = B' * a1 + c1t' */
FLA_Gemvc_external( FLA_TRANSPOSE, FLA_CONJUGATE, alpha, B, a1, FLA_ONE, c1t );
/*------------------------------------------------------------*/
FLA_Cont_with_1x3_to_1x2( &AL, /**/ &AR, A0, /**/ a1, A2,
FLA_RIGHT );
FLA_Cont_with_3x1_to_2x1( &CT, C0,
/* ** */ /* *** */
c1t,
&CB, C2, FLA_BOTTOM );
}
return FLA_SUCCESS;
}
FLA_Error FLA_Copyt_h_blk_var3( FLA_Obj A, FLA_Obj B, fla_copyt_t* cntl )
{
FLA_Obj AT, A0,
AB, A1,
A2;
FLA_Obj BL, BR, B0, B1, B2;
dim_t b;
FLA_Part_2x1( A, &AT,
&AB, 0, FLA_TOP );
FLA_Part_1x2( B, &BL, &BR, 0, FLA_LEFT );
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_1x2_to_1x3( BL, /**/ BR, &B0, /**/ &B1, &B2,
b, FLA_RIGHT );
/*------------------------------------------------------------*/
FLA_Copyt_internal( FLA_CONJ_TRANSPOSE, A1, B1,
FLA_Cntl_sub_copyt( cntl ) );
/*------------------------------------------------------------*/
FLA_Cont_with_3x1_to_2x1( &AT, A0,
A1,
/* ** */ /* ** */
&AB, A2, FLA_TOP );
FLA_Cont_with_1x3_to_1x2( &BL, /**/ &BR, B0, B1, /**/ B2,
FLA_LEFT );
}
return FLA_SUCCESS;
}
FLA_Error FLA_Gemm_nc_unb_var5( FLA_Obj alpha, FLA_Obj A, FLA_Obj B, FLA_Obj beta, FLA_Obj C )
{
FLA_Obj AL, AR, A0, a1, A2;
FLA_Obj BT, B0,
BB, b1t,
B2;
FLA_Scal_external( beta, C );
FLA_Part_1x2( A, &AL, &AR, 0, FLA_LEFT );
FLA_Part_2x1( B, &BT,
&BB, 0, FLA_TOP );
while ( FLA_Obj_width( AL ) < FLA_Obj_width( A ) ){
FLA_Repart_1x2_to_1x3( AL, /**/ AR, &A0, /**/ &a1, &A2,
1, FLA_RIGHT );
FLA_Repart_2x1_to_3x1( BT, &B0,
/* ** */ /* *** */
&b1t,
BB, &B2, 1, FLA_BOTTOM );
/*------------------------------------------------------------*/
/* C = a1 * b1t + C */
FLA_Gerc_external( FLA_NO_CONJUGATE, FLA_CONJUGATE, alpha, a1, b1t, C );
/*------------------------------------------------------------*/
FLA_Cont_with_1x3_to_1x2( &AL, /**/ &AR, A0, a1, /**/ A2,
FLA_LEFT );
FLA_Cont_with_3x1_to_2x1( &BT, B0,
b1t,
/* ** */ /* *** */
&BB, B2, FLA_TOP );
}
return FLA_SUCCESS;
}
FLA_Error FLA_Gemm_ht_unb_var4( FLA_Obj alpha, FLA_Obj A, FLA_Obj B, FLA_Obj beta, FLA_Obj C )
{
FLA_Obj BT, B0,
BB, b1t,
B2;
FLA_Obj CL, CR, C0, c1, C2;
FLA_Scal_external( beta, C );
FLA_Part_2x1( B, &BT,
&BB, 0, FLA_BOTTOM );
FLA_Part_1x2( C, &CL, &CR, 0, FLA_RIGHT );
while ( FLA_Obj_length( BB ) < FLA_Obj_length( B ) ){
FLA_Repart_2x1_to_3x1( BT, &B0,
&b1t,
/* ** */ /* *** */
BB, &B2, 1, FLA_TOP );
FLA_Repart_1x2_to_1x3( CL, /**/ CR, &C0, &c1, /**/ &C2,
1, FLA_LEFT );
/*------------------------------------------------------------*/
/* c1 = A' * b1t' + c1 */
FLA_Gemv_external( FLA_CONJ_TRANSPOSE, alpha, A, b1t, FLA_ONE, c1 );
/*------------------------------------------------------------*/
FLA_Cont_with_3x1_to_2x1( &BT, B0,
/* ** */ /* *** */
b1t,
&BB, B2, FLA_BOTTOM );
FLA_Cont_with_1x3_to_1x2( &CL, /**/ &CR, C0, /**/ c1, C2,
FLA_RIGHT );
}
return FLA_SUCCESS;
}
FLA_Error FLA_Gemm_tt_unb_var5( FLA_Obj alpha, FLA_Obj A, FLA_Obj B, FLA_Obj beta, FLA_Obj C )
{
FLA_Obj AT, A0,
AB, a1t,
A2;
FLA_Obj BL, BR, B0, b1, B2;
FLA_Scal_external( beta, C );
FLA_Part_2x1( A, &AT,
&AB, 0, FLA_TOP );
FLA_Part_1x2( B, &BL, &BR, 0, FLA_LEFT );
while ( FLA_Obj_length( AT ) < FLA_Obj_length( A ) ){
FLA_Repart_2x1_to_3x1( AT, &A0,
/* ** */ /* *** */
&a1t,
AB, &A2, 1, FLA_BOTTOM );
FLA_Repart_1x2_to_1x3( BL, /**/ BR, &B0, /**/ &b1, &B2,
1, FLA_RIGHT );
/*------------------------------------------------------------*/
/* C = a1t' * b1' + C */
FLA_Ger_external( alpha, a1t, b1, C );
/*------------------------------------------------------------*/
FLA_Cont_with_3x1_to_2x1( &AT, A0,
a1t,
/* ** */ /* *** */
&AB, A2, FLA_TOP );
FLA_Cont_with_1x3_to_1x2( &BL, /**/ &BR, B0, b1, /**/ B2,
FLA_LEFT );
}
return FLA_SUCCESS;
}
int Gemm_unb_var1( FLA_Obj A, FLA_Obj B, FLA_Obj C )
{
FLA_Obj AL, AR, A0, a1, A2;
FLA_Obj BT, B0,
BB, b1t,
B2;
FLA_Part_1x2( A, &AL, &AR, 0, FLA_LEFT );
FLA_Part_2x1( B, &BT,
&BB, 0, FLA_TOP );
while ( FLA_Obj_width( AL ) < FLA_Obj_width( A ) ){
FLA_Repart_1x2_to_1x3( AL, /**/ AR, &A0, /**/ &a1, &A2,
1, FLA_RIGHT );
FLA_Repart_2x1_to_3x1( BT, &B0,
/* ** */ /* *** */
&b1t,
BB, &B2, 1, FLA_BOTTOM );
/*------------------------------------------------------------*/
FLA_Ger( FLA_ONE, a1, b1t, C );
/*------------------------------------------------------------*/
FLA_Cont_with_1x3_to_1x2( &AL, /**/ &AR, A0, a1, /**/ A2,
FLA_LEFT );
FLA_Cont_with_3x1_to_2x1( &BT, B0,
b1t,
/* ** */ /* *** */
&BB, B2, FLA_TOP );
}
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_Trsm_rlt_blk_var3_ht( FLA_Diag diagA, FLA_Obj alpha, FLA_Obj A, FLA_Obj B, FLA_Trsm_t* cntl )
{
FLA_Obj BT, B0,
BB, B1,
B2;
int b;
FLA_Part_2x1( B, &BT,
&BB, 0, FLA_TOP );
while ( FLA_Obj_length( BT ) < FLA_Obj_length( B ) ){
b = 1;
FLA_Repart_2x1_to_3x1( BT, &B0,
/* ** */ /* ** */
&B1,
BB, &B2, b, FLA_BOTTOM );
/*------------------------------------------------------------*/
/* B1 = B1 / tril( A'); */
FLA_Trsm_external( FLA_RIGHT, FLA_LOWER_TRIANGULAR, FLA_TRANSPOSE, diagA,
alpha, *FLASH_OBJ_PTR_AT( A ), *FLASH_OBJ_PTR_AT( B1 ),
NULL );
/*------------------------------------------------------------*/
FLA_Cont_with_3x1_to_2x1( &BT, B0,
B1,
/* ** */ /* ** */
&BB, B2, FLA_TOP );
}
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;
}
void fill_eigenvalues( FLA_Obj l )
{
FLA_Obj lT, l0,
lB, lambda1,
l2;
FLA_Obj alpha;
FLA_Obj_create( FLA_Obj_datatype( l ), 1, 1, 0, 0, &alpha );
FLA_Copy( FLA_ONE, alpha );
FLA_Part_2x1( l, &lT,
&lB, 0, FLA_TOP );
while ( FLA_Obj_length( lT ) < FLA_Obj_length( l ) ){
FLA_Repart_2x1_to_3x1( lT, &l0,
/* ** */ /* ******* */
&lambda1,
lB, &l2, 1, FLA_BOTTOM );
/*------------------------------------------------------------*/
FLA_Copy( alpha, lambda1 );
