sgerq2()

subroutine sgerq2	(	integer	m,
		integer	n,
		real, dimension( lda, * )	a,
		integer	lda,
		real, dimension( * )	tau,
		real, dimension( * )	work,
		integer	info )

SGERQ2 computes the RQ factorization of a general rectangular matrix using an unblocked algorithm.

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Purpose:

!>
!> SGERQ2 computes an RQ factorization of a real m by n matrix A:
!> A = R * Q.
!> 

Parameters

[in]	M	!> M is INTEGER !> The number of rows of the matrix A. M >= 0. !>
[in]	N	!> N is INTEGER !> The number of columns of the matrix A. N >= 0. !>
[in,out]	A	!> A is 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). !>
[in]	LDA	!> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,M). !>
[out]	TAU	!> TAU is REAL array, dimension (min(M,N)) !> The scalar factors of the elementary reflectors (see Further !> Details). !>
[out]	WORK	!> WORK is REAL array, dimension (M) !>
[out]	INFO	!> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value !>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

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**T
!>
!>  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).
!>