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zgerqf.f(3) LAPACK zgerqf.f(3)

zgerqf.f -


subroutine zgerqf (M, N, A, LDA, TAU, WORK, LWORK, INFO)
 
ZGERQF

ZGERQF
Purpose:
 ZGERQF 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 min(m,n) 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 (MAX(1,LWORK))
          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK
          LWORK is INTEGER
          The dimension of the array WORK.  LWORK >= max(1,M).
          For optimum performance LWORK >= M*NB, where NB is
          the optimal blocksize.
If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.
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:
November 2011
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 139 of file zgerqf.f.

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Sat Nov 16 2013 Version 3.4.2

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