DGEQPF(3F)DGEQPF(3F)NAME
DGEQPF - compute a QR factorization with column pivoting of a real M-by-N
matrix A
SYNOPSIS
SUBROUTINE DGEQPF( M, N, A, LDA, JPVT, TAU, WORK, INFO )
INTEGER INFO, LDA, M, N
INTEGER JPVT( * )
DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
PURPOSE
DGEQPF computes a QR factorization with column pivoting of a real M-by-N
matrix A: A*P = Q*R.
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 triangular 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(i) .ne. 0, the i-th column of A is permuted to
the front of A*P (a leading column); if JPVT(i) = 0, the i-th
column of A is a free column. On exit, if JPVT(i) = k, then the
i-th column of A*P was the k-th column of A.
TAU (output) DOUBLE PRECISION array, dimension (min(M,N))
The scalar factors of the elementary reflectors.
WORK (workspace) DOUBLE PRECISION array, dimension (3*N)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
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DGEQPF(3F)DGEQPF(3F)FURTHER DETAILS
The matrix Q is represented as a product of elementary reflectors
Q = H(1)H(2) . . . H(n)
Each H(i) has the form
H = I - tau * v * v'
where tau is a real scalar, and v is a real 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).
The matrix P is represented in jpvt as follows: If
jpvt(j) = i
then the jth column of P is the ith canonical unit vector.
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