FLA_Househ2_UT.c File Reference

(r)

Functions
FLA_Error	FLA_Househ2_UT (FLA_Side side, FLA_Obj chi_1, FLA_Obj x2, FLA_Obj tau)
FLA_Error	FLA_Househ2_UT_l_ops (int m_x2, float *chi_1, float *x2, int inc_x2, float *tau)
FLA_Error	FLA_Househ2_UT_l_opd (int m_x2, double *chi_1, double *x2, int inc_x2, double *tau)
FLA_Error	FLA_Househ2_UT_l_opc (int m_x2, scomplex *chi_1, scomplex *x2, int inc_x2, scomplex *tau)
FLA_Error	FLA_Househ2_UT_l_opz (int m_x2, dcomplex *chi_1, dcomplex *x2, int inc_x2, dcomplex *tau)
FLA_Error	FLA_Househ2_UT_r_ops (int m_x2, float *chi_1, float *x2, int inc_x2, float *tau)
FLA_Error	FLA_Househ2_UT_r_opd (int m_x2, double *chi_1, double *x2, int inc_x2, double *tau)
FLA_Error	FLA_Househ2_UT_r_opc (int m_x2, scomplex *chi_1, scomplex *x2, int inc_x2, scomplex *tau)
FLA_Error	FLA_Househ2_UT_r_opz (int m_x2, dcomplex *chi_1, dcomplex *x2, int inc_x2, dcomplex *tau)

Function Documentation

FLA_Househ2_UT()

FLA_Error FLA_Househ2_UT	(	FLA_Side	side,
		FLA_Obj	chi_1,
		FLA_Obj	x2,
		FLA_Obj	tau
	)

{
  FLA_Datatype datatype;
  int          m_x2;
  int          inc_x2;
 
  datatype = FLA_Obj_datatype( x2 );
 
  m_x2     = FLA_Obj_vector_dim( x2 );
  inc_x2   = FLA_Obj_vector_inc( x2 );
 
  if ( FLA_Check_error_level() >= FLA_MIN_ERROR_CHECKING )
    FLA_Househ2_UT_check( side, chi_1, x2, tau );
 
  switch ( datatype )
  {
    case FLA_FLOAT:
    {
      float* chi_1_p = ( float* ) FLA_FLOAT_PTR( chi_1 );
      float* x2_p    = ( float* ) FLA_FLOAT_PTR( x2 );
      float* tau_p   = ( float* ) FLA_FLOAT_PTR( tau );
 
      if ( side == FLA_LEFT )
        FLA_Househ2_UT_l_ops( m_x2,
                              chi_1_p,
                              x2_p, inc_x2,
                              tau_p );
      else // if ( side == FLA_RIGHT )
        FLA_Househ2_UT_r_ops( m_x2,
                              chi_1_p,
                              x2_p, inc_x2,
                              tau_p );
 
      break;
    }
 
    case FLA_DOUBLE:
    {
      double* chi_1_p = ( double* ) FLA_DOUBLE_PTR( chi_1 );
      double* x2_p    = ( double* ) FLA_DOUBLE_PTR( x2 );
      double* tau_p   = ( double* ) FLA_DOUBLE_PTR( tau );
 
      if ( side == FLA_LEFT )
        FLA_Househ2_UT_l_opd( m_x2,
                              chi_1_p,
                              x2_p, inc_x2,
                              tau_p );
      else // if ( side == FLA_RIGHT )
        FLA_Househ2_UT_r_opd( m_x2,
                              chi_1_p,
                              x2_p, inc_x2,
                              tau_p );
 
      break;
    }
 
    case FLA_COMPLEX:
    {
      scomplex* chi_1_p = ( scomplex* ) FLA_COMPLEX_PTR( chi_1 );
      scomplex* x2_p    = ( scomplex* ) FLA_COMPLEX_PTR( x2 );
      scomplex* tau_p   = ( scomplex* ) FLA_COMPLEX_PTR( tau );
 
