FLA_Error FLA_Obj_create_complex_constant( double const_real, double const_imag, FLA_Obj *obj )
{
  int*      temp_i;
  float*    temp_s;
  double*   temp_d;
  scomplex* temp_c;
  dcomplex* temp_z;

  if ( FLA_Check_error_level() >= FLA_MIN_ERROR_CHECKING )
    FLA_Obj_create_complex_constant_check( const_real, const_imag, obj );

  FLA_Obj_create( FLA_CONSTANT, 1, 1, 0, 0, obj );

#ifdef FLA_ENABLE_SCC
  if ( !FLA_is_owner() )
    return FLA_SUCCESS;
#endif

  temp_i       = FLA_INT_PTR( *obj );
  temp_s       = FLA_FLOAT_PTR( *obj );
  temp_d       = FLA_DOUBLE_PTR( *obj );
  temp_c       = FLA_COMPLEX_PTR( *obj );
  temp_z       = FLA_DOUBLE_COMPLEX_PTR( *obj );

  *temp_i      = ( int   ) const_real;
  *temp_s      = ( float ) const_real;
  *temp_d      =           const_real;
  temp_c->real = ( float ) const_real;
  temp_c->imag = ( float ) const_imag;
  temp_z->real =           const_real;
  temp_z->imag =           const_imag;

  return FLA_SUCCESS;
}

FLA_Error FLA_Trinv_lu_opc_var2( int mn_A,
                                 scomplex* buff_A, int rs_A, int cs_A )
{
  scomplex* buff_m1 = FLA_COMPLEX_PTR( FLA_MINUS_ONE );
  int       i;

  for ( i = 0; i < mn_A; ++i )
  {
    scomplex* a21       = buff_A + (i  )*cs_A + (i+1)*rs_A;
    scomplex* A22       = buff_A + (i+1)*cs_A + (i+1)*rs_A;

    int       mn_ahead  = mn_A - i - 1;

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

    // FLA_Trsv_external( FLA_LOWER_TRIANGULAR, FLA_NO_TRANSPOSE, FLA_UNIT_DIAG, A22, a21 );
    bl1_ctrsv( BLIS1_LOWER_TRIANGULAR,
               BLIS1_NO_TRANSPOSE,
               BLIS1_UNIT_DIAG,
               mn_ahead,
               A22, rs_A, cs_A,
               a21, rs_A );

    // FLA_Scal_external( FLA_MINUS_ONE, a21 );
    bl1_cscalv( BLIS1_NO_CONJUGATE,
                mn_ahead,
                buff_m1,
                a21, rs_A );

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

  }

  return FLA_SUCCESS;
}

FLA_Error FLA_Chol_u_opt_var3( FLA_Obj A )
{
  FLA_Error    r_val = FLA_SUCCESS;
  FLA_Datatype datatype;
  int          mn_A;
  int          rs_A, cs_A;

  datatype = FLA_Obj_datatype( A );

  mn_A     = FLA_Obj_length( A );
  rs_A     = FLA_Obj_row_stride( A );
  cs_A     = FLA_Obj_col_stride( A );
  

  switch ( datatype )
  {
    case FLA_FLOAT:
    {
      float* buff_A = FLA_FLOAT_PTR( A );

      r_val = FLA_Chol_u_ops_var3( mn_A,
                                   buff_A, rs_A, cs_A );

      break;
    }

    case FLA_DOUBLE:
    {
      double* buff_A = FLA_DOUBLE_PTR( A );

      r_val = FLA_Chol_u_opd_var3( mn_A,
                                   buff_A, rs_A, cs_A );

      break;
    }

    case FLA_COMPLEX:
    {
      scomplex* buff_A = FLA_COMPLEX_PTR( A );

      r_val = FLA_Chol_u_opc_var3( mn_A,
                                   buff_A, rs_A, cs_A );

      break;
    }

    case FLA_DOUBLE_COMPLEX:
    {
      dcomplex* buff_A = FLA_DOUBLE_COMPLEX_PTR( A );

      r_val = FLA_Chol_u_opz_var3( mn_A,
                                   buff_A, rs_A, cs_A );

      break;
    }
  }

  return r_val;
}

FLA_Error FLA_Tevd_eigval_v_opt_var1( FLA_Obj G, FLA_Obj d, FLA_Obj e, FLA_Obj k )
{
	FLA_Datatype datatype;
	int          m_A, n_G;
	int          rs_G, cs_G;
	int          inc_d;
	int          inc_e;

	datatype = FLA_Obj_datatype( d );

	m_A      = FLA_Obj_vector_dim( d );
	n_G      = FLA_Obj_width( G );

	rs_G     = FLA_Obj_row_stride( G );
	cs_G     = FLA_Obj_col_stride( G );

	inc_d    = FLA_Obj_vector_inc( d );
	inc_e    = FLA_Obj_vector_inc( e );
	

	switch ( datatype )
	{
		case FLA_FLOAT:
		{
			scomplex* buff_G = FLA_COMPLEX_PTR( G );
			float*    buff_d = FLA_FLOAT_PTR( d );
			float*    buff_e = FLA_FLOAT_PTR( e );
			int*      buff_k = FLA_INT_PTR( k );

			FLA_Tevd_eigval_v_ops_var1( m_A,
			                            n_G,
			                            buff_G, rs_G, cs_G,
			                            buff_d, inc_d,
			                            buff_e, inc_e,
			                            buff_k );

			break;
		}

		case FLA_DOUBLE:
		{
			dcomplex* buff_G = FLA_DOUBLE_COMPLEX_PTR( G );
			double*   buff_d = FLA_DOUBLE_PTR( d );
			double*   buff_e = FLA_DOUBLE_PTR( e );
			int*      buff_k = FLA_INT_PTR( k );

