FLA_Tevd_eigval_v.h File Reference

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Functions
FLA_Error	FLA_Tevd_eigval_v_opt_var1 (FLA_Obj G, FLA_Obj d, FLA_Obj e, FLA_Obj n_iter)
FLA_Error	FLA_Tevd_eigval_v_ops_var1 (int m_A, int n_G, scomplex *buff_G, int rs_G, int cs_G, float *buff_d, int inc_d, float *buff_e, int inc_e, int *n_iter)
FLA_Error	FLA_Tevd_eigval_v_opd_var1 (int m_A, int n_G, dcomplex *buff_G, int rs_G, int cs_G, double *buff_d, int inc_d, double *buff_e, int inc_e, int *n_iter)
FLA_Error	FLA_Tevd_eigval_v_ops_var3 (int m_A, int m_U, int n_G, scomplex *buff_G, int rs_G, int cs_G, float *buff_d, int inc_d, float *buff_e, int inc_e, float *buff_l, int inc_l, int *buff_ls, int inc_ls, float *buff_pu, int inc_pu, int *n_iter)
FLA_Error	FLA_Tevd_eigval_v_opd_var3 (int m_A, int m_U, int n_G, dcomplex *buff_G, int rs_G, int cs_G, double *buff_d, int inc_d, double *buff_e, int inc_e, double *buff_l, int inc_l, int *buff_ls, int inc_ls, double *buff_pu, int inc_pu, int *n_iter)

Function Documentation

FLA_Tevd_eigval_v_opd_var1()

FLA_Error FLA_Tevd_eigval_v_opd_var1	(	int	m_A,
		int	n_G,
		dcomplex *	buff_G,
		int	rs_G,
		int	cs_G,
		double *	buff_d,
		int	inc_d,
		double *	buff_e,
		int	inc_e,
		int *	n_iter
	)

{
    FLA_Error r_val;
    double    eps;
    double    safmin;
    double*   e_last;
    double*   d_last;
    double*   d_last_m1;
    double    shift;
    int       k;
    int       n_iter_allowed = n_G;
 
    // Query epsilon and safmin, which are used in the test for convergence.
    eps    = FLA_Mach_params_opd( FLA_MACH_EPS );
    safmin = FLA_Mach_params_opd( FLA_MACH_SFMIN );
 
    // Initialize a pointer to the last sub-diagonal element and two
    // more to the last and second last
    e_last    = &buff_e[ (m_A-2)*inc_e ];
    d_last_m1 = &buff_d[ (m_A-2)*inc_d ];
    d_last    = &buff_d[ (m_A-1)*inc_d ];
 
    for ( k = 0; k < n_iter_allowed; ++k )
    {
        dcomplex* g1 = buff_G + (k  )*cs_G;
 
        /*------------------------------------------------------------*/
 
        // If we've converged, record k and return index of eigenvalue found.
        // The reason we check before the Francis step (rather than after)
        // is so we correctly handle situations where the last diagonal
        // element has already converged from previous eigenvalue searches
        // and thus no iteration is necessary. If we checked after the
        // Francis step, we would have unnecessarily executed an additional
        // Francis step's worth of rotations with a sub-optimal shift (since
        // it would be using a 2x2 that was not "centered" properly).
        if ( MAC_Tevd_eigval_converged_opd( eps, safmin, *d_last_m1, *e_last, *d_last ) )
        {
            *e_last = 0.0;
            *n_iter = k;
            return m_A - 1;
        }
 
        // Compute a Wilkinson shift with the last 2x2 matrix.
        FLA_Wilkshift_tridiag_opd( *d_last_m1,
                                   *e_last,
                                   *d_last,
                                   &shift );
 
        // Perform a Francis step.
        r_val = FLA_Tevd_francis_v_opd_var1( m_A,
                                             &shift,
                                             g1,     rs_G,
                                             buff_d, inc_d,
                                             buff_e, inc_e );
 
        // Check for internal deflation.
        if ( r_val != FLA_SUCCESS )
        {
#ifdef PRINTF
            printf( "FLA_Tevd_eigval_v_opt_var1: Internal deflation in col %d, eig %d\n", r_val, m_A - 1 );
            printf( "FLA_Tevd_eigval_v_opt_var1: alpha11         = %23.19e\n", buff_d[r_val*inc_d] );
            printf( "FLA_Tevd_eigval_v_opt_var1: alpha21 alpha22 = %23.19e %23.19e\n", buff_e[r_val*inc_e], buff_d[(r_val+1)*inc_d] );
#endif
 
            // Set the off-diagonal element to zero.
            buff_e[ r_val*inc_e ] = 0.0;
 
            *n_iter = k + 1;
            return r_val;
        }
 
        /*------------------------------------------------------------*/
    }
 
    *n_iter = n_iter_allowed;
    return FLA_FAILURE;
}

References FLA_Mach_params_opd(), FLA_Tevd_francis_v_opd_var1(), FLA_Wilkshift_tridiag_opd(), and i.

Referenced by FLA_Tevd_eigval_v_opt_var1(), and FLA_Tevd_iteracc_v_opd_var1().

