◆ zgelqf()

LQ factorization of a complex

Purpose: This routine computes a LQ factorization of a complex m x n matrix A.
A = L * Q

Parameters

[in]	m	Number of rows of the matrix A. (m >= 0) (If m = 0, returns without computation)
[in]	n	Number of columns of the matrix A. (n >= 0) (If n = 0, returns without computation)
[in]	lda	Leading dimension of the two dimensional array a[][]. (lda >= max(1, m))
[in,out]	a[][]	Array a[la][lda] (la >= n) [in] m x n matrix A. [out] The elements on and above the diagonal of the array contains the m x min(m, n) lower trapezoidal matrix L (L is lower triangular if m <= n); the elements above the diagonal, with the array tau[], represent the unitary matrix Q as a product of elementary reflectors (see Further Details).
[out]	tau[]	Array tau[ltau] (ltau >= min(m, n)) The scalar factors of the elementary reflectors (see Further Details).
[out]	work[]	Array work[lwork] Work array. On exit, if info = 0, work[0] returns the optimal lwork.
[in]	lwork	The dimension of the array work[]. (lwork >= max(1, m)) For optimal 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, and returns the value in work[0].
[out]	info	= 0: Successful exit = -1: The argument m had an illegal value (m < 0) = -2: The argument n had an illegal value (n < 0) = -3: The argument lda had an illegal value (lda < max(1, m)) = -7: The argument lwork had an illegal value (lwork too small)

Further Details: The matrix Q is represented as a product of elementary reflectors
Q = H(k) . . . H(2) H(1), where k = min(m, n).

Each H(i) has the form
H(i) = I - tau * v * v^H

where tau is a complex scalar, and v is a complex vector with v(1 to i-1) = 0 and v(i) = 1; v(i+1 to n) is stored on exit in a[i to n-1][i-1], and tau in tau[i-1].