      if ( side == FLA_LEFT )
        FLA_Househ2_UT_l_opc( m_x2,
                              chi_1_p,
                              x2_p, inc_x2,
                              tau_p );
      else // if ( side == FLA_RIGHT )
        FLA_Househ2_UT_r_opc( m_x2,
                              chi_1_p,
                              x2_p, inc_x2,
                              tau_p );
 
      break;
    }
 
    case FLA_DOUBLE_COMPLEX:
    {
      dcomplex* chi_1_p = ( dcomplex* ) FLA_DOUBLE_COMPLEX_PTR( chi_1 );
      dcomplex* x2_p    = ( dcomplex* ) FLA_DOUBLE_COMPLEX_PTR( x2 );
      dcomplex* tau_p   = ( dcomplex* ) FLA_DOUBLE_COMPLEX_PTR( tau );
 
      if ( side == FLA_LEFT )
        FLA_Househ2_UT_l_opz( m_x2,
                              chi_1_p,
                              x2_p, inc_x2,
                              tau_p );
      else // if ( side == FLA_RIGHT )
        FLA_Househ2_UT_r_opz( m_x2,
                              chi_1_p,
                              x2_p, inc_x2,
                              tau_p );
 
      break;
    }
  }
 
  return FLA_SUCCESS;
}

References FLA_Check_error_level(), FLA_Househ2_UT_check(), FLA_Househ2_UT_l_opc(), FLA_Househ2_UT_l_opd(), FLA_Househ2_UT_l_ops(), FLA_Househ2_UT_l_opz(), FLA_Househ2_UT_r_opc(), FLA_Househ2_UT_r_opd(), FLA_Househ2_UT_r_ops(), FLA_Househ2_UT_r_opz(), FLA_Obj_datatype(), FLA_Obj_vector_dim(), FLA_Obj_vector_inc(), and i.

Referenced by FLA_Bidiag_UT_u_step_unb_var1(), FLA_Bidiag_UT_u_step_unb_var2(), FLA_Bidiag_UT_u_step_unb_var3(), FLA_Bidiag_UT_u_step_unb_var4(), FLA_Bidiag_UT_u_step_unb_var5(), FLA_CAQR2_UT_unb_var1(), FLA_Hess_UT_step_unb_var1(), FLA_Hess_UT_step_unb_var2(), FLA_Hess_UT_step_unb_var3(), FLA_Hess_UT_step_unb_var4(), FLA_Hess_UT_step_unb_var5(), FLA_LQ_UT_unb_var1(), FLA_LQ_UT_unb_var2(), FLA_QR2_UT_unb_var1(), FLA_QR_UT_piv_unb_var1(), FLA_QR_UT_piv_unb_var2(), FLA_QR_UT_unb_var1(), FLA_QR_UT_unb_var2(), FLA_Tridiag_UT_l_step_unb_var1(), FLA_Tridiag_UT_l_step_unb_var2(), and FLA_Tridiag_UT_l_step_unb_var3().

FLA_Househ2_UT_l_opc()

FLA_Error FLA_Househ2_UT_l_opc	(	int	m_x2,
		scomplex *	chi_1,
		scomplex *	x2,
		int	inc_x2,
		scomplex *	tau
	)

{
  scomplex one_half = *FLA_COMPLEX_PTR( FLA_ONE_HALF );
  scomplex y[2];
  scomplex alpha;
  scomplex chi_1_minus_alpha;
  float    abs_chi_1;
  float    norm_x_2;
  float    norm_x;
  float    abs_chi_1_minus_alpha;
  float    norm_x_2_div_abs_chi_1_minus_alpha;
  int      i_one = 1;
  int      i_two = 2;
 
  //
  // Compute the 2-norm of x_2:
  //
  //   norm_x_2 := || x_2 ||_2
  //
 
  bl1_cnrm2( m_x2,
             x2, inc_x2,
             &norm_x_2 );
 
  //
  // If 2-norm of x_2 is zero, then return with trivial values.
  //
 
  if ( norm_x_2 == 0.0F )
  {
    chi_1->real = -(chi_1->real);
    chi_1->imag = -(chi_1->imag);
    tau->real   = one_half.real;
    tau->imag   = one_half.imag;
 
    return FLA_SUCCESS;
  }
 
  //
  // Compute the absolute value (magnitude) of chi_1, which equals the 2-norm
  // of chi_1:
  //
  //   abs_chi_1 :=  | chi_1 |  =  || chi_1 ||_2
  //
 
  bl1_cnrm2( i_one,
             chi_1, i_one,
             &abs_chi_1 );
 
