SGEQP3 - compute a QR factorization with column pivoting
of a matrix A
SYNOPSIS
SUBROUTINE SGEQP3( M, N, A, LDA, JPVT, TAU, WORK, LWORK,
INFO )
INTEGER INFO, LDA, LWORK, M, N
INTEGER JPVT( * )
REAL A( LDA, * ), TAU( * ), WORK( * )
PURPOSE
SGEQP3 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) REAL 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 col
umn. On exit, if JPVT(J)=K, then the J-th column
of A*P was the the K-th column of A.
TAU (output) REAL array, dimension (min(M,N))
The scalar factors of the elementary reflectors.
WORK (workspace/output) REAL array, dimension (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,
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 ille
gal 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/com
plex 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
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