---
name: "cgerq2"
section: "3lapack"
platform: "linux"
package: "liblapack-doc"
version: "3.2.1-8"
release: "Debian 6.0 (Squeeze)"
platforms: ["linux"]
url: "https://new.carta.tech/cgerq2/3lapack"
---

# cgerq2(3lapack)

computes an RQ factorization of a complex m by n matrix A

## NAME

CGERQ2 - computes an RQ factorization of a complex m by n matrix A

## SYNOPSIS

- SUBROUTINE CGERQ2(

  M, N, A, LDA, TAU, WORK, INFO )

- INTEGER

  INFO, LDA, M, N

- COMPLEX

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

## PURPOSE

CGERQ2 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 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 array, dimension (min(M,N))

  The scalar factors of the elementary reflectors (see Further Details).

- WORK (workspace) COMPLEX 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).\