Contents
cgeqp3 - compute a QR factorization with column pivoting of
a matrix A
SUBROUTINE CGEQP3(M, N, A, LDA, JPVT, TAU, WORK, LWORK, RWORK, INFO)
COMPLEX A(LDA,*), TAU(*), WORK(*)
INTEGER M, N, LDA, LWORK, INFO
INTEGER JPVT(*)
REAL RWORK(*)
SUBROUTINE CGEQP3_64(M, N, A, LDA, JPVT, TAU, WORK, LWORK, RWORK,
INFO)
COMPLEX A(LDA,*), TAU(*), WORK(*)
INTEGER*8 M, N, LDA, LWORK, INFO
INTEGER*8 JPVT(*)
REAL RWORK(*)
F95 INTERFACE
SUBROUTINE GEQP3([M], [N], A, [LDA], JPVT, TAU, [WORK], [LWORK],
[RWORK], [INFO])
COMPLEX, DIMENSION(:) :: TAU, WORK
COMPLEX, DIMENSION(:,:) :: A
INTEGER :: M, N, LDA, LWORK, INFO
INTEGER, DIMENSION(:) :: JPVT
REAL, DIMENSION(:) :: RWORK
SUBROUTINE GEQP3_64([M], [N], A, [LDA], JPVT, TAU, [WORK], [LWORK],
[RWORK], [INFO])
COMPLEX, DIMENSION(:) :: TAU, WORK
COMPLEX, DIMENSION(:,:) :: A
INTEGER(8) :: M, N, LDA, LWORK, INFO
INTEGER(8), DIMENSION(:) :: JPVT
REAL, DIMENSION(:) :: RWORK
C INTERFACE
#include <sunperf.h>
void cgeqp3(int m, int n, complex *a, int lda, int *jpvt,
complex *tau, int *info);
void cgeqp3_64(long m, long n, complex *a, long lda, long
*jpvt, complex *tau, long *info);
cgeqp3 computes a QR factorization with column pivoting of a
matrix A: A*P = Q*R using Level 3 BLAS.
M (input) The number of rows of the matrix A. M >= 0.
N (input) The number of columns of the matrix A. N >= 0.
A (input/output)
On entry, the M-by-N matrix A. On exit, the upper
triangle of the array contains the min(M,N)-by-N
upper trapezoidal matrix R; the elements below the
diagonal, together with the array TAU, represent
the unitary matrix Q as a product of min(M,N) ele-
mentary reflectors.
LDA (input)
The leading dimension of the array A. LDA >=
max(1,M).
JPVT (input/output)
On entry, if JPVT(J).ne.0, the J-th column of A is
permuted to the front of A*P (a leading column);
if JPVT(J)=0, the J-th column of A is a free
column. On exit, if JPVT(J)=K, then the J-th
column of A*P was the the K-th column of A.
TAU (output)
The scalar factors of the elementary reflectors.
WORK (workspace)
On exit, if INFO=0, WORK(1) returns the optimal
LWORK.
LWORK (input)
The dimension of the array WORK. LWORK >= N+1.
For optimal performance LWORK >= ( N+1 )*NB, where
NB is the optimal blocksize.
If LWORK = -1, then a workspace query is assumed;
the routine only calculates the optimal size of
the WORK array, returns this value as the first
entry of the WORK array, and no error message
related to LWORK is issued by XERBLA.
RWORK (workspace)
dimension(2*N)
INFO (output)
= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an ille-
gal value.
The matrix Q is represented as a product of elementary
reflectors
Q = H(1) H(2) . . . H(k), where k = min(m,n).
Each H(i) has the form
H(i) = I - tau * v * v'
where tau is a real/complex scalar, and v is a real/complex
vector with v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on
exit in A(i+1:m,i), and tau in TAU(i).
Based on contributions by
G. Quintana-Orti, Depto. de Informatica, Universidad Jaime
I, Spain
X. Sun, Computer Science Dept., Duke University, USA