  //
  // Compute the 2-norm of x via the two norms previously computed above:
  //
  //   norm_x :=  || x ||_2  =  || / chi_1 \ ||   =  || / || chi_1 ||_2 \ ||
  //                            || \  x_2  / ||_2    || \  || x_2 ||_2  / ||_2
  //
 
  y[0].real = abs_chi_1;
  y[0].imag = 0.0F;
 
  y[1].real = norm_x_2;
  y[1].imag = 0.0F;
 
  bl1_cnrm2( i_two,
             y, i_one,
             &norm_x );
 
  //
  // Compute alpha:
  //
  //   alpha := - || x ||_2 * chi_1 / | chi_1 |
  //
 
  if ( abs_chi_1 == 0.0F )
  {
    alpha.real = norm_x * ( -1.0F );
    alpha.imag = norm_x * ( -1.0F );
  }
  else
  {
    alpha.real = norm_x * ( -chi_1->real / abs_chi_1 );
    alpha.imag = norm_x * ( -chi_1->imag / abs_chi_1 );
  }
 
  //
  // Overwrite x_2 with u_2:
  //
  //   x_2 := x_2 / ( chi_1 - alpha )
  //
 
  chi_1_minus_alpha.real = chi_1->real - alpha.real;
  chi_1_minus_alpha.imag = chi_1->imag - alpha.imag;
 
  bl1_cinvscalv( BLIS1_NO_CONJUGATE,
                 m_x2,
                 &chi_1_minus_alpha,
                 x2, inc_x2 );
 
  //
  // Compute tau:
  //
  //   tau := ( 1 + u_2' * u_2 ) / 2
  //        = ( ( chi_1 - alpha ) * conj( chi_1 - alpha ) + x_2' * x_2 ) /
  //          ( 2 * ( chi_1 - alpha ) * conj( chi_1 - alpha ) )
  //        = 1/2 + ( || x ||_2 / | chi_1 - alpha | )^2
  //
 
  bl1_csabsval2( &chi_1_minus_alpha, &abs_chi_1_minus_alpha );
 
  norm_x_2_div_abs_chi_1_minus_alpha = norm_x_2 / abs_chi_1_minus_alpha;
  tau->real = one_half.real + one_half.real*(norm_x_2_div_abs_chi_1_minus_alpha * 
                                             norm_x_2_div_abs_chi_1_minus_alpha);
  tau->imag = 0.0F;
 
  //
  // Overwrite chi_1 with alpha:
  //
  //   chi_1 := alpha
  //
 
  chi_1->real = alpha.real;
  chi_1->imag = alpha.imag;
 
  return FLA_SUCCESS;
}

References bl1_cinvscalv(), bl1_cnrm2(), BLIS1_NO_CONJUGATE, FLA_ONE_HALF, and i.

Referenced by FLA_Bidiag_UT_u_step_ofc_var2(), FLA_Bidiag_UT_u_step_ofc_var3(), FLA_Bidiag_UT_u_step_ofc_var4(), FLA_Bidiag_UT_u_step_opc_var1(), FLA_Bidiag_UT_u_step_opc_var2(), FLA_Bidiag_UT_u_step_opc_var3(), FLA_Bidiag_UT_u_step_opc_var4(), FLA_Bidiag_UT_u_step_opc_var5(), FLA_CAQR2_UT_opc_var1(), FLA_Hess_UT_step_ofc_var2(), FLA_Hess_UT_step_ofc_var3(), FLA_Hess_UT_step_ofc_var4(), FLA_Hess_UT_step_opc_var1(), FLA_Hess_UT_step_opc_var2(), FLA_Hess_UT_step_opc_var3(), FLA_Hess_UT_step_opc_var4(), FLA_Hess_UT_step_opc_var5(), FLA_Househ2_UT(), FLA_Househ2_UT_r_opc(), FLA_QR2_UT_opc_var1(), FLA_QR_UT_opc_var1(), FLA_QR_UT_opc_var2(), FLA_Tridiag_UT_l_step_ofc_var2(), FLA_Tridiag_UT_l_step_ofc_var3(), FLA_Tridiag_UT_l_step_opc_var1(), FLA_Tridiag_UT_l_step_opc_var2(), and FLA_Tridiag_UT_l_step_opc_var3().

