---
name: "zgeqr2"
section: "3lapack"
platform: "linux"
package: "liblapack-doc"
version: "3.2.1-8"
release: "Debian 6.0 (Squeeze)"
platforms: ["linux"]
url: "https://new.carta.tech/zgeqr2/3lapack"
---

# zgeqr2(3lapack)

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 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).\