Computes the norm of an array.
Function Return Value
Norm of A. This is a scalar for the case where A is rank 1 or rank 2. For rank-3 arrays, the norms of each rank-2 array, in dimension 3, are computed. (Output)
Required Argument
A — An array of rank-1, rank-2, or rank-3, containing the values for which the norm is to be computed. It may be real, double, complex, or double complex. (Input)
Optional Arguments, Packaged Options
TYPE —Integer
indicating the type of norm to be computed.
1 = 
2 = 
(default)
huge(1) = 
Use of the option number ?_reset_default_norm will switch the
default from the to the 
norms. (Input)
The option and derived type names are given in the following tables:
|
Option Names for NORM |
Option Value |
|
?_norm_for_lin_sol_svd |
1 |
|
?_reset_default_norm |
2 |
|
Name of
Unallocated Option Array |
Use |
Derived Type |
|
?_norm_options(:) |
Use when setting options for calls hereafter. |
?_options |
|
?_norm_options_once(:) |
Use when setting options for next call only. |
?_options |
For a description on how to use these options, see Matrix Optional Data Changes. See lin_sol_svd located in Chapter 1, “Linear Systems” for the specific options for this routine.
FORTRAN 90 Interface
NORM (A [,…])
Description
Computes the , norm. The 
norms are likely to be less expensive to compute than the
l2 norm.
If the norm is required, this function uses
lin_sol_svd
(see Chapter 1, “Linear Systems”), to compute the
largest singular value of A. For the other norms, Fortran 90
intrinsics are used.
Examples
Compute three norms of an array
use norm_int
real (kind(1e0)) A(5), n_1, n_2, n_inf
A = rand (A)
! I1
n_1 = norm(A, TYPE=1)
write (*,*) n_1
! I2
n_2 = norm(A)
write (*,*) n_2
! I infinity
n_inf = norm(A, TYPE=huge(1))
write (*,*) n_inf
end
Parallel Example (parallel_ex14.f90)
A “Polar Decomposition” of several matrices are computed. The box data type and the SVD() function are used. Orthogonality and small residuals are checked to verify that the results are correct.
use linear_operators
use mpi_setup_int
implicit none
! This is Parallel Example 15 using operators and
! functions for a polar decomposition.
integer, parameter :: n=33, nr=3
real(kind(1d0)) :: one=1d0, zero=0d0
real(kind(1d0)),dimension(n,n,nr) :: A, P, Q, &
S_D(n,nr), U_D, V_D
real(kind(1d0)) TEMP1(nr), TEMP2(nr)
! Setup for MPI:
mp_nprocs = mp_setup()
! Generate a random matrix.
if(mp_rank == 0) A = rand(A)
! Compute the singular value decomposition.
S_D = SVD(A, U=U_D, V=V_D)
! Compute the (left) orthogonal factor.
P = U_D .xt. V_D
! Compute the (right) self-adjoint factor.
Q = V_D .x. diag(S_D) .xt. V_D
! Check the results for orthogonality and
! small residuals.
TEMP1 = NORM(spread(EYE(n),3,nr) - (p .xt. p))
TEMP2 = NORM(A -(P .X. Q)) / NORM(A)
if (ALL(TEMP1 <= sqrt(epsilon(one))) .and. &
ALL(TEMP2 <= sqrt(epsilon(one)))) then
if(mp_rank == 0)&
write (*,*) 'Parallel Example 15 is correct.'
end if
! See to any error messages and exit MPI.
mp_nprocs = mp_setup('Final')
end
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