subroutine zgeql2 (M, N, A, LDA, TAU, WORK, INFO)
subroutine zgeql2 (integerM, integerN, complex*16, dimension( lda, * )A, integerLDA, complex*16, dimension( * )TAU, complex*16, dimension( * )WORK, integerINFO)ZGEQL2 computes the QL factorization of a general rectangular matrix using an unblocked algorithm. Purpose:
ZGEQL2 computes a QL factorization of a complex m by n matrix A: A = Q * L.
M is INTEGER The number of rows of the matrix A. M >= 0.N
N is INTEGER The number of columns of the matrix A. N >= 0.A
A is COMPLEX*16 array, dimension (LDA,N) On entry, the m by n matrix A. On exit, if m >= n, the lower triangle of the subarray A(m-n+1:m,1:n) contains the n by n lower triangular matrix L; if m <= n, the elements on and below the (n-m)-th superdiagonal contain the m by n lower trapezoidal matrix L; the remaining elements, with the array TAU, represent the unitary matrix Q as a product of elementary reflectors (see Further Details).LDA
LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).TAU
TAU is COMPLEX*16 array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Details).WORK
WORK is COMPLEX*16 array, dimension (N)INFO
INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value
Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd.Date:
September 2012Further 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(m-k+i+1:m) = 0 and v(m-k+i) = 1; v(1:m-k+i-1) is stored on exit in A(1:m-k+i-1,n-k+i), and tau in TAU(i).