FLA_Hevd_lv_unb_var2.c File Reference

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Functions
FLA_Error	FLA_Hevd_lv_unb_var2 (dim_t n_iter_max, FLA_Obj A, FLA_Obj l, dim_t k_accum, dim_t b_alg)

Function Documentation

FLA_Hevd_lv_unb_var2()

FLA_Error FLA_Hevd_lv_unb_var2	(	dim_t	n_iter_max,
		FLA_Obj	A,
		FLA_Obj	l,
		dim_t	k_accum,
		dim_t	b_alg
	)

{
    FLA_Error    r_val;
    FLA_Uplo     uplo = FLA_LOWER_TRIANGULAR;
    FLA_Datatype dt;
    FLA_Datatype dt_real;
    FLA_Datatype dt_comp;
    FLA_Obj      scale, T, r, d, e, G, R, W;
    dim_t        mn_A;
    dim_t        n_G = k_accum;
 
    mn_A    = FLA_Obj_length( A );
    dt      = FLA_Obj_datatype( A );
    dt_real = FLA_Obj_datatype_proj_to_real( A );
    dt_comp = FLA_Obj_datatype_proj_to_complex( A );
 
    // If the matrix is a scalar, then the EVD is easy.
    if ( mn_A == 1 )
    {
        FLA_Copy( A, l );
        FLA_Set( FLA_ONE, A );
 
        return FLA_SUCCESS;
    }
 
    // Create a matrix to hold block Householder transformations.
    FLA_Tridiag_UT_create_T( A, &T );
 
    // Create a vector to hold the realifying scalars.
    FLA_Obj_create( dt,      mn_A,     1, 0, 0, &r );
 
    // Create vectors to hold the diagonal and sub-diagonal.
    FLA_Obj_create( dt_real, mn_A,     1, 0, 0, &d );
    FLA_Obj_create( dt_real, mn_A-1,   1, 0, 0, &e );
    FLA_Obj_create( dt_comp, mn_A-1, n_G, 0, 0, &G );
    FLA_Obj_create( dt_real, mn_A,  mn_A, 0, 0, &R );
    FLA_Obj_create( dt,      mn_A,  mn_A, 0, 0, &W );
 
    // Create a real scaling factor.
    FLA_Obj_create( dt_real, 1, 1, 0, 0, &scale );
 
    // Compute a scaling factor; If none is needed, sigma will be set to one.
    FLA_Hevd_compute_scaling( uplo, A, scale );
 
    // Scale the matrix if scale is non-unit.
    if ( !FLA_Obj_equals( scale, FLA_ONE ) )
        FLA_Scalr( uplo, scale, A );
 
    // Reduce the matrix to tridiagonal form.
    FLA_Tridiag_UT( uplo, A, T );
 
    // Apply scalars to rotate elements on the sub-diagonal to the real domain.
    FLA_Tridiag_UT_realify( uplo, A, r );
 
    // Extract the diagonal and sub-diagonal from A.
    FLA_Tridiag_UT_extract_real_diagonals( uplo, A, d, e );
 
    // Form Q, overwriting A.
    FLA_Tridiag_UT_form_Q( uplo, A, T, A );
 
    // Apply the scalars in r to Q.
    FLA_Apply_diag_matrix( FLA_RIGHT, FLA_CONJUGATE, r, A );
 
    // Perform an eigenvalue decomposition on the tridiagonal matrix.
    r_val = FLA_Tevd_v_opt_var2( n_iter_max, d, e, G, R, W, A, b_alg );
 
    // Copy the converged eigenvalues to the output vector.
    FLA_Copy( d, l );
 
    // Sort the eigenvalues and eigenvectors in ascending order.
    FLA_Sort_evd( FLA_FORWARD, l, A );
 
    // If the matrix was scaled, rescale the eigenvalues.
    if ( !FLA_Obj_equals( scale, FLA_ONE ) )
        FLA_Inv_scal( scale, l );
 
    FLA_Obj_free( &scale );
    FLA_Obj_free( &T );
    FLA_Obj_free( &r );
    FLA_Obj_free( &d );
    FLA_Obj_free( &e );
    FLA_Obj_free( &G );
    FLA_Obj_free( &R );
    FLA_Obj_free( &W );
 
    return r_val;
}

References FLA_Apply_diag_matrix(), FLA_Copy(), FLA_Hevd_compute_scaling(), FLA_Inv_scal(), FLA_Obj_create(), FLA_Obj_datatype(), FLA_Obj_datatype_proj_to_complex(), FLA_Obj_datatype_proj_to_real(), FLA_Obj_equals(), FLA_Obj_free(), FLA_Obj_length(), FLA_ONE, FLA_Scalr(), FLA_Set(), FLA_Sort_evd(), FLA_Tevd_v_opt_var2(), FLA_Tridiag_UT(), FLA_Tridiag_UT_create_T(), FLA_Tridiag_UT_extract_real_diagonals(), FLA_Tridiag_UT_form_Q(), FLA_Tridiag_UT_realify(), and i.