			FLA_Tevd_eigval_v_opd_var1( m_A,
			                            n_G,
			                            buff_G, rs_G, cs_G,
			                            buff_d, inc_d,
			                            buff_e, inc_e,
			                            buff_k );

			break;
		}
	}

	return FLA_SUCCESS;
}

FLA_Error FLA_Absolute_value( FLA_Obj alpha )
{
  FLA_Datatype datatype;

  if ( FLA_Check_error_level() >= FLA_MIN_ERROR_CHECKING )
    FLA_Absolute_value_check( alpha );

  datatype = FLA_Obj_datatype( alpha );
  
  switch ( datatype ){

  case FLA_FLOAT:
  {
    float *buff_alpha = ( float * ) FLA_FLOAT_PTR( alpha );

    *buff_alpha = ( float ) fabs( ( double ) *buff_alpha );

    break;
  }

  case FLA_DOUBLE:
  {
    double *buff_alpha = ( double * ) FLA_DOUBLE_PTR( alpha );

    *buff_alpha = fabs( *buff_alpha );

    break;
  }

  case FLA_COMPLEX:
  {
    scomplex *buff_alpha = ( scomplex * ) FLA_COMPLEX_PTR( alpha );

    buff_alpha->real = ( float ) sqrt( ( double ) buff_alpha->real * buff_alpha->real + 
                                                  buff_alpha->imag * buff_alpha->imag );
    buff_alpha->imag = 0.0F; 


    break;
  }

  case FLA_DOUBLE_COMPLEX:
  {
    dcomplex *buff_alpha = ( dcomplex * ) FLA_DOUBLE_COMPLEX_PTR( alpha );

    buff_alpha->real = sqrt( buff_alpha->real * buff_alpha->real + 
                             buff_alpha->imag * buff_alpha->imag );
    buff_alpha->imag = 0.0; 

    break;
  }

  }

  return FLA_SUCCESS;
}

FLA_Error FLA_Trinv_lu_opc_var3( int mn_A,
                                 scomplex* buff_A, int rs_A, int cs_A )
{
  scomplex* buff_1  = FLA_COMPLEX_PTR( FLA_ONE );
  scomplex* buff_m1 = FLA_COMPLEX_PTR( FLA_MINUS_ONE );
  int       i;

  for ( i = 0; i < mn_A; ++i )
  {
    scomplex* a10t      = buff_A + (0  )*cs_A + (i  )*rs_A;
    scomplex* A20       = buff_A + (0  )*cs_A + (i+1)*rs_A;
    scomplex* a21       = buff_A + (i  )*cs_A + (i+1)*rs_A;

    int       mn_ahead  = mn_A - i - 1;
    int       mn_behind = i;

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

    // FLA_Scal_external( FLA_MINUS_ONE, a21 );
    bl1_cscalv( BLIS1_NO_CONJUGATE,
                mn_ahead,
                buff_m1,
                a21, rs_A );

    // FLA_Ger_external( FLA_ONE, a21, a10t, A20 );
    bl1_cger( BLIS1_NO_CONJUGATE,
              BLIS1_NO_CONJUGATE,
              mn_ahead,
              mn_behind,
              buff_1,
              a21, rs_A,
              a10t, cs_A,
              A20, rs_A, cs_A );

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

  }

  return FLA_SUCCESS;
}

FLA_Error FLA_Fused_Ahx_Ax_opc_var1( int m_A,
                                     int n_A,
                                     scomplex* buff_A, int rs_A, int cs_A, 
                                     scomplex* buff_x, int inc_x, 
                                     scomplex* buff_v, int inc_v, 
                                     scomplex* buff_w, int inc_w )
{
  scomplex* buff_0  = FLA_COMPLEX_PTR( FLA_ZERO );
  int       i;

  bl1_csetv( m_A,
             buff_0,
             buff_w, inc_w );

  for ( i = 0; i < n_A; ++i )
  {
    scomplex* a1       = buff_A + (i  )*cs_A + (0  )*rs_A;
    scomplex* nu1      = buff_v + (i  )*inc_v;
    scomplex* x        = buff_x;
    scomplex* chi1     = buff_x + (i  )*inc_x;
    scomplex* w        = buff_w;

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

    bl1_cdot( BLIS1_CONJUGATE,
              m_A,
              a1, rs_A,
              x,  inc_x,
              nu1 );

    bl1_caxpyv( BLIS1_NO_CONJUGATE,
                m_A,
                chi1,
                a1, rs_A,
                w,  inc_w );
/*
    F77_caxpy( &m_A,
               chi1,
               a1, &rs_A,
               w,  &inc_w );
*/

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

  }

  return FLA_SUCCESS;
}

FLA_Error FLA_Ttmm_l_opc_var3( int mn_A,
                               scomplex* buff_A, int rs_A, int cs_A )
{
  scomplex* buff_1  = FLA_COMPLEX_PTR( FLA_ONE );
  int       i;

  for ( i = 0; i < mn_A; ++i )
  {
    scomplex* alpha11   = buff_A + (i  )*cs_A + (i  )*rs_A;
    scomplex* a21       = buff_A + (i  )*cs_A + (i+1)*rs_A;
    scomplex* A22       = buff_A + (i+1)*cs_A + (i+1)*rs_A;

    int       mn_ahead  = mn_A - i - 1;

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

    // FLA_Absolute_square( alpha11 );
    bl1_cabsqr( alpha11 );

    // FLA_Dotcs_external( FLA_CONJUGATE, FLA_ONE, a21, a21, FLA_ONE, alpha11 );
    bl1_cdots( BLIS1_CONJUGATE,
               mn_ahead,
               buff_1,
               a21, rs_A,
               a21, rs_A,
               buff_1,
               alpha11 );

    // FLA_Trmv_external( FLA_LOWER_TRIANGULAR, FLA_CONJ_TRANSPOSE, FLA_NONUNIT_DIAG, A22, a21 );
    bl1_ctrmv( BLIS1_LOWER_TRIANGULAR,
               BLIS1_CONJ_TRANSPOSE,
               BLIS1_NONUNIT_DIAG,
               mn_ahead,
               A22, rs_A, cs_A,
               a21, rs_A );

