
cgeqrf.f(3) LAPACK cgeqrf.f(3)
NAME
cgeqrf.f 
SYNOPSIS
Functions/Subroutines
subroutine cgeqrf (M, N, A, LDA, TAU, WORK, LWORK, INFO)
CGEQRF
Function/Subroutine Documentation
subroutine cgeqrf (integerM, integerN, complex, dimension( lda, * )A, integerLDA, complex,
dimension( * )TAU, complex, dimension( * )WORK, integerLWORK, integerINFO)
CGEQRF
Purpose:
CGEQRF computes a QR factorization of a complex MbyN matrix A:
A = Q * R.
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 array, dimension (LDA,N)
On entry, the MbyN matrix A.
On exit, the elements on and above the diagonal of the array
contain the min(M,N)byN upper trapezoidal matrix R (R is
upper triangular if m >= n); the elements below the diagonal,
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 array, dimension (min(M,N))
The scalar factors of the elementary reflectors (see Further
Details).
WORK
WORK is COMPLEX 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,N).
For optimum performance LWORK >= N*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 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(2) . . . H(k), 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(1:i1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
and tau in TAU(i).
Definition at line 137 of file cgeqrf.f.
Author
Generated automatically by Doxygen for LAPACK from the source code.
Version 3.4.2 Tue Sep 25 2012 cgeqrf.f(3) 
