zgerq2.f - Man Page

SRC/zgerq2.f

Synopsis

Functions/Subroutines

subroutine zgerq2 (m, n, a, lda, tau, work, info)
ZGERQ2 computes the RQ factorization of a general rectangular matrix using an unblocked algorithm.

Function/Subroutine Documentation

subroutine zgerq2 (integer m, integer n, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) tau, complex*16, dimension( * ) work, integer info)

ZGERQ2 computes the RQ factorization of a general rectangular matrix using an unblocked algorithm.  

Purpose:

 ZGERQ2 computes an RQ factorization of a complex m by n matrix A:
 A = R * Q.
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 upper triangle of the subarray
          A(1:m,n-m+1:n) contains the m by m upper triangular matrix R;
          if m >= n, the elements on and above the (m-n)-th subdiagonal
          contain the m by n upper trapezoidal matrix R; 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 (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(1)**H H(2)**H . . . H(k)**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(n-k+i+1:n) = 0 and v(n-k+i) = 1; conjg(v(1:n-k+i-1)) is stored on
  exit in A(m-k+i,1:n-k+i-1), and tau in TAU(i).

Definition at line 122 of file zgerq2.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.

Referenced By

The man page zgerq2(3) is an alias of zgerq2.f(3).

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