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

  }

  return FLA_SUCCESS;
}

FLA_Error FLA_Househ3UD_UT_opc( int       m_x1,
                                int       m_y2,
                                scomplex* chi_0,
                                scomplex* x1, int inc_x1,
                                scomplex* y2, int inc_y2,
                                scomplex* tau )
{
  scomplex one_half = *FLA_COMPLEX_PTR( FLA_ONE_HALF );
  scomplex alpha;
  scomplex chi_0_minus_alpha;
  scomplex neg_chi_0_minus_alpha;
  float    abs_chi_0;
  float    norm_x_1;
  float    norm_y_2;
  float    lambda;
  float    abs_sq_chi_0_minus_alpha;
  int      i_one = 1;

  //
  // Compute the 2-norms of x_1 and y_2:
  //
  //   norm_x_1 := || x_1 ||_2
  //   norm_y_2 := || y_2 ||_2
  //

  bl1_cnrm2( m_x1,
             x1, inc_x1,
             &norm_x_1 );

  bl1_cnrm2( m_y2,
             y2, inc_y2,
             &norm_y_2 );

  //
  // If 2-norms of x_1, y_2 are zero, then return with trivial tau, chi_0 values.
  //

  if ( norm_x_1 == 0.0F && 
       norm_y_2 == 0.0F )
  {
    chi_0->real = -(chi_0->real);
    chi_0->imag = -(chi_0->imag);
    tau->real   = one_half.real;
    tau->imag   = one_half.imag;

    return FLA_SUCCESS;
  }

  //
  // Compute the absolute value (magnitude) of chi_0, which equals the 2-norm
  // of chi_0:
  //
  //   abs_chi_0 :=  | chi_0 |  =  || chi_0 ||_2
  //

  bl1_cnrm2( i_one,
             chi_0, i_one,
             &abs_chi_0 );

  //
  // Compute lambda:
  //
  //   lambda := sqrt( conj(chi0) chi0 + x1' x1 - y2' y2 )
  //

  lambda = ( float ) sqrt( abs_chi_0 * abs_chi_0 + 
                           norm_x_1  * norm_x_1  -
                           norm_y_2  * norm_y_2 );
  
  //
  // Compute alpha:
  //
  //   alpha := - lambda * chi_0 / | chi_0 |
  //

  alpha.real = -chi_0->real * lambda / abs_chi_0;
  alpha.imag = -chi_0->imag * lambda / abs_chi_0;

  //
  // Overwrite x_1 and y_2 with u_1 and v_2, respectively:
  //
  //   x_1 := x_1 / ( chi_0 - alpha )
  //   y_2 := y_2 / -( chi_0 - alpha )
  //

  chi_0_minus_alpha.real = chi_0->real - alpha.real;
  chi_0_minus_alpha.imag = chi_0->imag - alpha.imag;

  bl1_cinvscalv( BLIS1_NO_CONJUGATE,
                 m_x1,
                 &chi_0_minus_alpha,
                 x1, inc_x1 );

  neg_chi_0_minus_alpha.real = -chi_0_minus_alpha.real;
  neg_chi_0_minus_alpha.imag = -chi_0_minus_alpha.imag;

  bl1_cinvscalv( BLIS1_NO_CONJUGATE,
                 m_y2,
                 &neg_chi_0_minus_alpha,
                 y2, inc_y2 );
//.........这里部分代码省略.........

FLA_Error FLA_LU_piv_opc_var5( int m_A,
                               int n_A,
                               scomplex* buff_A, int rs_A, int cs_A,
                               int*      buff_p, int inc_p )
{
  FLA_Error r_val   = FLA_SUCCESS;
  scomplex* buff_m1 = FLA_COMPLEX_PTR( FLA_MINUS_ONE );
  int       min_m_n = min( m_A, n_A );
  int       i;

  for ( i = 0; i < min_m_n; ++i )
  {
    scomplex  pivot_val = czero;
    scomplex* a10t      = buff_A + (0  )*cs_A + (i  )*rs_A;
    scomplex* alpha11   = buff_A + (i  )*cs_A + (i  )*rs_A;
    scomplex* a21       = buff_A + (i  )*cs_A + (i+1)*rs_A;
    scomplex* a12t      = buff_A + (i+1)*cs_A + (i  )*rs_A;
    scomplex* A22       = buff_A + (i+1)*cs_A + (i+1)*rs_A;

    int*      pi1       = buff_p + i*inc_p;

    int       m_ahead   = m_A - i - 1;
    int       n_ahead   = n_A - i - 1;

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

    // FLA_Merge_2x1( alpha11,
    //                    a21,      &aB1 );

    // FLA_Amax_external( aB1, pi1 );
    bl1_camax( m_ahead + 1,
               alpha11, rs_A,
               pi1 );

    // If a null pivot is encountered, return the index. 
    pivot_val = *(alpha11 + *pi1);
    if ( pivot_val.real == czero.real &&
         pivot_val.imag == czero.imag )  r_val = ( r_val == FLA_SUCCESS ? i : r_val );
    else 
    {
      // FLA_Merge_1x2( ABL, ABR,      &AB );
      
      // FLA_Apply_pivots( FLA_LEFT, FLA_NO_TRANSPOSE, pi1, AB );
      FLA_Apply_pivots_ln_opc_var1( n_A,
                                    a10t, rs_A, cs_A,
                                    0,
                                    0,
                                    pi1, inc_p );
      
      // FLA_Inv_scal_external( alpha11, a21 );
      bl1_cinvscalv( BLIS1_NO_CONJUGATE,
                     m_ahead,
                     alpha11,
                     a21, rs_A );
    }

    // FLA_Ger_external( FLA_MINUS_ONE, a21, a12t, A22 );
    bl1_cger( BLIS1_NO_CONJUGATE,
              BLIS1_NO_CONJUGATE,
              m_ahead,
              n_ahead,
              buff_m1,
              a21, rs_A,
              a12t, cs_A,
              A22, rs_A, cs_A );