FLA_Mult_add( FLA_ONE, FLA_ONE, alpha );
/*------------------------------------------------------------*/
FLA_Cont_with_3x1_to_2x1( &lT, l0,
lambda1,
/* ** */ /* ******* */
&lB, l2, FLA_TOP );
}
FLA_Obj_free( &alpha );
}
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;
}
int Symm_ll1_unb_var2( FLA_Obj A, FLA_Obj B, FLA_Obj C )
{
FLA_Obj ATL, ATR, A00, a01, A02,
ABL, ABR, a10t, alpha11, a12t,
A20, a21, A22;
FLA_Obj BT, B0,
BB, b1t,
B2;
FLA_Obj CT, C0,
CB, c1t,
C2;
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 ) ){
FLA_Repart_2x2_to_3x3( ATL, /**/ ATR, &A00, /**/ &a01, &A02,
/* ************* */ /* ************************** */
&a10t, /**/ &alpha11, &a12t,
ABL, /**/ ABR, &A20, /**/ &a21, &A22,
1, 1, FLA_BR );
FLA_Repart_2x1_to_3x1( BT, &B0,
/* ** */ /* *** */
&b1t,
BB, &B2, 1, FLA_BOTTOM );
FLA_Repart_2x1_to_3x1( CT, &C0,
/* ** */ /* *** */
&c1t,
CB, &C2, 1, FLA_BOTTOM );
/*------------------------------------------------------------*/
C0 = C0 + FLA_Transpose(A20T)*B2;
c1t = c1t - a10t*B0 - alpha11*b1t;
/* update line 1 */
/* : */
/* update line n */
/*------------------------------------------------------------*/
FLA_Cont_with_3x3_to_2x2( &ATL, /**/ &ATR, A00, a01, /**/ A02,
a10t, alpha11, /**/ a12t,
/* ************** */ /* ************************ */
&ABL, /**/ &ABR, A20, a21, /**/ A22,
FLA_TL );
FLA_Cont_with_3x1_to_2x1( &BT, B0,
b1t,
/* ** */ /* *** */
&BB, B2, FLA_TOP );
FLA_Cont_with_3x1_to_2x1( &CT, C0,
c1t,
/* ** */ /* *** */
&CB, C2, FLA_TOP );
}
return FLA_SUCCESS;
}
FLA_Error FLA_Apply_Q_UT_lhfr_blk_var1( FLA_Obj A, FLA_Obj T, FLA_Obj W, FLA_Obj B, fla_apqut_t* cntl )
{
/*
Apply the conjugate-transpose of a unitary matrix Q to a matrix B from the
left,
B := Q' B
where Q is the forward product of Householder transformations:
Q = H(0) H(1) ... H(k-1)
where H(i) corresponds to the Householder vector stored above the diagonal
in the ith row of A. Thus, the operation becomes:
B := Q' B
= ( H(0) H(1) ... H(k-1) )' B
= H(k-1)' ... H(1)' H(0)' B
From this, we can see that we must move through A from top-left to bottom-
right, since the Householder vector for H(0) was stored in the first row
of A. We intend to apply blocks of reflectors at a time, where a block
reflector H of b consecutive Householder transforms may be expressed as:
H = ( H(i) H(i+1) ... H(i+b-1) )'
= ( I - U inv(T) U' )'
where:
- U^T is the strictly upper trapezoidal (with implicit unit diagonal) matrix
of Householder vectors, stored above the diagonal of A in rows i through
i+b-1, corresponding to H(i) through H(i+b-1).
- T is the upper triangular block Householder matrix corresponding to
Householder vectors i through i+b-1.
Consider applying H to B as an intermediate step towards applying all of Q':
B := H B
= ( I - U inv(T) U' )' B
= ( I - U inv(T)' U' ) B
= B - U inv(T)' U' B
We must move from top-left to bottom-right. So, we partition:
U^T -> ( U11 U12 ) B -> / B1 \ T -> ( T1 T2 )
\ B2 /
where:
- U11 is stored in the strictly upper triangle of A11 with implicit unit
diagonal.
- U12 is stored in A12.
- T1 is an upper triangular block of row-panel matrix T.
Substituting repartitioned U, B, and T, we have:
/ B1 \ := / B1 \ - ( U11 U12 )^T inv(T1)' conj( U11 U12 ) / B1 \
\ B2 / \ B2 / \ B2 /
= / B1 \ - / U11^T \ inv(T1)' conj( U11 U12 ) / B1 \
\ B2 / \ U12^T / \ B2 /
= / B1 \ - / U11^T \ inv(T1)' ( conj(U11) B1 + conj(U12) B2 )
\ B2 / \ U12^T /
Thus, B1 is updated as:
B1 := B1 - U11^T inv(T1)' ( conj(U11) B1 + conj(U12) B2 )
And B2 is updated as:
B2 := B2 - U12^T inv(T1)' ( conj(U11) B1 + conj(U12) B2 )
Note that:
inv(T1)' ( conj(U11) B1 + conj(U12) B2 )
is common to both updates, and thus may be computed and stored in
workspace, and then re-used.
-FGVZ
*/
FLA_Obj ATL, ATR, A00, A01, A02,
ABL, ABR, A10, A11, A12,
A20, A21, A22;
FLA_Obj TL, TR, T0, T1, T2;
FLA_Obj T1T,
T2B;
FLA_Obj WTL, WTR,
WBL, WBR;
FLA_Obj BT, B0,
BB, B1,
B2;
dim_t b_alg, b;
// Query the algorithmic blocksize by inspecting the length of T.
b_alg = FLA_Obj_length( T );
FLA_Part_2x2( A, &ATL, &ATR,
&ABL, &ABR, 0, 0, FLA_TL );
FLA_Part_1x2( T, &TL, &TR, 0, FLA_LEFT );
FLA_Part_2x1( B, &BT,
&BB, 0, FLA_TOP );
while ( FLA_Obj_min_dim( ABR ) > 0 ){
b = min( b_alg, FLA_Obj_min_dim( ABR ) );
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( TL, /**/ TR, &T0, /**/ &T1, &T2,
b, FLA_RIGHT );
FLA_Repart_2x1_to_3x1( BT, &B0,
/* ** */ /* ** */
&B1,
BB, &B2, b, FLA_BOTTOM );
/*------------------------------------------------------------*/
FLA_Part_2x1( T1, &T1T,
&T2B, b, FLA_TOP );
FLA_Part_2x2( W, &WTL, &WTR,
&WBL, &WBR, b, FLA_Obj_width( B1 ), FLA_TL );
// WTL = B1;
FLA_Copyt_internal( FLA_NO_TRANSPOSE, B1, WTL,
FLA_Cntl_sub_copyt( cntl ) );
// U11 = triuu( A11 );
// U12 = A12;
//
// WTL = inv( triu(T1T) )' * ( conj(U11) * B1 + conj(U12) * B2 );
FLA_Trmm_internal( FLA_LEFT, FLA_UPPER_TRIANGULAR,
FLA_CONJ_NO_TRANSPOSE, FLA_UNIT_DIAG,
FLA_ONE, A11, WTL,
FLA_Cntl_sub_trmm1( cntl ) );
FLA_Gemm_internal( FLA_CONJ_NO_TRANSPOSE, FLA_NO_TRANSPOSE,
FLA_ONE, A12, B2, FLA_ONE, WTL,
FLA_Cntl_sub_gemm1( cntl ) );
FLA_Trsm_internal( FLA_LEFT, FLA_UPPER_TRIANGULAR,
FLA_CONJ_TRANSPOSE, FLA_NONUNIT_DIAG,
FLA_ONE, T1T, WTL,
FLA_Cntl_sub_trsm( cntl ) );
// B2 = B2 - U12^T * WTL;
// B1 = B1 - U11^T * WTL;
FLA_Gemm_internal( FLA_TRANSPOSE, FLA_NO_TRANSPOSE,
FLA_MINUS_ONE, A12, WTL, FLA_ONE, B2,
FLA_Cntl_sub_gemm2( cntl ) );
FLA_Trmm_internal( FLA_LEFT, FLA_UPPER_TRIANGULAR,
FLA_TRANSPOSE, FLA_UNIT_DIAG,
FLA_MINUS_ONE, A11, WTL,
FLA_Cntl_sub_trmm2( cntl ) );
FLA_Axpyt_internal( FLA_NO_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_1x3_to_1x2( &TL, /**/ &TR, T0, T1, /**/ T2,
FLA_LEFT );
FLA_Cont_with_3x1_to_2x1( &BT, B0,
