1ZGEQP3(1)                LAPACK routine (version 3.1)                ZGEQP3(1)
2
3
4

NAME

6       ZGEQP3 - a QR factorization with column pivoting of a matrix A
7

SYNOPSIS

9       SUBROUTINE ZGEQP3( M, N, A, LDA, JPVT, TAU, WORK, LWORK, RWORK, INFO )
10
11           INTEGER        INFO, LDA, LWORK, M, N
12
13           INTEGER        JPVT( * )
14
15           DOUBLE         PRECISION RWORK( * )
16
17           COMPLEX*16     A( LDA, * ), TAU( * ), WORK( * )
18

PURPOSE

20       ZGEQP3  computes a QR factorization with column pivoting of a matrix A:
21       A*P = Q*R  using Level 3 BLAS.
22
23

ARGUMENTS

25       M       (input) INTEGER
26               The number of rows of the matrix A. M >= 0.
27
28       N       (input) INTEGER
29               The number of columns of the matrix A.  N >= 0.
30
31       A       (input/output) COMPLEX*16 array, dimension (LDA,N)
32               On entry, the M-by-N matrix A.  On exit, the upper triangle  of
33               the  array  contains the min(M,N)-by-N upper trapezoidal matrix
34               R; the elements below the diagonal,  together  with  the  array
35               TAU,  represent  the  unitary matrix Q as a product of min(M,N)
36               elementary reflectors.
37
38       LDA     (input) INTEGER
39               The leading dimension of the array A. LDA >= max(1,M).
40
41       JPVT    (input/output) INTEGER array, dimension (N)
42               On entry, if JPVT(J).ne.0, the J-th column of A is permuted  to
43               the  front  of  A*P  (a leading column); if JPVT(J)=0, the J-th
44               column of A is a free column.  On exit, if JPVT(J)=K, then  the
45               J-th column of A*P was the the K-th column of A.
46
47       TAU     (output) COMPLEX*16 array, dimension (min(M,N))
48               The scalar factors of the elementary reflectors.
49
50       WORK    (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK))
51               On exit, if INFO=0, WORK(1) returns the optimal LWORK.
52
53       LWORK   (input) INTEGER
54               The  dimension  of  the  array WORK. LWORK >= N+1.  For optimal
55               performance LWORK >= ( N+1 )*NB, where NB is the optimal block‐
56               size.
57
58               If  LWORK  = -1, then a workspace query is assumed; the routine
59               only calculates the optimal size of  the  WORK  array,  returns
60               this  value  as the first entry of the WORK array, and no error
61               message related to LWORK is issued by XERBLA.
62
63       RWORK   (workspace) DOUBLE PRECISION array, dimension (2*N)
64
65       INFO    (output) INTEGER
66               = 0: successful exit.
67               < 0: if INFO = -i, the i-th argument had an illegal value.
68

FURTHER DETAILS

70       The matrix Q is represented as a product of elementary reflectors
71
72          Q = H(1) H(2) . . . H(k), where k = min(m,n).
73
74       Each H(i) has the form
75
76          H(i) = I - tau * v * v'
77
78       where tau is a real/complex scalar, and v is a real/complex vector with
79       v(1:i-1)  =  0  and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
80       and tau in TAU(i).
81
82       Based on contributions by
83         G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain
84         X. Sun, Computer Science Dept., Duke University, USA
85
86
87
88
89 LAPACK routine (version 3.1)    November 2006                       ZGEQP3(1)