FLA_Househ2_UT_l_opd()

FLA_Error FLA_Househ2_UT_l_opd	(	int	m_x2,
		double *	chi_1,
		double *	x2,
		int	inc_x2,
		double *	tau
	)

{
  double   one_half = *FLA_DOUBLE_PTR( FLA_ONE_HALF );
  double   y[2];
  double   alpha;
  double   chi_1_minus_alpha;
  double   abs_chi_1;
  double   norm_x_2;
  double   norm_x;
  double   abs_chi_1_minus_alpha;
  double   norm_x_2_div_abs_chi_1_minus_alpha;
  int      i_one = 1;
  int      i_two = 2;
 
  //
  // Compute the 2-norm of x_2:
  //
  //   norm_x_2 := || x_2 ||_2
  //
 
  bl1_dnrm2( m_x2,
             x2, inc_x2,
             &norm_x_2 );
 
  //
  // If 2-norm of x_2 is zero, then return with trivial values.
  //
 
  if ( norm_x_2 == 0.0 )
  {
    *chi_1 = -(*chi_1);
    *tau   = one_half;
 
    return FLA_SUCCESS;
  }
 
  //
  // Compute the absolute value (magnitude) of chi_1, which equals the 2-norm
  // of chi_1:
  //
  //   abs_chi_1 :=  | chi_1 |  =  || chi_1 ||_2
  //
 
  bl1_dnrm2( i_one,
             chi_1, i_one,
             &abs_chi_1 );
 
  //
  // Compute the 2-norm of x via the two norms previously computed above:
  //
  //   norm_x :=  || x ||_2  =  || / chi_1 \ ||   =  || / || chi_1 ||_2 \ ||
  //                            || \  x_2  / ||_2    || \  || x_2 ||_2  / ||_2
  //
 
  y[0] = abs_chi_1;
  y[1] = norm_x_2;
 
  bl1_dnrm2( i_two,
             y, i_one,
             &norm_x );
 
  //
  // Compute alpha:
  //
  //   alpha := - || x ||_2 * chi_1 / | chi_1 |
  //          = -sign( chi_1 ) * || x ||_2
  //
 
  alpha = -dsign( *chi_1 ) * norm_x;
 
  //
  // Overwrite x_2 with u_2:
  //
  //   x_2 := x_2 / ( chi_1 - alpha )
  //
 
  chi_1_minus_alpha = *chi_1 - alpha;
 
  bl1_dinvscalv( BLIS1_NO_CONJUGATE,
                 m_x2,
                 &chi_1_minus_alpha,
                 x2, inc_x2 );
 
  //
  // Compute tau:
  //
  //   tau := ( 1 + u_2' * u_2 ) / 2
  //        = ( ( chi_1 - alpha ) * conj( chi_1 - alpha ) + x_2' * x_2 ) /
  //          ( 2 * ( chi_1 - alpha ) * conj( chi_1 - alpha ) )
  //        = 1/2 + ( || x ||_2 / | chi_1 - alpha | )^2
  //
 
  bl1_dabsval2( &chi_1_minus_alpha, &abs_chi_1_minus_alpha );
 
  abs_chi_1_minus_alpha = (double)fabs(chi_1_minus_alpha);
 
  norm_x_2_div_abs_chi_1_minus_alpha = norm_x_2 / abs_chi_1_minus_alpha;
  *tau = one_half + one_half*(norm_x_2_div_abs_chi_1_minus_alpha * 
                              norm_x_2_div_abs_chi_1_minus_alpha);
 
  //
  // Overwrite chi_1 with alpha:
  //
  //   chi_1 := alpha
  //
 
  *chi_1 = alpha;
 
  return FLA_SUCCESS;
}

References bl1_dinvscalv(), bl1_dnrm2(), BLIS1_NO_CONJUGATE, FLA_ONE_HALF, and i.