B1,
/* ** */ /* ** */
&BB, B2, FLA_TOP );
}
return FLA_SUCCESS;
}
FLA_Error FLA_Syr2k_ln_unb_var4( FLA_Obj alpha, FLA_Obj A, FLA_Obj B, FLA_Obj beta, FLA_Obj C )
{
FLA_Obj AT, A0,
AB, a1t,
A2;
FLA_Obj BT, B0,
BB, b1t,
B2;
FLA_Obj CTL, CTR, C00, c01, C02,
CBL, CBR, c10t, gamma11, c12t,
C20, c21, C22;
FLA_Scalr_external( FLA_LOWER_TRIANGULAR, beta, C );
FLA_Part_2x1( A, &AT,
&AB, 0, FLA_TOP );
FLA_Part_2x1( B, &BT,
&BB, 0, FLA_TOP );
FLA_Part_2x2( C, &CTL, &CTR,
&CBL, &CBR, 0, 0, FLA_TL );
while ( FLA_Obj_length( AT ) < FLA_Obj_length( A ) ){
FLA_Repart_2x1_to_3x1( AT, &A0,
/* ** */ /* ** */
&a1t,
AB, &A2, 1, FLA_BOTTOM );
FLA_Repart_2x1_to_3x1( BT, &B0,
/* ** */ /* ** */
&b1t,
BB, &B2, 1, FLA_BOTTOM );
FLA_Repart_2x2_to_3x3( CTL, /**/ CTR, &C00, /**/ &c01, &C02,
/* ************* */ /* ************************** */
&c10t, /**/ &gamma11, &c12t,
CBL, /**/ CBR, &C20, /**/ &c21, &C22,
1, 1, FLA_BR );
/*------------------------------------------------------------*/
/* c21 = c21 + A2 * b1t' */
FLA_Gemv_external( FLA_NO_TRANSPOSE, alpha, A2, b1t, FLA_ONE, c21 );
/* c21 = c21 + B2 * a1t' */
FLA_Gemv_external( FLA_NO_TRANSPOSE, alpha, B2, a1t, FLA_ONE, c21 );
/* gamma11 = gamma11 + a1t * b1t' + b1t * a1t' */
FLA_Dot2s_external( alpha, a1t, b1t, FLA_ONE, gamma11 );
/*------------------------------------------------------------*/
FLA_Cont_with_3x1_to_2x1( &AT, A0,
a1t,
/* ** */ /* ** */
&AB, A2, FLA_TOP );
FLA_Cont_with_3x1_to_2x1( &BT, B0,
b1t,
/* ** */ /* ** */
&BB, B2, FLA_TOP );
FLA_Cont_with_3x3_to_2x2( &CTL, /**/ &CTR, C00, c01, /**/ C02,
c10t, gamma11, /**/ c12t,
/* ************** */ /* ************************ */
&CBL, /**/ &CBR, C20, c21, /**/ C22,
FLA_TL );
}
return FLA_SUCCESS;
}
FLA_Error FLA_Svd_uv_unb_var1( dim_t n_iter_max, FLA_Obj A, FLA_Obj s, FLA_Obj U, FLA_Obj V, dim_t k_accum, dim_t b_alg )
{
FLA_Error r_val = FLA_SUCCESS;
FLA_Datatype dt;
FLA_Datatype dt_real;
FLA_Datatype dt_comp;
FLA_Obj scale, T, S, rL, rR, d, e, G, H;
dim_t m_A, n_A;
dim_t min_m_n;
dim_t n_GH;
double crossover_ratio = 17.0 / 9.0;
n_GH = k_accum;
m_A = FLA_Obj_length( A );
n_A = FLA_Obj_width( A );
min_m_n = FLA_Obj_min_dim( A );
dt = FLA_Obj_datatype( A );
dt_real = FLA_Obj_datatype_proj_to_real( A );
dt_comp = FLA_Obj_datatype_proj_to_complex( A );
// Create matrices to hold block Householder transformations.
FLA_Bidiag_UT_create_T( A, &T, &S );
// Create vectors to hold the realifying scalars.
FLA_Obj_create( dt, min_m_n, 1, 0, 0, &rL );
FLA_Obj_create( dt, min_m_n, 1, 0, 0, &rR );
// Create vectors to hold the diagonal and sub-diagonal.
FLA_Obj_create( dt_real, min_m_n, 1, 0, 0, &d );
FLA_Obj_create( dt_real, min_m_n-1, 1, 0, 0, &e );
// Create matrices to hold the left and right Givens scalars.
FLA_Obj_create( dt_comp, min_m_n-1, n_GH, 0, 0, &G );
FLA_Obj_create( dt_comp, min_m_n-1, n_GH, 0, 0, &H );
// Create a real scaling factor.
FLA_Obj_create( dt_real, 1, 1, 0, 0, &scale );
// Compute a scaling factor; If none is needed, sigma will be set to one.
FLA_Svd_compute_scaling( A, scale );
// Scale the matrix if scale is non-unit.
if ( !FLA_Obj_equals( scale, FLA_ONE ) )
FLA_Scal( scale, A );
if ( m_A < crossover_ratio * n_A )
{
// Reduce the matrix to bidiagonal form.
// Apply scalars to rotate elements on the superdiagonal to the real domain.
// Extract the diagonal and superdiagonal from A.
FLA_Bidiag_UT( A, T, S );
FLA_Bidiag_UT_realify( A, rL, rR );
FLA_Bidiag_UT_extract_real_diagonals( A, d, e );
// Form U and V.
FLA_Bidiag_UT_form_U( A, T, U );
FLA_Bidiag_UT_form_V( A, S, V );
// Apply the realifying scalars in rL and rR to U and V, respectively.
{
FLA_Obj UL, UR;
FLA_Obj VL, VR;
FLA_Part_1x2( U, &UL, &UR, min_m_n, FLA_LEFT );
FLA_Part_1x2( V, &VL, &VR, min_m_n, FLA_LEFT );
FLA_Apply_diag_matrix( FLA_RIGHT, FLA_CONJUGATE, rL, UL );
FLA_Apply_diag_matrix( FLA_RIGHT, FLA_NO_CONJUGATE, rR, VL );
}
// Perform a singular value decomposition on the bidiagonal matrix.
r_val = FLA_Bsvd_v_opt_var1( n_iter_max, d, e, G, H, U, V, b_alg );
}
else // if ( crossover_ratio * n_A <= m_A )
{
FLA_Obj TQ, R;
FLA_Obj AT,
AB;
FLA_Obj UL, UR;
// Perform a QR factorization on A and form Q in U.
FLA_QR_UT_create_T( A, &TQ );
FLA_QR_UT( A, TQ );
FLA_QR_UT_form_Q( A, TQ, U );
FLA_Obj_free( &TQ );
// Set the lower triangle of R to zero and then copy the upper
// triangle of A to R.
FLA_Part_2x1( A, &AT,
&AB, n_A, FLA_TOP );
FLA_Obj_create( dt, n_A, n_A, 0, 0, &R );
FLA_Setr( FLA_LOWER_TRIANGULAR, FLA_ZERO, R );
FLA_Copyr( FLA_UPPER_TRIANGULAR, AT, R );
// Reduce the matrix to bidiagonal form.
// Apply scalars to rotate elements on the superdiagonal to the real domain.
// Extract the diagonal and superdiagonal from A.
FLA_Bidiag_UT( R, T, S );
FLA_Bidiag_UT_realify( R, rL, rR );
FLA_Bidiag_UT_extract_real_diagonals( R, d, e );
// Form V from right Householder vectors in upper triangle of R.
FLA_Bidiag_UT_form_V( R, S, V );
// Form U in R.
FLA_Bidiag_UT_form_U( R, T, R );
// Apply the realifying scalars in rL and rR to U and V, respectively.
FLA_Apply_diag_matrix( FLA_RIGHT, FLA_CONJUGATE, rL, R );
FLA_Apply_diag_matrix( FLA_RIGHT, FLA_NO_CONJUGATE, rR, V );
// Perform a singular value decomposition on the bidiagonal matrix.
r_val = FLA_Bsvd_v_opt_var1( n_iter_max, d, e, G, H, R, V, b_alg );
// Multiply R into U, storing the result in A and then copying back
// to U.
FLA_Part_1x2( U, &UL, &UR, n_A, FLA_LEFT );
FLA_Gemm( FLA_NO_TRANSPOSE, FLA_NO_TRANSPOSE,
FLA_ONE, UL, R, FLA_ZERO, A );
FLA_Copy( A, UL );
FLA_Obj_free( &R );
}
// Copy the converged eigenvalues to the output vector.
FLA_Copy( d, s );
// Sort the singular values and singular vectors in descending order.
