zgeqr2 (l)  Linux Man Pages
zgeqr2: computes a QR factorization of a complex m by n matrix A
NAME
ZGEQR2  computes a QR factorization of a complex m by n matrix ASYNOPSIS
 SUBROUTINE ZGEQR2(
 M, N, A, LDA, TAU, WORK, INFO )
 INTEGER INFO, LDA, M, N
 COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
PURPOSE
ZGEQR2 computes a QR factorization of a complex m by n matrix A: A = Q * R.ARGUMENTS
 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 ith argument had an illegal value
FURTHER DETAILS
The matrix Q is represented as a product of elementary reflectorsQ
Each H(i) has the form
H(i)
where tau is a complex scalar, and v is a complex vector with v(1:i1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i), and tau in TAU(i).