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Functions | |
FLA_Error | FLA_Tridiag_UT_l_unb_var2 (FLA_Obj A, FLA_Obj T) |
FLA_Error | FLA_Tridiag_UT_l_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_Dotc(), FLA_Gemv(), FLA_Hemv(), FLA_Her2(), 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_Obj_set_to_scalar(), FLA_ONE, FLA_Part_2x1(), FLA_Part_2x2(), FLA_Repart_2x1_to_3x1(), FLA_Repart_2x2_to_3x3(), FLA_Scal(), FLA_TWO, and FLA_ZERO.
Referenced by FLA_Tridiag_UT_l_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 uT, u01, uB, upsilon11, u21; FLA_Obj zT, z01, zB, zeta11, z21; FLA_Obj wT, w01, wB, omega11, w21; FLA_Obj u, z, w; FLA_Obj inv_tau11; FLA_Obj minus_inv_tau11; FLA_Obj first_elem; FLA_Obj beta; FLA_Obj minus_upsilon11; FLA_Obj minus_conj_upsilon11; FLA_Obj minus_zeta11; FLA_Obj minus_conj_zeta11; 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, &minus_upsilon11 ); FLA_Obj_create( datatype_A, 1, 1, 0, 0, &minus_conj_upsilon11 ); FLA_Obj_create( datatype_A, 1, 1, 0, 0, &minus_zeta11 ); FLA_Obj_create( datatype_A, 1, 1, 0, 0, &minus_conj_zeta11 ); FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &u ); FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &z ); FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &w ); 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( u, &uT, &uB, 0, FLA_TOP ); FLA_Part_2x1( z, &zT, &zB, 0, FLA_TOP ); FLA_Part_2x1( w, &wT, &wB, 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( uT, &u01, /* ** */ /* ********* */ &upsilon11, uB, &u21, 1, FLA_BOTTOM ); FLA_Repart_2x1_to_3x1( zT, &z01, /* ** */ /* ****** */ &zeta11, zB, &z21, 1, FLA_BOTTOM ); FLA_Repart_2x1_to_3x1( wT, &w01, /* ** */ /* ******* */ &omega11, wB, &w21, 1, FLA_BOTTOM ); /*------------------------------------------------------------*/ if ( FLA_Obj_length( ATL ) > 0 ) { FLA_Copy( upsilon11, minus_upsilon11 ); FLA_Scal( FLA_MINUS_ONE, minus_upsilon11 ); FLA_Copyt( FLA_CONJ_NO_TRANSPOSE, minus_upsilon11, minus_conj_upsilon11 ); FLA_Copy( zeta11, minus_zeta11 ); FLA_Scal( FLA_MINUS_ONE, minus_zeta11 ); FLA_Copyt( FLA_CONJ_NO_TRANSPOSE, minus_zeta11, minus_conj_zeta11 ); // alpha11 = alpha11 - upsilon11 * conj(zeta11) - zeta11 * conj(upsilon11); FLA_Axpyt( FLA_CONJ_NO_TRANSPOSE, minus_upsilon11, zeta11, alpha11 ); FLA_Axpyt( FLA_CONJ_NO_TRANSPOSE, minus_zeta11, upsilon11, alpha11 ); // a21 = a21 - conj(zeta11) * u21 - conj(upsilon11) * z21; FLA_Axpyt( FLA_NO_TRANSPOSE, minus_conj_zeta11, u21, a21 ); FLA_Axpyt( FLA_NO_TRANSPOSE, minus_conj_upsilon11, z21, a21 ); } if ( FLA_Obj_length( A22 ) > 0 ) { FLA_Part_2x1( a21, &a21_t, &a21_b, 1, FLA_TOP ); // [ x21, tau11, a21 ] = House( a21 ); FLA_Househ2_UT( FLA_LEFT, a21_t, a21_b, tau11 ); // inv_tau11 = 1 / tau11; // minus_inv_tau11 = -1 / tau11; FLA_Obj_set_to_scalar( 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_Obj_set_to_scalar( FLA_ONE, a21_t ); } if ( FLA_Obj_length( ATL ) > 0 ) { // A22 = A22 - u21 * z21' - z21 * u21'; FLA_Her2( FLA_LOWER_TRIANGULAR, FLA_MINUS_ONE, u21, z21, A22 ); } if ( FLA_Obj_length( A22 ) > 0 ) { // w21 = A22 * x21; FLA_Hemv( FLA_LOWER_TRIANGULAR, FLA_ONE, A22, a21, FLA_ZERO, w21 ); // u21 = x21; // z21 = w21; FLA_Copy( a21, u21 ); FLA_Copy( w21, z21 ); // beta = u21' * z21 / 2; FLA_Dotc( FLA_CONJUGATE, a21, z21, beta ); FLA_Inv_scal( FLA_TWO, beta ); // z21 = ( z21 - beta / tau * u21 ) / tau; FLA_Scal( minus_inv_tau11, beta ); FLA_Axpy( beta, a21, z21 ); FLA_Scal( inv_tau11, z21 ); // 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 ); } // 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_length( A22 ) > 0 ) { // A22 = A22 - u21 * y21' - z21 * u21'; FLA_Her2( FLA_LOWER_TRIANGULAR, FLA_MINUS_ONE, u21, z21, 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_3x1_to_2x1( &uT, u01, upsilon11, /* ** */ /* ********* */ &uB, u21, FLA_TOP ); FLA_Cont_with_3x1_to_2x1( &zT, z01, zeta11, /* ** */ /* ****** */ &zB, z21, FLA_TOP ); FLA_Cont_with_3x1_to_2x1( &wT, w01, omega11, /* ** */ /* ******* */ &wB, w21, 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( &minus_upsilon11 ); FLA_Obj_free( &minus_conj_upsilon11 ); FLA_Obj_free( &minus_zeta11 ); FLA_Obj_free( &minus_conj_zeta11 ); FLA_Obj_free( &u ); FLA_Obj_free( &z ); FLA_Obj_free( &w ); return FLA_SUCCESS; }
References FLA_Tridiag_UT_l_step_unb_var2().
Referenced by FLA_Tridiag_UT_l().
{ return FLA_Tridiag_UT_l_step_unb_var2( A, T ); }