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libflame
revision_anchor
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Functions | |
| FLA_Error | FLA_Hess_UT_blk_var5 (FLA_Obj A, FLA_Obj T) |
| FLA_Error FLA_Hess_UT_blk_var5 | ( | FLA_Obj | A, |
| FLA_Obj | T | ||
| ) |
References FLA_Apply_Q_UT(), FLA_Cont_with_1x3_to_1x2(), FLA_Cont_with_3x1_to_2x1(), FLA_Cont_with_3x3_to_2x2(), FLA_Copyt_external(), FLA_Gemm_external(), FLA_Hess_UT_step_opt_var5(), FLA_Merge_2x1(), FLA_MINUS_ONE, FLA_Obj_create(), FLA_Obj_datatype(), FLA_Obj_free(), FLA_Obj_length(), FLA_Obj_width(), FLA_ONE, FLA_Part_1x2(), FLA_Part_2x1(), FLA_Part_2x2(), FLA_Repart_1x2_to_1x3(), FLA_Repart_2x1_to_3x1(), FLA_Repart_2x2_to_3x3(), FLA_Trsm_external(), and FLA_ZERO.
Referenced by FLA_Hess_UT_internal().
{
FLA_Obj ATL, ATR, A00, A01, A02,
ABL, ABR, A10, A11, A12,
A20, A21, A22;
FLA_Obj UT, U0,
UB, U1,
U2;
FLA_Obj ZT, Z0,
ZB, Z1,
Z2;
FLA_Obj TL, TR, T0, T1, W12;
FLA_Obj U, Z;
FLA_Obj UB_l;
FLA_Obj ZB_l;
FLA_Obj WT_l;
FLA_Obj T1_tl;
FLA_Obj none, none2, none3;
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, &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( 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( ZT, &Z0,
/* ** */ /* ** */
&Z1,
ZB, &Z2, b, FLA_BOTTOM );
FLA_Repart_1x2_to_1x3( TL, /**/ TR, &T0, /**/ &T1, &W12,
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( UB, &UB_l, &none, bb, FLA_LEFT );
FLA_Part_1x2( ZB, &ZB_l, &none, bb, FLA_LEFT );
// [ ABR, UB, ZB, T1 ] = FLA_Hess_UT_step_unb_var5( ABR, UB, ZB, T1, b );
//FLA_Hess_UT_step_unb_var5( ABR, UB, ZB, T1_tl );
FLA_Hess_UT_step_opt_var5( ABR, UB, ZB, T1_tl );
// ATR = ATR - ATR * UB * inv( triu ( T1 ) ) * 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( T1 ) ).
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 );
}
// / A12 \ = Q11' * / / A12 \ - / Z1 \ * inv( triu( T1 ) ) * U2' \
// \ A22 / \ \ A22 / \ Z2 / /
//
// where Q11 corresponds to the block Householder transformation
// associated with UB and T1.
if ( FLA_Obj_width( A12 ) > 0 )
{
FLA_Obj ABR2, ABR2_b;
FLA_Obj UB_b;
// NOTE: Since A12.n > 0, we are guaranteed to not be at an edge case,
// namely the case where bb = b - 1 = ABR.m - 1, thus we are free to use
// the "full" matrix partitions in this scope block (ie: ZB instead of
// ZB_l).
// W12 = U2'
// W12 = inv( triu( T1 ) ) * W12;
FLA_Copyt_external( FLA_CONJ_TRANSPOSE, U2, W12 );
FLA_Trsm_external( FLA_LEFT, FLA_UPPER_TRIANGULAR, FLA_NO_TRANSPOSE,
FLA_NONUNIT_DIAG, FLA_ONE, T1_tl, W12 );
FLA_Merge_2x1( A12,
A22, &ABR2 );
// / A12 \ = / A12 \ - / Z1 \ * W12
// \ A22 / \ A22 / \ Z2 /
FLA_Gemm_external( FLA_NO_TRANSPOSE, FLA_NO_TRANSPOSE,
FLA_MINUS_ONE, ZB, W12, FLA_ONE, ABR2 );
// Omit the top row of UB so it has [implicit] unit diagonal, allowing us
// to use FLA_Apply_Q_UT() to apply the block Householder transformation
// corresponding to UB and T1. This trick is valid since the top row of
// ABR2 would normally be unchanged by the transformation (ie: multiplied
// by identity).
FLA_Part_2x1( UB, &none,
&UB_b, 1, FLA_TOP );
FLA_Part_2x1( ABR2, &none,
&ABR2_b, 1, FLA_TOP );
// Apply Q11' to A12 and A22 from the left:
//
// / A12 \ = / I - / U1 \ * inv( triu( T1 ) ) * / U1 \' \' / A12 \
// \ A22 / \ \ U2 / \ U2 / / \ A22 /
//
FLA_Apply_Q_UT( FLA_LEFT, FLA_CONJ_TRANSPOSE, FLA_FORWARD, FLA_COLUMNWISE,
UB_b, T1_tl, W12, ABR2_b );
}
/*------------------------------------------------------------*/
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( &ZT, Z0,
Z1,
/* ** */ /* ** */
&ZB, Z2, FLA_TOP );
FLA_Cont_with_1x3_to_1x2( &TL, /**/ &TR, T0, T1, /**/ W12,
FLA_LEFT );
}
FLA_Obj_free( &U );
FLA_Obj_free( &Z );
return FLA_SUCCESS;
}
1.7.6.1