FLA_Sort_svd( FLA_BACKWARD, s, U, V );
// If the matrix was scaled, rescale the singular values.
if ( !FLA_Obj_equals( scale, FLA_ONE ) )
FLA_Inv_scal( scale, s );
FLA_Obj_free( &scale );
FLA_Obj_free( &T );
FLA_Obj_free( &S );
FLA_Obj_free( &rL );
FLA_Obj_free( &rR );
FLA_Obj_free( &d );
FLA_Obj_free( &e );
FLA_Obj_free( &G );
FLA_Obj_free( &H );
return r_val;
}
FLA_Error FLA_Apply_Q_UT_lnfc_blk_var1( FLA_Obj A, FLA_Obj T, FLA_Obj W, FLA_Obj B, fla_apqut_t* cntl )
/*
Apply a unitary matrix Q to a matrix B from the left,
B := Q B
where Q is the forward product of Householder transformations:
Q = H(0) H(1) ... H(k-1)
where H(i) corresponds to the Householder vector stored below the diagonal
in the ith column of A. Thus, the operation becomes:
B := Q B
= H(0) H(1) ... H(k-1) B
From this, we can see that we must move through A from bottom-right to top-
left, since the Householder vector for H(k-1) was stored in the last column
of A. We intend to apply blocks of reflectors at a time, where a block
reflector H of b consecutive Householder transforms may be expressed as:
H = ( H(i) H(i+1) ... H(i+b-1) )
= ( I - U inv(T) U' )
where:
- U is the strictly lower trapezoidal (with implicit unit diagonal) matrix
of Householder vectors, stored below the diagonal of A in columns i through
i+b-1, corresponding to H(i) through H(i+b-1).
- T is the upper triangular block Householder matrix corresponding to
Householder vectors i through i+b-1.
Consider applying H to B as an intermediate step towards applying all of Q:
B := H B
= ( I - U inv(T) U' ) B
= B - U inv(T) U' B
We must move from bottom-right to top-left. So, we partition:
U -> / U11 \ B -> / B1 \ T -> ( T2 T1 )
\ U21 / \ B2 /
where:
- U11 is stored in strictly lower triangle of A11 with implicit unit
diagonal.
- U21 is stored in A21.
- T1 is an upper triangular block of row-panel matrix T.
Substituting repartitioned U, B, and T, we have:
/ B1 \ := / B1 \ - / U11 \ inv(T1) / U11 \' / B1 \
\ B2 / \ B2 / \ U21 / \ U21 / \ B2 /
= / B1 \ - / U11 \ inv(T1) ( U11' U21' ) / B1 \
\ B2 / \ U21 / \ B2 /
= / B1 \ - / U11 \ inv(T1) ( U11' B1 + U21' B2 )
\ B2 / \ U21 /
Thus, B1 is updated as:
B1 := B1 - U11 inv(T1) ( U11' B1 + U21' B2 )
And B2 is updated as:
B2 := B2 - U21 inv(T1) ( U11' B1 + U21' B2 )
Note that:
inv(T1) ( U11' B1 + U21' B2 )
is common to both updates, and thus may be computed and stored in
workspace, and then re-used.
-FGVZ
*/
{
FLA_Obj ATL, ATR, A00, A01, A02,
ABL, ABR, A10, A11, A12,
A20, A21, A22;
FLA_Obj TL, TR, T0, T1, T2;
FLA_Obj T1T,
T2B;
FLA_Obj WTL, WTR,
WBL, WBR;
FLA_Obj BT, B0,
BB, B1,
B2;
dim_t b_alg, b;
dim_t m_BR, n_BR;
// Query the algorithmic blocksize by inspecting the length of T.
b_alg = FLA_Obj_length( T );
// If m > n, then we have to initialize our partitionings carefully so
// that we begin in the proper location in A and B (since we traverse
// matrix A from BR to TL).
if ( FLA_Obj_length( A ) > FLA_Obj_width( A ) )
{
m_BR = FLA_Obj_length( A ) - FLA_Obj_width( A );
n_BR = 0;
}
else if ( FLA_Obj_length( A ) < FLA_Obj_width( A ) )
{
m_BR = 0;
n_BR = FLA_Obj_width( A ) - FLA_Obj_length( A );
}
else
{
m_BR = 0;
n_BR = 0;
}
FLA_Part_2x2( A, &ATL, &ATR,
&ABL, &ABR, m_BR, n_BR, FLA_BR );
// A and T are dependent; we determine T matrix w.r.t. A
FLA_Part_1x2( T, &TL, &TR, FLA_Obj_min_dim( A ), FLA_LEFT );
FLA_Part_2x1( B, &BT,
&BB, m_BR, FLA_BOTTOM );
while ( FLA_Obj_min_dim( ATL ) > 0 ){
b = min( b_alg, FLA_Obj_min_dim( ATL ) );
// Since T was filled from left to right, and since we need to access them
// in reverse order, we need to handle the case where the last block is
// smaller than the other b x b blocks.
if ( FLA_Obj_width( TR ) == 0 && FLA_Obj_width( T ) % b_alg > 0 )
b = FLA_Obj_width( T ) % b_alg;
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( TL, /**/ TR, &T0, &T1, /**/ &T2,
b, FLA_LEFT );
FLA_Repart_2x1_to_3x1( BT, &B0,
&B1,
/* ** */ /* ** */
BB, &B2, b, FLA_TOP );
/*------------------------------------------------------------*/
FLA_Part_2x1( T1, &T1T,
&T2B, b, FLA_TOP );
FLA_Part_2x2( W, &WTL, &WTR,
&WBL, &WBR, b, FLA_Obj_width( B1 ), FLA_TL );
// WTL = B1;
FLA_Copyt_internal( FLA_NO_TRANSPOSE, B1, WTL,
FLA_Cntl_sub_copyt( cntl ) );
// U11 = trilu( A11 );
// U21 = A21;
//
// WTL = inv( triu(T1T) ) * ( U11' * B1 + U21' * B2 );
FLA_Trmm_internal( FLA_LEFT, FLA_LOWER_TRIANGULAR,
FLA_CONJ_TRANSPOSE, FLA_UNIT_DIAG,
FLA_ONE, A11, WTL,
FLA_Cntl_sub_trmm1( cntl ) );
FLA_Gemm_internal( FLA_CONJ_TRANSPOSE, FLA_NO_TRANSPOSE,
FLA_ONE, A21, B2, FLA_ONE, WTL,
FLA_Cntl_sub_gemm1( cntl ) );
FLA_Trsm_internal( FLA_LEFT, FLA_UPPER_TRIANGULAR,
FLA_NO_TRANSPOSE, FLA_NONUNIT_DIAG,
FLA_ONE, T1T, WTL,
FLA_Cntl_sub_trsm( cntl ) );
// B2 = B2 - U21 * WTL;
// B1 = B1 - U11 * WTL;
FLA_Gemm_internal( FLA_NO_TRANSPOSE, FLA_NO_TRANSPOSE,
FLA_MINUS_ONE, A21, WTL, FLA_ONE, B2,
FLA_Cntl_sub_gemm2( cntl ) );
FLA_Trmm_internal( FLA_LEFT, FLA_LOWER_TRIANGULAR,
FLA_NO_TRANSPOSE, FLA_UNIT_DIAG,
FLA_MINUS_ONE, A11, WTL,
FLA_Cntl_sub_trmm2( cntl ) );
FLA_Axpyt_internal( FLA_NO_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_BR );
FLA_Cont_with_1x3_to_1x2( &TL, /**/ &TR, T0, /**/ T1, T2,
FLA_RIGHT );
FLA_Cont_with_3x1_to_2x1( &BT, B0,
/* ** */ /* ** */
B1,
&BB, B2, FLA_BOTTOM );
}
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;
}
void time_QR_UT(
int variant, int type, int nrepeats, int m, int n,
FLA_Obj A, FLA_Obj A_ref, FLA_Obj t, FLA_Obj T, FLA_Obj W, FLA_Obj b, FLA_Obj b_orig,
double *dtime, double *diff, double *gflops )
{
int
irep;
double
dtime_old = 1.0e9;
FLA_Obj
A_save, b_save, norm;
FLA_Obj_create_conf_to( FLA_NO_TRANSPOSE, A, &A_save );
FLA_Obj_create_conf_to( FLA_NO_TRANSPOSE, b, &b_save );
if ( FLA_Obj_is_single_precision( A ) )
FLA_Obj_create( FLA_FLOAT, 1, 1, 0, 0, &norm );
else
FLA_Obj_create( FLA_DOUBLE, 1, 1, 0, 0, &norm );
FLA_Copy_external( A, A_save );
FLA_Copy_external( b, b_save );
for ( irep = 0 ; irep < nrepeats; irep++ ){
FLA_Copy_external( A_save, A );
*dtime = FLA_Clock();
switch( variant ){
case 0:{
switch( type ){
case FLA_ALG_REFERENCE:
REF_QR_UT( A, t );
break;
case FLA_ALG_FRONT:
FLA_QR_UT( A, T );
break;
default:
