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FORTRAN 90: Determinant of a Matrix

Thus function finds the determinant of a square matrix of any order

Submitted By: Louisda16th

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Views: 6,070

Language: Other Languages

Last Modified: September 18, 2007

Instructions: !Example program:
PROGRAM MAT_DET
IMPLICIT NONE

REAL, ALLOCATABLE, DIMENSION(:,:) :: Matrix
REAL :: Determinant, FindDet
INTEGER :: n, i, j

PRINT*,"Enter order of matrix"
READ*, n

ALLOCATE(Matrix(n,n))

PRINT*,"Enter elements row-wise"

DO i = 1,n
READ*,(MATRIX(i,j),j=1,n)
END DO

Determinant = FindDet(Matrix,n)

PRINT*,"Determinant =",Determinant
END PROGRAM MAT_DET
!Function Source Here

Snippet

!Function to find the determinant of a square matrix
!Author : Louisda16th a.k.a Ashwith J. Rego
!Description: The subroutine is based on two key points:
!1] A determinant is unaltered when row operations are performed: Hence, using this principle,
!row operations (column operations would work as well) are used
!to convert the matrix into upper traingular form
!2]The determinant of a triangular matrix is obtained by finding the product of the diagonal elements
!
REAL FUNCTION FindDet(matrix, n)
IMPLICIT NONE
REAL, DIMENSION(n,n) :: matrix
INTEGER, INTENT(IN) :: n
REAL :: m, temp
INTEGER :: i, j, k, l
LOGICAL :: DetExists = .TRUE.
l = 1
!Convert to upper triangular form
DO k = 1, n-1
IF (matrix(k,k) == 0) THEN
DetExists = .FALSE.
DO i = k+1, n
IF (matrix(i,k) /= 0) THEN
DO j = 1, n
temp = matrix(i,j)
matrix(i,j)= matrix(k,j)
matrix(k,j) = temp
END DO
DetExists = .TRUE.
l=-l
EXIT
ENDIF
END DO
IF (DetExists .EQV. .FALSE.) THEN
FindDet = 0
return
END IF
ENDIF
DO j = k+1, n
m = matrix(j,k)/matrix(k,k)
DO i = k+1, n
matrix(j,i) = matrix(j,i) - m*matrix(k,i)
END DO
END DO
END DO
!Calculate determinant by finding product of diagonal elements
FindDet = l
DO i = 1, n
FindDet = FindDet * matrix(i,i)
END DO
END FUNCTION FindDet

Copy & Paste

!Function to find the determinant of a square matrix
!Author : Louisda16th a.k.a Ashwith J. Rego
!Description: The subroutine is based on two key points:
!1] A determinant is unaltered when row operations are performed: Hence, using this principle,
!row operations (column operations would work as well) are used
!to convert the matrix into upper traingular form
!2]The determinant of a triangular matrix is obtained by finding the product of the diagonal elements
!
REAL FUNCTION FindDet(matrix, n)
	IMPLICIT NONE
	REAL, DIMENSION(n,n) :: matrix
	INTEGER, INTENT(IN) :: n
	REAL :: m, temp
	INTEGER :: i, j, k, l
	LOGICAL :: DetExists = .TRUE.
	l = 1
	!Convert to upper triangular form
	DO k = 1, n-1
		IF (matrix(k,k) == 0) THEN
			DetExists = .FALSE.
			DO i = k+1, n
				IF (matrix(i,k) /= 0) THEN
					DO j = 1, n
						temp = matrix(i,j)
						matrix(i,j)= matrix(k,j)
						matrix(k,j) = temp
					END DO
					DetExists = .TRUE.
					l=-l
					EXIT
				ENDIF
			END DO
			IF (DetExists .EQV. .FALSE.) THEN
				FindDet = 0
				return
			END IF
		ENDIF
		DO j = k+1, n
			m = matrix(j,k)/matrix(k,k)
			DO i = k+1, n
				matrix(j,i) = matrix(j,i) - m*matrix(k,i)
			END DO
		END DO
	END DO
	
	!Calculate determinant by finding product of diagonal elements
	FindDet = l
	DO i = 1, n
		FindDet = FindDet * matrix(i,i)
	END DO
	
END FUNCTION FindDet