Calculate the Inner (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: out_prod_vec

Author: Christian Bolander

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

and can be added to a program using

$ gfortran program.f90 out_prod_vec.o

Description/Purpose: This routine will calculate the outer product, C, of two vectors, a and b, using

Input:

m : INTEGER - the length of vector a

n : INTEGER - the length of vector b

a : REAL - an arbitrary vector of length m

b : REAL - an arbitrary vector of length n

Output:

C : REAL - the outer product of a and b with size m x n

Usage/Example:

This routine can be implemented in a program as follows

INTEGER :: n, m, i
REAL*8, ALLOCATABLE :: a(:), b(:)
REAL*8, ALLOCATABLE :: C(:, :)

m = 4
n = 3
ALLOCATE(a(1:m), b(1:n), C(1:m, 1:n))
a = (/-3.2D0, 4.5D0, 8.7D0, 2.6D0/)
b = (/9.2D0, 4.6D0, -7.1D0/)
CALL out_prod_vec(m, n, a, b, C)
DO i = 1, m
	WRITE(*,*) C(i, :)
END DO

The output from the above code:

   -29.439999999999998       -14.719999999999999        22.719999999999999     
   41.399999999999999        20.699999999999999       -31.949999999999999     
   80.039999999999992        40.019999999999996       -61.769999999999989     
   23.919999999999998        11.959999999999999       -18.460000000000001 

which is the vector outer product of a and b.

Implementation/Code: The code for vec_cross_prod3 can be seen below.

SUBROUTINE out_prod_vec(m, n, a, b, C)
	IMPLICIT NONE
	
	! Takes as inputs two vectors, `a` and `b`, of length `m` and `n`
	! respectively. Outputs the outer product of `a` and `b`, a matrix
	! `C` of size `m` x `n`.
	INTEGER, INTENT(IN) :: m, n
	REAL*8, INTENT(IN) :: a(1:m), b(1:n)
	REAL*8, INTENT(OUT) :: C(1:m, 1:n)
	
	! Initialize two increment variables for looping.
	INTEGER :: i, j
	
	! Loop over all elements of `C` and multiply the appropriate
	! elements of `a` and `b` together to calculate the outer product.
	DO i = 1, m
		DO j = 1, n
			C(i, j) = a(i)*b(j)
		END DO
	END DO
END SUBROUTINE