libflame
revision_anchor
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Functions | |
FLA_Error | FLA_QR_UT_blk_var2 (FLA_Obj A, FLA_Obj T, fla_qrut_t *cntl) |
FLA_Error FLA_QR_UT_blk_var2 | ( | FLA_Obj | A, |
FLA_Obj | T, | ||
fla_qrut_t * | cntl | ||
) |
References FLA_Apply_Q_UT_internal(), FLA_Cont_with_3x3_to_2x2(), FLA_Copyt_external(), FLA_Determine_blocksize(), FLA_Gemm_external(), FLA_Merge_2x1(), FLA_Obj_min_dim(), FLA_Obj_width(), FLA_ONE, FLA_Part_2x2(), FLA_QR_UT_internal(), FLA_Repart_2x2_to_3x3(), and FLA_Trmm_external().
Referenced by FLA_QR_UT_internal().
{ FLA_Obj ATL, ATR, A00, A01, A02, ABL, ABR, A10, A11, A12, A20, A21, A22; FLA_Obj TTL, TTR, T00, T01, T02, TBL, TBR, T10, T11, W12, T20, T21, T22; FLA_Obj AB1, AB2; dim_t b; 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 ){ b = FLA_Determine_blocksize( ABR, FLA_BR, FLA_Cntl_blocksize( cntl ) ); FLA_Repart_2x2_to_3x3( ATL, /**/ ATR, &A00, /**/ &A01, &A02, /* ************* */ /* ******************** */ &A10, /**/ &A11, &A12, ABL, /**/ ABR, &A20, /**/ &A21, &A22, b, b, FLA_BR ); FLA_Repart_2x2_to_3x3( TTL, /**/ TTR, &T00, /**/ &T01, &T02, /* ************* */ /* ******************** */ &T10, /**/ &T11, &W12, TBL, /**/ TBR, &T20, /**/ &T21, &T22, b, b, FLA_BR ); /*------------------------------------------------------------*/ FLA_Merge_2x1( A11, A21, &AB1 ); // Perform a QR factorization via the UT transform on AB1: // // / A11 \ -> QB1 R11 // \ A21 / // // where: // - QB1 is formed from UB1 (which is stored column-wise below the // diagonal of AB1) and T11 (which is stored to the upper triangle // of T11). // - R11 is stored to the upper triangle of AB1. FLA_QR_UT_internal( AB1, T11, FLA_Cntl_sub_qrut( cntl ) ); if ( FLA_Obj_width( A12 ) > 0 ) { FLA_Merge_2x1( A12, A22, &AB2 ); // Apply the Householder transforms associated with UB1 and T11 to // AB2: // // / A12 \ := QB1' / A12 \ // \ A22 / \ A22 / // // where QB1 is formed from UB1 and T11. FLA_Apply_Q_UT_internal( FLA_LEFT, FLA_CONJ_TRANSPOSE, FLA_FORWARD, FLA_COLUMNWISE, AB1, T11, W12, AB2, FLA_Cntl_sub_apqut( cntl ) ); } // Update T // // T01 = A10' * U11 + A20' * U21; // // Recall: U11 = trilu( A11 ); // U21 = A21; FLA_Copyt_external( FLA_CONJ_TRANSPOSE, A10, T01 ); FLA_Trmm_external( FLA_RIGHT, FLA_LOWER_TRIANGULAR, FLA_NO_TRANSPOSE, FLA_UNIT_DIAG, FLA_ONE, A11, T01 ); FLA_Gemm_external( FLA_CONJ_TRANSPOSE, FLA_NO_TRANSPOSE, FLA_ONE, A20, A21, FLA_ONE, T01 ); /*------------------------------------------------------------*/ FLA_Cont_with_3x3_to_2x2( &ATL, /**/ &ATR, A00, A01, /**/ A02, A10, A11, /**/ A12, /* ************** */ /* ****************** */ &ABL, /**/ &ABR, A20, A21, /**/ A22, FLA_TL ); FLA_Cont_with_3x3_to_2x2( &TTL, /**/ &TTR, T00, T01, /**/ T02, T10, T11, /**/ W12, /* ************** */ /* ****************** */ &TBL, /**/ &TBR, T20, T21, /**/ T22, FLA_TL ); } return FLA_SUCCESS; }