1SGEQPF(1)       LAPACK deprecated driver routine (version 3.1)       SGEQPF(1)
2
3
4

NAME

6       SGEQPF - i deprecated and has been replaced by routine SGEQP3
7

SYNOPSIS

9       SUBROUTINE SGEQPF( M, N, A, LDA, JPVT, TAU, WORK, INFO )
10
11           INTEGER        INFO, LDA, M, N
12
13           INTEGER        JPVT( * )
14
15           REAL           A( LDA, * ), TAU( * ), WORK( * )
16

PURPOSE

18       This routine is deprecated and has been replaced by routine SGEQP3.
19
20       SGEQPF computes a QR factorization with column pivoting of a real M-by-
21       N matrix A: A*P = Q*R.
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) REAL 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 triangular matrix R;
34               the elements below the diagonal, together with the  array  TAU,
35               represent the orthogonal matrix Q as a product of min(m,n) ele‐
36               mentary 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(i) .ne. 0, the i-th column of A  is  permuted
43               to  the front of A*P (a leading column); if JPVT(i) = 0, the i-
44               th column of A is a free column.  On exit, if JPVT(i) = k, then
45               the i-th column of A*P was the k-th column of A.
46
47       TAU     (output) REAL array, dimension (min(M,N))
48               The scalar factors of the elementary reflectors.
49
50       WORK    (workspace) REAL array, dimension (3*N)
51
52       INFO    (output) INTEGER
53               = 0:  successful exit
54               < 0:  if INFO = -i, the i-th argument had an illegal value
55

FURTHER DETAILS

57       The matrix Q is represented as a product of elementary reflectors
58
59          Q = H(1) H(2) . . . H(n)
60
61       Each H(i) has the form
62
63          H = I - tau * v * v'
64
65       where tau is a real scalar, and v is a real vector with
66       v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i).
67
68       The matrix P is represented in jpvt as follows: If
69          jpvt(j) = i
70       then the jth column of P is the ith canonical unit vector.
71
72       Partial column norm updating strategy modified by
73         Z. Drmac and Z. Bujanovic, Dept. of Mathematics,
74         University of Zagreb, Croatia.
75         June 2006.
76       For more details see LAPACK Working Note 176.
77
78
79
80
81 LAPACK deprecated driver routineN(ovveermsbieorn230.016)                      SGEQPF(1)