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libflame
revision_anchor
|
Functions | |
| FLA_Error | FLA_Bidiag_UT_u_unb_var3 (FLA_Obj A, FLA_Obj TU, FLA_Obj TV) |
| FLA_Error | FLA_Bidiag_UT_u_step_unb_var3 (FLA_Obj A, FLA_Obj T, FLA_Obj S) |
| FLA_Error FLA_Bidiag_UT_u_step_unb_var3 | ( | FLA_Obj | A, |
| FLA_Obj | T, | ||
| FLA_Obj | S | ||
| ) |
References FLA_Axpy(), FLA_Axpyt(), FLA_Conjugate(), FLA_Cont_with_3x1_to_2x1(), FLA_Cont_with_3x3_to_2x2(), FLA_Copy(), FLA_Copyt(), FLA_Dotc(), FLA_Gemv(), FLA_Gemvc(), FLA_Gerc(), FLA_Househ2_UT(), FLA_Househ2s_UT(), FLA_Inv_scalc(), FLA_MINUS_ONE, FLA_Mult_add(), 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_2x1_to_3x1(), FLA_Repart_2x2_to_3x3(), FLA_Scal(), and FLA_ZERO.
Referenced by FLA_Bidiag_UT_u_unb_var3().
{
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 STL, STR, S00, s01, S02,
SBL, SBR, s10t, sigma11, s12t,
S20, s21, S22;
FLA_Obj wT, w01,
wB, omega11,
w21;
FLA_Obj apT, a01p,
apB, alpha11p,
a12p;
FLA_Obj uT, u01,
uB, upsilon11,
u21;
FLA_Obj uTp, u01p,
uBp, upsilon11p,
u21p;
FLA_Obj vT, v01,
vB, nu11,
v21;
FLA_Obj yT, y01,
yB, psi11,
y21;
FLA_Obj zT, z01,
zB, zeta11,
z21;
FLA_Obj w, ap, u, up, v, y, z;
FLA_Obj minus_inv_tau11;
FLA_Obj beta;
FLA_Obj alpha12;
FLA_Obj minus_conj_alpha12;
FLA_Obj psi11_minus_alpha12;
FLA_Obj minus_upsilon11;
FLA_Obj minus_conj_nu11;
FLA_Obj minus_conj_psi11;
FLA_Obj minus_zeta11;
FLA_Obj a12t_l, a12t_r;
FLA_Obj a12p_t,
a12p_b;
FLA_Obj A22_l, A22_r;
FLA_Obj v21_t,
v21_b;
FLA_Datatype datatype_A;
dim_t m_A, n_A;
dim_t b_alg;
b_alg = FLA_Obj_length( T );
datatype_A = FLA_Obj_datatype( A );
m_A = FLA_Obj_length( A );
n_A = FLA_Obj_width( A );
FLA_Obj_create( datatype_A, 1, 1, 0, 0, &minus_inv_tau11 );
FLA_Obj_create( datatype_A, 1, 1, 0, 0, &beta );
FLA_Obj_create( datatype_A, 1, 1, 0, 0, &alpha12 );
FLA_Obj_create( datatype_A, 1, 1, 0, 0, &minus_conj_alpha12 );
FLA_Obj_create( datatype_A, 1, 1, 0, 0, &psi11_minus_alpha12 );
FLA_Obj_create( datatype_A, 1, 1, 0, 0, &minus_upsilon11 );
FLA_Obj_create( datatype_A, 1, 1, 0, 0, &minus_conj_nu11 );
FLA_Obj_create( datatype_A, 1, 1, 0, 0, &minus_conj_psi11 );
FLA_Obj_create( datatype_A, 1, 1, 0, 0, &minus_zeta11 );
FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &w );
FLA_Obj_create( datatype_A, n_A, 1, 0, 0, &ap );
FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &u );
FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &up );
FLA_Obj_create( datatype_A, n_A, 1, 0, 0, &v );
FLA_Obj_create( datatype_A, n_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_2x2( S, &STL, &STR,