FLA_Tevd_eigval_v_opd_var3()

FLA_Error FLA_Tevd_eigval_v_opd_var3	(	int	m_A,
		int	m_U,
		int	n_G,
		dcomplex *	buff_G,
		int	rs_G,
		int	cs_G,
		double *	buff_d,
		int	inc_d,
		double *	buff_e,
		int	inc_e,
		double *	buff_l,
		int	inc_l,
		int *	buff_ls,
		int	inc_ls,
		double *	buff_pu,
		int	inc_pu,
		int *	n_iter
	)

{
    FLA_Error r_val;
    double    eps;
    double    safmin;
    double*   e_last;
    double*   d_last;
    double*   d_last_m1;
    double    shift;
    int       ij_shift;
    int       k;
    int       n_iter_allowed = n_G;
 
    // Query epsilon and safmin, which are used in the test for convergence.
    eps    = FLA_Mach_params_opd( FLA_MACH_EPS );
    safmin = FLA_Mach_params_opd( FLA_MACH_SFMIN );
 
    // Initialize a pointer to the last sub-diagonal element and two
    // more to the last and second last
    e_last    = &buff_e[ (m_A-2)*inc_e ];
    d_last_m1 = &buff_d[ (m_A-2)*inc_d ];
    d_last    = &buff_d[ (m_A-1)*inc_d ];
 
 
    for ( k = 0; k < n_iter_allowed; ++k )
    {
        dcomplex* g1 = buff_G + (k  )*cs_G;
 
        /*------------------------------------------------------------*/
 
        // If we've converged, record k and return index of eigenvalue found.
        // The reason we check before the Francis step (rather than after)
        // is so we correctly handle situations where the last diagonal
        // element has already converged from previous eigenvalue searches
        // and thus no iteration is necessary. If we checked after the
        // Francis step, we would have unnecessarily executed an additional
        // Francis step's worth of rotations with a sub-optimal shift (since
        // it would be using a 2x2 that was not "centered" properly).
        if ( MAC_Tevd_eigval_converged_opd( eps, safmin, *d_last_m1, *e_last, *d_last ) )
        {
            *e_last = 0.0;
            *n_iter = k;
            return m_A - 1;
        }
 
        FLA_Tevd_find_perfshift_opd( m_A,
                                     m_U,
                                     buff_d, inc_d,
                                     buff_e, inc_e,
                                     buff_l, inc_l,
                                     buff_ls, inc_ls,
                                     buff_pu, inc_pu,
                                     &ij_shift );
 
        if ( ij_shift == -1 )
        {
            FLA_Wilkshift_tridiag_opd( *d_last_m1,
                                       *e_last,
                                       *d_last,
                                       &shift );
        }
        else
        {
            shift = buff_l[ ij_shift*inc_l ];
        }
 
        // Perform a Francis step.
        r_val = FLA_Tevd_francis_v_opd_var1( m_A,
                                             &shift,
                                             g1,     rs_G,
                                             buff_d, inc_d,
                                             buff_e, inc_e );
 
        if ( ij_shift >= 0 &&
             MAC_Tevd_eigval_converged_opd( eps, safmin, *d_last_m1, *e_last, *d_last ) )
        {
            buff_ls[ ij_shift * inc_ls ] = 1;
            *e_last = 0.0;
            *n_iter = k + 1;
            return m_A - 1;
        }
 
        // Check for internal deflation.
        if ( r_val != FLA_SUCCESS )
        {
#ifdef PRINTF
            printf( "FLA_Tevd_eigval_v_opt_var3: Internal deflation in col %d, eig %d\n", r_val, m_A - 1 );
            printf( "FLA_Tevd_eigval_v_opt_var3: alpha11         = %23.19e\n", buff_d[r_val*inc_d] );
            printf( "FLA_Tevd_eigval_v_opt_var3: alpha21 alpha22 = %23.19e %23.19e\n", buff_e[r_val*inc_e], buff_d[(r_val+1)*inc_d] );
#endif
 
            // Set the off-diagonal element to zero.
            buff_e[ r_val*inc_e ] = 0.0;
 
            *n_iter = k + 1;
            return r_val;
        }
 
        /*------------------------------------------------------------*/
    }
 
    *n_iter = n_iter_allowed;
    return FLA_FAILURE;
}

References FLA_Mach_params_opd(), FLA_Tevd_find_perfshift_opd(), FLA_Tevd_francis_v_opd_var1(), FLA_Wilkshift_tridiag_opd(), and i.

Referenced by FLA_Tevd_iteracc_v_opd_var3().

FLA_Tevd_eigval_v_ops_var1()

FLA_Error FLA_Tevd_eigval_v_ops_var1	(	int	m_A,
		int	n_G,
		scomplex *	buff_G,
		int	rs_G,
		int	cs_G,
		float *	buff_d,
		int	inc_d,
		float *	buff_e,
		int	inc_e,
		int *	n_iter
	)

{
    return FLA_SUCCESS;
}

References i.

Referenced by FLA_Tevd_eigval_v_opt_var1().

FLA_Tevd_eigval_v_ops_var3()

FLA_Error FLA_Tevd_eigval_v_ops_var3	(	int	m_A,
		int	m_U,
		int	n_G,
		scomplex *	buff_G,
		int	rs_G,
		int	cs_G,
		float *	buff_d,
		int	inc_d,
		float *	buff_e,
		int	inc_e,
		float *	buff_l,
		int	inc_l,
		int *	buff_ls,
		int	inc_ls,
		float *	buff_pu,
		int	inc_pu,
		int *	n_iter
	)

{
    return FLA_SUCCESS;
}

References i.

FLA_Tevd_eigval_v_opt_var1()

FLA_Error FLA_Tevd_eigval_v_opt_var1	(	FLA_Obj	G,
		FLA_Obj	d,
		FLA_Obj	e,
		FLA_Obj	n_iter
	)

{
    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;
}

References FLA_Obj_col_stride(), FLA_Obj_datatype(), FLA_Obj_row_stride(), FLA_Obj_vector_dim(), FLA_Obj_vector_inc(), FLA_Obj_width(), FLA_Tevd_eigval_v_opd_var1(), FLA_Tevd_eigval_v_ops_var1(), and i.