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libflame
revision_anchor
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Functions | |
| FLA_Error | FLA_Hess_UT_unb_var4 (FLA_Obj A, FLA_Obj T) |
| FLA_Error | FLA_Hess_UT_step_unb_var4 (FLA_Obj A, FLA_Obj Y, FLA_Obj Z, FLA_Obj T) |
References FLA_Axpy(), FLA_Axpyt(), FLA_Cont_with_3x1_to_2x1(), FLA_Cont_with_3x3_to_2x2(), FLA_Copy(), FLA_Copyt(), FLA_Dot(), FLA_Dotc(), FLA_Gemv(), FLA_Gemvc(), FLA_Gerc(), FLA_Househ2_UT(), FLA_Inv_scal(), FLA_Inv_scalc(), FLA_Merge_2x1(), FLA_MINUS_ONE, FLA_Obj_create(), FLA_Obj_datatype(), FLA_Obj_free(), FLA_Obj_length(), FLA_ONE, FLA_Part_1x2(), FLA_Part_2x1(), FLA_Part_2x2(), FLA_Repart_2x1_to_3x1(), FLA_Repart_2x2_to_3x3(), FLA_Scal(), FLA_Set(), FLA_TWO, and FLA_ZERO.
Referenced by FLA_Hess_UT_unb_var4().
{
FLA_Obj ATL, ATR, A00, a01, A02,
ABL, ABR, a10t, alpha11, a12t,
A20, a21, A22;
FLA_Obj YTL, YTR, Y00, y01, Y02,
YBL, YBR, y10t, psi11, y12t,
Y20, y21, Y22;
FLA_Obj ZTL, ZTR, Z00, z01, Z02,
ZBL, ZBR, z10t, zeta11, z12t,
Z20, z21, Z22;
FLA_Obj TTL, TTR, T00, t01, T02,
TBL, TBR, t10t, tau11, t12t,
T20, t21, T22;
FLA_Obj dT, d0,
dB, delta1,
d2;
FLA_Obj eT, e0,
eB, epsilon1,
e2;
FLA_Obj fT, f0,
fB, phi1,
f2;
FLA_Obj d, e, f;
FLA_Obj inv_tau11;
FLA_Obj minus_inv_tau11;
FLA_Obj first_elem;
FLA_Obj last_elem;
FLA_Obj beta;
FLA_Obj conj_beta;
FLA_Obj dot_product;
FLA_Obj a10t_l, a10t_r;
FLA_Obj a21_t,
a21_b;
FLA_Obj a2;
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, &last_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, &d );
FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &e );
FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &f );
FLA_Set( FLA_ZERO, Y );
FLA_Set( FLA_ZERO, Z );
FLA_Part_2x2( A, &ATL, &ATR,
&ABL, &ABR, 0, 0, FLA_TL );
FLA_Part_2x2( Y, &YTL, &YTR,
&YBL, &YBR, 0, 0, FLA_TL );
FLA_Part_2x2( Z, &ZTL, &ZTR,
&ZBL, &ZBR, 0, 0, FLA_TL );
FLA_Part_2x2( T, &TTL, &TTR,
&TBL, &TBR, 0, 0, FLA_TL );
FLA_Part_2x1( d, &dT,
&dB, 0, FLA_TOP );
FLA_Part_2x1( e, &eT,
&eB, 0, FLA_TOP );
FLA_Part_2x1( f, &fT,
&fB, 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( YTL, /**/ YTR, &Y00, /**/ &y01, &Y02,
/* ************* */ /* ************************ */
&y10t, /**/ &psi11, &y12t,
YBL, /**/ YBR, &Y20, /**/ &y21, &Y22,
1, 1, FLA_BR );
FLA_Repart_2x2_to_3x3( ZTL, /**/ ZTR, &Z00, /**/ &z01, &Z02,
/* ************* */ /* ************************* */
&z10t, /**/ &zeta11, &z12t,
ZBL, /**/ ZBR, &Z20, /**/ &z21, &Z22,
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( dT, &d0,
/* ** */ /* ****** */
&delta1,
dB, &d2, 1, FLA_BOTTOM );
FLA_Repart_2x1_to_3x1( eT, &e0,
/* ** */ /* ******** */
&epsilon1,
eB, &e2, 1, FLA_BOTTOM );
FLA_Repart_2x1_to_3x1( fT, &f0,
/* ** */ /* **** */
&phi1,
fB, &f2, 1, FLA_BOTTOM );
/*------------------------------------------------------------*/
// Save first element of a10_r and set it to one so we can use a10t as
// u10t in subsequent computations. We will restore a10_r later on.