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

  }

  return r_val;
}

FLA_Error FLA_LU_piv_opt_var5( FLA_Obj A, FLA_Obj p )
{
  FLA_Error    r_val = FLA_SUCCESS;
  FLA_Datatype datatype;
  int          m_A, n_A;
  int          rs_A, cs_A;
  int          inc_p;

  datatype = FLA_Obj_datatype( A );

  m_A      = FLA_Obj_length( A );
  n_A      = FLA_Obj_width( A );
  rs_A     = FLA_Obj_row_stride( A );
  cs_A     = FLA_Obj_col_stride( A );

  inc_p    = FLA_Obj_vector_inc( p );


  switch ( datatype )
  {
    case FLA_FLOAT:
    {
      float* buff_A = FLA_FLOAT_PTR( A );
      int*   buff_p = FLA_INT_PTR( p );

      r_val = FLA_LU_piv_ops_var5( m_A,
                                   n_A,
                                   buff_A, rs_A, cs_A,
                                   buff_p, inc_p );
      
      break;
    }

    case FLA_DOUBLE:
    {
      double* buff_A = FLA_DOUBLE_PTR( A );
      int*    buff_p = FLA_INT_PTR( p );

      r_val = FLA_LU_piv_opd_var5( m_A,
                                   n_A,
                                   buff_A, rs_A, cs_A,
                                   buff_p, inc_p );

      break;
    }

    case FLA_COMPLEX:
    {
      scomplex* buff_A = FLA_COMPLEX_PTR( A );
      int*      buff_p = FLA_INT_PTR( p );

      r_val = FLA_LU_piv_opc_var5( m_A,
                                   n_A,
                                   buff_A, rs_A, cs_A,
                                   buff_p, inc_p );

      break;
    }

    case FLA_DOUBLE_COMPLEX:
    {
      dcomplex* buff_A = FLA_DOUBLE_COMPLEX_PTR( A );
      int*      buff_p = FLA_INT_PTR( p );

      r_val = FLA_LU_piv_opz_var5( m_A,
                                   n_A,
                                   buff_A, rs_A, cs_A,
                                   buff_p, inc_p );
      
      break;
    }
  }

  return r_val;
}

FLA_Error FLA_Trmm_external_gpu( FLA_Side side, FLA_Uplo uplo, FLA_Trans trans, FLA_Diag diag, FLA_Obj alpha, FLA_Obj A, void* A_gpu, FLA_Obj B, void* B_gpu )
{
  FLA_Datatype datatype;
  int          m_B, n_B;
  int          ldim_A;
  int          ldim_B;
  char         blas_side; 
  char         blas_uplo;
  char         blas_trans;
  char         blas_diag;

  if ( FLA_Check_error_level() == FLA_FULL_ERROR_CHECKING ) 
    FLA_Trmm_check( side, uplo, trans, diag, alpha, A, B );

  if ( FLA_Obj_has_zero_dim( B ) ) return FLA_SUCCESS;

  datatype = FLA_Obj_datatype( A );

  ldim_A   = FLA_Obj_length( A );

  m_B      = FLA_Obj_length( B );
  n_B      = FLA_Obj_width( B );
  ldim_B   = FLA_Obj_length( B );

  FLA_Param_map_flame_to_netlib_side( side, &blas_side );
  FLA_Param_map_flame_to_netlib_uplo( uplo, &blas_uplo );
  FLA_Param_map_flame_to_netlib_trans( trans, &blas_trans );
  FLA_Param_map_flame_to_netlib_diag( diag, &blas_diag );


  switch( datatype ){

  case FLA_FLOAT:
  {
    float *buff_alpha = ( float * ) FLA_FLOAT_PTR( alpha );

    cublasStrmm( blas_side,
                 blas_uplo, 
                 blas_trans,
                 blas_diag,
                 m_B,
                 n_B,
                 *buff_alpha,
                 ( float * ) A_gpu, ldim_A,
                 ( float * ) B_gpu, ldim_B );
    
    break;
  }

  case FLA_DOUBLE:
  {
    double *buff_alpha = ( double * ) FLA_DOUBLE_PTR( alpha );

    cublasDtrmm( blas_side,
                 blas_uplo, 
                 blas_trans,
                 blas_diag,
                 m_B,
                 n_B,
                 *buff_alpha,
                 ( double * ) A_gpu, ldim_A,
                 ( double * ) B_gpu, ldim_B );

    break;
  }

  case FLA_COMPLEX:
  {
    cuComplex *buff_alpha = ( cuComplex * ) FLA_COMPLEX_PTR( alpha );

    cublasCtrmm( blas_side,
                 blas_uplo, 
                 blas_trans,
                 blas_diag,
                 m_B,
                 n_B,
                 *buff_alpha,
                 ( cuComplex * ) A_gpu, ldim_A,
                 ( cuComplex * ) B_gpu, ldim_B );

    break;
  }

  case FLA_DOUBLE_COMPLEX:
  {
    cuDoubleComplex *buff_alpha = ( cuDoubleComplex * ) FLA_DOUBLE_COMPLEX_PTR( alpha );

    cublasZtrmm( blas_side,
                 blas_uplo, 
                 blas_trans,
                 blas_diag,
                 m_B,
                 n_B,
                 *buff_alpha,
                 ( cuDoubleComplex * ) A_gpu, ldim_A,
                 ( cuDoubleComplex * ) B_gpu, ldim_B );

    break;
  }

//.........这里部分代码省略.........

FLA_Error FLA_Hess_UT_step_opt_var4( FLA_Obj A, FLA_Obj Y, FLA_Obj Z, FLA_Obj T )
{
  FLA_Datatype datatype;
  int          m_A, m_T;
  int          rs_A, cs_A;
  int          rs_Y, cs_Y;
  int          rs_Z, cs_Z;
  int          rs_T, cs_T;

  datatype = FLA_Obj_datatype( A );

  m_A      = FLA_Obj_length( A );
  m_T      = FLA_Obj_length( T );

  rs_A     = FLA_Obj_row_stride( A );
  cs_A     = FLA_Obj_col_stride( A );

  rs_Y     = FLA_Obj_row_stride( Y );
  cs_Y     = FLA_Obj_col_stride( Y );

  rs_Z     = FLA_Obj_row_stride( Z );
  cs_Z     = FLA_Obj_col_stride( Z );

  rs_T     = FLA_Obj_row_stride( T );
  cs_T     = FLA_Obj_col_stride( T );
  

  switch ( datatype )
  {
    case FLA_FLOAT:
    {
      float* buff_A = FLA_FLOAT_PTR( A );
      float* buff_Y = FLA_FLOAT_PTR( Y );
      float* buff_Z = FLA_FLOAT_PTR( Z );
      float* buff_T = FLA_FLOAT_PTR( T );