printf("trouble\n");
}
break;
}
}
*dtime = FLA_Clock() - *dtime;
dtime_old = min( *dtime, dtime_old );
}
if ( type == FLA_ALG_REFERENCE )
{
FLA_Obj AT, AB;
FLA_Obj bT, bB;
FLA_Obj y;
FLA_Obj_create( FLA_Obj_datatype( b ), n, 1, 0, 0, &y );
FLA_Copy_external( b, b_orig );
if ( FLA_Obj_is_real( A ) )
FLA_Apply_Q_blk_external( FLA_LEFT, FLA_TRANSPOSE, FLA_COLUMNWISE, A, t, b );
else
FLA_Apply_Q_blk_external( FLA_LEFT, FLA_CONJ_TRANSPOSE, FLA_COLUMNWISE, A, t, b );
FLA_Part_2x1( A, &AT,
&AB, FLA_Obj_width( A ), FLA_TOP );
FLA_Part_2x1( b, &bT,
&bB, FLA_Obj_width( A ), FLA_TOP );
FLA_Trsm_external( FLA_LEFT, FLA_UPPER_TRIANGULAR, FLA_NO_TRANSPOSE,
FLA_NONUNIT_DIAG, FLA_ONE, AT, bT );
FLA_Gemv_external( FLA_NO_TRANSPOSE, FLA_MINUS_ONE, A_save, bT, FLA_ONE, b_orig );
FLA_Gemv_external( FLA_CONJ_TRANSPOSE, FLA_ONE, A_save, b_orig, FLA_ZERO, y );
FLA_Nrm2_external( y, norm );
FLA_Obj_extract_real_scalar( norm, diff );
FLA_Obj_free( &y );
}
else
{
FLA_Obj x, y;
FLA_Obj_create( FLA_Obj_datatype( b ), n, 1, 0, 0, &y );
FLA_Obj_create( FLA_Obj_datatype( b ), n, 1, 0, 0, &x );
FLA_Copy_external( b, b_orig );
FLA_QR_UT_solve( A, T, b, x );
FLA_Gemv_external( FLA_NO_TRANSPOSE, FLA_MINUS_ONE, A_save, x, FLA_ONE, b_orig );
FLA_Gemv_external( FLA_CONJ_TRANSPOSE, FLA_ONE, A_save, b_orig, FLA_ZERO, y );
FLA_Nrm2_external( y, norm );
FLA_Obj_extract_real_scalar( norm, diff );
FLA_Obj_free( &x );
FLA_Obj_free( &y );
}
*gflops = ( 2.0 * m * n * n -
( 2.0 / 3.0 ) * n * n * n ) /
dtime_old / 1e9;
if ( FLA_Obj_is_complex( A ) )
*gflops *= 4.0;
*dtime = dtime_old;
FLA_Copy_external( A_save, A );
FLA_Copy_external( b_save, b );
FLA_Obj_free( &A_save );
FLA_Obj_free( &b_save );
FLA_Obj_free( &norm );
}
FLA_Error FLA_Eig_gest_nl_opt_var5( FLA_Obj A, FLA_Obj Y, FLA_Obj B )
{
FLA_Datatype datatype;
int m_AB;
int rs_A, cs_A;
int rs_B, cs_B;
int inc_y;
FLA_Obj yT, yB;
datatype = FLA_Obj_datatype( A );
m_AB = FLA_Obj_length( A );
rs_A = FLA_Obj_row_stride( A );
cs_A = FLA_Obj_col_stride( A );
rs_B = FLA_Obj_row_stride( B );
cs_B = FLA_Obj_col_stride( B );
FLA_Part_2x1( Y, &yT,
&yB, 1, FLA_TOP );
inc_y = FLA_Obj_vector_inc( yT );
switch ( datatype )
{
case FLA_FLOAT:
{
float* buff_A = FLA_FLOAT_PTR( A );
float* buff_y = FLA_FLOAT_PTR( yT );
float* buff_B = FLA_FLOAT_PTR( B );
FLA_Eig_gest_nl_ops_var5( m_AB,
buff_A, rs_A, cs_A,
buff_y, inc_y,
buff_B, rs_B, cs_B );
break;
}
case FLA_DOUBLE:
{
double* buff_A = FLA_DOUBLE_PTR( A );
double* buff_y = FLA_DOUBLE_PTR( yT );
double* buff_B = FLA_DOUBLE_PTR( B );
FLA_Eig_gest_nl_opd_var5( m_AB,
buff_A, rs_A, cs_A,
buff_y, inc_y,
buff_B, rs_B, cs_B );
break;
}
case FLA_COMPLEX:
{
scomplex* buff_A = FLA_COMPLEX_PTR( A );
scomplex* buff_y = FLA_COMPLEX_PTR( yT );
scomplex* buff_B = FLA_COMPLEX_PTR( B );
FLA_Eig_gest_nl_opc_var5( m_AB,
buff_A, rs_A, cs_A,
buff_y, inc_y,
buff_B, rs_B, cs_B );
break;
}
case FLA_DOUBLE_COMPLEX:
{
dcomplex* buff_A = FLA_DOUBLE_COMPLEX_PTR( A );
dcomplex* buff_y = FLA_DOUBLE_COMPLEX_PTR( yT );
dcomplex* buff_B = FLA_DOUBLE_COMPLEX_PTR( B );
FLA_Eig_gest_nl_opz_var5( m_AB,
buff_A, rs_A, cs_A,
buff_y, inc_y,
buff_B, rs_B, cs_B );
break;
}
}
return FLA_SUCCESS;
}
FLA_Error FLA_Svd_uv_var2_components( dim_t n_iter_max, dim_t k_accum, dim_t b_alg,
FLA_Obj A, FLA_Obj s, FLA_Obj U, FLA_Obj V,
double* dtime_bred, double* dtime_bsvd, double* dtime_appq,
double* dtime_qrfa, double* dtime_gemm )
{
FLA_Error r_val = FLA_SUCCESS;
FLA_Datatype dt;
FLA_Datatype dt_real;
FLA_Datatype dt_comp;
FLA_Obj T, S, rL, rR, d, e, G, H, RG, RH, W;
dim_t m_A, n_A;
dim_t min_m_n;
dim_t n_GH;
double crossover_ratio = 17.0 / 9.0;
double dtime_temp;
n_GH = k_accum;
m_A = FLA_Obj_length( A );
n_A = FLA_Obj_width( A );
min_m_n = FLA_Obj_min_dim( A );
dt = FLA_Obj_datatype( A );
dt_real = FLA_Obj_datatype_proj_to_real( A );
dt_comp = FLA_Obj_datatype_proj_to_complex( A );
// If the matrix is a scalar, then the SVD is easy.
if ( min_m_n == 1 )
{
FLA_Copy( A, s );
FLA_Set_to_identity( U );
FLA_Set_to_identity( V );
return FLA_SUCCESS;
}
// Create matrices to hold block Householder transformations.
FLA_Bidiag_UT_create_T( A, &T, &S );
// Create vectors to hold the realifying scalars.
FLA_Obj_create( dt, min_m_n, 1, 0, 0, &rL );
FLA_Obj_create( dt, min_m_n, 1, 0, 0, &rR );
// Create vectors to hold the diagonal and sub-diagonal.
FLA_Obj_create( dt_real, min_m_n, 1, 0, 0, &d );
FLA_Obj_create( dt_real, min_m_n-1, 1, 0, 0, &e );
// Create matrices to hold the left and right Givens scalars.
FLA_Obj_create( dt_comp, min_m_n-1, n_GH, 0, 0, &G );
FLA_Obj_create( dt_comp, min_m_n-1, n_GH, 0, 0, &H );
// Create matrices to hold the left and right Givens matrices.
FLA_Obj_create( dt_real, min_m_n, min_m_n, 0, 0, &RG );
FLA_Obj_create( dt_real, min_m_n, min_m_n, 0, 0, &RH );
FLA_Obj_create( dt, m_A, n_A, 0, 0, &W );
if ( m_A >= n_A )
{
if ( m_A < crossover_ratio * n_A )
{
dtime_temp = FLA_Clock();
{
// Reduce the matrix to bidiagonal form.
// Apply scalars to rotate elements on the sub-diagonal to the real domain.
// Extract the diagonal and sub-diagonal from A.
FLA_Bidiag_UT( A, T, S );
FLA_Bidiag_UT_realify( A, rL, rR );
FLA_Bidiag_UT_extract_diagonals( A, d, e );
}
*dtime_bred = FLA_Clock() - dtime_temp;
dtime_temp = FLA_Clock();
{
// Form U and V.
FLA_Bidiag_UT_form_U( A, T, U );
FLA_Bidiag_UT_form_V( A, S, V );
}
*dtime_appq = FLA_Clock() - dtime_temp;
// Apply the realifying scalars in rL and rR to U and V, respectively.
{
FLA_Obj UL, UR;
FLA_Obj VL, VR;
FLA_Part_1x2( U, &UL, &UR, min_m_n, FLA_LEFT );
FLA_Part_1x2( V, &VL, &VR, min_m_n, FLA_LEFT );
FLA_Apply_diag_matrix( FLA_RIGHT, FLA_CONJUGATE, rL, UL );
FLA_Apply_diag_matrix( FLA_RIGHT, FLA_NO_CONJUGATE, rR, VL );
}
dtime_temp = FLA_Clock();
{
// Perform a singular value decomposition on the bidiagonal matrix.
r_val = FLA_Bsvd_v_opt_var2( n_iter_max, d, e, G, H, RG, RH, W, U, V, b_alg );
}
*dtime_bsvd = FLA_Clock() - dtime_temp;
}
else // if ( crossover_ratio * n_A <= m_A )
{
FLA_Obj TQ, R;
FLA_Obj AT,
AB;
FLA_Obj UL, UR;
//FLA_QR_UT_create_T( A, &TQ );
FLA_Obj_create( dt, 32, n_A, 0, 0, &TQ );
dtime_temp = FLA_Clock();
{
// Perform a QR factorization on A and form Q in U.
