LU Factorization of a General Matrix

Calling Sequence

CALL DGEFA	(DA, LDA, N, IPIVOT, INFO)
CALL SGEFA	(SA, LDA, N, IPIVOT, INFO)
CALL ZGEFA	(ZA, LDA, N, IPIVOT, INFO)
CALL CGEFA	(CA, LDA, N, IPIVOT, INFO)
void dgefa	(double *da, int lda, int n, int *ipivot, int *info)
void sgefa	(float *sa, int lda, int n, int *ipivot, int *info)
void zgefa	(doublecomplex *za, int lda, int n, int *ipivot, int *info)
void cgefa	(complex *ca, int lda, int n, int *ipivot, int *info)

Arguments

xA	On entry, the matrix A. On exit, an LU factorization of A.
LDA	Leading dimension of the array A as specified in a dimension or type statement. LDA max(1,N).
N	Order of the matrix A. N 0.
IPIVOT	On exit, a vector of pivot indices.
INFO	On exit:
	INFO = 0	Subroutine completed normally.
	INFO > 0	Returns a value k if U(k,k) = 0 to indicate that xGESL will divide by zero if called.

Sample Program

PROGRAM TEST

IMPLICIT NONE

C

INTEGER LDA, N

PARAMETER (N = 3)

PARAMETER (LDA = N)

C

DOUBLE PRECISION A(LDA,N)

INTEGER ICOL, INFO, IPIVOT(N), IROW

C

EXTERNAL DGEFA

C

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

C

C 100 2 3

C A = 100 202 6

C 100 202 306

C

DATA A / 1.0D2, 1.0D2, 1.0D2, 2.0D0, 2.02D2, 2.02D2,

$ 3.0D0, 6.0D0, 3.06D2 /

PRINT 1000

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

CALL DGEFA (A, LDA, N, IPIVOT, INFO)

IF (INFO .EQ. 0) THEN

PRINT 1020

PRINT 1030, (A(1,ICOL), ICOL = 1, N)

PRINT 1040, (A(2,ICOL), ICOL = 1, N)

PRINT 1050, (A(3,ICOL), ICOL = 1, N)

ELSE

PRINT 1060, INFO

END IF

C

1000 FORMAT (1X, 'A:')

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

1020 FORMAT (/8X, 'Multipliers', 19X, 'Upper')

1030 FORMAT (3X, ' 1.0', 17X, 3(2X, F5.1))

1040 FORMAT (3X, F5.1, 2X, ' 1.0', 17X, 2(2X, F5.1))

1050 FORMAT (1X, 2(2X, F5.1), 2X, ' 1.0', 17X, 2X, F5.1)

1060 FORMAT (1X, 'A appears singular at ', I2)

C

END

Sample Output

A:
100.0 2.0 3.0
100.0 202.0 6.0
100.0 202.0 306.0
Multipliers Upper
1.0 100.0 2.0 3.0
1.0 1.0 200.0 3.0
1.0 1.0 1.0 300.0