FLA_QR_UT_blk_var3.c File Reference

(r)

Functions
FLA_Error	FLA_QR_UT_blk_var3 (FLA_Obj A, FLA_Obj TW, fla_qrut_t *cntl)

---

Function Documentation

FLA_Error FLA_QR_UT_blk_var3	(	FLA_Obj	A,
		FLA_Obj	TW,
		fla_qrut_t *	cntl
	)

References FLA_Apply_Q_UT_internal(), FLA_Cont_with_3x3_to_2x2(), FLA_Determine_blocksize(), FLA_Merge_2x1(), FLA_Obj_min_dim(), FLA_Obj_width(), FLA_Part_2x2(), FLA_QR_UT_internal(), and FLA_Repart_2x2_to_3x3().

Referenced by FLA_QR_UT_internal().

{
  FLA_Obj ATL,   ATR,      A00, A01, A02, 
          ABL,   ABR,      A10, A11, A12,
                           A20, A21, A22;

  FLA_Obj TWTL,  TWTR,     TW00, TW01, TW02, 
          TWBL,  TWBR,     TW10,  T11,  W12,
                           TW20, TW21, TW22;

  FLA_Obj AB1,   AB2;

  dim_t   b;

  FLA_Part_2x2( A,    &ATL, &ATR,
                      &ABL, &ABR,     0, 0, FLA_TL );

  FLA_Part_2x2( TW,   &TWTL, &TWTR,
                      &TWBL, &TWBR,     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( TWTL, /**/ TWTR,     &TW00, /**/ &TW01, &TW02,
                        /* ************* */   /* ******************** */
                                                &TW10, /**/ &T11,   &W12,
                           TWBL, /**/ TWBR,     &TW20, /**/ &TW21, &TW22,
                           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 ) );
    }

    /*------------------------------------------------------------*/

    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( &TWTL, /**/ &TWTR,     TW00, TW01, /**/ TW02,
                                                     TW10,  T11, /**/  W12,
                            /* ************** */  /* ****************** */
                              &TWBL, /**/ &TWBR,     TW20, TW21, /**/ TW22,
                              FLA_TL );
  }

  return FLA_SUCCESS;
}