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Functions | |
FLA_Error | FLA_LQ_UT_unb_var2 (FLA_Obj A, FLA_Obj T) |
References FLA_Apply_H2_UT(), FLA_Cont_with_3x3_to_2x2(), FLA_Copyt_external(), FLA_Gemvc_external(), FLA_Househ2_UT(), FLA_Obj_min_dim(), FLA_ONE, FLA_Part_2x2(), and FLA_Repart_2x2_to_3x3().
Referenced by FLA_LQ_UT_internal().
{ 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_Part_2x2( A, &ATL, &ATR, &ABL, &ABR, 0, 0, FLA_TL ); FLA_Part_2x2( T, &TTL, &TTR, &TBL, &TBR, 0, 0, FLA_TL ); while ( FLA_Obj_min_dim( ABR ) > 0 ){ 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 ); /*------------------------------------------------------------*/ // Compute tau11 and u12t from alpha11 and a12t such that tau11 and u12t // determine a Householder transform H such that applying H from the // right to the row vector consisting of alpha11 and a12t annihilates // the entries in a12t (and updates alpha11). FLA_Househ2_UT( FLA_RIGHT, alpha11, a12t, tau11 ); // ( a21 A22 ) = ( a21 A22 ) H // // where H is formed from tau11 and u12t. FLA_Apply_H2_UT( FLA_RIGHT, tau11, a12t, a21, A22 ); // t01 = conj(a01) + conj(A02) * u12t^T; FLA_Copyt_external( FLA_CONJ_NO_TRANSPOSE, a01, t01 ); FLA_Gemvc_external( FLA_CONJ_NO_TRANSPOSE, FLA_NO_CONJUGATE, FLA_ONE, A02, a12t, 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( &TTL, /**/ &TTR, T00, t01, /**/ T02, t10t, tau11, /**/ t12t, /* ************** */ /* ********************** */ &TBL, /**/ &TBR, T20, t21, /**/ T22, FLA_TL ); } return FLA_SUCCESS; }