Create a Diagonally-Dominant Square Matrix

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

Routine Name: mat_dd

Author: Christian Bolander

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

and can be added to a program using

$ gfortran program.f90 mat_dd.o

Description/Purpose: This routine takes a square matrix, A, and fills each element of the matrix with a random number from 0 to 1 not including one. This matrix is then modified so that it is diagonally dominant, which means that

It can be used to quickly generate a matrix to be tested with other linear algebra routines.

Input:

n : INTEGER - number of rows and columns in the matrix

Output:

mat : REAL - a diagonally dominant matrix of size (n, n) containing random numbers

Usage/Example:

This routine has an input n and can be implemented in a program as follows

INTEGER :: n, i
REAL*8, ALLOCATABLE :: A(:, :)

n = 3
ALLOCATE(A(1:n, 1:n))
CALL mat_dd(n, A)
DO i = 1, n
	WRITE(*,*) A(i, :)
END DO

The outputs from the above code:

   1.6853128504659201       0.65315654864851747       0.13964096814871718     
   3.8754568170421222E-002  0.97335793596721065       0.23884389800574723     
  0.34318290516739380       0.75534218933621855        2.0417728343013199   

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

SUBROUTINE mat_dd(n, mat)
	IMPLICIT NONE
	
	! Takes in a value for the number of rows and columns in the
	! diagonally dominant matrix and outputs the matrix.
	INTEGER, INTENT(IN) :: n
	REAL*8, INTENT(OUT) :: mat(1:n, 1:n)
	
	! Intialize do loop incrementers and a row summation variable to
	! help enforce diagonal dominance.
	INTEGER :: i, j
	REAL*8 :: row_sum
	
	! Fills the matrix with random numbers in all elements from 0 to 1
	! non-inclusive.
	CALL RANDOM_NUMBER(mat)
	
	! Loops through all rows and calculates a value for the summation
	! of all elements in that row.
	DO i = 1, n
		row_sum = 0.D0
		DO j = 1, n
			row_sum = row_sum + mat(i, j)
		END DO
		! Adds the value of the row summation to the diagonal element.
		mat(i, i) = row_sum
	END DO
END SUBROUTINE