# cgerq2.f - Man Page

SRC/cgerq2.f

## Synopsis

### Functions/Subroutines

subroutine **cgerq2** (m, n, a, lda, tau, work, info)**CGERQ2** computes the RQ factorization of a general rectangular matrix using an unblocked algorithm.

## Function/Subroutine Documentation

### subroutine cgerq2 (integer m, integer n, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) tau, complex, dimension( * ) work, integer info)

**CGERQ2** computes the RQ factorization of a general rectangular matrix using an unblocked algorithm.

**Purpose:**

CGERQ2 computes an RQ factorization of a complex m by n matrix A: A = R * Q.

**Parameters***M*M is INTEGER The number of rows of the matrix A. M >= 0.

*N*N is INTEGER The number of columns of the matrix A. N >= 0.

*A*A is 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*LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).

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

*WORK*WORK is COMPLEX array, dimension (M)

*INFO*INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Further Details:**

The matrix Q is represented as a product of elementary reflectors Q = H(1)**H H(2)**H . . . H(k)**H, where k = min(m,n). Each H(i) has the form H(i) = I - tau * v * v**H 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).

Definition at line **122** of file **cgerq2.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page cgerq2(3) is an alias of cgerq2.f(3).

Tue Nov 28 2023 12:08:41 Version 3.12.0 LAPACK