FLA_QR_UT_piv_vars.h File Reference

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Functions
FLA_Error	FLA_QR_UT_piv_unb_var1 (FLA_Obj A, FLA_Obj T, FLA_Obj w, FLA_Obj p)
FLA_Error	FLA_QR_UT_piv_blk_var1 (FLA_Obj A, FLA_Obj T, FLA_Obj w, FLA_Obj p, fla_qrut_t *cntl)
FLA_Error	FLA_QR_UT_piv_unb_var2 (FLA_Obj A, FLA_Obj T, FLA_Obj w, FLA_Obj p)
FLA_Error	FLA_QR_UT_piv_blk_var2 (FLA_Obj A, FLA_Obj T, FLA_Obj w, FLA_Obj p, fla_qrut_t *cntl)
FLA_Error	FLA_Apply_H2_UT_piv_row (FLA_Obj tau, FLA_Obj a1t, FLA_Obj u1t, FLA_Obj W, FLA_Obj u2, FLA_Obj A2, FLA_Obj U2, FLA_Obj w1t, FLA_Obj vt)

Function Documentation

FLA_Apply_H2_UT_piv_row()

FLA_Error FLA_Apply_H2_UT_piv_row	(	FLA_Obj	tau,
		FLA_Obj	a1t,
		FLA_Obj	u1t,
		FLA_Obj	W,
		FLA_Obj	u2,
		FLA_Obj	A2,
		FLA_Obj	U2,
		FLA_Obj	w1t,
		FLA_Obj	vt
	)

{
  // a1t -= u1t W = 1 a1t -1 W^T u1t;
  FLA_Gemvc_external( FLA_TRANSPOSE, FLA_NO_CONJUGATE, 
                      FLA_MINUS_ONE, W, u1t, FLA_ONE, a1t );
 
  // w1t := a1t;
  FLA_Copy_external( a1t, w1t );
  
  // w1t += u2' A2 = 1 w1t + 1 A2^T conj(u2);
  FLA_Gemvc_external( FLA_TRANSPOSE, FLA_CONJUGATE, FLA_ONE, A2, u2, FLA_ONE, w1t );
 
  if ( FLA_Obj_min_dim( U2 ) > 0 ) 
  {
    FLA_Obj vtR;
 
    // Partition the workspace (a row vector matching the width of a1t)
    FLA_Part_1x2( vt, &vt, &vtR, FLA_Obj_width( U2 ), FLA_LEFT );
 
    // vt := u2'U2 = 0 vt + 1 U2^T conj(u2);
    FLA_Gemvc_external( FLA_TRANSPOSE, FLA_CONJUGATE, 
                        FLA_ONE, U2, u2, FLA_ZERO, vt );
 
    // w1t -= - vt W = 1 w1t -1 W^T vt;
    FLA_Gemvc_external( FLA_TRANSPOSE, FLA_NO_CONJUGATE, 
                        FLA_MINUS_ONE, W, vt, FLA_ONE, w1t );
  }
 
  // w1t = w1t / tau;
  FLA_Inv_scalc_external( FLA_NO_CONJUGATE, tau, w1t );
 
  // a1t  = a1t - w1t;
  FLA_Axpy_external( FLA_MINUS_ONE, w1t, a1t );
 
  return FLA_SUCCESS;
}

References FLA_Axpy_external(), FLA_Copy_external(), FLA_Gemvc_external(), FLA_Inv_scalc_external(), FLA_MINUS_ONE, FLA_Obj_min_dim(), FLA_Obj_width(), FLA_ONE, FLA_Part_1x2(), FLA_ZERO, and i.

Referenced by FLA_QR_UT_piv_unb_var2().

FLA_QR_UT_piv_blk_var1()

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

{
  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;
}

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(), FLA_Repart_2x2_to_3x3(), i, and w1.

Referenced by FLA_QR_UT_piv_internal().

