LAPACK
3.6.1
LAPACK: Linear Algebra PACKage
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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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SGERQ2 computes an RQ factorization of a real m by n matrix A: A = R * Q.
[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 |
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).
Definition at line 125 of file sgerq2.f.