      FLA_Hess_UT_step_ops_var4( m_A,
                                 m_T,
                                 buff_A, rs_A, cs_A,
                                 buff_Y, rs_Y, cs_Y,
                                 buff_Z, rs_Z, cs_Z,
                                 buff_T, rs_T, cs_T );

      break;
    }

    case FLA_DOUBLE:
    {
      double* buff_A = FLA_DOUBLE_PTR( A );
      double* buff_Y = FLA_DOUBLE_PTR( Y );
      double* buff_Z = FLA_DOUBLE_PTR( Z );
      double* buff_T = FLA_DOUBLE_PTR( T );

      FLA_Hess_UT_step_opd_var4( m_A,
                                 m_T,
                                 buff_A, rs_A, cs_A,
                                 buff_Y, rs_Y, cs_Y,
                                 buff_Z, rs_Z, cs_Z,
                                 buff_T, rs_T, cs_T );

      break;
    }

    case FLA_COMPLEX:
    {
      scomplex* buff_A = FLA_COMPLEX_PTR( A );
      scomplex* buff_Y = FLA_COMPLEX_PTR( Y );
      scomplex* buff_Z = FLA_COMPLEX_PTR( Z );
      scomplex* buff_T = FLA_COMPLEX_PTR( T );

      FLA_Hess_UT_step_opc_var4( m_A,
                                 m_T,
                                 buff_A, rs_A, cs_A,
                                 buff_Y, rs_Y, cs_Y,
                                 buff_Z, rs_Z, cs_Z,
                                 buff_T, rs_T, cs_T );

      break;
    }

    case FLA_DOUBLE_COMPLEX:
    {
      dcomplex* buff_A = FLA_DOUBLE_COMPLEX_PTR( A );
      dcomplex* buff_Y = FLA_DOUBLE_COMPLEX_PTR( Y );
      dcomplex* buff_Z = FLA_DOUBLE_COMPLEX_PTR( Z );
      dcomplex* buff_T = FLA_DOUBLE_COMPLEX_PTR( T );

      FLA_Hess_UT_step_opz_var4( m_A,
                                 m_T,
                                 buff_A, rs_A, cs_A,
                                 buff_Y, rs_Y, cs_Y,
                                 buff_Z, rs_Z, cs_Z,
                                 buff_T, rs_T, cs_T );

      break;
    }
  }

  return FLA_SUCCESS;
}

FLA_Error FLA_Herc_external( FLA_Uplo uplo, FLA_Conj conj, FLA_Obj alpha, FLA_Obj x, FLA_Obj A )
{
  FLA_Datatype datatype;
  int          m_A;
  int          rs_A, cs_A;
  int          inc_x; 
  uplo_t       blis_uplo;
  conj_t       blis_conj;

  if ( FLA_Check_error_level() == FLA_FULL_ERROR_CHECKING ) 
    FLA_Herc_check( uplo, conj, alpha, x, A );

  if ( FLA_Obj_has_zero_dim( A ) ) return FLA_SUCCESS;

  datatype = FLA_Obj_datatype( A );

  m_A      = FLA_Obj_length( A );
  rs_A     = FLA_Obj_row_stride( A );
  cs_A     = FLA_Obj_col_stride( A );

  inc_x    = FLA_Obj_vector_inc( x );

  FLA_Param_map_flame_to_blis_uplo( uplo, &blis_uplo );
  FLA_Param_map_flame_to_blis_conj( conj, &blis_conj );


  switch( datatype ){

  case FLA_FLOAT:
  {
    float *buff_A     = ( float * ) FLA_FLOAT_PTR( A );
    float *buff_x     = ( float * ) FLA_FLOAT_PTR( x );
    float *buff_alpha = ( float * ) FLA_FLOAT_PTR( alpha );

    bli_ssyr( blis_uplo,
              m_A,
              buff_alpha,
              buff_x, inc_x,
              buff_A, rs_A, cs_A ); 
    break;
  }

  case FLA_DOUBLE:
  {
    double *buff_A     = ( double * ) FLA_DOUBLE_PTR( A );
    double *buff_x     = ( double * ) FLA_DOUBLE_PTR( x );
    double *buff_alpha = ( double * ) FLA_DOUBLE_PTR( alpha );

    bli_dsyr( blis_uplo,
              m_A,
              buff_alpha,
              buff_x, inc_x,
              buff_A, rs_A, cs_A ); 
    break;
  }

  case FLA_COMPLEX:
  {
    scomplex *buff_A     = ( scomplex * ) FLA_COMPLEX_PTR( A );
    scomplex *buff_x     = ( scomplex * ) FLA_COMPLEX_PTR( x );
    float    *buff_alpha = ( float    * ) FLA_FLOAT_PTR( alpha );

    bli_cher( blis_uplo,
              blis_conj,
              m_A,
              buff_alpha,
              buff_x, inc_x,
              buff_A, rs_A, cs_A ); 

    break;
  }

  case FLA_DOUBLE_COMPLEX:
  {
    dcomplex *buff_A     = ( dcomplex * ) FLA_DOUBLE_COMPLEX_PTR( A );
    dcomplex *buff_x     = ( dcomplex * ) FLA_DOUBLE_COMPLEX_PTR( x );
    double   *buff_alpha = ( double   * ) FLA_DOUBLE_PTR( alpha );

    bli_zher( blis_uplo,
              blis_conj,
              m_A,
              buff_alpha,
              buff_x, inc_x,
              buff_A, rs_A, cs_A ); 