&SBL, &SBR, 0, 0, FLA_TL );
FLA_Part_2x1( w, &wT,
&wB, 0, FLA_TOP );
FLA_Part_2x1( ap, &apT,
&apB, 0, FLA_TOP );
FLA_Part_2x1( u, &uT,
&uB, 0, FLA_TOP );
FLA_Part_2x1( up, &uTp,
&uBp, 0, FLA_TOP );
FLA_Part_2x1( v, &vT,
&vB, 0, FLA_TOP );
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_2x2_to_3x3( STL, /**/ STR, &S00, /**/ &s01, &S02,
/* ************* */ /* ************************** */
&s10t, /**/ &sigma11, &s12t,
SBL, /**/ SBR, &S20, /**/ &s21, &S22,
1, 1, FLA_BR );
FLA_Repart_2x1_to_3x1( wT, &w01,
/* ** */ /* ***** */
&omega11,
wB, &w21, 1, FLA_BOTTOM );
FLA_Repart_2x1_to_3x1( apT, &a01p,
/* ** */ /* ***** */
&alpha11p,
apB, &a12p, 1, FLA_BOTTOM );
FLA_Repart_2x1_to_3x1( uT, &u01,
/* ** */ /* ***** */
&upsilon11,
uB, &u21, 1, FLA_BOTTOM );
FLA_Repart_2x1_to_3x1( uTp, &u01p,
/* ** */ /* ***** */
&upsilon11p,
uBp, &u21p, 1, FLA_BOTTOM );
FLA_Repart_2x1_to_3x1( vT, &v01,
/* ** */ /* ***** */
&nu11,
vB, &v21, 1, FLA_BOTTOM );
FLA_Repart_2x1_to_3x1( yT, &y01,
/* ** */ /* ***** */
&psi11,
yB, &y21, 1, FLA_BOTTOM );
FLA_Repart_2x1_to_3x1( zT, &z01,
/* ** */ /* ***** */
&zeta11,
zB, &z21, 1, FLA_BOTTOM );
/*------------------------------------------------------------*/
if ( FLA_Obj_length( ATL ) > 0 )
{
FLA_Copy( upsilon11, minus_upsilon11 );
FLA_Scal( FLA_MINUS_ONE, minus_upsilon11 );
FLA_Copy( zeta11, minus_zeta11 );
FLA_Scal( FLA_MINUS_ONE, minus_zeta11 );
FLA_Copyt( FLA_CONJ_NO_TRANSPOSE, psi11, minus_conj_psi11 );
FLA_Scal( FLA_MINUS_ONE, minus_conj_psi11 );
FLA_Copyt( FLA_CONJ_NO_TRANSPOSE, nu11, minus_conj_nu11 );
FLA_Scal( FLA_MINUS_ONE, minus_conj_nu11 );
// alpha11 = alpha11 - upsilon11 * conj(psi11) - zeta11 * conj(nu1);
FLA_Axpyt( FLA_NO_TRANSPOSE, minus_conj_psi11, upsilon11, alpha11 );
FLA_Axpyt( FLA_NO_TRANSPOSE, minus_conj_nu11, zeta11, alpha11 );
// a21 = a21 - u21 * conj(psi11) - z21 * conj(nu11);
FLA_Axpyt( FLA_NO_TRANSPOSE, minus_conj_psi11, u21, a21 );
FLA_Axpyt( FLA_NO_TRANSPOSE, minus_conj_nu11, z21, a21 );
// a12t = a12t - upsilon11 * y21' - zeta11 * v21';
FLA_Axpyt( FLA_CONJ_TRANSPOSE, minus_upsilon11, y21, a12t );
FLA_Axpyt( FLA_CONJ_TRANSPOSE, minus_zeta11, v21, a12t );
}
// [ alpha11, u21p, tau11 ] = House2( alpha11, a21 );
FLA_Househ2_UT( FLA_LEFT,
alpha11,
a21, tau11 );
FLA_Copy( a21, u21p );
if ( FLA_Obj_width( A22 ) > 0 )
{
// minus_inv_tau11 = - 1 / tau11;
FLA_Copy( FLA_MINUS_ONE, minus_inv_tau11 );
FLA_Inv_scalc( FLA_NO_CONJUGATE, tau11, minus_inv_tau11 );
// a12p = ( tau11 - 1 ) * a12t^T / tau11;
// = a12t^T - ( 1 / tau11 ) * a12t^T;
FLA_Copyt( FLA_TRANSPOSE, a12t, a12p );
FLA_Axpyt( FLA_TRANSPOSE, minus_inv_tau11, a12t, a12p );
