Calculate the L2 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: l2_vec_norm

Author: Christian Bolander

Language: Fortran. This code can be compiled using the GNU Fortran compiler by $ gfortran -c l2_vec_norm.f90

and can be added to a program using

$ gfortran program.f90 l2_vec_norm.o

Description/Purpose: This routine calculates the -norm or Euclidean 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 l2_vec_norm(a, n, norm)
WRITE(*,*) norm

The output from the above code:

     3.4641016151377544 

which is the -norm of the vector a.

Implementation/Code: The code for l2_vec_norm can be seen.

SUBROUTINE l2_vec_norm(a, n, norm)
IMPLICIT NONE

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

summation = 0.0D0

! Sum up the squares of each value in the vector a.
DO i = 1, n
	summation = summation + (a(i)*a(i))
END DO

! Find the l2 norm of the vector by taking the square root of the sum
! of the squares
norm = SQRT(summation)
END SUBROUTINE