cgeql2-f(3)

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 (integerM, integerN, complex, dimension( lda, * )A, integerLDA, complex, dimension( * )TAU, complex, dimension( * )WORK, integerINFO)

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

Purpose:

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

Parameters:

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

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

 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.

Date:

September 2012

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 124 of file cgeql2.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.