FLA_QR_UT_piv_blk_var2()

FLA_Error FLA_QR_UT_piv_blk_var2	(	FLA_Obj	A,
		FLA_Obj	T,
		FLA_Obj	w,
		FLA_Obj	p,
		fla_qrut_t *	cntl
	)

{
  FLA_Obj ATL,   ATR,      A00, A01, A02, 
          ABL,   ABR,      A10, A11, A12,
                           A20, A21, A22;
 
  FLA_Obj TL,    TR,       T0,  T1,  W12;
  FLA_Obj TT,    TB;
 
  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 );
 
  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 );
 
    /*------------------------------------------------------------*/
 
    // ** Reshape T matrices to match the blocksize b
    FLA_Part_2x1( TR,   &TT, 
                        &TB,    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 the upper-triangle of T1. 
    //  - R11 is stored to ( A11 A12 ).
    //  - W12 stores  T and partial updates for FLA_Apply_Q_UT_piv_var.
    FLA_QR_UT_piv_internal( ABR, TT, wB, p1, 
                            FLA_Cntl_sub_qrut( cntl ) );
 
    if ( FLA_Obj_width( A12 ) > 0 )
    {
      // ** Block update
      FLA_Part_2x1( W12,  &TT, 
                          &TB,    b, FLA_TOP );
 
      FLA_Gemm_external( FLA_NO_TRANSPOSE, FLA_NO_TRANSPOSE, 
                         FLA_MINUS_ONE, A21, TT, FLA_ONE, A22 );
    }
 
    // ** 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;
}

References FLA_Apply_pivots(), FLA_Cont_with_1x3_to_1x2(), FLA_Cont_with_3x1_to_2x1(), FLA_Cont_with_3x3_to_2x2(), FLA_Gemm_external(), 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_QR_UT_piv_internal(), FLA_Repart_1x2_to_1x3(), FLA_Repart_2x1_to_3x1(), FLA_Repart_2x2_to_3x3(), i, and w1.

Referenced by FLA_QR_UT_piv_internal().

FLA_QR_UT_piv_unb_var1()

FLA_Error FLA_QR_UT_piv_unb_var1	(	FLA_Obj	A,
		FLA_Obj	T,
		FLA_Obj	w,
		FLA_Obj	p
	)

{
  FLA_Obj AL,    AR;
 
  FLA_Obj ATL,   ATR,      A00,  a01,     A02, 
          ABL,   ABR,      a10t, alpha11, a12t,
                           A20,  a21,     A22;
 
  FLA_Obj AT,              A0,
          AB,              a1t,
                           A2;
  FLA_Obj AB1, AT1, at1;
 
  FLA_Obj TTL,   TTR,      T00,  t01,   T02, 
          TBL,   TBR,      t10t, tau11, t12t,
                           T20,  t21,   T22;
 
  FLA_Obj pT,              p0,
          pB,              pi1,
                           p2;
 
  FLA_Obj wT,              w0,
          wB,              omega1,
                           w2;
 
  dim_t   nb  = FLA_Obj_width ( A ) - FLA_Obj_width( T );
  //dim_t   mb  = FLA_Obj_length( A ) - FLA_Obj_width( T );
 
  FLA_Part_1x2( A,    &AL,  &AR,      nb, FLA_RIGHT );
 
  FLA_Part_2x2( AL,   &ATL, &ATR,
                      &ABL, &ABR,     0, 0, FLA_TL );
 
  FLA_Part_2x1( AR,   &AT,
                      &AB,            0, FLA_TOP );
 
  FLA_Part_2x2( T,    &TTL, &TTR,
                      &TBL, &TBR,     0, 0, FLA_TL );
 
  FLA_Part_2x1( p,    &pT,
                      &pB,            0, FLA_TOP );
 
  FLA_Part_2x1( w,    &wT,
                      &wB,            0, FLA_TOP );
 
  while ( FLA_Obj_min_dim( ABR ) > 0 ){
 
    FLA_Repart_2x2_to_3x3( ATL, /**/ ATR,       &A00,  /**/ &a01,     &A02,
                        /* ************* */   /* ************************** */
                                                &a10t, /**/ &alpha11, &a12t,
                           ABL, /**/ ABR,       &A20,  /**/ &a21,     &A22,
                           1, 1, FLA_BR );
 
    FLA_Repart_2x1_to_3x1( AT,                &A0,
                        /* ** */            /* *** */
                                              &a1t,
                           AB,                &A2,        1, FLA_BOTTOM );
 