if ( FLA_Obj_length( ATL ) > 0 )
{
FLA_Part_1x2( a10t, &a10t_l, &a10t_r, 1, FLA_RIGHT );
FLA_Copy( a10t_r, last_elem );
FLA_Set( FLA_ONE, a10t_r );
}
FLA_Merge_2x1( alpha11,
a21, &a2 );
// alpha11 = alpha11 - u10t * y10t' - z10t * u10t';
// a21 = a21 - U20 * y10t' - Z20 * u10t';
FLA_Gemvc( FLA_NO_TRANSPOSE, FLA_CONJUGATE, FLA_MINUS_ONE, ABL, y10t, FLA_ONE, a2 );
FLA_Gemvc( FLA_NO_TRANSPOSE, FLA_CONJUGATE, FLA_MINUS_ONE, ZBL, a10t, FLA_ONE, a2 );
// a12t = a12t - u10t * Y20' - z10t * U20';
FLA_Gemv( FLA_CONJ_NO_TRANSPOSE, FLA_MINUS_ONE, Y20, a10t, FLA_ONE, a12t );
FLA_Gemv( FLA_CONJ_NO_TRANSPOSE, FLA_MINUS_ONE, A20, z10t, FLA_ONE, a12t );
// Restore last element of a10t.
if ( FLA_Obj_length( ATL ) > 0 )
{
FLA_Copy( last_elem, a10t_r );
}
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.
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, y21 );
// z21 = A22 * u21;
FLA_Gemv( FLA_NO_TRANSPOSE, FLA_ONE, A22, a21, FLA_ZERO, z21 );
// y21 = y21 - Y20 * ( U20' * u21 ) - U20 * ( Z20' * u21 );
FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, A20, a21, FLA_ZERO, d0 );
FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, Y20, a21, FLA_ZERO, e0 );
FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, Z20, a21, FLA_ZERO, f0 );
FLA_Gemv( FLA_NO_TRANSPOSE, FLA_MINUS_ONE, Y20, d0, FLA_ONE, y21 );
FLA_Gemv( FLA_NO_TRANSPOSE, FLA_MINUS_ONE, A20, f0, FLA_ONE, y21 );
// t01 = U20' * u21;
FLA_Copy( d0, t01 );
// z21 = z21 - U20 * ( Y20' * u21 ) - Z20 * ( U20' * u21 );
FLA_Gemv( FLA_NO_TRANSPOSE, FLA_MINUS_ONE, A20, e0, FLA_ONE, z21 );
FLA_Gemv( FLA_NO_TRANSPOSE, FLA_MINUS_ONE, Z20, d0, FLA_ONE, z21 );
// beta = u21' * z21 / 2;
// conj_beta = conj(beta);
FLA_Dotc( FLA_CONJUGATE, a21, z21, 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, y21 );
FLA_Scal( inv_tau11, y21 );
// z21 = ( z21 - beta / tau * u21 ) / tau;
FLA_Scal( minus_inv_tau11, beta );
FLA_Axpy( beta, a21, z21 );
FLA_Scal( inv_tau11, z21 );
// 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, e0 );
FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, minus_inv_tau11, e0, a21, A02 );
// 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( &YTL, /**/ &YTR, Y00, y01, /**/ Y02,
y10t, psi11, /**/ y12t,
/* ************** */ /* ********************** */
&YBL, /**/ &YBR, Y20, y21, /**/ Y22,
FLA_TL );
FLA_Cont_with_3x3_to_2x2( &ZTL, /**/ &ZTR, Z00, z01, /**/ Z02,
z10t, zeta11, /**/ z12t,
/* ************** */ /* *********************** */
&ZBL, /**/ &ZBR, Z20, z21, /**/ Z22,
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( &dT, d0,
delta1,
/* ** */ /* ****** */
&dB, d2, FLA_TOP );
FLA_Cont_with_3x1_to_2x1( &eT, e0,
epsilon1,
/* ** */ /* ******** */
&eB, e2, FLA_TOP );
FLA_Cont_with_3x1_to_2x1( &fT, f0,
phi1,
/* ** */ /* **** */
&fB, f2, FLA_TOP );
}
FLA_Obj_free( &inv_tau11 );
FLA_Obj_free( &minus_inv_tau11 );
FLA_Obj_free( &first_elem );
FLA_Obj_free( &last_elem );
FLA_Obj_free( &beta );
FLA_Obj_free( &conj_beta );
FLA_Obj_free( &dot_product );
FLA_Obj_free( &d );
FLA_Obj_free( &e );
FLA_Obj_free( &f );
return FLA_SUCCESS;
}
| FLA_Error FLA_Hess_UT_unb_var4 | ( | FLA_Obj | A, |
| FLA_Obj | T | ||
| ) |
References FLA_Hess_UT_step_unb_var4(), FLA_Obj_create_conf_to(), and FLA_Obj_free().
Referenced by FLA_Hess_UT_internal().
{
FLA_Error r_val;
FLA_Obj Y, Z;
FLA_Obj_create_conf_to( FLA_NO_TRANSPOSE, A, &Y );
FLA_Obj_create_conf_to( FLA_NO_TRANSPOSE, A, &Z );
r_val = FLA_Hess_UT_step_unb_var4( A, Y, Z, T );
FLA_Obj_free( &Y );
FLA_Obj_free( &Z );
return r_val;
}
1.7.6.1