}
if ( FLA_Obj_length( ATL ) > 0 )
{
// A22 = A22 - u21 * y21' - z21 * v21';
FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, FLA_MINUS_ONE, u21, y21, A22 );
FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, FLA_MINUS_ONE, z21, v21, A22 );
}
if ( FLA_Obj_width( A22 ) > 0 )
{
// y21 = A22' * u21p;
FLA_Gemvc( FLA_CONJ_TRANSPOSE, FLA_NO_CONJUGATE, FLA_ONE, A22, u21p, FLA_ZERO, y21 );
// a12p = a12p - conj(y21) / tau11;
FLA_Axpyt( FLA_CONJ_NO_TRANSPOSE, minus_inv_tau11, y21, a12p );
// w21 = A22 * conj(a12p);
FLA_Gemvc( FLA_NO_TRANSPOSE, FLA_CONJUGATE, FLA_ONE, A22, a12p, FLA_ZERO, w21 );
// y21 = y21 + conj(a12t)^T;
FLA_Axpyt( FLA_CONJ_TRANSPOSE, FLA_ONE, a12t, y21 );
FLA_Part_1x2( a12t, &a12t_l, &a12t_r, 1, FLA_LEFT );
FLA_Part_2x1( v21, &v21_t,
&v21_b, 1, FLA_TOP );
FLA_Part_2x1( a12p, &a12p_t,
&a12p_b, 1, FLA_TOP );
// [ alpha12, psi11_minus_alpha12, sigma11 ] = House2s( a12p_t, a12p_b );
FLA_Househ2s_UT( FLA_RIGHT,
a12p_t,
a12p_b,
alpha12, psi11_minus_alpha12, sigma11 );
// v21 = conj( ( a12p - alpha12 * e0 ) / ( psi11 - alpha12 ) );
FLA_Copy( a12p, v21 );
FLA_Mult_add( FLA_MINUS_ONE, alpha12, v21_t );
FLA_Inv_scalc( FLA_NO_CONJUGATE, psi11_minus_alpha12, v21 );
FLA_Conjugate( v21_b );
// a12t_l = alpha12;
// a12t_r = v21_b^T;
FLA_Copyt( FLA_NO_TRANSPOSE, alpha12, a12t_l );
FLA_Copyt( FLA_TRANSPOSE, v21_b, a12t_r );
}
// u21 = u21p;
FLA_Copy( u21p, u21 );
if ( FLA_Obj_width( A22 ) > 0 )
{
// beta = - y21' * v21 / tau11;
FLA_Dotc( FLA_CONJUGATE, y21, v21, beta );
FLA_Scal( FLA_MINUS_ONE, beta );
FLA_Inv_scalc( FLA_NO_CONJUGATE, tau11, beta );
FLA_Part_1x2( A22, &A22_l, &A22_r, 1, FLA_LEFT );
// minus_conj_alpha12 = - conj(alpha12);
FLA_Copyt( FLA_CONJ_NO_TRANSPOSE, alpha12, minus_conj_alpha12 );
FLA_Scal( FLA_MINUS_ONE, minus_conj_alpha12 );
// z21 = ( w21 - conj(alpha12) * A22 * e0 ) / conj(psi11 - alpha12) + beta * u21;
FLA_Copy( w21, z21 );
FLA_Axpy( minus_conj_alpha12, A22_l, z21 );
FLA_Inv_scalc( FLA_CONJUGATE, psi11_minus_alpha12, z21 );
FLA_Axpy( beta, u21, z21 );
// y21 = y21 / tau11;
// z21 = z21 / sigma11;
FLA_Inv_scalc( FLA_NO_CONJUGATE, tau11, y21 );
FLA_Inv_scalc( FLA_NO_CONJUGATE, sigma11, z21 );
// s01 = conj(V02) * v21;
FLA_Gemv( FLA_CONJ_NO_TRANSPOSE, FLA_ONE, A02, v21, FLA_ZERO, s01 );
}
// t01 = a10t' + U20' * u21;
FLA_Copyt( FLA_CONJ_TRANSPOSE, a10t, t01 );
FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, A20, u21, FLA_ONE, t01 );
// Update A22 if this is the last iteration; this is needed when we're
// being called from the blocked routine so A22 is left in a valid state.