Referenced by FLA_Bidiag_UT_u_step_ofd_var2(), FLA_Bidiag_UT_u_step_ofd_var3(), FLA_Bidiag_UT_u_step_ofd_var4(), FLA_Bidiag_UT_u_step_opd_var1(), FLA_Bidiag_UT_u_step_opd_var2(), FLA_Bidiag_UT_u_step_opd_var3(), FLA_Bidiag_UT_u_step_opd_var4(), FLA_Bidiag_UT_u_step_opd_var5(), FLA_CAQR2_UT_opd_var1(), FLA_Hess_UT_step_ofd_var2(), FLA_Hess_UT_step_ofd_var3(), FLA_Hess_UT_step_ofd_var4(), FLA_Hess_UT_step_opd_var1(), FLA_Hess_UT_step_opd_var2(), FLA_Hess_UT_step_opd_var3(), FLA_Hess_UT_step_opd_var4(), FLA_Hess_UT_step_opd_var5(), FLA_Househ2_UT(), FLA_Househ2_UT_r_opd(), FLA_QR2_UT_opd_var1(), FLA_QR_UT_opd_var1(), FLA_QR_UT_opd_var2(), FLA_Tridiag_UT_l_step_ofd_var2(), FLA_Tridiag_UT_l_step_ofd_var3(), FLA_Tridiag_UT_l_step_opd_var1(), FLA_Tridiag_UT_l_step_opd_var2(), and FLA_Tridiag_UT_l_step_opd_var3().

FLA_Househ2_UT_l_ops()

FLA_Error FLA_Househ2_UT_l_ops	(	int	m_x2,
		float *	chi_1,
		float *	x2,
		int	inc_x2,
		float *	tau
	)

{
  float    one_half = *FLA_FLOAT_PTR( FLA_ONE_HALF );
  float    y[2];
  float    alpha;
  float    chi_1_minus_alpha;
  float    abs_chi_1;
  float    norm_x_2;
  float    norm_x;
  float    abs_chi_1_minus_alpha;
  float    norm_x_2_div_abs_chi_1_minus_alpha;
  int      i_one = 1;
  int      i_two = 2;
 
  //
  // Compute the 2-norm of x_2:
  //
  //   norm_x_2 := || x_2 ||_2
  //
 
  bl1_snrm2( m_x2,
             x2, inc_x2,
             &norm_x_2 );
 
  //
  // If 2-norm of x_2 is zero, then return with trivial values.
  //
 
  if ( norm_x_2 == 0.0F )
  {
    *chi_1 = -(*chi_1);
    *tau   = one_half;
 
    return FLA_SUCCESS;
  }
 
  //
  // Compute the absolute value (magnitude) of chi_1, which equals the 2-norm
  // of chi_1:
  //
  //   abs_chi_1 :=  | chi_1 |  =  || chi_1 ||_2
  //
 
  bl1_snrm2( i_one,
             chi_1, i_one,
             &abs_chi_1 );
 
  //
  // Compute the 2-norm of x via the two norms previously computed above:
  //
  //   norm_x :=  || x ||_2  =  || / chi_1 \ ||   =  || / || chi_1 ||_2 \ ||
  //                            || \  x_2  / ||_2    || \  || x_2 ||_2  / ||_2
  //
 
  y[0] = abs_chi_1;
  y[1] = norm_x_2;
 
  bl1_snrm2( i_two,
             y, i_one,
             &norm_x );
 
  //
  // Compute alpha:
  //
  //   alpha := - || x ||_2 * chi_1 / | chi_1 |
  //          = -sign( chi_1 ) * || x ||_2
  //
 
  alpha = -ssign( *chi_1 ) * norm_x;
 
  //
  // Overwrite x_2 with u_2:
  //
  //   x_2 := x_2 / ( chi_1 - alpha )
  //
 
  chi_1_minus_alpha = *chi_1 - alpha;
 
  bl1_sinvscalv( BLIS1_NO_CONJUGATE,
                 m_x2,
                 &chi_1_minus_alpha,
                 x2, inc_x2 );
 
