cgeqr2 man page on Scientific

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```CGEQR2(1)		 LAPACK routine (version 3.2)		     CGEQR2(1)

NAME
CGEQR2 - computes a QR factorization of a complex m by n matrix A

SYNOPSIS
SUBROUTINE CGEQR2( M, N, A, LDA, TAU, WORK, INFO )

INTEGER	  INFO, LDA, M, N

COMPLEX	  A( LDA, * ), TAU( * ), WORK( * )

PURPOSE
CGEQR2  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 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 dimenā
sion of the array A.  LDA >= max(1,M).

TAU     (output) COMPLEX array, dimension (min(M,N))
The scalar factors of the elementary  reflectors	 (see  Further
Details).

WORK    (workspace) COMPLEX 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)	 November 2008			     CGEQR2(1)
```
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