zgerqf (3)  Linux Manuals
NAME
zgerqf.f 
SYNOPSIS
Functions/Subroutines
subroutine zgerqf (M, N, A, LDA, TAU, WORK, LWORK, INFO)
ZGERQF
Function/Subroutine Documentation
subroutine zgerqf (integerM, integerN, complex*16, dimension( lda, * )A, integerLDA, complex*16, dimension( * )TAU, complex*16, dimension( * )WORK, integerLWORK, integerINFO)
ZGERQF
Purpose:

ZGERQF computes an RQ factorization of a complex MbyN matrix A: A = R * Q.
Parameters:

M
M is INTEGER The number of rows of the matrix A. M >= 0.
NN is INTEGER The number of columns of the matrix A. N >= 0.
AA is COMPLEX*16 array, dimension (LDA,N) On entry, the MbyN matrix A. On exit, if m <= n, the upper triangle of the subarray A(1:m,nm+1:n) contains the MbyM upper triangular matrix R; if m >= n, the elements on and above the (mn)th subdiagonal contain the MbyN 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).
LDALDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).
TAUTAU is COMPLEX*16 array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Details).
WORKWORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORKLWORK 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.
INFOINFO is INTEGER = 0: successful exit < 0: if INFO = i, the ith 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(nk+i+1:n) = 0 and v(nk+i) = 1; conjg(v(1:nk+i1)) is stored on exit in A(mk+i,1:nk+i1), and tau in TAU(i).
Definition at line 139 of file zgerqf.f.
Author
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