FLA_QR_UT_piv_blk_var1.c File Reference

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Functions
FLA_Error	FLA_QR_UT_piv_blk_var1 (FLA_Obj A, FLA_Obj T, FLA_Obj w, FLA_Obj p, fla_qrut_t *cntl)

---

Function Documentation

FLA_Error FLA_QR_UT_piv_blk_var1	(	FLA_Obj	A,
		FLA_Obj	T,
		FLA_Obj	w,
		FLA_Obj	p,
		fla_qrut_t *	cntl
	)

References FLA_Apply_pivots(), FLA_Cont_with_1x3_to_1x2(), FLA_Cont_with_3x1_to_2x1(), FLA_Cont_with_3x3_to_2x2(), FLA_Obj_length(), FLA_Obj_min_dim(), FLA_Part_1x2(), FLA_Part_2x1(), FLA_Part_2x2(), FLA_QR_UT_piv_internal(), FLA_Repart_1x2_to_1x3(), FLA_Repart_2x1_to_3x1(), and FLA_Repart_2x2_to_3x3().

Referenced by FLA_QR_UT_piv_internal().

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

  FLA_Obj TL,    TR,       T0,  T1,  W12;
  FLA_Obj T1T,   T2B;

  FLA_Obj pT,              p0,
          pB,              p1,
                           p2;

  FLA_Obj wT,              w0,
          wB,              w1,
                           w2;

  dim_t   b_alg, b;

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

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

  FLA_Part_1x2( T,    &TL,  &TR,      0, FLA_LEFT );

  FLA_Part_2x1( p,    &pT, 
                      &pB,            0, FLA_TOP );

  FLA_Part_2x1( w,    &wT, 
                      &wB,            0, FLA_TOP );

  // Loop over A; T is properly truncated.
  while ( FLA_Obj_min_dim( ABR ) > 0 ){

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

    FLA_Repart_2x2_to_3x3( ATL, /**/ ATR,       &A00, /**/ &A01, &A02,
                        /* ************* */   /* ******************** */
                                                &A10, /**/ &A11, &A12,
                           ABL, /**/ ABR,       &A20, /**/ &A21, &A22,
                           b, b, FLA_BR );

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

    FLA_Repart_2x1_to_3x1( pT,                &p0, 
                        /* ** */            /* ** */
                                              &p1, 
                           pB,                &p2,        b, FLA_BOTTOM );

    FLA_Repart_2x1_to_3x1( wT,                &w0, 
                        /* ** */            /* ** */
                                              &w1, 
                           wB,                &w2,        b, FLA_BOTTOM );

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

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

    // Perform a unblocked (BLAS2-oriented) QR factorization 
    // with pivoting via the UT transform on ABR:
    //
    //   ABR  -> QB1 R11
    //
    // where:
    //  - QB1 is formed from UB1 (which is stored column-wise below the
    //    diagonal of ( A11 A21 )^T and T1T (which is stored to the upper triangle
    //    of T11).
    //  - R11 is stored to ( A11 A12 ).
    FLA_QR_UT_piv_internal( ABR, T1T, wB, p1, 
                            FLA_Cntl_sub_qrut( cntl ) );

    // Apply pivots to previous columns.
    FLA_Apply_pivots( FLA_RIGHT, FLA_TRANSPOSE, p1, ATR );

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

    FLA_Cont_with_3x3_to_2x2( &ATL, /**/ &ATR,       A00, A01, /**/ A02,
                                                     A10, A11, /**/ A12,
                            /* ************** */  /* ****************** */
                              &ABL, /**/ &ABR,       A20, A21, /**/ A22,
                              FLA_TL );

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

    FLA_Cont_with_3x1_to_2x1( &pT,                p0, 
                                                  p1, 
                            /* ** */           /* ** */
                              &pB,                p2,     FLA_TOP );

    FLA_Cont_with_3x1_to_2x1( &wT,                w0, 
                                                  w1, 
                            /* ** */           /* ** */
                              &wB,                w2,     FLA_TOP );
  }

  return FLA_SUCCESS;
}