Sun Performance Library Reference Manual: 1

QL Factorization of a General Matrix

The subroutines described in this section compute a QL factorization of a general matrix A.

Calling Sequence


CALL DGEQLF	(M, N, DA, LDA, DTAU, DWORK, LDWORK, INFO)
CALL SGEQLF	(M, N, SA, LDA, STAU, SWORK, LDWORK, INFO)
CALL ZGEQLF	(M, N, ZA, LDA, ZTAU, ZWORK, LDWORK, INFO)
CALL CGEQLF	(M, N, CA, LDA, CTAU, CWORK, LDWORK, INFO)

void dgeqlf	(int m, int n, double da, int lda, double dtau, int *info)
void sgeqlf	(int m, int n, float sa, int lda, float stau, int *info)
void zgeqlf	(int m, int n, doublecomplex za, int lda, doublecomplex ztau, int *info)
void cgeqlf	(int m, int n, complex ca, int lda, complex ctau, int *info)

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, A and TAU contain a QL factorization of the matrix A.
LDA	Leading dimension of the array A as specified in a dimension or type statement. LDA max(1, M).
xTAU	On exit, the min(M, N) scalar factors of the elementary reflectors. The elementary reflectors in xTAU together with xA contain a QL factorization of the matrix A that can be used by other LAPACK subroutines that operate on the matrix A.
xWORK	Scratch array with a dimension of LDWORK.
LDWORK	Leading dimension of the array WORK as specified in a dimension or type statement. LDWORK max(1, N).
INFO	On exit:
	INFO = 0	Subroutine completed normally.
	INFO < 0	The ith argument, where i = \|INFO\|, had an illegal value.

Sample Program



PROGRAM TEST
IMPLICIT NONE
C
INTEGER LDA, LDL, LDWORK, M, N
PARAMETER (M = 4)
PARAMETER (N = 3)
PARAMETER (LDA = M)
PARAMETER (LDL = N)
PARAMETER (LDWORK = N)
C
DOUBLE PRECISION A(LDA,N), L(LDL,N), TAU(N), WORK(LDWORK)
INTEGER ICOL, INFO, IROW
C
EXTERNAL DCOPY, DGEQLF, DORGQL
INTRINSIC ABS
C
C Initialize the array A to store the matrix A shown below.
C
C 1 2 2
C A = 1 0 -2
C 1 0 2
C 1 -2 -2
C
DATA A / 1.0D0, 1.0D0, 1.0D0, 1.0D0,
$ 2.0D0, 0.0D0, 0.0D0, -2.0D0,
$ 2.0D0, -2.0D0, 2.0D0, -2.0D0 /
C
C Print the initial value of A.
C
PRINT 1000
PRINT 1010, ((A(IROW,ICOL), ICOL = 1, N), IROW = 1, M)
C
C Compute the QL factorization of A.
C
CALL DGEQLF (M, N, A, LDA, TAU, WORK, LDWORK, INFO)
IF (INFO .NE. 0) THEN
PRINT 1020, ABS(INFO)
STOP 1
END IF
DO 100, ICOL = 1, N
CALL DCOPY (N, A(M-N+1,ICOL), 1, L(1,ICOL), 1)
100 CONTINUE
C
C Compute and print the matrix Q used in the QL factorization
C of A.
C
CALL DORGQL (M, N, N, A, LDA, TAU, WORK, LDWORK, INFO)
IF (INFO .NE. 0) THEN
PRINT 1030, ABS(INFO)
STOP 2
END IF
PRINT 1040
PRINT 1010, ((A(IROW,ICOL), ICOL = 1, N), IROW = 1, M)
PRINT 1050
DO 110, IROW = 1, N
PRINT 1010, (L(IROW,ICOL), ICOL = 1, IROW),
$ (0.0D0, ICOL = IROW + 1, N)
110 CONTINUE
C
1000 FORMAT (1X, 'A:')
1010 FORMAT (3(3X, F8.4))
1020 FORMAT (1X, 'Illegal value for argument #', I1,
$ ' in DGEQLF.')
1030 FORMAT (1X, 'Illegal value for argument #', I1,
$ ' in DORGQL.')
1040 FORMAT (/1X, 'Q:')
1050 FORMAT (/1X, 'L:')
C
END

Sample Output