    break;
  }

  }

  return FLA_SUCCESS;
}

FLA_Error FLA_Symm_external( FLA_Side side, FLA_Uplo uplo, FLA_Obj alpha, FLA_Obj A, FLA_Obj B, FLA_Obj beta, FLA_Obj C )
{
  FLA_Datatype datatype;
  int          m_C, n_C;
  int          rs_A, cs_A;
  int          rs_B, cs_B;
  int          rs_C, cs_C;
  side_t       blis_side;
  uplo_t       blis_uplo; 

  if ( FLA_Check_error_level() == FLA_FULL_ERROR_CHECKING ) 
    FLA_Symm_check( side, uplo, alpha, A, B, beta, C );

  if ( FLA_Obj_has_zero_dim( C ) ) return FLA_SUCCESS;

  datatype = FLA_Obj_datatype( A );

  rs_A     = FLA_Obj_row_stride( A );
  cs_A     = FLA_Obj_col_stride( A );

  rs_B     = FLA_Obj_row_stride( B );
  cs_B     = FLA_Obj_col_stride( B );

  m_C      = FLA_Obj_length( C );
  n_C      = FLA_Obj_width( C );
  rs_C     = FLA_Obj_row_stride( C );
  cs_C     = FLA_Obj_col_stride( C );

  FLA_Param_map_flame_to_blis_side( side, &blis_side );
  FLA_Param_map_flame_to_blis_uplo( uplo, &blis_uplo );


  switch( datatype ){

  case FLA_FLOAT:
  {
    float *buff_A     = ( float * ) FLA_FLOAT_PTR( A );
    float *buff_B     = ( float * ) FLA_FLOAT_PTR( B );
    float *buff_C     = ( float * ) FLA_FLOAT_PTR( C );
    float *buff_alpha = ( float * ) FLA_FLOAT_PTR( alpha );
    float *buff_beta  = ( float * ) FLA_FLOAT_PTR( beta );

    bli_ssymm( blis_side, 
               blis_uplo, 
               m_C, 
               n_C, 
               buff_alpha,
               buff_A, rs_A, cs_A, 
               buff_B, rs_B, cs_B,
               buff_beta,  
               buff_C, rs_C, cs_C );

    break;
  }

  case FLA_DOUBLE:
  {
    double *buff_A     = ( double * ) FLA_DOUBLE_PTR( A );
    double *buff_B     = ( double * ) FLA_DOUBLE_PTR( B );
    double *buff_C     = ( double * ) FLA_DOUBLE_PTR( C );
    double *buff_alpha = ( double * ) FLA_DOUBLE_PTR( alpha );
    double *buff_beta  = ( double * ) FLA_DOUBLE_PTR( beta );

    bli_dsymm( blis_side, 
               blis_uplo, 
               m_C, 
               n_C, 
               buff_alpha,
               buff_A, rs_A, cs_A, 
               buff_B, rs_B, cs_B,
               buff_beta,  
               buff_C, rs_C, cs_C );

    break;
  }

  case FLA_COMPLEX:
  {
    scomplex *buff_A     = ( scomplex * ) FLA_COMPLEX_PTR( A );
    scomplex *buff_B     = ( scomplex * ) FLA_COMPLEX_PTR( B );
    scomplex *buff_C     = ( scomplex * ) FLA_COMPLEX_PTR( C );
    scomplex *buff_alpha = ( scomplex * ) FLA_COMPLEX_PTR( alpha );
    scomplex *buff_beta  = ( scomplex * ) FLA_COMPLEX_PTR( beta );

    bli_csymm( blis_side, 
               blis_uplo, 
               m_C, 
               n_C, 
               buff_alpha,
               buff_A, rs_A, cs_A, 
               buff_B, rs_B, cs_B,
               buff_beta,  
               buff_C, rs_C, cs_C );

    break;
  }

  case FLA_DOUBLE_COMPLEX:
  {
    dcomplex *buff_A     = ( dcomplex * ) FLA_DOUBLE_COMPLEX_PTR( A );
//.........这里部分代码省略.........

FLA_Bool FLA_Obj_equals( FLA_Obj A, FLA_Obj B )
{
  FLA_Datatype datatype_A;
  FLA_Datatype datatype_B;
  FLA_Datatype datatype;
  dim_t        m, n;
  dim_t        rs_A, cs_A;
  dim_t        rs_B, cs_B;
  dim_t        i, j;

  if ( FLA_Check_error_level() >= FLA_MIN_ERROR_CHECKING )
    FLA_Obj_equals_check( A, B );

  m      = FLA_Obj_length( A );
  n      = FLA_Obj_width( A );
  rs_A   = FLA_Obj_row_stride( A );
  cs_A   = FLA_Obj_col_stride( A );
  rs_B   = FLA_Obj_row_stride( B );
  cs_B   = FLA_Obj_col_stride( B );

  datatype_A = FLA_Obj_datatype( A );
  datatype_B = FLA_Obj_datatype( B );

  // If A is a non-FLA_CONSTANT object, then we should proceed based on the
  // value of datatype_A. In such a situation, either datatype_B is an exact
  // match and we're fine, or datatype_B is FLA_CONSTANT, in which case we're
  // also covered since FLA_CONSTANT encompassas all numerical types.
  // If A is an FLA_CONSTANT object, then we should proceed based on the value
  // of datatype_B. In this case, datatype_B is either a non-FLA_CONSTANT type,
  // which mirrors the second sub-case above, or datatype_B is FLA_CONSTANT,
  // in which case both types are FLA_CONSTANT and therefore we have to handle
  // that case. Only if both are FLA_CONSTANTs does the FLA_CONSTANT case
  // statement below execute.
  if ( datatype_A != FLA_CONSTANT )
    datatype = datatype_A;
  else
    datatype = datatype_B;

  switch ( datatype )
  {
    case FLA_CONSTANT:
    {
      // We require ALL floating-point fields to be the same.
      float*    buffs_A = ( float    * ) FLA_FLOAT_PTR( A );
      float*    buffs_B = ( float    * ) FLA_FLOAT_PTR( B );
      double*   buffd_A = ( double   * ) FLA_DOUBLE_PTR( A );
      double*   buffd_B = ( double   * ) FLA_DOUBLE_PTR( B );
      scomplex* buffc_A = ( scomplex * ) FLA_COMPLEX_PTR( A );
      scomplex* buffc_B = ( scomplex * ) FLA_COMPLEX_PTR( B );
      dcomplex* buffz_A = ( dcomplex * ) FLA_DOUBLE_COMPLEX_PTR( A );
      dcomplex* buffz_B = ( dcomplex * ) FLA_DOUBLE_COMPLEX_PTR( B );

