LAPACK: Linear Algebra PACKage
|subroutine||zgeqrf (M, N, A, LDA, TAU, WORK, LWORK, INFO)|
|ZGEQRF VARIANT: left-looking Level 3 BLAS of the algorithm. |
|complex*16, dimension( lda, * )||A,|
|complex*16, dimension( * )||TAU,|
|complex*16, dimension( * )||WORK,|
ZGEQRF VARIANT: left-looking Level 3 BLAS of the algorithm.
ZGEQRF computes a QR factorization of a real M-by-N matrix A: A = Q * R. This is the left-looking Level 3 BLAS version of the algorithm.
M is INTEGER The number of rows of the matrix A. M >= 0.
N is INTEGER The number of columns of the matrix A. N >= 0.
A is COMPLEX*16 array, dimension (LDA,N) On entry, the M-by-N matrix A. On exit, the elements on and above the diagonal of the array contain the min(M,N)-by-N 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).
LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).
TAU is COMPLEX*16 array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Details).
WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal 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 (K-NT), 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 ((K-NX)/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((N-M)*K, (N-M)*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.
INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value
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:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i), and tau in TAU(i).