FLA_CAQR2_UT_blk_var1.c File Reference

(r)

Functions
FLA_Error	FLA_CAQR2_UT_blk_var1 (FLA_Obj U, FLA_Obj D, FLA_Obj T, fla_caqr2ut_t *cntl)

---

Function Documentation

FLA_Error FLA_CAQR2_UT_blk_var1	(	FLA_Obj	U,
		FLA_Obj	D,
		FLA_Obj	T,
		fla_caqr2ut_t *	cntl
	)

References FLA_Axpy_internal(), FLA_CAQR2_UT_internal(), FLA_Cont_with_1x3_to_1x2(), FLA_Cont_with_3x3_to_2x2(), FLA_Copy_internal(), FLA_Gemm_internal(), FLA_Merge_2x1(), 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_CAQR2_UT_internal().

{
  FLA_Obj UTL,   UTR,      U00, U01, U02, 
          UBL,   UBR,      U10, U11, U12,
                           U20, U21, U22;

  FLA_Obj DTL,   DTR,      D00, D01, D02, 
          DBL,   DBR,      D10, D11, D12,
                           D20, D21, D22;

  FLA_Obj TL,    TR,       T0,  T1,  W12;

  FLA_Obj D1;

  FLA_Obj W12T, W12B;

  FLA_Obj T1T, T2B;

  dim_t   b_alg, b;
  dim_t   m_DT;

  // Query the algorithmic blocksize by inspecting the length of T.
  b_alg = FLA_Obj_length( T );

  // 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_1x2( T,    &TL,  &TR,      0, FLA_LEFT );

  while ( FLA_Obj_min_dim( UBR ) > 0 ){

    b = min( b_alg, FLA_Obj_min_dim( UBR ) );

    FLA_Repart_2x2_to_3x3( UTL, /**/ UTR,       &U00, /**/ &U01, &U02,
                        /* ************* */   /* ******************** */
                                                &U10, /**/ &U11, &U12,
                           UBL, /**/ UBR,       &U20, /**/ &U21, &U22,
                           b, b, FLA_BR );

    FLA_Repart_2x2_to_3x3( DTL, /**/ DTR,       &D00, /**/ &D01, &D02,
                        /* ************* */   /* ******************** */
                                                &D10, /**/ &D11, &D12,
                           DBL, /**/ DBR,       &D20, /**/ &D21, &D22,
                           b, b, FLA_BR );

    FLA_Repart_1x2_to_1x3( TL,  /**/ TR,        &T0, /**/ &T1, &W12,
                           b, FLA_RIGHT );

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

    // T1T = FLA_Top_part( T1, b );

    FLA_Part_2x1( T1,   &T1T, 
                        &T2B,    b, FLA_TOP );

    FLA_Merge_2x1( D01,
                   D11,   &D1 );

    // [ U11, ...
    //   D1, T1 ] = FLA_CAQR2_UT( U11
    //                            D1, T1T );

    FLA_CAQR2_UT_internal( U11,
                           D1, T1T, 
                           FLA_Cntl_sub_caqr2ut( cntl ) );


    if ( FLA_Obj_width( U12 ) > 0 )
    {
      // W12T = FLA_Top_part( W12, b );

      FLA_Part_2x1( W12,  &W12T, 
                          &W12B, b, FLA_TOP );

      // W12T = inv( triu( T1T ) )' * ( U12 + D1' * D2 );
      //      = inv( triu( T1T ) )' * ( U12 + D01' * D02 + D11' * D12 );

      FLA_Copy_internal( D12, W12T,
                         FLA_Cntl_sub_copy( cntl ) );

      FLA_Trmm_internal( FLA_LEFT, FLA_UPPER_TRIANGULAR, 
                         FLA_CONJ_TRANSPOSE, FLA_NONUNIT_DIAG, 
                         FLA_ONE, D11, W12T,
                         FLA_Cntl_sub_trmm1( cntl ) );

      FLA_Gemm_internal( FLA_CONJ_TRANSPOSE, FLA_NO_TRANSPOSE,
                         FLA_ONE, D01, D02, FLA_ONE, W12T,
                         FLA_Cntl_sub_gemm1( cntl ) );

      FLA_Axpy_internal( FLA_ONE, U12, W12T,
                         FLA_Cntl_sub_axpy1( cntl ) );

      FLA_Trsm_internal( FLA_LEFT, FLA_UPPER_TRIANGULAR, 
                         FLA_CONJ_TRANSPOSE, FLA_NONUNIT_DIAG, 
                         FLA_ONE, T1T, W12T,
                         FLA_Cntl_sub_trsm( cntl ) );

      // U12 = U12 - W12T;
      // D2  = D2  - D1 * W12T;
      //  => D02 = D02 - D01 * W12T;
      //     D12 = D12 - D11 * W12T;

      FLA_Axpy_internal( FLA_MINUS_ONE, W12T, U12,
                         FLA_Cntl_sub_axpy2( cntl ) );

      FLA_Gemm_internal( FLA_NO_TRANSPOSE, FLA_NO_TRANSPOSE, 
                         FLA_MINUS_ONE, D01, W12T, FLA_ONE, D02,
                         FLA_Cntl_sub_gemm2( cntl ) );

      FLA_Trmm_internal( FLA_LEFT, FLA_UPPER_TRIANGULAR, 
                         FLA_NO_TRANSPOSE, FLA_NONUNIT_DIAG, 
                         FLA_ONE, D11, W12T,
                         FLA_Cntl_sub_trmm2( cntl ) );

      FLA_Axpy_internal( FLA_MINUS_ONE, W12T, D12,
                         FLA_Cntl_sub_axpy3( cntl ) );
    }

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

    FLA_Cont_with_3x3_to_2x2( &UTL, /**/ &UTR,       U00, U01, /**/ U02,
                                                     U10, U11, /**/ U12,
                            /* ************** */  /* ****************** */
                              &UBL, /**/ &UBR,       U20, U21, /**/ U22,
                              FLA_TL );

    FLA_Cont_with_3x3_to_2x2( &DTL, /**/ &DTR,       D00, D01, /**/ D02,
                                                     D10, D11, /**/ D12,
                            /* ************** */  /* ****************** */
                              &DBL, /**/ &DBR,       D20, D21, /**/ D22,
                              FLA_TL );

    FLA_Cont_with_1x3_to_1x2( &TL,  /**/ &TR,        T0, T1, /**/ W12,
                              FLA_LEFT );

  }

  return FLA_SUCCESS;
}