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## man page of LAPACK-3

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

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NAME

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

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 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(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). LAPACK routine (version 3.2.2) March 2011 LAPACK-3(3)

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