DGEQP3(1) LAPACK routine (version 3.2) DGEQP3(1)NAME
DGEQP3 - computes a QR factorization with column pivoting of a matrix A
SYNOPSIS
SUBROUTINE DGEQP3( M, N, A, LDA, JPVT, TAU, WORK, LWORK, INFO )
INTEGER INFO, LDA, LWORK, M, N
INTEGER JPVT( * )
DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
PURPOSE
DGEQP3 computes a QR factorization with column pivoting of a matrix A:
A*P = Q*R using Level 3 BLAS.
ARGUMENTS
M (input) INTEGER
The number of rows of the matrix A. M >= 0.
N (input) INTEGER
The number of columns of the matrix A. N >= 0.
A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
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) INTEGER
The leading dimension of the array A. LDA >= max(1,M).
JPVT (input/output) INTEGER array, dimension (N)
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) DOUBLE PRECISION array, dimension (min(M,N))
The scalar factors of the elementary reflectors.
WORK (workspace/output) DOUBLE PRECISION array, dimension
(MAX(1,LWORK))
On exit, if INFO=0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
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) INTEGER
= 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
LAPACK routine (version 3.2) November 2008 DGEQP3(1)
