Determinant and Inverse of an LU-Factored General Matrix

Calling Sequence

CALL DGEDI	(DA, LDA, N, IPIVOT, DDET, DWORK, JOB)
CALL SGEDI	(SA, LDA, N, IPIVOT, SDET, SWORK, JOB)
CALL ZGEDI	(ZA, LDA, N, IPIVOT, ZDET, ZWORK, JOB)
CALL CGEDI	(CA, LDA, N, IPIVOT, CDET, CWORK, JOB)
void dgedi	(double *da, int lda, int n, int *ipivot, double *ddet, int job)
void sgedi	(float *sa, int lda, int n, int *ipivot, float *sdet, int job)
void zgedi	(doublecomplex *za, int lda, int n, int *ipivot, doublecomplex *zdet, int job)
void cgedi	(complex *ca, int lda, int n, int *ipivot, complex *cdet, int job)

Arguments

xA	On entry, the LU factorization of the matrix A, as computed by xGECO or xGEFA. On exit, the inverse of the original matrix A if the inverse was requested, otherwise it is unchanged.
LDA	Leading dimension of the array A as specified in a dimension or type statement. LDA max(1,N).
N	Order of the original matrix A. N 0.
IPIVOT	Pivot vector as computed by xGECO or xGEFA.
xDET	On exit, the determinant of the matrix A. The determinant is stored as b × 10expon where b is stored in DET(1) and expon is stored in DET(2). 1.0 |DET(1)| < 10.0 or DET(1) = 0.0.
xWORK	Scratch array with a dimension of N.
JOB	Determines which operation the subroutine will perform:
	11	both determinant and inverse
	01	inverse only
	10	determinant only

Sample Program

PROGRAM TEST

IMPLICIT NONE

C

INTEGER INVDET, LDA, N

PARAMETER (INVDET = 11)

PARAMETER (N = 4)

PARAMETER (LDA = N)

C

DOUBLE PRECISION A(LDA,N), DET(2), RCOND, WORK(N)

INTEGER ICOL, IPIVOT(N), IROW, JOB

C

EXTERNAL DGECO, DGEDI

C

C Initialize the array A to store the matrix A shown below.

C Its exact inverse also is shown below.

C

C -3 1 1 1 1 1 1

C A = 1 -2 1 A**(-1) = - --- * 1 3 3 3

C 1 -2 1 2 1 3 5 5

C 1 -1 1 3 5 7

C

DATA A / -3.0D0, 1.0D0, 2*0.0D0, 1.0D0, -2.0D0, 1.0D0,

$ 2*0.0D0, 1.0D0, -2.0D0, 1.0D0, 2*0.0D0, 1.0D0,

$ -1.0D0 /

C

PRINT 1000

PRINT 1010, ((A(IROW,ICOL), ICOL = 1, N), IROW = 1, N)

CALL DGECO (A, LDA, N, IPIVOT, RCOND, WORK)

JOB = INVDET

CALL DGEDI (A, LDA, N, IPIVOT, DET, WORK, JOB)

PRINT 1020

PRINT 1010, ((A(IROW,ICOL), ICOL = 1, N), IROW = 1, N)

PRINT 1030, DET(1) * (1.0D1 ** DET(2))

C

1000 FORMAT (1X, 'A:')

1010 FORMAT (4(3X, F5.1))

1020 FORMAT (/1X, 'A**(-1):')

1030 FORMAT (/1X, 'det(A) =', F6.1)

C

END

Sample Output

A:
-3.0 1.0 0.0 0.0
1.0 -2.0 1.0 0.0
0.0 1.0 -2.0 1.0
0.0 0.0 1.0 -1.0
A**(-1):
-0.5 -0.5 -0.5 -0.5
-0.5 -1.5 -1.5 -1.5
-0.5 -1.5 -2.5 -2.5
-0.5 -1.5 -2.5 -3.5
det(A) = 2.0