dgerqf (l) - Linux Manuals

dgerqf: computes an RQ factorization of a real M-by-N matrix A

NAME

DGERQF - computes an RQ factorization of a real M-by-N matrix A

SYNOPSIS

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 M-by-N 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 M-by-N matrix A. On exit, if m <= n, the upper triangle of the subarray A(1:m,n-m+1:n) contains the M-by-M upper triangular matrix R; if m >= n, the elements on and above the (m-n)-th subdiagonal contain the M-by-N 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 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 * vaq
where tau is a real scalar, and v is a real vector with
v(n-k+i+1:n) = 0 and v(n-k+i) = 1; v(1:n-k+i-1) is stored on exit in A(m-k+i,1:n-k+i-1), and tau in TAU(i).

Pages related to dgerqf

  • dgerqf (3)
  • dgerq2 (l) - computes an RQ factorization of a real m by n matrix A
  • dger (l) - performs the rank 1 operation A := alpha*x*yaq + A,
  • dgerfs (l) - improves the computed solution to a system of linear equations and provides error bounds and backward error estimates for the solution
  • dgerfsx (l) - DGERFSX improve the computed solution to a system of linear equations and provides error bounds and backward error estimates for the solution
  • dgebak (l) - forms the right or left eigenvectors of a real general matrix by backward transformation on the computed eigenvectors of the balanced matrix output by DGEBAL
  • dgebal (l) - balances a general real matrix A
  • dgebd2 (l) - reduces a real general m by n matrix A to upper or lower bidiagonal form B by an orthogonal transformation