Sun Performance Library Reference Manual: 1

QR Factorization with Column Pivoting of a General Matrix

The subroutines described in this section compute a QR factorization with column pivoting of a general matrix A.

Calling Sequence


CALL DGEQPF	(M, N, DA, LDA, JPIVOT, DTAU, DWORK, INFO)
CALL SGEQPF	(M, N, SA, LDA, JPIVOT, STAU, SWORK, INFO)
CALL ZGEQPF	(M, N, ZA, LDA, JPIVOT, ZTAU, ZWORK, DWORK2, INFO)
CALL CGEQPF	(M, N, CA, LDA, JPIVOT, CTAU, CWORK, SWORK2, INFO)

void dgeqpf	(int m, int n, double da, int lda, int jpivot, double dtau, int info)
void sgeqpf	(int m, int n, float sa, int lda, int jpivot, float stau, int info)
void zgeqpf	(int m, int n, doublecomplex za, int lda, int jpivot, doublecomplex ztau, int info)
void cgeqpf	(int m, int n, complex ca, int lda, int jpivot, 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 QR factorization of the matrix A.
LDA	Leading dimension of the array A as specified in a dimension or type statement. LDA max(1, M).
JPIVOT	On entry, if JPIVOT(i) 0 for 1 i N then the ith column of A is an initial column, otherwise it is a free column. Before the QR factorization of A, all initial columns are permuted to the leading positions. Only the remaining free columns are moved as a result of column pivoting during the factorization. On exit, if JPIVOT(i) = k, then the ith column of A was the kth column of A.
xTAU	On exit, the min(M, N) scalar factors of the elementary reflectors. The elementary reflectors in xTAU together with xA contain a QR 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 3 × N for real subroutines or N for complex subroutines.
xWORK2	Scratch array with a dimension of 2 × N for complex subroutines.
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, LDR, LDWORK, M, N
PARAMETER (M = 4)
PARAMETER (N = 3)
PARAMETER (LDA = M)
PARAMETER (LDR = N)
PARAMETER (LDWORK = 3 * N)
C
DOUBLE PRECISION A(LDA,N), R(LDR,N), TAU(N), WORK(LDWORK)
INTEGER ICOL, INFO, IPIVOT(N), IROW
C
EXTERNAL DCOPY, DGEQPF, DORGQR
INTRINSIC ABS
C
C Initialize the array A to store the matrix A shown below.
C
C 1 6 2
C A = 1 -2 -8
C 1 -2 4
C 1 6 14
C
DATA A / 4*1.0D0, 6.0D0, -2.0D0, -2.0D0, 6.0D0,
$ 2.0D0, -8.0D0, 4.0D0, 1.4D1 /
DATA IPIVOT / N*0 /
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 QR factorization of A with pivoting.
C
CALL DGEQPF (M, N, A, LDA, IPIVOT, TAU, WORK, INFO)
IF (INFO .NE. 0) THEN
PRINT 1020, ABS(INFO)
STOP 1
END IF
DO 100, ICOL = 1, N
CALL DCOPY (N, A(1,ICOL), 1, R(1,ICOL), 1)
100 CONTINUE
C
C Compute and print the matrix Q used in the QR factorization
C of A.
C
CALL DORGQR (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, (0.0D0, ICOL = 1, IROW - 1),
$ (R(IROW,ICOL), ICOL = IROW, N)
110 CONTINUE
C
1000 FORMAT (1X, 'A:')
1010 FORMAT (3(3X, F8.4))
1020 FORMAT (1X, 'Illegal value for argument #', I1,
$ ' in DGEQPF.')
1030 FORMAT (1X, 'Illegal value for argument #', I1,
$ ' in DORGQR.')
1040 FORMAT (/1X, 'Q:')
1050 FORMAT (/1X, 'R:')
C
END

Sample Output