Calculate the L1 Norm of a Vector

This is a part of the student software manual project for Math 5610: Computational Linear Algebra and Solution of Systems of Equations.

Routine Name: l1_vec_norm

Author: Christian Bolander

Language: Fortran. This code can be compiled using the GNU Fortran compiler by $ gfortran -c l1_vec_norm.f90

and can be added to a program using

$ gfortran program.f90 l1_vec_norm.o

Description/Purpose: This routine calculates the -norm of an arbitrary vector, a.

Input:

n : INTEGER - the length of the vector, a

a : REAL - an arbitrary vector of length n

Output:

norm : REAL - the -norm of the vector, a.

Usage/Example:

This routine can be implemented in a program as follows

n = 12
doo = 1.0D0
norm = 0.0D0
ALLOCATE(a(1:n))
DO i = 1, n
	a(i) = -doo
END DO
CALL l1_vec_norm(a, n, norm)
WRITE(*,*) norm

The output from the above code:

        12.000000000000000      

which is the -norm of the vector a.

Implementation/Code: The code for l1_vec_norm can be seen below.

SUBROUTINE l1_vec_norm(a, n, norm)
IMPLICIT NONE

INTEGER, INTENT(IN) :: n
REAL*8, INTENT(IN) :: a(1:n)
REAL*8, INTENT(OUT) :: norm
INTEGER :: i

norm = 0.0D0

! Sum up the absolute value of each value in the vector a to find
! the l1-norm of the vector.
DO i = 1, n
	norm = norm + ABS(a(i))
END DO
END SUBROUTINE