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libflame
revision_anchor
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Functions | |
| FLA_Error | FLA_Hess_UT_unb_var2 (FLA_Obj A, FLA_Obj T) |
| FLA_Error | FLA_Hess_UT_step_unb_var2 (FLA_Obj A, FLA_Obj T) |
| FLA_Error FLA_Hess_UT_step_unb_var2 | ( | FLA_Obj | A, |
| 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_Gerc(), FLA_Househ2_UT(), FLA_Inv_scal(), FLA_Inv_scalc(), FLA_MINUS_ONE, FLA_Obj_create(), FLA_Obj_datatype(), FLA_Obj_free(), FLA_Obj_length(), FLA_ONE, 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_var2().
{
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;
}
| FLA_Error FLA_Hess_UT_unb_var2 | ( | FLA_Obj | A, |
| FLA_Obj | T | ||
| ) |
References FLA_Hess_UT_step_unb_var2().
Referenced by FLA_Hess_UT_internal().
{
return FLA_Hess_UT_step_unb_var2( A, T );
}
1.7.6.1