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(*)
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
#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.
min(M,N)
elementary
reflectors.
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.
WORK(1)
returns the optimal LWORK.
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.
dimension(2*N)
= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an illegal 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