FLA_QR_UT( A, TQ );
}
*dtime_qrfa = FLA_Clock() - dtime_temp;
dtime_temp = FLA_Clock();
{
FLA_QR_UT_form_Q( A, TQ, U );
}
*dtime_appq = FLA_Clock() - dtime_temp;
FLA_Obj_free( &TQ );
// Set the lower triangle of R to zero and then copy the upper
// triangle of A to R.
FLA_Part_2x1( A, &AT,
&AB, n_A, FLA_TOP );
FLA_Obj_create( dt, n_A, n_A, 0, 0, &R );
FLA_Setr( FLA_LOWER_TRIANGULAR, FLA_ZERO, R );
FLA_Copyr( FLA_UPPER_TRIANGULAR, AT, R );
dtime_temp = FLA_Clock();
{
// Reduce the matrix to bidiagonal form.
// Apply scalars to rotate elements on the superdiagonal to the real domain.
// Extract the diagonal and superdiagonal from A.
FLA_Bidiag_UT( R, T, S );
FLA_Bidiag_UT_realify( R, rL, rR );
FLA_Bidiag_UT_extract_diagonals( R, d, e );
}
*dtime_bred = FLA_Clock() - dtime_temp;
dtime_temp = FLA_Clock();
{
// Form V from right Householder vectors in upper triangle of R.
FLA_Bidiag_UT_form_V( R, S, V );
// Form U in R.
FLA_Bidiag_UT_form_U( R, T, R );
}
*dtime_appq += FLA_Clock() - dtime_temp;
// Apply the realifying scalars in rL and rR to U and V, respectively.
FLA_Apply_diag_matrix( FLA_RIGHT, FLA_CONJUGATE, rL, R );
FLA_Apply_diag_matrix( FLA_RIGHT, FLA_NO_CONJUGATE, rR, V );
dtime_temp = FLA_Clock();
{
// Perform a singular value decomposition on the bidiagonal matrix.
r_val = FLA_Bsvd_v_opt_var2( n_iter_max, d, e, G, H, RG, RH, W, R, V, b_alg );
}
*dtime_bsvd = FLA_Clock() - dtime_temp;
dtime_temp = FLA_Clock();
{
// Multiply R into U, storing the result in A and then copying back
// to U.
FLA_Part_1x2( U, &UL, &UR, n_A, FLA_LEFT );
FLA_Gemm( FLA_NO_TRANSPOSE, FLA_NO_TRANSPOSE,
FLA_ONE, UL, R, FLA_ZERO, A );
FLA_Copy( A, UL );
}
*dtime_gemm = FLA_Clock() - dtime_temp;
FLA_Obj_free( &R );
}
}
else // if ( m_A < n_A )
{
FLA_Check_error_code( FLA_NOT_YET_IMPLEMENTED );
}
// Copy the converged eigenvalues to the output vector.
FLA_Copy( d, s );
// Sort the singular values and singular vectors in descending order.
FLA_Sort_svd( FLA_BACKWARD, s, U, V );
FLA_Obj_free( &T );
FLA_Obj_free( &S );
FLA_Obj_free( &rL );
FLA_Obj_free( &rR );
FLA_Obj_free( &d );
FLA_Obj_free( &e );
FLA_Obj_free( &G );
FLA_Obj_free( &H );
FLA_Obj_free( &RG );
FLA_Obj_free( &RH );
FLA_Obj_free( &W );
return r_val;
}
FLA_Error FLA_Her2k_un_unb_var6( FLA_Obj alpha, FLA_Obj A, FLA_Obj B, FLA_Obj beta, FLA_Obj C )
{
FLA_Obj AT, A0,
AB, a1t,
A2;
FLA_Obj BT, B0,
BB, b1t,
B2;
FLA_Obj CTL, CTR, C00, c01, C02,
CBL, CBR, c10t, gamma11, c12t,
C20, c21, C22;
FLA_Scalr_external( FLA_UPPER_TRIANGULAR, beta, C );
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 ) ){
FLA_Repart_2x1_to_3x1( AT, &A0,
&a1t,
/* ** */ /* ** */
AB, &A2, 1, FLA_TOP );
FLA_Repart_2x1_to_3x1( BT, &B0,
&b1t,
/* ** */ /* ** */
BB, &B2, 1, FLA_TOP );
FLA_Repart_2x2_to_3x3( CTL, /**/ CTR, &C00, &c01, /**/ &C02,
&c10t, &gamma11, /**/ &c12t,
/* ************* */ /* ************************** */
CBL, /**/ CBR, &C20, &c21, /**/ &C22,
1, 1, FLA_TL );
/*------------------------------------------------------------*/
/* c01 = c01 + A0 * b1t' */
FLA_Gemvc_external( FLA_NO_TRANSPOSE, FLA_CONJUGATE, alpha, A0, b1t, FLA_ONE, c01 );
/* c12t = c12t + b1t * A2' */
FLA_Gemv_external( FLA_CONJ_NO_TRANSPOSE, alpha, A2, b1t, FLA_ONE, c12t );
/* gamma11 = gamma11 + a1t * b1t' + b1t * a1t' */
FLA_Dot2cs_external( FLA_CONJUGATE, alpha, a1t, b1t, FLA_ONE, gamma11 );
/*------------------------------------------------------------*/
FLA_Cont_with_3x1_to_2x1( &AT, A0,
/* ** */ /* ** */
a1t,
&AB, A2, FLA_BOTTOM );
FLA_Cont_with_3x1_to_2x1( &BT, B0,
/* ** */ /* ** */
b1t,
&BB, B2, FLA_BOTTOM );
FLA_Cont_with_3x3_to_2x2( &CTL, /**/ &CTR, C00, /**/ c01, C02,
/* ************** */ /* ************************ */
c10t, /**/ gamma11, c12t,
&CBL, /**/ &CBR, C20, /**/ c21, C22,
FLA_BR );
}
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_omp2l_var1( FLA_Obj A, FLA_Obj C )
{
FLA_Obj AT, A0,
AB, A1,
A2;
FLA_Obj CTL, CTR, C00, C01, C02,
CBL, CBR, C10, C11, C12,
C20, C21, C22;
int b;
FLA_Part_2x1( A, &AT,
&AB, 0, FLA_TOP );
FLA_Part_2x2( C, &CTL, &CTR,
&CBL, &CBR, 0, 0, FLA_TL );
#pragma intel omp parallel taskq
{
while ( FLA_Obj_length( AT ) < FLA_Obj_length( A ) ){
b = FLA_Task_compute_blocksize( 0, A, AT, FLA_TOP );
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 );
/*------------------------------------------------------------*/
#pragma intel omp task captureprivate(A1, A0, C10)
{
/* C10 = C10 + A1 * A0' */
FLA_Gemm_external( FLA_NO_TRANSPOSE, FLA_TRANSPOSE, FLA_ONE, A1, A0, FLA_ONE, C10 );
}
/*------------------------------------------------------------*/
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 );
}
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_Task_compute_blocksize( 0, A, AT, FLA_TOP );
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 );
/*------------------------------------------------------------*/
#pragma intel omp task captureprivate(C11, A1)
{
/* C11 = C11 + A1 * A1' */
FLA_Syrk_external( FLA_LOWER_TRIANGULAR, FLA_NO_TRANSPOSE, FLA_ONE, A1, FLA_ONE, C11 );
}
/*------------------------------------------------------------*/
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_Hess_UT_blk_var4( FLA_Obj A, FLA_Obj T )
{
FLA_Obj ATL, ATR, A00, A01, A02,
ABL, ABR, A10, A11, A12,
A20, A21, A22;
FLA_Obj UT, U0,
UB, U1,
U2;
FLA_Obj YT, Y0,
YB, Y1,
Y2;
FLA_Obj ZT, Z0,
ZB, Z1,
Z2;
FLA_Obj TL, TR, T0, T1, T2;
FLA_Obj U, Y, Z;
FLA_Obj ABR_l;
FLA_Obj UB_l, U2_l;
FLA_Obj YB_l, Y2_l;
FLA_Obj ZB_l, Z2_l;
FLA_Obj WT_l;
FLA_Obj T1_tl;
FLA_Obj none, none2, none3;
FLA_Obj UB_tl,
UB_bl;
FLA_Datatype datatype_A;
dim_t m_A;
dim_t b_alg, b, bb;
b_alg = FLA_Obj_length( T );
