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Functions | |
FLA_Error | FLA_QR_UT_piv_unb_var1 (FLA_Obj A, FLA_Obj T, FLA_Obj w, FLA_Obj p) |
References FLA_Amax_external(), FLA_Apply_H2_UT(), FLA_Apply_pivots(), FLA_Cont_with_3x1_to_2x1(), FLA_Cont_with_3x3_to_2x2(), FLA_Copyt_external(), FLA_Gemv_external(), FLA_Househ2_UT(), FLA_Merge_1x2(), FLA_MINUS_ONE, FLA_Obj_le(), FLA_Obj_min_dim(), FLA_Obj_width(), FLA_ONE, FLA_Part_1x2(), FLA_Part_2x1(), FLA_Part_2x2(), FLA_QR_UT_piv_colnorm(), FLA_Repart_2x1_to_3x1(), FLA_Repart_2x2_to_3x3(), FLA_Set(), and FLA_ZERO.
Referenced by FLA_QR_UT_piv_internal().
{ FLA_Obj AL, AR; FLA_Obj ATL, ATR, A00, a01, A02, ABL, ABR, a10t, alpha11, a12t, A20, a21, A22; FLA_Obj AT, A0, AB, a1t, A2; FLA_Obj AB1, AT1, at1; FLA_Obj TTL, TTR, T00, t01, T02, TBL, TBR, t10t, tau11, t12t, T20, t21, T22; FLA_Obj pT, p0, pB, pi1, p2; FLA_Obj wT, w0, wB, omega1, w2; dim_t nb = FLA_Obj_width ( A ) - FLA_Obj_width( T ); //dim_t mb = FLA_Obj_length( A ) - FLA_Obj_width( T ); FLA_Part_1x2( A, &AL, &AR, nb, FLA_RIGHT ); FLA_Part_2x2( AL, &ATL, &ATR, &ABL, &ABR, 0, 0, FLA_TL ); FLA_Part_2x1( AR, &AT, &AB, 0, FLA_TOP ); FLA_Part_2x2( T, &TTL, &TTR, &TBL, &TBR, 0, 0, FLA_TL ); FLA_Part_2x1( p, &pT, &pB, 0, FLA_TOP ); FLA_Part_2x1( w, &wT, &wB, 0, FLA_TOP ); 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_2x1_to_3x1( AT, &A0, /* ** */ /* *** */ &a1t, AB, &A2, 1, FLA_BOTTOM ); 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( pT, &p0, /* ** */ /* *** */ &pi1, pB, &p2, 1, FLA_BOTTOM ); FLA_Repart_2x1_to_3x1( wT, &w0, /* ** */ /* *** */ &omega1, wB, &w2, 1, FLA_BOTTOM ); /*------------------------------------------------------------*/ // Ignore minus inputs for LAPACK compatability. if ( FLA_Obj_le( pi1, FLA_ZERO ) == FALSE ) { // Determine pivot index FLA_Amax_external( wB, pi1 ); FLA_Apply_pivots( FLA_LEFT, FLA_NO_TRANSPOSE, pi1, wB ); // Apply pivots FLA_Merge_1x2( ABR, AB, &AB1 ); FLA_Apply_pivots( FLA_RIGHT, FLA_TRANSPOSE, pi1, AB1 ); } else { // Do not pivot. FLA_Set( FLA_ZERO, pi1 ); } // Compute tau11 and u21 from alpha11 and a21 such that tau11 and u21 // determine a Householder transform H such that applying H from the // left to the column vector consisting of alpha11 and a21 annihilates // the entries in a21 (and updates alpha11). FLA_Househ2_UT( FLA_LEFT, alpha11, a21, tau11 ); // Apply H to (a12t A22)^T // / a12t \ = H / a12t \ // \ A22 / \ A22 / // // where H is formed from tau11 and u21. FLA_Merge_1x2( A22, A2, &AB1 ); FLA_Merge_1x2( a12t, a1t, &at1 ); FLA_Apply_H2_UT( FLA_LEFT, tau11, a21, at1, AB1 ); // t01 = a10t' + A20' * u21; FLA_Copyt_external( FLA_CONJ_TRANSPOSE, a10t, t01 ); FLA_Gemv_external( FLA_CONJ_TRANSPOSE, FLA_ONE, A20, a21, FLA_ONE, t01 ); // Apply pivots to previous rows if ( FLA_Obj_le( pi1, FLA_ZERO ) == FALSE ) { FLA_Merge_1x2( ATR, AT, &AT1 ); FLA_Apply_pivots( FLA_RIGHT, FLA_TRANSPOSE, pi1, AT1 ); } // Norm downdate w2 = alpha w2 + beta columnwisenorm2(a12t) FLA_QR_UT_piv_colnorm( FLA_MINUS_ONE, at1, w2 ); /*------------------------------------------------------------*/ FLA_Cont_with_3x3_to_2x2( &ATL, /**/ &ATR, A00, a01, /**/ A02, a10t, alpha11, /**/ a12t, /* ************** */ /* ************************ */ &ABL, /**/ &ABR, A20, a21, /**/ A22, FLA_TL ); FLA_Cont_with_3x1_to_2x1( &AT, A0, a1t, /* ** */ /* *** */ &AB, A2, FLA_TOP ); 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( &pT, p0, pi1, /* ** */ /* *** */ &pB, p2, FLA_TOP ); FLA_Cont_with_3x1_to_2x1( &wT, w0, omega1, /* ** */ /* *** */ &wB, w2, FLA_TOP ); } return FLA_SUCCESS; }