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Functions | |
FLA_Error | FLA_Apply_Q_UT_rhfc_blk_var1 (FLA_Obj A, FLA_Obj T, FLA_Obj W, FLA_Obj B, fla_apqut_t *cntl) |
FLA_Error FLA_Apply_Q_UT_rhfc_blk_var1 | ( | FLA_Obj | A, |
FLA_Obj | T, | ||
FLA_Obj | W, | ||
FLA_Obj | B, | ||
fla_apqut_t * | cntl | ||
) |
References FLA_Axpyt_internal(), FLA_Cont_with_1x3_to_1x2(), FLA_Cont_with_3x3_to_2x2(), FLA_Copyt_internal(), FLA_Gemm_internal(), FLA_MINUS_ONE, FLA_Obj_length(), FLA_Obj_min_dim(), FLA_Obj_width(), FLA_ONE, FLA_Part_1x2(), FLA_Part_2x1(), FLA_Part_2x2(), FLA_Repart_1x2_to_1x3(), FLA_Repart_2x2_to_3x3(), FLA_Trmm_internal(), and FLA_Trsm_internal().
Referenced by FLA_Apply_Q_UT_rhfc().
{ FLA_Obj ATL, ATR, A00, A01, A02, ABL, ABR, A10, A11, A12, A20, A21, A22; FLA_Obj TL, TR, T0, T1, T2; FLA_Obj T1T, T2B; FLA_Obj WTL, WTR, WBL, WBR; FLA_Obj BL, BR, B0, B1, B2; dim_t b_alg, b; dim_t m_BR, n_BR; // Query the algorithmic blocksize by inspecting the length of T. b_alg = FLA_Obj_length( T ); // If m > n, then we have to initialize our partitionings carefully so // that we begin in the proper location in A and B (since we traverse // matrix A from BR to TL). if ( FLA_Obj_length( A ) > FLA_Obj_width( A ) ) { m_BR = FLA_Obj_length( A ) - FLA_Obj_width( A ); n_BR = 0; } else { m_BR = 0; n_BR = 0; } FLA_Part_2x2( A, &ATL, &ATR, &ABL, &ABR, m_BR, n_BR, FLA_BR ); FLA_Part_1x2( T, &TL, &TR, 0, FLA_RIGHT ); FLA_Part_1x2( B, &BL, &BR, m_BR, FLA_RIGHT ); while ( FLA_Obj_min_dim( ATL ) > 0 ){ b = min( b_alg, FLA_Obj_min_dim( ATL ) ); // Since T was filled from left to right, and since we need to access them // in reverse order, we need to handle the case where the last block is // smaller than the other b x b blocks. if ( FLA_Obj_width( TR ) == 0 && FLA_Obj_width( T ) % b_alg > 0 ) b = FLA_Obj_width( T ) % b_alg; FLA_Repart_2x2_to_3x3( ATL, /**/ ATR, &A00, &A01, /**/ &A02, &A10, &A11, /**/ &A12, /* ************* */ /* ******************** */ ABL, /**/ ABR, &A20, &A21, /**/ &A22, b, b, FLA_TL ); FLA_Repart_1x2_to_1x3( TL, /**/ TR, &T0, &T1, /**/ &T2, b, FLA_LEFT ); FLA_Repart_1x2_to_1x3( BL, /**/ BR, &B0, &B1, /**/ &B2, b, FLA_LEFT ); /*------------------------------------------------------------*/ FLA_Part_2x1( T1, &T1T, &T2B, b, FLA_TOP ); FLA_Part_2x2( W, &WTL, &WTR, &WBL, &WBR, b, FLA_Obj_length( B1 ), FLA_TL ); // WTL = B1^T; FLA_Copyt_internal( FLA_TRANSPOSE, B1, WTL, FLA_Cntl_sub_copyt( cntl ) ); // U11 = trilu( A11 ); // U21 = A21; // Let WTL^T be conformal to B1. // // WTL^T = ( B1 * U11 + B2 * U21 ) * inv( triu(T1T)' ); // WTL = inv( conj(triu(T1T)) ) * ( U11^T * B1^T + U21^T * B2^T ); FLA_Trmm_internal( FLA_LEFT, FLA_LOWER_TRIANGULAR, FLA_TRANSPOSE, FLA_UNIT_DIAG, FLA_ONE, A11, WTL, FLA_Cntl_sub_trmm1( cntl ) ); FLA_Gemm_internal( FLA_TRANSPOSE, FLA_TRANSPOSE, FLA_ONE, A21, B2, FLA_ONE, WTL, FLA_Cntl_sub_gemm1( cntl ) ); FLA_Trsm_internal( FLA_LEFT, FLA_UPPER_TRIANGULAR, FLA_CONJ_NO_TRANSPOSE, FLA_NONUNIT_DIAG, FLA_ONE, T1T, WTL, FLA_Cntl_sub_trsm( cntl ) ); // B2 = B2 - WTL^T * U21'; // B1 = B1 - WTL^T * U11'; // = B1 - ( conj(U11) * WTL )^T; FLA_Gemm_internal( FLA_TRANSPOSE, FLA_CONJ_TRANSPOSE, FLA_MINUS_ONE, WTL, A21, FLA_ONE, B2, FLA_Cntl_sub_gemm2( cntl ) ); FLA_Trmm_internal( FLA_LEFT, FLA_LOWER_TRIANGULAR, FLA_CONJ_NO_TRANSPOSE, FLA_UNIT_DIAG, FLA_MINUS_ONE, A11, WTL, FLA_Cntl_sub_trmm2( cntl ) ); FLA_Axpyt_internal( FLA_TRANSPOSE, FLA_ONE, WTL, B1, FLA_Cntl_sub_axpyt( cntl ) ); /*------------------------------------------------------------*/ FLA_Cont_with_3x3_to_2x2( &ATL, /**/ &ATR, A00, /**/ A01, A02, /* ************** */ /* ****************** */ A10, /**/ A11, A12, &ABL, /**/ &ABR, A20, /**/ A21, A22, FLA_BR ); FLA_Cont_with_1x3_to_1x2( &TL, /**/ &TR, T0, /**/ T1, T2, FLA_RIGHT ); FLA_Cont_with_1x3_to_1x2( &BL, /**/ &BR, B0, /**/ B1, B2, FLA_RIGHT ); } return FLA_SUCCESS; }