FLA_Error FLA_Syrk_ln_unb_var4( FLA_Obj alpha, FLA_Obj A, FLA_Obj beta, FLA_Obj C )
{
FLA_Obj AT, A0,
AB, a1t,
A2;
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_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_2x2_to_3x3( CTL, /**/ CTR, &C00, &c01, /**/ &C02,
&c10t, &gamma11, /**/ &c12t,
/* ************* */ /* ************************** */
CBL, /**/ CBR, &C20, &c21, /**/ &C22,
1, 1, FLA_TL );
/*------------------------------------------------------------*/
/* c10t = c10t + A0 * a1t' */
FLA_Gemv_external( FLA_NO_TRANSPOSE, alpha, A0, a1t, FLA_ONE, c10t );
/* gamma11 = gamma11 + a1t * a1t' */
FLA_Dots_external( alpha, a1t, a1t, FLA_ONE, gamma11 );
/*------------------------------------------------------------*/
FLA_Cont_with_3x1_to_2x1( &AT, A0,
/* ** */ /* *** */
a1t,
&AB, A2, 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_LU_nopiv_unb_var3( FLA_Obj A )
{
FLA_Obj ATL, ATR, A00, a01, A02,
ABL, ABR, a10t, alpha11, a12t,
A20, a21, A22;
FLA_Part_2x2( A, &ATL, &ATR,
&ABL, &ABR, 0, 0, FLA_TL );
while ( FLA_Obj_length( ATL ) < FLA_Obj_length( A ) &&
FLA_Obj_width( ATL ) < FLA_Obj_width( A )){
FLA_Repart_2x2_to_3x3( ATL, /**/ ATR, &A00, /**/ &a01, &A02,
/* ************* */ /* ************************** */
&a10t, /**/ &alpha11, &a12t,
ABL, /**/ ABR, &A20, /**/ &a21, &A22,
1, 1, FLA_BR );
/*------------------------------------------------------------*/
// a01 = trilu( A00 ) \ a10
FLA_Trsv_external( FLA_LOWER_TRIANGULAR, FLA_NO_TRANSPOSE, FLA_UNIT_DIAG, A00, a01 );
// alpha11 = alpha11 - a10t * a01
FLA_Dots_external( FLA_MINUS_ONE, a10t, a01, FLA_ONE, alpha11 );
// a21 = a21 - A20 * a01
FLA_Gemv_external( FLA_NO_TRANSPOSE, FLA_MINUS_ONE, A20, a01, FLA_ONE, a21 );
// a21 = a21 / alpha11
FLA_Inv_scal_external( alpha11, a21 );
/*------------------------------------------------------------*/
FLA_Cont_with_3x3_to_2x2( &ATL, /**/ &ATR, A00, a01, /**/ A02,
a10t, alpha11, /**/ a12t,
/* ************** */ /* ************************ */
&ABL, /**/ &ABR, A20, a21, /**/ A22,
FLA_TL );
}
if ( FLA_Obj_width( ATR ) > 0 )
// ATR = trilu( ATL ) \ ATR
FLA_Trsm_external( FLA_LEFT, FLA_LOWER_TRIANGULAR,
FLA_NO_TRANSPOSE, FLA_UNIT_DIAG,
FLA_ONE, ATL, ATR );
return FLA_SUCCESS;
}
FLA_Error FLA_Syrk_lt_unb_var2( FLA_Obj alpha, FLA_Obj A, FLA_Obj beta, FLA_Obj C )
{
FLA_Obj AL, AR, A0, a1, A2;
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_1x2( A, &AL, &AR, 0, FLA_LEFT );
FLA_Part_2x2( C, &CTL, &CTR,
&CBL, &CBR, 0, 0, FLA_TL );
while ( FLA_Obj_width( AL ) < FLA_Obj_width( A ) ){
FLA_Repart_1x2_to_1x3( AL, /**/ AR, &A0, /**/ &a1, &A2,
1, FLA_RIGHT );