    FLA_Repart_2x2_to_3x3( TTL, /**/ TTR,       &T00,  /**/ &t01,   &T02,
                        /* ************* */   /* ************************ */
                                                &t10t, /**/ &tau11, &t12t,
                           TBL, /**/ TBR,       &T20,  /**/ &t21,   &T22,
                           1, 1, FLA_BR );
 
    FLA_Repart_2x1_to_3x1( pT,                &p0,
                        /* ** */            /* *** */
                                              &pi1,
                           pB,                &p2,        1, FLA_BOTTOM );
 
    FLA_Repart_2x1_to_3x1( wT,                &w0,
                        /* ** */            /* *** */
                                              &omega1,
                           wB,                &w2,        1, FLA_BOTTOM );
 
    /*------------------------------------------------------------*/
 
 
    // Ignore minus inputs for LAPACK compatability.
    if ( FLA_Obj_le( pi1, FLA_ZERO ) == FALSE )
    {
      // Determine pivot index
      FLA_Amax_external( wB, pi1 );
      FLA_Apply_pivots( FLA_LEFT, FLA_NO_TRANSPOSE, pi1, wB );
      
      // Apply pivots
      FLA_Merge_1x2( ABR, AB, &AB1 );
      FLA_Apply_pivots( FLA_RIGHT, FLA_TRANSPOSE, pi1, AB1 );
    }
    else
    {
      // Do not pivot.
      FLA_Set( FLA_ZERO, pi1 );
    }
 
    // Compute tau11 and u21 from alpha11 and a21 such that tau11 and u21
    // determine a Householder transform H such that applying H from the
    // left to the column vector consisting of alpha11 and a21 annihilates
    // the entries in a21 (and updates alpha11).
    FLA_Househ2_UT( FLA_LEFT,
                    alpha11,
                    a21, tau11 );
 
    // Apply H to (a12t A22)^T
    // / a12t \ =  H / a12t \
    // \ A22  /      \ A22  /
    //
    // where H is formed from tau11 and u21.
    FLA_Merge_1x2( A22,  A2,  &AB1 );
    FLA_Merge_1x2( a12t, a1t, &at1 );
 
    FLA_Apply_H2_UT( FLA_LEFT, tau11, a21, at1,
                                           AB1 );
 
    // t01 = a10t' + A20' * u21;
    FLA_Copyt_external( FLA_CONJ_TRANSPOSE, a10t, t01 );
    FLA_Gemv_external( FLA_CONJ_TRANSPOSE, FLA_ONE, A20, a21, FLA_ONE, t01 );
 
    // Apply pivots to previous rows
    if ( FLA_Obj_le( pi1, FLA_ZERO ) == FALSE )
    {
      FLA_Merge_1x2( ATR, AT, &AT1 );
      FLA_Apply_pivots( FLA_RIGHT, FLA_TRANSPOSE, pi1, AT1 );
    }
 
    // Norm downdate w2 = alpha w2 + beta columnwisenorm2(a12t)
    FLA_QR_UT_piv_colnorm( FLA_MINUS_ONE, at1, w2 );
 
    /*------------------------------------------------------------*/
 
    FLA_Cont_with_3x3_to_2x2( &ATL, /**/ &ATR,       A00,  a01,     /**/ A02,
                                                     a10t, alpha11, /**/ a12t,
                            /* ************** */  /* ************************ */
                              &ABL, /**/ &ABR,       A20,  a21,     /**/ A22,
                              FLA_TL );
 
    FLA_Cont_with_3x1_to_2x1( &AT,                A0,
                                                  a1t,
                            /* ** */           /* *** */
                              &AB,                A2,     FLA_TOP );
 
    FLA_Cont_with_3x3_to_2x2( &TTL, /**/ &TTR,       T00,  t01,   /**/ T02,
                                                     t10t, tau11, /**/ t12t,
                            /* ************** */  /* ********************** */
                              &TBL, /**/ &TBR,       T20,  t21,   /**/ T22,
                              FLA_TL );
 
    FLA_Cont_with_3x1_to_2x1( &pT,                p0,
                                                  pi1,
                            /* ** */           /* *** */
                              &pB,                p2,     FLA_TOP );
 
