NAME¶

SGERQ2 - computes an RQ factorization of a real m by n matrix A

SYNOPSIS¶

SUBROUTINE SGERQ2(

M, N, A, LDA, TAU, WORK, INFO )

INTEGER INFO, LDA, M, N REAL A( LDA, * ), TAU( * ), WORK( * )

PURPOSE¶

SGERQ2 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) REAL 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 elementary reflectors (see Further Details).

LDA (input) INTEGER

The leading dimension of the array A. LDA >= max(1,M).

TAU (output) REAL array, dimension (min(M,N))

The scalar factors of the elementary reflectors (see Further Details).

WORK (workspace) REAL array, dimension (M)

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 * v'
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).