libflame revision_anchor
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Functions | |
FLA_Error | FLA_Bidiag_UT_u_unb_var4 (FLA_Obj A, FLA_Obj TU, FLA_Obj TV) |
FLA_Error | FLA_Bidiag_UT_u_step_unb_var4 (FLA_Obj A, FLA_Obj Y, FLA_Obj Z, 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_Househ2_UT(), FLA_Househ2s_UT(), FLA_Inv_scalc(), FLA_Merge_2x1(), FLA_MINUS_ONE, FLA_Mult_add(), FLA_Obj_create(), FLA_Obj_datatype(), FLA_Obj_free(), FLA_Obj_length(), FLA_Obj_set_to_scalar(), 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_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 STL, STR, S00, s01, S02, SBL, SBR, s10t, sigma11, s12t, S20, s21, S22; FLA_Obj wT, w01, wB, omega11, w21; FLA_Obj alT, a01l, alB, alpha11l, a22l; 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 dT, d0, dB, delta1, d2; FLA_Obj eT, e0, eB, epsilon1, e2; FLA_Obj fT, f0, fB, phi1, f2; FLA_Obj gT, g0, gB, ghi1, g2; FLA_Obj w, al, ap, u, up, v; FLA_Obj d, e, f, g; FLA_Obj minus_inv_tau11; FLA_Obj last_elem; 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 a01_t, a01_b; FLA_Obj A02_l, A02_r; 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_Obj Y20_t, Y20_b; FLA_Obj a2; 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, &last_elem ); 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, m_A, 1, 0, 0, &al ); 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, &d ); FLA_Obj_create( datatype_A, n_A, 1, 0, 0, &e ); FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &f ); FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &g ); FLA_Obj_set_to_scalar( FLA_ZERO, Y ); FLA_Obj_set_to_scalar( 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_2x2( S, &STL, &STR, &SBL, &SBR, 0, 0, FLA_TL ); FLA_Part_2x1( w, &wT, &wB, 0, FLA_TOP ); FLA_Part_2x1( al, &alT, &alB, 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( d, &dT, &dB, 0, FLA_TOP ); FLA_Part_2x1( e, &eT, &eB, 0, FLA_TOP ); FLA_Part_2x1( f, &fT, &fB, 0, FLA_TOP ); FLA_Part_2x1( g, &gT, &gB, 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_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( alT, &a01l, /* ** */ /* ***** */ &alpha11l, alB, &a22l, 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( 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 ); FLA_Repart_2x1_to_3x1( gT, &g0, /* ** */ /* **** */ &ghi1, gB, &g2, 1, FLA_BOTTOM ); /*------------------------------------------------------------*/ // Save last element of a01 and set it to one so we can use a01 as // v10t^T in subsequent computations. We will restore a01_b later on. // Also note: V20^T is stored in A02. if ( FLA_Obj_length( ATL ) > 0 ) { FLA_Part_2x1( a01, &a01_t, &a01_b, 1, FLA_BOTTOM ); FLA_Copy( a01_b, last_elem ); FLA_Obj_set_to_scalar( FLA_ONE, a01_b ); } FLA_Merge_2x1( alpha11, a21, &a2 ); // alpha11 = alpha11 - u10t * y10t' - z10t * v10t'; // a21 = a21 - U20 * y10t' - Z20 * v10t'; 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, a01, FLA_ONE, a2 ); // a12t = a12t - u10t * Y20' - z10t * V20'; FLA_Gemv( FLA_CONJ_NO_TRANSPOSE, FLA_MINUS_ONE, Y20, a10t, FLA_ONE, a12t ); FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_MINUS_ONE, A02, z10t, FLA_ONE, a12t ); // Restore last element of a01. if ( FLA_Obj_length( ATL ) > 0 ) { FLA_Copy( last_elem, a01_b ); } // [ 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 ); // y21 = - Y20 * ( U20' * u21p ) - V20 * ( Z20' * u21p ); FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, A20, u21p, FLA_ZERO, d0 ); FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, Z20, u21p, FLA_ZERO, e0 ); FLA_Obj_set_to_scalar( FLA_ZERO, y21 ); FLA_Gemv( FLA_NO_TRANSPOSE, FLA_MINUS_ONE, Y20, d0, FLA_ONE, y21 ); FLA_Gemv( FLA_TRANSPOSE, FLA_MINUS_ONE, A02, e0, FLA_ONE, y21 ); // y21 = y21 + A22' * u21p; FLA_Gemv( FLA_CONJ_TRANSPOSE, FLA_ONE, A22, u21p, FLA_ONE, 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 ); // w21 = w21 - U20 * ( Y20' * conj(a12p) ) - Z20 * ( V20' * conj(a12p) ); FLA_Gemvc( FLA_CONJ_TRANSPOSE, FLA_CONJUGATE, FLA_ONE, Y20, a12p, FLA_ZERO, f0 ); FLA_Gemvc( FLA_CONJ_NO_TRANSPOSE, FLA_CONJUGATE, FLA_ONE, A02, a12p, FLA_ZERO, g0 ); FLA_Gemv( FLA_NO_TRANSPOSE, FLA_MINUS_ONE, A20, f0, FLA_ONE, w21 ); FLA_Gemv( FLA_NO_TRANSPOSE, FLA_MINUS_ONE, Z20, g0, FLA_ONE, w21 ); FLA_Part_1x2( A22, &A22_l, &A22_r, 1, FLA_LEFT ); FLA_Part_2x1( Y20, &Y20_t, &Y20_b, 1, FLA_TOP ); FLA_Part_1x2( A02, &A02_l, &A02_r, 1, FLA_LEFT ); // a22l = A22 * e0 - U20 * ( Y20' * e0 ) - Z20 * ( V20' * e0 ); FLA_Copy( A22_l, a22l ); FLA_Gemvc( FLA_NO_TRANSPOSE, FLA_CONJUGATE, FLA_MINUS_ONE, A20, Y20_t, FLA_ONE, a22l ); FLA_Gemvc( FLA_NO_TRANSPOSE, FLA_CONJUGATE, FLA_MINUS_ONE, Z20, A02_l, FLA_ONE, a22l ); // 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 ); // 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) * a22l ) / conj(psi11 - alpha12) + beta * u21; FLA_Copy( w21, z21 ); FLA_Axpy( minus_conj_alpha12, a22l, 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 ); /*------------------------------------------------------------*/ 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_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( &alT, a01l, alpha11l, /* ** */ /* ***** */ &alB, a22l, 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( &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_Cont_with_3x1_to_2x1( &gT, g0, ghi1, /* ** */ /* **** */ &gB, g2, FLA_TOP ); } FLA_Obj_free( &minus_inv_tau11 ); FLA_Obj_free( &last_elem ); 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( &al ); FLA_Obj_free( &ap ); FLA_Obj_free( &u ); FLA_Obj_free( &up ); FLA_Obj_free( &v ); FLA_Obj_free( &d ); FLA_Obj_free( &e ); FLA_Obj_free( &f ); FLA_Obj_free( &g ); return FLA_SUCCESS; }
References FLA_Bidiag_UT_u_step_unb_var4(), FLA_Obj_create(), FLA_Obj_datatype(), FLA_Obj_free(), FLA_Obj_length(), and FLA_Obj_width().
Referenced by FLA_Bidiag_UT_u().
{ FLA_Error r_val; FLA_Obj Y, Z; FLA_Datatype datatype_A; dim_t m_A, n_A; datatype_A = FLA_Obj_datatype( A ); m_A = FLA_Obj_length( A ); n_A = FLA_Obj_width( A ); FLA_Obj_create( datatype_A, n_A, n_A, 0, 0, &Y ); FLA_Obj_create( datatype_A, m_A, n_A, 0, 0, &Z ); r_val = FLA_Bidiag_UT_u_step_unb_var4( A, Y, Z, TU, TV ); FLA_Obj_free( &Y ); FLA_Obj_free( &Z ); return r_val; }