norm                 package:Matrix                 R Documentation

_N_o_r_m _o_f _a _M_a_t_r_i_x

_D_e_s_c_r_i_p_t_i_o_n:

     Computes a matrix norm of 'x' using Lapack.  The norm can be the
     one norm, the infinity norm, the Frobenius norm, or the maximum
     modulus among elements of a matrix, as determined by the value of
     'type'.

_U_s_a_g_e:

     ## S3 method for class 'Matrix':
     norm(x, type = "M", ...) 

_A_r_g_u_m_e_n_t_s:

       x: a real or complex matrix. 

    type: A character indicating the type of norm desired. '"O"' or
          '"o"' or '"1"' specifies the one norm, (maximum absolute
          column sum); '"I"' or '"i"' specifies the infinity norm
          (maximum absolute row sum); '"F"' or '"f"' specifies the
          Frobenius norm (the Euclidean norm of 'x' treated as if it
          were a vector); and '"M"' or '"m"' specifies the maximum
          modulus of all the elements in 'x'. The default is '"M"'.

          Only the first character of 'type[1]' is used. 

     ...: further arguments passed to or from other methods.

_D_e_t_a_i_l_s:

     Based on the Lapack functions 'dlange', 'dlansy', 'dlantr',
     'zlange',  'zlansy', and 'zlantr'.

_V_a_l_u_e:

     A numeric value of class '"norm"', representing the quantity
     chosen according to 'type'.

_R_e_f_e_r_e_n_c_e_s:

     Anderson, E., et al. (1994). _LAPACK User's Guide,_ 2nd edition,
     SIAM, Philadelphia.

_E_x_a_m_p_l_e_s:

     x <- hilbert(9)
     norm(x, "1")
     norm(x, "I")
     norm(x, "F")
     norm(x, "M")

