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revision_anchor
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Functions | |
FLA_Error | FLA_CAQR2_UT_unb_var1 (FLA_Obj U, FLA_Obj D, FLA_Obj T) |
FLA_Error FLA_CAQR2_UT_unb_var1 | ( | FLA_Obj | U, |
FLA_Obj | D, | ||
FLA_Obj | T | ||
) |
References FLA_Apply_H2_UT(), FLA_Cont_with_3x3_to_2x2(), FLA_Copy_external(), FLA_Gemv_external(), FLA_Househ2_UT(), FLA_Merge_2x1(), FLA_Obj_length(), FLA_Obj_min_dim(), FLA_Obj_width(), FLA_ONE, FLA_Part_2x1(), FLA_Part_2x2(), FLA_Repart_2x2_to_3x3(), and FLA_Trmv_external().
Referenced by FLA_CAQR2_UT_internal().
{ FLA_Obj UTL, UTR, U00, u01, U02, UBL, UBR, u10t, upsilon11, u12t, U20, u21, U22; FLA_Obj DTL, DTR, D00, d01, D02, DBL, DBR, d10t, delta11, d12t, D20, d21, D22; FLA_Obj TTL, TTR, T00, t01, T02, TBL, TBR, t10t, tau11, t12t, T20, t21, T22; FLA_Obj d1, D2; FLA_Obj d01T, d01B; FLA_Obj D00T, D00B; dim_t m_DT; // Begin partitioning diagonally through D with m - n rows above // the diagonal. m_DT = FLA_Obj_length( D ) - FLA_Obj_width( D ); FLA_Part_2x2( U, &UTL, &UTR, &UBL, &UBR, 0, 0, FLA_TL ); FLA_Part_2x2( D, &DTL, &DTR, &DBL, &DBR, m_DT, 0, FLA_TL ); FLA_Part_2x2( T, &TTL, &TTR, &TBL, &TBR, 0, 0, FLA_TL ); while ( FLA_Obj_min_dim( UBR ) > 0 ){ FLA_Repart_2x2_to_3x3( UTL, /**/ UTR, &U00, /**/ &u01, &U02, /* ************* */ /* ************************** */ &u10t, /**/ &upsilon11, &u12t, UBL, /**/ UBR, &U20, /**/ &u21, &U22, 1, 1, FLA_BR ); FLA_Repart_2x2_to_3x3( DTL, /**/ DTR, &D00, /**/ &d01, &D02, /* ************* */ /* ************************** */ &d10t, /**/ &delta11, &d12t, DBL, /**/ DBR, &D20, /**/ &d21, &D22, 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_Merge_2x1( d01, delta11, &d1 ); FLA_Merge_2x1( D02, d12t, &D2 ); // Compute tau11 and u2 from upsilon11 and d1 such that tau11 and u2 // determine a Householder transform H such that applying H from the // left to the column vector consisting of upsilon11 and d1 annihilates // the entries in d1 (and updates upsilon11). FLA_Househ2_UT( FLA_LEFT, upsilon11, d1, tau11 ); // / u12t \ = H / u12t \ // \ D2 / \ D2 / // // where H is formed from tau11 and d1. FLA_Apply_H2_UT( FLA_LEFT, tau11, d1, u12t, D2 ); FLA_Part_2x1( d01, &d01T, &d01B, m_DT, FLA_TOP ); FLA_Part_2x1( D00, &D00T, &D00B, m_DT, FLA_TOP ); // t01 = D00' * d01; // = D00T' * d01T + triu( D00B )' * d01B; FLA_Copy_external( d01B, t01 ); FLA_Trmv_external( FLA_UPPER_TRIANGULAR, FLA_CONJ_TRANSPOSE, FLA_NONUNIT_DIAG, D00B, t01 ); FLA_Gemv_external( FLA_CONJ_TRANSPOSE, FLA_ONE, D00T, d01T, FLA_ONE, t01 ); /*------------------------------------------------------------*/ FLA_Cont_with_3x3_to_2x2( &UTL, /**/ &UTR, U00, u01, /**/ U02, u10t, upsilon11, /**/ u12t, /* ************** */ /* ************************ */ &UBL, /**/ &UBR, U20, u21, /**/ U22, FLA_TL ); FLA_Cont_with_3x3_to_2x2( &DTL, /**/ &DTR, D00, d01, /**/ D02, d10t, delta11, /**/ d12t, /* ************** */ /* ************************ */ &DBL, /**/ &DBR, D20, d21, /**/ D22, 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; }