    FLA_Cont_with_3x1_to_2x1( &wT,                w0,
                                                  omega1,
                            /* ** */           /* *** */
                              &wB,                w2,     FLA_TOP );
  }
 
  return FLA_SUCCESS;
}

References FLA_Amax_external(), FLA_Apply_H2_UT(), FLA_Apply_pivots(), FLA_Cont_with_3x1_to_2x1(), FLA_Cont_with_3x3_to_2x2(), FLA_Copyt_external(), FLA_Gemv_external(), FLA_Househ2_UT(), FLA_Merge_1x2(), FLA_MINUS_ONE, FLA_Obj_le(), FLA_Obj_min_dim(), FLA_Obj_width(), FLA_ONE, FLA_Part_1x2(), FLA_Part_2x1(), FLA_Part_2x2(), FLA_QR_UT_piv_colnorm(), FLA_Repart_2x1_to_3x1(), FLA_Repart_2x2_to_3x3(), FLA_Set(), FLA_ZERO, i, and omega1.

Referenced by FLA_QR_UT_piv_internal().

FLA_QR_UT_piv_unb_var2()

FLA_Error FLA_QR_UT_piv_unb_var2	(	FLA_Obj	A,
		FLA_Obj	T,
		FLA_Obj	w,
		FLA_Obj	p
	)

{
  FLA_Obj ATL,   ATR,      A00,  a01,     A02, 
          ABL,   ABR,      a10t, alpha11, a12t,
                           A20,  a21,     A22;
 
  FLA_Obj TTL,   TTR,      T00,  t01,   T02, 
          TBL,   TBR,      t10t, tau11, t12t,
                           T20,  t21,   T22;
 
  FLA_Obj pT,              p0,
          pB,              pi1,
                           p2;
 
  FLA_Obj wT,              w0,
          wB,              omega1,
                           w2;
 
  FLA_Obj ab1, v;
 
  // Create workspace
  FLA_Obj_create( FLA_Obj_datatype( T ), 1, FLA_Obj_width( T ), 0, 0, &v );
 
  FLA_Part_2x2( A,    &ATL, &ATR,
                      &ABL, &ABR,     0, 0, FLA_TL );
 
  FLA_Part_2x2( T,    &TTL, &TTR,
                      &TBL, &TBR,     0, 0, FLA_TL );
 
  FLA_Part_2x1( p,    &pT,
                      &pB,            0, FLA_TOP );
 
  FLA_Part_2x1( w,    &wT,
                      &wB,            0, FLA_TOP );
 
  while ( FLA_Obj_min_dim( pB ) > 0 ) {
 
    FLA_Repart_2x2_to_3x3( ATL, /**/ ATR,       &A00,  /**/ &a01,     &A02,
                        /* ************* */   /* ************************** */
                                                &a10t, /**/ &alpha11, &a12t,
                           ABL, /**/ ABR,       &A20,  /**/ &a21,     &A22,
                           1, 1, FLA_BR );
 
    FLA_Repart_2x2_to_3x3( TTL, /**/ TTR,       &T00,  /**/ &t01,   &T02,
                        /* ************* */   /* ************************ */
                                                &t10t, /**/ &tau11, &t12t,
                           TBL, /**/ TBR,       &T20,  /**/ &t21,   &T22,
                           1, 1, FLA_BR );
 
    FLA_Repart_2x1_to_3x1( pT,                &p0,
                        /* ** */            /* *** */
                                              &pi1,
                           pB,                &p2,        1, FLA_BOTTOM );
 
    FLA_Repart_2x1_to_3x1( wT,                &w0,
                        /* ** */            /* *** */
                                              &omega1,
                           wB,                &w2,        1, FLA_BOTTOM );
 
    /*------------------------------------------------------------*/
 
 
    //  ** Ignore minus inputs for LAPACK compatability.
    if ( FLA_Obj_lt( pi1, FLA_ZERO ) == FALSE )
    {
      // ** Determine pivot index
      FLA_Amax_external( wB, pi1 );
 
