man zgeqr2 (Fonctions bibliothèques) - compute a QR factorization of a complex m by n matrix A

NAME

ZGEQR2 - compute a QR factorization of a complex m by n matrix A

ZGEQR2 computes a QR factorization of a complex m by n matrix A: A = Q * R.

M (input) INTEGER: The number of rows of the matrix A. M >= 0.
N (input) INTEGER: The number of columns of the matrix A. N >= 0.
A (input/output) COMPLEX*16 array, dimension (LDA,N): On entry, the m by n matrix A. On exit, the elements on and above the diagonal of the array contain the min(m,n) by n upper trapezoidal matrix R (R is upper triangular if m >= n); the elements below the diagonal, with the array TAU, represent the unitary matrix Q as a product of elementary reflectors (see Further Details). LDA (input) INTEGER The leading dimension of the array A. LDA >= max(1,M).
TAU (output) COMPLEX*16 array, dimension (min(M,N)): The scalar factors of the elementary reflectors (see Further Details).
WORK (workspace) COMPLEX*16 array, dimension (N)
INFO (output) 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'

where tau is a complex scalar, and v is a complex vector with v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i), and tau in TAU(i).