if ( FLA_Obj_length( ATL ) + 1 == b_alg &&
FLA_Obj_width( A22 ) > 0 )
{
// A22 = A22 - u21 * y21' - z21 * v21';
FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, FLA_MINUS_ONE, u21, y21, A22 );
FLA_Gerc( FLA_NO_CONJUGATE, FLA_CONJUGATE, FLA_MINUS_ONE, z21, v21, A22 );
}
/*------------------------------------------------------------*/
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_3x3_to_2x2( &STL, /**/ &STR, S00, s01, /**/ S02,
s10t, sigma11, /**/ s12t,
/* ************** */ /* ************************ */
&SBL, /**/ &SBR, S20, s21, /**/ S22,
FLA_TL );
FLA_Cont_with_3x1_to_2x1( &wT, w01,
omega11,
/* ** */ /* ***** */
&wB, w21, FLA_TOP );
FLA_Cont_with_3x1_to_2x1( &apT, a01p,
alpha11p,
/* ** */ /* ***** */
&apB, a12p, FLA_TOP );
FLA_Cont_with_3x1_to_2x1( &uT, u01,
upsilon11,
/* ** */ /* ***** */
&uB, u21, FLA_TOP );
FLA_Cont_with_3x1_to_2x1( &uTp, u01p,
upsilon11p,
/* ** */ /* ***** */
&uBp, u21p, FLA_TOP );
FLA_Cont_with_3x1_to_2x1( &vT, v01,
nu11,
/* ** */ /* ***** */
&vB, v21, FLA_TOP );
FLA_Cont_with_3x1_to_2x1( &yT, y01,
psi11,
/* ** */ /* ***** */
&yB, y21, FLA_TOP );
FLA_Cont_with_3x1_to_2x1( &zT, z01,
zeta11,
/* ** */ /* ***** */
&zB, z21, FLA_TOP );
}
FLA_Obj_free( &minus_inv_tau11 );
FLA_Obj_free( &beta );
FLA_Obj_free( &alpha12 );
FLA_Obj_free( &minus_conj_alpha12 );
FLA_Obj_free( &psi11_minus_alpha12 );
FLA_Obj_free( &minus_upsilon11 );
FLA_Obj_free( &minus_conj_nu11 );
FLA_Obj_free( &minus_conj_psi11 );
FLA_Obj_free( &minus_zeta11 );
FLA_Obj_free( &w );
FLA_Obj_free( &ap );
FLA_Obj_free( &u );
FLA_Obj_free( &up );
FLA_Obj_free( &v );
FLA_Obj_free( &y );
FLA_Obj_free( &z );
return FLA_SUCCESS;
}
| FLA_Error FLA_Bidiag_UT_u_unb_var3 | ( | FLA_Obj | A, |
| FLA_Obj | TU, | ||
| FLA_Obj | TV | ||
| ) |
References FLA_Bidiag_UT_u_step_unb_var3().
Referenced by FLA_Bidiag_UT_u().
{
return FLA_Bidiag_UT_u_step_unb_var3( A, TU, TV );
}
1.7.6.1