      if ( *buffs_A != *buffs_B ||
           *buffd_A != *buffd_B ||
           buffc_A->real != buffc_B->real ||
           buffc_A->imag != buffc_B->imag ||
           buffz_A->real != buffz_B->real ||
           buffz_A->imag != buffz_B->imag )
      {
        return FALSE;
      }

      break;
    }

    case FLA_INT:
    {
      int *buff_A = ( int * ) FLA_INT_PTR( A );
      int *buff_B = ( int * ) FLA_INT_PTR( B );

      for ( j = 0; j < n; j++ )
        for ( i = 0; i < m; i++ )
          if ( buff_A[ j * cs_A + i * rs_A ] != 
               buff_B[ j * cs_B + i * rs_B ] )
          {
            return FALSE;
          }

      break;
    }

    case FLA_FLOAT:
    {
      float *buff_A = ( float * ) FLA_FLOAT_PTR( A );
      float *buff_B = ( float * ) FLA_FLOAT_PTR( B );

      for ( j = 0; j < n; j++ )
        for ( i = 0; i < m; i++ )
          if ( buff_A[ j * cs_A + i * rs_A ] != 
               buff_B[ j * cs_B + i * rs_B ] )
          {
            return FALSE;
          }

      break;
    }

    case FLA_DOUBLE:
    {
      double *buff_A = ( double * ) FLA_DOUBLE_PTR( A );
//.........这里部分代码省略.........

FLA_Error FLA_Tridiag_UT_l_step_opc_var2( int m_A,
                                          int m_T,
                                          scomplex* buff_A, int rs_A, int cs_A, 
                                          scomplex* buff_T, int rs_T, int cs_T )
{
  scomplex* buff_2  = FLA_COMPLEX_PTR( FLA_TWO );
  scomplex* buff_1  = FLA_COMPLEX_PTR( FLA_ONE );
  scomplex* buff_0  = FLA_COMPLEX_PTR( FLA_ZERO );
  scomplex* buff_m1 = FLA_COMPLEX_PTR( FLA_MINUS_ONE );

  scomplex  first_elem;
  scomplex  beta;
  scomplex  inv_tau11;
  scomplex  minus_inv_tau11;
  scomplex  minus_upsilon11, minus_conj_upsilon11;
  scomplex  minus_zeta11, minus_conj_zeta11;
  int       i;

  // b_alg = FLA_Obj_length( T );
  int       b_alg = m_T;

  // FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &u );
  // FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &z );
  // FLA_Obj_create( datatype_A, m_A, 1, 0, 0, &w );
  scomplex* buff_u = ( scomplex* ) FLA_malloc( m_A * sizeof( *buff_A ) );
  scomplex* buff_z = ( scomplex* ) FLA_malloc( m_A * sizeof( *buff_A ) );
  scomplex* buff_w = ( scomplex* ) FLA_malloc( m_A * sizeof( *buff_A ) );
  int       inc_u  = 1;
  int       inc_z  = 1;
  int       inc_w  = 1;

  // Initialize some variables (only to prevent compiler warnings).
  first_elem      = *buff_0;
  minus_inv_tau11 = *buff_0;

  for ( i = 0; i < b_alg; ++i )
  {
    scomplex* A20      = buff_A + (0  )*cs_A + (i+1)*rs_A;
    scomplex* alpha11  = buff_A + (i  )*cs_A + (i  )*rs_A;
    scomplex* a21      = buff_A + (i  )*cs_A + (i+1)*rs_A;
    scomplex* A22      = buff_A + (i+1)*cs_A + (i+1)*rs_A;

    scomplex* t01      = buff_T + (i  )*cs_T + (0  )*rs_T;
    scomplex* tau11    = buff_T + (i  )*cs_T + (i  )*rs_T;

    scomplex* upsilon11= buff_u + (i  )*inc_u;
    scomplex* u21      = buff_u + (i+1)*inc_u;

    scomplex* zeta11   = buff_z + (i  )*inc_z;
    scomplex* z21      = buff_z + (i+1)*inc_z;

    scomplex* w21      = buff_w + (i+1)*inc_w;

    scomplex* a21_t    = a21    + (0  )*cs_A + (0  )*rs_A;
    scomplex* a21_b    = a21    + (0  )*cs_A + (1  )*rs_A;

    int       m_ahead  = m_A - i - 1;
    int       m_behind = i;
    int       n_behind = i;

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

    if ( m_behind > 0 )
    {
      // FLA_Copy( upsilon11, minus_upsilon11 );
      // FLA_Scal( FLA_MINUS_ONE, minus_upsilon11 );
      // FLA_Copy( minus_upsilon11, minus_conj_upsilon11 );
      bl1_cmult3( buff_m1, upsilon11, &minus_upsilon11 );
      bl1_ccopyconj( &minus_upsilon11, &minus_conj_upsilon11 );

      // FLA_Copy( zeta11, minus_zeta11 );
      // FLA_Scal( FLA_MINUS_ONE, minus_zeta11 );
      // FLA_Copy( minus_zeta11, minus_conj_zeta11 );
      bl1_cmult3( buff_m1, zeta11, &minus_zeta11 );
      bl1_ccopyconj( &minus_zeta11, &minus_conj_zeta11 );

      // FLA_Axpyt( FLA_CONJ_NO_TRANSPOSE, minus_upsilon11, zeta11,    alpha11 );
      // FLA_Axpyt( FLA_CONJ_NO_TRANSPOSE, minus_zeta11,    upsilon11, alpha11 );
      bl1_caxpyv( BLIS1_CONJUGATE,
                  1,
                  &minus_upsilon11,
                  zeta11,  1,
                  alpha11, 1 );
      bl1_caxpyv( BLIS1_CONJUGATE,
                  1,
                  &minus_zeta11,
                  upsilon11, 1,
                  alpha11,  1 );

      // FLA_Axpyt( FLA_NO_TRANSPOSE, minus_conj_zeta11,    u21, a21 );
      // FLA_Axpyt( FLA_NO_TRANSPOSE, minus_conj_upsilon11, z21, a21 );
      bl1_caxpyv( BLIS1_NO_CONJUGATE,
                  m_ahead,
                  &minus_conj_zeta11,
                  u21, inc_u,
                  a21, rs_A );
      bl1_caxpyv( BLIS1_NO_CONJUGATE,
                  m_ahead,
                  &minus_conj_upsilon11,
                  z21, inc_z,
//.........这里部分代码省略.........

