zgeql2.f (3) - Linux Manuals

NAME

zgeql2.f -

SYNOPSIS

Functions/Subroutines

subroutine zgeql2 (M, N, A, LDA, TAU, WORK, INFO)
ZGEQL2 computes the QL factorization of a general rectangular matrix using an unblocked algorithm.

Function/Subroutine Documentation

subroutine zgeql2 (integerM, integerN, complex*16, dimension( lda, * )A, integerLDA, complex*16, dimension( * )TAU, complex*16, dimension( * )WORK, integerINFO)

ZGEQL2 computes the QL factorization of a general rectangular matrix using an unblocked algorithm.

Purpose:

 ZGEQL2 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*16 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*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.

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 zgeql2.f.

Author

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