  //
  // Compute tau:
  //
  //   tau := ( 1 + u_2' * u_2 ) / 2
  //        = ( ( chi_1 - alpha ) * conj( chi_1 - alpha ) + x_2' * x_2 ) /
  //          ( 2 * ( chi_1 - alpha ) * conj( chi_1 - alpha ) )
  //        = 1/2 + ( || x ||_2 / | chi_1 - alpha | )^2
  //
 
  bl1_sabsval2( &chi_1_minus_alpha, &abs_chi_1_minus_alpha );
 
  norm_x_2_div_abs_chi_1_minus_alpha = norm_x_2 / abs_chi_1_minus_alpha;
  *tau = one_half + one_half*(norm_x_2_div_abs_chi_1_minus_alpha * 
                              norm_x_2_div_abs_chi_1_minus_alpha);
 
  //
  // Overwrite chi_1 with alpha:
  //
  //   chi_1 := alpha
  //
 
  *chi_1 = alpha;
 
  return FLA_SUCCESS;
}

References bl1_sinvscalv(), bl1_snrm2(), BLIS1_NO_CONJUGATE, FLA_ONE_HALF, and i.

Referenced by FLA_Bidiag_UT_u_step_ofs_var2(), FLA_Bidiag_UT_u_step_ofs_var3(), FLA_Bidiag_UT_u_step_ofs_var4(), FLA_Bidiag_UT_u_step_ops_var1(), FLA_Bidiag_UT_u_step_ops_var2(), FLA_Bidiag_UT_u_step_ops_var3(), FLA_Bidiag_UT_u_step_ops_var4(), FLA_Bidiag_UT_u_step_ops_var5(), FLA_CAQR2_UT_ops_var1(), FLA_Hess_UT_step_ofs_var2(), FLA_Hess_UT_step_ofs_var3(), FLA_Hess_UT_step_ofs_var4(), FLA_Hess_UT_step_ops_var1(), FLA_Hess_UT_step_ops_var2(), FLA_Hess_UT_step_ops_var3(), FLA_Hess_UT_step_ops_var4(), FLA_Hess_UT_step_ops_var5(), FLA_Househ2_UT(), FLA_Househ2_UT_r_ops(), FLA_QR2_UT_ops_var1(), FLA_QR_UT_ops_var1(), FLA_QR_UT_ops_var2(), FLA_Tridiag_UT_l_step_ofs_var2(), FLA_Tridiag_UT_l_step_ofs_var3(), FLA_Tridiag_UT_l_step_ops_var1(), FLA_Tridiag_UT_l_step_ops_var2(), and FLA_Tridiag_UT_l_step_ops_var3().

FLA_Househ2_UT_l_opz()

FLA_Error FLA_Househ2_UT_l_opz	(	int	m_x2,
		dcomplex *	chi_1,
		dcomplex *	x2,
		int	inc_x2,
		dcomplex *	tau
	)

{
  dcomplex one_half = *FLA_DOUBLE_COMPLEX_PTR( FLA_ONE_HALF );
  dcomplex y[2];
  dcomplex alpha;
  dcomplex chi_1_minus_alpha;
  double   abs_chi_1;
  double   norm_x_2;
  double   norm_x;
  double   abs_chi_1_minus_alpha;
  double   norm_x_2_div_abs_chi_1_minus_alpha;
  int      i_one = 1;
  int      i_two = 2;
 
  //
  // Compute the 2-norm of x_2:
  //
  //   norm_x_2 := || x_2 ||_2
  //
 
  bl1_znrm2( m_x2,
             x2, inc_x2,
             &norm_x_2 );
 
  //
  // If 2-norm of x_2 is zero, then return with trivial values.
  //
 
  if ( norm_x_2 == 0.0 )
  {
    chi_1->real = -(chi_1->real);
    chi_1->imag = -(chi_1->imag);
    tau->real   = one_half.real;
    tau->imag   = one_half.imag;
 
    return FLA_SUCCESS;
  }
 
  //
  // Compute the absolute value (magnitude) of chi_1, which equals the 2-norm
  // of chi_1:
  //
  //   abs_chi_1 :=  | chi_1 |  =  || chi_1 ||_2
  //
 
  bl1_znrm2( i_one,
             chi_1, i_one,
             &abs_chi_1 );
 
