subroutine zgelq2 (M, N, A, LDA, TAU, WORK, INFO)
subroutine zgelq2 (integerM, integerN, complex*16, dimension( lda, * )A, integerLDA, complex*16, dimension( * )TAU, complex*16, dimension( * )WORK, integerINFO)ZGELQ2 computes the LQ factorization of a general rectangular matrix using an unblocked algorithm. Purpose:
ZGELQ2 computes an LQ factorization of a complex m by n matrix A: A = L * Q.
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, the elements on and below the diagonal of the array contain the m by 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).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 (M)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 . . . H(2)**H H(1)**H, 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:i-1) = 0 and v(i) = 1; conjg(v(i+1:n)) is stored on exit in A(i,i+1:n), and tau in TAU(i).