LU Factorization of a General Matrix

Calling Sequence

CALL DGETRF	(M, N, DA, LDA, IPIVOT, INFO)
CALL SGETRF	(M, N, SA, LDA, IPIVOT, INFO)
CALL ZGETRF	(M, N, ZA, LDA, IPIVOT, INFO)
CALL CGETRF	(M, N, CA, LDA, IPIVOT, INFO)
void dgetrf	(int m, int n, double *da, int lda, int *ipivot, int *info)
void sgetrf	(int m, int n, float *sa, int lda, int *ipivot, int *info)
void zgetrf	(int m, int n, doublecomplex *za, int lda, int *ipivot, int *info)
void cgetrf	(int m, int n, complex *ca, int lda, int *ipivot, int *info)

Arguments

M	Number of rows of the matrix A. M 0.
N	Number of columns of the matrix A. N 0.
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, M).
IPIVOT	On exit, the pivot indices. During factorization, row i was exchanged with row IPIVOT(i) for 1 i min(M, N).
INFO	On exit:
	INFO = 0	Subroutine completed normally.
	INFO < 0	The ith argument, where i = |INFO|, had an illegal value.
	INFO > 0	U(i,i), where i = INFO, is exactly zero and U is therefore singular. The factorization has been completed, but division by zero will occur if this factorization is used to solve a linear system.

Sample Program

PROGRAM TEST

IMPLICIT NONE

C

INTEGER LDA, LDB, M, N, NRHS, SIZEB

PARAMETER (M = 3)

PARAMETER (N = 3)

PARAMETER (NRHS = 1)

PARAMETER (LDA = M)

PARAMETER (LDB = LDA)

PARAMETER (SIZEB = LDB * NRHS)

C

DOUBLE PRECISION A(LDA,N), B(LDB,NRHS)

INTEGER ICOL, INFO, IROW, IPIVOT(N)

C

EXTERNAL DGETRF, DGETRS

C

C Initialize the array A to store the coefficient matrix A

C shown below. Initialize the array B to store the right

C hand side vector b shown below.

C

C 1 2 2 15

C A = 2 1 2 b = 15

C 2 2 1 15

C

DATA A / 1.0D0, 3*2.0D0, 1.0D0, 3*2.0D0, 1.0D0 /

DATA B / SIZEB*1.5D1 /

C

C Print the initial value of the arrays.

C

PRINT 1000

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

PRINT 1020

PRINT 1030, B

C

C Factor A, solve the system, and print the solution.

C

CALL DGETRF (M, N, A, LDA, IPIVOT, INFO)

IF (INFO .EQ. 0) THEN

CALL DGETRS ('NO TRANSPOSE A', N, NRHS, A, LDA, IPIVOT,

$ B, LDB, INFO)

IF (INFO .EQ. 0) THEN

PRINT 1040

PRINT 1030, B

ELSE

PRINT 1050, INFO

END IF

ELSE

PRINT 1060, INFO

END IF

C

1000 FORMAT (1X, 'A:')

1010 FORMAT (3(3X, F4.1))

1020 FORMAT (/1X, 'b:')

1030 FORMAT (1X, 2X, F4.1)

1040 FORMAT (/1X, 'x:')

1050 FORMAT (1X, 'Solve failed with INFO = ', I6)

1060 FORMAT (1X, 'Factorization failed with INFO = ', I6)

C

END

Sample Output

A:
1.0 2.0 2.0
2.0 1.0 2.0
2.0 2.0 1.0
b:
15.0
15.0
15.0
x:
3.0
3.0
3.0