DECLARE SUB CDIV (Z1#(), Z2#(), Z#())
DECLARE SUB CMUL (Z1#(), Z2#(), Z#())
'************************************************************
'*  This program calculates the determinant of a complex    *
'* square matrix using Function CFindDet (see ref. below).  *
'* -------------------------------------------------------- *
'* SAMPLE RUN:                                              *
'*                                                          *
'* Calculate the deteminant of square matrix:               *
'*                                                          *
'*           ! 0  -1  -1  -1 !                              *
'*           ! 1   0  -1  -1 !                              *
'*           ! 1   1   0  -1 !                              *
'*           ! 1   1   1   0 !                              *
'*                                                          *
'*  Determinant =  (1.000000, 0.000000)                     *
'*                                                          *
'* -------------------------------------------------------- *
'*                                                          *
'*                    Basic Version By J-P Moreau, Paris.   *
'************************************************************
DEFINT I-N
DEFDBL A-H, O-Z

n = 4

DIM A(n, n, 2) 'Complex matrix of size N*N
DIM D(2) 'Complex determinant
 
A(1, 1, 1) = 0!: A(1, 1, 2) = 0!
A(2, 1, 1) = 1!: A(2, 1, 2) = 0!
A(3, 1, 1) = 1!: A(3, 1, 2) = 0!
A(4, 1, 1) = 1!: A(4, 1, 2) = 0!

A(1, 2, 1) = -1!: A(1, 2, 2) = 0!
A(2, 2, 1) = 0!: A(2, 2, 2) = 0!
A(3, 2, 1) = 1!: A(3, 2, 2) = 0!
A(4, 2, 1) = 1!: A(4, 2, 2) = 0!

A(1, 3, 1) = -1!: A(1, 3, 2) = 0!
A(2, 3, 1) = -1!: A(2, 3, 2) = 0!
A(3, 3, 1) = 0!: A(3, 3, 2) = 0!
A(4, 3, 1) = 1!: A(4, 3, 2) = 0!

A(1, 4, 1) = -1!: A(1, 4, 2) = 0!
A(2, 4, 1) = -1!: A(2, 4, 2) = 0!
A(3, 4, 1) = -1!: A(3, 4, 2) = 0!
A(4, 4, 1) = 0!: A(4, 4, 2) = 0!

GOSUB 1000 'D = CFindDet(A, N)

PRINT
PRINT " Determinant = ("; D(1); ","; D(2); ")"
PRINT

END
 
'-----------------------------------------------------------------------------------------------------
'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
'-----------------------------------------------------------------------------------------------------
1000 'FUNCTION CFindDet(A, n)
DIM cm(2), temp(2), temp1(2), CONE(2), CZERO(2) 'Complex numbers
DIM DetExists AS INTEGER 'Boolean
DIM FALSE, TRUE AS INTEGER
l = 1
FALSE = 0: TRUE = 1
DetExists = TRUE
CZERO(1) = 0: CZERO(2) = 0
CONE(1) = 1!: CONE(2) = 0!
'Convert to upper triangular form
FOR k = 1 TO n - 1
    IF A(k, k, 1) = CZERO(1) AND A(k, k, 2) = CZERO(2) THEN
        DetExists = FALSE
        FOR i = k + 1 TO n
            IF A(i, k, 1) <> CZERO(1) OR A(i, k, 2) <> CZERO(2) THEN
                FOR j = 1 TO n
                    temp(1) = A(i, j, 1): temp(2) = A(i, j, 2)
                    A(i, j, 1) = A(k, j, 1): A(i, j, 2) = A(k, j, 2)
                    A(k, j, 1) = temp(1): A(k, j, 2) = temp(2)
                NEXT j
                DetExists = TRUE
                l = -l
                GOTO 10
            END IF
        NEXT i
        10 IF DetExists = FALSE THEN
            D(1) = CZERO(1): D(2) = CZERO(2)
            RETURN
        END IF
    END IF
    FOR j = k + 1 TO n
        'm = A(j,k)/A(k,k)
        temp(1) = A(j, k, 1): temp(2) = A(j, k, 2)
        temp1(1) = A(k, k, 1): temp1(2) = A(k, k, 2)
        CALL CDIV(temp(), temp1(), cm())
        FOR i = k + 1 TO n
            'A(j,i) = A(j,i) - m*A(k,i)
            temp1(1) = A(k, i, 1): temp1(2) = A(k, i, 2)
            CALL CMUL(cm(), temp1(), temp())
            A(j, i, 1) = A(j, i, 1) - temp(1)
            A(j, i, 2) = A(j, i, 2) - temp(2)
        NEXT i
    NEXT j
NEXT k
     
'Calculate determinant by finding product of diagonal elements
D(1) = 1#: D(2) = 0#
FOR i = 1 TO n
    D(1) = D(1) * A(i, i, 1)
    D(2) = D(2) * A(i, i, 2)
NEXT i
     
RETURN

'end of file cfinddet.bas

SUB CDIV (Z1(), Z2(), Z())
DIM C1(2)
D1 = Z2(1) ^ 2 + Z2(2) ^ 2
IF D1 < 2E-12 THEN
    PRINT #2, " Complex Divide by zero!"
ELSE
    C1(1) = Z2(1): C1(2) = -Z2(2)
    CMUL Z1(), C1(), Z()
    Z(1) = Z(1) / D1: Z(2) = Z(2) / D1
END IF
END SUB

SUB CMUL (Z1(), Z2(), Z())
Z(1) = Z1(1) * Z2(1) - Z1(2) * Z2(2)
Z(2) = Z1(1) * Z2(2) + Z1(2) * Z2(1)
END SUB