dgeqp3(3P) Sun Performance Library dgeqp3(3P)NAMEdgeqp3 - compute a QR factorization with column pivoting of a matrix A
SYNOPSIS
SUBROUTINE DGEQP3(M, N, A, LDA, JPVT, TAU, WORK, LWORK, INFO)
INTEGER M, N, LDA, LWORK, INFO
INTEGER JPVT(*)
DOUBLE PRECISION A(LDA,*), TAU(*), WORK(*)
SUBROUTINE DGEQP3_64(M, N, A, LDA, JPVT, TAU, WORK, LWORK, INFO)
INTEGER*8 M, N, LDA, LWORK, INFO
INTEGER*8 JPVT(*)
DOUBLE PRECISION A(LDA,*), TAU(*), WORK(*)
F95 INTERFACE
SUBROUTINE GEQP3([M], [N], A, [LDA], JPVT, TAU, [WORK], [LWORK],
[INFO])
INTEGER :: M, N, LDA, LWORK, INFO
INTEGER, DIMENSION(:) :: JPVT
REAL(8), DIMENSION(:) :: TAU, WORK
REAL(8), DIMENSION(:,:) :: A
SUBROUTINE GEQP3_64([M], [N], A, [LDA], JPVT, TAU, [WORK], [LWORK],
[INFO])
INTEGER(8) :: M, N, LDA, LWORK, INFO
INTEGER(8), DIMENSION(:) :: JPVT
REAL(8), DIMENSION(:) :: TAU, WORK
REAL(8), DIMENSION(:,:) :: A
C INTERFACE
#include <sunperf.h>
void dgeqp3(int m, int n, double *a, int lda, int *jpvt, double *tau,
int *info);
void dgeqp3_64(long m, long n, double *a, long lda, long *jpvt, double
*tau, long *info);
PURPOSEdgeqp3 computes a QR factorization with column pivoting of a matrix A:
A*P = Q*R using Level 3 BLAS.
ARGUMENTS
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 orthogonal matrix Q as a product of
min(M,N) elementary 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 >= 3*N+1. For optimal
performance LWORK >= 2*N+( 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.
INFO (output)
= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an illegal value.
FURTHER DETAILS
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
6 Mar 2009 dgeqp3(3P)
