# zgelq2.f - Man Page

SRC/zgelq2.f

## Synopsis

### Functions/Subroutines

subroutine **zgelq2** (m, n, a, lda, tau, work, info)**ZGELQ2** computes the LQ factorization of a general rectangular matrix using an unblocked algorithm.

## Function/Subroutine Documentation

### subroutine zgelq2 (integer m, integer n, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) tau, complex*16, dimension( * ) work, integer info)

**ZGELQ2** computes the LQ factorization of a general rectangular matrix using an unblocked algorithm.

**Purpose:**

ZGELQ2 computes an LQ factorization of a complex m-by-n matrix A: A = ( L 0 ) * Q where: Q is a n-by-n orthogonal matrix; L is a lower-triangular m-by-m matrix; 0 is a m-by-(n-m) zero matrix, if m < n.

**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*16 array, dimension (LDA,N) On entry, the m by n matrix A. On exit, the elements on and below the diagonal of the array contain the m by min(m,n) lower trapezoidal matrix L (L is lower triangular if m <= n); the elements above the diagonal, 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*16 array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Details).

*WORK*WORK is COMPLEX*16 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(k)**H . . . H(2)**H H(1)**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(1:i-1) = 0 and v(i) = 1; conjg(v(i+1:n)) is stored on exit in A(i,i+1:n), and tau in TAU(i).

Definition at line **128** of file **zgelq2.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page zgelq2(3) is an alias of zgelq2.f(3).

Tue Nov 28 2023 12:08:42 Version 3.12.0 LAPACK