FLA_Error FLA_Househ3UD_UT( FLA_Obj chi_0, FLA_Obj x1, FLA_Obj y2, FLA_Obj tau )
/*
  Compute an up-and-downdating UT Householder transformation

          / / 1 0 0 \            / 1 0  0 \  / 1  \ ( 1  u1' v2' ) \
    H  =  | | 0 I 0 | - inv(tau) | 0 I  0 |  | u1 |                |
          \ \ 0 0 I /            \ 0 0 -I /  \ v2 /                /

  by computing tau, u1, and v2 such that the following is satisfied:

      / chi_0 \   / alpha \
    H |  x1   | = |   0   |
      \  y2   /   \   0   /

  where

    alpha  = - lambda * chi_0 / | chi_0 |

    lambda =  sqrt( conj(chi0) chi0 + x1' x1 - y2' y2 )

              / chi_0 \
    x      =  |  x1   |
              \  y2   /

    tau    =  ( 1 + u1' u1 - v2' v2 ) / 2

    u1     =  x1 / ( chi_0 - alpha )

    v2     =  -y2 / ( chi_0 - alpha )

  Upon completion, alpha, u1, and v2 have overwritten objects chi_0, x1,
  and y2, respectively.

  -FGVZ
*/
{
  FLA_Datatype datatype;
  int          m_x1;
  int          m_y2;
  int          inc_x1;
  int          inc_y2;

  datatype = FLA_Obj_datatype( x1 );

  m_x1     = FLA_Obj_vector_dim( x1 );
  m_y2     = FLA_Obj_vector_dim( y2 );
  inc_x1   = FLA_Obj_vector_inc( x1 );
  inc_y2   = FLA_Obj_vector_inc( y2 );

  if ( FLA_Check_error_level() >= FLA_MIN_ERROR_CHECKING )
    FLA_Househ3UD_UT_check( chi_0, x1, y2, tau );

  switch ( datatype )
  {
    case FLA_FLOAT:
    {
      float* chi_0_p = ( float* ) FLA_FLOAT_PTR( chi_0 );
      float* x1_p    = ( float* ) FLA_FLOAT_PTR( x1 );
      float* y2_p    = ( float* ) FLA_FLOAT_PTR( y2 );
      float* tau_p   = ( float* ) FLA_FLOAT_PTR( tau );

      FLA_Househ3UD_UT_ops( m_x1,
                            m_y2,
                            chi_0_p,
                            x1_p, inc_x1,
                            y2_p, inc_y2,
                            tau_p );
      break;
    }

    case FLA_DOUBLE:
    {
      double* chi_0_p = ( double* ) FLA_DOUBLE_PTR( chi_0 );
      double* x1_p    = ( double* ) FLA_DOUBLE_PTR( x1 );
      double* y2_p    = ( double* ) FLA_DOUBLE_PTR( y2 );
      double* tau_p   = ( double* ) FLA_DOUBLE_PTR( tau );

      FLA_Househ3UD_UT_opd( m_x1,
                            m_y2,
                            chi_0_p,
                            x1_p, inc_x1,
                            y2_p, inc_y2,
                            tau_p );
      break;
    }

    case FLA_COMPLEX:
    {
      scomplex* chi_0_p = ( scomplex* ) FLA_COMPLEX_PTR( chi_0 );
      scomplex* x1_p    = ( scomplex* ) FLA_COMPLEX_PTR( x1 );
      scomplex* y2_p    = ( scomplex* ) FLA_COMPLEX_PTR( y2 );
      scomplex* tau_p   = ( scomplex* ) FLA_COMPLEX_PTR( tau );

      FLA_Househ3UD_UT_opc( m_x1,
                            m_y2,
                            chi_0_p,
                            x1_p, inc_x1,
                            y2_p, inc_y2,
                            tau_p );
      break;
//.........这里部分代码省略.........

FLA_Error FLA_Fused_Gerc2_opt_var1( FLA_Obj alpha, FLA_Obj u, FLA_Obj y, FLA_Obj z, FLA_Obj v, FLA_Obj A )
{
/*
   Effective computation:
   A = A + alpha * ( u * y' + z * v' );
*/
  FLA_Datatype datatype;
  int          m_A, n_A;
  int          rs_A, cs_A;
  int          inc_u, inc_y, inc_z, inc_v;

  datatype = FLA_Obj_datatype( A );

  m_A      = FLA_Obj_length( A );
  n_A      = FLA_Obj_width( A );

  rs_A     = FLA_Obj_row_stride( A );
  cs_A     = FLA_Obj_col_stride( A );

  inc_u    = FLA_Obj_vector_inc( u );
  inc_y    = FLA_Obj_vector_inc( y );
  inc_z    = FLA_Obj_vector_inc( z );
  inc_v    = FLA_Obj_vector_inc( v );
  

  switch ( datatype )
  {
    case FLA_FLOAT:
    {
      float* buff_A = FLA_FLOAT_PTR( A );
      float* buff_u = FLA_FLOAT_PTR( u );
      float* buff_y = FLA_FLOAT_PTR( y );
      float* buff_z = FLA_FLOAT_PTR( z );
      float* buff_v = FLA_FLOAT_PTR( v );
      float* buff_alpha = FLA_FLOAT_PTR( alpha );

      FLA_Fused_Gerc2_ops_var1( m_A,
                                n_A,
                                buff_alpha,