dgerqf (l)  Linux Manuals
dgerqf: computes an RQ factorization of a real MbyN matrix A
NAME
DGERQF  computes an RQ factorization of a real MbyN matrix ASYNOPSIS
 SUBROUTINE DGERQF(
 M, N, A, LDA, TAU, WORK, LWORK, INFO )
 INTEGER INFO, LDA, LWORK, M, N
 DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
PURPOSE
DGERQF computes an RQ factorization of a real MbyN matrix A: A = R * Q.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 MbyN matrix A. On exit, if m <= n, the upper triangle of the subarray A(1:m,nm+1:n) contains the MbyM upper triangular matrix R; if m >= n, the elements on and above the (mn)th subdiagonal contain the MbyN upper trapezoidal matrix R; the remaining elements, with the array TAU, represent the orthogonal matrix Q as a product of min(m,n) elementary reflectors (see Further Details). LDA (input) INTEGER The leading dimension of the array A. LDA >= max(1,M).
 TAU (output) DOUBLE PRECISION array, dimension (min(M,N))
 The scalar factors of the elementary reflectors (see Further Details).
 WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK))
 On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
 LWORK (input) INTEGER
 The dimension of the array WORK. LWORK >= max(1,M). For optimum performance LWORK >= M*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.
 INFO (output) INTEGER

= 0: successful exit
< 0: if INFO = i, the ith argument had an illegal value
FURTHER DETAILS
The matrix Q is represented as a product of elementary reflectorsQ
Each H(i) has the form
H(i)
where tau is a real scalar, and v is a real vector with
v(nk+i+1:n) = 0 and v(nk+i) = 1; v(1:nk+i1) is stored on exit in A(mk+i,1:nk+i1), and tau in TAU(i).