Computes the mathematical rank of a matrix.
Function Return Value
Integer rank of A. The output function value is an integer with a value equal to the number of singular values that are greater than a tolerance. (Output)
Required Argument
A — Matrix for which the rank is to be computed. The argument must be rank-2 or rank-3 (box) array of type single, double, complex, or double complex. (Input)
Optional Arguments, Packaged Options
This function uses lin_sol_svd to compute the singular values of the argument. The singular values are then compared with the value of the tolerance to compute the rank.
The option and derived type names are given in the following tables:
|
Option Names for RANK |
Option Value |
|
?_rank_set_small |
1 |
|
?_rank_for_lin_sol_svd |
2 |
|
Name of
Unallocated Option Array |
Use |
Derived Type |
|
?_rank_options(:) |
Use when setting options for calls hereafter. |
?_options |
|
?_rank_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
RANK (A)
Description
Computes the mathematical rank of a rank-2 or rank-3 array.
The output function value is an integer with a value equal to the number of
singular values that are greater than a tolerance. The default value for
this tolerance is 
,
where 
is machine
precision and 
is the
largest singular value of the matrix.
Examples
use linear_operators
real (kind(1e0)) A(5,5)
A = rand (A)
write (*,*) rank(A)
A=1.0
write (*,*) rank(A)
end
Output
5
1
Parallel Example
use linear_operators
use mpi_setup_int
integer, parameter :: N=3, nr=4
integer r(nr)
real (kind(1.e0)) s_mat(N,N), s_box(N,N,nr)
! Setup for MPI
mp_nprocs = mp_setup()
if (mp_rank == 0) then
s_mat = reshape((/1.,0.,0.,epsilon(1.0e0)/),(/n,n/))
s_box = spread(s_mat,dim=3,ncopies=nr)
end if
r = rank(s_box)
mp_nprocs = mp_setup ('Final')
end
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