CGEQP3(3S)CGEQP3(3S)NAME
CGEQP3 - compute a QR factorization with column pivoting of a matrix A
SYNOPSIS
SUBROUTINE CGEQP3( M, N, A, LDA, JPVT, TAU, WORK, LWORK, RWORK, INFO )
INTEGER INFO, LDA, LWORK, M, N
INTEGER JPVT( * )
REAL RWORK( * )
COMPLEX A( LDA, * ), TAU( * ), WORK( * )
IMPLEMENTATION
These routines are part of the SCSL Scientific Library and can be loaded
using either the -lscs or the -lscs_mp option. The -lscs_mp option
directs the linker to use the multi-processor version of the library.
When linking to SCSL with -lscs or -lscs_mp, the default integer size is
4 bytes (32 bits). Another version of SCSL is available in which integers
are 8 bytes (64 bits). This version allows the user access to larger
memory sizes and helps when porting legacy Cray codes. It can be loaded
by using the -lscs_i8 option or the -lscs_i8_mp option. A program may use
only one of the two versions; 4-byte integer and 8-byte integer library
calls cannot be mixed.
PURPOSE
CGEQP3 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) COMPLEX 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 unitary 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
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CGEQP3(3S)CGEQP3(3S)
J-th column of A*P was the the K-th column of A.
TAU (output) COMPLEX array, dimension (min(M,N))
The scalar factors of the elementary reflectors.
WORK (workspace/output) COMPLEX array, dimension (LWORK)
On exit, if INFO=0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
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) REAL array, dimension (2*N)
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
SEE ALSOINTRO_LAPACK(3S), INTRO_SCSL(3S)
This man page is available only online.
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