datatype_A = FLA_Obj_datatype( A );
m_A = FLA_Obj_length( A );
FLA_Obj_create( datatype_A, m_A, b_alg, 0, 0, &U );
FLA_Obj_create( datatype_A, m_A, b_alg, 0, 0, &Y );
FLA_Obj_create( datatype_A, m_A, b_alg, 0, 0, &Z );
FLA_Part_2x2( A, &ATL, &ATR,
&ABL, &ABR, 0, 0, FLA_TL );
FLA_Part_2x1( U, &UT,
&UB, 0, FLA_TOP );
FLA_Part_2x1( Y, &YT,
&YB, 0, FLA_TOP );
FLA_Part_2x1( Z, &ZT,
&ZB, 0, FLA_TOP );
FLA_Part_1x2( T, &TL, &TR, 0, FLA_LEFT );
while ( FLA_Obj_length( ATL ) < FLA_Obj_length( A ) )
{
b = min( FLA_Obj_length( ABR ), b_alg );
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( UT, &U0,
/* ** */ /* ** */
&U1,
UB, &U2, b, FLA_BOTTOM );
FLA_Repart_2x1_to_3x1( YT, &Y0,
/* ** */ /* ** */
&Y1,
YB, &Y2, b, FLA_BOTTOM );
FLA_Repart_2x1_to_3x1( ZT, &Z0,
/* ** */ /* ** */
&Z1,
ZB, &Z2, b, FLA_BOTTOM );
FLA_Repart_1x2_to_1x3( TL, /**/ TR, &T0, /**/ &T1, &T2,
b, FLA_RIGHT );
/*------------------------------------------------------------*/
FLA_Part_2x2( T1, &T1_tl, &none,
&none2, &none3, b, b, FLA_TL );
bb = min( FLA_Obj_length( ABR ) - 1, b_alg );
FLA_Part_1x2( ABR, &ABR_l, &none, bb, FLA_LEFT );
FLA_Part_1x2( UB, &UB_l, &none, bb, FLA_LEFT );
FLA_Part_1x2( YB, &YB_l, &none, bb, FLA_LEFT );
FLA_Part_1x2( ZB, &ZB_l, &none, bb, FLA_LEFT );
FLA_Part_2x1( UB_l, &none,
&U2_l, b, FLA_TOP );
FLA_Part_2x1( YB_l, &none,
&Y2_l, b, FLA_TOP );
FLA_Part_2x1( ZB_l, &none,
&Z2_l, b, FLA_TOP );
// [ ABR, YB, ZB, T1 ] = FLA_Hess_UT_step_unb_var4( ABR, YB, ZB, T1, b );
//FLA_Hess_UT_step_unb_var4( ABR, YB, ZB, T1_tl );
//FLA_Hess_UT_step_ofu_var4( ABR, YB, ZB, T1_tl );
FLA_Hess_UT_step_opt_var4( ABR, YB, ZB, T1_tl );
// Build UB from ABR, with explicit unit subdiagonal and zeros.
FLA_Copy_external( ABR_l, UB_l );
FLA_Part_2x1( UB_l, &UB_tl,
&UB_bl, 1, FLA_TOP );
FLA_Triangularize( FLA_LOWER_TRIANGULAR, FLA_UNIT_DIAG, UB_bl );
FLA_Set( FLA_ZERO, UB_tl );
// ATR = ATR - ATR * UB * inv( triu( T ) ) * UB' );
if ( FLA_Obj_length( ATR ) > 0 )
{
// NOTE: We use ZT as temporary workspace.
FLA_Part_1x2( ZT, &WT_l, &none, bb, FLA_LEFT );
FLA_Part_2x2( T1, &T1_tl, &none,
&none2, &none3, bb, bb, FLA_TL );
// WT_l = ATR * UB_l * inv( triu( T ) ).
FLA_Gemm_external( FLA_NO_TRANSPOSE, FLA_NO_TRANSPOSE,
FLA_ONE, ATR, UB_l, FLA_ZERO, WT_l );
FLA_Trsm_external( FLA_RIGHT, FLA_UPPER_TRIANGULAR,
FLA_NO_TRANSPOSE, FLA_NONUNIT_DIAG, FLA_ONE, T1_tl, WT_l );
// ATR = ATR - WT_l * UB_l'
FLA_Gemm_external( FLA_NO_TRANSPOSE, FLA_CONJ_TRANSPOSE,
FLA_MINUS_ONE, WT_l, UB_l, FLA_ONE, ATR );
}
// A22 = A22 - U2 * Y2' - Z2 * U2';
FLA_Gemm_external( FLA_NO_TRANSPOSE, FLA_CONJ_TRANSPOSE,
FLA_MINUS_ONE, U2_l, Y2_l, FLA_ONE, A22 );
FLA_Gemm_external( FLA_NO_TRANSPOSE, FLA_CONJ_TRANSPOSE,
FLA_MINUS_ONE, Z2_l, U2_l, FLA_ONE, A22 );
/*------------------------------------------------------------*/
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( &UT, U0,
U1,
/* ** */ /* ** */
&UB, U2, FLA_TOP );
FLA_Cont_with_3x1_to_2x1( &YT, Y0,
Y1,
/* ** */ /* ** */
&YB, Y2, FLA_TOP );
FLA_Cont_with_3x1_to_2x1( &ZT, Z0,
Z1,
/* ** */ /* ** */
&ZB, Z2, FLA_TOP );
FLA_Cont_with_1x3_to_1x2( &TL, /**/ &TR, T0, T1, /**/ T2,
FLA_LEFT );
}
FLA_Obj_free( &U );
FLA_Obj_free( &Y );
FLA_Obj_free( &Z );
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_Symm_lu_unb_var1( FLA_Obj alpha, FLA_Obj A, FLA_Obj B, FLA_Obj beta, FLA_Obj C )
{
FLA_Obj ATL, ATR, A00, a01, A02,
ABL, ABR, a10t, alpha11, a12t,
A20, a21, A22;
FLA_Obj BT, B0,
BB, b1t,
B2;
FLA_Obj CT, C0,
CB, c1t,
C2;
FLA_Scal_external( beta, C );
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 ) ){
FLA_Repart_2x2_to_3x3( ATL, /**/ ATR, &A00, /**/ &a01, &A02,
/* ************* */ /* ************************** */
&a10t, /**/ &alpha11, &a12t,
ABL, /**/ ABR, &A20, /**/ &a21, &A22,
1, 1, FLA_BR );
FLA_Repart_2x1_to_3x1( BT, &B0,
/* ** */ /* ** */
&b1t,
BB, &B2, 1, FLA_BOTTOM );
FLA_Repart_2x1_to_3x1( CT, &C0,
/* ** */ /* ** */
&c1t,
CB, &C2, 1, FLA_BOTTOM );
/*------------------------------------------------------------*/
/* C0 = C0 + a01 * b1t */
FLA_Ger_external( alpha, a01, b1t, C0 );
/* c1t = c1t + a01' * B0 */
/* c1t' = c1t' + B0' * a01 */
FLA_Gemv_external( FLA_TRANSPOSE, alpha, B0, a01, FLA_ONE, c1t );
/* c1t = c1t + alpha11 * b1t */
FLA_Axpys_external( alpha, alpha11, b1t, FLA_ONE, c1t );
/*------------------------------------------------------------*/
FLA_Cont_with_3x3_to_2x2( &ATL, /**/ &ATR, A00, a01, /**/ A02,
a10t, alpha11, /**/ a12t,
/* ************** */ /* ************************ */
&ABL, /**/ &ABR, A20, a21, /**/ A22,
FLA_TL );
FLA_Cont_with_3x1_to_2x1( &BT, B0,
b1t,
/* ** */ /* ** */
&BB, B2, FLA_TOP );
FLA_Cont_with_3x1_to_2x1( &CT, C0,
c1t,
/* ** */ /* ** */
&CB, C2, FLA_TOP );
}
return FLA_SUCCESS;
}
FLA_Error FLA_Hemm_ll_unb_var5( FLA_Obj alpha, FLA_Obj A, FLA_Obj B, FLA_Obj beta, FLA_Obj C )
{
FLA_Obj ATL, ATR, A00, a01, A02,
ABL, ABR, a10t, alpha11, a12t,
A20, a21, A22;
FLA_Obj BT, B0,
BB, b1t,
B2;
FLA_Obj CT, C0,
CB, c1t,
C2;
FLA_Scal_external( beta, C );
FLA_Part_2x2( A, &ATL, &ATR,
&ABL, &ABR, 0, 0, FLA_BR );
FLA_Part_2x1( B, &BT,
&BB, 0, FLA_BOTTOM );
FLA_Part_2x1( C, &CT,
&CB, 0, FLA_BOTTOM );
while ( FLA_Obj_length( ABR ) < FLA_Obj_length( A ) ){
FLA_Repart_2x2_to_3x3( ATL, /**/ ATR, &A00, &a01, /**/ &A02,
&a10t, &alpha11, /**/ &a12t,
/* ************* */ /* ************************** */
ABL, /**/ ABR, &A20, &a21, /**/ &A22,
1, 1, FLA_TL );
FLA_Repart_2x1_to_3x1( BT, &B0,
&b1t,
/* ** */ /* ** */
BB, &B2, 1, FLA_TOP );
FLA_Repart_2x1_to_3x1( CT, &C0,
&c1t,
/* ** */ /* ** */
CB, &C2, 1, FLA_TOP );
/*------------------------------------------------------------*/
