# zgeqr2.f - Man Page

SRC/zgeqr2.f

## Synopsis

### Functions/Subroutines

subroutine **zgeqr2** (m, n, a, lda, tau, work, info)**ZGEQR2** computes the QR factorization of a general rectangular matrix using an unblocked algorithm.

## Function/Subroutine Documentation

### subroutine zgeqr2 (integer m, integer n, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) tau, complex*16, dimension( * ) work, integer info)

**ZGEQR2** computes the QR factorization of a general rectangular matrix using an unblocked algorithm. Ā

**Purpose:**

ZGEQR2 computes a QR factorization of a complex m-by-n matrix A: A = Q * ( R ), ( 0 ) where: Q is a m-by-m orthogonal matrix; R is an upper-triangular n-by-n matrix; 0 is a (m-n)-by-n 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 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*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 (N)

*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(2) . . . H(k), 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; v(i+1:m) is stored on exit in A(i+1:m,i), and tau in TAU(i).

Definition at line **129** of file **zgeqr2.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page zgeqr2(3) is an alias of zgeqr2.f(3).

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