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; }