/* c1t = c1t + alpha11 * b1t */
FLA_Axpys_external( alpha, alpha11, b1t, FLA_ONE, c1t );
/* c1t = c1t + a21' * B2 */
/* c1t' = c1t' + B2' * a21 */
FLA_Gemvc_external( FLA_TRANSPOSE, FLA_CONJUGATE, alpha, B2, a21, FLA_ONE, c1t );
/* C2 = C2 + a21 * b1t */
FLA_Ger_external( alpha, a21, b1t, C2 );
/*------------------------------------------------------------*/
FLA_Cont_with_3x3_to_2x2( &ATL, /**/ &ATR, A00, /**/ a01, A02,
/* ************** */ /* ************************ */
a10t, /**/ alpha11, a12t,
&ABL, /**/ &ABR, A20, /**/ a21, A22,
FLA_BR );
FLA_Cont_with_3x1_to_2x1( &BT, B0,
/* ** */ /* ** */
b1t,
&BB, B2, FLA_BOTTOM );
FLA_Cont_with_3x1_to_2x1( &CT, C0,
/* ** */ /* ** */
c1t,
&CB, C2, FLA_BOTTOM );
}
return FLA_SUCCESS;
}
FLA_Error FLA_Hess_UT_step_unb_var2( FLA_Obj A, FLA_Obj T )
{
FLA_Obj ATL, ATR, A00, a01, A02,
ABL, ABR, a10t, alpha11, a12t,
A20, a21, A22;
FLA_Obj TTL, TTR, T00, t01, T02,
TBL, TBR, t10t, tau11, t12t,
T20, t21, T22;
FLA_Obj yT, y0,
yB, psi1,
y2;
FLA_Obj zT, z0,
zB, zeta1,
z2;
FLA_Obj y, z;
FLA_Obj inv_tau11;
FLA_Obj minus_inv_tau11;
FLA_Obj first_elem;
FLA_Obj beta;
FLA_Obj conj_beta;
FLA_Obj dot_product;
FLA_Obj a21_t,
a21_b;
FLA_Datatype datatype_A;
dim_t m_A;
dim_t b_alg;
b_alg = FLA_Obj_length( T );
datatype_A = FLA_Obj_datatype( A );
m_A = FLA_Obj_length( A );
FLA_Obj_create( datatype_A, 1, 1, 0, 0, &inv_tau11 );
FLA_Obj_create( datatype_A, 1, 1, 0, 0, &minus_inv_tau11 );
FLA_Obj_create( datatype_A, 1, 1, 0, 0, &first_elem );
FLA_Obj_create( datatype_A, 1, 1, 0, 0, &beta );
FLA_Obj_create( datatype_A, 1, 1, 0, 0, &conj_beta );
FLA_Obj_create( datatype_A, 1, 1, 0, 0, &dot_product );
FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &y );
FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &z );
FLA_Part_2x2( A, &ATL, &ATR,
&ABL, &ABR, 0, 0, FLA_TL );
FLA_Part_2x2( T, &TTL, &TTR,
&TBL, &TBR, 0, 0, FLA_TL );
FLA_Part_2x1( y, &yT,
&yB, 0, FLA_TOP );
FLA_Part_2x1( z, &zT,
&zB, 0, FLA_TOP );
while ( FLA_Obj_length( ATL ) < b_alg )
{
FLA_Repart_2x2_to_3x3( ATL, /**/ ATR, &A00, /**/ &a01, &A02,
/* ************* */ /* ************************** */
&a10t, /**/ &alpha11, &a12t,
ABL, /**/ ABR, &A20, /**/ &a21, &A22,
1, 1, FLA_BR );
FLA_Repart_2x2_to_3x3( TTL, /**/ TTR, &T00, /**/ &t01, &T02,
/* ************* */ /* ************************** */
&t10t, /**/ &tau11, &t12t,
TBL, /**/ TBR, &T20, /**/ &t21, &T22,
1, 1, FLA_BR );
FLA_Repart_2x1_to_3x1( yT, &y0,
/* ** */ /* **** */
&psi1,
yB, &y2, 1, FLA_BOTTOM );
FLA_Repart_2x1_to_3x1( zT, &z0,
/* ** */ /* ***** */
&zeta1,
zB, &z2, 1, FLA_BOTTOM );
/*------------------------------------------------------------*/
if ( FLA_Obj_length( A22 ) > 0 )
{
FLA_Part_2x1( a21, &a21_t,
&a21_b, 1, FLA_TOP );
// [ u21, tau11, a21 ] = House( a21 );
FLA_Househ2_UT( FLA_LEFT,
a21_t,
a21_b, tau11 );
// inv_tau11 = 1 / tau11;
// minus_inv_tau11 = -1 / tau11;
FLA_Set( FLA_ONE, inv_tau11 );
FLA_Inv_scalc( FLA_NO_CONJUGATE, tau11, inv_tau11 );
FLA_Copy( inv_tau11, minus_inv_tau11 );
FLA_Scal( FLA_MINUS_ONE, minus_inv_tau11 );
// Save first element of a21_t and set it to one so we can use a21 as
// u21 in subsequent computations. We will restore a21_t later on.
FLA_Copy( a21_t, first_elem );
FLA_Set( FLA_ONE, a21_t );
// y21 = A22' * u21;
FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, A22, a21, FLA_ZERO, y2 );
// z21 = A22 * u21;
FLA_Gemv( FLA_NO_TRANSPOSE, FLA_ONE, A22, a21, FLA_ZERO, z2 );
// beta = u21' * z21 / 2;
// conj_beta = conj(beta);
FLA_Dotc( FLA_CONJUGATE, a21, z2, beta );
FLA_Inv_scal( FLA_TWO, beta );
FLA_Copyt( FLA_CONJ_NO_TRANSPOSE, beta, conj_beta );
// y21' = ( y21' - beta / tau * u21' ) / tau;
// y21 = ( y21 - conj(beta) / tau * u21 ) / tau;
FLA_Scal( minus_inv_tau11, conj_beta );
FLA_Axpy( conj_beta, a21, y2 );
FLA_Scal( inv_tau11, y2 );
// z21 = ( z21 - beta / tau * u21 ) / tau;
FLA_Scal( minus_inv_tau11, beta );
FLA_Axpy( beta, a21, z2 );
FLA_Scal( inv_tau11, z2 );
// a12t = a12t * ( I - u21 * u21' / tau );
// = a12t - ( a12t * u21 ) * u21' / tau;
FLA_Dot( a12t, a21, dot_product );
FLA_Scal( minus_inv_tau11, dot_product );
FLA_Axpyt( FLA_CONJ_TRANSPOSE, dot_product, a21, a12t );
// A02 = A02 * ( I - u21 * u21' / tau );
// = A02 - ( A02 * u21 ) * u21' / tau;
FLA_Gemv( FLA_NO_TRANSPOSE, FLA_ONE, A02, a21, FLA_ZERO, y0 );
FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, minus_inv_tau11, y0, a21, A02 );
// A22 = A22 - u21 * y21' - z21 * u21';
FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, FLA_MINUS_ONE, a21, y2, A22 );
FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, FLA_MINUS_ONE, z2, a21, A22 );
// t01 = U20' * u21;
FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, A20, a21, FLA_ZERO, t01 );
// Restore first element of a21.
FLA_Copy( first_elem, a21_t );
}
/*------------------------------------------------------------*/
FLA_Cont_with_3x3_to_2x2( &ATL, /**/ &ATR, A00, a01, /**/ A02,
a10t, alpha11, /**/ a12t,
/* ************** */ /* ************************ */
&ABL, /**/ &ABR, A20, a21, /**/ A22,
FLA_TL );
FLA_Cont_with_3x3_to_2x2( &TTL, /**/ &TTR, T00, t01, /**/ T02,
t10t, tau11, /**/ t12t,
/* ************** */ /* ************************ */
&TBL, /**/ &TBR, T20, t21, /**/ T22,
FLA_TL );
FLA_Cont_with_3x1_to_2x1( &yT, y0,
psi1,
/* ** */ /* **** */
&yB, y2, FLA_TOP );
FLA_Cont_with_3x1_to_2x1( &zT, z0,
zeta1,
/* ** */ /* ***** */
&zB, z2, FLA_TOP );
}
FLA_Obj_free( &inv_tau11 );
FLA_Obj_free( &minus_inv_tau11 );
FLA_Obj_free( &first_elem );
FLA_Obj_free( &beta );
FLA_Obj_free( &conj_beta );
FLA_Obj_free( &dot_product );
FLA_Obj_free( &y );
FLA_Obj_free( &z );
return FLA_SUCCESS;
}