      // ** BLIS returns -1 if it fails to search the maximum value
      if ( FLA_Obj_lt( pi1, FLA_ZERO ) == TRUE )
        FLA_Set( FLA_ZERO, pi1 );
 
      // ** Apply a pivot on column norms
      FLA_Apply_pivots( FLA_LEFT, FLA_NO_TRANSPOSE, pi1, wB );
 
      // ** Apply a pivot on ABR
      FLA_Apply_pivots( FLA_RIGHT, FLA_TRANSPOSE, pi1, ABR );
 
      // ** Apply a pivot on TTR
      FLA_Apply_pivots( FLA_RIGHT, FLA_TRANSPOSE, pi1, TTR );
    }
    else
    {
      // ** Do not pivot.
      FLA_Set( FLA_ZERO, pi1 );
    }
 
    // ** Update the pivot column
    FLA_Merge_2x1( alpha11,
                   a21, &ab1 );
 
    // ab1 = ab1 - ABL t01
    FLA_Gemv_external( FLA_NO_TRANSPOSE, FLA_MINUS_ONE, ABL, t01, FLA_ONE, ab1 );
 
    // ** Find the householder reflector on that column
    FLA_Househ2_UT( FLA_LEFT, alpha11,
                              a21,     tau11 );
 
    // ** Update the pivot row
    FLA_Apply_H2_UT_piv_row( tau11, a12t, a10t, T02,
                             a21,   A22,  A20,  t12t,
                             v );
 
    // ** Apply pivots on ATR 
    FLA_Apply_pivots( FLA_RIGHT, FLA_TRANSPOSE, pi1, ATR );
 
    // ** Norm downdate w2 = w2 - columnwisenorm2(a12t)
    FLA_QR_UT_piv_colnorm( FLA_MINUS_ONE, a12t, w2 );
 
    // ** Update T matrix
    // t01 = a10t' + A20' * u21; 
    FLA_Copyt_external( FLA_CONJ_TRANSPOSE, a10t, t01 );
    FLA_Gemv_external( FLA_CONJ_TRANSPOSE, FLA_ONE, A20, a21, FLA_ONE, t01 );
 
    /*------------------------------------------------------------*/
 
    FLA_Cont_with_3x3_to_2x2( &ATL, /**/ &ATR,       A00,  a01,     /**/ A02,
                                                     a10t, alpha11, /**/ a12t,
                            /* ************** */  /* ************************ */
                              &ABL, /**/ &ABR,       A20,  a21,     /**/ A22,
                              FLA_TL );
 
    FLA_Cont_with_3x3_to_2x2( &TTL, /**/ &TTR,       T00,  t01,   /**/ T02,
                                                     t10t, tau11, /**/ t12t,
                            /* ************** */  /* ********************** */
                              &TBL, /**/ &TBR,       T20,  t21,   /**/ T22,
                              FLA_TL );
 
    FLA_Cont_with_3x1_to_2x1( &pT,                p0,
                                                  pi1,
                            /* ** */           /* *** */
                              &pB,                p2,     FLA_TOP );
 
    FLA_Cont_with_3x1_to_2x1( &wT,                w0,
                                                  omega1,
                            /* ** */           /* *** */
                              &wB,                w2,     FLA_TOP );
  }
 
  // Free the workspace
  FLA_Obj_free( &v);
 
  return FLA_SUCCESS;
}

References FLA_Amax_external(), FLA_Apply_H2_UT_piv_row(), FLA_Apply_pivots(), FLA_Cont_with_3x1_to_2x1(), FLA_Cont_with_3x3_to_2x2(), FLA_Copyt_external(), FLA_Gemv_external(), FLA_Househ2_UT(), FLA_Merge_2x1(), FLA_MINUS_ONE, FLA_Obj_create(), FLA_Obj_datatype(), FLA_Obj_free(), FLA_Obj_lt(), FLA_Obj_min_dim(), FLA_Obj_width(), FLA_ONE, FLA_Part_2x1(), FLA_Part_2x2(), FLA_QR_UT_piv_colnorm(), FLA_Repart_2x1_to_3x1(), FLA_Repart_2x2_to_3x3(), FLA_Set(), FLA_ZERO, i, and omega1.

Referenced by FLA_QR_UT_piv_internal().