zgerq2 (l)  Linux Man Pages
zgerq2: computes an RQ factorization of a complex m by n matrix A
NAME
ZGERQ2  computes an RQ factorization of a complex m by n matrix ASYNOPSIS
 SUBROUTINE ZGERQ2(
 M, N, A, LDA, TAU, WORK, INFO )
 INTEGER INFO, LDA, M, N
 COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
PURPOSE
ZGERQ2 computes an RQ factorization of a complex m by n matrix A: A = R * Q.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, if m <= n, the upper triangle of the subarray A(1:m,nm+1:n) contains the m by m upper triangular matrix R; if m >= n, the elements on and above the (mn)th subdiagonal contain the m by n upper trapezoidal matrix R; the remaining elements, 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 (M)
 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(nk+i+1:n) = 0 and v(nk+i) = 1; conjg(v(1:nk+i1)) is stored on exit in A(mk+i,1:nk+i1), and tau in TAU(i).