  //
  // Compute the 2-norm of x via the two norms previously computed above:
  //
  //   norm_x :=  || x ||_2  =  || / chi_1 \ ||   =  || / || chi_1 ||_2 \ ||
  //                            || \  x_2  / ||_2    || \  || x_2 ||_2  / ||_2
  //
 
  y[0].real = abs_chi_1;
  y[0].imag = 0.0;
 
  y[1].real = norm_x_2;
  y[1].imag = 0.0;
 
  bl1_znrm2( i_two,
             y, i_one,
             &norm_x );
 
  //
  // Compute alpha:
  //
  //   alpha := - || x ||_2 * chi_1 / | chi_1 |
  //
 
  if ( abs_chi_1 == 0.0 )
  {
    alpha.real = norm_x * ( -1.0 );
    alpha.imag = norm_x * ( -1.0 );
  }
  else
  {
    alpha.real = norm_x * ( -chi_1->real / abs_chi_1 );
    alpha.imag = norm_x * ( -chi_1->imag / abs_chi_1 );
  }
 
  //
  // Overwrite x_2 with u_2:
  //
  //   x_2 := x_2 / ( chi_1 - alpha )
  //
 
  chi_1_minus_alpha.real = chi_1->real - alpha.real;
  chi_1_minus_alpha.imag = chi_1->imag - alpha.imag;
 
  bl1_zinvscalv( BLIS1_NO_CONJUGATE,
                 m_x2,
                 &chi_1_minus_alpha,
                 x2, inc_x2 );
 
  //
  // Compute tau:
  //
  //   tau := ( 1 + u_2' * u_2 ) / 2
  //        = ( ( chi_1 - alpha ) * conj( chi_1 - alpha ) + x_2' * x_2 ) /
  //          ( 2 * ( chi_1 - alpha ) * conj( chi_1 - alpha ) )
  //        = 1/2 + ( || x ||_2 / | chi_1 - alpha | )^2
  //
 
  bl1_zdabsval2( &chi_1_minus_alpha, &abs_chi_1_minus_alpha );
 
  norm_x_2_div_abs_chi_1_minus_alpha = norm_x_2 / abs_chi_1_minus_alpha;
  tau->real = one_half.real + one_half.real*(norm_x_2_div_abs_chi_1_minus_alpha * 
                                             norm_x_2_div_abs_chi_1_minus_alpha);
  tau->imag = 0.0;
 
  //
  // Overwrite chi_1 with alpha:
  //
  //   chi_1 := alpha
  //
 
  chi_1->real = alpha.real;
  chi_1->imag = alpha.imag;
 
  return FLA_SUCCESS;
}

References bl1_zinvscalv(), bl1_znrm2(), BLIS1_NO_CONJUGATE, FLA_ONE_HALF, and i.

Referenced by FLA_Bidiag_UT_u_step_ofz_var2(), FLA_Bidiag_UT_u_step_ofz_var3(), FLA_Bidiag_UT_u_step_ofz_var4(), FLA_Bidiag_UT_u_step_opz_var1(), FLA_Bidiag_UT_u_step_opz_var2(), FLA_Bidiag_UT_u_step_opz_var3(), FLA_Bidiag_UT_u_step_opz_var4(), FLA_Bidiag_UT_u_step_opz_var5(), FLA_CAQR2_UT_opz_var1(), FLA_Hess_UT_step_ofz_var2(), FLA_Hess_UT_step_ofz_var3(), FLA_Hess_UT_step_ofz_var4(), FLA_Hess_UT_step_opz_var1(), FLA_Hess_UT_step_opz_var2(), FLA_Hess_UT_step_opz_var3(), FLA_Hess_UT_step_opz_var4(), FLA_Hess_UT_step_opz_var5(), FLA_Househ2_UT(), FLA_Househ2_UT_r_opz(), FLA_QR2_UT_opz_var1(), FLA_QR_UT_opz_var1(), FLA_QR_UT_opz_var2(), FLA_Tridiag_UT_l_step_ofz_var2(), FLA_Tridiag_UT_l_step_ofz_var3(), FLA_Tridiag_UT_l_step_opz_var1(), FLA_Tridiag_UT_l_step_opz_var2(), and FLA_Tridiag_UT_l_step_opz_var3().

