# cgeql2.f - Man Page

SRC/cgeql2.f

## Synopsis

### Functions/Subroutines

subroutine **cgeql2** (m, n, a, lda, tau, work, info)**CGEQL2** computes the QL factorization of a general rectangular matrix using an unblocked algorithm.

## Function/Subroutine Documentation

### subroutine cgeql2 (integer m, integer n, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) tau, complex, dimension( * ) work, integer info)

**CGEQL2** computes the QL factorization of a general rectangular matrix using an unblocked algorithm. Ā

**Purpose:**

CGEQL2 computes a QL factorization of a complex m by n matrix A: A = Q * L.

**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 lower triangle of the subarray A(m-n+1:m,1:n) contains the n by n lower triangular matrix L; if m <= n, the elements on and below the (n-m)-th superdiagonal contain the m by n lower trapezoidal matrix L; 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 (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(k) . . . H(2) H(1), 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(m-k+i+1:m) = 0 and v(m-k+i) = 1; v(1:m-k+i-1) is stored on exit in A(1:m-k+i-1,n-k+i), and tau in TAU(i).

Definition at line **122** of file **cgeql2.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page cgeql2(3) is an alias of cgeql2.f(3).

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