Calculate the Dot Product of Two Vectors

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

Routine Name: vec_dot_prod

Author: Christian Bolander

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

and can be added to a program using

$ gfortran program.f90 vec_dot_prod.o

Description/Purpose: This routine will calculate the dot product of two vectors, a and b of the same size n, using

Input:

n : INTEGER - the length of the vectors for which the dot product is being calculated

a : REAL - an arbitrary vector of length n

b : REAL - an arbitrary vector of length n

Output:

dotprod : REAL - the dot product of a and b

Usage/Example:

This routine can be implemented in a program as follows

n = 3
ALLOCATE(a(1:n), b(1:n))
a(1) = 1
a(2) = 3
a(3) = -5
b(1) = 4
b(2) = -2
b(3) = -1
CALL vec_dot_prod(a, b, n, norm)
WRITE(*,*) norm

The output from the above code:

   3.0000000000000000  

which is the vector dot product of a and b.

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

SUBROUTINE vec_dot_prod(a, b, n, dotprod)
	IMPLICIT NONE
	
	! I/O variables
	INTEGER, INTENT(IN) :: n
	REAL*8, INTENT(IN) :: a(1:n), b(1:n)
	REAL*8, INTENT(OUT) :: dotprod
	
	! Initialize subroutine variables
	INTEGER :: i
	
	dotprod = 0.D0
	
	! Calculate the dot product of the vectors a and b by multiplying
	! the elements together and summing them up
	DO i = 1, n
		dotprod = dotprod + a(i)*b(i)
	END DO
END SUBROUTINE