FLA_Househ2_UT_r_opc()

FLA_Error FLA_Househ2_UT_r_opc	(	int	m_x2,
		scomplex *	chi_1,
		scomplex *	x2,
		int	inc_x2,
		scomplex *	tau
	)

{
  FLA_Househ2_UT_l_opc( m_x2,
                        chi_1,
                        x2, inc_x2,
                        tau );
 
  bl1_cconjv( m_x2,
              x2, inc_x2 );
 
  return FLA_SUCCESS;
}

References bl1_cconjv(), FLA_Househ2_UT_l_opc(), and i.

Referenced by FLA_Bidiag_UT_u_step_ofc_var2(), FLA_Bidiag_UT_u_step_opc_var1(), FLA_Bidiag_UT_u_step_opc_var2(), FLA_Bidiag_UT_u_step_opc_var5(), FLA_Househ2_UT(), FLA_LQ_UT_opc_var1(), and FLA_LQ_UT_opc_var2().

FLA_Househ2_UT_r_opd()

FLA_Error FLA_Househ2_UT_r_opd	(	int	m_x2,
		double *	chi_1,
		double *	x2,
		int	inc_x2,
		double *	tau
	)

{
  FLA_Househ2_UT_l_opd( m_x2,
                        chi_1,
                        x2, inc_x2,
                        tau );
 
  return FLA_SUCCESS;
}

References FLA_Househ2_UT_l_opd(), and i.

Referenced by FLA_Bidiag_UT_u_step_ofd_var2(), FLA_Bidiag_UT_u_step_opd_var1(), FLA_Bidiag_UT_u_step_opd_var2(), FLA_Bidiag_UT_u_step_opd_var5(), FLA_Househ2_UT(), FLA_LQ_UT_opd_var1(), and FLA_LQ_UT_opd_var2().

FLA_Househ2_UT_r_ops()

FLA_Error FLA_Househ2_UT_r_ops	(	int	m_x2,
		float *	chi_1,
		float *	x2,
		int	inc_x2,
		float *	tau
	)

{
  FLA_Househ2_UT_l_ops( m_x2,
                        chi_1,
                        x2, inc_x2,
                        tau );
 
  return FLA_SUCCESS;
}

References FLA_Househ2_UT_l_ops(), and i.

Referenced by FLA_Bidiag_UT_u_step_ofs_var2(), FLA_Bidiag_UT_u_step_ops_var1(), FLA_Bidiag_UT_u_step_ops_var2(), FLA_Bidiag_UT_u_step_ops_var5(), FLA_Househ2_UT(), FLA_LQ_UT_ops_var1(), and FLA_LQ_UT_ops_var2().

FLA_Househ2_UT_r_opz()

FLA_Error FLA_Househ2_UT_r_opz	(	int	m_x2,
		dcomplex *	chi_1,
		dcomplex *	x2,
		int	inc_x2,
		dcomplex *	tau
	)

{
  FLA_Househ2_UT_l_opz( m_x2,
                        chi_1,
                        x2, inc_x2,
                        tau );
 
  bl1_zconjv( m_x2,
              x2, inc_x2 );
 
  return FLA_SUCCESS;
}

References bl1_zconjv(), FLA_Househ2_UT_l_opz(), and i.

Referenced by FLA_Bidiag_UT_u_step_ofz_var2(), FLA_Bidiag_UT_u_step_opz_var1(), FLA_Bidiag_UT_u_step_opz_var2(), FLA_Bidiag_UT_u_step_opz_var5(), FLA_Househ2_UT(), FLA_LQ_UT_opz_var1(), and FLA_LQ_UT_opz_var2().