Computes the 1-norm of a complex band matrix in band storage mode.
Required Arguments
A — Complex (NUCA + NLCA + 1) by N array containing the N by N band matrix in band storage mode. (Input)
NLCA — Number of lower codiagonals of A. (Input)
NUCA — Number of upper codiagonals of A. (Input)
ANORM — Real scalar containing the 1-norm of A. (Output)
Optional Arguments
N — Order of the
matrix. (Input)
Default: N = size
(A,2).
LDA — Leading
dimension of A
exactly as specified in the dimension statement of the calling
program. (Input)
Default: LDA = size
(A,1).
FORTRAN 90 Interface
Generic: CALL NR1CB (A, NLCA, NUCA, ANORM [,…])
Specific: The specific interface names are S_NR1CB and D_NR1CB.
FORTRAN 77 Interface
Single: CALL NR1CB (N, A, LDA, NLCA, NUCA, ANORM)
Double: The double precision name is DNR1CB.
Description
The routine NR1CB computes the 1-norm of a complex band matrix A. The 1-norm of a complex matrix A is
Example
Compute the 1-norm of a complex matrix of order 4 in band storage mode.
USE NR1CB_INT
USE UMACH_INT
IMPLICIT NONE
! Declare variables
INTEGER LDA, N, NLCA, NUCA
PARAMETER (LDA=4, N=4, NLCA=2, NUCA=1)
!
INTEGER NOUT
REAL ANORM
COMPLEX A(LDA,N)
!
! Set values for A (in band mode)
! A = ( 0.0+0.0i 2.0+3.0i -1.0+1.0i -2.0-1.0i )
! ( -2.0+3.0i 1.0+0.0i -4.0-1.0i 0.0-4.0i )
! ( 2.0+2.0i 4.0+6.0i 3.0+2.0i 0.0+0.0i )
! ( 0.0-1.0i 2.0+1.0i 0.0+0.0i 0.0+0.0i )
!
DATA A/(0.0,0.0), (-2.0,3.0), (2.0,2.0), (0.0,-1.0), (2.0,3.0), &
(1.0,0.0), (4.0,6.0), (2.0,1.0), (-1.0,1.0), (-4.0,-1.0), &
(3.0,2.0), (0.0,0.0), (-2.0,-1.0), (0.0,-4.0), (0.0,0.0), &
(0.0,0.0)/
! Compute the L1 norm of A
CALL NR1CB (A, NLCA, NUCA, ANORM)
! Print results
CALL UMACH (2, NOUT)
WRITE (NOUT,*) ' The 1-norm of A is ', ANORM
END
Output
The 1-norm of A is 19.0000
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