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' * a1 */
FLA_Gemv_external( FLA_TRANSPOSE, alpha, A2, a1, FLA_ONE, c21 );
/* gamma11 = gamma11 + a1' * a1 */
FLA_Dots_external( alpha, a1, a1, FLA_ONE, gamma11 );
/*------------------------------------------------------------*/
FLA_Cont_with_1x3_to_1x2( &AL, /**/ &AR, A0, a1, /**/ A2,
FLA_LEFT );
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_LU_piv_unb_var3( FLA_Obj A, FLA_Obj p )
{
FLA_Obj ATL, ATR, A00, a01, A02,
ABL, ABR, a10t, alpha11, a12t,
A20, a21, A22;
FLA_Obj AL, AR, A0, a1, A2;
FLA_Obj pT, p0,
pB, pi1,
p2;
FLA_Obj AB0, aB1;
FLA_Part_2x2( A, &ATL, &ATR,
&ABL, &ABR, 0, 0, FLA_TL );
FLA_Part_1x2( A, &AL, &AR, 0, FLA_LEFT );
FLA_Part_2x1( p, &pT,
&pB, 0, FLA_TOP );
while ( FLA_Obj_length( ATL ) < FLA_Obj_length( A ) &&
FLA_Obj_width( ATL ) < FLA_Obj_width( 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_1x2_to_1x3( AL, /**/ AR, &A0, /**/ &a1, &A2,
1, FLA_RIGHT );
FLA_Repart_2x1_to_3x1( pT, &p0,
/* ** */ /* *** */
&pi1,
pB, &p2, 1, FLA_BOTTOM );
/*------------------------------------------------------------*/
// Apply previously computed pivots
FLA_Apply_pivots( FLA_LEFT, FLA_NO_TRANSPOSE, p0, a1 );
// a01 = trilu( A00 ) \ a01
FLA_Trsv_external( FLA_LOWER_TRIANGULAR, FLA_NO_TRANSPOSE, FLA_UNIT_DIAG, A00, a01 );
// alpha11 = alpha11 - a10t * a01
FLA_Dots_external( FLA_MINUS_ONE, a10t, a01, FLA_ONE, alpha11 );
// a21 = a21 - A20 * a01
FLA_Gemv_external( FLA_NO_TRANSPOSE, FLA_MINUS_ONE, A20, a01, FLA_ONE, a21 );
// aB1 = / alpha11 \
// \ a21 /
FLA_Merge_2x1( alpha11,
a21, &aB1 );
// Determine pivot index
FLA_Amax_external( aB1, pi1 );
// Apply pivots to current column
FLA_Apply_pivots( FLA_LEFT, FLA_NO_TRANSPOSE, pi1, aB1 );
// a21 = a21 / alpha11
FLA_Inv_scal_external( alpha11, a21 );
// AB0 = / a10t \
// \ A20 /
FLA_Merge_2x1( a10t,
A20, &AB0 );
// Apply pivots to previous columns
FLA_Apply_pivots( FLA_LEFT, FLA_NO_TRANSPOSE, pi1, AB0 );
/*------------------------------------------------------------*/
FLA_Cont_with_3x3_to_2x2( &ATL, /**/ &ATR, A00, a01, /**/ A02,
a10t, alpha11, /**/ a12t,
/* ************** */ /* ************************ */
&ABL, /**/ &ABR, A20, a21, /**/ A22,
FLA_TL );
FLA_Cont_with_1x3_to_1x2( &AL, /**/ &AR, A0, a1, /**/ A2,
FLA_LEFT );
FLA_Cont_with_3x1_to_2x1( &pT, p0,
pi1,
/* ** */ /* *** */
&pB, p2, FLA_TOP );
}
if ( FLA_Obj_width( ATR ) > 0 )
{
/* Apply pivots to untouched columns */
FLA_Apply_pivots( FLA_LEFT, FLA_NO_TRANSPOSE, p, ATR );
/* ATR = trilu( ATL ) \ ATR */
FLA_Trsm_external( FLA_LEFT, FLA_LOWER_TRIANGULAR,
FLA_NO_TRANSPOSE, FLA_UNIT_DIAG,
FLA_ONE, ATL, ATR );
}
return FLA_SUCCESS;
}
