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## man page of LAPACK-3

### LAPACK-3: computes an RQ factorization of a complex m by n matrix A

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## NAME

LAPACK-3 - computes an RQ factorization of a complex m by n matrix A## SYNOPSIS

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,n-m+1:n) contains the m by m upper triangular matrix R; if m >= n, the elements on and above the (m-n)-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 i-th argument had an illegal value## FURTHER DETAILS

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(n-k+i+1:n) = 0 and v(n-k+i) = 1; conjg(v(1:n-k+i-1)) is stored on exit in A(m-k+i,1:n-k+i-1), and tau in TAU(i). LAPACK routine (version 3.2.2) March 2011 LAPACK-3(3)

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