LAPACK
3.4.2
LAPACK: Linear Algebra PACKage

Go to the source code of this file.
Functions/Subroutines  
subroutine  zgeqrf (M, N, A, LDA, TAU, WORK, LWORK, INFO) 
ZGEQRF VARIANT: leftlooking Level 3 BLAS of the algorithm. 
subroutine zgeqrf  (  integer  M, 
integer  N,  
complex*16, dimension( lda, * )  A,  
integer  LDA,  
complex*16, dimension( * )  TAU,  
complex*16, dimension( * )  WORK,  
integer  LWORK,  
integer  INFO  
) 
ZGEQRF VARIANT: leftlooking Level 3 BLAS of the algorithm.
Purpose:
ZGEQRF computes a QR factorization of a real MbyN matrix A: A = Q * R. This is the leftlooking Level 3 BLAS version of the algorithm.
[in]  M  M is INTEGER The number of rows of the matrix A. M >= 0. 
[in]  N  N is INTEGER The number of columns of the matrix A. N >= 0. 
[in,out]  A  A is COMPLEX*16 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 orthogonal matrix Q as a product of min(m,n) elementary reflectors (see Further Details). 
[in]  LDA  LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M). 
[out]  TAU  TAU is COMPLEX*16 array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Details). 
[out]  WORK  WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK. 
[in]  LWORK  LWORK is INTEGER The dimension of the array WORK. The dimension can be divided into three parts. 1) The part for the triangular factor T. If the very last T is not bigger than any of the rest, then this part is NB x ceiling(K/NB), otherwise, NB x (KNT), where K = min(M,N) and NT is the dimension of the very last T 2) The part for the very last T when T is bigger than any of the rest T. The size of this part is NT x NT, where NT = K  ceiling ((KNX)/NB) x NB, where K = min(M,N), NX is calculated by NX = MAX( 0, ILAENV( 3, 'ZGEQRF', ' ', M, N, 1, 1 ) ) 3) The part for dlarfb is of size max((NM)*K, (NM)*NB, K*NB, NB*NB) So LWORK = part1 + part2 + part3 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. 
[out]  INFO  INFO is INTEGER = 0: successful exit < 0: if INFO = i, the ith argument had an illegal value 
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' where tau is a real scalar, and v is a real 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 150 of file zgeqrf.f.